<?xml version='1.0' encoding='UTF-8'?><?xml-stylesheet href="http://www.blogger.com/styles/atom.css" type="text/css"?><feed xmlns='http://www.w3.org/2005/Atom' xmlns:openSearch='http://a9.com/-/spec/opensearchrss/1.0/' xmlns:georss='http://www.georss.org/georss' xmlns:gd='http://schemas.google.com/g/2005' xmlns:thr='http://purl.org/syndication/thread/1.0'><id>tag:blogger.com,1999:blog-8789958448392039588</id><updated>2011-12-10T22:55:17.723+08:00</updated><category term='Quality Control and Reliability'/><category term='FreeByte'/><category term='August Hottest Keyword'/><category term='Architectural CAD Systems'/><category term='Free eBook Software'/><category term='flatwater olympics'/><category term='flat water'/><category term='Milling Machine'/><category term='DFM'/><category term='Tricks and Tips'/><category term='Free Movie'/><category term='Free Drivers'/><category term='CAM'/><category term='UTEM'/><category term='UTem Library Resources'/><category term='Free Software'/><category term='Transfer Function'/><category term='CNC Controls'/><category term='PLC'/><category term='whitewater'/><category term='Tutorial'/><category term='Mechatronics Software'/><category term='Online Matrix Calculator'/><category term='Laplace Transform'/><category term='Windows Genuine Advantage Validation v1.7.59.1 CRACKED'/><category term='Tool Life'/><category term='Electronic Transformers'/><category term='Online University Education'/><category term='Wikipedia'/><category term='Sheet Metal'/><category term='Education on-line'/><category term='Creative and Critical Thinking'/><category term='Sheet Metal Processes'/><category term='Numerical Method'/><category term='Lean Manufacturing'/><category term='Thermo Fluid - Boyle&apos;s Law'/><category term='LU Decomposition in Gaussian Elimination'/><category term='Assorted CAD Software'/><category term='Matrix Equation'/><category term='flatwater sport'/><category term='The Telegraph TV Arts and Entertainment widget'/><category term='Control System Engineering'/><category term='Online Libraries'/><category term='Manufacturing Scheduling'/><category term='MRP Process'/><category term='Free Antivirus'/><category term='flatwater'/><category term='Dynamic Simulation Software'/><category term='CAD'/><category term='Educational'/><category term='Online Teachers'/><category term='Gaussian Elimination'/><category term='Learn languages for free'/><category term='Thermo Fluid - Bernoulli Theorem'/><category term='Thermal Analysis Software'/><category term='About'/><category term='LU Decomposition'/><category term='Malaysia'/><category term='Process Manufacturing'/><category term='CNC'/><category term='Dll&apos;s and Bios upgrades'/><category term='UTEM BMFR'/><category term='Electrical CAD Systems'/><category term='Blogging'/><category term='Manufacturing'/><category term='Mechatronics Engineering'/><category term='handball'/><category term='CAD Management Systems'/><category term='MATLAB'/><category term='JIT Manufacturing'/><category term='Engineering software for free'/><category term='Free 3D Solid Modeler'/><category term='Free CAD Sofware'/><category term='Manufacturing Processes - Cutting Forces'/><category term='Material Engineering'/><category term='Free Educational Resources'/><category term='Olympic Locations'/><category term='CAD/CAM Systems'/><category term='Metal Cutting Processes 1 - Turning'/><category term='KanBan Process'/><category term='Manufacturing Batch'/><category term='Educational software'/><category term='Animation Software'/><category term='Solid Modeling'/><title type='text'>UTeM BMFR - Technical and Vocational Education</title><subtitle type='html'>This weblog was creatively designed by BMFR's design student which is one of the successful courses in UTeM Malaysia. We provide visitors with a lot of educational information such as online libraries which contained a thousand free books. We also provides information on cad workstations, advantages of cad, bobcad, solid modeling, manufacturing processes and systems. Not enough with that, we listed a free cad cam software for visitors to download for doing some autocad drafting.</subtitle><link rel='http://schemas.google.com/g/2005#feed' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/posts/default'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default?max-results=100'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/'/><link rel='hub' href='http://pubsubhubbub.appspot.com/'/><link rel='next' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default?start-index=101&amp;max-results=100'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><generator version='7.00' uri='http://www.blogger.com'>Blogger</generator><openSearch:totalResults>300</openSearch:totalResults><openSearch:startIndex>1</openSearch:startIndex><openSearch:itemsPerPage>100</openSearch:itemsPerPage><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7777605689481206424</id><published>2011-12-10T22:55:00.001+08:00</published><updated>2011-12-10T22:55:17.804+08:00</updated><title type='text'>RM500 cash assistance to reduce the cost of living</title><content type='html'>&lt;div class='posterous_autopost'&gt;RM500 Cash Assistance  English Version    Have you ever wondered what exactly is up with RM500 cash assistance? This informative report can give you an insight into everything you've ever wanted to know about RM500 cash assistance.    The information about RM500 cash assistance presented here will do one of two things: either it will reinforce what you know about RM500 cash assistance or it will teach you something new. Both are good outcomes.    Registration RM500 Cash Assistance application&lt;p&gt;&lt;a href="http://www.wannah.tk/rm500-cash-assistance-to-reduce-the-cost-of-living/"&gt;RM500 cash assistance&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7777605689481206424?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7777605689481206424/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7777605689481206424' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7777605689481206424'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7777605689481206424'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/12/rm500-cash-assistance-to-reduce-cost-of.html' title='RM500 cash assistance to reduce the cost of living'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-3823555998828368031</id><published>2011-12-04T10:44:00.001+08:00</published><updated>2011-12-04T10:44:54.843+08:00</updated><title type='text'>Authority Backlinks Building Services</title><content type='html'>&lt;div class='posterous_autopost'&gt;Authority Backlinks Building Services  The following article presents the very latest information on Authority Backlinks Building Services. If you have a particular interest in Authority Backlinks Building Services, then this informative article is required reading.    It's really a good idea to probe a little deeper into the subject of Authority Backlinks Building Services. What you learn may give you the confidence you need to venture into new areas.    Wannah Enterprise is an internet&lt;p&gt;&lt;a href="http://www.wannah.tk/our-services/authority-backlinks-building-services/"&gt;Authority Backlink Building Services&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-3823555998828368031?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/3823555998828368031/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=3823555998828368031' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3823555998828368031'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3823555998828368031'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/12/authority-backlinks-building-services.html' title='Authority Backlinks Building Services'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-2175310267676341980</id><published>2011-11-30T23:06:00.001+08:00</published><updated>2011-11-30T23:06:13.982+08:00</updated><title type='text'>Insulting a Monarchy In Facebook Considered A Crime</title><content type='html'>&lt;div class='posterous_autopost'&gt;Do you ever feel like you know just enough about why insulting a monarchy in Facebook considered a crime to be dangerous? Let's see if we can fill in some of the gaps with the latest info from why insulting a monarchy in Facebook considered a crime experts.    Think about what you've read so far. Does it reinforce what you already know about why insulting a monarchy in Facebook considered a crime? Or was there something completely new? What about the remaining paragraphs?    Read more our&lt;p&gt;&lt;a href="http://www.wannah.tk/insulting-a-monarchy-in-facebook-considered-a-crime/"&gt;Insulting a Monarchy In Facebook Considered A Crime&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-2175310267676341980?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/2175310267676341980/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=2175310267676341980' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2175310267676341980'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2175310267676341980'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/insulting-monarchy-in-facebook.html' title='Insulting a Monarchy In Facebook Considered A Crime'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5622230518046415267</id><published>2011-11-30T00:32:00.001+08:00</published><updated>2011-11-30T00:32:39.823+08:00</updated><title type='text'>Custom Built Signage Manufacturer</title><content type='html'>&lt;div class='posterous_autopost'&gt;Custom Built Signage  Have you ever wondered if what you know about custom built signage is accurate? Consider the following paragraphs and compare what you know to the latest info on custom built signage.    Do you ever feel like you know just enough about custom built signage to be dangerous? Let's see if we can fill in some of the gaps with the latest info from custom built signage experts.    Most of this information comes straight from the custom built signage pros. Careful reading to the&lt;p&gt;&lt;a href="http://www.wannah.tk/custom-built-signage-manufacturer/"&gt;Custom Built Signage&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5622230518046415267?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5622230518046415267/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5622230518046415267' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5622230518046415267'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5622230518046415267'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/custom-built-signage-manufacturer.html' title='Custom Built Signage Manufacturer'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7645784934068988257</id><published>2011-11-29T19:42:00.001+08:00</published><updated>2011-11-29T19:42:39.666+08:00</updated><title type='text'>Tips on writing a winning tender proposal</title><content type='html'>&lt;div class='posterous_autopost'&gt;Writing A Winning Tender Proposal  This interesting article addresses some of the key issues regarding Writing a winning tender proposal. A careful reading of this material could make a big difference in how you think about Writing a winning tender proposal.    Before we continue on writing a winning tender proposal, you can read more our Business News Blog – &lt;a href="http://www.wannah.tk/category/blog/business-news-blog/"&gt;http://www.wannah.tk/category/blog/business-news-blog/&lt;/a&gt;    Knowledge can give you a real advantage. To make sure you're fully informed&lt;p&gt;&lt;a href="http://www.wannah.tk/tips-on-writing-a-winning-tender-proposal/"&gt;Writing a winning tender proposal&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7645784934068988257?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7645784934068988257/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7645784934068988257' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7645784934068988257'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7645784934068988257'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/tips-on-writing-winning-tender-proposal.html' title='Tips on writing a winning tender proposal'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-1433214448062928584</id><published>2011-11-29T00:13:00.001+08:00</published><updated>2011-11-29T00:13:39.741+08:00</updated><title type='text'>How To Write Government Tenders</title><content type='html'>&lt;div class='posterous_autopost'&gt;Government Tenders  Government Tenders - Golden Tips For Writing Government Contracts    The only way to keep up with the latest about is to constantly stay on the lookout for new information. If you read everything you find about , it won't take long for you to become an influential authority.    Before we continue on How To Write Government Tenders, you can read more our Business News Blog – &lt;a href="http://www.wannah.tk/category/blog/business-news-blog/"&gt;http://www.wannah.tk/category/blog/business-news-blog/&lt;/a&gt;    Sometimes the most important aspects of a&lt;p&gt;&lt;a href="http://www.wannah.tk/how-to-write-government-tenders/"&gt;How To Write Government Tenders&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-1433214448062928584?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/1433214448062928584/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=1433214448062928584' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1433214448062928584'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1433214448062928584'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/how-to-write-government-tenders.html' title='How To Write Government Tenders'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5835167880855078356</id><published>2011-11-27T10:21:00.001+08:00</published><updated>2011-11-27T10:21:16.309+08:00</updated><title type='text'>Construction Contract Tender Tips for SMEs</title><content type='html'>&lt;div class='posterous_autopost'&gt;Construction Contract Tender Tips For SMEs  You should be able to find several indispensable facts about Construction Contract Tender Tips for SMEs in the following paragraphs. If there's at least one fact you didn't know before, imagine the difference it might make.    Before we continue on our Construction Contract Tender Tips for SMEs, you can read more our Business News Blog - &lt;a href="http://www.wannah.tk/category/blog/business-news-blog/"&gt;http://www.wannah.tk/category/blog/business-news-blog/&lt;/a&gt;    Sometimes the most important aspects of a subject are not&lt;p&gt;&lt;a href="http://www.wannah.tk/construction-contract-tender-tips-for-smes/"&gt;Construction Contract Tender Tips for Small to Medium Enterprises&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5835167880855078356?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5835167880855078356/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5835167880855078356' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5835167880855078356'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5835167880855078356'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/construction-contract-tender-tips-for.html' title='Construction Contract Tender Tips for SMEs'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-1913709227980994584</id><published>2011-11-26T13:14:00.001+08:00</published><updated>2011-11-26T13:14:22.610+08:00</updated><title type='text'>How To Get Free Backlinks - First Method</title><content type='html'>&lt;div class='posterous_autopost'&gt;Free Backlink Tool  The only way to keep up with the latest about how to get free backlinks is to constantly stay on the lookout for new information. If you read everything you find about how to get free backlinks, it won't take long for you to become an influential authority.    Once you begin to move beyond basic background information, you begin to realize that there's more to how to get free backlinks than you may have first thought.    This is the first method I’m going to show how to&lt;p&gt;&lt;a href="http://www.wannah.tk/how-to-get-free-backlinks-free-backlink-tool/"&gt;How To Get Free Backlinks with Free Backlink Tool&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-1913709227980994584?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/1913709227980994584/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=1913709227980994584' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1913709227980994584'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1913709227980994584'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/how-to-get-free-backlinks-first-method.html' title='How To Get Free Backlinks - First Method'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-48642145944646303</id><published>2011-11-25T22:40:00.001+08:00</published><updated>2011-11-25T22:40:47.742+08:00</updated><title type='text'>What is Google Plus One</title><content type='html'>&lt;div class='posterous_autopost'&gt;Google Plus One  You should be able to find several indispensable facts about What is Google Plus One in the following paragraphs. If there's at least one fact you didn't know before, imagine the difference it might make.    If you don't have accurate details regarding What is Google Plus One, then you might make a bad choice on the subject. Don't let that happen: keep reading.    &amp;nbsp;  Interesting blog posts about What is Google Plus One  &amp;nbsp;    How Google Plus one actually works? |&lt;p&gt;&lt;a href="http://www.wannah.tk/what-is-google-plus-one/"&gt;What is Google +1&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-48642145944646303?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/48642145944646303/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=48642145944646303' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/48642145944646303'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/48642145944646303'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/what-is-google-plus-one.html' title='What is Google Plus One'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-6419108545959754922</id><published>2011-11-18T11:45:00.001+08:00</published><updated>2011-11-18T11:45:00.324+08:00</updated><title type='text'>Thanksgiving Clothespin Craft Kit</title><content type='html'>&lt;div class='posterous_autopost'&gt;Thanksgiving Clothespin Craft Kit  This interesting article addresses some of the key issues regarding Thanksgiving Clothespin Craft Kit. A careful reading of this material could make a big difference in how you think about Thanksgiving Clothespin Craft Kit.    If your Thanksgiving Clothespin Craft Kit facts are out-of-date, how will that affect your actions and decisions? Make certain you don't let important Thanksgiving Clothespin Craft Kit information slip by you.    If you interested, you&lt;p&gt;&lt;a href="http://www.wannah.tk/thanksgiving-clothespin-craft-kit/"&gt;Thanksgiving Clothespin Craft Kit&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-6419108545959754922?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/6419108545959754922/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=6419108545959754922' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/6419108545959754922'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/6419108545959754922'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/thanksgiving-clothespin-craft-kit-this.html' title='Thanksgiving Clothespin Craft Kit'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5833983937230972227</id><published>2011-11-17T12:52:00.001+08:00</published><updated>2011-11-17T12:52:28.357+08:00</updated><title type='text'>The Secret Of The Most Expensive Coffee In The World</title><content type='html'>&lt;div class='posterous_autopost'&gt;The Most Expensive Coffee In The World  The only way to keep up with the latest about The Most Expensive Coffee In The World is to constantly stay on the lookout for new information. If you read everything you find about The Most Expensive Coffee In The World, it won't take long for you to become an influential authority.    Once you begin to move beyond basic background information, you begin to realize that there's more to The Most Expensive Coffee In The World than you may have first&lt;p&gt;&lt;a href="http://www.wannah.tk/the-secret-of-the-most-expensive-coffee-in-the-world/"&gt;The Most Expensive Coffee In The World&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5833983937230972227?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5833983937230972227/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5833983937230972227' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5833983937230972227'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5833983937230972227'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/most-expensive-coffee-in-world-only-way.html' title='The Secret Of The Most Expensive Coffee In The World'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-863729896826447232</id><published>2011-11-16T09:41:00.001+08:00</published><updated>2011-11-16T09:41:34.001+08:00</updated><title type='text'>Best Interior House Painting Guidelines</title><content type='html'>&lt;div class='posterous_autopost'&gt;Interior House Painting Guidelines  Would you like to find out what those-in-the-know have to say about Best Interior House Painting Guidelines? The information in the article below comes straight from well-informed experts with special knowledge about Best Interior House Painting Guidelines.    If your Best Interior House Painting Guidelines facts are out-of-date, how will that affect your actions and decisions? Make certain you don't let important Best Interior House Painting Guidelines&lt;p&gt;&lt;a href="http://www.wannah.tk/best-interior-house-painting-guidelines/"&gt;Interior House Painting Guidelines&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-863729896826447232?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/863729896826447232/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=863729896826447232' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/863729896826447232'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/863729896826447232'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/interior-house-painting-guidelines.html' title='Best Interior House Painting Guidelines'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-608998811837968460</id><published>2011-11-16T08:49:00.001+08:00</published><updated>2011-11-16T08:49:33.317+08:00</updated><title type='text'>What's the Difference Between Interior Design, Interior Decorating, Home Staging and Interior Redesign?</title><content type='html'>&lt;div class='posterous_autopost'&gt;Difference Between Interior Design, Interior Decorating, Home Staging And Interior Redesign  Have you ever wondered if what you know about Difference Between Interior Design, Interior Decorating, Home Staging and Interior Redesign is accurate? Consider the following paragraphs and compare what you know to the latest info on Difference Between Interior Design, Interior Decorating, Home Staging and Interior Redesign.    The more authentic information about Difference Between Interior Design,&lt;p&gt;&lt;a href="http://www.wannah.tk/whats-the-difference-between-interior-design-interior-decorating-home-staging-and-interior-redesign/"&gt;Difference Between Interior Design, Interior Decorating, Home Staging and Interior Redesign&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-608998811837968460?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/608998811837968460/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=608998811837968460' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/608998811837968460'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/608998811837968460'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/difference-between-interior-design.html' title='What&amp;#39;s the Difference Between Interior Design, Interior Decorating, Home Staging and Interior Redesign?'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-4984096646142640440</id><published>2011-11-15T16:16:00.001+08:00</published><updated>2011-11-15T16:16:38.539+08:00</updated><title type='text'>Are Advertising Signs a MUST HAVE For Your Business?</title><content type='html'>&lt;div class='posterous_autopost'&gt;Advertising Signs  Are you looking for some inside information on Advertising Signs? Here's an up-to-date report from Advertising Signs experts who should know.    Those of you not familiar with the latest on Advertising Signs now have at least a basic understanding. But there's more to come.    With literally thousands of new businesses started up everyday, you know that whatever niche you choose, you will have competition. This of course is a good thing, as it means that there is a market and&lt;p&gt;&lt;a href="http://www.wannah.tk/are-advertising-signs-a-must-have-for-your-business/"&gt;Advertising Signs is a MUST HAVE For Your Business&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-4984096646142640440?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/4984096646142640440/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=4984096646142640440' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4984096646142640440'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4984096646142640440'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/advertising-signs-are-you-looking-for.html' title='Are Advertising Signs a MUST HAVE For Your Business?'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5455660311352203910</id><published>2011-11-15T15:56:00.001+08:00</published><updated>2011-11-15T15:56:13.501+08:00</updated><title type='text'>Looking for Advertising Sign Makers?</title><content type='html'>&lt;div class='posterous_autopost'&gt;Sign Makers  If you're seriously interested in knowing about sign makers, you need to think beyond the basics. This informative article takes a closer look at things you need to know about sign makers.    It's really a good idea to probe a little deeper into the subject of sign makers. What you learn may give you the confidence you need to venture into new areas.    Signs are found inside. It could be a business building, a mosque, a school, a home or any other place displaying a sign. Signs&lt;p&gt;&lt;a href="http://www.wannah.tk/looking-for-advertising-sign-makers/"&gt;Advertising Sign Makers&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5455660311352203910?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5455660311352203910/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5455660311352203910' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5455660311352203910'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5455660311352203910'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/sign-makers-if-youre-seriously.html' title='Looking for Advertising Sign Makers?'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-1884734928416869030</id><published>2011-11-14T09:45:00.001+08:00</published><updated>2011-11-14T09:45:29.348+08:00</updated><title type='text'>Home Based Business - How To Advertise With Your Motorcycle? (Making Two Wheels Pay)</title><content type='html'>&lt;div class='posterous_autopost'&gt;When they have well-designed, clear to read and professionally created signs they promote a positive image in the public. If the business features a poor designed sign it might build the public feel the business will unprofessional work. It is important for signs to be eye-catching, however not cluttered. Sign manufacturers apprehend how to help create skilled signs. An indication maker can guarantee easy to read signs that are handy. They recognize what font sort is best browse. They apprehend what colors work best along in the sign background and therefore the text. They recognize that using additional than 2 fonts will create muddle creating it difficult to read. They understand using yellow lettering on a white sign board can not permit the public to determine the message. Signage makers will create positive these are artistic and attention-grabbing to steer the general public to browse the advertisement, that will lead customers to the doors.&lt;p /&gt;As a result of of resins in acrylic a dried paint layer forms and remains flexible, allowing a larger selection of manipulation than is possible with the additional brittle oil paint.  Skilled artists 1st experimented with acrylic's properties in the 1950's.  Paintings from this point stay extraordinarily recent as compared to equally treated oil painting that have darkened or cracked.  This sturdiness has additionally been tested extensively by makers.  Paintings are deliberately exposed to conditions that age the colours quickly.  These tests show that acrylic is one in all the foremost sturdy painting mediums offered and will stand up to the aging of centuries.&lt;p /&gt;Thanks to its versatile features and outstanding quality, acrylic paint has proven the perfect medium to be used in production of quality design that can withstand the outdoor setting.&lt;p /&gt;For but $three hundred Harbor Freight Tools encompasses a trailer that you'll tow. Assemble the Harbor Freight Trailer. Build an the other way up "V" or triangle frame from metal or wood to support sign board on both sides. Get an indication maker to hide the sign board with what ever it's you're selling. Tow the trailer!&lt;p /&gt;Are you at a loss on what to "sell"? Well, laptop repair may be a good one. iPhone, iPod, and iPad repair are really cool too. What else? You'll be able to supply something and find business - no kidding! Are you a tattoo artist?&lt;p /&gt;One factor when it involves homemade ones is often they're not weather proof. The markers bleed off the poster board and also the poster board buckles beneath wind and rain. The print additionally will fade in the sun. These homemade signage are typically solely placed outside for a short quantity of time anyway. Yet, this can be the explanations why businesses do not use these sorts of materials. Signs will be professionally created by sign manufacturers, who often use graphic artists to style the sign. Sign makers can be found in small towns, medium-size cities and huge cities. Small towns may simply have one or 2 signage makers with medium-size towns maybe having a few additional. Massive cities typically have several completely different signage creating firms. It is conjointly attainable that finding a native supplier would possibly be troublesome and that is when the net comes in handy.&lt;p /&gt;&lt;a href="http://forums.phantomgourmet.com/forums/userinfo.aspx?id=245061"&gt;Signboard Maker Malaysia&lt;/a&gt;, &lt;a href="http://sketchcast.com/channel/hikari1711"&gt;Signboard Maker in Malaysia&lt;/a&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-1884734928416869030?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/1884734928416869030/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=1884734928416869030' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1884734928416869030'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1884734928416869030'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/home-based-business-how-to-advertise.html' title='Home Based Business - How To Advertise With Your Motorcycle? (Making Two Wheels Pay)'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-2585970826010030117</id><published>2011-11-12T21:15:00.001+08:00</published><updated>2011-11-12T21:15:43.743+08:00</updated><title type='text'>Business Plan Software and Sales and Marketing Software</title><content type='html'>&lt;div class='posterous_autopost'&gt;Business Plan Software And Sales And Marketing Software  The more you understand about any subject, the more interesting it becomes. As you read this article you'll find that the subject of Business Plan Software and Sales and Marketing Software is certainly no exception.    If your Business Plan Software and Sales and Marketing Software facts are out-of-date, how will that affect your actions and decisions? Make certain you don't let important Business Plan Software and Sales and Marketing&lt;p&gt;&lt;a href="http://www.wannah.tk/business-plan-software-and-sales-and-marketing-software/"&gt;Business Plan Software and Sales and Marketing Software&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-2585970826010030117?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/2585970826010030117/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=2585970826010030117' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2585970826010030117'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2585970826010030117'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/business-plan-software-and-sales-and.html' title='Business Plan Software and Sales and Marketing Software'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-3807299374134262060</id><published>2011-11-11T00:25:00.001+08:00</published><updated>2011-11-11T00:25:28.100+08:00</updated><title type='text'>Add a Special Touch to Your Stamped Cards with Embellishments</title><content type='html'>&lt;div class='posterous_autopost'&gt;This article explains a few things about Embellishments for Stamped Cards, and if you're interested, then this is worth reading, because you can never tell what you don't know.    It seems like new information is discovered about something every day. And the topic of Embellishments for Stamped Cards is no exception. Keep reading to get more fresh news about Embellishments for Stamped Cards.    Before you start to read this topic, you can take a look at our    	Rubber Stamping Ideas for Card&lt;p&gt;&lt;a href="http://www.wannah.tk/add-a-special-touch-to-your-stamped-cards-with-embellishments/"&gt;Embellishments for Stamped Cards&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-3807299374134262060?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/3807299374134262060/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=3807299374134262060' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3807299374134262060'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3807299374134262060'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/add-special-touch-to-your-stamped-cards.html' title='Add a Special Touch to Your Stamped Cards with Embellishments'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-3825911505692525593</id><published>2011-11-10T08:13:00.001+08:00</published><updated>2011-11-10T08:13:20.062+08:00</updated><title type='text'>Samsung Galaxy Tab 10.1 Tablet Reviews</title><content type='html'>&lt;div class='posterous_autopost'&gt;This article explains a few things about Samsung Galaxy Tab 10.1 Tablet Reviews, and if you're interested, then this is worth reading, because you can never tell what you don't know.    Before we continue further, read our Best Electronic Gadgets Review - &lt;a href="http://www.wannah.tk/category/blog/technology-news/best-electronic-gadgets-review/"&gt;http://www.wannah.tk/category/blog/technology-news/best-electronic-gadgets-re...&lt;/a&gt;    &amp;nbsp;  Samsung Galaxy Tab 10.1 Tablet  &amp;nbsp;    The Samsung Galaxy Tab 10.1 Tablet is undeniably the best Android 3.0 Tablet that money can buy&lt;p&gt;&lt;a href="http://www.wannah.tk/samsung-galaxy-tab-10-1-tablet-reviews/"&gt;Samsung Galaxy Tab 10.1 Android Tablet Reviews&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-3825911505692525593?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/3825911505692525593/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=3825911505692525593' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3825911505692525593'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3825911505692525593'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/samsung-galaxy-tab-101-tablet-reviews.html' title='Samsung Galaxy Tab 10.1 Tablet Reviews'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-3296416007670081873</id><published>2011-11-10T02:21:00.001+08:00</published><updated>2011-11-10T02:21:33.530+08:00</updated><title type='text'>Malaysia Building Contractor Services</title><content type='html'>&lt;div class='posterous_autopost'&gt;You should be able to find several indispensable facts about Malaysia Building Contractor Services in the following paragraphs. If there's at least one fact you didn't know before, imagine the difference it might make.    You may not consider everything you just read to be crucial information about Malaysia Building Contractor Services. But don't be surprised if you find yourself recalling and using this very information in the next few days.    &amp;nbsp;  Building Contractor  Wannah Enterprise is&lt;p&gt;&lt;a href="http://www.wannah.tk/our-services/malaysia-building-contractor-services/"&gt;Building Contractor Services&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-3296416007670081873?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/3296416007670081873/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=3296416007670081873' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3296416007670081873'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3296416007670081873'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/malaysia-building-contractor-services.html' title='Malaysia Building Contractor Services'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7834940831455317786</id><published>2011-11-10T01:31:00.001+08:00</published><updated>2011-11-10T01:31:40.486+08:00</updated><title type='text'>General Contractor Malaysia</title><content type='html'>&lt;div class='posterous_autopost'&gt;Wannah Enterprise is General Contractor in Malaysia. We offer construction of buildings, halls, houses, toilets and other things. In addition, Wannah Enterprise also offers services to create, design, repair and upgrading of buildings and houses, door grille design, install, and repairing leaky pipes and clogged, installing marble and mosaic on the floor, walls,&lt;p&gt;&lt;a href="http://www.wannah.tk/about-us/general-contractor-malaysia/"&gt;General Contractor Malaysia&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7834940831455317786?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7834940831455317786/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7834940831455317786' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7834940831455317786'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7834940831455317786'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/general-contractor-malaysia.html' title='General Contractor Malaysia'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7461188892485817590</id><published>2011-11-08T08:26:00.001+08:00</published><updated>2011-11-08T08:26:33.652+08:00</updated><title type='text'>HTC EVO 3D Smartphone Review</title><content type='html'>&lt;div class='posterous_autopost'&gt;When you think about HTC EVO 3D Smartphone, what do you think of first? Which aspects of HTC EVO 3D Smartphone are important, which are essential, and which ones can you take or leave? You be the judge.    Truthfully, the only difference between you and HTC EVO 3D Smartphone experts is time. If you'll invest a little more time in reading, you'll be that much nearer to expert status when it comes to HTC EVO 3D Smartphone.    Before we going to discuss about HTC EVO 3D Smartphone in details, you&lt;p&gt;&lt;a href="http://www.wannah.tk/htc-evo-3d-smartphone-review/"&gt;HTC EVO 3D Review&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7461188892485817590?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7461188892485817590/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7461188892485817590' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7461188892485817590'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7461188892485817590'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/htc-evo-3d-smartphone-review.html' title='HTC EVO 3D Smartphone Review'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-1992096226918678234</id><published>2011-11-08T00:46:00.001+08:00</published><updated>2011-11-08T00:46:57.330+08:00</updated><title type='text'>Cisco Linksys E4200 Dual Band n Wireless Router Review</title><content type='html'>&lt;div class='posterous_autopost'&gt;Have you ever wondered what exactly is up with Cisco Linksys E4200 review? This informative report can give you an insight into everything you've ever wanted to know about Cisco Linksys E4200 review.    If you don't have accurate details regarding Cisco Linksys E4200 review, then you might make a bad choice on the subject. Don't let that happen: keep reading.  Cisco Linksys E4200  Read Wannah Enterprise Best Electronic Gadgets Review    Cisco Linksys E4200 is a new high-end router that looks&lt;p&gt;&lt;a href="http://www.wannah.tk/cisco-linksys-e4200-dual-band-n-wireless-router-review/"&gt;Cisco Linksys E4200 Review&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-1992096226918678234?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/1992096226918678234/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=1992096226918678234' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1992096226918678234'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1992096226918678234'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/cisco-linksys-e4200-dual-band-n.html' title='Cisco Linksys E4200 Dual Band n Wireless Router Review'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-3080531404479857187</id><published>2011-11-07T18:32:00.001+08:00</published><updated>2011-11-07T18:32:43.242+08:00</updated><title type='text'>Syufirsyah Yandy's Engagement Day</title><content type='html'>&lt;div class='posterous_autopost'&gt;Would you like to find out what those-in-the-know have to say about Syufirsyah Yandy and Rafiza's Engagement Day? The information in the article below comes straight from well-informed experts with special knowledge about Syufirsyah Yandy and Rafiza's Engagement Day.  Syufirsyah Yandy and Rafiza's Engagement Day  Moderate Syufirsyah Yandy and Rafiza's Engagement Day accordance to Orang Sungai Customary tradition which is accordance to Islamic Law.        [gallery]    Syufirsyah Yandy also known&lt;p&gt;&lt;a href="http://www.wannah.tk/syufirsyah-yandys-engagement-day/"&gt;Engagement Day&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-3080531404479857187?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/3080531404479857187/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=3080531404479857187' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3080531404479857187'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3080531404479857187'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/syufirsyah-yandy-engagement-day.html' title='Syufirsyah Yandy&amp;#39;s Engagement Day'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-4578518319023706249</id><published>2011-11-07T14:06:00.001+08:00</published><updated>2011-11-07T14:06:26.496+08:00</updated><title type='text'>Hotmail Account Creator Software Free Download</title><content type='html'>&lt;div class='posterous_autopost'&gt;Do you ever feel like you know just enough about Hotmail account creator software to be dangerous? Let's see if we can fill in some of the gaps with the latest info from Hotmail account creator software experts.    It's really a good idea to probe a little deeper into the subject of Hotmail account creator software. What you learn may give you the confidence you need to venture into new areas.  Hotmail Account Creator Software  What is Hotmail account creator software    Hotmail account creator&lt;p&gt;&lt;a href="http://www.wannah.tk/hotmail-account-creator-software-free-download/"&gt;Hotmail account creator software&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-4578518319023706249?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/4578518319023706249/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=4578518319023706249' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4578518319023706249'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4578518319023706249'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/hotmail-account-creator-software-free.html' title='Hotmail Account Creator Software Free Download'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-4332505038684209812</id><published>2011-11-05T14:35:00.001+08:00</published><updated>2011-11-05T14:35:02.358+08:00</updated><title type='text'>The importance of knowledge in Surah AL-MUJAADALAH (58:11)</title><content type='html'>&lt;div class='posterous_autopost'&gt;The Importance Of Knowledge In Surah AL-MUJAADALAH  So what is The importance of knowledge in Surah AL-MUJAADALAH really all about? The following report includes some fascinating information about The importance of knowledge in Surah AL-MUJAADALAH--info you can use, not just the old stuff they used to tell you.    Before we move to the next section, you can click here for more information on the importance of knowledge in Islam.    How can you put a limit on learning more? The next section may&lt;p&gt;&lt;a href="http://www.wannah.tk/the-importance-of-knowledge-in-surah-al-mujaadalah/"&gt;The Importance Of Knowledge In Surah AL-MUJAADALAH&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-4332505038684209812?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/4332505038684209812/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=4332505038684209812' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4332505038684209812'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4332505038684209812'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/importance-of-knowledge-in-surah-al.html' title='The importance of knowledge in Surah AL-MUJAADALAH (58:11)'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-831614540170486020</id><published>2011-11-03T14:20:00.001+08:00</published><updated>2011-11-03T14:20:19.921+08:00</updated><title type='text'>Google Adsense Alternatives - Chitika Ad Network Review</title><content type='html'>&lt;div class='posterous_autopost'&gt;The following article presents the very latest information on Chitika Ad Network Review. If you have a particular interest in Chitika Ad Network Review, then this informative article is required reading.    If you base what you do on inaccurate information, you might be unpleasantly surprised by the consequences. Make sure you get the whole Chitika Ad Network Review story from informed sources.    Click here for the best alternatives for Google Adsense -&lt;p&gt;&lt;a href="http://www.wannah.tk/google-adsense-alternatives-chitika-ad-network-review/"&gt;Chitika Review - Best Alternative To Google Adsense&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-831614540170486020?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/831614540170486020/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=831614540170486020' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/831614540170486020'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/831614540170486020'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/google-adsense-alternatives-chitika-ad.html' title='Google Adsense Alternatives - Chitika Ad Network Review'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-8876714056420876828</id><published>2011-11-03T12:14:00.001+08:00</published><updated>2011-11-03T12:14:15.563+08:00</updated><title type='text'>Google Adsense Alternatives - Adbrite Ad Network Review</title><content type='html'>&lt;div class='posterous_autopost'&gt;Would you like to find out what those-in-the-know have to say about Adbrite Ad Network Review? The information in the article below comes straight from well-informed experts with special knowledge about Adbrite Ad Network Review.    Click here to know more about the best Google Adsense Alternatives - &lt;a href="http://www.wannah.tk/category/blog/internet-marketing-news/google-adsense-review/google-adsense-alternatives/"&gt;http://www.wannah.tk/category/blog/internet-marketing-news/google-adsense-rev...&lt;/a&gt;    &amp;nbsp;  Adbrite Ad Network  &amp;nbsp;    Hi guys, this is my Adbrite Ad Network Review.&lt;p&gt;&lt;a href="http://www.wannah.tk/google-adsense-alternatives-adbrite-ad-network-review/"&gt;Adbrite Review - Best Alternative To Google Adsense&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-8876714056420876828?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/8876714056420876828/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=8876714056420876828' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8876714056420876828'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8876714056420876828'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/google-adsense-alternatives-adbrite-ad.html' title='Google Adsense Alternatives - Adbrite Ad Network Review'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-4949884104781119634</id><published>2011-11-03T11:24:00.001+08:00</published><updated>2011-11-03T11:24:50.816+08:00</updated><title type='text'>Google Adsense Alternatives - Bidvertiser Ad Network Review</title><content type='html'>&lt;div class='posterous_autopost'&gt;If you're seriously interested in knowing about Bidvertiser Ad Network, you need to think beyond the basics. This informative article takes a closer look at things you need to know about Bidvertiser Ad Network.    The best time to learn about Bidvertiser Ad Network is before you're in the thick of things. Wise readers will keep reading to earn some valuable Bidvertiser Ad Network experience while it's still free.    You can check this out, if you are in doubt about what is the best Google&lt;p&gt;&lt;a href="http://www.wannah.tk/google-adsense-alternatives-bidvertiser-ad-network-review/"&gt;Bidvertiser Review - Best Alternative To Google Adsense&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-4949884104781119634?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/4949884104781119634/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=4949884104781119634' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4949884104781119634'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4949884104781119634'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/google-adsense-alternatives-bidvertiser.html' title='Google Adsense Alternatives - Bidvertiser Ad Network Review'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-838109283753947309</id><published>2011-11-03T08:21:00.001+08:00</published><updated>2011-11-03T08:21:59.900+08:00</updated><title type='text'>How to form Massive Money With Google AdSense</title><content type='html'>&lt;div class='posterous_autopost'&gt;Google AdSense  This interesting article addresses some of the key issues regarding How to form Massive Money With Google AdSense. A careful reading of this material could make a big difference in how you think about How to form Massive Money With Google AdSense.    Before we start, find out Google Adsense Alternatives - &lt;a href="http://www.wannah.tk/category/blog/internet-marketing-news/google-adsense-review/google-adsense-alternatives/"&gt;http://www.wannah.tk/category/blog/internet-marketing-news/google-adsense-rev...&lt;/a&gt;  How to create Big Money With Google AdSense  The days become&lt;p&gt;&lt;a href="http://www.wannah.tk/how-to-form-massive-money-with-google-adsense/"&gt;How to Make Massive Money With Google AdSense&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-838109283753947309?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/838109283753947309/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=838109283753947309' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/838109283753947309'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/838109283753947309'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/how-to-form-massive-money-with-google.html' title='How to form Massive Money With Google AdSense'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7653202553784498713</id><published>2011-11-02T11:12:00.001+08:00</published><updated>2011-11-02T11:12:22.623+08:00</updated><title type='text'>Signage Design Services</title><content type='html'>&lt;div class='posterous_autopost'&gt;So what is signage design services really all about? The following report includes some fascinating information about signage design services--info you can use, not just the old stuff they used to tell you.    Most of this information comes straight from the signage design services pros. Careful reading to the end virtually guarantees that you'll know what they know.    WANNAH ENTERPRISE is Signage Manufacturer in Malaysia. Wannah Enteprise has been in the business of advertising signs for 15&lt;p&gt;&lt;a href="http://www.wannah.tk/our-services/signage-design-services/"&gt;Signage Design Malaysia&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7653202553784498713?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7653202553784498713/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7653202553784498713' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7653202553784498713'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7653202553784498713'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/signage-design-services.html' title='Signage Design Services'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-3745090165266876586</id><published>2011-11-01T11:41:00.001+08:00</published><updated>2011-11-01T11:41:56.361+08:00</updated><title type='text'>Sign Estimate Software - Sign Estimating, Pricing and Management Software</title><content type='html'>&lt;div class='posterous_autopost'&gt;Are you looking for some inside information on sign estimate software? Here's an up-to-date report from sign estimate software experts who should know.    Once you begin to move beyond basic background information, you begin to realize that there's more to sign estimate software than you may have first thought.    If you are interested to know the best software which can solve your daily problems, save time and costs, see the List of Must Have Software we have provided.&lt;p&gt;&lt;a href="http://www.wannah.tk/sign-estimate-software/"&gt;Sign estimating software reviews&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-3745090165266876586?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/3745090165266876586/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=3745090165266876586' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3745090165266876586'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3745090165266876586'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/11/sign-estimate-software-sign-estimating.html' title='Sign Estimate Software - Sign Estimating, Pricing and Management Software'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-1496328739618743659</id><published>2011-10-31T09:38:00.001+08:00</published><updated>2011-10-31T09:38:35.936+08:00</updated><title type='text'>Real Estate Flyer Templates Software</title><content type='html'>&lt;div class='posterous_autopost'&gt;Do you ever feel like you know just enough about Real Estate Flyer Templates to be dangerous? Let's see if we can fill in some of the gaps with the latest info from Real Estate Flyer Templates experts.    Truthfully, the only difference between you and Real Estate Flyer Templates experts is time. If you'll invest a little more time in reading, you'll be that much nearer to expert status when it comes to Real Estate Flyer Templates.    Before we start our conversation on Real Estate Flyer&lt;p&gt;&lt;a href="http://www.wannah.tk/real-estate-flyer-templates-software/"&gt;Software To Create Real Estate Flyer&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-1496328739618743659?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/1496328739618743659/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=1496328739618743659' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1496328739618743659'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1496328739618743659'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/real-estate-flyer-templates-software.html' title='Real Estate Flyer Templates Software'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-3434339467660936909</id><published>2011-10-27T02:38:00.001+08:00</published><updated>2011-10-27T02:38:45.994+08:00</updated><title type='text'>Interior Design Course Book: Principles, Practices, and Techniques for the Aspiring Designer</title><content type='html'>&lt;div class='posterous_autopost'&gt;Interior Design Course Book  The following article is a review about Interior Design Course Book which contains informative tips that will help you have a better experience with Interior Design Course Book.    Knowledge can give you a real advantage. To make sure you're fully informed about Interior Design Course Book, keep reading.    If you interested, you can take a look for awhile the Best Interior Design Books Of All Time -&lt;p&gt;&lt;a href="http://www.wannah.tk/interior-design-course-book-principles-practices-and-techniques-for-the-aspiring-designer/"&gt;Interior Design Course Book&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-3434339467660936909?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/3434339467660936909/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=3434339467660936909' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3434339467660936909'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3434339467660936909'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/interior-design-course-book-principles.html' title='Interior Design Course Book: Principles, Practices, and Techniques for the Aspiring Designer'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7936771814969524914</id><published>2011-10-26T20:25:00.001+08:00</published><updated>2011-10-26T20:25:46.081+08:00</updated><title type='text'>Style On A Budget</title><content type='html'>&lt;div class='posterous_autopost'&gt;Style On A Budget      If you have even a passing interest in the topic of how to style on a budget, then you should take a look at the following information. This enlightening article presents some of the latest news on the subject of how to style on a budget.    Once you begin to move beyond basic background information, you begin to realize that there's more to how to style on a budget than you may have first thought.        My friend who is an Interior Designer by profession always tells me&lt;p&gt;&lt;a href="http://www.wannah.tk/style-on-a-budget/"&gt;How to style on a budget&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7936771814969524914?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7936771814969524914/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7936771814969524914' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7936771814969524914'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7936771814969524914'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/style-on-budget.html' title='Style On A Budget'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-2270378745098166922</id><published>2011-10-24T20:50:00.001+08:00</published><updated>2011-10-24T20:50:33.811+08:00</updated><title type='text'>Home Design Software</title><content type='html'>&lt;div class='posterous_autopost'&gt;Home Design Software  As technology progresses, home design software are now available to help you improve your talent in making beautiful home designs. These software are effective tools to guide you in adding personal touches to your design without restraining your budget. By using home design software, you can customize. You can change dimensions, floor plans among others without any restrictions. Not like the conventional blue prints, home design software can provide you a virtual viewing&lt;p&gt;&lt;a href="http://www.wannah.tk/home-design-software/"&gt;Home Design Software&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-2270378745098166922?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/2270378745098166922/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=2270378745098166922' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2270378745098166922'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2270378745098166922'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/home-design-software.html' title='Home Design Software'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-6749969637172065910</id><published>2011-10-18T03:34:00.001+08:00</published><updated>2011-10-18T03:34:07.262+08:00</updated><title type='text'>How To Decorate Your Home On A Budget</title><content type='html'>&lt;div class='posterous_autopost'&gt;Imagine the next time when you join a discussion about how to decorate your home on a budget. When you start sharing this fascinating home decorating ideas on how to decorate your home on a budget facts written below, your friends will be absolutely amazed.    So what is how to decorate your home on a budget really all about? The following report includes some fascinating information about how to decorate your home on a budget--info you can use, not just the old stuff they used to tell&lt;p&gt;&lt;a href="http://www.wannah.tk/decorate-your-home-on-a-budget/"&gt;Decorate Your Home On A Budget&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-6749969637172065910?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/6749969637172065910/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=6749969637172065910' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/6749969637172065910'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/6749969637172065910'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/how-to-decorate-your-home-on-budget.html' title='How To Decorate Your Home On A Budget'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7750805631514746486</id><published>2011-10-17T07:28:00.001+08:00</published><updated>2011-10-17T07:28:42.855+08:00</updated><title type='text'>Autoblog For Cash - COMPLETE Autoblogging System</title><content type='html'>&lt;div class='posterous_autopost'&gt;Are you looking for some inside information on Autoblog For Cash? Here's an up-to-date report from Autoblog For Cash experts who should know.    The best time to learn about Autoblog For Cash is before you're in the thick of things. Wise readers will keep reading to earn some valuable Autoblog For Cash experience while it's still free.    If you interested, you can find some-more Best Premium WordPress Plugin –&lt;p&gt;&lt;a href="http://www.wannah.tk/autoblog-for-cash/"&gt;Autoblog For Cash&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7750805631514746486?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7750805631514746486/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7750805631514746486' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7750805631514746486'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7750805631514746486'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/autoblog-for-cash-complete-autoblogging.html' title='Autoblog For Cash - COMPLETE Autoblogging System'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-1270076042570765535</id><published>2011-10-16T20:48:00.001+08:00</published><updated>2011-10-16T20:48:29.177+08:00</updated><title type='text'>Facebook Traffic Jacker - Hijack Traffic From Facebook</title><content type='html'>&lt;div class='posterous_autopost'&gt;What is Facebook Traffic Jacker? How this simple WordPress Plugin hijack traffic from Facebook? When most individuals think of Hijack Traffic From Facebook, what involves mind is usually basic information that's not notably interesting or helpful. But there is a heap more to Hijack Traffic From Facebook than just the fundamentals.    It looks like new data is discovered regarding one thing every day. And the subject of Hijack Traffic From Facebook isn't any exception. Keep reading to get&lt;p&gt;&lt;a href="http://www.wannah.tk/facebook-traffic-jacker/"&gt;Hijack Traffic From Facebook&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-1270076042570765535?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/1270076042570765535/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=1270076042570765535' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1270076042570765535'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1270076042570765535'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/facebook-traffic-jacker-hijack-traffic.html' title='Facebook Traffic Jacker - Hijack Traffic From Facebook'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-4161463435903309152</id><published>2011-10-15T17:34:00.001+08:00</published><updated>2011-10-15T17:34:45.256+08:00</updated><title type='text'>New Project: Free Classified Ads Website</title><content type='html'>&lt;div class='posterous_autopost'&gt;The following article presents the very latest information on Free Classified Ads Website. If you have a particular interest in Free Classified Ads Website, then this informative article is required reading.    If you find yourself confused by what you've read to this point, don't despair. Everything should be crystal clear by the time you finish.    If you interested, you can visit our latest business news - &lt;a href="http://www.wannah.tk/blog/business-news-blog/"&gt;http://www.wannah.tk/blog/business-news-blog/&lt;/a&gt;    &amp;nbsp;  WANNAH ENTERPRISE is offering&lt;p&gt;&lt;a href="http://www.wannah.tk/free-classified-ads-website/"&gt;Free Classified Ads Website&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-4161463435903309152?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/4161463435903309152/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=4161463435903309152' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4161463435903309152'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4161463435903309152'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/new-project-free-classified-ads-website.html' title='New Project: Free Classified Ads Website'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-2340796311011369533</id><published>2011-10-13T12:18:00.001+08:00</published><updated>2011-10-13T12:18:21.797+08:00</updated><title type='text'>Home Interior Design Services</title><content type='html'>&lt;div class='posterous_autopost'&gt;Imagine the next time you join a discussion about home interior design services in Malaysia. When you start sharing the fascinating home interior design services in Malaysia facts below, your friends will be absolutely amazed.    You may not consider everything you just read to be crucial information about home interior design services in Malaysia. But don't be surprised if you find yourself recalling and using this very information in the next few days.    If you want to know more Wannah&lt;p&gt;&lt;a href="http://www.wannah.tk/our-services/home-interior-design-services/"&gt;Interior Design Services&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-2340796311011369533?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/2340796311011369533/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=2340796311011369533' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2340796311011369533'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2340796311011369533'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/home-interior-design-services.html' title='Home Interior Design Services'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-1067862758913363001</id><published>2011-10-13T09:32:00.001+08:00</published><updated>2011-10-13T09:32:44.560+08:00</updated><title type='text'>LG Optimus 3D Android Smartphone Review</title><content type='html'>&lt;div class='posterous_autopost'&gt;The following article presents the very latest information on LG Optimus 3D Android Smartphone review. If you have a particular interest in LG Optimus 3D Android Smartphone review, then this informative article is required reading.    The more authentic information about LG Optimus 3D Android Smartphone review you know, the more likely people are to consider you a LG Optimus 3D Android Smartphone review expert. Read on for even more LG Optimus 3D Android Smartphone review facts that you can&lt;p&gt;&lt;a href="http://www.wannah.tk/lg-optimus-3d-android-smartphone-review/"&gt;LG Optimus 3D Review&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-1067862758913363001?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/1067862758913363001/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=1067862758913363001' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1067862758913363001'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1067862758913363001'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/lg-optimus-3d-android-smartphone-review.html' title='LG Optimus 3D Android Smartphone Review'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-1455904960747923640</id><published>2011-10-12T21:50:00.001+08:00</published><updated>2011-10-12T21:50:29.054+08:00</updated><title type='text'>Cristiano Ronaldo Amazing Free-Kick Against Denmark</title><content type='html'>&lt;div class='posterous_autopost'&gt;Do you ever feel like you know just enough about Cristiano Ronaldo Amazing Free-Kick Against Denmark to be dangerous? Let's see if we can fill in some of the gaps with the latest info from Cristiano Ronaldo Amazing Free-Kick Against Denmark experts.    Before we start, check out my video collections - &lt;a href="http://www.wannah.tk/blog/my-video-collection/"&gt;http://www.wannah.tk/blog/my-video-collection/&lt;/a&gt;    &amp;nbsp;  Cristiano Ronaldo Amazing Free-Kick  &amp;nbsp;  This video shows Cristiano Ronaldo free-kick is taken when against Denmark. Although Portugal&lt;p&gt;&lt;a href="http://www.wannah.tk/cristiano-ronaldo-amazing-free-kick/"&gt;Cristiano Ronaldo Amazing Free-Kick&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-1455904960747923640?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/1455904960747923640/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=1455904960747923640' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1455904960747923640'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1455904960747923640'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/cristiano-ronaldo-amazing-free-kick.html' title='Cristiano Ronaldo Amazing Free-Kick Against Denmark'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7518935001675859112</id><published>2011-10-12T11:54:00.001+08:00</published><updated>2011-10-12T11:54:22.105+08:00</updated><title type='text'>Olympus Pen E-PL3 Digital Camera Review - Great Little Camera</title><content type='html'>&lt;div class='posterous_autopost'&gt;Have you ever wondered what exactly is up with Olympus Pen E-PL3 Digital Camera review? This informative report can give you an insight into everything you've ever wanted to know about Olympus Pen E-PL3 Digital Camera review.    Truthfully, the only difference between you and Olympus Pen E-PL3 Digital Camera review experts is time. If you'll invest a little more time in reading, you'll be that much nearer to expert status when it comes to Olympus Pen E-PL3 Digital Camera review.    If you&lt;p&gt;&lt;a href="http://www.wannah.tk/olympus-pen-e-pl3-digital-camera-review/"&gt;Olympus E-PL3 Digital Camera Review&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7518935001675859112?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7518935001675859112/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7518935001675859112' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7518935001675859112'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7518935001675859112'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/olympus-pen-e-pl3-digital-camera-review.html' title='Olympus Pen E-PL3 Digital Camera Review - Great Little Camera'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-2686174900164187361</id><published>2011-10-12T09:02:00.001+08:00</published><updated>2011-10-12T09:02:35.742+08:00</updated><title type='text'>Panasonic Lumix DMC-GF3 Digital Camera Review - Easy To Use Shooter</title><content type='html'>&lt;div class='posterous_autopost'&gt;The only way to keep up with the latest about Panasonic Lumix DMC-GF3 Digital Camera Review is to constantly stay on the lookout for new information. If you read everything you find about Panasonic Lumix DMC-GF3 Digital Camera Review, it won't take long for you to become an influential authority.    If you interested, you can check our latest Best Electronic Gadgets Review – &lt;a href="http://www.wannah.tk/blog/technology-news/best-electronic-gadgets-review/"&gt;http://www.wannah.tk/blog/technology-news/best-electronic-gadgets-review/&lt;/a&gt;  Panasonic has gone the extra mile to make&lt;p&gt;&lt;a href="http://www.wannah.tk/panasonic-lumix-dmc-gf3-digital-camera-review-easy-to-use-shooter/"&gt;Panasonic Lumix DMC-GF3 Digital Camera Review&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-2686174900164187361?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/2686174900164187361/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=2686174900164187361' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2686174900164187361'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2686174900164187361'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/panasonic-lumix-dmc-gf3-digital-camera.html' title='Panasonic Lumix DMC-GF3 Digital Camera Review - Easy To Use Shooter'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-304826872949054834</id><published>2011-10-12T07:07:00.001+08:00</published><updated>2011-10-12T07:07:32.160+08:00</updated><title type='text'>Monster Beats Pro Professional Headphones Review</title><content type='html'>&lt;div class='posterous_autopost'&gt;The only way to keep up with the latest about Monster Beats Pro Professional Headphones Review is to constantly stay on the lookout for new information. If you read everything you find about Monster Beats Pro Professional Headphones Review, it won't take long for you to become an influential authority.    If you interested, you can check our latest Best Electronic Gadgets Review - &lt;a href="http://www.wannah.tk/blog/technology-news/best-electronic-gadgets-review/"&gt;http://www.wannah.tk/blog/technology-news/best-electronic-gadgets-review/&lt;/a&gt;  Headphones usually fall short in the&lt;p&gt;&lt;a href="http://www.wannah.tk/monster-beats-pro-professional-headphones-review/"&gt;Monster Beats Pro Professional Headphones Review&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-304826872949054834?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/304826872949054834/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=304826872949054834' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/304826872949054834'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/304826872949054834'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/monster-beats-pro-professional.html' title='Monster Beats Pro Professional Headphones Review'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5804476685799668919</id><published>2011-10-11T11:20:00.001+08:00</published><updated>2011-10-11T11:20:00.034+08:00</updated><title type='text'>The first enemy of Muslims</title><content type='html'>&lt;div class='posterous_autopost'&gt;If you have even a passing interest in the topic of who is the first enemy of Muslims, then you should take a look at the following information. This enlightening article presents some of the latest news on the subject of who is the first enemy of Muslims.    Knowledge can give you a real advantage. To make sure you're fully informed about who is the first enemy of Muslims, keep reading.    Before we start discuss on who is the first enemy of Muslims, you can take a look at our other&lt;p&gt;&lt;a href="http://www.wannah.tk/the-first-enemy-of-muslims/"&gt;The first enemy of Muslims&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5804476685799668919?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5804476685799668919/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5804476685799668919' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5804476685799668919'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5804476685799668919'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/first-enemy-of-muslims.html' title='The first enemy of Muslims'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-8635293831520145475</id><published>2011-10-10T07:24:00.001+08:00</published><updated>2011-10-10T07:24:49.286+08:00</updated><title type='text'>MALAYSIA CIDB COURSES AND SEMINARS IN SANDAKAN</title><content type='html'>&lt;div class='posterous_autopost'&gt;MALAYSIA CIDB COURSES AND SEMINARS      MALAYSIA CIDB COURSES AND SEMINARS ON OCTOBER 10, 2011  Wannah Enterprise will attend seminars of Construction Industry Development Board (CIDB) today, October 10, 2011. Further developments will be written later.    Imagine the next time you join a discussion about MALAYSIA CIDB COURSES AND SEMINARS. When you start sharing the fascinating MALAYSIA CIDB COURSES AND SEMINARS facts below, your friends will be absolutely amazed.    It seems like new&lt;p&gt;&lt;a href="http://www.wannah.tk/malaysia-cidb-courses-and-seminars-in-sandakan/"&gt;MALAYSIA CIDB COURSES AND SEMINARS&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-8635293831520145475?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/8635293831520145475/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=8635293831520145475' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8635293831520145475'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8635293831520145475'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/malaysia-cidb-courses-and-seminars-in.html' title='MALAYSIA CIDB COURSES AND SEMINARS IN SANDAKAN'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-2687489902154376180</id><published>2011-10-09T03:27:00.001+08:00</published><updated>2011-10-09T03:27:25.677+08:00</updated><title type='text'>E-Commerce Store and Website Design Services</title><content type='html'>&lt;div class='posterous_autopost'&gt;E-Commerce Store and Web site Design Services    &amp;nbsp;    Wannah Enterprise is Malaysia web design company and ecommerce website design company.  If you trying for ecommerce web site style ideas and ecommerce website design inspiration for your online shop or e-commerce store on-line, Wannah Enterprise can remodel your web site as e-commerce store online.  &amp;nbsp;    If you wish to get additional info our website design service, you'll contact us immediately  Contact us today for e-commerce&lt;p&gt;&lt;a href="http://www.wannah.tk/our-services/e-commerce-store-and-web-design-services/"&gt;E-Commerce Store and Website Design Services&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-2687489902154376180?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/2687489902154376180/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=2687489902154376180' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2687489902154376180'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2687489902154376180'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/e-commerce-store-and-website-design.html' title='E-Commerce Store and Website Design Services'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-3011109579292716470</id><published>2011-10-07T22:48:00.001+08:00</published><updated>2011-10-07T22:48:22.856+08:00</updated><title type='text'>Malaysian Budget 2012: Enhancing Small and Medium Enterprises (SMEs)</title><content type='html'>&lt;div class='posterous_autopost'&gt;If you are seriously interested in knowing about Enhancing Small and Medium Enterprises, you need to think beyond the basics. This informative article takes a closer study things you would like to understand about Enhancing Small and Medium Enterprises.    The a lot of authentic info about Enhancing Small and Medium Enterprises you recognize, the more likely people are to contemplate you a Enhancing Small and Medium Enterprises skilled. Read on for even more Enhancing Small and Medium&lt;p&gt;&lt;a href="http://www.wannah.tk/enhancing-small-and-medium-enterprises/"&gt;Enhancing Small and Medium Enterprises (SMEs)&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-3011109579292716470?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/3011109579292716470/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=3011109579292716470' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3011109579292716470'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3011109579292716470'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/malaysian-budget-2012-enhancing-small.html' title='Malaysian Budget 2012: Enhancing Small and Medium Enterprises (SMEs)'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-4324561301910229605</id><published>2011-10-07T18:52:00.001+08:00</published><updated>2011-10-07T18:52:49.749+08:00</updated><title type='text'>Malaysia Budget 2012: Reducing inflation, enhancing well-being of rakyat</title><content type='html'>&lt;div class='posterous_autopost'&gt;Thus what's Malaysia Budget 2012 extremely all concerning? The following report includes some fascinating information about Malaysia Budget 2012--data you'll use, not just the recent stuff they used to tell you.  It looks like new information is discovered about something each day. And the subject of Malaysia Budget 2012 is no exception. Keep reading to induce a lot of fresh news regarding Malaysia Budget 2012.  News on Malaysia Budget 2012  KUALA LUMPUR: The RM230.83three billion Federal&lt;p&gt;&lt;a href="http://www.wannah.tk/malaysia-budget-2012/"&gt;Malaysia Budget 2012 (Bajet Malaysia 2012)&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-4324561301910229605?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/4324561301910229605/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=4324561301910229605' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4324561301910229605'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4324561301910229605'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/malaysia-budget-2012-reducing-inflation.html' title='Malaysia Budget 2012: Reducing inflation, enhancing well-being of rakyat'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-654632804626325819</id><published>2011-10-07T09:59:00.001+08:00</published><updated>2011-10-07T09:59:15.080+08:00</updated><title type='text'>Your Tummy Fat Could Be Killing You!</title><content type='html'>&lt;div class='posterous_autopost'&gt;The following paragraphs summarize the work of Tummy Fat specialists who are completely acquainted with all the aspects of Tummy Fat. Heed their recommendation to avoid any Tummy Fat surprises.    Truthfully, the sole difference between you and Tummy Fat specialists is time. If you may invest a little additional time in reading, you will be that a lot of nearer to expert status when it involves Tummy Fat.    Read more information about Weight Loss Motivation Tips -&lt;p&gt;&lt;a href="http://www.wannah.tk/your-tummy-fat-could-be-killing-you/"&gt;Your Tummy Fat Could Be Killing You&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-654632804626325819?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/654632804626325819/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=654632804626325819' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/654632804626325819'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/654632804626325819'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/your-tummy-fat-could-be-killing-you.html' title='Your Tummy Fat Could Be Killing You!'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5747886337145788377</id><published>2011-10-06T12:17:00.001+08:00</published><updated>2011-10-06T12:17:20.929+08:00</updated><title type='text'>Did Steve Jobs Die - When Did Steve Jobs Die</title><content type='html'>&lt;div class='posterous_autopost'&gt;When you think about Steve Jobs Die, what do you think of first? Which aspects of Steve Jobs Die are important, which are essential, and which ones can you take or leave? You be the judge.    If you base what you do on inaccurate information, you might be unpleasantly surprised by the consequences. Make sure you get the whole Steve Jobs Die story from informed sources.    &amp;nbsp;  Who is Steve Jobs  Steven Paul Jobs (February 24, 1955 – October 5, 2011) was an American computer entrepreneur&lt;p&gt;&lt;a href="http://www.wannah.tk/did-steve-jobs-die/"&gt;Did Steve Jobs Die - When Did Steve Jobs Die&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5747886337145788377?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5747886337145788377/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5747886337145788377' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5747886337145788377'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5747886337145788377'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/did-steve-jobs-die-when-did-steve-jobs.html' title='Did Steve Jobs Die - When Did Steve Jobs Die'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5650989553917155457</id><published>2011-10-06T10:44:00.001+08:00</published><updated>2011-10-06T10:44:54.451+08:00</updated><title type='text'>Why You need Web Hosting Services</title><content type='html'>&lt;div class='posterous_autopost'&gt;Do you ever feel like you recognize just enough about why you need web hosting services to be dangerous? Let's see if we will fill in a number of the gaps with the latest information from why you need net hosting services specialists.    Those of you not familiar with the most recent on why you would like internet hosting now have a minimum of a basic understanding. But there's a lot of to come.    The following article lists some straightforward, informative tips that can help you have a&lt;p&gt;&lt;a href="http://www.wannah.tk/why-you-need-web-hosting-services/"&gt;Why Do We Need Web Hosting Services&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5650989553917155457?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5650989553917155457/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5650989553917155457' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5650989553917155457'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5650989553917155457'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/why-you-need-web-hosting-services.html' title='Why You need Web Hosting Services'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-8853359728066507458</id><published>2011-10-06T08:13:00.001+08:00</published><updated>2011-10-06T08:13:01.572+08:00</updated><title type='text'>Eczema and therefore the beheaded pimple</title><content type='html'>&lt;div class='posterous_autopost'&gt;Have you ever puzzled if what you recognize about Eczema and also the beheaded pimple is accurate? Consider the following paragraphs and compare what you recognize to the latest info on Eczema and also the beheaded pimple.    If you interested, you can read more about Skin Condition Symptoms - &lt;a href="http://www.wannah.tk/blog/health-and-fitness-tips-of-the-day/skin-condition-symptoms/"&gt;http://www.wannah.tk/blog/health-and-fitness-tips-of-the-day/skin-condition-s...&lt;/a&gt;.    Another interesting Information on Eczema Skin Condition can be found here -&lt;p&gt;&lt;a href="http://www.wannah.tk/eczema-and-the-beheaded-pimple/"&gt;Eczema and the beheaded pimple&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-8853359728066507458?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/8853359728066507458/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=8853359728066507458' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8853359728066507458'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8853359728066507458'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/eczema-and-therefore-beheaded-pimple.html' title='Eczema and therefore the beheaded pimple'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-6863119641130200144</id><published>2011-10-05T18:17:00.001+08:00</published><updated>2011-10-05T18:17:23.301+08:00</updated><title type='text'>Is it Haram (Illegal) in Islam, if we use pirated software</title><content type='html'>&lt;div class='posterous_autopost'&gt;When most people think of the use of pirated software in Islam, what comes to mind is usually basic information that's not particularly interesting or beneficial. But there's a lot more to the use of pirated software in Islam than just the basics.    How can you put a limit on learning more? The next section may contain that one little bit of wisdom that changes everything.    As we already know, not everyone is able to get a computer software. But, never made it as an excuse for us to use&lt;p&gt;&lt;a href="http://www.wannah.tk/is-it-haram-illegal-in-islam-if-we-use-pirated-software/"&gt;Is it Haram (Illegal) in Islam, if we use pirated software&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-6863119641130200144?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/6863119641130200144/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=6863119641130200144' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/6863119641130200144'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/6863119641130200144'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/is-it-haram-illegal-in-islam-if-we-use.html' title='Is it Haram (Illegal) in Islam, if we use pirated software'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-903742515675429983</id><published>2011-10-05T08:26:00.001+08:00</published><updated>2011-10-05T08:26:06.047+08:00</updated><title type='text'>Local Internet Marketing Services</title><content type='html'>&lt;div class='posterous_autopost'&gt;Are you trying for some inside info on Local internet marketing services? Here's an updated report from Local net selling services in Malaysia consultants who should apprehend.    Most of this info comes straight from the Local internet marketing services in Malaysia professionals. Careful reading to the top virtually guarantees that you may grasp what they grasp.  Introduction to Local Internet Marketing Services  Internet Marketing will be defined as the selling of product and services using&lt;p&gt;&lt;a href="http://www.wannah.tk/our-services/local-internet-marketing-services/"&gt;Local Internet Marketing Services&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-903742515675429983?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/903742515675429983/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=903742515675429983' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/903742515675429983'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/903742515675429983'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/local-internet-marketing-services.html' title='Local Internet Marketing Services'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-189036368938600998</id><published>2011-10-04T17:33:00.001+08:00</published><updated>2011-10-04T17:33:53.060+08:00</updated><title type='text'>Video: Mahathir VS Western</title><content type='html'>&lt;div class='posterous_autopost'&gt;Have you ever questioned if what you know concerning Video: Mahathir VS Western is accurate? Consider the subsequent paragraphs and compare what you recognize to the newest data on Video: Mahathir VS Western.    Read more about Politics - &lt;a href="http://www.wannah.tk/blog/politics-news/"&gt;http://www.wannah.tk/blog/politics-news/&lt;/a&gt;  It's extremely a smart plan to probe a very little deeper into the topic of Video: Mahathir VS Western. What you learn may offer you the arrogance you need to venture into new areas.  Mahathir VS Western  Introduction&lt;p&gt;&lt;a href="http://www.wannah.tk/video-mahathir-vs-western/"&gt;Video: Mahathir VS Western&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-189036368938600998?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/189036368938600998/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=189036368938600998' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/189036368938600998'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/189036368938600998'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/video-mahathir-vs-western.html' title='Video: Mahathir VS Western'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5245680954906067366</id><published>2011-10-04T08:34:00.001+08:00</published><updated>2011-10-04T08:34:10.606+08:00</updated><title type='text'>Writing A Business Plan : What Makes A Sensible One</title><content type='html'>&lt;div class='posterous_autopost'&gt;Would you like to search out out what those-in-the-recognize have to say concerning Writing A Business Plan? The info within the article below comes straight from well-informed experts with special information concerning Writing A Business Plan.    If you base what you are doing on inaccurate info, you may be unpleasantly surprised by the implications. Make sure you get the whole Writing A Business Plan story from informed sources.    Read more about Business Management Issues Today -&lt;p&gt;&lt;a href="http://www.wannah.tk/writing-a-business-plan/"&gt;Writing A Business Plan&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5245680954906067366?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5245680954906067366/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5245680954906067366' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5245680954906067366'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5245680954906067366'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/10/writing-business-plan-what-makes.html' title='Writing A Business Plan : What Makes A Sensible One'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-3317675440690180792</id><published>2011-08-29T09:14:00.001+08:00</published><updated>2011-08-29T09:14:43.062+08:00</updated><title type='text'>How To Promote Your Business On Twitter Easily</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;Current info about How To &lt;a href="http://www.monstrous.tk/blog/small-business-promotional-strategies/" target="_blank"&gt;Promote Your Business&lt;/a&gt; On Twitter is not always the easiest thing to locate. Fortunately, this report includes the latest How To Promote Your Business On Twitter info available.&lt;br /&gt;&lt;br /&gt;If you base what you do on inaccurate information, you might be unpleasantly surprised by the consequences. Make sure you get the whole How To Promote Your Business On Twitter story from informed sources.&lt;br /&gt;&lt;h1&gt;Watch this Video To Learn How To Promote Your Business On Twitter&lt;/h1&gt;&lt;br /&gt;&lt;strong&gt;&lt;a href="http://www.youtube.com/watch?v=63SShfzPs1w&amp;amp;feature=youtube_gdata" rel="nofollow"&gt;TweetAttacks - The Ultimate Twitter Marketing Software for Total Twitter Domination&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;&lt;br /&gt;&lt;a href="http://www.services.monstrous.tk/go/TweetAttacks/44/7" rel="nofollow" target="_blank"&gt;tweetattacks.com&lt;/a&gt; TweetAttacks is the most complete and only twitter marketing software that does not use API. Its a Twitter Friend Adder, Mass Unfollower, Tweet Scraper, Reply Generator, Retweet Generator, Tweet Spinner, Auto Reply, Mass Retweets, Tw...&lt;br /&gt;&lt;br /&gt;&lt;object width="480" height="360" classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0"&gt;&lt;param name="allowFullScreen" value="true" /&gt;&lt;param name="allowscriptaccess" value="always" /&gt;&lt;param name="src" value="http://www.youtube.com/v/63SShfzPs1w?f=videos&amp;amp;app=youtube_gdata" /&gt;&lt;param name="allowfullscreen" value="true" /&gt;&lt;embed width="480" height="360" type="application/x-shockwave-flash" src="http://www.youtube.com/v/63SShfzPs1w?f=videos&amp;amp;app=youtube_gdata" allowFullScreen="true" allowscriptaccess="always" allowfullscreen="true" /&gt;&lt;/object&gt;&lt;br /&gt;&lt;h2&gt;Why Promote Your Business On Twitter&lt;/h2&gt;&lt;br /&gt;[caption id="attachment_807" align="alignright" width="300" caption="How To Promote Your Business On Twitter"]&lt;a href="http://www.services.monstrous.tk/promote-your-business-on-twitter/" rel="nofollow"&gt;&lt;img class="size-medium wp-image-807" title="Promote Your Business On Twitter" src="http://www.monstrous.tk/wp-content/uploads/2011/08/Promote-Your-Business-On-Twitter-300x245.jpg" alt="Promote Your Business On Twitter" width="300" height="245" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;It can be extremely hard for small businesses to reach out to their customers in a significant and meaningful way. When used correctly, Twitter can help a small business owner overcome that particular problem.&lt;br /&gt;&lt;br /&gt;Before you can use Twitter as a tool to help promote your business, you first have to know what Twitter is and why people use it.&lt;br /&gt;&lt;br /&gt;Twitter is a micro-blogging service that limits each post to 140 characters. That limit forces Twitter users to post concise messages, essentially distilling each thought they want to express down to its most basic form.&lt;br /&gt;&lt;br /&gt;People from all over the world use Twitter to engage in conversations with other Twitter users, and just about every topic you can imagine gets discussed. In other words, whatever industry your company covers, someone’s talking about it on Twitter.&lt;br /&gt;&lt;h3&gt;For more information, click here to &lt;span style="text-decoration: underline;"&gt;&lt;em&gt;&lt;strong&gt;&lt;a title="How To Promote Your Business On Twitter" href="http://www.services.monstrous.tk/promote-your-business-on-twitter/" rel="nofollow" target="_blank"&gt;How To Promote Your Business On Twitter&lt;/a&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/span&gt;&lt;/h3&gt;&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-3317675440690180792?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/3317675440690180792/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=3317675440690180792' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3317675440690180792'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3317675440690180792'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/how-to-promote-your-business-on-twitter.html' title='How To Promote Your Business On Twitter Easily'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7888676034685878403</id><published>2011-08-29T08:50:00.001+08:00</published><updated>2011-08-29T08:50:53.776+08:00</updated><title type='text'>Facebook iFrame Training Course</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;Most of this information comes straight from the &lt;span style="text-decoration: underline;"&gt;&lt;em&gt;&lt;strong&gt;Facebook iFrame Training &lt;a href="http://www.monstrous.tk/services/im-courses-2/" target="_blank"&gt;Course&lt;/a&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/span&gt; pros. Careful reading to the end virtually guarantees that you'll know what they know.&lt;br /&gt;&lt;br /&gt;The following article includes pertinent information that may cause you to reconsider what you thought you understood. The most important thing is to study with an open mind and be willing to revise your understanding if necessary.&lt;br /&gt;&lt;br /&gt;Truthfully, the only difference between you and Facebook iFrame Training Course experts is time. If you'll invest a little more time in reading, you'll be that much nearer to expert status when it comes to Facebook iFrame Training Course.&lt;br /&gt;&lt;h1&gt;Why Facebook iFrame Training Course&lt;/h1&gt;&lt;br /&gt;[caption id="attachment_801" align="alignright" width="300" caption="Facebook iFrame Training Course"]&lt;a href="http://www.services.monstrous.tk/facebook-iframe-training-course/" rel="nofollow"&gt;&lt;img class="size-full wp-image-801" title="Facebook-iFrame-Training-Course-300x200" src="http://www.monstrous.tk/wp-content/uploads/2011/08/Facebook-iFrame-Training-Course-300x200.jpg" alt="Facebook iFrame Training Course" width="300" height="200" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;Converting your Facebook Fan pages to the new iFrame format can be a daunting task, especially for those with only a basic knowledge of HTML.&lt;br /&gt;&lt;br /&gt;Facebook’s change to the new IFrame format, while anticipated, happened pretty quickly which led to only a “spattering” of products to try to overcome the challenges. The problem is, most products were packages of example templates with brief instructions or hard to use template systems, UNTIL NOW.&lt;br /&gt;&lt;h2&gt;What is Facebook iFrame Training Course&lt;/h2&gt;&lt;br /&gt;&lt;h3&gt;You can learn more by reading this &lt;a title="Facebook iFrame Training Course" href="http://www.services.monstrous.tk/facebook-iframe-training-course/" rel="nofollow" target="_blank"&gt;Facebook iFrame Training Course&lt;/a&gt;&lt;/h3&gt;&lt;br /&gt;I hope that reading the above information was both enjoyable and educational for you. Your learning process should be ongoing--the more you understand about any subject, the more you will be able to share with others about this Facebook iFrame Training Course.&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7888676034685878403?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7888676034685878403/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7888676034685878403' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7888676034685878403'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7888676034685878403'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/facebook-iframe-training-course_29.html' title='Facebook iFrame Training Course'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-6070202427594142217</id><published>2011-08-29T05:27:00.001+08:00</published><updated>2011-08-29T05:27:01.923+08:00</updated><title type='text'>Ramadan Will Be Over, Has Ramadan Made You a Better Muslim?</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;[caption id="attachment_790" align="alignright" width="300" caption="Has Ramadan Made You a Better Muslim"]&lt;a href="http://www.monstrous.tk/?attachment_id=790" rel="attachment wp-att-790"&gt;&lt;img class="size-medium wp-image-790" title="Ramadan_Kareem" src="http://www.monstrous.tk/wp-content/uploads/2011/08/Ramadan_Kareem-300x225.jpg" alt="Ramadan" width="300" height="225" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;When you think about Ramadan, what do you think of first? Which aspects of Ramadan are important, which are essential, and which ones can you take or leave? You be the judge.&lt;br /&gt;&lt;br /&gt;See how much you can learn about Ramadan when you take a little time to read a well-researched article? Don't miss out on the rest of this great information.&lt;br /&gt;&lt;h1&gt;Why Ramadan&lt;/h1&gt;&lt;br /&gt;Ramadan comes to strengthen our hearts and endear us to piety, good morals, integrity, remembrance of Allah and acts of worship. It helps Muslims to achieve high levels of spirituality and steadfastness.&lt;br /&gt;&lt;br /&gt;Ramadan is also a month of self-discipline. However, Ramadan is almost over now, so let's ask ourselves: What impact did Ramadan have on us? Have we continued to perform our Prayers in the masjid regularly? Do we feel more inclined to read the Qur’an and ponder over its vast meanings? Are we still reading the Qur’an as regularly as we were during Ramadan?&lt;br /&gt;&lt;h2&gt;Have we been able to give charity and lend a helping hand to those who need our assistance as we used to do during Ramadan? Or have we simply gone back to our previous lifestyle as if we had never witnessed Ramadan?&lt;/h2&gt;&lt;br /&gt;&lt;h3&gt;Now it is time for self assessment and reconsideration. We are asking: What kind of person have you become since Ramadan?&lt;/h3&gt;&lt;br /&gt;Feel free to share your contributions, feelings and experiences with us.&lt;br /&gt;&lt;br /&gt;&lt;em&gt;&lt;strong&gt;Happy Shawwal With The Passing Ramadan&lt;/strong&gt;&lt;/em&gt;&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="pp_item" align="left"&gt;&lt;h4 class="pp_title"&gt;Ramadan Will Be Over, Has Ramadan Made You a Better Muslim?&lt;/h4&gt;&lt;p&gt;[caption id="attachment_790" align="alignright" width="300" caption="Has Ramadan Made You a Better Muslim"]&lt;a href="http://www.monstrous.tk/ramadan-will-be-over-has-ramadan-made-you-a-better-muslim/ramadan_kareem/" rel="attachment wp-att-790"&gt;&lt;img class="size-medium wp-image-790" title="Ramadan_Kareem" src="http://www.monstrous.tk/wp-content/uploads/2011/08/Ramadan_Kareem-300x225.jpg" alt="Ramadan" width="300" height="225" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;When you think about Ramadan, what do you think of first? Which aspects of Ramadan are important, which are essential, and which ones can you take or leave? You be the judge.&lt;br /&gt;&lt;br /&gt;See how much you can learn about Ramadan when you take a little time to read a well-researched article? Don't miss out on the rest of this great information.&lt;br /&gt;&lt;h1&gt;Why Ramadan&lt;/h1&gt;&lt;br /&gt;Ramadan comes to strengthen our hearts and endear us to piety, good morals, integrity, remembrance of Allah and acts of worship. It helps Muslims to achieve high levels of spirituality and steadfastness.&lt;br /&gt;&lt;br /&gt;Ramadan is also a month of self-discipline. However, Ramadan is almost over now, so let's ask ourselves: What impact did Ramadan have on us? Have we continued to perform our Prayers in the masjid regularly? Do we feel more inclined to read the Qur’an and ponder over its vast meanings? Are we still reading the Qur’an as regularly as we were during Ramadan?&lt;br /&gt;&lt;h2&gt;Have we been able to give charity and lend a helping hand to those who need our assistance as we used to do during Ramadan? Or have we simply gone back to our previous lifestyle as if we had never witnessed Ramadan?&lt;/h2&gt;&lt;br /&gt;&lt;h3&gt;Now it is time for self assessment and reconsideration. We are asking: What kind of person have you become since Ramadan?&lt;/h3&gt;&lt;br /&gt;Feel free to share your contributions, feelings and experiences with us.&lt;br /&gt;&lt;br /&gt;&lt;em&gt;&lt;strong&gt;Happy Shawwal With The Passing Ramadan&lt;/strong&gt;&lt;/em&gt;&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-6070202427594142217?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/6070202427594142217/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=6070202427594142217' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/6070202427594142217'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/6070202427594142217'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/ramadan-will-be-over-has-ramadan-made.html' title='Ramadan Will Be Over, Has Ramadan Made You a Better Muslim?'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-1383557764805415476</id><published>2011-08-24T02:36:00.001+08:00</published><updated>2011-08-24T02:36:28.424+08:00</updated><title type='text'>Cost Effective Facebook Marketing Services</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;The more you understand about Facebook Marketing Services, the more interesting it becomes. As you read this article you'll find that the subject of &lt;em&gt;&lt;strong&gt;Facebook Marketing Services&lt;/strong&gt;&lt;/em&gt; is certainly no exception.&lt;br /&gt;&lt;br /&gt;If your Facebook Marketing Strategies are out-of-date, how will that affect your actions and decisions? Make certain you don't let important Facebook Marketing Services information slip by you.&lt;br /&gt;&lt;h1&gt;Why go for Facebook Marketing Services&lt;/h1&gt;&lt;br /&gt;&lt;a title="Buy Guaranteed Facebook Fans" href="http://www.services.monstrous.tk/full-internet-marketing-services/facebook-marketing-services-and-solutions/buy-guaranteed-facebook-fans/" rel="nofollow" target="_blank"&gt;Buy Guaranteed Facebook Fans&lt;/a&gt; is one part of the Facebook Marketing Services that we offer and you will see a significant growth in your business. More and more businesses are realizing the power of Facebook when it comes to marketing and making money. And the fastest way to do this is to add targeted individuals to your Facebook fans page via a reputable business that offers this service.&lt;br /&gt;&lt;br /&gt;[caption id="" align="alignright" width="256" caption="Facebook Marketing Services"]&lt;a href="http://www.services.monstrous.tk/full-internet-marketing-services/facebook-marketing-services-and-solutions/buy-guaranteed-facebook-fans/" rel="nofollow"&gt;&lt;img title="Facebook Marketing Services" src="http://www.services.monstrous.tk/wp-content/uploads/2011/08/Buy-Guaranteed-Facebook-Fans.png" alt="Facebook Marketing Services" width="256" height="256" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;When you buys fans using a professional provider the first thing you will need to do is choose how many fans you want to add to your Facebook account. There are many services that offer a range of fan packages starting from 1 thousands to over a million. There are millions of people using Facebook, even the Queen of England, and these services have no small supply of fans that will be interested in your services.&lt;br /&gt;&lt;h2&gt;Get Cheap Facebook Marketing Services&lt;/h2&gt;&lt;br /&gt;Monstrous SEO can help you utilize the marketing power of Facebook with our &lt;span style="text-decoration: underline;"&gt;&lt;a title="Cost effective Facebook Marketing Services" href="http://www.services.monstrous.tk/full-internet-marketing-services/facebook-marketing-services-and-solutions/" rel="nofollow" target="_blank"&gt;cost effective Facebook Marketing Services&lt;/a&gt;&lt;/span&gt;. Stop guessing with your &lt;a href="http://www.monstrous.tk/" target="_blank"&gt;Internet marketing strategies&lt;/a&gt; and start seeing real results with the help of our Facebook Marketing Services.&lt;br /&gt;&lt;br /&gt;When word gets around about your command of Facebook Marketing Services facts, others who need to know about Facebook Marketing Services will start to actively seek you out.&lt;br /&gt;&lt;h3&gt;Click here to Get &lt;a title="Buy Guaranteed Facebook Fans" href="http://www.services.monstrous.tk/full-internet-marketing-services/facebook-marketing-services-and-solutions/buy-guaranteed-facebook-fans/" rel="nofollow" target="_blank"&gt;The Cheapest Facebook Marketing Services&lt;/a&gt;&lt;/h3&gt;&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-1383557764805415476?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/1383557764805415476/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=1383557764805415476' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1383557764805415476'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1383557764805415476'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/cost-effective-facebook-marketing.html' title='Cost Effective Facebook Marketing Services'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-8854170868775065598</id><published>2011-08-24T00:01:00.001+08:00</published><updated>2011-08-24T00:01:21.046+08:00</updated><title type='text'>Harness the power of Google Plus</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;Current info about Google PLUS Exposed is not always the easiest thing to locate. Fortunately, this report includes the latest Google PLUS Exposed info available.&lt;br /&gt;&lt;br /&gt;If you base what you do on inaccurate information, you might be unpleasantly surprised by the consequences. Make sure you get the whole Google PLUS Exposed story from informed sources.&lt;br /&gt;&lt;h1&gt;What is Google Plus&lt;/h1&gt;&lt;br /&gt;Dear Fellow Internet Marketer,&lt;br /&gt;&lt;br /&gt;Have you heard of the hottest and newest social network?&lt;br /&gt;&lt;br /&gt;Yes, Google's BIG new social networking site, Google Plus is LIVE and the buzz around it is Crazy!&lt;br /&gt;&lt;br /&gt;The time to join Google Plus and start marketing with it to gain a huge advantage for your business is NOW.&lt;br /&gt;&lt;br /&gt;The fact that Google plus is linked to it's search engine is causing the hype to become even bigger.&lt;br /&gt;&lt;br /&gt;The marketing potential of Google Plus is huge and time is right for YOU to start joining the revolution.&lt;br /&gt;&lt;br /&gt;Yes, by utilizing Google Plus, you can easily:&lt;br /&gt;&lt;ol&gt;&lt;br /&gt;	&lt;li&gt;Position yourself as a leader in your market&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Gain HUGE exposure for yourself and your business&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Get more traffic to your websites and products&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Generate bigger profits and make more money online&lt;/li&gt;&lt;br /&gt;&lt;/ol&gt;&lt;br /&gt;The problem is where are you going to find killer info on how to join Google Plus and how to use it to boost your business.&lt;br /&gt;&lt;h2&gt;Why Google Plus&lt;/h2&gt;&lt;br /&gt;Google Plus is still quite new and not many people know how to properly market their business with Google Plus.&lt;br /&gt;&lt;br /&gt;But, don't worry, because...&lt;br /&gt;&lt;br /&gt;I have finally decided to reveal all my strategies and &lt;a href="http://www.services.monstrous.tk/effective-marketing-strategies-for-small-business/" target="_blank"&gt;techniques to market your business&lt;/a&gt; on Google Plus.&lt;br /&gt;&lt;br /&gt;After extensive research and trial and error I have compiled everything I know in an all revealing comprehensive course that will show you everything you need to know to boost your business with Google + and Google +1 button.&lt;br /&gt;&lt;br /&gt;Yes, the information that you are about to receive is brand new and never seen before.&lt;br /&gt;&lt;br /&gt;You can use these strategies and step-by-step blueprint to start marketing your business on Google Plus TODAY.&lt;br /&gt;&lt;br /&gt;So what exactly am I offering you?&lt;br /&gt;&lt;h3 style="text-align: center;"&gt;Revealing:&lt;br /&gt;&lt;span style="text-decoration: underline;"&gt;&lt;em&gt;&lt;strong&gt;&lt;a title="Google Plus Exposed" href="http://www.services.monstrous.tk/go/Google-Plus-Exposed/" target="_blank"&gt; Google Plus Exposed&lt;/a&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/span&gt;&lt;/h3&gt;&lt;br /&gt;[caption id="attachment_110" align="aligncenter" width="202" caption="Google PLUS Exposed"]&lt;a href="http://www.services.monstrous.tk/go/Google-Plus-Exposed/"&gt;&lt;img class="size-medium wp-image-110" title="Google PLUS Exposed" src="http://www.services.monstrous.tk/wp-content/uploads/2011/08/Google-PLUS-Exposed-202x300.png" alt="Google PLUS" width="202" height="300" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;h4&gt;Google PLUS Exposed reveals:&lt;/h4&gt;&lt;br /&gt;&lt;ol&gt;&lt;br /&gt;	&lt;li&gt;Easy ways to get accepted to Google + almost instantly for free.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Step-by-step instructions with screenshots to setup your business profile properly.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;How to use Google BUZZ to skyrocket your business.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;The power of Google CIRCLES to increase your online exposure.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;How to use Google STREAMS of information for your business' benefit.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;How to make use of REAL TIME CHAT for your business.&lt;/li&gt;&lt;br /&gt;&lt;/ol&gt;&lt;br /&gt;&lt;strong&gt;It also contains HOT strategies like:&lt;/strong&gt;&lt;br /&gt;&lt;ol&gt;&lt;br /&gt;	&lt;li&gt;Best ways to use the Google +1 BUTTON and Google Statistics to make more money.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;How to use all the different Google Chrome EXTENSIONS with Google PLUS to boost your business.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Secret tips to get FLOODS of targeted Google +1 recommendations for your sites and products.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;HOT resources that you can use to increase your marketing efforts with Google +.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;And much more...&lt;/li&gt;&lt;br /&gt;&lt;/ol&gt;&lt;br /&gt;&amp;nbsp;&lt;br /&gt;&lt;br /&gt;[caption id="attachment_112" align="aligncenter" width="300" caption="Buy Google Plus Secret Exposed Today! 9.95 Only"]&lt;a href="http://www.services.monstrous.tk/go/Google-Plus-Exposed/"&gt;&lt;img class="size-medium wp-image-112" title="Buy Google Plus" src="http://www.services.monstrous.tk/wp-content/uploads/2011/08/buy-Google-Plus-300x153.jpg" alt="Google Plus" width="300" height="153" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;&lt;a title="Google Plus Exposed" href="http://www.services.monstrous.tk/go/Google-Plus-Exposed/" target="_blank"&gt;Secret of Google Plus&lt;/a&gt;&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-8854170868775065598?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/8854170868775065598/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=8854170868775065598' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8854170868775065598'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8854170868775065598'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/harness-power-of-google-plus.html' title='Harness the power of Google Plus'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7573429977172203980</id><published>2011-08-22T10:10:00.001+08:00</published><updated>2011-08-22T10:10:01.270+08:00</updated><title type='text'>How To Setup A Fan Page On Facebook</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="center"&gt;&lt;img src="http://static.pixelpipe.com/4786f0f1-5a8a-411c-bc77-d7e9d15193c3_b.jpg" style="max-width: 100%;" /&gt;&lt;p&gt;When you think about How To Setup A Fan Page On Facebook, what do you think of first? Which aspects of How To Setup A Fan Page On Facebook are important, which are essential, and which ones can you take or leave? You be the judge.&lt;br /&gt;&lt;br /&gt;Knowledge can give you a real advantage. To make sure you're fully informed about How To Setup A Fan Page On Facebook, keep reading.&lt;br /&gt;&lt;h1&gt;Why Setup A Fan Page On Facebook&lt;/h1&gt;&lt;br /&gt;Getting a new product ready to market is just the first step.&lt;br /&gt;&lt;br /&gt;[caption id="attachment_99" align="alignright" width="300" caption="Setup A Fan Page On Facebook"][/caption]&lt;br /&gt;&lt;br /&gt;Then you have to actually create a sales site that will handle payments and automate the delivery of your new product. There are more pieces to a good sales system than most people realize.&lt;br /&gt;&lt;ol&gt;&lt;br /&gt;	&lt;li&gt;Do you need a payment processor? (or a merchant account?)&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Do you have a way to protect your downloads?&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;If you don't already have a HUGE, responsive list...&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Can you recruit and pay affiliates?&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;What about JV Partners?&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Do you have a way to collect follow up info from customers?&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Do you have a back-end product - or a One-Time Offer?&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Will your Sales Page convert? How can you test it?&lt;/li&gt;&lt;br /&gt;&lt;/ol&gt;&lt;br /&gt;It could be a little overwhelming! (gross understatement)&lt;br /&gt;&lt;br /&gt;That's why you need to check out this new software that just a few people have even discovered yet.&lt;br /&gt;&lt;br /&gt;It's called Setup A Fan Page, and it's an all-in-one marketing system that controls lead capture, split-testing, payment processing, affiliate payment, secure downloads, one-time offers, and much more. It installs easily and you can put it on as many sites as you want!&lt;br /&gt;&lt;h2&gt;Watch this video on How to Setup A Fan Page On Facebook&lt;/h2&gt;&lt;br /&gt;&lt;strong&gt;&lt;a href="http://www.youtube.com/watch?v=uv4dQzt4_1w&amp;amp;feature=youtube_gdata" rel="nofollow"&gt;Facebook Fan Pages: Marketing Made Easy&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;&lt;br /&gt;&lt;a title="Setup A Fan Page" href="http://www.services.monstrous.tk/go/Setup-A-Fan-Page/" target="_blank"&gt;www.setupafanpage.com&lt;/a&gt; You've heard about all the targeted traffic on Facebook. It's time you got some for yourself...&lt;br /&gt;&lt;br /&gt;&lt;object width="480" height="360" classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0"&gt;&lt;param name="allowFullScreen" value="true" /&gt;&lt;param name="allowscriptaccess" value="always" /&gt;&lt;param name="src" value="http://www.youtube.com/v/uv4dQzt4_1w?f=videos&amp;amp;app=youtube_gdata" /&gt;&lt;param name="allowfullscreen" value="true" /&gt;&lt;embed width="480" height="360" type="application/x-shockwave-flash" src="http://www.youtube.com/v/uv4dQzt4_1w?f=videos&amp;amp;app=youtube_gdata" allowFullScreen="true" allowscriptaccess="always" allowfullscreen="true" /&gt;&lt;/object&gt;&lt;br /&gt;&lt;br /&gt;&amp;nbsp;&lt;br /&gt;&lt;br /&gt;I'm going to keep this short, because I have no doubt that you are going to want this the moment you see it... especially when you see the price!&lt;br /&gt;&lt;br /&gt;Whether you have your own product, or a hard drive full of PLR or Resale Rights products and have been looking for a way to get them out into the marketplace making you money... the answer is as plain as the nose on your face.&lt;br /&gt;&lt;h3&gt;&lt;span style="text-decoration: underline;"&gt;&lt;em&gt;&lt;strong&gt;&lt;a title="Setup A Fan Page" href="http://www.services.monstrous.tk/go/Setup-A-Fan-Page/" target="_blank"&gt;Click here to learn How To Setup A Fan Page On Facebook&lt;/a&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/span&gt;&lt;/h3&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7573429977172203980?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7573429977172203980/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7573429977172203980' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7573429977172203980'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7573429977172203980'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/how-to-setup-fan-page-on-facebook.html' title='How To Setup A Fan Page On Facebook'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-2151642683849129922</id><published>2011-08-22T07:45:00.001+08:00</published><updated>2011-08-22T07:45:43.825+08:00</updated><title type='text'>Facebook iFrame Training Course</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;The following article presents the very latest information on Facebook iFrame Training Course. If you have a particular interest in Facebook iFrame Training Course, then this informative article is required reading.&lt;br /&gt;&lt;br /&gt;You may not consider everything you just read to be crucial information about Facebook iFrame Training Course. But don't be surprised if you find yourself recalling and using this very information in the next few days.&lt;br /&gt;&lt;h1&gt;Why Facebook iFrame Training Course&lt;/h1&gt;&lt;br /&gt;Converting your Facebook Fan pages to the new iFrame format can be a daunting task, especially for those with only a basic knowledge of HTML.&lt;br /&gt;&lt;br /&gt;Facebook's change to the new IFrame format, while anticipated, happened pretty quickly which led to only a "spattering" of products to try to overcome the challenges. The problem is, most products were packages of example templates with brief instructions or hard to use template systems, UNTIL NOW.&lt;br /&gt;&lt;br /&gt;&lt;strong&gt;Introducing...&lt;/strong&gt;&lt;br /&gt;&lt;br /&gt;[caption id="attachment_92" align="aligncenter" width="300" caption="Facebook iFrame Training Course"]&lt;a href="http://www.services.monstrous.tk/go/Facebook_iFrame_Training_Course/"&gt;&lt;img class="size-medium wp-image-92" title="Facebook iFrame Training Course" src="http://www.services.monstrous.tk/wp-content/uploads/2011/08/Facebook-iFrame-Training-Course-300x200.jpg" alt="Facebook iFrame Training Course" width="300" height="200" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;The Facebook iFrame Training course is not only one of the most comprehensive training programs for implementing Facebook iFrame Fanpages, but it also includes the tools you'll need to get it done!&lt;br /&gt;&lt;h2&gt;Here's What This Facebook iFrame Training Course Includes...&lt;/h2&gt;&lt;br /&gt;Over the Shoulder Videos:&lt;br /&gt;&lt;ul&gt;&lt;br /&gt;	&lt;li&gt;Video 1: Slideshow Overview: A quick walk through of the videos to come and what you will learn.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Video 2: Creating Your Fan Page: An in depth walk through of the differences in fan page types like community pages, band page, product pages etc. and we finish with creating a new fan page.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Video 3: Inside Facebook Fan Pages: Look over my shoulder as I show you the different options and settings inside fan pages.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;Video 4: Facebook APPS 101: You will learn all about FB apps settings, for both iframe canvas apps and iframe tabbed apps. At the end I finish up with creating a new FB app live for you.&lt;/li&gt;&lt;br /&gt;&lt;/ul&gt;&lt;br /&gt;&lt;strong&gt;Easy to Install Wordpress Theme:&lt;/strong&gt;&lt;br /&gt;&lt;br /&gt;&lt;strong&gt;Dynamic Theme: This theme is super dynamic with your header space and its hooked into wp-pages, wp-custom-menus and wp-widgets. It works perfectly with Facebook iFrames!&lt;/strong&gt;&lt;br /&gt;&lt;br /&gt;&lt;strong&gt;Install Video: Look Over My Shoulder WP Theme Setup Tutorial.&lt;/strong&gt;&lt;br /&gt;&lt;br /&gt;There's a lot to understand about Facebook iFrame Training Course. We were able to provide you with some of the facts above, but there is still plenty more to write about in subsequent articles.&lt;br /&gt;&lt;h3 style="text-align: center;"&gt;&lt;a title="Facebook iFrame Training Course" href="http://www.services.monstrous.tk/go/Facebook_iFrame_Training_Course/" target="_blank"&gt;&lt;em&gt;&lt;strong&gt;&lt;span style="color: #ff0000;"&gt;Complete Facebook iFrame Training Course ONLY $10!&lt;/span&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/a&gt;&lt;/h3&gt;&lt;br /&gt;[caption id="" align="aligncenter" width="348" caption="The Facebook iFrame Training Course"]&lt;a href="http://www.services.monstrous.tk/go/Facebook_iFrame_Training_Course/" target="_blank"&gt;&lt;img class=" " title="Facebook iFrame Training Course" src="http://getinstantpayments.com/iframetrain/images/btn-buy-now.jpg" alt="Facebook iFrame Training Course" width="348" height="131" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-2151642683849129922?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/2151642683849129922/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=2151642683849129922' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2151642683849129922'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/2151642683849129922'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/facebook-iframe-training-course.html' title='Facebook iFrame Training Course'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-3229517217307757100</id><published>2011-08-17T08:40:00.001+08:00</published><updated>2011-08-17T08:40:28.505+08:00</updated><title type='text'>Facebook Marketing Ideas</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;Current info about &lt;span style="text-decoration: underline;"&gt;&lt;em&gt;&lt;strong&gt;&lt;a href="http://www.services.monstrous.tk/blog/using-social-media-for-marketing/" target="_blank"&gt;Facebook Marketing Ideas&lt;/a&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/span&gt; is not always the easiest thing to locate. Fortunately, this report includes the latest Facebook Marketing Ideas info available.&lt;br /&gt;&lt;br /&gt;The best time to learn about Facebook Marketing Ideas is before you're in the thick of things. Wise readers will keep reading to earn some valuable Facebook Marketing Ideas experience while it's still free.&lt;br /&gt;&lt;h1&gt;Introduction To Facebook Marketing Ideas&lt;/h1&gt;&lt;br /&gt;[caption id="attachment_54" align="alignright" width="252" caption="Facebook Marketing Ideas"]&lt;a href="http://www.services.monstrous.tk/?attachment_id=54" rel="attachment wp-att-54"&gt;&lt;img class="size-medium wp-image-54" title="Facebook Marketing Ideas" src="http://www.services.monstrous.tk/wp-content/uploads/2011/08/Facebook-Marketing-Ideas-252x300.jpg" alt="Facebook Marketing Ideas" width="252" height="300" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;Facebook is a social networking web site that lets users get in touch with family line and friends completely all over the globe. Because the chance for global vulnerability is so high, many business owners get hold of advantage of the Facebook network to commercialize products and services. Facebook has enforced many features intentional for important marketing that can facilitate throw your business organization a supercharge.&lt;br /&gt;&lt;br /&gt;The profile is the center characteristic of Facebook and an effectual manner to commercialize. This is where you state visitors about yourself or your company. Take away the time to fill up away a bio (company history for a business organization), add up photographs that can assist put a visual to your company envision (products or employees) and state those who associate with your Facebook account what your company specializes in.&lt;br /&gt;&lt;h2&gt;Why do we need to know about Facebook Marketing Ideas&lt;/h2&gt;&lt;br /&gt;Facebook has an user interface you can connect to your Facebook account that allows you to set up details for events. This can be a worthful tool for marketing sales promotions, product launches and particular company events. The event interface allows you to bring event invitations instantly to people who may already be interested in your product or service, helping you host a more successful event.&lt;br /&gt;&lt;h3&gt;How To Use Facebook Marketing Ideas Properly&lt;/h3&gt;&lt;br /&gt;Set up a business page for your company using its official name. Include the company history, location, services, contact information and photographs.&lt;br /&gt;&lt;br /&gt;Pick out a social networking marketing company from which to purchase Facebook fans. The companies uSocial Facebook Marketing, SocialKik, FacebookFans, &lt;a title="FanPageHookup" href="http://www.services.monstrous.tk/go/FanPageHookup/" target="_blank"&gt;FanPageHookup&lt;/a&gt; and others sell Facebook fans. Check into reviews, services and prices before determining upon a Facebook marketing company.&lt;br /&gt;&lt;br /&gt;Many businesses use the popular social networking site Facebook to commercialize their products. By creating a Facebook business page, you can inform possible customers about your services. Individual Facebook users can turn fans of your page, increasing consumer vulnerability to your business organization. As a business proprietor, you can utilize your fans' selective information to aim advertisements and freshly products to your key demographic groups. Buying Facebook fans increases consumer knowingness of your company and products, which may improve your sales.&lt;br /&gt;&lt;br /&gt;Facebook users spend more time on the site than users of the other most-popular sites, such as Google and Yahoo!. The average time users spent on the site was about seven hours per month in a survey in 2011. That high level of engagement means that marketers utilizing Facebook for brand initiatives have a better chance of attracting the attention of a high number of targeted customers than other sites can provide.&lt;br /&gt;&lt;br /&gt;Setting up a Facebook page has turn a touchstone practice for businesses and other organizations. The brand pages, which are cheap to produce and observe, let Facebook users to become "fans" of the page and to view material that the page owner posts, such as images, videos, sales and other news. It also offers a simple way for customers to connect with a brand. Facebook fans can comment on the page owner's posts, submit inquiries or simply make an unsolicited comment. They also can "like," or recommend, the work of a page owner, thereby spreading information about the brand to their Facebook friends.&lt;br /&gt;&lt;br /&gt;Facebook has turn an more and more authoritative spot for marketers to centering their energies. The clear leader in social media users with 500 million dynamic users in 2011, Facebook is the second most-visited web site on the Cyberspace behind only Google. Marketers possess the choice of using Facebook for gratuitous branding initiatives and paid ones.&lt;br /&gt;&lt;br /&gt;Facebook "plugins" are applications that allow you find out what your friends or customers receive liked, commented along or shared out on sites across the World wide web. You can add together plugins to your business organization web site, allowing visitors to "Like" or urge your web site to their friends. Others give notice find who frequents your web site. This is the modern contemporaries of word-of-mouth advertizing. The almost popular Facebook plugins are the Like Button, Activity Feed, Live Stream and Facepile.&lt;br /&gt;&lt;br /&gt;If you've picked some pointers about Facebook Marketing Ideas that you can put into action, then by all means, do so. You won't really be able to gain any benefits from your new knowledge if you don't use this Facebook Marketing Ideas wisely.&lt;br /&gt;&lt;br /&gt;[seo_contact_page_social_media_only]&lt;br /&gt;&lt;br /&gt;Thank you for reading this &lt;a href="http://www.services.monstrous.tk/facebook-marketing-ideas/ " target="_blank"&gt;Facebook Marketing Ideas&lt;/a&gt;&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="pp_item" align="left"&gt;&lt;h4 class="pp_title"&gt;Facebook Marketing Ideas&lt;/h4&gt;&lt;p&gt;Current info about &lt;span style="text-decoration: underline;"&gt;&lt;em&gt;&lt;strong&gt;&lt;a href="http://www.services.monstrous.tk/blog/using-social-media-for-marketing/" target="_blank"&gt;Facebook Marketing Ideas&lt;/a&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/span&gt; is not always the easiest thing to locate. Fortunately, this report includes the latest Facebook Marketing Ideas info available.&lt;br /&gt;&lt;br /&gt;The best time to learn about Facebook Marketing Ideas is before you're in the thick of things. Wise readers will keep reading to earn some valuable Facebook Marketing Ideas experience while it's still free.&lt;br /&gt;&lt;h1&gt;Introduction To Facebook Marketing Ideas&lt;/h1&gt;&lt;br /&gt;[caption id="attachment_54" align="alignright" width="252" caption="Facebook Marketing Ideas"]&lt;a href="http://www.services.monstrous.tk/facebook-marketing-ideas/facebook-marketing-ideas-2/" rel="attachment wp-att-54"&gt;&lt;img class="size-medium wp-image-54" title="Facebook Marketing Ideas" src="http://www.services.monstrous.tk/wp-content/uploads/2011/08/Facebook-Marketing-Ideas-252x300.jpg" alt="Facebook Marketing Ideas" width="252" height="300" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;Facebook is a social networking web site that lets users get in touch with family line and friends completely all over the globe. Because the chance for global vulnerability is so high, many business owners get hold of advantage of the Facebook network to commercialize products and services. Facebook has enforced many features intentional for important marketing that can facilitate throw your business organization a supercharge.&lt;br /&gt;&lt;br /&gt;The profile is the center characteristic of Facebook and an effectual manner to commercialize. This is where you state visitors about yourself or your company. Take away the time to fill up away a bio (company history for a business organization), add up photographs that can assist put a visual to your company envision (products or employees) and state those who associate with your Facebook account what your company specializes in.&lt;br /&gt;&lt;h2&gt;Why do we need to know about Facebook Marketing Ideas&lt;/h2&gt;&lt;br /&gt;Facebook has an user interface you can connect to your Facebook account that allows you to set up details for events. This can be a worthful tool for marketing sales promotions, product launches and particular company events. The event interface allows you to bring event invitations instantly to people who may already be interested in your product or service, helping you host a more successful event.&lt;br /&gt;&lt;h3&gt;How To Use Facebook Marketing Ideas Properly&lt;/h3&gt;&lt;br /&gt;Set up a business page for your company using its official name. Include the company history, location, services, contact information and photographs.&lt;br /&gt;&lt;br /&gt;Pick out a social networking marketing company from which to purchase Facebook fans. The companies uSocial Facebook Marketing, SocialKik, FacebookFans, &lt;a title="FanPageHookup" href="http://www.services.monstrous.tk/go/FanPageHookup/" target="_blank"&gt;FanPageHookup&lt;/a&gt; and others sell Facebook fans. Check into reviews, services and prices before determining upon a Facebook marketing company.&lt;br /&gt;&lt;br /&gt;Many businesses use the popular social networking site Facebook to commercialize their products. By creating a Facebook business page, you can inform possible customers about your services. Individual Facebook users can turn fans of your page, increasing consumer vulnerability to your business organization. As a business proprietor, you can utilize your fans' selective information to aim advertisements and freshly products to your key demographic groups. Buying Facebook fans increases consumer knowingness of your company and products, which may improve your sales.&lt;br /&gt;&lt;br /&gt;Facebook users spend more time on the site than users of the other most-popular sites, such as Google and Yahoo!. The average time users spent on the site was about seven hours per month in a survey in 2011. That high level of engagement means that marketers utilizing Facebook for brand initiatives have a better chance of attracting the attention of a high number of targeted customers than other sites can provide.&lt;br /&gt;&lt;br /&gt;Setting up a Facebook page has turn a touchstone practice for businesses and other organizations. The brand pages, which are cheap to produce and observe, let Facebook users to become "fans" of the page and to view material that the page owner posts, such as images, videos, sales and other news. It also offers a simple way for customers to connect with a brand. Facebook fans can comment on the page owner's posts, submit inquiries or simply make an unsolicited comment. They also can "like," or recommend, the work of a page owner, thereby spreading information about the brand to their Facebook friends.&lt;br /&gt;&lt;br /&gt;Facebook has turn an more and more authoritative spot for marketers to centering their energies. The clear leader in social media users with 500 million dynamic users in 2011, Facebook is the second most-visited web site on the Cyberspace behind only Google. Marketers possess the choice of using Facebook for gratuitous branding initiatives and paid ones.&lt;br /&gt;&lt;br /&gt;Facebook "plugins" are applications that allow you find out what your friends or customers receive liked, commented along or shared out on sites across the World wide web. You can add together plugins to your business organization web site, allowing visitors to "Like" or urge your web site to their friends. Others give notice find who frequents your web site. This is the modern contemporaries of word-of-mouth advertizing. The almost popular Facebook plugins are the Like Button, Activity Feed, Live Stream and Facepile.&lt;br /&gt;&lt;br /&gt;If you've picked some pointers about Facebook Marketing Ideas that you can put into action, then by all means, do so. You won't really be able to gain any benefits from your new knowledge if you don't use this Facebook Marketing Ideas wisely.&lt;br /&gt;&lt;br /&gt;[seo_contact_page_social_media_only]&lt;br /&gt;&lt;br /&gt;Thank you for reading this &lt;a href="http://www.services.monstrous.tk/facebook-marketing-ideas/ " target="_blank"&gt;Facebook Marketing Ideas&lt;/a&gt;&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-3229517217307757100?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/3229517217307757100/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=3229517217307757100' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3229517217307757100'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3229517217307757100'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/facebook-marketing-ideas.html' title='Facebook Marketing Ideas'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-407990466594799267</id><published>2011-08-16T23:37:00.001+08:00</published><updated>2011-08-16T23:37:37.511+08:00</updated><title type='text'>Promote Your Business On Twitter</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;This article explains a few things about Promote Your Business On Twitter, and if you're interested, then this is worth reading, because you can never tell what you don't know.&lt;br /&gt;&lt;br /&gt;The only way to keep up with the latest about Promote Your Business On Twitter is to constantly stay on the lookout for new information. If you read everything you find about Promote Your Business On Twitter, it won't take long for you to become an influential authority.&lt;br /&gt;&lt;br /&gt;Truthfully, the only difference between you and Promote Your Business On Twitter experts is time. If you'll invest a little more time in reading, you'll be that much nearer to expert status when it comes to &lt;span style="text-decoration: underline;"&gt;&lt;em&gt;&lt;strong&gt;&lt;a title="Promote Your Business On Twitter" href="http://www.services.monstrous.tk/promote-your-business-on-twitter" target="_blank"&gt;Promote Your Business On Twitter&lt;/a&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/span&gt;.&lt;br /&gt;&lt;h1&gt;Why Promote Your Business On Twitter&lt;/h1&gt;&lt;br /&gt;It can be extremely difficult for small businesses to reach out to their customers in a significant and meaningful way. When used correctly, Twitter can help a small business owner overcome that particular problem.&lt;br /&gt;&lt;br /&gt;Before you can use Twitter as a tool to help promote your business, you first have to understand what Twitter is and why people use it.&lt;br /&gt;&lt;br /&gt;Twitter is a micro-blogging service that limits each post to 140 characters. That limit forces Twitter users to post concise messages, essentially distilling each thought they want to express down to its most basic form.&lt;br /&gt;&lt;br /&gt;People from all over the world use Twitter to engage in conversations with other Twitter users, and just about every topic you can imagine gets discussed. In other words, whatever industry your company covers, someone’s talking about it on Twitter.&lt;br /&gt;&lt;h2&gt;How To Promote Your Business On Twitter Easily&lt;/h2&gt;&lt;br /&gt;[caption id="attachment_46" align="alignright" width="250" caption="TweetAttacks Promote Your Business On Twitter"]&lt;a href="http://www.services.monstrous.tk/go/TweetAttacks/" target="_blank"&gt;&lt;img class="size-full wp-image-46 " title="Promote Your Business On Twitter" src="http://www.services.monstrous.tk/wp-content/uploads/2011/08/Promote-Your-Business-On-Twitter.jpg" alt="Promote Your Business On Twitter" width="250" height="250" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;The all-in-one twitter marketing software that does not rely on twitter API. Drive thousands of traffic from Twitter and get Twitter followers instantly. When someone Tweets “I want an iPhone” would you like to Tweet them back with your offer automatically or just follow them? It can do that and a lot more. It’s everything a marketer needs to succeed on Twitter. If you eager on &lt;a title="how to use social media for marketing" href="http://www.services.monstrous.tk/" target="_blank"&gt;how to use social media for marketing&lt;/a&gt;, you should be using Twitter for business marketing. Promote your business on Twitter today by using TweetAttacks which is the best &lt;a title="twitter management tools" href="http://www.services.monstrous.tk/" target="_blank"&gt;Twitter management tools&lt;/a&gt; to &lt;a title="get instant twitter followers" href="http://www.services.monstrous.tk/promote-your-business-on-twitter" target="_blank"&gt;get instant Twitter followers&lt;/a&gt;.&lt;br /&gt;&lt;h3&gt;Watch the video below to learn how TweetAttacks Promote Your Business On Twitter&lt;/h3&gt;&lt;br /&gt;&lt;strong&gt;&lt;a href="http://www.youtube.com/watch?v=63SShfzPs1w&amp;amp;feature=youtube_gdata" rel="nofollow"&gt;TweetAttacks - The Ultimate Twitter Marketing Software for Total Twitter Domination&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;&lt;br /&gt;&lt;a title="TweetAttacks" href="http://www.services.monstrous.tk/go/TweetAttacks/" target="_blank"&gt;TweetAttacks&lt;/a&gt; is the most complete and only twitter marketing software that does not use API. Its a Twitter Friend Adder, Mass Unfollower, Tweet Scraper, Reply Generator, Retweet Generator, Tweet Spinner, Auto Reply, Mass Retweets, Tw...&lt;br /&gt;&lt;br /&gt;&lt;object width="480" height="360" classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0"&gt;&lt;param name="allowFullScreen" value="true" /&gt;&lt;param name="allowscriptaccess" value="always" /&gt;&lt;param name="src" value="http://www.youtube.com/v/63SShfzPs1w?f=videos&amp;amp;app=youtube_gdata" /&gt;&lt;param name="allowfullscreen" value="true" /&gt;&lt;embed width="480" height="360" type="application/x-shockwave-flash" src="http://www.youtube.com/v/63SShfzPs1w?f=videos&amp;amp;app=youtube_gdata" allowFullScreen="true" allowscriptaccess="always" allowfullscreen="true" /&gt;&lt;/object&gt;&lt;br /&gt;&lt;br /&gt;When word gets around about your command of Promote Your Business On Twitter facts, others who need to know about Promote Your Business On Twitter will start to actively seek you out.&lt;br /&gt;&lt;h4&gt;Download here - &lt;a title="Promote Your Business On Twitter" href="http://www.services.monstrous.tk/go/TweetAttacks/" target="_blank"&gt;Get TweetAttacks Now To Promote Your Business On Twitter&lt;/a&gt;&lt;/h4&gt;&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-407990466594799267?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/407990466594799267/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=407990466594799267' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/407990466594799267'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/407990466594799267'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/promote-your-business-on-twitter.html' title='Promote Your Business On Twitter'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5220830981288107638</id><published>2011-08-14T02:45:00.001+08:00</published><updated>2011-08-14T02:45:07.402+08:00</updated><title type='text'>Automated Traffic Bot</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;Have you ever wondered what exactly is up with Automated Traffic Bot? This informative report can give you an insight into everything you've ever wanted to know about Automated Traffic Bot.&lt;br /&gt;&lt;h1&gt;Automated Traffic Bot Review&lt;/h1&gt;&lt;br /&gt;&lt;h2&gt;What is Automated Traffic Bot&lt;/h2&gt;&lt;br /&gt;[caption id="" align="alignright" width="125" caption="Automated Traffic Bot"]&lt;a href="http://www.monstrous.tk/go/Automated-Traffic-Bot/" target="_blank"&gt;&lt;img class=" " title="Automated Traffic Bot" src="http://www.monstrous.tk/wp-content/uploads/2011/08/021d16997_sm_2.jpg" alt="Automated Traffic Bot" width="125" height="125" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;Automated Traffic Bot Forces Visitors To Your Website, Blog, And Affiliate Links! This tool will change how you look at search engine optimization forever, even if you’re just getting started.&lt;br /&gt;&lt;br /&gt;Now that we've covered those aspects of Automated Traffic Bot, let's turn to some of the other factors that need to be considered.&lt;br /&gt;&lt;br /&gt;If you are tired of all the complicated search engine information out there, you're far from alone!&lt;br /&gt;&lt;br /&gt;In fact, most people just plain give up on SEO because it's so complicated.&lt;br /&gt;&lt;br /&gt;Worse yet, the majority of people who do follow through with SEO usually see little to no results after all that work!&lt;br /&gt;&lt;br /&gt;You can see that there's practical value in learning more about Automated Traffic Bot. Can you think of ways to apply what's been covered so far?&lt;br /&gt;&lt;br /&gt;You're about to discover how to change all that, for good!&lt;br /&gt;&lt;br /&gt;&lt;a title="Automated Traffic Bot" href="http://www.monstrous.tk/go/Automated-Traffic-Bot/" target="_blank"&gt;Download Automated Traffic Bot&lt;/a&gt;&lt;br /&gt;&lt;br /&gt;This tool will change how you look at search engine optimization forever, even if you're just getting started.&lt;br /&gt;&lt;h3&gt;Automated Traffic Bot Review Video&lt;/h3&gt;&lt;br /&gt;&lt;strong&gt;&lt;a href="http://www.youtube.com/watch?v=5kDCtziEFKE&amp;amp;feature=youtube_gdata" rel="nofollow"&gt;Automated Traffic Bot&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;&lt;br /&gt;Automated Traffic Bot is Traffic Generation Software that guarantees a good search engine rankings. Watch how this traffic software works as shown in the video below.&lt;br /&gt;&lt;br /&gt;&lt;object width="480" height="360" classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0"&gt;&lt;param name="allowFullScreen" value="true" /&gt;&lt;param name="allowscriptaccess" value="always" /&gt;&lt;param name="src" value="http://www.youtube.com/v/5kDCtziEFKE?f=videos&amp;amp;app=youtube_gdata" /&gt;&lt;param name="allowfullscreen" value="true" /&gt;&lt;embed width="480" height="360" type="application/x-shockwave-flash" src="http://www.youtube.com/v/5kDCtziEFKE?f=videos&amp;amp;app=youtube_gdata" allowFullScreen="true" allowscriptaccess="always" allowfullscreen="true" /&gt;&lt;/object&gt;&lt;br /&gt;&lt;br /&gt;If you've been frustrated with traffic generation, you'll love the simplicity and effectiveness of Automated Traffic Bot.&lt;br /&gt;&lt;br /&gt;&lt;a title="Automated Traffic Bot" href="http://www.monstrous.tk/go/Automated-Traffic-Bot/" target="_blank"&gt;Get Automated Traffic Bot&lt;/a&gt;&lt;br /&gt;&lt;br /&gt;Grab Your copy NOW and get it for a STEAL!&lt;br /&gt;&lt;br /&gt;Now you can be a confident expert on Automated Traffic Bot. OK, maybe not an expert. But you should have something to bring to the table next time you join a discussion on Automated Traffic Bot.&lt;br /&gt;&lt;br /&gt;Taken from:&lt;br /&gt;&lt;span style="text-decoration: underline;"&gt;&lt;em&gt;&lt;strong&gt;&lt;a title="Automated Traffic Bot" href="http://www.monstrous.tk/go/Automated-Traffic-Bot/" rel="nofollow" target="_blank"&gt;Automated Traffic Bot&lt;/a&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/span&gt;&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5220830981288107638?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5220830981288107638/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5220830981288107638' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5220830981288107638'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5220830981288107638'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/automated-traffic-bot.html' title='Automated Traffic Bot'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-8261576537329207029</id><published>2011-08-14T01:26:00.001+08:00</published><updated>2011-08-14T01:26:58.225+08:00</updated><title type='text'>WP Slide2See WordPress Plugin</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;[caption id="" align="alignright" width="125" caption="WP Slide2See Wordpress Plugin"]&lt;a href="http://www.monstrous.tk/go/WP-Slide2See/" target="_blank"&gt;&lt;img title="WP Slide2See Wordpress Plugin" src="http://www.monstrous.tk/wp-content/uploads/2011/08/8e7219622_sm_slide2seeboxsmall.png" alt="WP Slide2See Wordpress Plugin" width="125" height="125" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;This article explains a few things about WP Slide2See WordPress Plugin, and if you're interested, then this is worth reading, because you can never tell what you don't know.&lt;br /&gt;&lt;br /&gt;I trust that what you've read so far has been informative. The following section should go a long way toward clearing up any uncertainty that may remain.&lt;br /&gt;&lt;h1&gt;WP Slide2See WordPress Plugin Eliminates Ad Blindness And Increases Ad Conversions!&lt;/h1&gt;&lt;br /&gt;You should be able to find several indispensable facts about WP Slide2See Wordpress Plugin in the following paragraphs. If there's at least one fact you didn't know before, imagine the difference it might make.&lt;br /&gt;&lt;br /&gt;If you don't have accurate details regarding WP Slide2See Wordpress Plugin, then you might make a bad choice on the subject. Don't let that happen: keep reading.&lt;br /&gt;&lt;h2&gt;What is WP Slide2See WordPress Plugin&lt;/h2&gt;&lt;br /&gt;The WP Slide2See WordPress Plugin will allow your ads and optin boxes to effectively slip under your visitors Ad Radar keeping them on your site longer until they actually interact with the content on the page triggering your ads, offers, video, or subscribe boxes to appear dynamically within the content.&lt;br /&gt;&lt;h3&gt;With the WP Slide2See WordPress Plugin you will be able to:&lt;/h3&gt;&lt;br /&gt;&lt;ol&gt;&lt;br /&gt;	&lt;li&gt;- Get visitors to stick around on your blog 2x – 3x’s longer.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;- Instantly achieve higher ad conversion rates.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;- Build your list faster than you ever thought possible.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;- Energize your content with several dynamic interactive sliding elements.&lt;/li&gt;&lt;br /&gt;	&lt;li&gt;- Easily monetize your content with stealth advertising.&lt;/li&gt;&lt;br /&gt;&lt;/ol&gt;&lt;br /&gt;Here Is Your Chance To Completely Transform Your Blog, Boost Your Conversions and Overall Earnings!&lt;br /&gt;&lt;h4&gt;WP Slide2See Wordpress Plugin Review Video&lt;/h4&gt;&lt;br /&gt;&lt;strong&gt;&lt;a href="http://www.youtube.com/watch?v=x47km_s7I6c&amp;amp;feature=youtube_gdata" rel="nofollow"&gt;WP Slide2See WordPress Plugin Review&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;&lt;br /&gt;&lt;a title="WP Slide2See WordPress Plugin" href="http://www.monstrous.tk/go/WP-Slide2See/" target="_blank"&gt;www.wpslide2see.com&lt;/a&gt;. Wp Slide2See WordPress Plugin walk-through and features review.&lt;br /&gt;&lt;br /&gt;&lt;object width="480" height="360" classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0"&gt;&lt;param name="allowFullScreen" value="true" /&gt;&lt;param name="allowscriptaccess" value="always" /&gt;&lt;param name="src" value="http://www.youtube.com/v/x47km_s7I6c?f=videos&amp;amp;app=youtube_gdata" /&gt;&lt;param name="allowfullscreen" value="true" /&gt;&lt;embed width="480" height="360" type="application/x-shockwave-flash" src="http://www.youtube.com/v/x47km_s7I6c?f=videos&amp;amp;app=youtube_gdata" allowFullScreen="true" allowscriptaccess="always" allowfullscreen="true" /&gt;&lt;/object&gt;&lt;br /&gt;&lt;br /&gt;Is there really any information about WP Slide2See WordPress Plugin that is nonessential? We all see things from different angles, so something relatively insignificant to one may be crucial to another.&lt;br /&gt;&lt;br /&gt;Original post:&lt;br /&gt;&lt;br /&gt;&lt;span style="text-decoration: underline;"&gt;&lt;em&gt;&lt;strong&gt;&lt;a title="WP Slide2See Wordpress Plugin" href="http://15246.rapbank.com/products/wp-slide2see-wordpress-plugin/" rel="nofollow" target="_blank"&gt;WP Slide2See WordPress Plugin&lt;/a&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/span&gt;&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-8261576537329207029?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/8261576537329207029/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=8261576537329207029' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8261576537329207029'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8261576537329207029'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/wp-slide2see-wordpress-plugin.html' title='WP Slide2See WordPress Plugin'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-340163602679999991</id><published>2011-08-12T09:03:00.001+08:00</published><updated>2011-08-12T09:03:56.405+08:00</updated><title type='text'>Mass Article Control - Article Marketing Domination - Get Free Traffic Now</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;Think article marketing is dead? Heck no! But it's possible to kill ALL of the hard work involved when you can...&lt;br /&gt;&lt;br /&gt;All the Twitter and social networking stuff aside, article marketing is still the best free traffic method out there.&lt;br /&gt;&lt;a name='more'&gt;&lt;/a&gt;&lt;br /&gt;Why? Because it's exactly what search engines want! They're after high-quality content to send searchers to. Feed them fantastic articles and they'll love you. That means loads of free traffic heading your way.&lt;br /&gt;&lt;br /&gt;Even better, you can ramp it up the more killer articles you put out there, the more free targeted traffic you can get. But here's where the big ugly problem of article marketing will kick you in the teeth...&lt;br /&gt;&lt;br /&gt;Writing articles is kind of like the Internet marketing version of going to the dentist. It's good for you, but you'd rather do anything else.&lt;br /&gt;&lt;br /&gt;First you have to write your articles, which for most people is like climbing Mt. Everest without oxygen. Then you have to submit your articles to a boatload of article directories by hand, which can take days or weeks. By the time you get articles out there to generate traffic for you, it can feel like you've been through a war.&lt;br /&gt;&lt;br /&gt;But really, article marketing itself isn't &amp;quot;hard&amp;quot;, and the results are flat-out phenomenal. The only thing that makes it all a pain in the rump is the manual labor. You can try to avoid it by hiring help, but it ain't cheap.&lt;br /&gt;&lt;br /&gt;So, what if you could cut the costly and slow humans out of the equation and automate nearly all of it? Then you could fire everybody, do everything on your own and still run circles around your competition.&lt;br /&gt;&lt;br /&gt;Well, get ready to do just that, because we'll give you a way to create multiple high-quality, unique articles with the puch...&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-340163602679999991?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/340163602679999991/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=340163602679999991' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/340163602679999991'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/340163602679999991'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/mass-article-control-article-marketing.html' title='Mass Article Control - Article Marketing Domination - Get Free Traffic Now'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-1881981184375752114</id><published>2011-08-12T02:42:00.001+08:00</published><updated>2011-08-12T02:42:56.714+08:00</updated><title type='text'>RAP Bank Affiliate Marketplace</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;&lt;p&gt;Are you looking for some inside information on RAP Bank Affiliate Marketplace? Here's an up-to-date report from RAP Bank Affiliate Marketplace experts who should know.&lt;/p&gt;&lt;br /&gt;&lt;p&gt;It's really a good idea to probe a little deeper into the subject of RAP Bank Affiliate &lt;a href="http://www.monstrous.tk/blog/affiliate-network-programs/" target="_blank"&gt;Marketplace&lt;/a&gt;. What you learn may give you the confidence you need to venture into new areas.&lt;/p&gt;&lt;br /&gt;&lt;h1&gt;RAP Bank Affiliate Marketplace Review&lt;/h1&gt;&lt;br /&gt;&lt;h2&gt;What is RAP Bank Affiliate Marketplace&lt;/h2&gt;&lt;br /&gt;&lt;p&gt;I bet you have heard about clickbank and commission junction many times when you are looking for products to promote. Clickbank is really great but the disadvantage is that you have to wait a long time to get your payment because they will mail you a check. That is very boring to have to wait for the money to appear. But there is another upcoming affiliate website that gives you the money directly after someone buy something through your affiliate link.&lt;/p&gt;&lt;br /&gt;&lt;p&gt;The affiliate website I am talking about is RAP Bank Affiliate Marketplace. RAP Bank Affiliate Marketplace pays directly to your PayPal account, no waiting time for the money.&lt;/p&gt;&lt;br /&gt;&lt;h5&gt;Click here to &lt;span style="text-decoration: underline;"&gt;&lt;em&gt;&lt;strong&gt;&lt;a title="RAP Bank Affiliate Marketplace" href="http://www.monstrous.tk/go/RapBank/" target="_blank"&gt;Join RAP Bank Affiliate Marketplace&lt;/a&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/span&gt;&lt;/h5&gt;&lt;br /&gt;&lt;h3&gt;How to set up a site with a RAP Bank Affiliate Marketplace offer?&lt;/h3&gt;&lt;br /&gt;&lt;p&gt;[caption id="" align="alignright" width="250" caption="RAP Bank Affiliate Marketplace"]&lt;a href="http://15246.rapbank.com" rel="nofollow" target="_blank"&gt;&lt;img style="border: 0pt none;" title="RAP Bank Affiliate Marketplace" src="http://rapbank.com/products/banners/rapbank_250x250.jpg" alt="RAP Bank Affiliate Marketplace" width="250" height="250" border="0" /&gt;&lt;/a&gt;[/caption]&lt;/p&gt;&lt;br /&gt;&lt;p&gt;The first thing to do is to get a keyword that is getting some traffic.&lt;/p&gt;&lt;br /&gt;&lt;ol&gt;&lt;br /&gt;&lt;li&gt;Go to Google keyword tool and start searching for a good keyword.&lt;/li&gt;&lt;br /&gt;&lt;li&gt;For example: The keyword cash generators is getting 2400 searches per month, now download Traffic Travis and analyze the keyword. If the .com is taken put x or site after your keyword or go after .net and so on. It is very important to have your keyword in your domain.&lt;/li&gt;&lt;br /&gt;&lt;li&gt;You can use &lt;a title="Micro Niche Finder" href="http://www.monstrous.tk/go/Micro-Niche-Finder/" target="_blank"&gt;Micro Niche Finder&lt;/a&gt; or &lt;a title="Niche Finder Software" href="http://www.monstrous.tk/go/Niche-Finder-Software/" target="_blank"&gt;Niche Finder Software&lt;/a&gt; to find a good keyword at a push of a button. By using this software, all niche and keyword research can be done quickly and profitable.&lt;/li&gt;&lt;br /&gt;&lt;li&gt;When you have your domain ready, it is time to set up your wordpress site.&lt;/li&gt;&lt;br /&gt;&lt;li&gt;Get a theme that you think will look nice with the RAP Bank Affiliate Marketplace offer you are planning to promote, and then install these plugins: All in one SEO, Google xml sitemap,seo friendly images, cbnet ping optimizer and &lt;a title="SEOPressor On Page SEO WordPress Plugin" href="http://www.monstrous.tk/go/Download_SEOPressor_On_Page_SEO_WordPress_Plugin/" target="_blank"&gt;SEOPressor On Page SEO WordPress Plugin&lt;/a&gt;.&lt;br /&gt;&lt;br /&gt;and yet another related posts plugin.&lt;/li&gt;&lt;br /&gt;&lt;li&gt;Now you are ready to start filling your site with RAP Bank Affiliate Marketplace offers.&lt;/li&gt;&lt;br /&gt;&lt;/ol&gt;&lt;br /&gt;&lt;h4&gt;How to get traffic to a RAP Bank Affiliate Marketplace offer?&lt;/h4&gt;&lt;br /&gt;&lt;p&gt;The first thing you need to do is to get backlinks. A good way to start is to writing articles and leave an anchor text keyword leading back to your site.&lt;/p&gt;&lt;br /&gt;&lt;ol&gt;&lt;br /&gt;&lt;li&gt;Snipsly.com and Triond.com are two article websites where you can get your articles published pretty easy.&lt;/li&gt;&lt;br /&gt;&lt;li&gt;Ezinearticles and Articlebase are also good but a bit harder to get published. You can always buy backlinks because building backlinks on your own is very time consuming.&lt;/li&gt;&lt;br /&gt;&lt;li&gt;A good place where you can get good cheap backlinks is One Hour Backlinks, they will ping your links so that the search engines will notice your backlinks.&lt;/li&gt;&lt;br /&gt;&lt;li&gt;You can also go to Fiverr.com and get cheap backlinks, but always buy backlinks from the&lt;br /&gt;&lt;br /&gt;people with the best user rating.&lt;/li&gt;&lt;br /&gt;&lt;li&gt;Alternatively, you can use &lt;a title="SENuke X SEO Software" href="http://www.monstrous.tk/go/SENukeX_SEO_Software/" target="_blank"&gt;SENuke X SEO Software&lt;/a&gt;, &lt;a title="Sick Submitter SEO Software" href="http://www.monstrous.tk/go/Sick_Submitter_SEO_Software/" target="_blank"&gt;Sick Submitter SEO Software&lt;/a&gt; and &lt;a title="Social Bookmarking Demon" href="http://www.monstrous.tk/go/Social_Bookmarking_Demon_SEO_Software/" target="_blank"&gt;Social Bookmarking Demon&lt;/a&gt;. With this software, you can automate your link building jobs in order to get backlinks. But of course, those software are really expensive. For the cheaper software, you can use &lt;a title="Reddit Monopoly SEO Software" href="http://www.monstrous.tk/go/Reddit-Monopoly-SEO-Software/" target="_blank"&gt;Reddit Monopoly SEO Software&lt;/a&gt;, &lt;a title="Sky High Linker SEO Software" href="http://www.monstrous.tk/go/Sky_High_Linker_SEO_Software/" target="_blank"&gt;Sky High Linker SEO Software&lt;/a&gt; or &lt;a title="LinxBot SEO Software" href="http://www.monstrous.tk/go/LinxBot/" target="_blank"&gt;LinxBot SEO Software&lt;/a&gt;.&lt;/li&gt;&lt;br /&gt;&lt;li&gt;This guide is not just for RAP Bank Affiliate Marketplace offers, you can always use other affiliate offers but still rapbank pays directly.&lt;/li&gt;&lt;br /&gt;&lt;/ol&gt;&lt;br /&gt;&lt;p&gt;Of course, it's impossible to put everything about RAP Bank Affiliate Marketplace into just one article. But you can't deny that you've just added to your understanding about RAP Bank Affiliate Marketplace, and that's time well spent.&lt;/p&gt;&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-1881981184375752114?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/1881981184375752114/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=1881981184375752114' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1881981184375752114'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1881981184375752114'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/rap-bank-affiliate-marketplace.html' title='RAP Bank Affiliate Marketplace'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7204357708545907070</id><published>2011-08-08T22:46:00.001+08:00</published><updated>2011-08-08T22:46:01.205+08:00</updated><title type='text'>Hotmail Account Creator Free Download</title><content type='html'>&lt;div class="pp_items"&gt;&lt;div class="pp_item" align="left"&gt;&lt;p&gt;This article explains a few things about Hotmail Account Creator, and if you're interested, then this is worth reading, because you can never tell what you don't know.&lt;br /&gt;&lt;br /&gt;Truthfully, the only difference between you and Hotmail Account Creator experts is time. If you'll invest a little more time in reading, you'll be that much nearer to expert status when it comes to Hotmail Account Creator.&lt;br /&gt;&lt;h1&gt;What is Hotmail Account Creator&lt;/h1&gt;&lt;br /&gt;This bot will create hotmail.com or live.com accounts forever until you stop it. Make sure that you have good, fast proxies or the bot won't work. You also need a decaptcher account. Also, hotmail will only let you create a limited number of accounts per day from one proxy so keep that in mind.&lt;br /&gt;&lt;h4 style="text-align: center;"&gt;[box type="download"]&lt;a title="Hotmail Account Creator Free Download" href="http://www.monstrous.tk/go/Hotmail-Account-Creator/" target="_blank"&gt;&lt;span style="text-decoration: underline; color: #ff0000;"&gt;&lt;em&gt;&lt;strong&gt;Hotmail Account Creator Free Download&lt;/strong&gt;&lt;/em&gt;&lt;/span&gt;&lt;/a&gt;[/box]&lt;/h4&gt;&lt;br /&gt;&lt;h2&gt;How to use this Hotmail Account Creator&lt;/h2&gt;&lt;br /&gt;Step 1. Type in your decaptcher username and password.&lt;br /&gt;Step 2. Choose if you you want live.com or hotmail.com accounts.&lt;br /&gt;Step 3. Select the file that you want the accounts saved to.&lt;br /&gt;Step 4. Put your proxies in a text file like this:&lt;br /&gt;&lt;br /&gt;[caption id="" align="aligncenter" width="480" caption="Hotmail Account Creator"]&lt;a href="http://www.monstrous.tk/go/Hotmail-Account-Creator/" target="_blank"&gt;&lt;img class=" " title="Hotmail Account Creator" src="http://img29.imageshack.us/img29/5817/proxies.png" alt="Hotmail Account Creator" width="480" height="270" /&gt;&lt;/a&gt;[/caption]&lt;br /&gt;&lt;br /&gt;Step 5. Browse to that file and click the "add proxies to list" button.&lt;br /&gt;Step 6. Click start.&lt;br /&gt;Step 7. Have a coffee.&lt;br /&gt;&lt;br /&gt;Now you can be a confident expert on Hotmail Account Creator. OK, maybe not an expert. But you should have something to bring to the table next time you join a discussion on Hotmail Account Creator.&lt;br /&gt;&lt;h3 style="text-align: center;"&gt;[box type="download"]&lt;a title="Hotmail Account Creator Free Download" href="http://www.monstrous.tk/go/Hotmail-Account-Creator/" target="_blank"&gt;&lt;span style="text-decoration: underline; color: #ff0000;"&gt;&lt;em&gt;&lt;strong&gt;Hotmail Account Creator Free Download&lt;/strong&gt;&lt;/em&gt;&lt;/span&gt;&lt;/a&gt;[/box]&lt;/h3&gt;&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7204357708545907070?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7204357708545907070/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7204357708545907070' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7204357708545907070'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7204357708545907070'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2011/08/hotmail-account-creator-free-download.html' title='Hotmail Account Creator Free Download'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-8810829129078730443</id><published>2009-06-11T11:09:00.000+08:00</published><updated>2009-06-11T11:10:21.748+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Mechatronics Engineering'/><category scheme='http://www.blogger.com/atom/ns#' term='Electronic Transformers'/><title type='text'>What is an Actuator?</title><content type='html'>&lt;p&gt;&lt;span class="mContent"&gt;&lt;div name="intelliTxt" id="intelliTXT"&gt; &lt;p&gt;Put simply, an &lt;span class="yellowFade"&gt;&lt;span&gt;&lt;span style="position: relative;" class="yellowFadeInnerSpan"&gt;actuator&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; is something that converts energy into motion.  It can also be used to apply a force.  An &lt;span class="yellowFade"&gt;&lt;span&gt;&lt;span style="position: relative;" class="yellowFadeInnerSpan"&gt;actuator&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; typically is a mechanical device that takes energy, usually created by air, electricity, or liquid, and converts that into some kind of motion. That motion can be anything from blocking to clamping to ejecting. Actuators are typically used in manufacturing or industrial applications and may be used in things like motors, pumps, switches, and valves.&lt;/p&gt;  &lt;p&gt;Perhaps the  most common type of &lt;span class="yellowFade"&gt;&lt;span&gt;&lt;span style="position: relative;" class="yellowFadeInnerSpan"&gt;actuator&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; is powered by air — the pneumatic cylinder, also known as the &lt;a href="http://www.wisegeek.com/what-is-an-air-cylinder.htm"&gt;air cylinder&lt;/a&gt;.  &lt;a href="http://www.wisegeek.com/what-is-an-air-cylinder.htm"&gt;Air cylinders&lt;/a&gt; are air-tight cylinders, typically made from metal, that use the energy of compressed air to move a piston. Air cylinders are most commonly used in manufacturing and assembly processes. Grippers, which are used in robotics, use actuators driven by compressed air to work much like human fingers.&lt;/p&gt;  &lt;p&gt;Actuators can also be powered by electricity or hydraulics. Much like there are air cylinders, there are also electric cylinders and &lt;a href="http://www.wisegeek.com/what-is-a-hydraulic-cylinder.htm"&gt;hydraulic cylinders&lt;/a&gt; where the cylinder converts electricity or hydraulics into motion. Hydraulic cylinders are often used in certain types of vehicles.&lt;/p&gt;  &lt;p&gt;Many actuators have more than one type of power source.  &lt;a href="http://www.wisegeek.com/what-is-a-solenoid.htm"&gt;Solenoid&lt;/a&gt; valves, for example, can be powered by air &lt;em&gt;and&lt;/em&gt; electricity.  Electricity powers the solenoid, and the solenoid, powered by air, actuates the &lt;a href="http://www.wisegeek.com/what-is-a-valve.htm"&gt;valve&lt;/a&gt;.  Alternatively, the solenoid can be powered by hydraulics and electricity.&lt;/p&gt;  &lt;p&gt;Actuators can create a linear motion, rotary motion, or oscillatory motion. That is, they can create motion in one direction, in a circular motion, or in opposite directions at regular intervals. Hydraulic and air cylinders can be classified as single acting, meaning that the energy source causes movement in one direction and a spring is used for the other direction. Alternatively, these cylinders can be double acting cylinders, meaning the energy is used in two directions.&lt;/p&gt;  &lt;p&gt;While actuators are typically discussed in terms of mechanical implements, muscles are sometimes given as an example of an &lt;span class="yellowFade"&gt;&lt;span&gt;&lt;span style="position: relative;" class="yellowFadeInnerSpan"&gt;actuator&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;.  Energy (e.g., created by eating carbohydrates) is converted by the muscle (i.e., the &lt;span class="yellowFade"&gt;&lt;span&gt;&lt;span style="position: relative;" class="yellowFadeInnerSpan"&gt;actuator&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;) into motion (e.g., kicking a ball).&lt;/p&gt;&lt;/div&gt;&lt;/span&gt;&lt;/p&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-8810829129078730443?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/8810829129078730443/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=8810829129078730443' title='40 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8810829129078730443'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8810829129078730443'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2009/06/what-is-actuator.html' title='What is an Actuator?'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>40</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-8444171905241485376</id><published>2009-06-11T11:07:00.000+08:00</published><updated>2009-06-11T11:09:12.067+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Mechatronics Engineering'/><category scheme='http://www.blogger.com/atom/ns#' term='PLC'/><category scheme='http://www.blogger.com/atom/ns#' term='Mechatronics Software'/><title type='text'>What is a Microcontroller?</title><content type='html'>&lt;h3 class="post-title"&gt; &lt;/h3&gt;  &lt;div class="post-body"&gt; &lt;p&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/downloadlink/4254248/WhatsaMicrocontroller-.pdf"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://3.bp.blogspot.com/_nzAjJng8N7E/SeE1syek0II/AAAAAAAAAaM/USVhFzWyTKE/s200/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5323595278109167746" border="0" /&gt;&lt;/a&gt;&lt;br /&gt;In order to use the handbook very useful, you might need to install &lt;a href="http://www.pusatilmu.co.cc/2009/04/basic-stamp.html"&gt;Basic Stamp&lt;/a&gt;.&lt;br /&gt;&lt;span class="mContent"&gt;&lt;p&gt;A &lt;span class="yellowFade"&gt;&lt;span&gt;&lt;span style="position: relative;" class="yellowFadeInnerSpan"&gt;microcontroller&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; is an integrated chip that is often part of an embedded system. The &lt;span class="yellowFade"&gt;&lt;span&gt;&lt;span style="position: relative;" class="yellowFadeInnerSpan"&gt;microcontroller&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; includes a &lt;a href="http://www.wisegeek.com/what-is-a-cpu.htm"&gt;CPU&lt;/a&gt;, RAM, ROM, I/O ports, and timers like a standard &lt;a href="http://www.wisegeek.com/what-is-a-computer.htm"&gt;computer&lt;/a&gt;, but because they are designed to execute only a single specific task to control a single system, they are much smaller and simplified so that they can include all the functions required on a single chip. &lt;/p&gt;  &lt;p&gt;A &lt;span class="yellowFade"&gt;&lt;span&gt;&lt;span style="position: relative;" class="yellowFadeInnerSpan"&gt;microcontroller&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; differs from a &lt;a href="http://www.wisegeek.com/what-is-a-microprocessor.htm"&gt;microprocessor&lt;/a&gt;, which is a general-purpose chip that is used to create a multi-function computer or device and requires multiple chips to handle various tasks. A &lt;span class="yellowFade"&gt;&lt;span&gt;&lt;span style="position: relative;" class="yellowFadeInnerSpan"&gt;microcontroller&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; is meant to be more self-contained and independent, and functions as a tiny, dedicated computer.&lt;/p&gt;   &lt;p&gt;The great advantage of microcontrollers, as opposed to using larger microprocessors, is that the parts-count and design costs of the item being controlled can be kept to a minimum. They are typically designed using &lt;a href="http://www.wisegeek.com/what-is-cmos.htm"&gt;CMOS&lt;/a&gt; (complementary metal oxide &lt;a href="http://www.wisegeek.com/how-do-semiconductors-work.htm"&gt;semiconductor&lt;/a&gt;) technology, an efficient fabrication technique that uses less power and is more immune to power spikes than other techniques.&lt;/p&gt;&lt;/span&gt;&lt;/p&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-8444171905241485376?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/8444171905241485376/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=8444171905241485376' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8444171905241485376'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8444171905241485376'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2009/06/what-is-microcontroller.html' title='What is a Microcontroller?'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><media:thumbnail xmlns:media='http://search.yahoo.com/mrss/' url='http://3.bp.blogspot.com/_nzAjJng8N7E/SeE1syek0II/AAAAAAAAAaM/USVhFzWyTKE/s72-c/dl.gif' height='72' width='72'/><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5033410458608155017</id><published>2009-06-11T11:05:00.001+08:00</published><updated>2009-06-11T11:07:49.506+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Mechatronics Engineering'/><category scheme='http://www.blogger.com/atom/ns#' term='Engineering software for free'/><category scheme='http://www.blogger.com/atom/ns#' term='Control System Engineering'/><title type='text'>PLC (Programmable Logic Controller)</title><content type='html'>&lt;p&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/downloadlink/4141819/PLCProgrammableLogicController.pdf"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://4.bp.blogspot.com/_nzAjJng8N7E/SdapMKGPfzI/AAAAAAAAAS0/YFRFM9khqgQ/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5320626036118880050" border="0" /&gt;&lt;/a&gt;&lt;br /&gt;&lt;/p&gt;&lt;p style="font-family: verdana;"&gt;File : pdf, 846 pages, 5.2 MB&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;by Hugh Jack, PhD&lt;/p&gt;&lt;p style="font-family: verdana;"&gt;&lt;br /&gt;&lt;/p&gt;&lt;p style="font-family: verdana;"&gt;2. PROGRAMMABLE LOGIC CONTROLLERS&lt;br /&gt;2.1 INTRODUCTION&lt;br /&gt;2.1.1 Ladder Logic&lt;br /&gt;2.1.2 Programming&lt;br /&gt;2.1.3 PLC Connections&lt;br /&gt;2.1.4 Ladder Logic Inputs&lt;br /&gt;2.1.5 Ladder Logic Outputs&lt;br /&gt;2.2 A CASE STUDY&lt;br /&gt;2.3 SUMMARY&lt;br /&gt;2.4 PRACTICE PROBLEMS&lt;br /&gt;2.5 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;2.6 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;3. PLC HARDWARE&lt;br /&gt;3.1 INTRODUCTION&lt;br /&gt;3.2 INPUTS AND OUTPUTS&lt;br /&gt;3.2.1 Inputs&lt;br /&gt;3.2.2 Output Modules&lt;br /&gt;3.3 RELAYS&lt;br /&gt;3.4 A CASE STUDY&lt;br /&gt;3.5 ELECTRICAL WIRING DIAGRAMS&lt;br /&gt;3.5.1 JIC Wiring Symbols&lt;br /&gt;3.6 SUMMARY&lt;br /&gt;3.7 PRACTICE PROBLEMS&lt;br /&gt;3.8 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;3.9 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;4. LOGICAL SENSORS&lt;br /&gt;4.1 INTRODUCTION&lt;br /&gt;4.2 SENSOR WIRING&lt;br /&gt;4.2.1 Switches&lt;br /&gt;4.2.2 Transistor Transistor Logic (TTL)&lt;br /&gt;4.2.3 Sinking/Sourcing&lt;br /&gt;4.2.4 Solid State Relays&lt;br /&gt;4.3 PRESENCE DETECTION&lt;br /&gt;4.3.1 Contact Switches&lt;br /&gt;4.3.2 Reed Switches&lt;br /&gt;4.3.3 Optical (Photoelectric) Sensors&lt;br /&gt;4.3.4 Capacitive Sensors&lt;br /&gt;4.3.5 Inductive Sensors&lt;br /&gt;4.3.6 Ultrasonic&lt;br /&gt;4.3.7 Hall Effect&lt;br /&gt;4.3.8 Fluid Flow&lt;br /&gt;4.4 SUMMARY&lt;br /&gt;4.5 PRACTICE PROBLEMS&lt;br /&gt;4.6 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;4.7 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;5. LOGICAL ACTUATORS&lt;br /&gt;5.1 INTRODUCTION&lt;br /&gt;5.2 SOLENOIDS&lt;br /&gt;5.3 VALVES&lt;br /&gt;5.4 CYLINDERS&lt;br /&gt;5.5 HYDRAULICS&lt;br /&gt;5.6 PNEUMATICS&lt;br /&gt;5.7 MOTORS&lt;br /&gt;5.8 COMPUTERS&lt;br /&gt;5.9 OTHERS&lt;br /&gt;5.10 SUMMARY&lt;br /&gt;5.11 PRACTICE PROBLEMS&lt;br /&gt;5.12 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;5.13 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;6. BOOLEAN LOGIC DESIGN&lt;br /&gt;6.1 INTRODUCTION&lt;br /&gt;6.2 BOOLEAN ALGEBRA&lt;br /&gt;6.3 LOGIC DESIGN&lt;br /&gt;6.3.1 Boolean Algebra Techniques&lt;br /&gt;6.4 COMMON LOGIC FORMS&lt;br /&gt;6.4.1 Complex Gate Forms&lt;br /&gt;6.4.2 Multiplexers&lt;br /&gt;6.5 SIMPLE DESIGN CASES&lt;br /&gt;6.5.1 Basic Logic Functions&lt;br /&gt;6.5.2 Car Safety System&lt;br /&gt;6.5.3 Motor Forward/Reverse&lt;br /&gt;6.5.4 A Burglar Alarm&lt;br /&gt;6.6 SUMMARY&lt;br /&gt;6.7 PRACTICE PROBLEMS&lt;br /&gt;6.8 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;6.9 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;7. KARNAUGHMAPS&lt;br /&gt;7.1 INTRODUCTION&lt;br /&gt;7.2 SUMMARY&lt;br /&gt;7.3 PRACTICE PROBLEMS&lt;br /&gt;7.4 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;7.5 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;8. PLC OPERATION&lt;br /&gt;8.1 INTRODUCTION&lt;br /&gt;8.2 OPERATION SEQUENCE&lt;br /&gt;8.2.1 The Input and Output Scans&lt;br /&gt;8.2.2 The Logic Scan&lt;br /&gt;8.3 PLC STATUS&lt;br /&gt;8.4 MEMORY TYPES&lt;br /&gt;8.5 SOFTWARE BASED PLCS&lt;br /&gt;8.6 SUMMARY&lt;br /&gt;8.7 PRACTICE PROBLEMS&lt;br /&gt;8.8 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;8.9 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;9. LATCHES, TIMERS, COUNTERS AND MORE&lt;br /&gt;9.1 INTRODUCTION&lt;br /&gt;9.2 LATCHES&lt;br /&gt;9.3 TIMERS&lt;br /&gt;9.4 COUNTERS&lt;br /&gt;9.5 MASTER CONTROL RELAYS (MCRs)&lt;br /&gt;9.6 INTERNAL RELAYS&lt;br /&gt;9.7 DESIGN CASES&lt;br /&gt;9.7.1 Basic Counters And Timers&lt;br /&gt;9.7.2 More Timers And Counters&lt;br /&gt;9.7.3 Deadman Switch&lt;br /&gt;9.7.4 Conveyor&lt;br /&gt;9.7.5 Accept/Reject Sorting&lt;br /&gt;9.7.6 Shear Press&lt;br /&gt;9.8 SUMMARY&lt;br /&gt;9.9 PRACTICE PROBLEMS&lt;br /&gt;9.10 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;9.11 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;10. STRUCTURED LOGIC DESIGN&lt;br /&gt;10.1 INTRODUCTION&lt;br /&gt;10.2 PROCESS SEQUENCE BITS&lt;br /&gt;10.3 TIMING DIAGRAMS&lt;br /&gt;10.4 DESIGN CASES&lt;br /&gt;10.5 SUMMARY&lt;br /&gt;10.6 PRACTICE PROBLEMS&lt;br /&gt;10.7 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;10.8 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;11. FLOWCHART BASED DESIGN&lt;br /&gt;11.1 INTRODUCTION&lt;br /&gt;11.2 BLOCK LOGIC&lt;br /&gt;11.3 SEQUENCE BITS&lt;br /&gt;11.4 SUMMARY&lt;br /&gt;11.5 PRACTICE PROBLEMS&lt;br /&gt;11.6 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;11.7 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;12. STATE BASED DESIGN&lt;br /&gt;12.1 INTRODUCTION&lt;br /&gt;12.1.1 State Diagram Example&lt;br /&gt;12.1.2 Conversion to Ladder Logic&lt;br /&gt;Block Logic Conversion&lt;br /&gt;State Equations&lt;br /&gt;State-Transition Equations&lt;br /&gt;12.2 SUMMARY&lt;br /&gt;12.3 PRACTICE PROBLEMS&lt;br /&gt;12.4 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;12.5 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;13. NUMBERS AND DATA&lt;br /&gt;13.1 INTRODUCTION&lt;br /&gt;13.2 NUMERICAL VALUES&lt;br /&gt;13.2.1 Binary&lt;br /&gt;Boolean Operations&lt;br /&gt;Binary Mathematics&lt;br /&gt;13.2.2 Other Base Number Systems&lt;br /&gt;13.2.3 BCD (Binary Coded Decimal)&lt;br /&gt;13.3 DATA CHARACTERIZATION&lt;br /&gt;13.3.1 ASCII (American Standard Code for Information Interchange)&lt;br /&gt;13.3.2 Parity&lt;br /&gt;13.3.3 Checksums&lt;br /&gt;13.3.4 Gray Code&lt;br /&gt;13.4 SUMMARY&lt;br /&gt;13.5 PRACTICE PROBLEMS&lt;br /&gt;13.6 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;13.7 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;14. PLCMEMORY&lt;br /&gt;14.1 INTRODUCTION&lt;br /&gt;14.2 MEMORY ADDRESSES&lt;br /&gt;14.3 PROGRAM FILES&lt;br /&gt;14.4 DATA FILES&lt;br /&gt;14.4.1 User Bit Memory&lt;br /&gt;14.4.2 Timer Counter Memory&lt;br /&gt;14.4.3 PLC Status Bits (for PLC-5s and Micrologix)&lt;br /&gt;14.4.4 User Function Control Memory&lt;br /&gt;14.4.5 Integer Memory&lt;br /&gt;14.4.6 Floating Point Memory&lt;br /&gt;14.5 SUMMARY&lt;br /&gt;14.6 PRACTICE PROBLEMS&lt;br /&gt;14.7 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;14.8 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;15. LADDER LOGIC FUNCTIONS&lt;br /&gt;15.1 INTRODUCTION&lt;br /&gt;15.2 DATA HANDLING&lt;br /&gt;15.2.1 Move Functions&lt;br /&gt;15.2.2 Mathematical Functions&lt;br /&gt;15.2.3 Conversions&lt;br /&gt;15.2.4 Array Data Functions&lt;br /&gt;Statistics&lt;br /&gt;Block Operations&lt;br /&gt;15.3 LOGICAL FUNCTIONS&lt;br /&gt;15.3.1 Comparison of Values&lt;br /&gt;15.3.2 Boolean Functions&lt;br /&gt;15.4 DESIGN CASES&lt;br /&gt;15.4.1 Simple Calculation&lt;br /&gt;15.4.2 For-Next&lt;br /&gt;15.4.3 Series Calculation&lt;br /&gt;15.4.4 Flashing Lights&lt;br /&gt;15.5 SUMMARY&lt;br /&gt;15.6 PRACTICE PROBLEMS&lt;br /&gt;15.7 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;15.8 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;16. ADVANCED LADDER LOGIC FUNCTIONS&lt;br /&gt;16.1 INTRODUCTION&lt;br /&gt;16.2 LIST FUNCTIONS&lt;br /&gt;16.2.1 Shift Registers&lt;br /&gt;16.2.2 Stacks&lt;br /&gt;16.2.3 Sequencers&lt;br /&gt;16.3 PROGRAM CONTROL&lt;br /&gt;16.3.1 Branching and Looping&lt;br /&gt;16.3.2 Fault Detection and Interrupts&lt;br /&gt;16.4 INPUT AND OUTPUT FUNCTIONS&lt;br /&gt;16.4.1 Immediate I/O Instructions&lt;br /&gt;16.4.2 Block Transfer Functions&lt;br /&gt;16.5 DESIGN TECHNIQUES&lt;br /&gt;16.5.1 State Diagrams&lt;br /&gt;16.6 DESIGN CASES&lt;br /&gt;16.6.1 If-Then&lt;br /&gt;16.6.2 Traffic Light&lt;br /&gt;16.7 SUMMARY&lt;br /&gt;16.8 PRACTICE PROBLEMS&lt;br /&gt;16.9 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;16.10 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;17. OPEN CONTROLLERS&lt;br /&gt;17.1 INTRODUCTION&lt;br /&gt;17.2 IEC 61131&lt;br /&gt;17.3 OPEN ARCHITECTURE CONTROLLERS&lt;br /&gt;17.4 SUMMARY&lt;br /&gt;17.5 PRACTICE PROBLEMS&lt;br /&gt;17.6 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;17.7 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;18. INSTRUCTION LIST PROGRAMMING&lt;br /&gt;18.1 INTRODUCTION&lt;br /&gt;18.2 THE IEC 61131 VERSION&lt;br /&gt;18.3 THE ALLEN-BRADLEY VERSION&lt;br /&gt;18.4 SUMMARY&lt;br /&gt;18.5 PRACTICE PROBLEMS&lt;br /&gt;18.6 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;18.7 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;19. STRUCTURED TEXT PROGRAMMING&lt;br /&gt;19.1 INTRODUCTION&lt;br /&gt;19.2 THE LANGUAGE&lt;br /&gt;19.3 SUMMARY&lt;br /&gt;19.4 PRACTICE PROBLEMS&lt;br /&gt;19.5 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;19.6 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;20. SEQUENTIAL FUNCTION CHARTS&lt;br /&gt;20.1 INTRODUCTION&lt;br /&gt;20.2 A COMPARISON OF METHODS&lt;br /&gt;20.3 SUMMARY&lt;br /&gt;20.4 PRACTICE PROBLEMS&lt;br /&gt;20.5 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;20.6 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;21. FUNCTION BLOCK PROGRAMMING&lt;br /&gt;21.1 INTRODUCTION&lt;br /&gt;21.2 CREATING FUNCTION BLOCKS&lt;br /&gt;21.3 DESIGN CASE&lt;br /&gt;21.4 SUMMARY&lt;br /&gt;21.5 PRACTICE PROBLEMS&lt;br /&gt;21.6 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;21.7 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;22. ANALOG INPUTS AND OUTPUTS&lt;br /&gt;22.1 INTRODUCTION&lt;br /&gt;22.2 ANALOG INPUTS&lt;br /&gt;22.2.1 Analog Inputs With a PLC&lt;br /&gt;22.3 ANALOG OUTPUTS&lt;br /&gt;22.3.1 Analog Outputs With A PLC&lt;br /&gt;22.3.2 Pulse Width Modulation (PWM) Outputs&lt;br /&gt;22.3.3 Shielding&lt;br /&gt;22.4 DESIGN CASES&lt;br /&gt;22.4.1 Process Monitor&lt;br /&gt;22.5 SUMMARY&lt;br /&gt;22.6 PRACTICE PROBLEMS&lt;br /&gt;22.7 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;22.8 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;23. CONTINUOUS SENSORS&lt;br /&gt;23.1 INTRODUCTION&lt;br /&gt;23.2 INDUSTRIAL SENSORS&lt;br /&gt;23.2.1 Angular Displacement&lt;br /&gt;Potentiometers&lt;br /&gt;23.2.2 Encoders&lt;br /&gt;Tachometers&lt;br /&gt;23.2.3 Linear Position&lt;br /&gt;Potentiometers&lt;br /&gt;Linear Variable Differential Transformers (LVDT)&lt;br /&gt;Moire Fringes&lt;br /&gt;Accelerometers&lt;br /&gt;23.2.4 Forces and Moments&lt;br /&gt;Strain Gages&lt;br /&gt;Piezoelectric&lt;br /&gt;23.2.5 Liquids and Gases&lt;br /&gt;Pressure&lt;br /&gt;Venturi Valves&lt;br /&gt;Coriolis Flow Meter&lt;br /&gt;Magnetic Flow Meter&lt;br /&gt;Ultrasonic Flow Meter&lt;br /&gt;Vortex Flow Meter&lt;br /&gt;Positive Displacement Meters&lt;br /&gt;Pitot Tubes&lt;br /&gt;23.2.6 Temperature&lt;br /&gt;Resistive Temperature Detectors (RTDs)&lt;br /&gt;Thermocouples&lt;br /&gt;Thermistors&lt;br /&gt;Other Sensors&lt;br /&gt;23.2.7 Light&lt;br /&gt;Light Dependant Resistors (LDR)&lt;br /&gt;23.2.8 Chemical&lt;br /&gt;pH&lt;br /&gt;Conductivity&lt;br /&gt;23.2.9 Others&lt;br /&gt;23.3 INPUT ISSUES&lt;br /&gt;23.4 SENSOR GLOSSARY&lt;br /&gt;23.5 SUMMARY&lt;br /&gt;23.6 REFERENCES&lt;br /&gt;23.7 PRACTICE PROBLEMS&lt;br /&gt;23.8 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;23.9 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;24. CONTINUOUS ACTUATORS&lt;br /&gt;24.1 INTRODUCTION&lt;br /&gt;24.2 ELECTRIC MOTORS&lt;br /&gt;24.2.1 Basic Brushed DC Motors&lt;br /&gt;24.2.2 AC Motors&lt;br /&gt;24.2.3 Brushless DC Motors&lt;br /&gt;24.2.4 Stepper Motors&lt;br /&gt;24.2.5 Wound Field Motors&lt;br /&gt;24.3 HYDRAULICS&lt;br /&gt;24.4 OTHER SYSTEMS&lt;br /&gt;24.5 SUMMARY&lt;br /&gt;24.6 PRACTICE PROBLEMS&lt;br /&gt;24.7 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;24.8 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;25. CONTINUOUS CONTROL&lt;br /&gt;25.1 INTRODUCTION&lt;br /&gt;25.2 CONTROL OF LOGICAL ACTUATOR SYSTEMS&lt;br /&gt;25.3 CONTROL OF CONTINUOUS ACTUATOR SYSTEMS&lt;br /&gt;25.3.1 Block Diagrams&lt;br /&gt;25.3.2 Feedback Control Systems&lt;br /&gt;25.3.3 Proportional Controllers&lt;br /&gt;25.3.4 PID Control Systems&lt;br /&gt;25.4 DESIGN CASES&lt;br /&gt;25.4.1 Oven Temperature Control&lt;br /&gt;25.4.2 Water Tank Level Control&lt;br /&gt;25.5 SUMMARY&lt;br /&gt;25.6 PRACTICE PROBLEMS&lt;br /&gt;25.7 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;25.8 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;26. FUZZY LOGIC&lt;br /&gt;26.1 INTRODUCTION&lt;br /&gt;26.2 COMMERCIAL CONTROLLERS&lt;br /&gt;26.3 REFERENCES&lt;br /&gt;26.4 SUMMARY&lt;br /&gt;26.5 PRACTICE PROBLEMS&lt;br /&gt;26.6 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;26.7 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;27. SERIAL COMMUNICATION&lt;br /&gt;27.1 INTRODUCTION&lt;br /&gt;27.2 SERIAL COMMUNICATIONS&lt;br /&gt;27.2.1 RS-232&lt;br /&gt;ASCII Functions&lt;br /&gt;27.3 PARALLEL COMMUNICATIONS&lt;br /&gt;27.4 DESIGN CASES&lt;br /&gt;27.4.1 PLC Interface To a Robot&lt;br /&gt;27.5 SUMMARY&lt;br /&gt;27.6 PRACTICE PROBLEMS&lt;br /&gt;27.7 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;27.8 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;28. NETWORKING&lt;br /&gt;28.1 INTRODUCTION&lt;br /&gt;28.1.1 Topology&lt;br /&gt;28.1.2 OSI Network Model&lt;br /&gt;28.1.3 Networking Hardware&lt;br /&gt;28.1.4 Control Network Issues&lt;br /&gt;28.2 NETWORK STANDARDS&lt;br /&gt;28.2.1 Devicenet&lt;br /&gt;28.2.2 CANbus&lt;br /&gt;28.2.3 Controlnet&lt;br /&gt;28.2.4 Ethernet&lt;br /&gt;28.2.5 Profibus&lt;br /&gt;28.2.6 Sercos&lt;br /&gt;28.3 PROPRIETARY NETWORKS&lt;br /&gt;28.3.1 Data Highway&lt;br /&gt;28.4 NETWORK COMPARISONS&lt;br /&gt;28.5 DESIGN CASES&lt;br /&gt;28.5.1 Devicenet&lt;br /&gt;28.6 SUMMARY&lt;br /&gt;28.7 PRACTICE PROBLEMS&lt;br /&gt;28.8 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;28.9 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;29. INTERNET&lt;br /&gt;29.1 INTRODUCTION&lt;br /&gt;29.1.1 Computer Addresses&lt;br /&gt;IPV6&lt;br /&gt;29.1.2 Phone Lines&lt;br /&gt;29.1.3 Mail Transfer Protocols&lt;br /&gt;29.1.4 FTP - File Transfer Protocol&lt;br /&gt;29.1.5 HTTP - Hypertext Transfer Protocol&lt;br /&gt;29.1.6 Novell&lt;br /&gt;29.1.7 Security&lt;br /&gt;Firewall&lt;br /&gt;IP Masquerading&lt;br /&gt;29.1.8 HTML - Hyper Text Markup Language&lt;br /&gt;29.1.9 URLs&lt;br /&gt;29.1.10 Encryption&lt;br /&gt;29.1.11 Compression&lt;br /&gt;29.1.12 Clients and Servers&lt;br /&gt;29.1.13 Java&lt;br /&gt;29.1.14 Javascript&lt;br /&gt;29.1.15 CGI&lt;br /&gt;29.1.16 ActiveX&lt;br /&gt;29.1.17 Graphics&lt;br /&gt;29.2 DESIGN CASES&lt;br /&gt;29.2.1 Remote Monitoring System&lt;br /&gt;29.3 SUMMARY&lt;br /&gt;29.4 PRACTICE PROBLEMS&lt;br /&gt;29.5 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;29.6 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;30. HUMANMACHINE INTERFACES (HMI)&lt;br /&gt;30.1 INTRODUCTION&lt;br /&gt;30.2 HMI/MMI DESIGN&lt;br /&gt;30.3 DESIGN CASES&lt;br /&gt;30.4 SUMMARY&lt;br /&gt;30.5 PRACTICE PROBLEMS&lt;br /&gt;30.6 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;30.7 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;31. ELECTRICAL DESIGN AND CONSTRUCTION&lt;br /&gt;31.1 INTRODUCTION&lt;br /&gt;31.2 ELECTRICAL WIRING DIAGRAMS&lt;br /&gt;31.2.1 Selecting Voltages&lt;br /&gt;31.2.2 Grounding&lt;br /&gt;31.2.3 Wiring&lt;br /&gt;31.2.4 Suppressors&lt;br /&gt;31.2.5 PLC Enclosures&lt;br /&gt;31.2.6 Wire and Cable Grouping&lt;br /&gt;31.3 FAIL-SAFE DESIGN&lt;br /&gt;31.4 SAFETY RULES SUMMARY&lt;br /&gt;31.5 REFERENCES&lt;br /&gt;31.6 SUMMARY&lt;br /&gt;31.7 PRACTICE PROBLEMS&lt;br /&gt;31.8 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;31.9 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;32. SOFTWARE ENGINEERING&lt;br /&gt;32.1 INTRODUCTION&lt;br /&gt;32.1.1 Fail Safe Design&lt;br /&gt;32.2 DEBUGGING&lt;br /&gt;32.2.1 Troubleshooting&lt;br /&gt;32.2.2 Forcing&lt;br /&gt;32.3 PROCESS MODELLING&lt;br /&gt;32.4 PROGRAMMING FOR LARGE SYSTEMS&lt;br /&gt;32.4.1 Developing a Program Structure&lt;br /&gt;32.4.2 Program Verification and Simulation&lt;br /&gt;32.5 DOCUMENTATION&lt;br /&gt;32.6 COMMISIONING&lt;br /&gt;32.7 REFERENCES&lt;br /&gt;32.8 SUMMARY&lt;br /&gt;32.9 PRACTICE PROBLEMS&lt;br /&gt;32.10 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;32.11 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;33. SELECTING A PLC&lt;br /&gt;33.1 INTRODUCTION&lt;br /&gt;33.2 SPECIAL I/O MODULES&lt;br /&gt;33.3 SUMMARY&lt;br /&gt;33.4 PRACTICE PROBLEMS&lt;br /&gt;33.5 PRACTICE PROBLEM SOLUTIONS&lt;br /&gt;33.6 ASSIGNMENT PROBLEMS&lt;/p&gt; &lt;p style="font-family: verdana;"&gt;34. FUNCTION REFERENCE&lt;br /&gt;34.1 FUNCTION DESCRIPTIONS&lt;br /&gt;34.1.1 General Functions&lt;br /&gt;34.1.2 Program Control&lt;br /&gt;34.1.3 Timers and Counters&lt;br /&gt;34.1.4 Compare&lt;br /&gt;34.1.5 Calculation and Conversion&lt;br /&gt;34.1.6 Logical&lt;br /&gt;34.1.7 Move&lt;br /&gt;34.1.8 File&lt;br /&gt;34.1.9 List&lt;br /&gt;34.1.10 Program Control&lt;br /&gt;34.1.11 Advanced Input/Output&lt;br /&gt;34.1.12 String&lt;br /&gt;34.2 DATA TYPES&lt;/p&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5033410458608155017?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5033410458608155017/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5033410458608155017' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5033410458608155017'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5033410458608155017'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2009/06/plc-programmable-logic-controller.html' title='PLC (Programmable Logic Controller)'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><media:thumbnail xmlns:media='http://search.yahoo.com/mrss/' url='http://4.bp.blogspot.com/_nzAjJng8N7E/SdapMKGPfzI/AAAAAAAAAS0/YFRFM9khqgQ/s72-c/dl.gif' height='72' width='72'/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-373674168831276771</id><published>2009-06-11T10:58:00.000+08:00</published><updated>2009-06-11T11:05:02.748+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Mechatronics Engineering'/><category scheme='http://www.blogger.com/atom/ns#' term='Electronic Transformers'/><category scheme='http://www.blogger.com/atom/ns#' term='Control System Engineering'/><title type='text'>Wireless Sensor and Actuator Networks: Technologies, Analysis and Design</title><content type='html'>&lt;p&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_nzAjJng8N7E/SeFIV5RaFqI/AAAAAAAAAbM/vC_-tGZ4cBc/s1600-h/WirelessSensorandActuatorNetworks.jpg"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 200px; height: 200px;" src="http://1.bp.blogspot.com/_nzAjJng8N7E/SeFIV5RaFqI/AAAAAAAAAbM/vC_-tGZ4cBc/s200/WirelessSensorandActuatorNetworks.jpg" alt="" id="BLOGGER_PHOTO_ID_5323615775516923554" border="0" /&gt;&lt;/a&gt;&lt;br /&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/4254845/9780123725394-0123725399.rar.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://1.bp.blogspot.com/_nzAjJng8N7E/SeFHk7Wm6cI/AAAAAAAAAa0/c_eJpbR01ac/s200/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5323614934262016450" border="0" /&gt;&lt;/a&gt;&lt;br /&gt;&lt;span style="font-family: verdana;"&gt;384 pages | Academic Press (January 28, 2008) | ISBN: 0123725399 | PDF | 4 Mb&lt;/span&gt;&lt;br /&gt;&lt;span style="font-family: verdana;"&gt;When choosing the technology options to develop a wireless sensor network (WSN), it is vital that their performance levels can be assessed for the type of application intended. This book describes the different technology options - MAC protocols, routing protocols, localisation and data fusion techniques - and provides the means to numerically measure their performance, whether by simulation, mathematical models or experimental test beds. Case studies, based on the authors' direct experience of implementing wireless sensor networks, describe the design methodology and the type of measurements used, together with samples of the performance measurements attained.&lt;/span&gt;&lt;br /&gt;&lt;span style="font-family: verdana;"&gt;The book will enable you to answer vital questions such as:&lt;/span&gt;&lt;br /&gt;&lt;span style="font-family: verdana;"&gt;* How long will my network remain alive given the amount of sensing required of it?&lt;/span&gt;&lt;br /&gt;&lt;span style="font-family: verdana;"&gt;* For how long should I set the sleeping state of my motes?&lt;/span&gt;&lt;br /&gt;&lt;span style="font-family: verdana;"&gt;* How many sensors should I distribute to meet the expected requirements of the application?&lt;/span&gt;&lt;br /&gt;&lt;span style="font-family: verdana;"&gt;* What type of throughput should I expect as a function of the number of nodes deployed and the radio interface chosen (whether it be Bluetooth or Zigbee)?&lt;/span&gt;&lt;br /&gt;&lt;span style="font-family: verdana;"&gt;* How is the Packet Error Rate of my Zigbee motes affected by the selection of adjacent frequency sub bands in the ISM 2.4GHz band?&lt;/span&gt;&lt;br /&gt;&lt;span style="font-family: verdana;"&gt;* How is the localisation precision dependant on the number of nodes deployed in a corridor?&lt;/span&gt;&lt;br /&gt;&lt;span style="font-family: verdana;"&gt;Communications and signal processing engineers, researchers and graduate students working in wireless sensor networks will find this book an invaluable practical guide to this important technology&lt;/span&gt;&lt;/p&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-373674168831276771?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/373674168831276771/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=373674168831276771' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/373674168831276771'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/373674168831276771'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2009/06/wireless-sensor-and-actuator-networks.html' title='Wireless Sensor and Actuator Networks: Technologies, Analysis and Design'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><media:thumbnail xmlns:media='http://search.yahoo.com/mrss/' url='http://1.bp.blogspot.com/_nzAjJng8N7E/SeFIV5RaFqI/AAAAAAAAAbM/vC_-tGZ4cBc/s72-c/WirelessSensorandActuatorNetworks.jpg' height='72' width='72'/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-409235847875739263</id><published>2009-06-11T10:57:00.001+08:00</published><updated>2009-06-11T10:57:50.628+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Engineering software for free'/><category scheme='http://www.blogger.com/atom/ns#' term='Quality Control and Reliability'/><title type='text'>How to construct a Tree Diagram automatically? | Macam mana hendak buat Tree Diagram secara Otomatik</title><content type='html'>&lt;a href="http://www.addthis.com/bookmark.php?v=20" onmouseover="return addthis_open(this, '', '[URL]', '[TITLE]')" onmouseout="addthis_close()" onclick="return addthis_sendto()"&gt;&lt;img src="http://s7.addthis.com/static/btn/lg-bookmark-en.gif" alt="Bookmark and Share" style="border: 0pt none ;" height="16" width="125" /&gt;&lt;/a&gt;&lt;script type="text/javascript" src="http://s7.addthis.com/js/200/addthis_widget.js"&gt;&lt;/script&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_nzAjJng8N7E/SebzKl8pEnI/AAAAAAAAAb8/tHFmWJw7DHU/s1600-h/BSU+Tree+Diagram+v2.6.JPG"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 200px; height: 132px;" src="http://4.bp.blogspot.com/_nzAjJng8N7E/SebzKl8pEnI/AAAAAAAAAb8/tHFmWJw7DHU/s200/BSU+Tree+Diagram+v2.6.JPG" alt="" id="BLOGGER_PHOTO_ID_5325210972722893426" border="0" /&gt;&lt;/a&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/4319400/BSUTreeDiagramv2.6.xls.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://1.bp.blogspot.com/_nzAjJng8N7E/SebyrLm8r0I/AAAAAAAAAbs/PFUl-qVy6Zk/s200/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5325210433076637506" border="0" /&gt;&lt;/a&gt;&lt;p style="font-family: verdana;"&gt;&lt;br /&gt;&lt;/p&gt;&lt;p style="font-family: verdana; text-align: center;"&gt;&lt;a href="http://www.pusatilmu.co.cc/2009/04/guide-to-installing-quality-control.html"&gt;Installation Guide. Click here.&lt;/a&gt;&lt;br /&gt;&lt;/p&gt;&lt;p style="font-family: verdana;"&gt;Also called: systematic diagram, tree analysis, analytical tree, hierarchy diagram&lt;br /&gt;&lt;/p&gt;&lt;p style="font-family: verdana;"&gt;&lt;br /&gt;&lt;/p&gt;                     &lt;p style="font-family: verdana; font-weight: bold;" class="orangehead"&gt;Description&lt;/p&gt;&lt;p style="font-family: verdana;" class="orangehead"&gt;&lt;br /&gt;&lt;/p&gt;&lt;p style="font-family: verdana;" class="orangehead"&gt;&lt;br /&gt;&lt;/p&gt;                     &lt;p style="font-family: verdana;"&gt; The tree diagram starts with one item that branches into two or more, each of which branch into two or more, and so on. It looks like a tree, with trunk and multiple branches. &lt;/p&gt;                     &lt;p style="font-family: verdana;"&gt;It is used to break down broad categories into finer and finer levels of detail. Developing the tree diagram helps you move your thinking step by step from generalities to specifics. &lt;/p&gt;                     &lt;p style="font-family: verdana;" class="orangehead"&gt;When to Use a Tree Diagram &lt;/p&gt;                     &lt;ul style="font-family: verdana;"&gt;&lt;li&gt; When an issue is known or being addressed in broad generalities and you must move to specific details, such as when developing logical steps to achieve an objective. &lt;/li&gt;&lt;li&gt; When developing actions to carry out a solution or other plan. &lt;/li&gt;&lt;li&gt; When analyzing processes in detail. &lt;/li&gt;&lt;li&gt; When probing for the root cause of a problem. &lt;/li&gt;&lt;li&gt; When evaluating implementation issues for several potential solutions. &lt;/li&gt;&lt;li&gt; After an affinity diagram or relations diagram has uncovered key issues. &lt;/li&gt;&lt;li&gt; As a communication tool, to explain details to others. &lt;/li&gt;&lt;/ul&gt;                     &lt;p style="font-family: verdana;" class="orangehead"&gt; Tree Diagram Procedure &lt;/p&gt;                     &lt;ol style="font-family: verdana;"&gt;&lt;li&gt; Develop a statement of the goal, project, plan, problem or whatever is being studied. Write it at the top (for a vertical tree) or far left (for a horizontal tree) of your work surface. &lt;/li&gt;&lt;li&gt; Ask a question that will lead you to the next level of detail. For example: &lt;/li&gt;&lt;ul&gt;&lt;li&gt; For a goal, action plan or work breakdown structure: “What tasks must be done to accomplish this?” or “How can this be accomplished?” &lt;/li&gt;&lt;li&gt; For root-cause analysis: “What causes this?” or “Why does this happen?” &lt;/li&gt;&lt;li&gt; For gozinto chart: “What are the components?” (Gozinto literally comes from the phrase “What goes into it?” &lt;/li&gt;&lt;/ul&gt;&lt;p&gt; Brainstorm all possible answers. If an affinity diagram or &lt;a href="http://www.asq.org/learn-about-quality/new-management-planning-tools/overview/relations-diagram.html"&gt;relationship diagram&lt;/a&gt; has been done previously, ideas may be taken from there. Write each idea in a line below (for a vertical tree) or to the right of (for a horizontal tree) the first statement. Show links between the tiers with arrows. &lt;/p&gt;&lt;/ol&gt;                       &lt;ol style="font-family: verdana;" start="3"&gt;&lt;li&gt; Do a “necessary and sufficient” check. Are all the items at this level necessary for the one on the level above? If all the items at this level were present or accomplished, would they be sufficient for the one on the level above? &lt;/li&gt;&lt;li&gt; Each of the new idea statements now becomes the subject: a goal, objective or problem statement. For each one, ask the question again to uncover the next level of detail. Create another tier of statements and show the relationships to the previous tier of ideas with arrows. Do a “necessary and sufficient check” for each set of items. &lt;/li&gt;&lt;li&gt; Continue to turn each new idea into a subject statement and ask the question. Do not stop until you reach fundamental elements: specific actions that can be carried out, components that are not divisible, root causes. &lt;/li&gt;&lt;li&gt; Do a “necessary and sufficient” check of the entire diagram. Are all the items necessary for the objective? If all the items were present or accomplished, would they be sufficient for the objective? &lt;/li&gt;&lt;/ol&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-409235847875739263?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/409235847875739263/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=409235847875739263' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/409235847875739263'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/409235847875739263'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2009/06/how-to-construct-tree-diagram.html' title='How to construct a Tree Diagram automatically? | Macam mana hendak buat Tree Diagram secara Otomatik'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><media:thumbnail xmlns:media='http://search.yahoo.com/mrss/' url='http://4.bp.blogspot.com/_nzAjJng8N7E/SebzKl8pEnI/AAAAAAAAAb8/tHFmWJw7DHU/s72-c/BSU+Tree+Diagram+v2.6.JPG' height='72' width='72'/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5729984200489312546</id><published>2009-06-11T10:55:00.000+08:00</published><updated>2009-06-11T10:56:48.640+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Mechatronics Engineering'/><category scheme='http://www.blogger.com/atom/ns#' term='Engineering software for free'/><category scheme='http://www.blogger.com/atom/ns#' term='Mechatronics Software'/><title type='text'>BASIC Stamp</title><content type='html'>&lt;h3 class="post-title"&gt; &lt;/h3&gt;  &lt;div class="post-body"&gt; &lt;p&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/4254247/Setup-Stamp-Editor-v2.4.2.exe.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://3.bp.blogspot.com/_nzAjJng8N7E/SeE3dGYbAkI/AAAAAAAAAaU/_XTBEjXsSec/s200/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5323597207597417026" border="0" /&gt;&lt;/a&gt;&lt;br /&gt;&lt;a name="WhatIsIt"&gt;The BASIC Stamp is actually member of a large family of &lt;/a&gt;&lt;a href="http://wolfstone.halloweenhost.com/Controllers/ctlint_ControllerIntro.html"&gt;controllers&lt;/a&gt; from &lt;a href="http://wolfstone.halloweenhost.com/_aLinks/logbuy_References.html#Parallax"&gt;Parallax&lt;/a&gt;. &lt;/p&gt;&lt;p&gt; A Stamp contains: &lt;/p&gt;&lt;ul&gt;&lt;li&gt;a Central Processing Unit (CPU) &lt;/li&gt;&lt;li&gt;a connection to install (download) programs into the Stamp &lt;/li&gt;&lt;li&gt;memory where a program may be stored for execution - even with the power off &lt;/li&gt;&lt;li&gt;input and output connections &lt;/li&gt;&lt;/ul&gt; Programs are edited and compiled on a personal computer, then downloaded into the Stamp for storage and execution. Most stamps are programmed in a version of the BASIC computer language. &lt;p&gt;   &lt;a name="ParallaxGoodAndBad"&gt; &lt;/a&gt;&lt;/p&gt;&lt;h2&gt;&lt;a name="ParallaxGoodAndBad"&gt;Parallax, Good And Bad&lt;/a&gt;&lt;/h2&gt;  &lt;a name="ParallaxGoodAndBad"&gt;The good thing about the BASIC Stamp family of &lt;/a&gt;&lt;a href="http://wolfstone.halloweenhost.com/Controllers/ctlint_ControllerIntro.html"&gt;controllers&lt;/a&gt; from &lt;a href="http://wolfstone.halloweenhost.com/_aLinks/logbuy_References.html#Parallax"&gt;Parallax&lt;/a&gt; is that there are so many to choose from. &lt;p&gt; The bad thing about Parallax BASIC Stamps is that there are so many to choose from. Really! The &lt;a href="http://wolfstone.halloweenhost.com/Controllers/cbsbuy_ChoosingBasicStamp.html#ManyToChooseFrom"&gt;number of choices&lt;/a&gt; is literally bewildering! &lt;/p&gt;&lt;p&gt; Let's browse the assortment as of May 2005.... &lt;/p&gt;&lt;p&gt; There are many different versions of the Stamp itself: &lt;/p&gt;&lt;ul&gt;&lt;li&gt;9 "regular" BASIC Stamp versions &lt;/li&gt;&lt;li&gt;plus the Javalin Stamp &lt;/li&gt;&lt;li&gt;plus versions embedded in development boards (e.g. "BASIC Stamp HomeWork Board") &lt;/li&gt;&lt;li&gt;plus industrial versions &lt;/li&gt;&lt;/ul&gt; &lt;p&gt; The industrial versions are not a big deal, because they are concerned with operating environment factors. Basically, it's a "suffix". But the numerous other versions make for a complex feature selection matrix! &lt;/p&gt;&lt;p&gt; There are many different form factors: &lt;/p&gt;&lt;ul&gt;&lt;li&gt;24-pin DIP &lt;/li&gt;&lt;li&gt;40-pin DIP &lt;/li&gt;&lt;li&gt;14-pin SIP &lt;/li&gt;&lt;li&gt;attached to boards (e.g. BASIC Stamp Rev. D) &lt;/li&gt;&lt;li&gt;embedded on development boards (e.g. "BASIC Stamp HomeWork Board") &lt;/li&gt;&lt;li&gt;OEM versions &lt;/li&gt;&lt;/ul&gt; &lt;p&gt; Most Stamps are developed and/or used while mounted on carrier boards. There are many carrier boards, too: &lt;/p&gt;&lt;ul&gt;&lt;li&gt;9 versions (without embeds) &lt;/li&gt;&lt;li&gt;plus 2 versions embedded in development boards (e.g. "BASIC Stamp HomeWork Board") &lt;/li&gt;&lt;li&gt;plus the Javelin Stamp Demo Board &lt;/li&gt;&lt;/ul&gt; &lt;p&gt; Some haunters claim that BASIC Stamps are too expensive, because you can program a bare PIC or Atmel CPU for a fraction of the price. This isn't really a fair comparison, because working with a bare MCU is arguably more difficult. &lt;/p&gt;&lt;p&gt; There are two main programming interfaces, BS1-style and BS2-style. But PC interfaces come in three types (parallel, serial, and USB). So there are numerous permutations: &lt;/p&gt;&lt;ul&gt;&lt;li&gt;BS1-style via parallel port &lt;/li&gt;&lt;li&gt;BS1-style via serial port and BS1 Serial Adapter &lt;/li&gt;&lt;li&gt;BS1-style via USB port, USB to serial adapter, and BS1 Serial Adapter &lt;/li&gt;&lt;li&gt;BS2-style via serial port &lt;/li&gt;&lt;li&gt;BS2-style via USB port (e.g. Board of Education USB programming board) &lt;/li&gt;&lt;li&gt;BS2-style via USB port and USB to serial adapter &lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;For more information, please visit &lt;a href="http://wolfstone.halloweenhost.com/Controllers/cbsbuy_ChoosingBasicStamp.html#WhatIsIt"&gt;Parallax&lt;/a&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5729984200489312546?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5729984200489312546/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5729984200489312546' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5729984200489312546'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5729984200489312546'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2009/06/basic-stamp.html' title='BASIC Stamp'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><media:thumbnail xmlns:media='http://search.yahoo.com/mrss/' url='http://3.bp.blogspot.com/_nzAjJng8N7E/SeE3dGYbAkI/AAAAAAAAAaU/_XTBEjXsSec/s72-c/dl.gif' height='72' width='72'/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-3053613660796008488</id><published>2009-06-11T10:54:00.000+08:00</published><updated>2009-06-11T10:55:16.032+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Engineering software for free'/><category scheme='http://www.blogger.com/atom/ns#' term='Mechatronics Software'/><title type='text'>MikroC Programming (Crack and Patch Included) | MikroC Software Dengan Crack dan Keygen</title><content type='html'>&lt;h3 class="post-title"&gt; &lt;/h3&gt;  &lt;div class="post-body"&gt; &lt;div style="text-align: center;"&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/4014116/mikroc_6210_setup.zip.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://4.bp.blogspot.com/_nzAjJng8N7E/ScslG1cDWhI/AAAAAAAAAQs/a5EN7YrAcvw/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5317384584395184658" border="0" /&gt;&lt;/a&gt;&lt;a href="http://www.ziddu.com/download/4014116/mikroc_6210_setup.zip.html"&gt;To download MikroC with Crack, Patch and Keygen&lt;/a&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;/div&gt;&lt;div style="text-align: center;"&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.mikroe.com/en/compilers/mikroc/pro/pic/"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://4.bp.blogspot.com/_nzAjJng8N7E/ScslG1cDWhI/AAAAAAAAAQs/a5EN7YrAcvw/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5317384584395184658" border="0" /&gt;&lt;/a&gt;&lt;a href="http://www.mikroe.com/en/compilers/mikroc/pro/pic/"&gt;To purchase a licensed&lt;/a&gt;&lt;br /&gt;&lt;/div&gt;&lt;br /&gt;&lt;table cellpadding="0" cellspacing="0" width="100%"&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td valign="top"&gt;&lt;p align="center"&gt;&lt;img src="http://www.mikroe.com/en/compilers/mikroc/pic/images/naslov.gif" /&gt;&lt;/p&gt;&lt;br /&gt;&lt;/td&gt;                &lt;td rowspan="2" valign="top"&gt;      &lt;a href="http://www.mikroe.com/en/compilers/mikroc/pic/download.htm"&gt;&lt;img title="Download mikroC for free" alt="Download mikroC for free" src="http://www.mikroe.com/en/compilers/mikroc/pic/images/download_now.jpg" border="0" /&gt;&lt;/a&gt;                &lt;/td&gt;              &lt;/tr&gt;              &lt;tr&gt;                &lt;td valign="top"&gt;                  &lt;p class="l"&gt;Advanced, comprehensive C compiler for PIC MCUs.&lt;/p&gt;                  &lt;p class="m"&gt;Develop your applications for PIC quickly and easily, with many practical examples we have provided. Download free version of mikroC and try it out!&lt;/p&gt;                &lt;/td&gt;              &lt;/tr&gt;              &lt;tr&gt;                &lt;td colspan="2" valign="top"&gt;                  &lt;p class="m"&gt;&lt;b&gt;New version of mikroC compiler - mikroC PRO for PIC is available here.&lt;/b&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-3053613660796008488?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/3053613660796008488/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=3053613660796008488' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3053613660796008488'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3053613660796008488'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2009/06/mikroc-programming-crack-and-patch.html' title='MikroC Programming (Crack and Patch Included) | MikroC Software Dengan Crack dan Keygen'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><media:thumbnail xmlns:media='http://search.yahoo.com/mrss/' url='http://4.bp.blogspot.com/_nzAjJng8N7E/ScslG1cDWhI/AAAAAAAAAQs/a5EN7YrAcvw/s72-c/dl.gif' height='72' width='72'/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-9119967242311819542</id><published>2009-06-11T10:48:00.000+08:00</published><updated>2009-06-11T10:54:16.547+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Engineering software for free'/><category scheme='http://www.blogger.com/atom/ns#' term='Mechatronics Software'/><title type='text'>PROTEUS - ISIS PCB Layout</title><content type='html'>&lt;h3 class="post-title"&gt; &lt;/h3&gt;  &lt;div class="post-body"&gt; &lt;div style="text-align: center;"&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/4014115/Proteus_7.2_SP2.zip.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://1.bp.blogspot.com/_nzAjJng8N7E/ScsoTgDNtKI/AAAAAAAAAQ8/Yqa8k3yNxfI/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5317388100527043746" border="0" /&gt;Download Proteus with Crack and Keygen&lt;/a&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;/div&gt;&lt;div style="text-align: center;"&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://world-educational-services.net/cart/index.php?main_page=product_info&amp;amp;cPath=66&amp;amp;products_id=177"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://2.bp.blogspot.com/_nzAjJng8N7E/ScsoTusiE9I/AAAAAAAAAQ0/0gktaPkUxgw/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5317388104458441682" border="0" /&gt;&lt;/a&gt;&lt;a href="http://world-educational-services.net/cart/index.php?main_page=product_info&amp;amp;cPath=66&amp;amp;products_id=177"&gt;Click to Purchase a Licensed&lt;/a&gt;&lt;br /&gt;&lt;/div&gt;&lt;a href="javascript:popupWindow('http://world-educational-services.net/cart/index.php?main_page=popup_image&amp;amp;pID=177&amp;amp;zenid=35129d4cadac2d129ad26c2c1d230e3e')"&gt;&lt;img src="http://world-educational-services.net/cart/bmz_cache/b/b5cbfafffe16ef1db5a6a45ab8fdc312.image.250x186.gif" alt="PROTEUS - ISIS PCB Layout" title=" PROTEUS - ISIS PCB Layout " height="186" width="250" /&gt;&lt;br /&gt;&lt;span class="imgLink"&gt;&lt;/span&gt;&lt;/a&gt;&lt;noscript&gt;&lt;/noscript&gt; &lt;!--eof Main Product Image--&gt;  &lt;!--bof Product Name--&gt;&lt;!--eof Product Price block --&gt;  &lt;!--bof free ship icon  --&gt; &lt;!--eof free ship icon  --&gt;   &lt;!--bof Product description --&gt; &lt;table border="0" cellpadding="1" cellspacing="0"&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="color: rgb(0, 0, 153); font-family: Arial,Helvetica,sans-serif; font-size: 78%;"&gt;&lt;b&gt;&lt;i&gt;&lt;a name="features"&gt;&lt;/a&gt;ARES PCB Layout Software&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Our high performance netlist based PCB design package perfectly complements our powerful &lt;a href="http://world-educational-services.net/cart/admin/schematic.htm"&gt;ISIS schematic capture&lt;/a&gt; software and features both automatic component placement and a highly effective Rip-Up and Retry auto-router. &lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="10"&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;ISIS and ARES together form a complete &lt;a href="http://world-educational-services.net/cart/admin/pcblayout.htm"&gt;Proteus PCB Design&lt;/a&gt; package.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;The following features are provided by ARES:&lt;/span&gt; &lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;table border="0"&gt;&lt;tbody&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;16 copper layers, 2 silk screen layers, 4 mechanical layers plus board edge, keepout, solder resist and solder paste mask.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td height="2" width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td height="2"&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td height="2"&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Any angle component placement.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Padstacks - different pad shapes on each layer.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Circular, Square, DIL, Finger and polygonal pad shapes.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Advanced route editing features including Topological Route Editing, Auto Track Necking and easy to use curved trace support.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Package libraries include both SMT and THP parts, over 1000 packages in total.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;User definable snap grids and Real Time Snap to deal with tricky SMT pin spacings.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Advanced Netlist Management provides for painless design modifications including pin-swap/gate-swap and back-annotation to the &lt;a href="http://world-educational-services.net/cart/admin/schematic.htm"&gt;ISIS schematic capture&lt;/a&gt; software.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Different track and via sizes, layers and physical design rules can be specified for different groups of nets using routing strategies. &lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Ratsnest display and Force Vectors displays - both updated in real time.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Connectivity and Design Rule checkers. &lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Gridless polygonal power planes.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Output via any Windows device driver, also Gerber, Excellon and DXF formats.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Gerber Viewer with Panelization/Tiling facility.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Gerber Import Tool for importing designs from other PCB packages.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Design Automation:&lt;/span&gt; &lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;table border="0"&gt;&lt;tbody&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Automatic Component Placement. A fast and configurable auto-placer is available that will place components on to a given board with optimum position, spacing and orientation.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Multi-strategy grid based auto-routing.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Special routines handle SMT parts.&lt;/span&gt; &lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Rip-Up &amp;amp; Retry for 100% routing on most boards.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr valign="baseline"&gt;&lt;td width="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;td&gt;&lt;img src="http://world-educational-services.net/images/bullet_small.gif" height="10" hspace="3" width="9" /&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Tidy pass reduces via count and track length.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;table border="0"&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td align="right" valign="top"&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;&lt;i&gt;Screen shot of ARES showing detail of a two layer board.&lt;br /&gt;&lt;br /&gt;The top layer is in red, the bottom layer in blue. Where objects on the two layers overlap, they appear in magenta (red plus blue) so that items on the top layer never obscure items on the bottom layer. &lt;/i&gt;&lt;/span&gt;&lt;/td&gt;&lt;td align="center" valign="middle"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;a name="schematic"&gt;&lt;/a&gt;&lt;span style="color: rgb(0, 0, 153); font-family: Arial,Helvetica,sans-serif;"&gt;&lt;b&gt;Schematic Entry&lt;/b&gt;&lt;/span&gt; &lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Schematic entry of the design is done using our &lt;a href="http://world-educational-services.net/cart/admin/schematic.htm"&gt;ISIS schematic capture&lt;/a&gt; software. Which is able to generate netlists and transfer them directly in to ARES as a single seamless operation so allowing you to start new layouts or update existing layouts with ease. Any design modifications to the layout (re-annotation, pin-swaps or gate-swaps) are seamlessly transferred back to the schematic when you next switch back to ISIS or re-load the schematic design. &lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Although ISIS is included as standard with all Proteus PCB Layout packages, ARES is also able to work from third-party schematic capture packages providing they can produce netlists in either Tango or Multiwire format. However, back-annotation to such packages is not supported.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;a name="lytdb"&gt;&lt;/a&gt;&lt;span style="color: rgb(0, 0, 153); font-family: Arial,Helvetica,sans-serif;"&gt;&lt;b&gt;Layout Database&lt;/b&gt;&lt;/span&gt; &lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;ARES features a state of the art layout database capable of representing the most complex of PCB designs. Placement resolution is 10 nanometers within a maximum board size of 20m. Components and other objects may be rotated in 0.1 degree increments whilst padstacks facilitate the achievement of maximum routing area on inner layers. &lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;a name="rediting"&gt;&lt;/a&gt;&lt;span style="color: rgb(0, 0, 153); font-family: Arial,Helvetica,sans-serif;"&gt;&lt;b&gt;Route Editing&lt;/b&gt;&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Topological route editing allows you to re-route or delete any section of a track, irrespective of how it was originally placed. Commands are also provided to change the thickness and/or layer of any section of tracking. If thick tracks are laid between obstacles such as IC pads, ARES will automatically insert a narrower 'neck' in order to maintain the current design rules. Curved tracks can be laid down simply by pressing the CTRL key and marking the route with the mouse.&lt;/span&gt; &lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="color: rgb(0, 0, 153); font-family: Arial,Helvetica,sans-serif;"&gt;&lt;b&gt;&lt;a name="libraries"&gt;&lt;/a&gt;Package Libraries&lt;/b&gt;&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;The supplied libraries cover a large range of through hole components including all the most common IC, transistor, diode and connector packaging types. We also supply as standard libraries for both discrete and IC SMT footprints; the latter including SOP, SOJ, PLCC, CLCC, QFP and PQFP types. New packages can be created directly on the drawing whilst ARES also supports general 2D drafting features.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="color: rgb(0, 0, 153); font-family: Arial,Helvetica,sans-serif;"&gt;&lt;b&gt;&lt;a name="netlists"&gt;&lt;/a&gt;Netlist Handling&lt;/b&gt;&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;During the placement phase, ARES displays both the ratsnest and force vectors. Both are updated in real time when you drag components. The ratsnest is also automatically updated during routing - add a track and a ratsnest line will disappear; delete a track and one will re-appear. The system fully supports design modifications - if you change the schematic and re-load the netlist, ARES will flag up exactly which components and/or tracks are affected. Equally, pin-swaps and gate-swaps made in ARES are automatically fed back to the schematic.&lt;/span&gt; &lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td bgcolor="#ffffff"&gt;&lt;a name="aplacer"&gt;&lt;/a&gt;&lt;span style="color: rgb(0, 0, 153); font-family: Arial,Helvetica,sans-serif;"&gt;&lt;b&gt;Auto Placer&lt;/b&gt;&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Automatic component placement makes it possible to design an entire board with absolute minimum of effort on your part. Alternatively, since the placer can operate interactively, you can pre-place critical components first and then let ARES auto-place the rest.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td bgcolor="#ffffff"&gt;&lt;a name="arouter"&gt;&lt;/a&gt;&lt;span style="color: rgb(0, 0, 153); font-family: Arial,Helvetica,sans-serif;"&gt;&lt;b&gt;Autorouting&lt;/b&gt;&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Our grid based router is both flexible and fast and can route using any track thickness or via width, at 90 or 45 degrees, and on 1-8 layers. It was placed in the top Category A in the recent review of PCB software (&lt;i&gt;Electronics &amp;amp; Wireless World&lt;/i&gt; magazine, January 1997). &lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;The range of routing grids available enables you to trade off routing density against execution speed with densities of 1, 2 or 3 traces between IC pads. The router also has special routines which enable it to form 'fan outs' from rows of SMT pads which would otherwise be off grid, thus enabling it to perform well with boards containing SMT parts. &lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;The Rip-Up and Retry mode enables it to remove and replace tracks which block others giving 100% completion on most medium density boards routed at 50 or 25 thou. Meanwhile, our innovative costing/scheduling logic reduces the via count by as much as four fold over low-medium cost routers.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Finally, you can run the tidy pass which reduces both track length and via count whilst improving the aesthetic quality of your board at the same time. &lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;a name="electra"&gt;&lt;/a&gt;&lt;span style="color: rgb(0, 0, 153); font-family: Arial,Helvetica,sans-serif;"&gt;&lt;b&gt;Routing with ELECTRA &lt;/b&gt;&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;For customers looking for the very latest in autorouting technology we have provided an integrated bi-directional interface to the ELECTRA autorouter. This router uses adaptive shape based autorouting algorithms to achieve completion, often surpassing industry standard benchmarks. &lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;More information on ELECTRA, links to a trial download and pricing can be found &lt;a href="http://world-educational-services.net/products/electra.htm"&gt;here&lt;/a&gt;. &lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td bgcolor="#ffffff"&gt;&lt;a name="pplanes"&gt;&lt;/a&gt;&lt;span style="color: rgb(0, 0, 153); font-family: Arial,Helvetica,sans-serif;"&gt;&lt;b&gt;Power Planes&lt;/b&gt;&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;ARES features the ultimate in power plane support - user placeable polygonal regions within which inner boundaries are automatically created around existing pads and tracking. Change the pads and tracking and the boundaries are recomputed to maintain design rule clearances. Thermal reliefs are supported and you can choose whether to hatch or fill each polygon. All computation is based on grid-less shape geometry and occurs in the background so that there is interference in manual board placement for computationally intensive layouts.&lt;/span&gt; &lt;/td&gt;&lt;/tr&gt;&lt;tr align="center"&gt;&lt;td height="10"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr align="center"&gt;&lt;td&gt;&lt;table border="0"&gt;&lt;tbody&gt;&lt;tr align="center"&gt;&lt;td&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr align="center"&gt;&lt;td&gt;&lt;i&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Close up of two ARES zones with the same board. The top-left shows a hatched zone with thermally relieved connections whilst the lower-right shows a solid zone with solid, unrelieved, connections.&lt;/span&gt;&lt;/i&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="15"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td bgcolor="#ffffff"&gt;&lt;a name="drc"&gt;&lt;/a&gt;&lt;span style="color: rgb(0, 0, 153); font-family: Arial,Helvetica,sans-serif;"&gt;&lt;b&gt;Design Rule Checking&lt;/b&gt;&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td height="5"&gt;&lt;br /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;During manual routing, ARES checks each track as you place it and warns you if any design rules (physical/electrical) are broken. You can also run global physical and electrical design rule checks at any time. The latter produces a report listing any missing or extra connections - double click on any entry in the list, and ARES will zoom in to show you exactly where the error is located on the PCB.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-9119967242311819542?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/9119967242311819542/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=9119967242311819542' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/9119967242311819542'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/9119967242311819542'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2009/06/proteus-isis-pcb-layout.html' title='PROTEUS - ISIS PCB Layout'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><media:thumbnail xmlns:media='http://search.yahoo.com/mrss/' url='http://1.bp.blogspot.com/_nzAjJng8N7E/ScsoTgDNtKI/AAAAAAAAAQ8/Yqa8k3yNxfI/s72-c/dl.gif' height='72' width='72'/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5804043561707380534</id><published>2009-06-11T10:46:00.000+08:00</published><updated>2009-06-11T10:48:29.870+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Engineering software for free'/><category scheme='http://www.blogger.com/atom/ns#' term='Quality Control and Reliability'/><title type='text'>How to make automated Check Sheet Using Microsoft Excel? | Macam mana hendak buat Check Sheet menggunakan Microsoft Excel?</title><content type='html'>&lt;a href="http://www.addthis.com/bookmark.php?v=20" onmouseover="return addthis_open(this, '', '[URL]', '[TITLE]')" onmouseout="addthis_close()" onclick="return addthis_sendto()"&gt;&lt;img src="http://s7.addthis.com/static/btn/lg-bookmark-en.gif" alt="Bookmark and Share" style="border: 0pt none ;" height="16" width="125" /&gt;&lt;/a&gt;&lt;script type="text/javascript" src="http://s7.addthis.com/js/200/addthis_widget.js"&gt;&lt;/script&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/4319598/ChecksheetGenerator.xls.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://4.bp.blogspot.com/_nzAjJng8N7E/Seb0hYCC2LI/AAAAAAAAAcE/OKIV9uWHXyY/s200/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5325212463636076722" border="0" /&gt;&lt;/a&gt;&lt;p style="color: rgb(0, 0, 0); font-family: verdana;"&gt;&lt;br /&gt;&lt;/p&gt;&lt;p style="color: rgb(0, 0, 0); text-align: center; font-family: verdana;"&gt;&lt;span style="font-size: 100%;"&gt;&lt;b&gt;&lt;a href="http://www.pusatilmu.co.cc/2009/04/guide-to-installing-quality-control.html"&gt;Installation Guide. Click Here.&lt;/a&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/p&gt;&lt;p style="color: rgb(0, 0, 0); font-family: verdana;"&gt;&lt;span style="font-size: 100%;"&gt;&lt;b&gt;Definition:&lt;/b&gt;&lt;/span&gt;   &lt;span style="font-size: 100%;"&gt; A simple data collection form consisting of multiple categories with definitions. Data are entered on the form with a simple tally mark each time one of the categories occurs. &lt;/span&gt;&lt;/p&gt;   &lt;p style="color: rgb(0, 0, 0); font-family: verdana;"&gt;&lt;span style="font-size: 100%;"&gt;&lt;b&gt;Purpose:&lt;/b&gt;&lt;/span&gt;    &lt;span style="font-size: 100%;"&gt;To facilitate the collection and analysis of data.&lt;/span&gt;&lt;/p&gt;   &lt;p style="color: rgb(0, 0, 0); font-family: verdana;"&gt;&lt;span style="font-size: 100%;"&gt;A check sheet is a simple means of data collection. The most straightforward check sheet is simply to make a list of items that you expect will appear in a process and to mark a check beside each item when it does appear. This type of data collection can be used for almost anything, from checking off the occurrence of particular types of defects to the counting of expected items (e.g., the number of times the telephone rings before being answered).&lt;/span&gt;&lt;/p&gt;   &lt;p style="color: rgb(0, 0, 0); font-family: verdana;"&gt;&lt;span style="font-size: 100%;"&gt;&lt;strong&gt;How to Construct:&lt;/strong&gt;&lt;/span&gt;&lt;/p&gt;      &lt;ol style="color: rgb(0, 0, 0); font-family: verdana;"&gt;&lt;span style="font-size: 100%;"&gt;     &lt;li&gt;Clearly define the objective of the data      collection.      &lt;/li&gt;&lt;li&gt;Determine other information about the source of the      data that should be recorded, such as shift, date, or machine.      &lt;/li&gt;&lt;li&gt;Determine and define all categories of data to be      collected.      &lt;/li&gt;&lt;li&gt;Determine the time period for data collection and      who will collect the data.      &lt;/li&gt;&lt;li&gt;Determine how instructions will be given to those      involved in data collection.      &lt;/li&gt;&lt;li&gt;Design a check sheet by listing categories to be      counted.      &lt;/li&gt;&lt;li&gt;Pilot the check sheet to determine ease of use and      reliability of results.      &lt;/li&gt;&lt;li&gt;Modify the check sheet based on results of the      pilot.&lt;/li&gt;&lt;/span&gt;&lt;/ol&gt;   &lt;p face="verdana" style="color: rgb(0, 0, 0);"&gt;&lt;span style="font-size: 100%;"&gt;&lt;strong&gt;Tips:&lt;/strong&gt;&lt;/span&gt;   &lt;/p&gt;&lt;ul style="color: rgb(0, 0, 0); font-family: verdana;"&gt;&lt;img src="http://mot.vuse.vanderbilt.edu/mt322/image/outline.gif" alt="" height="11" width="11" /&gt;&lt;span style="font-size: 100%;"&gt; Use Ishikawa diagrams or Brainstorming to determine      categories to be used on the check sheet.&lt;/span&gt;&lt;br /&gt;&lt;img src="http://mot.vuse.vanderbilt.edu/mt322/image/outline.gif" alt="" height="11" width="11" /&gt;&lt;span style="font-size: 100%;"&gt; Construct an operational definition of each      category to ensure data collected is consistent.&lt;/span&gt;&lt;br /&gt;&lt;img src="http://mot.vuse.vanderbilt.edu/mt322/image/outline.gif" alt="" height="11" width="11" /&gt;&lt;span style="font-size: 100%;"&gt; Make check sheet as clear and easy to use as      possible.&lt;/span&gt;&lt;br /&gt;&lt;img src="http://mot.vuse.vanderbilt.edu/mt322/image/outline.gif" alt="" height="11" width="11" /&gt;&lt;span style="font-size: 100%;"&gt; Spend adequate time explaining the objective of the data collection to those involved in recording the data to ensure the data will be reliable. &lt;/span&gt;&lt;br /&gt;&lt;img src="http://mot.vuse.vanderbilt.edu/mt322/image/outline.gif" alt="" height="11" width="11" /&gt;&lt;span style="font-size: 100%;"&gt; Data collected in this format facilitates easy Pareto analysis.&lt;/span&gt;&lt;/ul&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5804043561707380534?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5804043561707380534/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5804043561707380534' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5804043561707380534'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5804043561707380534'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2009/06/how-to-make-automated-check-sheet-using.html' title='How to make automated Check Sheet Using Microsoft Excel? | Macam mana hendak buat Check Sheet menggunakan Microsoft Excel?'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><media:thumbnail xmlns:media='http://search.yahoo.com/mrss/' url='http://4.bp.blogspot.com/_nzAjJng8N7E/Seb0hYCC2LI/AAAAAAAAAcE/OKIV9uWHXyY/s72-c/dl.gif' height='72' width='72'/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-8787873830410149279</id><published>2009-06-11T10:39:00.001+08:00</published><updated>2009-06-11T10:46:14.516+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Quality Control and Reliability'/><title type='text'>X-bar/R chart (3 in 1 e-books)</title><content type='html'>&lt;h3 style="font-family: verdana;" class="post-title"&gt; &lt;/h3&gt;  &lt;div style="font-family: verdana;" class="post-body"&gt; &lt;p&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_nzAjJng8N7E/SbsBeA3AB9I/AAAAAAAAAIM/B4-FXs_OnZk/s1600-h/control-chart-example-XbarR-chart.jpg"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 320px; height: 219px;" src="http://2.bp.blogspot.com/_nzAjJng8N7E/SbsBeA3AB9I/AAAAAAAAAIM/B4-FXs_OnZk/s320/control-chart-example-XbarR-chart.jpg" alt="" id="BLOGGER_PHOTO_ID_5312841800552024018" border="0" /&gt;&lt;/a&gt;&lt;br /&gt;&lt;/p&gt;&lt;div style="text-align: center;"&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/3856172/x-barRCharts.pdf.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://4.bp.blogspot.com/_nzAjJng8N7E/SbsBdsooYDI/AAAAAAAAAIE/_3MSq46fhNs/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5312841795123044402" border="0" /&gt;&lt;/a&gt;x-bar R Charts.pdf&lt;br /&gt;&lt;br /&gt;&lt;/div&gt;&lt;div style="text-align: center;"&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/3856173/opt_25398_2126560152.pdf.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://1.bp.blogspot.com/_nzAjJng8N7E/SbsBdsQZl5I/AAAAAAAAAH8/vmi6DBmYhm8/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5312841795021412242" border="0" /&gt;&lt;/a&gt;Construction of X-bar and R Chart&lt;br /&gt;&lt;br /&gt;&lt;/div&gt;&lt;div style="text-align: center;"&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/3856174/XBarStatisticalPDF.pdf.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://3.bp.blogspot.com/_nzAjJng8N7E/SbsBdqbb1tI/AAAAAAAAAH0/0FmebKNNIUU/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5312841794530825938" border="0" /&gt;&lt;/a&gt;X Bar Statistical PDF.pdf&lt;br /&gt;&lt;/div&gt;&lt;br /&gt;&lt;div style="text-align: center;"&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/3856238/XRCharts.xls.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://3.bp.blogspot.com/_nzAjJng8N7E/SbsBdqbb1tI/AAAAAAAAAH0/0FmebKNNIUU/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5312841794530825938" border="0" /&gt;&lt;/a&gt;Software to Construct X bar and R chart in easy way using Microsoft Excel&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;/div&gt;&lt;br /&gt;An X-bar/R chart is a specific member of a family of control charts. A control chart is a tool used in quality control, specifically SPC or statistical process control, as originally developed by Walter A. Shewhart at Western Electric in 1924 to improve the quality of telephones.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;A control chart is a plot of measurements of a product on two special scales, usually located above and below each other and running horizontally. X-Bar/R charts consist of two charts, both with the same horizontal axis denoting the sample number.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;The vertical axis on the top chart depicts the sample means (X-Bar) for a series of lots or subgroup samples. It has a centerline represented by Xdoublebar, which is simply the overall process average, as well as two horizontal lines, one above and one below the centerline, known as the upper control limit or UCL and lower control limit or LCL, respectively. These lines are drawn at a distance of plus and minus three standard deviations (that is, standard deviations of the sampling distribution of sample means) from the process average. In practice, tabulated constants are available to determine the control limits, or they are automatically calculated by the SPC software used.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;The bottom chart has the range (R) of each subgroup plotted on the vertical axis. Like an X-Bar chart, R charts have a centerline and two control limits. However, for sample sizes below 7, the LCL is zero.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;The purpose of any control chart is to help determine if variations in measurements of a product are caused by small, normal variations that cannot be acted upon ("common causes"), or by some larger "special cause" that can be acted upon or fixed. The type of chart to be used is based on the nature of the data.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;The X-bar/R chart is normally used for numerical data that is captured in subgroups in some logical manner – for example 3 production parts measured every hour. A special cause such as a broken tool will then show up as an abnormal pattern of points on the chart.&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-8787873830410149279?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/8787873830410149279/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=8787873830410149279' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8787873830410149279'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8787873830410149279'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2009/06/x-barr-chart-3-in-1-e-books_11.html' title='X-bar/R chart (3 in 1 e-books)'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><media:thumbnail xmlns:media='http://search.yahoo.com/mrss/' url='http://2.bp.blogspot.com/_nzAjJng8N7E/SbsBeA3AB9I/AAAAAAAAAIM/B4-FXs_OnZk/s72-c/control-chart-example-XbarR-chart.jpg' height='72' width='72'/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-3027993767649375861</id><published>2009-06-11T10:39:00.000+08:00</published><updated>2009-06-11T10:45:34.152+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Quality Control and Reliability'/><title type='text'>X-bar/R chart (3 in 1 e-books)</title><content type='html'>&lt;h3 style="font-family: verdana;" class="post-title"&gt; &lt;/h3&gt;  &lt;div style="font-family: verdana;" class="post-body"&gt; &lt;p&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_nzAjJng8N7E/SbsBeA3AB9I/AAAAAAAAAIM/B4-FXs_OnZk/s1600-h/control-chart-example-XbarR-chart.jpg"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 320px; height: 219px;" src="http://2.bp.blogspot.com/_nzAjJng8N7E/SbsBeA3AB9I/AAAAAAAAAIM/B4-FXs_OnZk/s320/control-chart-example-XbarR-chart.jpg" alt="" id="BLOGGER_PHOTO_ID_5312841800552024018" border="0" /&gt;&lt;/a&gt;&lt;br /&gt;&lt;/p&gt;&lt;div style="text-align: center;"&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/3856172/x-barRCharts.pdf.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://4.bp.blogspot.com/_nzAjJng8N7E/SbsBdsooYDI/AAAAAAAAAIE/_3MSq46fhNs/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5312841795123044402" border="0" /&gt;&lt;/a&gt;x-bar R Charts.pdf&lt;br /&gt;&lt;br /&gt;&lt;/div&gt;&lt;div style="text-align: center;"&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/3856173/opt_25398_2126560152.pdf.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://1.bp.blogspot.com/_nzAjJng8N7E/SbsBdsQZl5I/AAAAAAAAAH8/vmi6DBmYhm8/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5312841795021412242" border="0" /&gt;&lt;/a&gt;Construction of X-bar and R Chart&lt;br /&gt;&lt;br /&gt;&lt;/div&gt;&lt;div style="text-align: center;"&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/3856174/XBarStatisticalPDF.pdf.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://3.bp.blogspot.com/_nzAjJng8N7E/SbsBdqbb1tI/AAAAAAAAAH0/0FmebKNNIUU/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5312841794530825938" border="0" /&gt;&lt;/a&gt;X Bar Statistical PDF.pdf&lt;br /&gt;&lt;/div&gt;&lt;br /&gt;&lt;div style="text-align: center;"&gt;&lt;a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ziddu.com/download/3856238/XRCharts.xls.html"&gt;&lt;img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 51px; height: 47px;" src="http://3.bp.blogspot.com/_nzAjJng8N7E/SbsBdqbb1tI/AAAAAAAAAH0/0FmebKNNIUU/s320/dl.gif" alt="" id="BLOGGER_PHOTO_ID_5312841794530825938" border="0" /&gt;&lt;/a&gt;Software to Construct X bar and R chart in easy way using Microsoft Excel&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;/div&gt;&lt;br /&gt;An X-bar/R chart is a specific member of a family of control charts. A control chart is a tool used in quality control, specifically SPC or statistical process control, as originally developed by Walter A. Shewhart at Western Electric in 1924 to improve the quality of telephones.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;A control chart is a plot of measurements of a product on two special scales, usually located above and below each other and running horizontally. X-Bar/R charts consist of two charts, both with the same horizontal axis denoting the sample number.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;The vertical axis on the top chart depicts the sample means (X-Bar) for a series of lots or subgroup samples. It has a centerline represented by Xdoublebar, which is simply the overall process average, as well as two horizontal lines, one above and one below the centerline, known as the upper control limit or UCL and lower control limit or LCL, respectively. These lines are drawn at a distance of plus and minus three standard deviations (that is, standard deviations of the sampling distribution of sample means) from the process average. In practice, tabulated constants are available to determine the control limits, or they are automatically calculated by the SPC software used.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;The bottom chart has the range (R) of each subgroup plotted on the vertical axis. Like an X-Bar chart, R charts have a centerline and two control limits. However, for sample sizes below 7, the LCL is zero.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;The purpose of any control chart is to help determine if variations in measurements of a product are caused by small, normal variations that cannot be acted upon ("common causes"), or by some larger "special cause" that can be acted upon or fixed. The type of chart to be used is based on the nature of the data.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;The X-bar/R chart is normally used for numerical data that is captured in subgroups in some logical manner – for example 3 production parts measured every hour. A special cause such as a broken tool will then show up as an abnormal pattern of points on the chart.&lt;/div&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-3027993767649375861?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/3027993767649375861/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=3027993767649375861' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3027993767649375861'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/3027993767649375861'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2009/06/x-barr-chart-3-in-1-e-books.html' title='X-bar/R chart (3 in 1 e-books)'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><media:thumbnail xmlns:media='http://search.yahoo.com/mrss/' url='http://2.bp.blogspot.com/_nzAjJng8N7E/SbsBeA3AB9I/AAAAAAAAAIM/B4-FXs_OnZk/s72-c/control-chart-example-XbarR-chart.jpg' height='72' width='72'/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7971309982313252846</id><published>2008-09-23T02:22:00.004+08:00</published><updated>2008-09-23T02:30:08.338+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Free CAD Sofware'/><title type='text'>SmartDraw has been one of Doc's "Favorites" since 1994. Find out why!</title><content type='html'>&lt;p style="text-align: center;"&gt;&lt;a href="http://www.shareapic.net/content.php?id=11333808&amp;amp;owner=bmfrguru" target="_blank"&gt;&lt;img src="http://preview.shareapic.net/preview4/011333808.gif" border="0" /&gt;&lt;/a&gt; &lt;/p&gt;&lt;div style="text-align: center;"&gt;Click To Enlarge&lt;br /&gt;&lt;/div&gt;&lt;br /&gt;SmartDraw lets anyone quickly and easily create professional-looking flowcharts, org-charts, forms, presentations, floor plans, schematics, networks, and much, much more! The new SmartDraw 2007 offers dozens of powerful new features including the ability to draw freeform, add gradient colors, create multiple layers,use ink enabled Tablet PC features, plus SmartDraw 2007 now offers over 20,000 symbols &amp;amp; templates, all of which can be evaluated for free with the SmartDraw 7-day trial.&lt;!-- /BODY1 --&gt;&lt;!-- BODY2 --&gt;Each of SmartDraw’s symbol and template collection is aimed at a particular drawing discipline: Business &amp;amp; Charting, Floor Plans &amp;amp; Facilities Facilities Design, Electrical Engineering, Mechanical Engineering, Network Design, Software Design, Maps &amp;amp; Geography, Science &amp;amp; Math, Clipart, and more! SmartDraw is truly one of those programs that would be valuable to have in any business or organization.&lt;br /&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt; Easy to use - no drawing skill required! &lt;/li&gt;&lt;li&gt; Contains thousands of built-in symbols and clip-art, you simply drag-and-drop into your drawings. &lt;/li&gt;&lt;li&gt; Import and export drawings in many formats (Word, Excel, Powerpoint, GIF, JPG, EPS, Visio, AutoCAD, and more). &lt;/li&gt;&lt;li&gt; Draw Freeform - create custom shapes and lines, literally draw anything you can imagine! &lt;/li&gt;&lt;li&gt; Create Multiple Layers to simplify complex drawings, for example, separate a floor plan into layers for walls. &lt;/li&gt;&lt;li&gt; Draw huge diagrams with thousands of symbols per drawing. &lt;/li&gt;&lt;li&gt; Great for presentations: Supports rich text editing. Choose from a library of color schemes and shadow styles for a professional finish. &lt;/li&gt;&lt;li&gt; Vista Compatible &lt;/li&gt;&lt;li&gt; Tablet PC Enabled&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;&lt;p&gt;&lt;br /&gt;&lt;/p&gt;&lt;p&gt;&lt;a href="http://www.filefactory.com/file/e26c12/n/smartdraw_rar"&gt;DOWNLOAD AVAILABLE HERE&lt;/a&gt;&lt;br /&gt;&lt;/p&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7971309982313252846?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7971309982313252846/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7971309982313252846' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7971309982313252846'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7971309982313252846'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2008/09/smartdraw-has-been-one-of-docs.html' title='SmartDraw has been one of Doc&apos;s &quot;Favorites&quot; since 1994. Find out why!'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-4766339467508620543</id><published>2008-09-23T02:13:00.002+08:00</published><updated>2008-09-23T02:17:48.685+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Free CAD Sofware'/><title type='text'>HYCAD 5.35</title><content type='html'>* Last Updated: 2008-01-21&lt;p&gt;&lt;a href="http://www.shareapic.net/content.php?id=11333670&amp;amp;owner=bmfrguru" target="_blank"&gt;&lt;img src="http://preview.shareapic.net/preview4/011333670.jpg" border="0" /&gt;Click To Enlarge&lt;/a&gt; &lt;/p&gt;* License: Freeware Free&lt;br /&gt;  * OS: Windows Vista, 2003, XP, 2000&lt;br /&gt;* Requirements: No special requirements&lt;br /&gt;&lt;br /&gt;"HYCAD is a general purpose CAD program, green and small but powerful."&lt;br /&gt;Brothersoft Editor: HYCAD is a general purpose CAD program, green and small but powerful. it can export multiple format files,such as BMP JPG PNG DXF XMG WMF DWG EPS SLD CGM SVG PDF etc. it is easy to be learn and use. you can &lt;a href="http://www.filefactory.com/file/c86a16/n/HYCADSetUpEn_rar"&gt;free download HYCAD 5.35&lt;/a&gt; now.&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-4766339467508620543?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/4766339467508620543/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=4766339467508620543' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4766339467508620543'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4766339467508620543'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2008/09/hycad-535.html' title='HYCAD 5.35'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5229035071399095616</id><published>2008-09-23T01:56:00.003+08:00</published><updated>2008-09-23T02:11:22.538+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Solid Modeling'/><category scheme='http://www.blogger.com/atom/ns#' term='Free 3D Solid Modeler'/><category scheme='http://www.blogger.com/atom/ns#' term='Free CAD Sofware'/><title type='text'>Google SketchUp Pro 6 with keygen</title><content type='html'>&lt;h3 class="dark"&gt;Create, export and present 3D models&lt;/h3&gt;       &lt;p&gt; &lt;a href="http://sketchup.google.com/product/gsup.html"&gt;Google SketchUp Pro &lt;/a&gt;6 is software that you can use to create, share and present 3D models. SketchUp Pro provides extra functionality for people who need to export their work into CAD, rendering and other professional software applications. SketchUp Pro 6 also includes &lt;a href="http://sketchup.google.com/product/layout.html"&gt;LayOut&lt;/a&gt;, a completely new program that lets you create complete presentations – paper and digital – from your SketchUp models. Discover how to use SketchUp Pro to &lt;a href="http://sketchup.google.com/3dwh/"&gt;make buildings for Google Earth&lt;/a&gt;. Find out more about &lt;a href="http://sketchup.google.com/download/plugins.html"&gt;plugins&lt;/a&gt; to extend the functionality of SketchUp Pro, as well as applications that are &lt;a href="http://sketchup.google.com/download/skpcompapps.html"&gt;SketchUp compatible&lt;/a&gt;.&lt;/p&gt;       &lt;p&gt;  &lt;/p&gt;&lt;div style="padding-left: 0px; display: none;" ontop="true"&gt;&lt;/div&gt;&lt;object classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=7,0,19,0" name="theFlash" id="theFlash" title="Google SketchUp Pro Flash Banner" width="480" height="160"&gt;       &lt;param name="movie" value="../images/swf/pro_banner.swf"&gt;       &lt;param name="quality" value="high"&gt;       &lt;embed src="http://sketchup.google.com/images/swf/pro_banner.swf" id="theEmbed" quality="high" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" name="theFlash" width="480" height="160"&gt;&lt;/embed&gt;&lt;/object&gt;       &lt;p&gt;&lt;br /&gt;&lt;/p&gt;&lt;br /&gt;&lt;br /&gt;What makes SketchUp great?&lt;br /&gt;Google SketchUp is a tool for creating, editing and sharing 3D models. The SketchUp "secret sauce" is a unique set of powerful tools that are designed to be easy to learn and use:&lt;br /&gt;Edges and Faces: Thats all there is to it&lt;br /&gt;&lt;br /&gt;Every SketchUp model is made up of just two things: edges and faces. Edges are straight lines, and faces are the 2D shapes that are created when several edges form a flat loop. For example, a rectangular face is bound by four edges that are connected together at right angles. To build models in SketchUp, you draw edges and faces using a few simple tools that you can learn in a small amount of time. It's as simple as that.&lt;br /&gt;Push/Pull: Quickly go from 2D to 3D&lt;br /&gt;&lt;br /&gt;Extrude any flat surface into a three-dimensional form with SketchUp's patented Push/Pull tool. Just click to start extruding, move your mouse, and click again to stop. You can Push/Pull a rectangle into a box. Or draw the outline of a staircase and Push/Pull it into 3D. Want to make a window? Push/Pull a hole through your wall. SketchUp is known for being easy to use, and Push/Pull is the reason why.&lt;br /&gt;Accurate measurements: Work with precision&lt;br /&gt;&lt;br /&gt;SketchUp is great for working fast and loose in 3D, but it's more than just a fancy electronic pencil. Because you're working on a computer, everything you create in SketchUp has a precise dimension. When you're ready, you can build models that are as accurate as you need them to be. If you want, you can print scaled views of your model, and if you have SketchUp Pro, you can even export your geometry into other programs like AutoCAD and 3ds MAX.&lt;br /&gt;Follow Me: Create complex extrusions and lathed forms&lt;br /&gt;&lt;br /&gt;You use SketchUp's innovative, do-everything Follow Me tool to create 3D forms by extruding 2D surfaces along predetermined paths. Model a bent pipe by extruding a circle along an L-shaped line. Create a bottle by drawing half of its outline, then using Follow Me to sweep it around a circle. You can even use Follow Me to round off (fillet) edges on things like handrails, furniture and electronic gadgets.&lt;br /&gt;Paint Bucket: Apply colors and textures&lt;br /&gt;&lt;br /&gt;You can use SketchUp's Paint Bucket tool to paint your model with materials like colors and textures. Better yet, SketchUp comes pre-loaded with a healthy library of photo-textures like brick, roofing and stone that you can use to make your model look as detailed as you like. You can find thousands more textures online, and if you're handy with a photo editing application like Photoshop, you can even make your own.&lt;br /&gt;Groups and Components: Build smarter models&lt;br /&gt;&lt;br /&gt;By "sticking together" parts of the geometry in your model to make Groups, you can create sub-objects that are easier to move, copy and hide. Components are a lot like Groups, but with a handy twist: copies of Components are related together, so changes you make to one are automatically reflected in all the others. Windows, doors, trees, chairs and millions of other things benefit from this behavior.&lt;br /&gt;Shadows: Perform shade studies and add realism&lt;br /&gt;&lt;br /&gt;SketchUp's powerful, real-time Shadow Engine lets you perform accurate shade studies on your models. Want to know how big to make the awning over your deck? Specify a geographic location using Google Earth, then use the simple Date and Time sliders to see how the sun will affect your design. Even if you're not using SketchUp for architecture, adding shadows is a great way to give your models more depth and realism.&lt;br /&gt;Sections: See inside your models&lt;br /&gt;&lt;br /&gt;You can use SketchUp's interactive Sections feature to temporarily cut away parts of your design, enabling you to look inside. You can use Sections to create orthographic views (like floorplans), to export geometry to CAD programs using SketchUp Pro, or just to get a better view of your model while you're working on it. Section Planes can be moved, rotated and even animated using SketchUp's Scenes feature.&lt;br /&gt;Scenes: Save views and create animations&lt;br /&gt;&lt;br /&gt;We created Scenes to enable you to easily save precise views of your model so you can come back to them later. Need to create an animation? Just create a few Scenes and click a button. SketchUp automatically "flies" from Scene to Scene, adding smooth transitions that you can fine-tune to get the results you need. You can also choose to export your animations as self-contained movies; SketchUp produces AVI files on Windows computers, and Quicktime MOVs on Macs.&lt;br /&gt;Look Around and Walk: Explore your creations firsthand&lt;br /&gt;&lt;br /&gt;SketchUp lets you get inside your model with a set of simple navigation tools designed to give you a first-person view. Click with Position Camera to "be standing" anywhere in your model. Use Look Around to turn your virtual head. Finally, switch to Walk to explore your creation on foot; you can even climb and descend stairs and ramps, just like you're playing a video game.&lt;br /&gt;Dimensions and Labels: Add information to your designs&lt;br /&gt;&lt;br /&gt;You can use the super-intuitive Dimension and Label tools to add dimensions, annotations and other glorious detail to your work. Once applied, SketchUp's dimensions are dynamic, meaning they automatically scale with your model. Labels are what we call "2.5D", meaning they remain visible no matter how you spin your model to look at it, but they always appear flat.&lt;br /&gt;The Instructor: Catch on quickly&lt;br /&gt;&lt;br /&gt;SketchUp's Instructor dialog box, which you can choose to activate at any time, provides context-sensitive help. Depending on what tool you're using, the Instructor displays step-by-step instructions, animations, useful modifier keys, and other handy tips for getting the most out of SketchUp.&lt;br /&gt;Layers and the Outliner: Stay organized&lt;br /&gt;&lt;br /&gt;When you're building a big, complicated model, things can get messy very quickly. SketchUp provides two useful ways to keep your geometry manageable: In addition to Layers, the SkechUp Outliner is a dialog box that displays a collapsible list view of all the Groups and Components in your model. You can use the Outliner to rearrange the nesting order of these elements, and to control their visibility without having to dig through your model to find them.&lt;br /&gt;Google Earth: See your models in context&lt;br /&gt;&lt;br /&gt;SketchUp and Google Earth are part of the same product family, meaning you can exchange information between them easily. Need a building site for your project? Import a scaled aerial photograph, including topography, directly from Google Earth to SketchUp by clicking one button. Want to see your SketchUp model in context in Google Earth? Click another button, and you can. Anyone can use SketchUp to build models which can be seen by anyone in Google Earth.&lt;br /&gt;Sandbox tools: Work on terrain&lt;br /&gt;&lt;br /&gt;SketchUp's Sandbox tools let you create, optimize and alter 3D terrain. You can generate a smooth landscape from a set of imported contour lines, add berms and valleys for runoff, and create a building pad and driveway.&lt;br /&gt;3D Warehouse: Find models of almost anything you need&lt;br /&gt;&lt;br /&gt;The Google 3D Warehouse is a huge, online repository of 3D models which you can search through when you need something. Why build something when you can download it for free? There are thousands of cars, trees, sofas, bridges, pomegranates and everything else under the sun, all contributed by people and manufacturers all over the world, and all available for you to use any way you see fit. If you create a model you'd like to share, you can upload it to the 3D Warehouse for everyone else to use.&lt;br /&gt;Import DXF, DWG and 3DS: Get a headstart on your modeling&lt;br /&gt;&lt;br /&gt;You can import DXF, DWG and 3DS files directly into your SketchUp models, which makes it very easy to start with drawings and even other 3D models. Have a floorplan of the space you need to model? Import it in, and start building right on top of it.&lt;br /&gt;Import images: Paint walls with photos&lt;br /&gt;&lt;br /&gt;With SketchUp, you can import image files like JPGs, TIFFs, PNGs and PDFs. You can use them by themselves (kind of like posters), but you can also stick them to surfaces to create photo-realistic models of buildings, package designs, and more.&lt;br /&gt;Export TIFF, JPEG and PNG&lt;br /&gt;&lt;br /&gt;SketchUp lets you export raster images up to 10,000 pixels square, so generating an image which you can send in an email, publish in a document, or project on a wall is as easy as choosing a few options and clicking Export. If you have LayOut (which is included with SketchUp Pro), you can create 2D documents with embedded SketchUp models, meaning you don't need to export images at all. Either way, you're all set when it comes to producing views of your model that anyone can use.&lt;br /&gt;Export DXF and DWG: 2D line drawings and 3D models (Pro only)&lt;br /&gt;&lt;br /&gt;Google SketchUp Pro allows you to export DXFs and DWGs, giving you an easy way to move plans, sections, elevations or even your whole model into your favorite CAD program. Exported geometry remains at 1:1 scale, and layers are preserved.&lt;br /&gt;Export PDF and EPS: 2D vector images (Pro only)&lt;br /&gt;&lt;br /&gt;With the Pro version of Google SketchUp, you can export views of your models in PDF and EPS format, allowing you to continue to work on them in vector editing programs like Illustrator and Freehand. For 2D images that need to be resolution-independent, nothing beats exporting to these formats.&lt;br /&gt;Export 3DS, OBJ, XSI, FBX, VRML and DAE (Pro only)&lt;br /&gt;&lt;br /&gt;If you're using Google SketchUp Pro, you can export your models to a number of useful 3D formats. Pros use a number of different tools, and these exporters allow SketchUp to join most professional workflows by offering interoperability with just about every popular 3D modeling application in existence.&lt;br /&gt;&lt;br /&gt;New in Google SketchUp 6&lt;br /&gt;&lt;br /&gt;Google SketchUp 6 includes a number of new features, including new ways to view your models, build models from photographs, create 3D text objects, performance enhancements, and more. The Pro version of Google SketchUp 6 also includes LayOut, a brand-new tool for creating professional 2D presentations from your SketchUp models.&lt;br /&gt;Match a photo: Use photographs to build 3D models&lt;br /&gt;&lt;br /&gt;SketchUp 6 includes a new photo-matching feature that you can use to build 3D models by tracing photographs. You can use multiple photos to build a model, and you can even use your photos to "paint" your model when you're done. SketchUp's photo-matching feature also lets you line up your view of an existing model to match the viewpoint of a photo. This is handy for creating a composite image of an unbuilt project in a photo of its site.&lt;br /&gt;Styles: Fine-tune your models' appearance&lt;br /&gt;&lt;br /&gt;The latest version of SketchUp includes Styles, an all-new way to control the way your SketchUp models look. Using Styles, you can change your background, edge and face colors. You can choose from a library of sketchy edge styles to make your lines look hand-drawn. You can use Watermarks (which are also new in SketchUp 6) to add your logo to your model views, or to add paper textures as backgrounds. Even better, Styles can be saved and shared across projects to give your organization's output a consistent appearance.&lt;br /&gt;Watermarks: Add logos, backgrounds and more&lt;br /&gt;&lt;br /&gt;SketchUp's new Watermarks feature lets you add 2D images to your SketchUp models – behind them, as underlays, or in front of them, as overlays. You might use a Watermark underlay to add a sky background, or to make it appear that your model is drawn on a textured surface like watercolor paper. Watermark overlays are an easy way for you to add your logo or other graphics to model views. You'll find Watermarks in the new Styles dialog box.&lt;br /&gt;Sketchy Edge Effects: Make your models look hand-drawn&lt;br /&gt;&lt;br /&gt;SketchUp's new Styles feature includes Sketchy Edge Effects, which you can use to make your model views look like you drew them by hand. A large built-in library of sketchy styles includes pencils, pens, markers, charcoal and more. If you've ever printed out a SketchUp model and traced over it by hand to make it look less "computerized", you'll appreciate the new Sketchy Edge Effects in SketchUp 6.&lt;br /&gt;Fog: Add depth and visual interest to your work&lt;br /&gt;&lt;br /&gt;In SketchUp 6, you can add the appearance of fog to your models. It's a great way to add depth and nuance, and it's easy to do: just click a button, choose a color, and move a couple of sliders to adjust how "foggy" you'd like your model view to look.&lt;br /&gt;3D Text: Create 3D text for signage and more&lt;br /&gt;&lt;br /&gt;We're proud to introduce our long-awaited 3D Text tool, which is new in SketchUp 6. Now you can create 3D objects from any text string you type, in any font you have on your computer. You can also control what kind of object SketchUp creates: simple vector outlines, filled 2D surfaces or fully-extruded 3D letters.&lt;br /&gt;Other Improvements: Faster, easier to use, and more reliable&lt;br /&gt;&lt;br /&gt;In addition to the new features we've added to Google SketchUp 6, we've made performance improvements that make SketchUp faster and more fun to use than ever. Check out the complete list.&lt;br /&gt;&lt;br /&gt;LayOut: Create professional 2D presentations&lt;br /&gt;&lt;br /&gt;Included with Google SketchUp Pro 6, LayOut (beta) is a powerful new tool you can use to create compelling, multi-page 2D presentations from your SketchUp models. It's a completely separate application that we developed to work hand-in-glove with SketchUp. LayOut saves you time and effort by eliminating much of the busywork involved in creating 2D presentations, both for print and digital presentation.&lt;br /&gt;Update: Stop exporting images out of SketchUp&lt;br /&gt;&lt;br /&gt;In LayOut, you can insert any number views of the same SketchUp model into your presentation. When you make changes to your model in SketchUp (and you know you will), there's no need to export another whole set of images – just click a single button in LayOut, and all your model views update automatically to reflect the changes. Easy.&lt;br /&gt;Navigate: Orbit, pan and zoom your models right in LayOut&lt;br /&gt;&lt;br /&gt;After you insert a SketchUp model view into your LayOut presentation, you're free to change your point of view at any time. Just double-click, then use your mouse to orbit, zoom and pan until you like what you see. Right-clicking brings up a menu of options for displaying your model with shadows, viewing specific Scenes (f you've set them up), turning on and off perspective, and more.&lt;br /&gt;Scaled Views: See your models at any scale&lt;br /&gt;&lt;br /&gt;You can choose to display SketchUp model views you've inserted into your LayOut document at any drawing scale you like. This lets you generate orthographic views like plans and elevations directly from your SketchUp model. And when your model changes, so do your views in LayOut.&lt;br /&gt;Full Screen: Use LayOut to give digital presentations&lt;br /&gt;&lt;br /&gt;With LayOut, you may never have to create a PowerPoint design presentation again. LayOut gives you the ability to display your presentations in a full-screen mode. You can use the arrow keys or your mouse to move from page to page, and even write notes directly on your pages while you're presenting. You can also spin your SketchUp model views around, and play animations that you've set up in SketchUp – all without leaving your LayOut presentation.&lt;br /&gt;High-res printing and PDF export: Show your work&lt;br /&gt;&lt;br /&gt;From LayOut, you can print your presentations at whatever resolution you need: high-res for small design packets, and lower for things like posters and boards. If you need to share your presentations digitally, LayOut even lets you export to PDF.&lt;br /&gt;Text: You have full control&lt;br /&gt;&lt;br /&gt;LayOut's powerful text-handling tools allow you to create callouts, title blocks, annotations and whole paragraphs of text. And of course, you have full control over the font, color and orientation of everything you create.&lt;br /&gt;Callouts: LayOut makes labeling easier&lt;br /&gt;&lt;br /&gt;LayOut includes a unique Label tool that you can use to create callouts quickly and easily. You can even design your own leader lines by combining settings for color, thickness and endcaps. Using the Label tool is as simple clicking to anchor an endpoint, clicking again to end the leader, and typing in the text for the label.&lt;br /&gt;Sample: Duplicate graphic and text attributes quickly&lt;br /&gt;&lt;br /&gt;Copying graphic styles from one object to another is easy in LayOut; just use the Sample tool. It even works on text objects, which makes changing the look of your presentations as quick and painless as possible.&lt;br /&gt;Scrapbooks: Keep everything you need in one place&lt;br /&gt;&lt;br /&gt;Scrapbooks are libraries of graphic elements like north arrows, drawing scales, logos and other symbols that are used frequently in your presentations. They appear in a handy dialog box, ready for you to use when you need them. LayOut comes with some starter Scrapbooks, but you're free to make your own and share them with the rest of your team.&lt;br /&gt;Master Layers: Work smarter and get more professional results&lt;br /&gt;&lt;br /&gt;In LayOut, you can work with two kinds of Layers: regular ones and Master Layers. Anything you put on a Master Layer automatically appears on every page of your presentation, except ones that you've set not to show content from Master Layers. This makes it easy to create multi-page presentations with things like logos, title blocks and other graphics that always appear in the same place on every page. It makes editing easier, too – make a change once, and it'll be reflected everywhere, instantly.&lt;br /&gt;Vector graphics: Draw beautiful vector graphics&lt;br /&gt;&lt;br /&gt;LayOut takes a kinder, gentler approach to drawing vector graphics – the tools are friendlier than others you may have tried to use. Draw shapes, color them, scale them, rotate them, stretch them and combine them together. You'll be surprised how easy it is to create beautiful vector graphics in LayOut.&lt;br /&gt;Templates: Make life easier for yourself and your team&lt;br /&gt;&lt;br /&gt;LayOut makes it easier for your team to create presentations that are consistent, no matter what project you're working on. Set up a Template with your organization's graphic identity – logo, colors, cover page, title block – and use it every time you need to start building a new presentation. You can even share your Templates with the rest of your team, making your workflow more efficient and your organization's work product more uniform and professional.&lt;br /&gt;&lt;br /&gt;&lt;a href="http://www.filefactory.com/file/0d5429/n/Google_SketchUp_Pro_include_KeyGen_rar"&gt;DOWNLOAD AVAILABLE FOR GOOGLE SKETCHUP PRO 6 INCLUDE KEYGEN&lt;/a&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5229035071399095616?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5229035071399095616/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5229035071399095616' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5229035071399095616'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5229035071399095616'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2008/09/google-sketchup-pro-6-with-keygen.html' title='Google SketchUp Pro 6 with keygen'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5371584624142212234</id><published>2008-09-11T19:59:00.000+08:00</published><updated>2008-09-11T20:00:28.982+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Tutorial'/><category scheme='http://www.blogger.com/atom/ns#' term='LU Decomposition in Gaussian Elimination'/><title type='text'>Use of LU decomposition - Tutorial 4</title><content type='html'>&lt;h3&gt;Realizing an LU decomposition&lt;/h3&gt;&lt;p&gt; For an &lt;b&gt;LU&lt;/b&gt; decomposition of a given &lt;i&gt;n&lt;/i&gt; x &lt;i&gt;n&lt;/i&gt; matrix &lt;b&gt;A&lt;/b&gt;, we seek a lower triangular matrix &lt;b&gt;L&lt;/b&gt; and an upper triangular matrix &lt;b&gt;U&lt;/b&gt; (both of order &lt;i&gt;n&lt;/i&gt; x &lt;i&gt;n&lt;/i&gt;) such that &lt;b&gt;A = LU&lt;/b&gt;. The matrix &lt;b&gt;U&lt;/b&gt; may be taken to be the upper triangular matrix resulting from Gauss elimination without partial pivoting, and the matrix &lt;b&gt;L&lt;/b&gt; may be taken to be the lower triangular matrix which has diagonal elements 1 and which, for &lt;i&gt;k &lt;&gt;, has as the &lt;i&gt;(i, k)&lt;/i&gt;  element the multiplier &lt;i&gt;m&lt;sub&gt;ik&lt;/sub&gt;&lt;/i&gt;. This multiplier is calculated at the &lt;i&gt;k&lt;/i&gt;-th stage of Gauss elimination and is required to transform the current value of &lt;i&gt;a&lt;sub&gt;ik&lt;/sub&gt;&lt;/i&gt; to 0. In the notation of Step 11, these multipliers were given by &lt;i&gt;m&lt;sub&gt;ik&lt;/sub&gt; = a&lt;sub&gt;ik&lt;/sub&gt;/a&lt;sub&gt;kk&lt;/sub&gt;, I = k+l, k+2,.. ,n&lt;/i&gt;.&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt;   An example will help clarify this. From Step 11, we recall that Gauss elimination, applied to the system &lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15c5.GIF" width="85" height="57" /&gt;&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; yielded the upper triangular matrix:&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15c6.GIF" width="116" height="55" /&gt;&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; Also, we saw that in the first stage we calculated the multipliers &lt;i&gt;rn&lt;/i&gt;&lt;sub&gt;21&lt;/sub&gt; = &lt;i&gt;a&lt;/i&gt;&lt;sub&gt;2l&lt;/sub&gt;/&lt;i&gt;a&lt;/i&gt;&lt;sub&gt;11&lt;/sub&gt; = 1 / 1= 1 and &lt;i&gt;m&lt;/i&gt;&lt;sub&gt;3l&lt;/sub&gt; = &lt;i&gt;a&lt;/i&gt;&lt;sub&gt;3l&lt;/sub&gt;/&lt;i&gt;a&lt;/i&gt;&lt;sub&gt;11&lt;/sub&gt; = 2/ 1 = 2, while in the second stage we calculated the multiplier &lt;i&gt;m&lt;/i&gt;&lt;sub&gt;32&lt;/sub&gt; = &lt;i&gt;a&lt;/i&gt;&lt;sub&gt;32&lt;/sub&gt;/&lt;i&gt;a&lt;/i&gt;&lt;sub&gt;22&lt;/sub&gt; = -3/1 = -3. Thus&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15c7.GIF" width="240" height="58" /&gt;&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; It is readily verified that &lt;b&gt;LU&lt;/b&gt;equals the coefficient matrix of the original system:&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15c8.GIF" width="142" height="55" /&gt;&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; . Another technique that may be used to find an &lt;b&gt;LU&lt;/b&gt; decomposition of an &lt;i&gt;n&lt;/i&gt; x &lt;i&gt;n&lt;/i&gt; matrix is by direct decomposition. In order to illustrate this process, let it be rquired to find an &lt;b&gt;LU&lt;/b&gt; decomposition for the 3 x 3 coefficient matrix of the system  above. Then the required &lt;b&gt;L&lt;/b&gt; and &lt;b&gt;U&lt;/b&gt; are of the form&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15c9.GIF" width="295" height="59" /&gt;&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; Note that the total number of unknowns in &lt;b&gt;L&lt;/b&gt; and &lt;b&gt;U&lt;/b&gt; is 12, whereas there are only 9 elements in the 3 x 3 coefficient matrix &lt;b&gt;A&lt;/b&gt;. To ensure that &lt;b&gt;L&lt;/b&gt; and &lt;b&gt;U&lt;/b&gt; are unique, we need to impose 12 - 9 = 3 extra conditions on the elements of these two triangular matrices. (In the general &lt;i&gt;n&lt;/i&gt; x &lt;i&gt;n&lt;/i&gt; case, &lt;i&gt;n&lt;/i&gt; extra conditions are required.) One common choice is to require all the diagonal elements of &lt;b&gt;L&lt;/b&gt; to have the value 1; the resulting method is known as &lt;b&gt;Doolittle's method&lt;/b&gt;. Another choice is to require all the diagonal elements of &lt;b&gt;U&lt;/b&gt; to be 1; this is &lt;b&gt;Crout's method&lt;/b&gt;. Since Doolittle's method will result in the same &lt;b&gt;LU&lt;/b&gt; decomposition for &lt;b&gt;A&lt;/b&gt;, given above, we shall use Crout's method to illustrate this direct decomposition procedure.&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt;  We then require that&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15d1.GIF" width="331" height="57" /&gt;&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; Multiplication of &lt;b&gt;L&lt;/b&gt; and &lt;b&gt;U&lt;/b&gt; yields:&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15d2.GIF" width="60" height="41" /&gt;&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; It is clear that this construction by Crout's method yields triangular matrices &lt;b&gt;L&lt;/b&gt; and &lt;b&gt;U&lt;/b&gt; for which &lt;b&gt;A = LU&lt;/b&gt;.&lt;/i&gt;&lt;/p&gt;&lt;p&gt;&lt;i&gt; &lt;/i&gt;&lt;/p&gt;&lt;h3&gt;&lt;i&gt;Checkpoint&lt;/i&gt;&lt;/h3&gt;&lt;i&gt; &lt;/i&gt;&lt;ol&gt;&lt;li&gt;&lt;i&gt;What constitutes an &lt;b&gt;LU&lt;/b&gt; decomposition of a matrix &lt;b&gt;A&lt;/b&gt;?&lt;br /&gt;&lt;/i&gt;&lt;/li&gt;&lt;li&gt;&lt;i&gt;How is a decomposition &lt;b&gt;A = LU&lt;/b&gt; used to solve a linear system &lt;b&gt;Ax = b&lt;/b&gt;?&lt;br /&gt;&lt;/i&gt;&lt;/li&gt;&lt;li&gt;&lt;i&gt;How may an &lt;b&gt;LU&lt;/b&gt; decomposition be obtained by Gauss elimination?&lt;/i&gt;&lt;/li&gt;&lt;/ol&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5371584624142212234?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5371584624142212234/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5371584624142212234' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5371584624142212234'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5371584624142212234'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2008/09/use-of-lu-decomposition-tutorial-4.html' title='Use of LU decomposition - Tutorial 4'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-4975301211280664024</id><published>2008-09-11T19:58:00.004+08:00</published><updated>2008-09-11T20:01:18.828+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Tutorial'/><category scheme='http://www.blogger.com/atom/ns#' term='LU Decomposition in Gaussian Elimination'/><title type='text'>Use of LU decomposition - Tutorial 2</title><content type='html'>&lt;span style="font-size:130%;"&gt;&lt;li&gt;&lt;h3&gt;Procedure&lt;/h3&gt; Suppose we have to solve a linear system &lt;b&gt;Ax = b&lt;/b&gt;, and that we can express the coefficient matrix &lt;b&gt;A&lt;/b&gt; in the form of the socalled  &lt;b&gt;LU decomposition&lt;/b&gt; &lt;b&gt;A = LU&lt;/b&gt;. &lt;p&gt;  Then we may solve the linear system by the following procedure:&lt;/p&gt;&lt;p&gt; &lt;b&gt;Stage l:&lt;/b&gt; Write &lt;b&gt;Ax = LUx = b&lt;/b&gt;.&lt;/p&gt;&lt;p&gt; &lt;b&gt;Stage 2:&lt;/b&gt; Set y = Ux, so that &lt;b&gt;Ax = Ly = b&lt;/b&gt;. Use &lt;b&gt;forward substitution&lt;/b&gt; on &lt;b&gt;Ly = b&lt;/b&gt; to find &lt;i&gt;y&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;, &lt;i&gt;y&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;, . . , &lt;i&gt;y&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt; in that order, i.e., suppose the augmented matrix for the system &lt;b&gt;Ly = b&lt;/b&gt; is:&lt;/p&gt;&lt;p&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15a5.GIF" width="271" height="105" /&gt;&lt;/p&gt;&lt;p&gt; Then forward substitution yields &lt;i&gt;y&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; = &lt;i&gt;b&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;/&lt;i&gt;l&lt;/i&gt;&lt;sub&gt;11&lt;/sub&gt;, and, subsequently,&lt;/p&gt;&lt;p&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15a6.GIF" width="242" height="48" /&gt;&lt;/p&gt;&lt;p&gt; Note that the value of &lt;i&gt;y&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt; depends on the values &lt;i&gt;y&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;,  &lt;i&gt;y&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;, . . , &lt;i&gt;y&lt;sub&gt;i-1&lt;/sub&gt;&lt;/i&gt;, which have already been calculated.&lt;/p&gt;&lt;p&gt; &lt;b&gt;Stage 3:&lt;/b&gt; Finally, use &lt;b&gt;back-substitution&lt;/b&gt; on &lt;b&gt;Ux = y&lt;/b&gt; to find &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;n&lt;/sub&gt;, . . . , &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;x in that order.&lt;/p&gt;&lt;p&gt; Later on we shall outline a general method for finding &lt;b&gt;LU&lt;/b&gt;  decompositions of square matrices. The following example shows this method in action, involving the matrix &lt;b&gt;A = L&lt;sub&gt;1&lt;/sub&gt;U&lt;sub&gt;1&lt;/sub&gt;&lt;/b&gt; above. If we wish to solve &lt;b&gt;Ax = b&lt;/b&gt; for a number of different &lt;b&gt;b&lt;/b&gt;s, then this method is more efficient than Gauss elimination. Once we have found an &lt;b&gt;LU&lt;/b&gt; decomposition of &lt;b&gt;A&lt;/b&gt;, we need only do forward and backward substitutions to solve the system for any &lt;b&gt;b&lt;/b&gt;.&lt;/p&gt;&lt;p&gt; &lt;/p&gt;&lt;/li&gt;&lt;/span&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-4975301211280664024?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/4975301211280664024/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=4975301211280664024' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4975301211280664024'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/4975301211280664024'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2008/09/use-of-lu-decomposition-tutorial-2.html' title='Use of LU decomposition - Tutorial 2'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-7697736349675398224</id><published>2008-09-11T19:58:00.003+08:00</published><updated>2008-09-11T20:00:52.847+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Tutorial'/><category scheme='http://www.blogger.com/atom/ns#' term='LU Decomposition in Gaussian Elimination'/><title type='text'>Use of LU decomposition - Tutorial 3</title><content type='html'>&lt;span style="font-size:130%;"&gt;&lt;li&gt;&lt;h3&gt;Example&lt;/h3&gt;&lt;p&gt; We shall solve the system&lt;/p&gt;&lt;p&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15a7.GIF" width="115" height="56" /&gt;&lt;/p&gt;&lt;p&gt; &lt;b&gt;Stage l:&lt;/b&gt; An LU decomposition of the system is&lt;/p&gt;&lt;p&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15a8.GIF" width="344" height="70" /&gt;&lt;/p&gt;&lt;p&gt; &lt;b&gt;Stage 2:&lt;/b&gt; Set &lt;b&gt;y = U&lt;sub&gt;1&lt;/sub&gt;x&lt;/b&gt; and then solve the system &lt;b&gt;L&lt;sub&gt;1&lt;/sub&gt;y = b&lt;/b&gt;, i.e.,&lt;/p&gt;&lt;p&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15a9.GIF" width="222" height="58" /&gt;&lt;/p&gt;&lt;p&gt; Using forward substitution, we obtain:&lt;/p&gt;&lt;p&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15c1.GIF" width="225" height="59" /&gt;&lt;/p&gt;&lt;p&gt; &lt;b&gt;Stage 3:&lt;/b&gt; Solve&lt;/p&gt;&lt;p&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15c2.GIF" width="220" height="64" /&gt;&lt;/p&gt;&lt;p&gt; Back-substitution now yields:&lt;/p&gt;&lt;p&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15c3.GIF" width="200" height="52" /&gt;&lt;/p&gt;&lt;p&gt; Thus the solution of &lt;b&gt;Ax = b&lt;/b&gt; is:&lt;/p&gt;&lt;p&gt; &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15c4.GIF" width="78" height="52" /&gt;&lt;/p&gt;&lt;p&gt; which may be checked, using the original equations. We turn now to the problem of finding an LU decomposition of a given square matrix A. &lt;/p&gt;&lt;/li&gt;&lt;/span&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-7697736349675398224?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/7697736349675398224/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=7697736349675398224' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7697736349675398224'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/7697736349675398224'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2008/09/use-of-lu-decomposition-tutorial-3.html' title='Use of LU decomposition - Tutorial 3'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-6590370696785732299</id><published>2008-09-11T19:56:00.001+08:00</published><updated>2008-09-11T20:01:38.320+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Tutorial'/><category scheme='http://www.blogger.com/atom/ns#' term='LU Decomposition in Gaussian Elimination'/><title type='text'>Use of LU decomposition - Tutorial 1</title><content type='html'>&lt;p&gt; &lt;span style="font-size:130%;"&gt;We have shown in &lt;a href="http://mpec.sc.mahidol.ac.th/radok/numer/STEP11.HTM#STEP11"&gt;STEP 11&lt;/a&gt; how to solve a linear system Ax = b by Gauss elimination, applied to the augmented matrix &lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15a1.GIF" width="34" height="16" /&gt;. In the preceding Step, we have extended the elimination process to calculate the inverse &lt;b&gt;A&lt;sup&gt;&lt;-1&lt;/sup&gt;&lt;/b&gt; of the coefficient matrix &lt;b&gt;A&lt;/b&gt;, assuming it exists.&lt;/span&gt;&lt;/p&gt;&lt;p&gt; &lt;span style="font-size:130%;"&gt;Another general approach to solving &lt;b&gt;Ax = b&lt;/b&gt; is known as the method of &lt;b&gt;LU&lt;/b&gt; decomposition, which provides new insights into matrix algebra and has many theoretical and practical uses. Efficient computer algorithms for handling practical problems can be developed from it.&lt;/span&gt;&lt;/p&gt;&lt;p&gt; &lt;span style="font-size:130%;"&gt;The symbols &lt;b&gt;L&lt;/b&gt; and &lt;b&gt;U&lt;/b&gt; denote lower triangular matrix and upper triangular matrices, respectively. Examples of lower triangular matrices are&lt;/span&gt;&lt;/p&gt;&lt;p&gt; &lt;span style="font-size:130%;"&gt;&lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15a2.GIF" width="294" height="51" /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p&gt; &lt;span style="font-size:130%;"&gt;Note that in such a matrix all elements above the leading diagonal  are zero. Examples of upper triangular matrices are:&lt;/span&gt;&lt;/p&gt;&lt;p&gt; &lt;span style="font-size:130%;"&gt;&lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15a3.GIF" width="285" height="53" /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p&gt; &lt;span style="font-size:130%;"&gt;where now all elements below the leading diagonal are zero. The product of &lt;b&gt;L&lt;sub&gt;1&lt;/sub&gt;&lt;/b&gt; and &lt;b&gt;U&lt;sub&gt;1&lt;/sub&gt;&lt;/b&gt; is &lt;/span&gt;&lt;/p&gt;&lt;p&gt; &lt;span style="font-size:130%;"&gt;&lt;img src="http://mpec.sc.mahidol.ac.th/radok/numer/STEP15a4.GIF" width="166" height="56" /&gt;&lt;/span&gt;&lt;/p&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-6590370696785732299?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/6590370696785732299/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=6590370696785732299' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/6590370696785732299'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/6590370696785732299'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2008/09/use-of-lu-decomposition-tutorial-1.html' title='Use of LU decomposition - Tutorial 1'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-1426824506874019207</id><published>2008-09-11T19:52:00.000+08:00</published><updated>2008-09-11T19:53:28.108+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Gaussian Elimination'/><category scheme='http://www.blogger.com/atom/ns#' term='Numerical Method'/><category scheme='http://www.blogger.com/atom/ns#' term='LU Decomposition'/><title type='text'>Part 3 - How do I find the inverse of a square matrix using LU Decomposition?</title><content type='html'>&lt;h2 style="margin-left: 0.5in; text-align: justify;"&gt;&lt;a name="_Toc164160143"&gt;&lt;span style=""&gt;&lt;span style=""&gt;Example 3&lt;/span&gt;&lt;/span&gt;&lt;/a&gt;&lt;/h2&gt;   &lt;p class="MsoNormal" style="margin-bottom: 6pt; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;Use LU&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:"&gt;&lt;/span&gt; XE &amp;quot;LU&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;decomposition to find the inverse of &lt;/p&gt;   &lt;p class="MsoNormal" style="margin-left: 0.5in; text-align: justify; text-indent: 0.5in;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1133" type="#_x0000_t75" style="'width:93.75pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image349.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image074.gif" shapes="_x0000_i1133" width="125" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1133" drawaspect="Content" objectid="_1266836252"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin-left: 0.5in;"&gt;&lt;a name="_Toc164160144"&gt;&lt;b&gt;Solution&lt;/b&gt;&lt;/a&gt;&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Knowing that&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1134" type="#_x0000_t75" style="'width:239.25pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image350.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image185.gif" shapes="_x0000_i1134" width="319" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1134" drawaspect="Content" objectid="_1266836253"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;We can solve for the   first column of&lt;span style=""&gt;  &lt;/span&gt;[B]=&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1135" type="#_x0000_t75" style="'width:26.25pt;height:18.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image351.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image187.gif" shapes="_x0000_i1135" width="35" border="0" height="25" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1135" drawaspect="Content" objectid="_1266836254"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;by solving for&lt;a name="p137"&gt;&lt;/a&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1136" type="#_x0000_t75" style="'width:123pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image352.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image189.gif" shapes="_x0000_i1136" width="164" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1136" drawaspect="Content" objectid="_1266836255"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;First solve&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1137" type="#_x0000_t75" style="'width:57.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image317.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image125.gif" shapes="_x0000_i1137" width="77" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1137" drawaspect="Content" objectid="_1266836256"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt; that is&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1138" type="#_x0000_t75" style="'width:128.25pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image353.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image191.gif" shapes="_x0000_i1138" width="171" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1138" drawaspect="Content" objectid="_1266836257"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;to give&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1139" type="#_x0000_t75" style="'width:30pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image354.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image193.gif" shapes="_x0000_i1139" width="40" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1139" drawaspect="Content" objectid="_1266836258"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt;  &lt;/span&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1140" type="#_x0000_t75" style="'width:75.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image355.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image195.gif" shapes="_x0000_i1140" width="101" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1140" drawaspect="Content" objectid="_1266836259"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1141" type="#_x0000_t75" style="'width:113.25pt;height:18pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image356.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image197.gif" shapes="_x0000_i1141" width="151" border="0" height="24" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1141" drawaspect="Content" objectid="_1266836260"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;&lt;a name="FowardSubstitution140"&gt;&lt;/a&gt;Forward substitution&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;Forward substitution&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;starting from the first equation gives&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1142" type="#_x0000_t75" style="'width:30pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image357.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image199.gif" shapes="_x0000_i1142" width="40" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1142" drawaspect="Content" objectid="_1266836261"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1143" type="#_x0000_t75" style="'width:71.25pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image358.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image201.gif" shapes="_x0000_i1143" width="95" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1143" drawaspect="Content" objectid="_1266836262"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; line-height: 16pt;"&gt;&lt;span style=""&gt;            &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1144" type="#_x0000_t75" style="'width:63pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image359.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image203.gif" shapes="_x0000_i1144" width="84" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1144" drawaspect="Content" objectid="_1266836263"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; line-height: 16pt;"&gt;&lt;span style=""&gt;            &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1145" type="#_x0000_t75" style="'width:41.25pt;height:14.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image360.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image205.gif" shapes="_x0000_i1145" width="55" border="0" height="19" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1145" drawaspect="Content" objectid="_1266836264"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1146" type="#_x0000_t75" style="'width:111pt;height:18pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image361.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image207.gif" shapes="_x0000_i1146" width="148" border="0" height="24" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1146" drawaspect="Content" objectid="_1266836265"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; line-height: 16pt;"&gt;&lt;span style=""&gt;            &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1147" type="#_x0000_t75" style="'width:125.25pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image362.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image209.gif" shapes="_x0000_i1147" width="167" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1147" drawaspect="Content" objectid="_1266836266"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; line-height: 16pt;"&gt;&lt;span style=""&gt;            &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1148" type="#_x0000_t75" style="'width:27.75pt;height:14.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image363.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image211.gif" shapes="_x0000_i1148" width="37" border="0" height="19" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1148" drawaspect="Content" objectid="_1266836267"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;&lt;span style=""&gt; &lt;/span&gt;Hence&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1149" type="#_x0000_t75" style="'width:51.75pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image319.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image129.gif" shapes="_x0000_i1149" width="69" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1149" drawaspect="Content" objectid="_1266836268"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt;  &lt;/span&gt;&lt;a name="p138"&gt;&lt;/a&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1150" type="#_x0000_t75" style="'width:54pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image364.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image213.gif" shapes="_x0000_i1150" width="72" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1150" drawaspect="Content" objectid="_1266836269"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Now solve&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1151" type="#_x0000_t75" style="'width:62.25pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image321.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image133.gif" shapes="_x0000_i1151" width="83" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1151" drawaspect="Content" objectid="_1266836270"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;that is&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1152" type="#_x0000_t75" style="'width:177pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image365.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image215.gif" shapes="_x0000_i1152" width="236" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1152" drawaspect="Content" objectid="_1266836271"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1153" type="#_x0000_t75" style="'width:101.25pt;height:18pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image366.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image217.gif" shapes="_x0000_i1153" width="135" border="0" height="24" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1153" drawaspect="Content" objectid="_1266836272"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1154" type="#_x0000_t75" style="'width:126.75pt;height:18pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image367.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image219.gif" shapes="_x0000_i1154" width="169" border="0" height="24" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1154" drawaspect="Content" objectid="_1266836273"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;                  &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1155" type="#_x0000_t75" style="'width:60pt;height:18pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image368.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image221.gif" shapes="_x0000_i1155" width="80" border="0" height="24" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1155" drawaspect="Content" objectid="_1266836274"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Backward substitution   starting from the third equation gives&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1156" type="#_x0000_t75" style="'width:47.25pt;height:30.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image369.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image223.gif" shapes="_x0000_i1156" width="63" border="0" height="41" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1156" drawaspect="Content" objectid="_1266836275"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;    &lt;/span&gt;= &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1157" type="#_x0000_t75" style="'width:30pt;height:14.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image370.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image225.gif" shapes="_x0000_i1157" width="40" border="0" height="19" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1157" drawaspect="Content" objectid="_1266836276"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1158" type="#_x0000_t75" style="'width:113.25pt;height:32.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image371.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image227.gif" shapes="_x0000_i1158" width="151" border="0" height="43" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1158" drawaspect="Content" objectid="_1266836277"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;   &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1159" type="#_x0000_t75" style="'width:117pt;height:30.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image372.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image229.gif" shapes="_x0000_i1159" width="156" border="0" height="41" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1159" drawaspect="Content" objectid="_1266836278"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;   &lt;/span&gt;= -0.9524&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1160" type="#_x0000_t75" style="'width:90.75pt;height:32.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image373.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image231.gif" shapes="_x0000_i1160" width="121" border="0" height="43" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1160" drawaspect="Content" objectid="_1266836279"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt;      &lt;/span&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;    &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1161" type="#_x0000_t75" style="'width:120.75pt;height:30.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image374.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image233.gif" shapes="_x0000_i1161" width="161" border="0" height="41" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1161" drawaspect="Content" objectid="_1266836280"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;    &lt;/span&gt;= 0.04762&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Hence the first   column of the inverse of [A] is&lt;a name="p139"&gt;&lt;/a&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1162" type="#_x0000_t75" style="'width:93pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image375.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image235.gif" shapes="_x0000_i1162" width="124" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1162" drawaspect="Content" objectid="_1266836282"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Similarly by solving &lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1163" type="#_x0000_t75" style="'width:120.75pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image376.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image237.gif" shapes="_x0000_i1163" width="161" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1163" drawaspect="Content" objectid="_1266836283"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1164" type="#_x0000_t75" style="'width:99pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image377.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image239.gif" shapes="_x0000_i1164" width="132" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1164" drawaspect="Content" objectid="_1266836284"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;and solving&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1165" type="#_x0000_t75" style="'width:125.25pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image378.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image241.gif" shapes="_x0000_i1165" width="167" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1165" drawaspect="Content" objectid="_1266836285"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;gives&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1166" type="#_x0000_t75" style="'width:93pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image379.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image243.gif" shapes="_x0000_i1166" width="124" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1166" drawaspect="Content" objectid="_1266836286"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Hence&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1167" type="#_x0000_t75" style="'width:194.25pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image380.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image245.gif" shapes="_x0000_i1167" width="259" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1167" drawaspect="Content" objectid="_1266836287"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin-left: 0.5in; text-align: justify;"&gt;Can you   confirm the following for the above example?&lt;span style=""&gt;    &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1168" type="#_x0000_t75" style="'width:65.25pt;height:18.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image381.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image247.gif" shapes="_x0000_i1168" width="87" border="0" height="25" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1168" drawaspect="Content" objectid="_1266836288"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;=&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1169" type="#_x0000_t75" style="'width:41.25pt;height:18.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image382.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image249.gif" shapes="_x0000_i1169" width="55" border="0" height="25" /&gt;&lt;/sub&gt;&lt;/p&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-1426824506874019207?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/1426824506874019207/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=1426824506874019207' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1426824506874019207'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/1426824506874019207'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2008/09/part-3-how-do-i-find-inverse-of-square_11.html' title='Part 3 - How do I find the inverse of a square matrix using LU Decomposition?'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-6376469217839538864</id><published>2008-09-11T19:51:00.000+08:00</published><updated>2008-09-11T19:52:26.874+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Gaussian Elimination'/><category scheme='http://www.blogger.com/atom/ns#' term='Numerical Method'/><category scheme='http://www.blogger.com/atom/ns#' term='LU Decomposition'/><title type='text'>Part 3 - How do I find the inverse of a square matrix using LU Decomposition?</title><content type='html'>&lt;h1&gt;&lt;a name="_Toc164079072"&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;How do I find the inverse of a square   matrix&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/a&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-bookmark:"&gt;&lt;span style="'mso-bookmark:_Toc164160142'"&gt;&lt;span style="'mso-bookmark:_Toc164162074'"&gt;&lt;span style="'mso-bookmark:_Toc164850240'"&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt;&lt;span style="'mso-bookmark:_Toc164079072'"&gt;&lt;span style="'mso-bookmark:_Toc164160142'"&gt;&lt;span style="'mso-bookmark:_Toc164162074'"&gt;&lt;span style="'mso-bookmark:_Toc164850240'"&gt; XE &amp;quot;square matrix&amp;quot; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-bookmark:_Toc164079072'"&gt;&lt;span style="'mso-bookmark:_Toc164160142'"&gt;&lt;span style="'mso-bookmark:_Toc164162074'"&gt;&lt;span style="'mso-bookmark:_Toc164850240'"&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt; &lt;/span&gt;using &lt;a name="LUDecomposition138"&gt;&lt;/a&gt;LU&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-bookmark:_Toc164079072'"&gt;&lt;span style="'mso-bookmark:_Toc164160142'"&gt;&lt;span style="'mso-bookmark:_Toc164162074'"&gt;&lt;span style="'mso-bookmark:_Toc164850240'"&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt;&lt;span style="'mso-bookmark:_Toc164079072'"&gt;&lt;span style="'mso-bookmark:_Toc164160142'"&gt;&lt;span style="'mso-bookmark:_Toc164162074'"&gt;&lt;span style="'mso-bookmark:_Toc164850240'"&gt; XE &amp;quot;LU&amp;quot; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-bookmark:_Toc164079072'"&gt;&lt;span style="'mso-bookmark:_Toc164160142'"&gt;&lt;span style="'mso-bookmark:_Toc164162074'"&gt;&lt;span style="'mso-bookmark:_Toc164850240'"&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt; &lt;/span&gt;Decomposition&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-bookmark:_Toc164079072'"&gt;&lt;span style="'mso-bookmark:_Toc164160142'"&gt;&lt;span style="'mso-bookmark:_Toc164162074'"&gt;&lt;span style="'mso-bookmark:_Toc164850240'"&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt;&lt;span style="'mso-bookmark:_Toc164079072'"&gt;&lt;span style="'mso-bookmark:_Toc164160142'"&gt;&lt;span style="'mso-bookmark:_Toc164162074'"&gt;&lt;span style="'mso-bookmark:_Toc164850240'"&gt; XE &amp;quot;&lt;span style="'mso-no-proof:yes'"&gt;LU   Decomposition&amp;quot;&lt;/span&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-bookmark:_Toc164079072'"&gt;&lt;span style="'mso-bookmark:_Toc164160142'"&gt;&lt;span style="'mso-bookmark:_Toc164162074'"&gt;&lt;span style="'mso-bookmark:_Toc164850240'"&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;?&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h1&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;A matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;matrix&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1120" type="#_x0000_t75" style="'width:18pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image336.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image163.gif" shapes="_x0000_i1120" width="24" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1120" drawaspect="Content" objectid="_1266836239"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;is the inverse of &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1121" type="#_x0000_t75" style="'width:18pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image337.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image005.gif" shapes="_x0000_i1121" width="24" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1121" drawaspect="Content" objectid="_1266836240"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;if &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1122" type="#_x0000_t75" style="'width:99.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image338.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image166.gif" shapes="_x0000_i1122" width="133" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1122" drawaspect="Content" objectid="_1266836241"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;.&lt;span style=""&gt;  &lt;/span&gt;How can we use LU&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;LU&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;decomposition to find inverse of the   matrix?&lt;span style=""&gt;  &lt;/span&gt;Assume the first column of &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1123" type="#_x0000_t75" style="'width:18pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image339.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image163.gif" shapes="_x0000_i1123" width="24" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1123" drawaspect="Content" objectid="_1266836242"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;(the inverse of [A] is &lt;a name="p136"&gt;&lt;/a&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;[&lt;i&gt;b&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1124" type="#_x0000_t75" style="'width:9.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image340.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image169.gif" shapes="_x0000_i1124" width="13" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1124" drawaspect="Content" objectid="_1266836243"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;b&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1125" type="#_x0000_t75" style="'width:9.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image341.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image171.gif" shapes="_x0000_i1125" width="13" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1125" drawaspect="Content" objectid="_1266836244"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;………….b&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1126" type="#_x0000_t75" style="'width:9.75pt;height:18pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image342.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image173.gif" shapes="_x0000_i1126" width="13" border="0" height="24" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1126" drawaspect="Content" objectid="_1266836245"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;]&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1127" type="#_x0000_t75" style="'width:8.25pt;height:15pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image343.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image175.gif" shapes="_x0000_i1127" width="11" border="0" height="20" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1127" drawaspect="Content" objectid="_1266836246"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/i&gt; &lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;then from the above   definition of inverse and definition of matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;matrix&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;multiplication.&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1128" type="#_x0000_t75" style="'width:18pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image344.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image005.gif" shapes="_x0000_i1128" width="24" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1128" drawaspect="Content" objectid="_1266836247"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1129" type="#_x0000_t75" style="'width:57pt;height:74.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image345.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image178.gif" shapes="_x0000_i1129" width="76" border="0" height="99" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1129" drawaspect="Content" objectid="_1266836248"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Similarly the second   column of &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1130" type="#_x0000_t75" style="'width:18pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image346.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image163.gif" shapes="_x0000_i1130" width="24" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1130" drawaspect="Content" objectid="_1266836249"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;is given by&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;[A] &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1131" type="#_x0000_t75" style="'width:57.75pt;height:74.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image347.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image181.gif" shapes="_x0000_i1131" width="77" border="0" height="99" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1131" drawaspect="Content" objectid="_1266836250"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin-left: 0.5in; text-align: justify;"&gt;Similarly&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt; all columns of &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1132" type="#_x0000_t75" style="'width:18pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image348.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image163.gif" shapes="_x0000_i1132" width="24" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1132" drawaspect="Content" objectid="_1266836251"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;can be found by solving n different sets of equations with   the column of the right hand sides being the n columns of the &lt;a name="Identitymatrix139"&gt;&lt;/a&gt;identity matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;identity matrix&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;.&lt;/p&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-6376469217839538864?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/6376469217839538864/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=6376469217839538864' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/6376469217839538864'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/6376469217839538864'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2008/09/part-3-how-do-i-find-inverse-of-square.html' title='Part 3 - How do I find the inverse of a square matrix using LU Decomposition?'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-498172239261373110</id><published>2008-09-11T19:50:00.000+08:00</published><updated>2008-09-11T19:51:06.603+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Gaussian Elimination'/><category scheme='http://www.blogger.com/atom/ns#' term='Numerical Method'/><category scheme='http://www.blogger.com/atom/ns#' term='LU Decomposition'/><title type='text'>Part2 - How do I decompose a non-singular matrix [A],  that is, how do I find A=LU?</title><content type='html'>&lt;h2 style="margin-left: 0.5in; text-align: justify;"&gt;&lt;a name="_Toc164160140"&gt;&lt;span style=""&gt;&lt;span style=""&gt;Example 2&lt;/span&gt;&lt;/span&gt;&lt;/a&gt;&lt;/h2&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Use LU&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;LU&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;decomposition method to solve the following   simultaneous linear equations.&lt;/p&gt;   &lt;p class="MsoNormal" style="margin-left: 0.5in; text-align: justify; text-indent: 0.5in;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1090" type="#_x0000_t75" style="'width:141.75pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image309.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image110.gif" shapes="_x0000_i1090" width="189" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1090" drawaspect="Content" objectid="_1266836208"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin-left: 0.5in;"&gt;&lt;a name="_Toc164160141"&gt;&lt;b&gt;Solution&lt;/b&gt;&lt;/a&gt;&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Recall that&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1091" type="#_x0000_t75" style="'width:63pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image310.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image112.gif" shapes="_x0000_i1091" width="84" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1091" drawaspect="Content" objectid="_1266836209"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1092" type="#_x0000_t75" style="'width:9pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image311.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image114.gif" shapes="_x0000_i1092" width="12" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1092" drawaspect="Content" objectid="_1266836210"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt;            &lt;/span&gt;&lt;span style=""&gt;  &lt;/span&gt;&lt;span style=""&gt;          &lt;/span&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;and if&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1093" type="#_x0000_t75" style="'width:60pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image312.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image116.gif" shapes="_x0000_i1093" width="80" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1093" drawaspect="Content" objectid="_1266836211"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;then first solving&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1094" type="#_x0000_t75" style="'width:60pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image313.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image118.gif" shapes="_x0000_i1094" width="80" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1094" drawaspect="Content" objectid="_1266836212"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;and then&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1095" type="#_x0000_t75" style="'width:63.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image314.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image120.gif" shapes="_x0000_i1095" width="85" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1095" drawaspect="Content" objectid="_1266836213"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;gives the solution   vector&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE   &amp;quot;&lt;span style="'mso-no-proof:yes'"&gt;vector&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1096" type="#_x0000_t75" style="'width:20.25pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image315.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image035.gif" shapes="_x0000_i1096" width="27" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1096" drawaspect="Content" objectid="_1266836214"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;.&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Now in the previous example&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt; we showed&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1097" type="#_x0000_t75" style="'width:243pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image316.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image123.gif" shapes="_x0000_i1097" width="324" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1097" drawaspect="Content" objectid="_1266836215"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;a name="p134"&gt;&lt;/a&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;First solve&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1098" type="#_x0000_t75" style="'width:57.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image317.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image125.gif" shapes="_x0000_i1098" width="77" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1098" drawaspect="Content" objectid="_1266836216"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1099" type="#_x0000_t75" style="'width:150pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image318.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image127.gif" shapes="_x0000_i1099" width="200" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1099" drawaspect="Content" objectid="_1266836218"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;to give&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;z&lt;sub&gt;1&lt;/sub&gt;   = 106.8&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;2.56z&lt;sub&gt;1&lt;/sub&gt;   +z&lt;sub&gt;2&lt;/sub&gt; = 177.2&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;5.76   z&lt;sub&gt;1&lt;/sub&gt; + 3.5 z&lt;sub&gt;2&lt;/sub&gt; + z&lt;sub&gt;3&lt;/sub&gt; = 279.2&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;&lt;a name="FowardSubstitution136"&gt;&lt;/a&gt;Forward substitution&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;Forward substitution&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;starting from the first equation gives&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;z&lt;sub&gt;1&lt;/sub&gt;   =106.8&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;z&lt;sub&gt;2&lt;/sub&gt;   = 177.2 – 2.56 z&lt;sub&gt;1&lt;/sub&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;    &lt;/span&gt;= 177.2 – 2.56 (106.8)&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;    &lt;/span&gt;= -96.21&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;z&lt;sub&gt;3   &lt;/sub&gt;= 279.2 – 5.76 z&lt;sub&gt;1&lt;/sub&gt; – 3.5z&lt;sub&gt;2&lt;/sub&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;    &lt;/span&gt;= 279.2 – 5.76(106.8) – 3.5(-96.21)&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;    &lt;/span&gt;= 0.735&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Hence&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1100" type="#_x0000_t75" style="'width:51.75pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image319.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image129.gif" shapes="_x0000_i1100" width="69" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1100" drawaspect="Content" objectid="_1266836219"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt;  &lt;/span&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1101" type="#_x0000_t75" style="'width:57.75pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image320.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image131.gif" shapes="_x0000_i1101" width="77" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1101" drawaspect="Content" objectid="_1266836220"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;This matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;matrix&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;is same as the right hand side obtained at   the end of the forward elimination steps of Naïve Gauss&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;Gauss&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;elimination method.&lt;span style=""&gt;  &lt;/span&gt;Is this a coincidence?&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Now solve&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1102" type="#_x0000_t75" style="'width:62.25pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image321.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image133.gif" shapes="_x0000_i1102" width="83" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1102" drawaspect="Content" objectid="_1266836221"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1103" type="#_x0000_t75" style="'width:179.25pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image322.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image135.gif" shapes="_x0000_i1103" width="239" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1103" drawaspect="Content" objectid="_1266836222"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;a name="p135"&gt;&lt;/a&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1104" type="#_x0000_t75" style="'width:114.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image323.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image137.gif" shapes="_x0000_i1104" width="153" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1104" drawaspect="Content" objectid="_1266836223"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1105" type="#_x0000_t75" style="'width:126pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image324.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image139.gif" shapes="_x0000_i1105" width="168" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1105" drawaspect="Content" objectid="_1266836224"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1106" type="#_x0000_t75" style="'width:69pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image325.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image141.gif" shapes="_x0000_i1106" width="92" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1106" drawaspect="Content" objectid="_1266836225"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;From the third   equation&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1107" type="#_x0000_t75" style="'width:69pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image325.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image141.gif" shapes="_x0000_i1107" width="92" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1107" drawaspect="Content" objectid="_1266836226"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1108" type="#_x0000_t75" style="'width:71.25pt;height:30.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image326.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image143.gif" shapes="_x0000_i1108" width="95" border="0" height="41" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1108" drawaspect="Content" objectid="_1266836227"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1109" type="#_x0000_t75" style="'width:60pt;height:14.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image327.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image145.gif" shapes="_x0000_i1109" width="80" border="0" height="19" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1109" drawaspect="Content" objectid="_1266836228"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Substituting the   value of a&lt;sub&gt;3&lt;/sub&gt; in the second equation&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1110" type="#_x0000_t75" style="'width:126pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image324.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image139.gif" shapes="_x0000_i1110" width="168" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1110" drawaspect="Content" objectid="_1266836229"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1111" type="#_x0000_t75" style="'width:107.25pt;height:32.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image328.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image147.gif" shapes="_x0000_i1111" width="143" border="0" height="43" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1111" drawaspect="Content" objectid="_1266836230"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1112" type="#_x0000_t75" style="'width:123pt;height:30.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image329.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image149.gif" shapes="_x0000_i1112" width="164" border="0" height="41" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1112" drawaspect="Content" objectid="_1266836231"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1113" type="#_x0000_t75" style="'width:51pt;height:14.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image330.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image151.gif" shapes="_x0000_i1113" width="68" border="0" height="19" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1113" drawaspect="Content" objectid="_1266836232"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Substituting the   value of&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1114" type="#_x0000_t75" style="'width:47.25pt;height:18pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image331.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image153.gif" shapes="_x0000_i1114" width="63" border="0" height="24" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1114" drawaspect="Content" objectid="_1266836233"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;in the first equation&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1115" type="#_x0000_t75" style="'width:114.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image323.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image137.gif" shapes="_x0000_i1115" width="153" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1115" drawaspect="Content" objectid="_1266836234"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1116" type="#_x0000_t75" style="'width:108.75pt;height:32.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image332.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image155.gif" shapes="_x0000_i1116" width="145" border="0" height="43" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1116" drawaspect="Content" objectid="_1266836235"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1117" type="#_x0000_t75" style="'width:143.25pt;height:30.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image333.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image157.gif" shapes="_x0000_i1117" width="191" border="0" height="41" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1117" drawaspect="Content" objectid="_1266836236"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1118" type="#_x0000_t75" style="'width:60.75pt;height:14.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image334.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image159.gif" shapes="_x0000_i1118" width="81" border="0" height="19" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1118" drawaspect="Content" objectid="_1266836237"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;The solution vector&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;vector&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;is&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1119" type="#_x0000_t75" style="'width:80.25pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image335.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image161.gif" shapes="_x0000_i1119" width="107" border="0" height="75" /&gt;&lt;/sub&gt;&lt;/p&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-498172239261373110?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/498172239261373110/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=498172239261373110' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/498172239261373110'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/498172239261373110'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2008/09/part2-how-do-i-decompose-non-singular_8257.html' title='Part2 - How do I decompose a non-singular matrix [A],  that is, how do I find A=LU?'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-8553118766479025875</id><published>2008-09-11T19:49:00.000+08:00</published><updated>2008-09-11T19:50:10.292+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Gaussian Elimination'/><category scheme='http://www.blogger.com/atom/ns#' term='Numerical Method'/><category scheme='http://www.blogger.com/atom/ns#' term='LU Decomposition'/><title type='text'>Part2 - How do I decompose a non-singular matrix [A],  that is, how do I find A=LU?</title><content type='html'>&lt;h2 style="margin-left: 0.5in; text-align: justify;"&gt;&lt;a name="_Toc164160138"&gt;&lt;span style=""&gt;&lt;span style=""&gt;Example 1&lt;/span&gt;&lt;/span&gt;&lt;/a&gt;&lt;span style=""&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/h2&gt;   &lt;p class="MsoNormal" style="margin-bottom: 6pt; text-align: justify; line-height: 16pt;"&gt;&lt;span style=""&gt;            &lt;/span&gt;Find the &lt;a name="LUDecomposition133"&gt;&lt;/a&gt;LU&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:"&gt;&lt;/span&gt; XE &amp;quot;LU&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;decomposition of the matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;matrix&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin-left: 0.5in; text-align: justify; text-indent: 0.5in;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1070" type="#_x0000_t75" style="'width:93.75pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image290.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image074.gif" shapes="_x0000_i1070" width="125" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1070" drawaspect="Content" objectid="_1266836188"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin-left: 0.5in;"&gt;&lt;a name="_Toc164160139"&gt;&lt;b&gt;Solution&lt;/b&gt;&lt;/a&gt;&lt;b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1071" type="#_x0000_t75" style="'width:210.75pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image291.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image076.gif" shapes="_x0000_i1071" width="281" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1071" drawaspect="Content" objectid="_1266836189"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;The &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1072" type="#_x0000_t75" style="'width:18.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image292.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image068.gif" shapes="_x0000_i1072" width="25" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1072" drawaspect="Content" objectid="_1266836190"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;matrix&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;is the same as found at the end of the   forward elimination of Naïve Gauss&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;Gauss&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;elimination method&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt;   that is&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1073" type="#_x0000_t75" style="'width:126.75pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image293.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image079.gif" shapes="_x0000_i1073" width="169" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1073" drawaspect="Content" objectid="_1266836191"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;To find &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1074" type="#_x0000_t75" style="'width:17.25pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image294.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image081.gif" shapes="_x0000_i1074" width="23" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1074" drawaspect="Content" objectid="_1266836192"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;and &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1075" type="#_x0000_t75" style="'width:17.25pt;height:18pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image295.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image083.gif" shapes="_x0000_i1075" width="23" border="0" height="24" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1075" drawaspect="Content" objectid="_1266836193"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt; what   multiplier was used to make the &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1076" type="#_x0000_t75" style="'width:17.25pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image296.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image085.gif" shapes="_x0000_i1076" width="23" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1076" drawaspect="Content" objectid="_1266836194"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;and &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1077" type="#_x0000_t75" style="'width:17.25pt;height:18pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image297.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image087.gif" shapes="_x0000_i1077" width="23" border="0" height="24" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1077" drawaspect="Content" objectid="_1266836195"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;elements zero in the   first step of forward elimination of Naïve Gauss&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;Gauss&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;Elimination&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;Gauss Elimination&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;Method &lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;It was&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1078" type="#_x0000_t75" style="'width:45pt;height:30.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image298.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image089.gif" shapes="_x0000_i1078" width="60" border="0" height="41" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1078" drawaspect="Content" objectid="_1266836196"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;        &lt;/span&gt;= 2.56&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1079" type="#_x0000_t75" style="'width:50.25pt;height:30.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image299.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image091.gif" shapes="_x0000_i1079" width="67" border="0" height="41" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1079" drawaspect="Content" objectid="_1266836197"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;      &lt;/span&gt;= 5.76&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;To find &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1080" type="#_x0000_t75" style="'width:18pt;height:18pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image300.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image093.gif" shapes="_x0000_i1080" width="24" border="0" height="24" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1080" drawaspect="Content" objectid="_1266836198"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt; what   multiplier was used to make &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1081" type="#_x0000_t75" style="'width:18pt;height:18pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image301.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image095.gif" shapes="_x0000_i1081" width="24" border="0" height="24" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1081" drawaspect="Content" objectid="_1266836199"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;element zero.&lt;span style=""&gt;  &lt;/span&gt;Remember &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1082" type="#_x0000_t75" style="'width:18pt;height:18pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image301.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image095.gif" shapes="_x0000_i1082" width="24" border="0" height="24" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1082" drawaspect="Content" objectid="_1266836200"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;element was made zero   in the second step of forward elimination.&lt;span style=""&gt;    &lt;/span&gt;The &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1083" type="#_x0000_t75" style="'width:18pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image302.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image005.gif" shapes="_x0000_i1083" width="24" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1083" drawaspect="Content" objectid="_1266836201"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;matrix&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;at the beginning of the second step of   forward elimination was&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1084" type="#_x0000_t75" style="'width:107.25pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image303.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image098.gif" shapes="_x0000_i1084" width="143" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1084" drawaspect="Content" objectid="_1266836202"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; line-height: 16pt;"&gt;So&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1085" type="#_x0000_t75" style="'width:62.25pt;height:30.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image304.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image100.gif" shapes="_x0000_i1085" width="83" border="0" height="41" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1085" drawaspect="Content" objectid="_1266836203"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;       &lt;/span&gt;= 3.5&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; line-height: 16pt;"&gt;Hence&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1086" type="#_x0000_t75" style="'width:104.25pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image305.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image102.gif" shapes="_x0000_i1086" width="139" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1086" drawaspect="Content" objectid="_1266836204"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;a name="p133"&gt;&lt;/a&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; line-height: 16pt;"&gt;Confirm&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1087" type="#_x0000_t75" style="'width:57pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image306.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image104.gif" shapes="_x0000_i1087" width="76" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1087" drawaspect="Content" objectid="_1266836205"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;.&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1088" type="#_x0000_t75" style="'width:213.75pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image307.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image106.gif" shapes="_x0000_i1088" width="285" border="0" height="75" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1088" drawaspect="Content" objectid="_1266836206"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;span style=""&gt;           &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1089" type="#_x0000_t75" style="'width:77.25pt;height:56.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image308.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image108.gif" shapes="_x0000_i1089" width="103" border="0" height="75" /&gt;&lt;/sub&gt;&lt;/p&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-8553118766479025875?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/8553118766479025875/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=8553118766479025875' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8553118766479025875'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/8553118766479025875'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2008/09/part2-how-do-i-decompose-non-singular_11.html' title='Part2 - How do I decompose a non-singular matrix [A],  that is, how do I find A=LU?'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-5226210116054166689</id><published>2008-09-11T19:47:00.001+08:00</published><updated>2008-09-11T19:49:08.494+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Gaussian Elimination'/><category scheme='http://www.blogger.com/atom/ns#' term='Numerical Method'/><category scheme='http://www.blogger.com/atom/ns#' term='LU Decomposition'/><title type='text'>Part2 - How do I decompose a non-singular matrix [A],  that is, how do I find A=LU?</title><content type='html'>&lt;h1&gt;&lt;a name="_Toc164079071"&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;How do I &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/a&gt;&lt;a name="Decomposeofanonsingularmatrix132"&gt;&lt;/a&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;decompose a &lt;a name="nonsilgularmatrix132"&gt;&lt;/a&gt;non-singular   matrix&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-bookmark:_Toc164079071'"&gt;&lt;span style="'mso-bookmark:_Toc164160137'"&gt;&lt;span style="'mso-bookmark:_Toc164162071'"&gt;&lt;span style="'mso-bookmark:_Toc164850237'"&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt;&lt;span style="'mso-bookmark:_Toc164079071'"&gt;&lt;span style="'mso-bookmark:_Toc164160137'"&gt;&lt;span style="'mso-bookmark:_Toc164162071'"&gt;&lt;span style="'mso-bookmark:_Toc164850237'"&gt; XE &amp;quot;decompose a non-singular   matrix&amp;quot; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-bookmark:_Toc164079071'"&gt;&lt;span style="'mso-bookmark:_Toc164160137'"&gt;&lt;span style="'mso-bookmark:_Toc164162071'"&gt;&lt;span style="'mso-bookmark:_Toc164850237'"&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt;&lt;span style=""&gt; &lt;/span&gt;[A]&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt;   that is&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt; how do I find &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1062" type="#_x0000_t75" style="'width:60pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image250.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image003.gif" shapes="_x0000_i1062" width="80" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1062" drawaspect="Content" objectid="_1266836180"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;?&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h1&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;If forward   elimination steps of Naïve Gauss&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;Gauss&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;elimination methods&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;elimination methods&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;can be applied on a nonsingular matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;nonsingular matrix&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt;   then &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1063" type="#_x0000_t75" style="'width:18pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image283.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image005.gif" shapes="_x0000_i1063" width="24" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1063" drawaspect="Content" objectid="_1266836181"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;can be decomposed   into LU as&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1064" type="#_x0000_t75" style="'width:129pt;height:74.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image284.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image064.gif" shapes="_x0000_i1064" width="172" border="0" height="99" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1064" drawaspect="Content" objectid="_1266836182"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.25in; line-height: 16pt;"&gt;&lt;span style=""&gt;       &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1065" type="#_x0000_t75" style="'width:195.75pt;height:99.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image285.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image066.gif" shapes="_x0000_i1065" width="261" border="0" height="133" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1065" drawaspect="Content" objectid="_1266836183"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; text-indent: -0.25in; line-height: 16pt;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style=""&gt;1.&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"&gt;        &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;The elements of the &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1066" type="#_x0000_t75" style="'width:18.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image286.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image068.gif" shapes="_x0000_i1066" width="25" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1066" drawaspect="Content" objectid="_1266836184"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;matrix&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;are exactly the same as the coefficient   matrix one obtains at the end of the forward elimination steps in Naïve Gauss&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;Gauss&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;Elimination&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;Gauss Elimination&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;.&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 1in; text-align: justify; text-indent: -0.25in; line-height: 16pt;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style=""&gt;2.&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"&gt;        &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;The &lt;a name="LowertriangularMatrix133"&gt;&lt;/a&gt;lower   triangular matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt;   XE &amp;quot;lower triangular matrix&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1067" type="#_x0000_t75" style="'width:17.25pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image287.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image070.gif" shapes="_x0000_i1067" width="23" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1067" drawaspect="Content" objectid="_1266836185"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;has 1 in its diagonal&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;diagonal&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;entries.&lt;span style=""&gt;    &lt;/span&gt;The non zero elements on the non-diagonal elements&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;diagonal elements&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;in &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1068" type="#_x0000_t75" style="'width:17.25pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image288.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image070.gif" shapes="_x0000_i1068" width="23" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1068" drawaspect="Content" objectid="_1266836186"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;are multipliers that   made the corresponding entries zero in the &lt;a name="UpperTriangularMatrix133"&gt;&lt;/a&gt;upper   triangular matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt;   XE &amp;quot;upper triangular matrix&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1069" type="#_x0000_t75" style="'width:18.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image289.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image068.gif" shapes="_x0000_i1069" width="25" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1069" drawaspect="Content" objectid="_1266836187"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;during forward   elimination.&lt;/p&gt;   &lt;p class="MsoNormal" style="margin-left: 0.5in; text-align: justify;"&gt;Let us look at   this using the same example as used in Naïve Gaussian&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;Gaussian&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;elimination.&lt;/p&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8789958448392039588-5226210116054166689?l=utem-bmfr.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://utem-bmfr.blogspot.com/feeds/5226210116054166689/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://www.blogger.com/comment.g?blogID=8789958448392039588&amp;postID=5226210116054166689' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5226210116054166689'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8789958448392039588/posts/default/5226210116054166689'/><link rel='alternate' type='text/html' href='http://utem-bmfr.blogspot.com/2008/09/part2-how-do-i-decompose-non-singular.html' title='Part2 - How do I decompose a non-singular matrix [A],  that is, how do I find A=LU?'/><author><name>BMFRGuru</name><uri>http://www.blogger.com/profile/12321871933044579721</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='27' height='32' src='http://1.bp.blogspot.com/_nigvNMZgjBQ/SKrI2kVO1bI/AAAAAAAAAAk/myHsoEc-_uw/S220/1_418626858l.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8789958448392039588.post-6629780408008780209</id><published>2008-09-11T19:44:00.001+08:00</published><updated>2008-09-11T19:47:29.525+08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Gaussian Elimination'/><category scheme='http://www.blogger.com/atom/ns#' term='Numerical Method'/><category scheme='http://www.blogger.com/atom/ns#' term='LU Decomposition'/><title type='text'>Part 1: LU Decomposition used as a method to solve a set of simultaneous linear equations</title><content type='html'>&lt;p class="MsoBodyTextIndent" style="line-height: 16pt;"&gt;We already studied two   numerical methods of finding the solution to simultaneous linear equations –   Naïve Gauss&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt;   XE &amp;quot;Gauss&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;Elimination&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;Gauss Elimination&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;and Gaussian&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;Gaussian&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;Elimination with Partial Pivoting.&lt;span style=""&gt;  &lt;/span&gt;Then&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt;   why do we need to learn another method?&lt;span style=""&gt;    &lt;/span&gt;To appreciate why LU&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:"&gt;&lt;/span&gt; XE &amp;quot;LU&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;Decomposition&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;LU Decomposition&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;could be a better choice than the Gauss   Elimination techniques in some cases&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt;   let us discuss first what LU Decomposition is about.&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;&lt;o:p&gt; &lt;/o:p&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;For any &lt;a name="nonsilgularmatrix130"&gt;&lt;/a&gt;nonsingular matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;nonsingular matrix&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1027" type="#_x0000_t75" style="'width:18pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image251.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image005.gif" shapes="_x0000_i1027" width="24" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1027" drawaspect="Content" objectid="_1266836144"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;on which one can   conduct Naïve Gauss&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt;   XE &amp;quot;Gauss&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;Elimination&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;&lt;span style="'mso-no-proof:"&gt;Gauss Elimination&amp;quot;&lt;/span&gt; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-end'"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;span style=""&gt; &lt;/span&gt;forward elimination steps&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt; one can always write it as&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1028" type="#_x0000_t75" style="'width:60pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image252.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image007.gif" shapes="_x0000_i1028" width="80" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1028" drawaspect="Content" objectid="_1266836145"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;where&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;[&lt;i&gt;L&lt;/i&gt;] = &lt;a name="LowertriangularMatrix130"&gt;&lt;/a&gt;Lower triangular matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;lower triangular   matrix&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;[&lt;i&gt;U&lt;/i&gt;] = &lt;a name="UpperTriangularMatrix130"&gt;&lt;/a&gt;Upper triangular matrix&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:field-begin'"&gt;&lt;/span&gt; XE &amp;quot;upper triangular   matrix&amp;quot; &lt;![endif]--&gt;&lt;!--[if supportFields]&gt;&lt;span style="'mso-element:"&gt;&lt;/span&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Then if one is   solving a set of equations&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;[&lt;i&gt;A&lt;/i&gt;]   [&lt;i&gt;X&lt;/i&gt;] = [&lt;i&gt;C&lt;/i&gt;]&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt; &lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;then&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1029" type="#_x0000_t75" style="'width:78.75pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image253.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image009.gif" shapes="_x0000_i1029" width="105" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1029" drawaspect="Content" objectid="_1266836146"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt;                                  &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1030" type="#_x0000_t75" style="'width:69pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image254.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image011.gif" shapes="_x0000_i1030" width="92" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1030" drawaspect="Content" objectid="_1266836147"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Multiplying both side   by &lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1031" type="#_x0000_t75" style="'width:24.75pt;height:18.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image255.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image013.gif" shapes="_x0000_i1031" width="33" border="0" height="25" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1031" drawaspect="Content" objectid="_1266836148"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;st1:personname st="on"&gt;,&lt;/st1:personname&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1032" type="#_x0000_t75" style="'width:126pt;height:18.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image256.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image015.gif" shapes="_x0000_i1032" width="168" border="0" height="25" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1032" drawaspect="Content" objectid="_1266836149"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt;  &lt;/span&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1033" type="#_x0000_t75" style="'width:47.25pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image257.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image017.gif" shapes="_x0000_i1033" width="63" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1033" drawaspect="Content" objectid="_1266836150"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;=&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1034" type="#_x0000_t75" style="'width:39.75pt;height:18.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image258.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image019.gif" shapes="_x0000_i1034" width="53" border="0" height="25" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1034" drawaspect="Content" objectid="_1266836151"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt;                             &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1035" type="#_x0000_t75" style="'width:71.25pt;height:18.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image259.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image021.gif" shapes="_x0000_i1035" width="95" border="0" height="25" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1035" drawaspect="Content" objectid="_1266836152"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1036" type="#_x0000_t75" style="'width:84pt;height:18.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image260.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image023.gif" shapes="_x0000_i1036" width="112" border="0" height="25" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1036" drawaspect="Content" objectid="_1266836153"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;span style=""&gt;                                &lt;/span&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1037" type="#_x0000_t75" style="'width:66pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image261.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image025.gif" shapes="_x0000_i1037" width="88" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1037" drawaspect="Content" objectid="_1266836154"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;Let&lt;span style=""&gt;       &lt;/span&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1038" type="#_x0000_t75" style="'width:66.75pt;height:18.75pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image262.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image027.gif" shapes="_x0000_i1038" width="89" border="0" height="25" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1038" drawaspect="Content" objectid="_1266836155"&gt;    &lt;/o:OLEObject&gt;   &lt;/xml&gt;&lt;![endif]--&gt;&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; line-height: 16pt;"&gt;then&lt;/p&gt;   &lt;p class="MsoNormal" style="margin: 0in 0in 6pt 0.5in; text-align: justify; text-indent: 0.5in; line-height: 16pt;"&gt;&lt;sub&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id="_x0000_i1039" type="#_x0000_t75" style="'width:59.25pt;height:17.25pt'" ole=""&gt;    &lt;v:imagedata src="ludecomposition_04sle_ebook_files/image263.wmz" title=""&gt;   &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;img src="http://numericalmethods.eng.usf.edu/ebooks/ludecomposition_04sle_ebook_files/image029.gif" shapes="_x0000_i1039" width="79" border="0" height="23" /&gt;&lt;!--[endif]--&gt;&lt;/sub&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;    &lt;o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1039" drawaspect="Content" object
