<?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:blogger='http://schemas.google.com/blogger/2008' 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-3111627990970613378</id><updated>2024-09-04T17:09:49.900-07:00</updated><title type='text'>computers science</title><subtitle type='html'>computer science overview</subtitle><link rel='http://schemas.google.com/g/2005#feed' type='application/atom+xml' href='http://computerscience113.blogspot.com/feeds/posts/default'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default?redirect=false'/><link rel='alternate' type='text/html' href='http://computerscience113.blogspot.com/'/><link rel='hub' href='http://pubsubhubbub.appspot.com/'/><author><name>fabrice otepa</name><uri>http://www.blogger.com/profile/13017780185308872185</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><generator version='7.00' uri='http://www.blogger.com'>Blogger</generator><openSearch:totalResults>10</openSearch:totalResults><openSearch:startIndex>1</openSearch:startIndex><openSearch:itemsPerPage>25</openSearch:itemsPerPage><entry><id>tag:blogger.com,1999:blog-3111627990970613378.post-1559551433438943365</id><published>2011-07-24T04:57:00.000-07:00</published><updated>2011-07-24T04:57:05.260-07:00</updated><title type='text'>database assgnement</title><content type='html'>&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Question 1&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraph&quot; style=&quot;line-height: normal; mso-list: l3 level1 lfo1; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;a.&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;A company operates four departments&lt;/span&gt;&lt;/b&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;. Although the company operates four departments now, it may later decide to combine operations or to expand them. Clearly, the company operates at least one department.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal; mso-list: l3 level1 lfo1; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;b.&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Each department in part (a) employs employees&lt;/span&gt;&lt;/b&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;. To exist, a department must have at least one employee. To simplify payroll procedure, an employee is likely to be assigned to just one department. How many people must be involved in a given operation before a department can be formed? The answer to that question depends on company policy, which dictates the appropriate business rule. Thus the business rule(s) will ultimately decide the cardinalities.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; mso-list: l3 level1 lfo1; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;c.&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Each of the employees in part b may or may not have one or more dependents&lt;/span&gt;&lt;/b&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;. Since an employee is not required to claim a dependent, DEPENDENT is optional to EMPLOYEE. Remember a company cannot permit the existence who is not claimed by an employee.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; mso-list: l3 level1 lfo1; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;d.&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Each employee is part (c) may or may not have an employment history&lt;/span&gt;&lt;/b&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;. Each employee may have an employment history. If a newly hired employee has no prior work experience, the employee will not have an employment history, so the EMP_HIST is &lt;i style=&quot;mso-bidi-font-style: normal;&quot;&gt;optional&lt;/i&gt; to EMPLOYEE. An employee may have worked for more than one previous employer or may have worked in several other departments prior to the current assignment.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpLast&quot;&gt;&lt;br /&gt;
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&lt;/tbody&gt;&lt;/table&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;!--[if !mso &amp; !vml]--&gt;&amp;nbsp;&lt;!--[endif]--&gt;&lt;!--[if !vml]--&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id=&quot;_x0000_s1034&quot; type=&quot;#_x0000_t110&quot;
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    font-family:&quot;Times New Roman&quot;,&quot;serif&quot;&#39;&gt;Manage/wor_&lt;span
    style=&#39;mso-spacerun:yes&#39;&gt;    &lt;/span&gt;for&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;&lt;/div&gt;&lt;![if !mso]&gt;&lt;/td&gt;    &lt;/tr&gt;
&lt;/table&gt;&lt;![endif]&gt;&lt;/v:textbox&gt; &lt;/v:shape&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;span style=&quot;height: 135px; margin-left: 475px; margin-top: 76px; mso-ignore: vglayout; position: absolute; width: 130px; z-index: 251664384;&quot;&gt;&lt;img alt=&quot;Flowchart: Decision: Manage/wor_    for&quot; height=&quot;135&quot; src=&quot;file:///C:/Users/user/AppData/Local/Temp/msohtmlclip1/01/clip_image014.gif&quot; v:shapes=&quot;_x0000_s1034&quot; width=&quot;130&quot; /&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;span style=&quot;mso-spacerun: yes;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;br /&gt;
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&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shapetype
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&lt;tr&gt;   &lt;td height=&quot;21&quot; width=&quot;465&quot;&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;tr&gt;   &lt;td&gt;&lt;/td&gt;   &lt;td&gt;&lt;img height=&quot;137&quot; src=&quot;file:///C:/Users/user/AppData/Local/Temp/msohtmlclip1/01/clip_image015.gif&quot; v:shapes=&quot;_x0000_s1027&quot; width=&quot;150&quot; /&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;o:p&gt;&amp;nbsp;&lt;/o:p&gt;&lt;/span&gt;&lt;br /&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;br clear=&quot;ALL&quot; style=&quot;mso-ignore: vglayout;&quot; /&gt;  &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Question 2&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal; mso-list: l1 level1 lfo2; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;a)&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;How many records does the file contain, and how many fields are there per record?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;There are 4 records and five fields.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal; mso-list: l1 level1 lfo2; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;b)&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;What problem would you encounter if you wanted to produce a report that would list the cities?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;How would you solve this problem by changing the file structure?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;This problem can be solved by adding three more attributes such as&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;(Project_Code, Project_Manager, Manager_Address)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal; mso-list: l1 level1 lfo2; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;c)&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;If you wanted to produce a listing of the file contents by last name, area code, city, state, or ZIPCODE, how would you alter the file structure?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;PROJECT_CODE,FNAME,LNAME,AREA_CODE,PHONE_NO,CITY,STATE,&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;ZIP_CODE.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;It contained multivalued attributes, which have to be normalized.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraph&quot; style=&quot;line-height: normal; mso-list: l1 level1 lfo2; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;d)&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;What data redundancies do you detect, and how could these redundancies lead to anomalies?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal; mso-list: l1 level1 lfo2; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;e)&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Create the relational schema by using two relational database tables, PROJECT and MANAGER, eliminate the redundancies discovered in Problem 2d.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpLast&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Question 3&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal; mso-list: l4 level1 lfo3; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;a)&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Give an example of a table with a multi-valued attribute?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Employee table has multivalued attributes for example Address, Phone Number.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal; mso-list: l4 level1 lfo3; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;b)&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Create a relation schema containing a composite attribute?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;span style=&quot;mso-spacerun: yes;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;!--[if gte vml 1]&gt;&lt;v:rect
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&lt;/tbody&gt;&lt;/table&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;!--[if !mso &amp; !vml]--&gt;&amp;nbsp;&lt;!--[endif]--&gt;&lt;!--[if !vml]--&gt;&lt;/td&gt;  &lt;/tr&gt;
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&lt;/tbody&gt;&lt;/table&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;!--[if !mso &amp; !vml]--&gt;&amp;nbsp;&lt;!--[endif]--&gt;&lt;!--[if !vml]--&gt;&lt;/td&gt;  &lt;/tr&gt;
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&lt;/tbody&gt;&lt;/table&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;!--[if !mso &amp; !vml]--&gt;&amp;nbsp;&lt;!--[endif]--&gt;&lt;!--[if !vml]--&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id=&quot;_x0000_s1064&quot; type=&quot;#_x0000_t32&quot;
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&lt;tr&gt;   &lt;td bgcolor=&quot;white&quot; height=&quot;40&quot; style=&quot;background: white; border: .75pt solid white; vertical-align: top;&quot; width=&quot;127&quot;&gt;&lt;!--[endif]--&gt;&lt;!--[if !mso]--&gt;&lt;span style=&quot;left: 0pt; mso-ignore: vglayout; position: absolute; z-index: 251685888;&quot;&gt;   &lt;table cellpadding=&quot;0&quot; cellspacing=&quot;0&quot;&gt;&lt;tbody&gt;
&lt;tr&gt;     &lt;td&gt;&lt;!--[endif]--&gt;     &lt;div class=&quot;shape&quot; style=&quot;padding: 4.35pt 7.95pt 4.35pt 7.95pt;&quot; v:shape=&quot;_x0000_s1055&quot;&gt;     &lt;div class=&quot;MsoNormal&quot;&gt;Street_ Address&lt;/div&gt;&lt;/div&gt;&lt;!--[if !mso]--&gt;&lt;/td&gt;    &lt;/tr&gt;
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&lt;tr&gt;   &lt;td height=&quot;40&quot;&gt;&lt;/td&gt;   &lt;td bgcolor=&quot;white&quot; height=&quot;40&quot; style=&quot;background: white; border: .75pt solid black; vertical-align: top;&quot; width=&quot;92&quot;&gt;&lt;!--[endif]--&gt;&lt;!--[if !mso]--&gt;&lt;span style=&quot;left: 0pt; mso-ignore: vglayout; position: absolute; z-index: 251699200;&quot;&gt;   &lt;table cellpadding=&quot;0&quot; cellspacing=&quot;0&quot;&gt;&lt;tbody&gt;
&lt;tr&gt;     &lt;td&gt;&lt;!--[endif]--&gt;     &lt;div class=&quot;shape&quot; style=&quot;padding: 4.35pt 7.95pt 4.35pt 7.95pt;&quot; v:shape=&quot;_x0000_s1068&quot;&gt;     &lt;div class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;&quot;&gt;EMPLOYEE&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;/div&gt;&lt;!--[if !mso]--&gt;&lt;/td&gt;    &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;!--[if !mso &amp; !vml]--&gt;&amp;nbsp;&lt;!--[endif]--&gt;&lt;!--[if !vml]--&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;tr&gt;   &lt;td height=&quot;13&quot;&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;tr&gt;   &lt;td height=&quot;34&quot;&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;o:p&gt;&amp;nbsp;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;br clear=&quot;ALL&quot; style=&quot;mso-ignore: vglayout;&quot; /&gt;  &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape
 id=&quot;_x0000_s1071&quot; type=&quot;#_x0000_t32&quot; style=&#39;position:absolute;left:0;
 text-align:left;margin-left:278.25pt;margin-top:1.3pt;width:48.75pt;height:.05pt;
 z-index:251702272&#39; o:connectortype=&quot;straight&quot;/&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;span style=&quot;height: 2px; left: 0px; margin-left: 370px; margin-top: 1px; mso-ignore: vglayout; position: absolute; width: 67px; z-index: 251702272;&quot;&gt;&lt;img height=&quot;2&quot; src=&quot;file:///C:/Users/user/AppData/Local/Temp/msohtmlclip1/01/clip_image024.gif&quot; v:shapes=&quot;_x0000_s1071&quot; width=&quot;67&quot; /&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape id=&quot;_x0000_s1069&quot;
 type=&quot;#_x0000_t32&quot; style=&#39;position:absolute;left:0;text-align:left;
 margin-left:104.25pt;margin-top:1.25pt;width:57pt;height:.05pt;z-index:251700224&#39;
 o:connectortype=&quot;straight&quot;/&gt;&lt;![endif]--&gt;&lt;!--[if !vml]--&gt;&lt;span style=&quot;height: 2px; left: 0px; margin-left: 138px; margin-top: 1px; mso-ignore: vglayout; position: absolute; width: 78px; z-index: 251700224;&quot;&gt;&lt;img height=&quot;2&quot; src=&quot;file:///C:/Users/user/AppData/Local/Temp/msohtmlclip1/01/clip_image025.gif&quot; v:shapes=&quot;_x0000_s1069&quot; width=&quot;78&quot; /&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;span style=&quot;mso-spacerun: yes;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Question 4&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Consider the following six relations for and order-processing database application in a company:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;CUSTOMER (City, CustNo., CName)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;ORDER (Order#, Odate, CustNo., Ord_Amt)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;ORDER_ITEM (Order#, ItemID, Qty)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;ITEM (ItemID, Unit_Price)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;SHIPMENT (Order#, WarehouseID, Ship_date)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;WAREHOUSE (City, WarehouseID)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Here, Ord_Amt refers to total dollar amount of an order; Odate is the date the order was placed; Ship_date is the date an order is shipped from the warehouse. Assume that an order can be shipped from several warehouses.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto; mso-list: l2 level1 lfo4; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;a.&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Specify Primary keys for this schema,&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-left: .5in;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;CUSTOMER (City, &lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;u&gt;CustNo.&lt;/u&gt;&lt;/b&gt;, CName)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;ORDER (&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;u&gt;Order#&lt;/u&gt;&lt;/b&gt;, Odate, CustNo., Ord_Amt)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;ORDER_ITEM (Order#, ItemID, Qty)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;ITEM (&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;u&gt;ItemID&lt;/u&gt;&lt;/b&gt;, Unit_Price)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;SHIPMENT (Order#, WarehouseID, Ship_date)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;WAREHOUSE (City, &lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;u&gt;WarehouseID&lt;/u&gt;)&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto; mso-list: l2 level1 lfo4; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;b.&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Specify foreign keys for this schema, stating any assumptions you make.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;CUSTOMER (City, CustNo., CName)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;ORDER (Order#, Odate, &lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;u&gt;CustNo.,&lt;/u&gt;&lt;/b&gt; Ord_Amt)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;ORDER_ITEM (&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;u&gt;Order#&lt;/u&gt;&lt;/b&gt;, &lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;u&gt;ItemID&lt;/u&gt;&lt;/b&gt;, Qty)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;ITEM (ItemID, Unit_Price)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;SHIPMENT (&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;u&gt;Order#&lt;/u&gt;&lt;/b&gt;, &lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;u&gt;WarehouseID&lt;/u&gt;&lt;/b&gt;, Ship_date)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;WAREHOUSE (City, WarehouseID)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Question 5&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto; mso-list: l0 level1 lfo5; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;a.&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Assume is in First Normal form, In what normal form is the following relation schema in below figure, briefly justifies your answer?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Second Normalization Form since it has only one primary key.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto; mso-list: l0 level1 lfo5; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;b.&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;How would you successively normalize it completely?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;LOTS&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;table border=&quot;1&quot; cellpadding=&quot;0&quot; cellspacing=&quot;0&quot; class=&quot;MsoTableGrid&quot; style=&quot;border-collapse: collapse; border: none; margin-left: 41.4pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;&quot;&gt;&lt;tbody&gt;
&lt;tr style=&quot;height: 25.6pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0; mso-yfti-lastrow: yes;&quot;&gt;   &lt;td style=&quot;border: solid windowtext 1.0pt; height: 25.6pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 103.5pt;&quot; valign=&quot;top&quot; width=&quot;138&quot;&gt;   &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;u&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;PROPERTY_ID#&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/u&gt;&lt;/b&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 25.6pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;&quot; valign=&quot;top&quot; width=&quot;156&quot;&gt;   &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;COUNTRY_NAME&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 25.6pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.4pt;&quot; valign=&quot;top&quot; width=&quot;65&quot;&gt;   &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;LOT#&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 25.6pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 44.85pt;&quot; valign=&quot;top&quot; width=&quot;60&quot;&gt;   &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;AREA&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 25.6pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.15pt;&quot; valign=&quot;top&quot; width=&quot;64&quot;&gt;   &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;PRICE&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 25.6pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 75.5pt;&quot; valign=&quot;top&quot; width=&quot;101&quot;&gt;   &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;TAX_RATE&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;2&lt;sup&gt;ND&lt;/sup&gt; NF&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-left: .75in; mso-add-space: auto;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;LOTS1&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;table border=&quot;1&quot; cellpadding=&quot;0&quot; cellspacing=&quot;0&quot; class=&quot;MsoTableGrid&quot; style=&quot;border-bottom-style: none; border-collapse: collapse; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-left: 41.4pt; width: 596px;&quot;&gt;&lt;tbody&gt;
&lt;tr style=&quot;height: 25.6pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0; mso-yfti-lastrow: yes;&quot;&gt;   &lt;td style=&quot;border: solid windowtext 1.0pt; height: 25.6pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 103.5pt;&quot; valign=&quot;top&quot; width=&quot;138&quot;&gt;   &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto;&quot;&gt;&lt;u&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;PROPERTY_ID#&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/u&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 25.6pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;&quot; valign=&quot;top&quot; width=&quot;156&quot;&gt;   &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;COUNTRY_NAME&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 25.6pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 49.5pt;&quot; valign=&quot;top&quot; width=&quot;66&quot;&gt;   &lt;div align=&quot;center&quot; class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto; text-align: center;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;LOT#&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 25.6pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 45.0pt;&quot; valign=&quot;top&quot; width=&quot;60&quot;&gt;   &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;AREA&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 25.6pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 45.0pt;&quot; valign=&quot;top&quot; width=&quot;60&quot;&gt;   &lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;PRICE&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border: none; height: 25.6pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 87.15pt;&quot; valign=&quot;top&quot; width=&quot;116&quot;&gt;   &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;span style=&quot;mso-spacerun: yes;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;LOTS2&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;table border=&quot;1&quot; cellpadding=&quot;0&quot; cellspacing=&quot;0&quot; class=&quot;MsoTableGrid&quot; style=&quot;border-collapse: collapse; border: none; margin-left: 41.4pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;&quot;&gt;&lt;tbody&gt;
&lt;tr style=&quot;height: 21.75pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0; mso-yfti-lastrow: yes;&quot;&gt;   &lt;td style=&quot;border: solid windowtext 1.0pt; height: 21.75pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 107.9pt;&quot; valign=&quot;top&quot; width=&quot;144&quot;&gt;   &lt;div align=&quot;center&quot; class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto; text-align: center;&quot;&gt;&lt;u&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;COUNTY_NAME&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/u&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 21.75pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 99.1pt;&quot; valign=&quot;top&quot; width=&quot;132&quot;&gt;   &lt;div align=&quot;center&quot; class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto; text-align: center;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;TAX_RATE&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;3&lt;sup&gt;RD&lt;/sup&gt; NF&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;LOTS1A&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;table border=&quot;1&quot; cellpadding=&quot;0&quot; cellspacing=&quot;0&quot; class=&quot;MsoTableGrid&quot; style=&quot;border-bottom-style: none; border-collapse: collapse; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-left: 0.5in; width: 403px;&quot;&gt;&lt;tbody&gt;
&lt;tr style=&quot;height: 24.35pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0; mso-yfti-lastrow: yes;&quot;&gt;   &lt;td style=&quot;border: solid windowtext 1.0pt; height: 24.35pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 111.2pt;&quot; valign=&quot;top&quot; width=&quot;148&quot;&gt;   &lt;div align=&quot;center&quot; class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto; text-align: center;&quot;&gt;&lt;u&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;PROPERTY_ID#&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/u&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 24.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 102.15pt;&quot; valign=&quot;top&quot; width=&quot;136&quot;&gt;   &lt;div align=&quot;center&quot; class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto; text-align: center;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;COUNTY_NAME&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 24.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 44.05pt;&quot; valign=&quot;top&quot; width=&quot;59&quot;&gt;   &lt;div align=&quot;center&quot; class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto; text-align: center;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;LOT#&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 24.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 45.0pt;&quot; valign=&quot;top&quot; width=&quot;60&quot;&gt;   &lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin: 0in; mso-add-space: auto;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;AREA&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;span style=&quot;mso-spacerun: yes;&quot;&gt;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; mso-add-space: auto;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;LOTS1B&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;table align=&quot;left&quot; border=&quot;1&quot; cellpadding=&quot;0&quot; cellspacing=&quot;0&quot; class=&quot;MsoTableGrid&quot; style=&quot;border-bottom-style: none; border-collapse: collapse; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-left: 6.75pt; margin-right: 6.75pt; width: 171px;&quot;&gt;&lt;tbody&gt;
&lt;tr style=&quot;height: 27.1pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0; mso-yfti-lastrow: yes;&quot;&gt;   &lt;td style=&quot;border: solid windowtext 1.0pt; height: 27.1pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 64.25pt;&quot; valign=&quot;top&quot; width=&quot;86&quot;&gt;   &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 104.05pt; mso-element-top: 10.5pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly;&quot;&gt;&lt;u&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;AREA&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/u&gt;&lt;/div&gt;&lt;/td&gt;   &lt;td style=&quot;border-left: none; border: solid windowtext 1.0pt; height: 27.1pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 64.25pt;&quot; valign=&quot;top&quot; width=&quot;86&quot;&gt;   &lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 104.05pt; mso-element-top: 10.5pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;PRICE&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;span style=&quot;mso-spacerun: yes;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;span style=&quot;mso-spacerun: yes;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;br /&gt;
&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Question 6&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Create an ER diagram for each of the following descriptions and show their respective min and max cardinality:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: normal; mso-list: l5 level1 lfo6; text-indent: -.25in;&quot;&gt;&lt;!--[if !supportLists]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;a.&lt;span style=&quot;font: 7.0pt &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;Each company operates four departments, and each department belongs to one &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;company.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: normal;&quot;&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape
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&lt;tr&gt;   &lt;td height=&quot;55&quot;&gt;&lt;/td&gt;  &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;&lt;!--[endif]--&gt;&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 12.0pt;&quot;&gt;&lt;o:p&gt;&amp;nbsp;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;br /&gt;
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&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://computerscience113.blogspot.com/feeds/1559551433438943365/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://computerscience113.blogspot.com/2011/07/database-assgnement.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/1559551433438943365'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/1559551433438943365'/><link rel='alternate' type='text/html' href='http://computerscience113.blogspot.com/2011/07/database-assgnement.html' title='database assgnement'/><author><name>fabrice otepa</name><uri>http://www.blogger.com/profile/13017780185308872185</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-3111627990970613378.post-4884910036229917153</id><published>2011-02-25T09:50:00.000-08:00</published><updated>2011-02-25T09:50:08.731-08:00</updated><title type='text'>Quantum Mechanics and Information</title><content type='html'>&lt;img src=&quot;http://www.dailygalaxy.com/photos/uncategorized/2007/09/06/quantum_computing_internet_3.jpg&quot; /&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Quantum-mechanical thermodynamics is the heart of thermodynamics, accounting for such&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;phenomena as spin-statistics, correct Boltzmann counting, and most of the interesting manybody system characteristics such as superfluidity and Fermi pressure. At its most basic level, to&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;put this discipline in an information-theoretic context requires generalizing the idea of&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;information.&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Because of the intricate correlations that quantum systems can possess, they are difficult to&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;interpret within the bounds of classical information theory. But a complete theory which&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;accounts for both the quantum and classical cases has been developed (Cer97b). The von&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Neumann entropy for a quantum system, represented by a density matrix ρA, where A is a&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;quantum system or quantum source,&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;H(A) = - A A&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Trρ log ρ&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;is familiar to students of statistical mechanics for being a measure of the disorder of a quantum&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;system (see the explanation in I.1.i.), but it was recently established that H(A) is the minimum&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;number of qubits needed to losslessly code an ensemble of quantum states, thus giving&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;information-theoretic importance to this representation – see the argument later in this section&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;for a summary of the proof (Sch95). Further, if ρΑ is composed of orthogonal quantum states it&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;clearly reduces to a classical Shannon entropy H(A), since we can just diagonalize ρA in the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;orthogonal basis; we will discuss this fact later in the context of quantum channels. For two&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;operators A, B, the definitions of joint, conditional, and mutual entropy can be defined as&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;follows, where ρAB is the joint density matrix: &amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;H (A, B) = −Tr{ρ AB&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;log ρ AB&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;{&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;H (A | B) = −Tr{ρ AB&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;log ρ A|B&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;{&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;I (A, B) = Tr{ρ AB&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;log ρ A;B&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;{&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;The definitions of ρA|B and ρA ;B are surprisingly subtle. They are given by&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;AB&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;A B&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;σ&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;ρ&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;−&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;= 2&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;|&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&amp;nbsp;,&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;[ ( )]&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;n&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;n&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;AB&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;n&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;A B&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;n&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;A B&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;1/ 1/&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;lim&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;−&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;∞→&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;ρ = ρ ⊗ ρ ρ&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;respectively, where&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;σAB = 1A ⊗ log2ρΑΒ - log2ρAB&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;and&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;ρΑ = TrB{ρΑΒ}, ρΒ = TrA{ρΑΒ}.&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(As noted earlier, TrB means to take the partial trace of the density matrix; e.g.,&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;a a ab AB&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;a b&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;b&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;A&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;ρ &#39; = ∑ ρ &#39; .&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;This is where the duality between projection operators and density matrices becomes useful.)&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;img src=&quot;http://z.about.com/d/physics/1/0/r/-/-/-/BlackHole.jpg&quot; /&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;The justification of these choices is basically by analogy: as ρΑΒ becomes diagonal, for example,&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;the quantum conditional entropy converges to its classical value; also, ρA;B satisfies the classical&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;identity I(A,B) = H(A)+H(B) - H(A,B). But ρA|B and ρA ;B are not true density matrices. For&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;example, ρA|B may have eigenvalues greater than 1, when σAB has negative eigenvalues – in such&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;situations one obtains negative conditional entropies! It has been shown that a separable density&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;matrix ρΑΒ (i.e., one that can be expanded in the form &amp;nbsp;35&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;⊗ ∑&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;B&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i A&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;a ρ ρ&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;and therefore can’t be told apart from a classical ensemble containing two completely decoupled&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;systems) must have positive semidefinite σAB and thus positive conditional entropies (Cer97a),&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;but sufficiently entangled systems can indeed guarantee strange behavior like negative&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;conditional entropies. And oddly enough, I(A, B) can exceed the entropy of each individual set of&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;variables! The above definitions and generalizations thereof have been applied to quantum&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;teleportation and superdense coding (i.e., where two classical bits are encoded in one qubit) in&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;the paper (Cer97b). In this paper the authors treat entangled qubits as virtual conjugate particles&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;e, &amp;nbsp;e (collectively called ebits, or entangled qubits), carrying opposite information content ( +1&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;qubit each), and suggest that &amp;nbsp;e may be visualized as e going backwards through time! One can,&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;for example, draw a Feynman diagram for ultradense coding (consumption of a shared entangled&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;state, plus transmission of one qubit, is equivalent to transmission of two classical bits). Thus&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;these ‘information quanta’ suddenly have many properties analogous to those of virtual particles&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;in relativistic quantum field theory – in particular, only through interactions that result in&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;classical bits may they become visible to the world. Importantly, this formalism allows an&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;intuitive picture of conserved information flows. Ebits can be created simply by transmitting one&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;bit of a Bell pair while keeping the other, but one cannot create a qubit directly from an ebit&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(some classical bits are required). An interesting point is that if the ebit used for teleportation or&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;superdense coding is only partly entangled, then the transmission will appear noisy.&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;The Schmidt decomposition, sometimes called the polar decomposition, is a way of representing&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;an entangled pure state in the form&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;d&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;= ∑c a ⊗ b&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;=1&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;ψ&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;where the ci&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&amp;nbsp;are positive real coefficients, and&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;a ,&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;b are appropriately chosen orthonormal&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;states of two subsystems A, B, which may perhaps be located far apart from one another&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(Ben95b) (Sch95). It is useful to note that local operations cannot increase the number of&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;nonzero terms in the Schmidt decomposition; i.e., one cannot create entanglement with purely&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;local operations (although by consuming other entangled bits, one can increase the entanglement&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;of another subsystem). Local unitary operations on subsystem A can only change the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;eigenvectors of A (not the eigenvalues), and cannot affect B’s observations at all. As noted&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;above, in this basis σAB is positive semidefinite. If A makes an observation of his part of the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;system, this is equivalent to him first tracing over the degrees of freedom of B’s subsystem&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(which results in an apparent mixed state of his subsystem, represented by a diagonal density&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;matrix ρA in the Schmidt basis), then making an observation on this reduced density matrix:&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;d&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;A B i i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Tr ∑c a a&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;=&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;= =&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;1&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;ρ ψ ψ&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Then the entropy of entanglement is defined to be&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;∑&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;=&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;− = − = − =&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;d&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;A A B B i i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;E Tr Tr c c&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;1&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;2 2&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;ρ log(ρ ) ρ log(ρ ) log( ) .&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Note that it is just the Shannon entropy of the squared density matrix coefficients in the Schmidt&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;basis. E = 0 for a direct product, and E = 1 for a Bell state. It can be proven (Pop97) that this is&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;the unique measure of entanglement for pure states. The argument, like Shannon’s definition of 36&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;information, is based on two axioms: it is impossible to increase entanglement purely by local&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;operations, and it is possible to reversibly transfer entanglement from some set of shared ebits to&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;previously unentangled qubits (leaving the original ebits unentangled) (Ben96c). (The last&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;statement is true asymptotically; one can reversibly transform k systems in one entangled state&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;into n systems in pure singlet states only in the limit n,k →∞ ; in fact n/k is often asymptotically&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;an &amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;irrational number, so due to incommensurability such reversible procedures can’t even exist&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;except in the infinite limit!) Formally these two statements are akin to the Second Law of&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;thermodynamics and the statement that all reversible heat engines are equally efficient, so the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;derivation of the entropy of entanglement is completely analogous to the derivation of entropy in&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;thermodynamics! Thus, proceeding as in thermodynamics, we require the degree of&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;entanglement to be extensive, we can measure the entanglement of an arbitrary state by&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;transforming it into a set of singlet states (which are defined to have entanglement equal to 1),&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;and so on. Unfortunately this definition is only good in the quantum analogy to the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;‘thermodynamic limit,’ meaning access to infinitely many pure ebits, which rarely occurs in real&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;life. Also, nobody has come up with a measure of entanglement for a mixed state, since no on&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;has exhibited a reversible way to convert a density matrix into pure states; candidates include the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;number of singlets that can be packed into a density matrix, or the number which can be&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;extracted – sometimes these two values can be different (Ben96d). Therefore many other&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;definitions may be more practical, if appropriately justified; it is difficult to imagine what&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;physical manifestation this measure of mixed-state entanglement might take. Indeed, the recent&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;literature indicates that even respectable scientists occasionally need reprimanding due to the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;ambiguity of dealing with issues as nonintuitive as entanglement (Unr).&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;One interesting manifestation of these results is that two people with many partially-entangled&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;qubits can increase the degree of entanglement of a few qubits to arbitrary purity, at the expense&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;of the others. Note that this is not in contradiction of our above statements, since only the total&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;entanglement is required to be conserved. For a large number n of entangled pairs of two-state&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;particles, each with entropy of entanglement E &amp;lt; 1, the yield of pure singlets goes like nE–&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;O(log(n)) (compare this to the pure state yield of bulk spin resonance quantum computation,&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;below). The process of Schmidt projection is as follows: suppose that the initial system is in the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;product state &amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(cos sin 2 2&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;1&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;1 1 i i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;n&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;i i ∏ a b a b&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;=&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;ψ = θ + θ&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;which has 2&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;n&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&amp;nbsp;terms, each with one of n + 1 distinct coefficients cos(θ)&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;n-k&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;sin(θ)&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;k&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&amp;nbsp;We can treat .&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;these states as n + 1 orthogonal subspaces, labed by the power k of sin(θ) in the coefficient. A&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;and B project the state ψ onto one of these subspaces by making an observation, and obtaining&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;some k; this collapses the state down into a maximally entangled state, which occupies a 2n!/(nk)!k! dimensional subspace of the original space; if lucky, one can get even more ebits than one&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;started with (but the expected entanglement cannot be greater than before). It’s analogous to the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;method of taking a biased coin, say with probability of heads .3, and getting an unbiased random&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;bit by flipping the coin and keeping sequences HT = 1 and TH = 0 (probability .21 each), and&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;discarding TT and HH (probability .49 and .09, respectively). In our case, measuring a power k&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;symmetrizes our state by selecting all possible combinations with some equal probability&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(although we cannot actively choose that probability) and discarding all the states with 37&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;probabilities that differ from it. One can transform this new state formally into singlets as&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;follows: measure k for each of m batches, each containing n entangled pairs, getting ki&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;, i = 1..m.&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Let Dm be the product of all the coefficients n!/ki&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;!(n-ki&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;)!, i = 1..m, and continue until Dm∈[2&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;l&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&amp;nbsp;,&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;l&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(1+ε)], where ε is the desired maximum error in the entanglement, and l is some integer. Then&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;A and B make a measurement on the system which projects it into one of two subspaces, one of&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;dimension 2&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;l+1&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&amp;nbsp;(which is in a maximally entangled state of two 2&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;l&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;-dimensional subsystems) and&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;one of dimension 2(Dm –2&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;l&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;) (which discards all the entanglement). In the former case, we have&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;again effectively symmetrized the state; in the latter, we lose everything. (Such is the risky&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;nature of quantum engineering.) Finally, another round of Schmidt decomposition arranges the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;density matrix into a product of l singlets. &amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Quantum channels, over which qubit messages are sent, are a useful abstraction. In classical&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;information theory, a source A produces messages ai&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&amp;nbsp;with probability p(ai&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;), and the fidelity of the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;coding system is the probability that the decoded message is the same as the transmitted one; in&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;quantum information theory a quantum source codes each messages a from a source A into a&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;signal state &amp;nbsp;M&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;a of a system M; the ensemble of messages is then representable by a density&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;matrix &amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;ρ = &amp;nbsp;∑&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;a&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;a&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;p a)π ( , where πa = &amp;nbsp;M M&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;a a ,&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;and the fidelity for a channel where ra is received when πa is transmitted is defined to be &amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;f &amp;nbsp;( = ) )Tr( a a&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;a&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;∑ p a π r&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(so that for perfect noiseless channels f = 1) (Sch95). Compare this to our definition of classical&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;probability fidelity in I.1.ii.; we will unite these pictures in the next paragraph. Another possible&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;definition of a quantum channel W, which lends itself more to problems involving noise, is to&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;consider a channel to be a probability distribution on unitary transformations U which act upon&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Hsignal ⊗ Henvironment&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;; before reading a quantum channel, one must take a partial trace over&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Henvironment&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;, and one can define the fidelity as &amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;x W x&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;all &amp;nbsp;signals &amp;nbsp;x&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;min&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(Cal96). Note that there are subtleties for the quantum channel which one does not have to&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;consider in the classical case: for example, one cannot copy an arbitrary quantum signal (the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;“no-cloning” theorem (Woo82)); the proof follows immediately from the linearity of quantum&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;mechanics. Only if the signals are orthogonal can they be copied (i.e., measuring a system which&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;is known to be in an eigenstate is trivial, and yields all the information available about the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;system). Fundamental to quantum communication is the idea of transposition, or placing a&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;system Y in the same state as a system X (perhaps resetting X to a useless state in the process);&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;unitary tranposition from system X to system Y can occur iff the states in X have the same inner&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;products as the corresponding states in Y, e.g. &amp;nbsp;ax bx = ay by , which occurs iff the Hilbert&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;space of Y is of dimension no less than the Hilbert space of X, for obvious reasons. If a message&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;is unitarily transposed from a source A to a system M, which upon transmission is decoded into a&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;message A’ (on an isomorphic quantum system) by the inverse of the unitary coding operator,&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;A → M → A’&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;then we say M is the quantum channel for the communication. The question arises, when is the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;quantum channel M big enough for a particular quantum source A?&amp;nbsp;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://computerscience113.blogspot.com/feeds/4884910036229917153/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://computerscience113.blogspot.com/2011/02/quantum-mechanics-and-information.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/4884910036229917153'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/4884910036229917153'/><link rel='alternate' type='text/html' href='http://computerscience113.blogspot.com/2011/02/quantum-mechanics-and-information.html' title='Quantum Mechanics and Information'/><author><name>fabrice otepa</name><uri>http://www.blogger.com/profile/13017780185308872185</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-3111627990970613378.post-4930089843623572772</id><published>2011-02-25T09:42:00.000-08:00</published><updated>2011-02-25T09:42:59.584-08:00</updated><title type='text'>QUANTUM COMPUTATION</title><content type='html'>&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif; font-size: large;&quot;&gt;Quantum Computation: Theory and Implementation&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif; font-size: large;&quot;&gt;&lt;img src=&quot;http://www.lbl.gov/Science-Articles/Archive/sabl/2005/June/assets/img/02_Schenkel_Shen.jpg&quot; /&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Quantum computation is a new field bridging many disciplines, including theoretical physics,&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;functional analysis and group theory, electrical engineering, algorithmic computer science, and&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;quantum chemistry. The goal of this thesis is to explore the fundamental knowledge base of&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;quantum computation, to demonstrate how to extract the necessary design criteria for a&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;functioning tabletop quantum computer, and to report on the construction of a portable NMR&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;spectrometer which can characterize materials and hopefully someday perform quantum&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;computation. This thesis concentrates on the digital and system-level issues. Preliminary data&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;and relevant code, schematics, and technology are discussed.&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;div style=&quot;font-size: x-large;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;font-size: x-large;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;img src=&quot;http://www.datacenterknowledge.com/wp-content/uploads/2009/12/dwave.jpg&quot; /&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;font-size: x-large;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/div&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Why build a quantum computer? Because it’s not there, for one thing, and the theory of quantum&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;computation, which far outstrips the degree of implementation as of today, suggests that a&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;quantum computer would be a incredible machine to have around. It could factor numbers&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;exponentially faster than any known algorithm, and it could extract information from unordered&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;databases in square-root the number of instructions required of a classical computer. As&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;computation is a nebulous field, the power of quantum computing to solve problems of&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;traditional complexity theory is essentially unknown. A quantum computer would also have&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;profound applications for pure physics. By their very nature, quantum computers would take&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;exponentially less space and time than classical computers to simulate real quantum systems, and&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;proposals have been made for efficiently simulating many-body systems using a quantum&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;computer. A more exotic application is the creation of new states which do not appear in nature:&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;for example, a highly entangled state experimentally unrealizable through other means, the 3-&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;qubit Greenberger-Horne-Zeilinger state &amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;000 + 111 ,&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;has been prepared on an NMR quantum computer with only 3 operations, a Y(π/2) pulse&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;followed by 2 CNOTs, applied to the spins of trichloroethylene (Laf97). Computational&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;approaches to NMR are interesting for their own sake: Warren has coupled spins as far as&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;millimeters apart, taking advantage of the properties of a phenomenon known as zero-quantum&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;coherence to make very detailed MRI images (War98). Performing fixed-point analyses on&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;iterated schemes for population inversion can result in very broadband spin-flipping operators –&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;in such a scheme, the Liouville space of operators is contracted towards a fixed point, so that&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;operators that are imperfect (due to irregularities in the magnetic field, end effects of the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;stimulating coil, impurities in the sample, etc.) nevertheless result in near-perfect operations&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(Tyc85) (Fre79). These simple uses of nonlinear dynamics and the properties of solution have&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;shed light on certain computational aspects of nuclear magnetic resonance.&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;But performing a quantum computation as simple as factoring 15 will involve the creation and&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;processing of dozens of coherences over extended periods of time. This presents an incredible&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;engineering challenge, and may open up new understandings on both computation and quantum&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;mechanics.&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Undoubtedly we will someday have quantum computers, if only to maintain progress in&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;computation. It has been widely speculated that within a few decades, the incredible growth&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;which characterizes today’s silicon age will come to a gradual halt, simply because there will be&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;no more room left at the bottom: memory bits and circuit traces will essentially be single atoms&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;on chips, the cost of a fabrication plant will be “the GNP of the planet,” and there will probably&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;be lots of interesting problems to solve which require still more computing power. This power&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;will have to come from elsewhere – that is, by stepping outside of the classical computation&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;paradigm.&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&amp;nbsp;&amp;nbsp;8&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Other fields related to quantum computing, which might be said to fall into&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;‘quantum control,’ include quantum teleportation, quantum manipulation, and quantum&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;cryptography. Quantum teleportation is an appealing way to send quantum states over long&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;distances, something no amount of classical information can ever do (probably), and has been&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;realized for distances exceeding 100 kilometers (Bra96). Quantum means of cryptography are&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;unbreakable according to the laws of physics, and using quantum states to send messages&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;guarantees that eavesdroppers can be detected (Lo99).&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Furthermore quantum computing joins two of the most abstruse and surprisingly nonintuitive&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;subjects known to humans: computation and quantum mechanics. Both have the power to shock&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;the human mind, the former with its strange powers and weaknesses, and the latter with its&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;nonintuitive picture of nature. Perhaps the conjunction of these two areas will yield new insights&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;into each. For the novice in this field, past overview papers on quantum computing include&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(Bar96) (Llo95) (Ste97).&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;There are powerful alternatives to quantum computing which may have more immediate&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;significance for the computing community. Incremental improvements in silicon fabrication&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;(such as MEMS-derived insights, low-power and reversible design principles, copper wiring&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;strategies, intergate trench isolation, and the use of novel dielectrics), reconfigurable computing&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;and field programmable gate arrays, single-electron transistors, superconducting rapid singleflux quantum logic, stochastic and defect-tolerant computers, ballistically-transporting&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;conductors, printable and wearable computers, dynamical systems capable of computation,&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;memory devices consisting of quantum dots and wells, and many other technologies are vying&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;for the forefront. Any of them, if lucky and well-engineered, could jump to the forefront and&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;perhaps render the remainder obsolete, much like the alternatives to silicon in the heyday of&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Bardeen and Intel. It is more likely that these diverse technologies will find a variety of niches in&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;the world, given the amazing number of problems that people want to solve nowadays.&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;This paper begins with a comprehensive critique of much of the knowledge in the quantum&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;computation community, since that is perhaps fundamental to understanding why and how&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;quantum computers should be built. Part I.1. covers elementary quantum mechanics, information&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;theory, and computation theory, which is a prerequisite for what follows. Much of this was&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;written over the past year to teach the author how all of these pictures can contribute to a&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;coherent picture of the physics of computation. Part I.1. can also be thought of an ensemble of&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;collected material, in preparation for a book which delves into the theories and experiments&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;behind the physics of computation; it is the opinion of the author that the definitive book on the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;physics of computation has not yet been written, and that the world needs one. It is noted that&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;very little synthesis has been performed on the information here presented; most of the&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;paragraphs are summaries of various different sources, assembled for easy reference and as an&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;aid to thinking. Some of these notes were presented at (Bab98).&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;div style=&quot;font-size: x-large;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://computerscience113.blogspot.com/feeds/4930089843623572772/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://computerscience113.blogspot.com/2011/02/quantum-computation.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/4930089843623572772'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/4930089843623572772'/><link rel='alternate' type='text/html' href='http://computerscience113.blogspot.com/2011/02/quantum-computation.html' title='QUANTUM COMPUTATION'/><author><name>fabrice otepa</name><uri>http://www.blogger.com/profile/13017780185308872185</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-3111627990970613378.post-3065611119608950916</id><published>2011-02-24T06:53:00.001-08:00</published><updated>2011-02-24T06:53:59.932-08:00</updated><title type='text'></title><content type='html'>&lt;script type=&quot;text/javascript&quot;&gt;

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&lt;/script&gt;</content><link rel='replies' type='application/atom+xml' href='http://computerscience113.blogspot.com/feeds/3065611119608950916/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://computerscience113.blogspot.com/2011/02/var-gaq-gaq-gaq.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/3065611119608950916'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/3065611119608950916'/><link rel='alternate' type='text/html' href='http://computerscience113.blogspot.com/2011/02/var-gaq-gaq-gaq.html' title=''/><author><name>fabrice otepa</name><uri>http://www.blogger.com/profile/13017780185308872185</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-3111627990970613378.post-2929887693526819599</id><published>2011-02-23T05:47:00.000-08:00</published><updated>2011-02-23T13:46:53.747-08:00</updated><title type='text'>Information Technology Industry</title><content type='html'>&lt;img src=&quot;http://www.theinnovestgroup.com/resources/Man+in+Datacenter.jpg&quot; /&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;iframe align=&quot;left&quot; frameborder=&quot;0&quot; marginheight=&quot;0&quot; marginwidth=&quot;0&quot; scrolling=&quot;no&quot; src=&quot;http://rcm.amazon.com/e/cm?t=widgetsamazon-20&amp;amp;o=1&amp;amp;p=8&amp;amp;l=bpl&amp;amp;asins=1442152311&amp;amp;fc1=000000&amp;amp;IS2=1&amp;amp;lt1=_blank&amp;amp;m=amazon&amp;amp;lc1=0000FF&amp;amp;bc1=000000&amp;amp;bg1=FFFFFF&amp;amp;f=ifr&quot; style=&quot;align: left; height: 245px; padding-right: 10px; padding-top: 5px; width: 131px;&quot;&gt;&lt;/iframe&gt;&lt;br /&gt;
&lt;div style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Information technology (IT) is both a huge industry in itself, and the source of dramatic changes in business practices in all other sectors. The term IT covers a number of related disciplines and areas, from semiconductor design and production (also covered in the profile of the electronics sector), through hardware manufacture (mainframes, servers, PCs, and mobile devices), to software, data storage, backup and retrieval, networking, and, of course, the internet.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;On top of this, there has been a convergence between IT and telephony, driven by transforming voice traffic from an analogue signal to a digital packet, indistinguishable from other data packets travelling through a computer network. IT in the leisure sector is already about enabling interaction with video, movies, and TV, and this trend is increasingly carrying into the business space.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Each of the major sub-areas in IT is itself capable of being divided into its component parts. Storage, for example, breaks down into disk drives, tape drives, and optical drives, and into attached storage and networked storage. PCs break down into utility-business desktop PCs, high-end work stations, and “extreme” gaming PCs for games enthusiasts—the computer and console games industry has already produced “blockbusters” that outsell top releases from Hollywood.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;iframe align=&quot;left&quot; frameborder=&quot;0&quot; marginheight=&quot;0&quot; marginwidth=&quot;0&quot; scrolling=&quot;no&quot; src=&quot;http://rcm.amazon.com/e/cm?t=widgetsamazon-20&amp;amp;o=1&amp;amp;p=8&amp;amp;l=bpl&amp;amp;asins=0470095210&amp;amp;fc1=000000&amp;amp;IS2=1&amp;amp;lt1=_blank&amp;amp;m=amazon&amp;amp;lc1=0000FF&amp;amp;bc1=000000&amp;amp;bg1=FFFFFF&amp;amp;f=ifr&quot; style=&quot;align: left; height: 245px; padding-right: 10px; padding-top: 5px; width: 131px;&quot;&gt;&lt;/iframe&gt;Software subdivides into numerous specialist areas, from relational database technologies to enterprise applications, to “horizontal” office applications characterized by Microsoft Office 2007, for example.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Somewhat off the main track of IT at present, but very much related to both increases in processor power, and to work in simulation and artificial intelligence, is the field of robotics. This lies outside the scope of this profile, but the linkages between robotics and IT are already transforming both manufacturing and defense.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;In addition, the IT arena is characterized by a number of key trends and emerging technologies which, again, have the potential to transform the way businesses currently use IT, and carry out their operations. An example of a trend would be the outsourcing of IT services, such as desktop PC support, or whole IT-supported functions, such as accounts processing. An example of a technology trend would be virtualization. This refers to the ability of large servers to be subdivided into a number of virtual machines, which can be either virtual PCs or virtual servers.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;img src=&quot;http://www.med.govt.nz/upload/19533/it-stats-2003-10.gif&quot; /&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Virtualization carries with it a number of benefits, including stopping what, at one stage, looked like an endless proliferation of servers inside companies. One large server can now be split into a number of virtual servers, enabling the organization to reduce the number of boxes it has to manage. Server virtualization should not be confused with another powerful trend, the creation of virtual environments inside the machine. The fact that desktop processors are now powerful enough to mimic real-world physics in computer space is transforming both design and entertainment.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;iframe align=&quot;left&quot; frameborder=&quot;0&quot; marginheight=&quot;0&quot; marginwidth=&quot;0&quot; scrolling=&quot;no&quot; src=&quot;http://rcm.amazon.com/e/cm?t=widgetsamazon-20&amp;amp;o=1&amp;amp;p=8&amp;amp;l=bpl&amp;amp;asins=0691118523&amp;amp;fc1=000000&amp;amp;IS2=1&amp;amp;lt1=_blank&amp;amp;m=amazon&amp;amp;lc1=0000FF&amp;amp;bc1=000000&amp;amp;bg1=FFFFFF&amp;amp;f=ifr&quot; style=&quot;align: left; height: 245px; padding-right: 10px; padding-top: 5px; width: 131px;&quot;&gt;&lt;/iframe&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;All these trends have enabled the IT industry to continue to generate a strong demand for the next generation of servers, PCs, and laptops. However, in a recession, companies of all sizes generally postpone upgrading their IT, or implementing major IT projects that are not already in hand. This makes the sector vulnerable to downturns in the economy, and the current global downturn is already having a major impact on revenues in&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Times New Roman&#39;; line-height: normal;&quot;&gt;&lt;img src=&quot;http://www.quality-web-solutions.com/images/offshoring.gif&quot; /&gt;&lt;/span&gt;&amp;nbsp;&lt;/span&gt;&lt;/div&gt;&lt;h2 style=&quot;color: black; font-family: Georgia, &#39;Times New Roman&#39;, Times, Verdana, sans-serif; font-size: 1.6em; font-weight: lighter; line-height: 1.2em; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0.8em; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;Market Analysis&lt;/h2&gt;&lt;div style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;According to the IT market analysis firm, Gartner, worldwide server shipments and revenues saw double-digit declines in the&amp;nbsp;&lt;a class=&quot;dlink&quot; href=&quot;http://www.qfinance.com/dictionary/fourth-quarter&quot; style=&quot;border-bottom-color: rgb(0, 0, 0); border-bottom-style: dotted; border-bottom-width: 1px; color: black; text-decoration: none;&quot; title=&quot;Look up term in QFINANCE Dictionary&quot;&gt;fourth quarter&lt;/a&gt;&amp;nbsp;of 2008. By comparison with the same quarter in 2007, shipment numbers declined by 11.7% while revenue dropped by 15.1%. Commenting on the figures, Heeral Kota, a senior research analyst at Gartner, said: “The weakening economic environment had a deep impact on server market revenues in the&amp;nbsp;&lt;a class=&quot;dlink&quot; href=&quot;http://www.qfinance.com/dictionary/fourth-quarter&quot; style=&quot;border-bottom-color: rgb(0, 0, 0); border-bottom-style: dotted; border-bottom-width: 1px; color: black; text-decoration: none;&quot; title=&quot;Look up term in QFINANCE Dictionary&quot;&gt;fourth quarter&lt;/a&gt;, as companies put a hold on spending across most&amp;nbsp;&lt;a class=&quot;dlink&quot; href=&quot;http://www.qfinance.com/dictionary/market-segment&quot; style=&quot;border-bottom-color: rgb(0, 0, 0); border-bottom-style: dotted; border-bottom-width: 1px; color: black; text-decoration: none;&quot; title=&quot;Look up term in QFINANCE Dictionary&quot;&gt;market segments&lt;/a&gt;. Almost all segments exhibited similar behavior, as users sought to reduce costs and spending, deferring projects where possible.”&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Gartner said that the fall in shipments and revenue was reported across all regions apart from Japan, which managed a 4.7% revenue increase. Europe, the Middle East, and Africa (EMEA) suffered the worst decline, with revenues falling by 20.6%. Even the emerging regions of Latin America and Asia-Pacific suffered, with declines of 12.5% and 14.8%, respectively. North America server revenue declined by 14.6%.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;The scale of the IT server sector as an industry can be seen from the fact that IBM, the&amp;nbsp;&lt;a class=&quot;dlink&quot; href=&quot;http://www.qfinance.com/dictionary/market-leader&quot; style=&quot;border-bottom-color: rgb(0, 0, 0); border-bottom-style: dotted; border-bottom-width: 1px; color: black; text-decoration: none;&quot; title=&quot;Look up term in QFINANCE Dictionary&quot;&gt;market leader&lt;/a&gt;, ended 2008 with revenues of US$4 billion from server shipments, with almost exactly one-third of the global market. However, IBM saw revenues decline by 17.4% as a result of the downturn. Hewlett-Packard was next, with revenues of just under US$4 billion and with a 30%&amp;nbsp;&lt;a class=&quot;dlink&quot; href=&quot;http://www.qfinance.com/dictionary/market-share&quot; style=&quot;border-bottom-color: rgb(0, 0, 0); border-bottom-style: dotted; border-bottom-width: 1px; color: black; text-decoration: none;&quot; title=&quot;Look up term in QFINANCE Dictionary&quot;&gt;market share&lt;/a&gt;.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;The figures in server shipments for 2008 chart the impact of the downturn fairly starkly. The sector had been enjoying fairly strong results during the first half of 2008, but a severe decline in sales set in as the intensity of the downturn began to bite, Gartner said.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;If things are bleak on the server front, the outlook is just as bad for PCs. Gartner is predicting that the PC industry will suffer its sharpest unit decline in history in 2009. Gartner expects some 257 million PCs to ship worldwide through 2009. This would represent an 11.9% contraction on the numbers sold in 2008. Even after the dot.com bubble burst in 2001, global PC unit shipments only contracted 3.2%.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;To view these statistics in perspective, it is important to remember that setting up a new chip-fabrication plant to make the next generation of PCs costs some US$3 billion. With margins on PCs being at an all-time low, it is very difficult for the industry to sustain itself if companies and households stop upgrading to the latest generation of PC.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;According to Gartner, both developed&amp;nbsp;&lt;a class=&quot;dlink&quot; href=&quot;http://www.qfinance.com/dictionary/market-economy&quot; style=&quot;border-bottom-color: rgb(0, 0, 0); border-bottom-style: dotted; border-bottom-width: 1px; color: black; text-decoration: none;&quot; title=&quot;Look up term in QFINANCE Dictionary&quot;&gt;market economies&lt;/a&gt;&amp;nbsp;and&amp;nbsp;&lt;a class=&quot;dlink&quot; href=&quot;http://www.qfinance.com/dictionary/emerging-market&quot; style=&quot;border-bottom-color: rgb(0, 0, 0); border-bottom-style: dotted; border-bottom-width: 1px; color: black; text-decoration: none;&quot; title=&quot;Look up term in QFINANCE Dictionary&quot;&gt;emerging markets&lt;/a&gt;&amp;nbsp;are forecast to go through tremendous slowdowns. After the telecoms and dot.com crash in 2001, sales of PCs in mature markets contracted by 7.9%, Gartner says, while sales growth in&amp;nbsp;&lt;a class=&quot;dlink&quot; href=&quot;http://www.qfinance.com/dictionary/emerging-market&quot; style=&quot;border-bottom-color: rgb(0, 0, 0); border-bottom-style: dotted; border-bottom-width: 1px; color: black; text-decoration: none;&quot; title=&quot;Look up term in QFINANCE Dictionary&quot;&gt;emerging markets&lt;/a&gt;&amp;nbsp;slowed to 11.1% in 2002. Both these low points will be substantially exceeded in 2009. The impact will be deepened by hardware suppliers, who will act prudently and maintain inventories at an all-time low to avoid losses.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;However, all is not total gloom. The trend for corporates and home users to switch to mobile PCs, rather than desktop units, will keep growth going for worldwide mobile PC shipments. Gartner is forecasting sales of 155.6 million units, up 9% from 2008. By way of contrast, desktop PC shipments will struggle to exceed 101 million, a drop of almost 32% on 2008. The most popular form in the mobile space will continue to be the mini-notebook, Gartner says. In particular, users are moving to higher-specification notebook PCs with larger screens, of around 8.9 inches. Prices, however, will continue to fall. Gartner is predicting that the price of a mid-specification mini-notebook PC with a large screen will fall, from an average of US$450 in 2008 to under US$400 by the end of 2009.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Another plus point is that the industry as a whole learned some valuable lessons in the crash of 2001, and is already demonstrating that it is much more agile, and better able to react to changing market conditions in 2009.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Not surprisingly, with all this bad news about slowing demand on actual “built” hardware, the downturn is also hitting demand for chip production. In fact, Gartner’s prediction here is that it will be at least 2013 before the semiconductor industry sees revenues comparable to those it achieved in 2008, when revenues peaked at US$256.4 billion. Over the course of 2009, the sector will see a drop in excess of 24%, with total global semiconductor revenues estimated to top out at US$194.5 billion. There is a precedent for this prediction, in that after the 2001 recession, the semiconductor industry took four years to get back to the revenues it had generated in 2000.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;The contraction predicted for 2009 is considerably more gloomy than a prediction made by Gartner six months ago, when it was only predicting a contraction for the sector of 16%. On the plus side, modest single-digit growth should return in 2010.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Apart from semiconductor chip manufacturers, the other huge area in the field is memory chips, or, more specifically, DRAM chips. According to Gartner, DRAM suppliers lost more than US$13 billion in 2007 and 2008, due to massive overcapacity in the market and soft pricing. But many suppliers are now reducing supply, which should push DRAM prices back up, and put the industry on a better footing.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;While the industry is absorbing all this bad news, there are positive trends that manufacturers, systems houses,&amp;nbsp;&lt;a class=&quot;dlink&quot; href=&quot;http://www.qfinance.com/dictionary/value-added&quot; style=&quot;border-bottom-color: rgb(0, 0, 0); border-bottom-style: dotted; border-bottom-width: 1px; color: black; text-decoration: none;&quot; title=&quot;Look up term in QFINANCE Dictionary&quot;&gt;value-added&lt;/a&gt;&amp;nbsp;resellers, and consultancies can focus on. The move to replace tens or even hundreds of individual servers with large virtual servers is picking up pace, and is not going to be stopped by the recession. It is a cost-saver and efficiency driver, so companies will press ahead with virtualization programs. This, in turn, will drive sales of larger servers, and could drive applications upgrades as well. According to Gartner, worldwide virtualization software revenue will increase by 43%, from US$1.9 billion in 2008 to US$2.7 billion in 2009. Virtualization also plays well to the green agenda, and greening up IT by lowering its carbon footprint is another unstoppable trend for 2009 and 2010. Virtualization plays to this on a number of fronts. First, it is more power-efficient to run a single, large server than a number of smaller servers. Second, the manufacturing carbon footprint is lower, and, third, if the virtualization exercise extends to the desktop, then one server can replace dozens of PCs. Revenue from hosted virtual desktops (HVDs) is expected to more than triple, from US$74.1 million to US$298.6 million through 2009, Gartner says.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;img src=&quot;http://www.dreamstime.com/high-technology-industry-business-concepts--thumb6575969.jpg&quot; /&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Storage systems in IT tend to be divided into external disk storage, where the disks are being “managed” in some way independently of processor resources, and attached storage, as in the typical PC or low-end server that comes with one or two hard drives already installed. According to the market analysis company, IDC, the worldwide external-disk storage market showed its first year-on-year fall for five years, for the&amp;nbsp;&lt;a class=&quot;dlink&quot; href=&quot;http://www.qfinance.com/dictionary/last-quarter&quot; style=&quot;border-bottom-color: rgb(0, 0, 0); border-bottom-style: dotted; border-bottom-width: 1px; color: black; text-decoration: none;&quot; title=&quot;Look up term in QFINANCE Dictionary&quot;&gt;last quarter&lt;/a&gt;&amp;nbsp;of 2008. IDC reports a fall of 0.5%, with revenues totaling US$5.3 billion that quarter. Total disk-storage systems capacity shipped amounted to 2,460 petabytes, a growth of just 27.3% on the volume shipped in 2007. (The point here is that with e-mail and, now, live video, demand for storage should be vastly ahead of this figure).&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Again on a positive note, one area where large and medium companies, as well as some service providers, can be expected to continue spending through the downturn is on the new IT concept known as “cloud computing.” IDC expects worldwide spending on cloud computing and cloud services to reach US$42 billion by 2012. Cloud computing is a term that essentially refers to the delivery of services to communities of users over the internet, instead of via a data centre located in the same building. Access to the service is via a web browser, and everything from storage to the processor power that drives the service is located remotely. The term itself comes from the way the internet is depicted in computer network diagrams (a non-specific “cloud”), and points to the fact that all the complexity of infrastructure that makes the service possible is hidden “in the cloud.”&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;According to a survey IDC conducted with almost 700 IT executives across the Asia-Pacific region, some 11% said they were already using cloud-based solutions. A further 41% indicated that they are either evaluating cloud-based solutions, or are piloting such solutions. Gartner, on the other hand, claims that cloud-computing application infrastructure technologies will still need some seven years to mature. It sees three phases of evolution for cloud computing going up to 2015 and beyond. Up to 2011, applications will be mostly opportunistic and tactical in nature, and will have little impact on mainstream IT, Gartner argues. By 2015, however, it expects cloud computing to have been commoditized, and to have become the preferred solution for many kinds of corporate &lt;iframe align=&quot;left&quot; frameborder=&quot;0&quot; marginheight=&quot;0&quot; marginwidth=&quot;0&quot; scrolling=&quot;no&quot; src=&quot;http://rcm.amazon.com/e/cm?t=widgetsamazon-20&amp;amp;o=1&amp;amp;p=8&amp;amp;l=bpl&amp;amp;asins=B000WKPHI8&amp;amp;fc1=000000&amp;amp;IS2=1&amp;amp;lt1=_blank&amp;amp;m=amazon&amp;amp;lc1=0000FF&amp;amp;bc1=000000&amp;amp;bg1=FFFFFF&amp;amp;f=ifr&quot; style=&quot;align: left; height: 245px; padding-right: 10px; padding-top: 5px; width: 131px;&quot;&gt;&lt;/iframe&gt;applications that are now run in-house on standard IT equipment.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;librios-pflindent&quot; style=&quot;line-height: 16px; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;In summary, the immediate future for IT looks like being a period of tough belt-tightening. However, the underlying innovation in the sector, and its ability to transform mainstream business processes while enabling new kinds of business practice is undiminished, and should re-emerge to drive revenue growth once the global upturn starts to gain momentum.&lt;/span&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://computerscience113.blogspot.com/feeds/2929887693526819599/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://computerscience113.blogspot.com/2011/02/information-technology-industry.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/2929887693526819599'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/2929887693526819599'/><link rel='alternate' type='text/html' href='http://computerscience113.blogspot.com/2011/02/information-technology-industry.html' title='Information Technology Industry'/><author><name>fabrice otepa</name><uri>http://www.blogger.com/profile/13017780185308872185</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-3111627990970613378.post-4215822706129503727</id><published>2011-02-23T05:42:00.000-08:00</published><updated>2011-02-23T13:48:02.488-08:00</updated><title type='text'>Statewide Solutions to Address Information Technology Industry Workforce Needs</title><content type='html'>&lt;div style=&quot;font-family: Tahoma, Geneva, sans-serif; font-size: 13px; line-height: 17px; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;iframe align=&quot;left&quot; frameborder=&quot;0&quot; marginheight=&quot;0&quot; marginwidth=&quot;0&quot; scrolling=&quot;no&quot; src=&quot;http://rcm.amazon.com/e/cm?t=widgetsamazon-20&amp;amp;o=1&amp;amp;p=8&amp;amp;l=bpl&amp;amp;asins=0789742535&amp;amp;fc1=000000&amp;amp;IS2=1&amp;amp;lt1=_blank&amp;amp;m=amazon&amp;amp;lc1=0000FF&amp;amp;bc1=000000&amp;amp;bg1=FFFFFF&amp;amp;f=ifr&quot; style=&quot;align: left; height: 245px; padding-right: 10px; padding-top: 5px; width: 131px;&quot;&gt;&lt;/iframe&gt;The U.S. Department of Labor has announced a series of investments totaling more than $7.8 million to address the workforce needs of the information technology industry. In preparing for these investments, the U.S. Department of Labor hosted forums with IT industry leaders, educators, and the public workforce system.&lt;/div&gt;&lt;div style=&quot;font-family: Tahoma, Geneva, sans-serif; font-size: 13px; line-height: 17px; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;On February 26, 2004, ETA convened an IT Industry Executive Forum at CompTIA Headquarters in Oakbrook Terrace, IL. Executives representing 18 companies from sectors such as IT hardware, software, cross-industry end users, and service providers discussed a wide range of workforce issues concerning the information technology industry including the role for government in the IT industry&#39;s workforce initiatives, the need to develop the workforce soft skills, transferable IT skills, and the development of an industry competency model.&lt;/div&gt;&lt;div style=&quot;font-family: Tahoma, Geneva, sans-serif; font-size: 13px; line-height: 17px; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;DOL has sought to understand and implement industry-identified strategies to confront critical workforce shortages. It has listened to employers, industry association representatives, and others associated with the information technology industry regarding some of their efforts to identify challenges and implement effective workforce strategies. DOL&#39;s Employment and Training Administration is supporting comprehensive business, education, and workforce development partnerships that have developed innovative approaches that address the workforce needs of business while also effectively helping workers find good jobs with good wages and promising career pathways in the information technology industry.&lt;/div&gt;&lt;div style=&quot;font-family: Tahoma, Geneva, sans-serif; font-size: 13px; line-height: 17px; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;iframe align=&quot;left&quot; frameborder=&quot;0&quot; marginheight=&quot;0&quot; marginwidth=&quot;0&quot; scrolling=&quot;no&quot; src=&quot;http://rcm.amazon.com/e/cm?t=widgetsamazon-20&amp;amp;o=1&amp;amp;p=8&amp;amp;l=bpl&amp;amp;asins=0789742535&amp;amp;fc1=000000&amp;amp;IS2=1&amp;amp;lt1=_blank&amp;amp;m=amazon&amp;amp;lc1=0000FF&amp;amp;bc1=000000&amp;amp;bg1=FFFFFF&amp;amp;f=ifr&quot; style=&quot;align: left; height: 245px; padding-right: 10px; padding-top: 5px; width: 131px;&quot;&gt;&lt;/iframe&gt;&lt;iframe align=&quot;left&quot; frameborder=&quot;0&quot; marginheight=&quot;0&quot; marginwidth=&quot;0&quot; scrolling=&quot;no&quot; src=&quot;http://rcm.amazon.com/e/cm?t=widgetsamazon-20&amp;amp;o=1&amp;amp;p=8&amp;amp;l=bpl&amp;amp;asins=0470534834&amp;amp;fc1=000000&amp;amp;IS2=1&amp;amp;lt1=_blank&amp;amp;m=amazon&amp;amp;lc1=0000FF&amp;amp;bc1=000000&amp;amp;bg1=FFFFFF&amp;amp;f=ifr&quot; style=&quot;align: left; height: 245px; padding-right: 10px; padding-top: 5px; width: 131px;&quot;&gt;&lt;/iframe&gt;This set of workforce solutions is based on the information technology industry&#39;s priorities that address issues such as:&lt;/div&gt;&lt;ul style=&quot;font-family: Tahoma, Geneva, sans-serif; font-size: 13px; line-height: 17px; list-style-image: url(http://www.doleta.gov/images/bullet-black.gif); list-style-position: initial; list-style-type: square; margin-bottom: 0.5em; margin-left: 1em; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;&lt;li style=&quot;margin-bottom: 0.5em; margin-left: 1em; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;Over 90% of IT workers are performing jobs outside the IT industry, therefore it is necessary to have both IT training and complementary training in a respective business sector such as health care, manufacturing, and financial services.&lt;/li&gt;
&lt;li style=&quot;margin-bottom: 0.5em; margin-left: 1em; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;Government may serve as an honest broker for specific issues such as promotion and image, forecasting the future of the workforce and their training needs.&lt;/li&gt;
&lt;li style=&quot;margin-bottom: 0.5em; margin-left: 1em; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;Educators should expose kids to the new dynamic, global workplace and teach more about today&#39;s business culture.&lt;/li&gt;
&lt;li style=&quot;margin-bottom: 0.5em; margin-left: 1em; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;Incumbent worker training has helped retain workers.&lt;/li&gt;
&lt;li style=&quot;margin-bottom: 0.5em; margin-left: 1em; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;When recruiting for high-end jobs, the industry sees a need to develop soft skills, as well as transferable &quot;umbrella skills.&quot;&lt;/li&gt;
&lt;/ul&gt;&lt;div style=&quot;font-family: Tahoma, Geneva, sans-serif; font-size: 13px; line-height: 17px; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;&quot;&gt;The grants are intended to provide genuine solutions, leadership, and models for partnerships that can be replicated in different parts of the country.&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://computerscience113.blogspot.com/feeds/4215822706129503727/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://computerscience113.blogspot.com/2011/02/statewide-solutions-to-address.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/4215822706129503727'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/4215822706129503727'/><link rel='alternate' type='text/html' href='http://computerscience113.blogspot.com/2011/02/statewide-solutions-to-address.html' title='Statewide Solutions to Address Information Technology Industry Workforce Needs'/><author><name>fabrice otepa</name><uri>http://www.blogger.com/profile/13017780185308872185</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-3111627990970613378.post-320767731312875730</id><published>2011-02-20T06:44:00.000-08:00</published><updated>2011-02-22T14:57:05.002-08:00</updated><title type='text'>BRIEF ABOUT COMPUTER SCIENCE</title><content type='html'>DEFINITION ABOUT COMPUTER SCIENCE&lt;br /&gt;
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&lt;img height=&quot;244&quot; src=&quot;http://www.rhythmeering.com/wp-content/uploads/2009/07/it.jpg&quot; width=&quot;320&quot; /&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;line-height: 19px;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&lt;b&gt;Computer science&lt;/b&gt;&amp;nbsp;or&amp;nbsp;&lt;b&gt;computing science&lt;/b&gt;&amp;nbsp;(abbreviated&amp;nbsp;&lt;b&gt;CS&lt;/b&gt;) is the study of the theoretical foundations of&amp;nbsp;information&amp;nbsp;andcomputation&amp;nbsp;and of practical techniques for their implementation and application in&amp;nbsp;computer&amp;nbsp;systems.&lt;/span&gt;&lt;br /&gt;
&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;&amp;nbsp;Computer scientists inventalgorithmic&amp;nbsp;processes that create, describe, and transform information and formulate suitable&amp;nbsp;abstractions&amp;nbsp;to model complex systems.&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;Computer science has many&amp;nbsp;sub-fields; some, such as&amp;nbsp;computational complexity theory, study the properties of&amp;nbsp;computational problems, while others, such as&amp;nbsp;computer graphics, emphasize the computation of specific results. Still others focus on the challenges in implementing computations. For example,&amp;nbsp;programming language theory&amp;nbsp;studies approaches to describe computations, while&amp;nbsp;computer programming&amp;nbsp;applies specific&amp;nbsp;programming languages&amp;nbsp;to solve specific computational problems, and&amp;nbsp;human-computer interaction&amp;nbsp;focuses on the challenges in making computers and computations useful, usable, and universally accessible to&amp;nbsp;people.&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: &#39;Trebuchet MS&#39;, sans-serif;&quot;&gt;The general public sometimes confuses computer science with careers that deal with computers (such as&amp;nbsp;information technology), or think that it relates to their own experience of computers, which typically involves activities such as gaming, web-browsing, and word-processing. However, the focus of computer science is more on understanding the properties of the programs used to implement software such as games and web-browsers, and using that understanding to create new programs or improve existing ones.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-2&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-2&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; text-decoration: none; white-space: nowrap;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;color: black;&quot;&gt;&lt;span style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; text-decoration: none; white-space: nowrap;&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;Apple-style-span&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; white-space: nowrap;&quot;&gt;3&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;iframe allowfullscreen=&#39;allowfullscreen&#39; webkitallowfullscreen=&#39;webkitallowfullscreen&#39; mozallowfullscreen=&#39;mozallowfullscreen&#39; width=&#39;320&#39; height=&#39;266&#39; src=&#39;https://www.youtube.com/embed/zQLUPjefuWA?feature=player_embedded&#39; frameborder=&#39;0&#39;&gt;&lt;/iframe&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;iframe allowfullscreen=&#39;allowfullscreen&#39; webkitallowfullscreen=&#39;webkitallowfullscreen&#39; mozallowfullscreen=&#39;mozallowfullscreen&#39; width=&#39;320&#39; height=&#39;266&#39; src=&#39;https://www.youtube.com/embed/k6U-i4gXkLM?feature=player_embedded&#39; frameborder=&#39;0&#39;&gt;&lt;/iframe&gt;&lt;/div&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;The early foundations of what would become computer science predate the invention of the modern&amp;nbsp;digital computer. Machines for calculating fixed numerical tasks, such as the&amp;nbsp;abacus, have existed since antiquity.&amp;nbsp;Wilhelm Schickard&amp;nbsp;designed the first mechanical calculator in 1623, but did not complete its construction.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-3&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-3&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[4]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;Blaise Pascaldesigned and constructed the first working mechanical calculator, the&amp;nbsp;Pascaline, in 1642.&amp;nbsp;Charles Babbage&amp;nbsp;designed a&amp;nbsp;difference engine&amp;nbsp;and then a general-purposeAnalytical Engine&amp;nbsp;in&amp;nbsp;Victorian&amp;nbsp;times&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-4&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-4&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[5]&lt;/a&gt;&lt;/sup&gt;, for which&amp;nbsp;Ada Lovelace&amp;nbsp;wrote a manual. Because of this work she is regarded today as the world&#39;s first&amp;nbsp;programmer.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-5&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-5&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[6]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;Around 1900,punch-card machines&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-6&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-6&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[7]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;were introduced. However, these machines were constrained to perform a single task, or at best some subset of all possible tasks.&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;During the 1940s, as newer and more powerful computing machines were developed, the term&amp;nbsp;&lt;i&gt;computer&lt;/i&gt;&amp;nbsp;came to refer to the machines rather than their human predecessors.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-7&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-7&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[8]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;As it became clear that computers could be used for more than just mathematical calculations, the field of computer science broadened to studycomputation&amp;nbsp;in general. Computer science began to be established as a distinct academic discipline in the 1950s and early 1960s.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-Denning_cs_discipline_8-0&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-Denning_cs_discipline-8&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[9]&lt;/a&gt;&lt;/sup&gt;&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-9&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-9&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[10]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;The first computer science degree program in the United States was formed at&amp;nbsp;Purdue University&amp;nbsp;in 1962.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-10&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-10&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[11]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;Since practical computers became available, many applications of computing have become distinct areas of study in their own right.&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;Although many initially believed it was impossible that computers themselves could actually be a scientific field of study, in the late fifties it gradually became accepted among the greater academic population.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-Levy1984_11-0&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-Levy1984-11&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[12]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;It is the now well-known&amp;nbsp;IBM&amp;nbsp;brand that formed part of the computer science revolution during this time. IBM (short for International Business Machines) released the IBM 704 and later the IBM 709 computers, which were widely used during the exploration period of such devices. &quot;Still, working with the IBM [computer] was frustrating...if you had misplaced as much as one letter in one instruction, the program would crash, and you would have to start the whole process over again&quot;.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-Levy1984_11-1&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-Levy1984-11&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[12]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;During the late 1950s, the computer science discipline was very much in its developmental stages, and such issues were commonplace.&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;Time has seen significant improvements in the usability and effectiveness of computer science technology. Modern society has seen a significant shift from computers being used solely by experts or professionals to a more widespread user base. Initially, computers were quite costly, and for their most-effective use, some degree of human aid was needed, in part by professional computer operators. However, as computers became widespread and far more affordable, less human assistance was needed, although residues of the original assistance still remained.&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;/div&gt;&lt;h3 style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; border-bottom-color: initial; border-bottom-style: none; border-bottom-width: initial; color: black; font-weight: bold; margin-bottom: 0.3em; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0.17em; padding-top: 0.5em; width: auto;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;span class=&quot;mw-headline&quot; id=&quot;Applied_computer_science&quot;&gt;Applied computer science&lt;/span&gt;&lt;/span&gt;&lt;/h3&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;Despite its name, a significant amount of computer science does not involve the study of computers themselves. Because of this, several alternative names have been proposed. Certain departments of major universities prefer the term&amp;nbsp;&lt;i&gt;computing science&lt;/i&gt;, to emphasize precisely that difference. Danish scientist&amp;nbsp;Peter Naur&amp;nbsp;suggested the term&amp;nbsp;&lt;i&gt;datalogy&lt;/i&gt;, to reflect the fact that the scientific discipline revolves around data and data treatment, while not necessarily involving computers. The first scientific institution to use the term was the Department of Datalogy at the University of Copenhagen, founded in 1969, with Peter Naur being the first professor in datalogy. The term is used mainly in the Scandinavian countries. Also, in the early days of computing, a number of terms for the practitioners of the field of computing were suggested in the&lt;i&gt;Communications of the ACM&lt;/i&gt;&amp;nbsp;–&amp;nbsp;&lt;i&gt;turingineer&lt;/i&gt;,&amp;nbsp;&lt;i&gt;turologist&lt;/i&gt;,&amp;nbsp;&lt;i&gt;flow-charts-man&lt;/i&gt;,&amp;nbsp;&lt;i&gt;applied meta-mathematician&lt;/i&gt;, and&amp;nbsp;&lt;i&gt;applied epistemologist&lt;/i&gt;.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-22&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-22&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[23]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;Three months later in the same journal,&lt;i&gt;comptologist&lt;/i&gt;&amp;nbsp;was suggested, followed next year by&amp;nbsp;&lt;i&gt;hypologist&lt;/i&gt;.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-23&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-23&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[24]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;The term&amp;nbsp;&lt;i&gt;computics&lt;/i&gt;&amp;nbsp;has also been suggested.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-24&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-24&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[25]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;In continental Europe, names such as&amp;nbsp;&lt;i&gt;informatique&lt;/i&gt;(French),&amp;nbsp;&lt;i&gt;Informatik&lt;/i&gt;&amp;nbsp;(German) or&amp;nbsp;&lt;i&gt;informatica&lt;/i&gt;&amp;nbsp;(Dutch), derived from information and possibly mathematics or automatic, are more common than names derived from computer/computation.&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;The renowned computer scientist&amp;nbsp;Edsger Dijkstra&amp;nbsp;stated, &quot;Computer science is no more about computers than astronomy is about telescopes.&quot; The design and deployment of computers and computer systems is generally considered the province of disciplines other than computer science. For example, the study of&amp;nbsp;computer hardware&amp;nbsp;is usually considered part of&amp;nbsp;computer engineering, while the study of commercial&amp;nbsp;computer systems&amp;nbsp;and their deployment is often called&amp;nbsp;information technology&amp;nbsp;or&amp;nbsp;information systems. However, there has been much cross-fertilization of ideas between the various computer-related disciplines. Computer science research has also often crossed into other disciplines, such as&amp;nbsp;philosophy,&amp;nbsp;cognitive science,&amp;nbsp;linguistics,&amp;nbsp;mathematics,&amp;nbsp;physics,&amp;nbsp;statistics, and&amp;nbsp;economics.&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;Computer science is considered by some to have a much closer relationship with mathematics than many scientific disciplines, with some observers saying that computing is a mathematical science.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-Denning_cs_discipline_8-2&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-Denning_cs_discipline-8&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[9]&lt;/a&gt;&lt;/sup&gt;&amp;nbsp;Early computer science was strongly influenced by the work of mathematicians such as&amp;nbsp;Kurt Gödel&amp;nbsp;and&amp;nbsp;Alan Turing, and there continues to be a useful interchange of ideas between the two fields in areas such as&amp;nbsp;mathematical logic,&amp;nbsp;category theory,&amp;nbsp;domain theory, and&amp;nbsp;algebra.&lt;/span&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;iframe allowfullscreen=&#39;allowfullscreen&#39; webkitallowfullscreen=&#39;webkitallowfullscreen&#39; mozallowfullscreen=&#39;mozallowfullscreen&#39; width=&#39;320&#39; height=&#39;266&#39; src=&#39;https://www.youtube.com/embed/KkMDCCdjyW8?feature=player_embedded&#39; frameborder=&#39;0&#39;&gt;&lt;/iframe&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;The relationship between computer science and&amp;nbsp;software engineering&amp;nbsp;is a contentious issue, which is further muddied by&amp;nbsp;disputes&amp;nbsp;over what the term &quot;software engineering&quot; means, and how computer science is defined.&amp;nbsp;David Parnas, taking a cue from the relationship between other engineering and science disciplines, has claimed that the principal focus of computer science is studying the properties of computation in general, while the principal focus of software engineering is the design of specific computations to achieve practical goals, making the two separate but complementary disciplines.&lt;sup class=&quot;reference&quot; id=&quot;cite_ref-25&quot; style=&quot;font-style: normal; font-weight: normal; line-height: 1em;&quot;&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Computer_science#cite_note-25&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;&lt;span style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;color: #0645ad;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; white-space: nowrap;&quot;&gt;26&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; color: #0645ad; text-decoration: none; white-space: nowrap;&quot;&gt;]&lt;/span&gt;&lt;/a&gt;&lt;/sup&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;img src=&quot;http://www.westmont.edu/_offices/it/images/righttop.jpg&quot; /&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style=&quot;line-height: 1.5em; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.4em;&quot;&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-family: Arial, Helvetica, sans-serif;&quot;&gt;The academic, political, and funding aspects of computer science tend to depend on whether a department formed with a mathematical emphasis or with an engineering emphasis. Computer science departments with a mathematics emphasis and with a numerical orientation consider alignment with&amp;nbsp;computational science. Both types of departments tend to make efforts to bridge the field educationally if not across all research.&lt;/span&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://computerscience113.blogspot.com/feeds/320767731312875730/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://computerscience113.blogspot.com/2011/02/computer-science.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/320767731312875730'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/3111627990970613378/posts/default/320767731312875730'/><link rel='alternate' type='text/html' href='http://computerscience113.blogspot.com/2011/02/computer-science.html' title='BRIEF ABOUT COMPUTER SCIENCE'/><author><name>fabrice otepa</name><uri>http://www.blogger.com/profile/13017780185308872185</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-3111627990970613378.post-5563513823789191565</id><published>2011-02-20T06:36:00.000-08:00</published><updated>2011-02-20T06:36:45.174-08:00</updated><title type='text'>Social sciences - 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