text:
User talk:Peterrawsthorne

Copyright problems on photos
Hello. There is a problem with one or more files you have uploaded. Every file you upload must have a clear statement of the copyright position. If you took the photos yourself, add PD-self if you are placing it unreservedly in the public domain. If you wish to retain minimal rights, add Cc-by-sa-3.0. If you did not take the photo, please add an explanation of why it can be hosted here. I am afraid that if you do not do this, the file wil be deleted. Let me know if you have any problems.--Collingwood (talk) 12:11, 6 July 2012 (UTC)

I am very sorry if the above was unclear. I confirm that File:PPMCycle.jpg is fine. However, the following require copyright information:

 * File:MobileDevice.svg
 * File:MvcPatternwMobile.jpg
 * File:MvcPattern.jpg
 * File:RedBadgeSrvr.png
 * File:RedBadgeBusi.png
 * File:GreenBadgeSrvr.png
 * File:GreenBadgeBusi.png
 * File:OrangeBadgeSrvr.png
 * File:OrangeBadgeBusi.png
 * File:YellowBadgeSrvr.png
 * File:YellowBadgeBusi.png
 * File:RedBadgeMobi.png
 * File:GreenBadgeMobi.png
 * File:OrangeBadgeMobi.png
 * File:WhiteBadgeSrvr.png
 * File:WhiteBadgeBusi.png
 * File:YellowBadgeMobi.png
 * File:WhiteBadgeMobi.png
 * File:RackedServers.svg

Thank you for your many contributions. Please let me know if you have any problems.--Collingwood (talk) 19:58, 6 July 2012 (UTC)

Files Missing License Information
Thank you for uploading files to Wikiversity. See Media for copyright and license requirements for Wikiversity files. All files must have copyright and/or license information added to the file.

Instructions for adding copyright and/or license information are available at License tags. Files must be updated within seven days or they may be removed without further notice. See Requests For Deletion for more information.

The following files are missing copyright and/or license information:
 * File:1css-Nhtml.jpg
 * File:Badge-diagram-2.2.jpg
 * File:BadgeJSON.jpg
 * File:DeviceAndroid.JPG
 * File:DeviceDesktop.jpg
 * File:GreenBadgeBusi.png
 * File:GreenBadgeMobi.png
 * File:GreenBadgeSrvr.png
 * File:LoadDesktopCSS.jpg
 * File:LoadPhoneCSS.jpg
 * File:LoadTabletCSS.jpg
 * File:MobileWebApplication.ConceptMap.jpg
 * File:MvcPattern.jpg
 * File:MvcPatternwMobile.jpg
 * File:Ncss-1html.jpg
 * File:OBI-DisplayerTechStack.png
 * File:OBI-EarnerTechStack.png
 * File:OBI-IssuerTechStack.png
 * File:OnPhDCandidateBadge.png
 * File:RackedServers.svg
 * File:RedBadgeBusi.png
 * File:RedBadgeMobi.png
 * File:RedBadgeSrvr.png
 * File:Tech-diagram-v3 updated.png

MaintenanceBot (discuss • contribs) 03:51, 11 November 2013 (UTC)

Files Missing Information
Thanks for uploading files to Wikiversity. All files must have source and license information to stay at Wikiversity. The following files are missing and/or License tags, and will be deleted if the missing information is not added. See Uploading files for more information.

 * File:Coding.svg

MaintenanceBot (discuss • contribs) 15:30, 16 April 2016 (UTC)

title: User talk:Peterrawsthorne


text:
User talk:Arided/ParagogyPaper

My view is that the paper would be best if it was refactored so that we had a section for each of the 5 paragogical principles, instead of repeating them within each theme we take up. I think it would look better to repeat the themes within the principles. Arided 15:56, 22 January 2011 (UTC)

The outline might look like the one here: http://piratepad.net/paragogy-outline Arided 16:20, 22 January 2011 (UTC)
 * http://www.danoff.org/paragogy-outline-latest-20110122.html version from --Charles Jeffrey Danoff 19:50, 22 January 2011 (UTC)

We should review the docs at http://p2pfoundation.net/Category:Education --Arided 18:08, 16 February 2011 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:Arided/ParagogyPaper


text:
User talk:MigueldelosSantos

 Hello MigueldelosSantos, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twiter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Ottava Rima (talk) 16:15, 22 January 2011 (UTC)

title: User talk:MigueldelosSantos


text:
User talk:Kierkk

 Hello Kierkk, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twiter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Ottava Rima (talk) 16:15, 22 January 2011 (UTC)

title: User talk:Kierkk


text: File:PEA1 lecture40 figure1.svg

title: File:PEA1 lecture40 figure1.svg


text: File:PEA1 lecture40 figure2.svg

title: File:PEA1 lecture40 figure2.svg


text:
User talk:Ivan Gospodinov

 Hello Ivan Gospodinov, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twiter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Ottava Rima (talk) 17:17, 22 January 2011 (UTC)

title: User talk:Ivan Gospodinov


text:
User talk:Tensils99/Dr. Jagatjit S Kohli

I have moved this page to user space to give the author time to recover the text for other possible use. The page was inappropriate for Wikiversity mainspace for sure, and probably anywhere here. If there are any questions, please contact me at User talk:Abd or by email through the Wikiversity email interface. --Abd 18:10, 22 January 2011 (UTC)


text:
User:Raghith/guestbook

'' Thanks for visiting my Guest Book.Please sign by adding (Optional friendly message) ~

title: User:Raghith/guestbook


title: File:Fe1.s11.mtg10.djvu


text:
Template:T5title1

= =

title: Template:T5title1


text:
User:Egm6341.s11.team5.shin/HW

Problem statement
Let $$\displaystyle f(x)= \frac{e^x-1}{x}$$. Find $$\displaystyle \lim_{x \to 0}f(x)$$ and plot $$\displaystyle f(x)$$ for $$\displaystyle x \in [0,1] $$.

Solution
Using L'Hospital's Rule, the limit can be evaluated. L'Hospital's Rule:
 * $$\lim_{x \to 0}\frac{g(x)}{h(x)}=\lim_{x \to 0}\frac{g^{'}(x)}{h^{'}(x)}$$

Applying the Rule:

As a result, the limit is shown below.
 * $$\displaystyle g(x)=e^x-1$$ || $$\displaystyle g^{'}(x)=e^x$$
 * $$\displaystyle h(x)=x$$ || $$\displaystyle h^{'}(x)=1$$
 * }
 * $$\displaystyle h(x)=x$$ || $$\displaystyle h^{'}(x)=1$$
 * }
 * $$\lim_{x \to 0}\frac{e^x-1}{x}=\lim_{x \to 0}\frac{e^x}{1}$$
 * $$\lim_{x \to 0}\frac{e^x}{1}=\frac{1}{1}=1$$

Plot: Matlab code:

Problem statement
Find $$\displaystyle P_n(x)$$ and $$\displaystyle R_{n+1}(x)$$ of $$\displaystyle e^x$$ and $$\displaystyle \frac{e^x-1}{x}$$.

Solution
From the class note, $$\displaystyle P_n(x)$$ and $$\displaystyle R_{n+1}(x)$$ is defined as

title: User:Egm6341.s11.team5.shin/HW


text:
User:Egm6341.s11.team5.shin/HW1

= Problem 1 - L'Hôpital's rule = From (meeting 3 page 1)

If $$\displaystyle f(x)= \frac{e^x-1}{x}$$,

Find

 * $$\displaystyle \lim_{x \to 0}f(x)$$ and plot $$\displaystyle f(x)$$ for $$\displaystyle x \in [0,1] $$.

Solution
Using L'Hospital's Rule, the limit can be evaluated. L'Hospital's Rule:
 * {| style="width:100%" border="0" align="left"

\lim_{x \to 0}\frac{g(x)}{h(x)}=\lim_{x \to 0}\frac{g^{'}(x)}{h^{'}(x)} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (1)
 * }
 * }

Applying the Rule:

As a result, the limit is computed as follows.
 * $$\displaystyle g(x)=e^x-1$$, || $$\displaystyle g^{'}(x)=e^x$$
 * $$\displaystyle h(x)=x$$, || $$\displaystyle h^{'}(x)=1$$
 * }
 * $$\displaystyle h(x)=x$$, || $$\displaystyle h^{'}(x)=1$$
 * }
 * $$\lim_{x \to 0}\frac{e^x-1}{x}=\lim_{x \to 0}\frac{e^x}{1}$$
 * $$\lim_{x \to 0}\frac{e^x}{1}=\frac{1}{1}=1$$

Hence,
 * {| style="width:100%" border="0" align="left"

$$\displaystyle \ \lim_{x\rightarrow 0} \frac{e^{x}-1}{x} \ = \ 1 $$
 * style="width:30%; padding:10px; border:2px solid #8888aa" align="center" |
 * style="width:30%; padding:10px; border:2px solid #8888aa" align="center" |
 * }
 * }
 * }

Plot: Matlab code:
 * {| style="width:100%" border="0" align="left"

Plot: Matlab code:
 * style="width:30%; padding:10px; border:1px solid #888888" align="center" |
 * style="width:30%; padding:10px; border:1px solid #888888" align="center" |
 * }
 * }
 * }
 * {| style="width:100%" border="0" align="left"

= Problem 2 - Taylor series expansion = From (meeting 3 page 4)
 * style="width:30%; padding:10px; border:1px solid #888888" align="center" |
 * style="width:30%; padding:10px; border:1px solid #888888" align="center" |
 * }
 * }
 * }

If $$\displaystyle f(x)= \frac{e^x-1}{x}$$,

Find

 * $$\displaystyle P_n(x)$$ and $$\displaystyle R_{n+1}(x)$$ of $$\displaystyle e^x$$ and $$\displaystyle \frac{e^x-1}{x}$$.

Solution
Through Taylor series, a function $$\displaystyle f(x) $$ can be decomposed into $$\displaystyle P_n(x)$$ and $$\displaystyle R_{n+1}(x)$$. From the lecture notes p.3-3, $$\displaystyle P_n(x)$$ and $$\displaystyle R_{n+1}(x)$$ is defined as

 * {| style="width:100%" border="0" align="left"

P_{n}(x)=f(x_{0})+\frac{(x-x_{0})}{1!}f^{(1)}(x_{0})+\cdots+\frac{(x-x_{0})^{n}}{n!}f^{(n)}(x_{0}) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (2)
 * }
 * }

 * {| style="width:100%" border="0" align="left"

R_{n+1}(x)=\frac{1}{n!}\int_{x_{0}}^{x}(x-t)^{n}f^{(n+1)}(t)dt=\frac{(x-x_{0})^{n+1}}{(n+1)!}f^{(n+1)}(\xi), \quad \xi\in[x_{0},x] $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (3)
 * }
 * }
 * }

 * $$\displaystyle f(x)=e^x $$
 * We know that n-th derivative of function $$\displaystyle e^x$$.
 * {| style="width:100%" border="0" align="left"

\frac{d^{(n)}}{dx^{(n)}}(e^x) = e^x $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (4)
 * }
 * Substitute Eq.(4) into Eq.(2) to obtain $$\displaystyle P_n(x)$$.
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

P_n(x)=e^{x_0}+\frac{(x-x_0)}{1!}e^{x_0}+\cdots+\frac{(x-x_0)^n}{n!}e^{x_0} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (5)
 * }
 * Simplify Eq.(5).
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

\begin{align} P_n(x)&=\bigl(1+\frac{(x-x_0)}{1!}+\cdots+\frac{(x-x_0)^n}{n!}\bigr)e^{x_0}\\ &=\sum_{i=0}^{n}\bigl(\frac{(x-x_0)^i}{i!}\bigr)e^{x_0} \end{align} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (6)
 * }
 * }

 * Substitute Eq.(4) into Eq.(3) to obtain $$\displaystyle R_{n+1}(x)$$.
 * {| style="width:100%" border="0" align="left"

R_{n+1}(x)=\frac{(x-x_{0})^{n+1}}{(n+1)!}e^{\xi}, \quad \xi\in[x_{0},x] $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (7)
 * }
 * The result of Taylor series expansion on $$\displaystyle f(x)=e^x $$ is shown below.
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

$$\displaystyle \begin{align} P_n(x)&=\sum_{i=0}^{n}\bigl(\frac{(x-x_0)^i}{i!}\bigr)e^{x_0} \\ R_{n+1}(x)&=\frac{(x-x_{0})^{n+1}}{(n+1)!}e^{\xi}, \quad \xi\in[x_{0},x] \end{align} $$
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * }
 * Also, the expansion becomes as below if $$\displaystyle x_0=0 $$.
 * }
 * Also, the expansion becomes as below if $$\displaystyle x_0=0 $$.

 * {| style="width:100%" border="0" align="left"

$$\displaystyle \begin{align} P_n(x)&=\sum_{i=0}^{n}\bigl(\frac{x^i}{i!}\bigr) \\ R_{n+1}(x)&=\frac{x^{n+1}}{(n+1)!}e^{\xi}, \quad \xi\in[0,x] \end{align} $$
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * $$\displaystyle (8)$$
 * }
 * }

 * $$\displaystyle f(x)=\frac{e^x-1}{x} $$
 * To perform Taylor series expansion on $$\displaystyle f(x)=\frac{e^x-1}{x} $$, we need to exploit Eq.(8). Assume the result of the expansion is $$\displaystyle P^{'}_n(x) $$ and the remainder is $$\displaystyle R^{'}_n(x) $$.
 * Then, $$\displaystyle P^{'}_n(x) $$ can be obtained as follows.
 * {| style="width:100%" border="0" align="left"

\begin{align} P_n(x)-1&=\sum_{i=0}^{n}\frac{x^i}{i!}-1 \\ &=\bigl(1+\sum_{i=1}^{n}\frac{x^i}{i!}\bigr)-1 \\ &=\sum_{i=1}^{n}\frac{x^i}{i!} \end{align} $$ \begin{align} P^'_n(x)&=\frac{P_n(x)-1}{x} \\ &=\sum_{i=1}^{n}\frac{x^{i-1}}{i!} \end{align} $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (9) $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (10) $$
 * }
 * Similarly, $$\displaystyle R^'_{n+1}(x)$$ can be computed. Note here that the term $$\displaystyle -1$$ in the function $$\displaystyle f(x)$$ is already taken into account in $$\displaystyle P^'_n(x)$$. Therefore, $$\displaystyle R^'_{n+1}(x)$$ can be computed by dividing $$\displaystyle R_{n+1}(x)$$ by $$\displaystyle x $$.
 * {| style="width:100%" border="0" align="left"

\begin{align} R^'_{n+1}(x)&=\frac{R_{n+1}(x)}{x} \\ &=\frac{x^n}{(n+1)!}e^{\xi}, \quad \xi\in[0,x] \end{align} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (11)
 * }
 * Hence, the expansion result of $$\displaystyle f(x)=\frac{e^x-1}{x} $$ is shown as:
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

$$\displaystyle \begin{align} P^'_n(x)&=\sum_{i=1}^{n}\frac{x^{i-1}}{i!} \\ R^'_{n+1}(x)&=\frac{x^n}{(n+1)!}e^{\xi}, \quad \xi\in[0,x] \end{align} $$
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * $$\displaystyle (12)$$
 * }
 * }

title: User:Egm6341.s11.team5.shin/HW1


text:
Template:T5title2

Comment :

title: Template:T5title2


text:
Template:T5box1

Comment:
 * {| style="width:100% padding:0px" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |

 * }
 * }
 * }

title: Template:T5box1


text: File:Paragogy-final.pdf

title: File:Paragogy-final.pdf


text:
User:Eml5526.s11.team3.akj

 * User:Eml5526.s11.team3.akj/Homework 1
 * User:Eml5526.s11.team3.akj/Homework 2
 * User:Eml5526.s11.team3.akj/Homework 3
 * User:Eml5526.s11.team3.akj/Homework 4
 * User:Eml5526.s11.team3.akj/Homework 5
 * User:Eml5526.s11.team3.akj/Homework 6
 * User:Eml5526.s11.team3.akj/Homework 7

title: User:Eml5526.s11.team3.akj


title: File:Hw1.4fx.jpg


title: File:Hw1.4gx.jpg


text:
User:Egm6341.s11.team2.lee

=Problem 1.3=

Find
Plot f, g and find $$ {\left\| f \right\|_\infty } {\left\| g \right\|_\infty } {\left\| {f - g} \right\|_\infty }$$

Given
$$ f(x) = 3x + 5{x^3},x \in [0,1]; g(x) = \sinh x,x \in [0,1] $$

Solution
Because $$ {f^'}(x) = 3 + 15{x^2} > 0,\;\;x \in [0,1], {g^'}(x) = {(\sinh x)^'} = {(\frac{2})^'} = \frac{2} > 0,\;\;x \in [0,1] {\left( {f(x) - g(x)} \right)^'} = 3 + 15{x^2} - \cosh x > 0,\;\;x \in [0,1]$$

Which means that f(x) keeps increasing at [0,1], and g(x) and f(x)-g(x) as well

So $$ {\left\| f \right\|_\infty } = \max \left| {f(x)} \right| = {\left. {\left| {f(x)} \right|} \right|_{x = 1}} = 8 $$

$$ {\left\| g \right\|_\infty } = \max \left| {g(x)} \right| = {\left. {\left| {g(x)} \right|} \right|_{x = 1}} = \frac{1}{2}(e - \frac{1}{e}) \approx 1.71520 $$

$$ {\left\| {f - g} \right\|_\infty } = \max \left| {f(x) - g(x)} \right| = {\left. {\left| {f(x) - g(x)} \right|} \right|_{x = 1}} = 8 - \frac{1}{2}(e - \frac{1}{e}) \approx 6.82479  $$

Using the following Fortran code

program main real,allocatable::x,f,g integer::i,n real::e=2.71828 open (unit=10, file="input", status="old") read(10,*)n allocate(x(n+1),f(n+1),g(n+1)) do i=1,n+1 x(i)=-1.0+2.0/n*(i-1) f(i)=3.0*x(i)+5*x(i)**3 g(i)=0.5*(e**x(i)-e**(-1.0*x(i))) end do  open (unit=11, file="hw1.4.plt", status="replace") do i=1,n+1 write(11,"(3F12.4)") x(i),f(i),g(i) end do   end program main

We can easily get the image of f(x) and g(x) as following

title: User:Egm6341.s11.team2.lee


text:
User:EML5526.s11.team6

Useful Links
Egm6341 Course Wiki

Homework
Homework #1

Homework #2

Homework #3

Homework #4

Members
Lee

title: User:EML5526.s11.team6


text:
User:Eml5526.s11.team6/hwk1

Homework 1 = Elastic Bar PDE, Dynamic situation.=

Find
Derive the following equation by performing a balance of forces:

$$ \frac{\partial}{\partial x}\left [ A(x)E(x)\frac{\partial u}{\partial x} \right ]+f(x,t)=A(x) \rho(x)\cdot \frac{\partial ^{2}u}{\partial t^{2}}\ $$

Solution
Consider the FBD of an infinitesimally small section of length dx of the 1-D elastic bar with varying material properties at a distance x from the origin. Where, A(x) - Varying cross section of the elastic bar, E(x) - Modulus of elasticity, rho (x) - Mass density, u - Displacement constrained only to x- axis (1-D bar), t - Time.

 * {| style="width:100%" border="0"

Where, $$\; {A}'=A(x) (dx)\cdot \rho (x)\cdot\frac{\partial^{2}u }{\partial t^{2}} =mass\cdot acceleration=Inertia\, Force$$
 * $$\displaystyle (Eq. 1.1) $$
 * }
 * }

As per Newton's law of motion, the involved forces should contribute to inertia force.

Force equilibrium in the x-direction yields:

$$\sum F_{x}=0 $$

 * {| style="width:100%" border="0"

$$\sum F_{x}=-N(x,t)+N(x+dx,t)+f(x,t) dx-m(x)\cdot \frac{\partial ^{2}u}{\partial t^{2}}=0$$
 * $$\displaystyle (Eq. 1.2) $$
 * }
 * }

 * {| style="width:100%" border="0"

Where, $$\;\; m(x)=A(x)(dx)\rho (x)$$
 * $$\displaystyle (Eq. 1.3) $$
 * }
 * }

Including Taylor series expansion for $$N(x+dx,t)$$ and neglecting the higher order terms (h.o.t) yields:

$$ \cancel {-N(x,t)}+[\cancel {N(x,t)}+\frac {\partial }{\partial x}(N(x,t))+(h.o.t)]+f(x,t)=\frac{m(x)}{dx}\cdot\frac{\partial ^{2} u}{\partial t^{2}}$$

 * {| style="width:100%" border="0"

$$\frac{\partial }{\partial x}(N(x,t))+f(x,t)=\frac{m(x)}{dx}\cdot\frac{\partial ^{2} u}{\partial t^{2}}$$
 * $$\displaystyle (Eq. 1.4) $$
 * }
 * }

 * {| style="width:100%" border="0"

$$Also,\; N(x,t)=A(x) \cdot \sigma (x)=A(x) \cdot [E(x)\cdot \epsilon (x,t)] $$
 * $$\displaystyle (Eq. 1.5) $$
 * }
 * }

 * {| style="width:100%" border="0"

$$\;\;\;\;\;\;\;\;\;\;\;\Rightarrow N(x,t)= A(x)\cdot E(x) \cdot\frac{\partial u}{\partial x}(x,t)$$
 * $$\displaystyle (Eq. 1.6) $$
 * }
 * }

Thus proving:

 * {| style="width:100%" border="0"

 * $$\displaystyle (Eq. 1.7) $$
 * }
 * }

= Modified Case=

Find
Discuss the case in which the bar has a rectangular cross section shown below.

Solution
We have from reference of class notes for mtg 2, eq(3) pg.2-3,

 * {| style="width:100%" border="0"

$$m=\rho (x) \cdot A(x) $$
 * $$\displaystyle (Eq. 2.1) $$
 * }
 * }

Also with reference to class notes for mtg 6, pg 6-1, point 2), for A(x)=bˑh(h),

 * {| style="width:100%" border="0"

$$m=\rho \left ( x+\frac{dx}{2} \right )\cdot \frac{1}{2}\left [ h(x)+h(x+dx) \right ]b $$
 * $$\displaystyle (Eq. 2.2) $$
 * }
 * }

Substituting Eq 2.1 and Eq 2.2 into Eq 1.7 for case of A(x)=bˑh(x),
 * {| style="width:100%" border="0"

$$\frac{\partial}{\partial x}\left [ \left ( b\cdot h(x)\cdot E(x)\cdot \frac{\partial u}{\partial x}\right ) \right ]+f(x,t)=\frac{1}{2}\left [ h(x)+h(x+dx) \right ]\rho (x+dx)\cdot \frac{\partial^{2} u}{\partial t^{2}}\cdot b$$
 * $$\displaystyle (Eq. 2.3) $$
 * }
 * }

Note:

1) $$\left [ \frac{1}{2}\left [ h(x)+h(x+dx) \right ]\rho (x+dx) \right ]$$ denotes mass per unit length at a distance of (x+dx/2), which is the middle of the elementary section considered in Figure 1.2.

2) $$\frac {1}{2}\left [h(x)+h(x+dx) \right ]$$ denotes average height of elementary section of figure 1.2.

3) Since we are considering an infinitesimally small section (dx) of the entire bar, we can write,

$$h(x)\approx h(x+dx)$$

$$\Rightarrow \frac{1}{2}\left [ h(x)+h(x+dx) \right ]\approx h(x)$$

4) Also, b is the width of the cross section and is constant and ρ(x+dx) is approximately equal to ρ(x) for a small section as in 3) above.

Eq 2.3 converts to the following:

 * {| style="width:100%" border="0"

 * $$\displaystyle (Eq. 2.4) $$
 * }
 * }

Eq 2.4 is the modified form of Eq 1.7 for the specific case of A(x)=bˑh(x).

=Contributing Members= Eml5526.s11.team6.gravois 20:59, 25 January 2011 (UTC)

eml5526.s11.team6.lee 21:11, 25 January 2011 (UTC)

Eml5526.s11.team6.kurth 10:31, 26 January 2011 (UTC)

Eml5526.s11.team6.tupsakhare 11:30, 26 January 2011 (UTC)

Eml5526.s11.team6.vork 11:35, 26 January 2011 (UTC)

Eml5526.s11.team6.joglekar 20:39, 26 January 2011 (UTC)

Eml5526.s11.team6.deshpande 20:51, 26 January 2011 (UTC)

title: User:Eml5526.s11.team6/hwk1


text:
Psycholinguistics/Neural Basis of Speech Perception

This chapter is limited to the neural basis of speech perception. For information on the non-neural models please refer to the chapter on the Models of Speech Perception

Introduction
The study of the neuroanatomy of speech perception has been a topic of interest for over 130 years. However, the full characterization of speech perception has yet to become complete. In the 1870s, Carl Wernicke developed the first hypothesis in understanding the functional neuroanatomy of speech perception. Wernicke hypothesized that the auditory cortex supports speech perception from patients of his with auditory language comprehension disorders, typically with left superior temporal gyrus (STG) lesions (see Figure 1 for neuroanatomical location). Patients with these symptoms were later termed Wernicke aphasics. In the 1980s, Damasio & Damasio found that large lesions to the left superior temporal gyrus did not lead to auditory speech comprehension problems, but rather deficits in speech production. These discrepancies in the literature created some ambiguity as to whether the STG was involved in speech perception or not. Damage to the left frontal, or inferior parietal areas created deficits in identification and discrimination of speech syllable tasks. This discovery raises the question of the involvement of a frontal-parietal circuit in speech perception. The development of functional magnetic resonance imaging (fMRI), the ambiguity was not eliminated with the use of passive listening tasks as hoped. Activations were visible in all of these areas including the STG bilaterally. Using syllable discriminations tasks Zatorre and collegues found prominent activation in the left inferior frontal lobe. However, many authors have suggested that the inferior frontal lobe may have been activated as a result of task-dependent phonological working memory processes.

The goal of these various studies is to understand the neural processes supporting the processing of speech sounds that ultimately link up with the mental lexicon, and result in auditory comprehension. From as early as the last 1800s research shows much conflicting evidence as to the neural origins of speech recognition as a whole. This is in part because of the use of some sub-lexical tasks, the problem being that speech perception and speech recognition are double dissociated. This means that speech perception doesn’t always necessarily result in speech recognition, the abilities are distinct computationally. Sub-lexical tasks aim to only measure early stages of processing phonemes of syllabic representations, yet their are people who cannot accurately perform these tasks yet have accurate comprehension. So in failing the sub-lexical tasks, these people appear to have comprehension deficits even though they do not. The main difference between the two is that speech perception requires the listener to maintain a sub-lexical representation active while completing the task. Whereas speech recognition does involve lexical access processes. .

In the 1870s, when Carl Wernicke, depicted in figure 2, developed the first hypothesis to speech processing, he also developed the first notion of two streams of auditory information processing. It wasn’t until 2007 that Hickok and Poeppel expanded and furthered this idea into what is now called the dual-stream model, which accounted for both speech perception and speech recognition. The publication of their dual-stream model has helped incorporate some of these afore mentioned discrepancies in the literature into a working model. Their descriptive account of the dual stream model is based around the central claim that proposes there is a ventral stream and a dorsal stream in processing verbal auditory stimuli. Speech articulation tasks rely on the dorsal stream system that is mostly left lateralized, and speech perception and recognition rely more heavily on the ventral stream system that is primarily bilaterally organized. The two streams have a common area of tissue in the left superior temporal gyrus (STG), and this therefore would explain the double dissociations that are observed. The common area of tissue in the STG auditory-responsive fields provides the early cortical stages for speech perception bilaterally. It is beyond this point that the system diverges into two streams for continued processing, the ventral and dorsal streams. Here, the focus will be on the ventral stream as it is more relevant to the neural aspects of speech perception, however, the dorsal stream will be discussed as it assists in explaining the frontal activations observed in some of the literature.

To understand spoken language, one must first transform the acoustic speech stimuli, recognize it as speech and not tones or non-speech sounds, and then convert it into a conceptual phonological representation that can then be assessed for meaning upon access to the mental lexicon. The chapter on acoustic phonetics covers the transformation of the acoustic signal, so in this chapter we will pick up at the processing of phonological (creating phonological representations) and semantic (linking of phonological representations with the syntactic and morphological operations) information that leads to comprehension. To eliminate confusion, the use of the term speech processing in this chapter will refer to any task that uses aurally presented speech stimuli. Speech perception then will refer to the sublexical tasks like syllable discrimination. Finally, the term speech recognition in this chapter will refer to a set of computations used to the perception information into a representation that will link up with the mental lexicon. The chapter makes use of the dual-stream model to assist in breaking down the various aspects of speech processing. However, although the heading is the dual-stream model all other evidence is included as well, some supporting and some opposing. There also may be other models proposed out there, but generally the information gathered fits well with this model.

Dual-Stream Model
The dual-stream model of the auditory system shows similarities to the speech processing dual-stream model proposed by Hickok and Poeppel in 2007. The ventral stream is analogous to the auditory 'what' stream, and processes speech signals for speech recognition and comprehension. The dorsal stream, analogous to the 'where' stream, is involved in the translation of speech signals to articulatory representations for speech production. The auditory-motor integration function of the dorsal stream has been suggested as where the language processing dorsal stream and the auditory 'where' stream deviate. In order to grasp the understanding of the dual-stream model, in terms of speech perception, we must break down the ventral stream into phonological and semantic processing. It is also necessary to incorporate other (and sometimes conflicting) studies to generate a more full view of the current research.

Ventral Stream
In the literature there appears to be an undetermined fact as to what exact aspects of phonological processing are included in the ventral stream and which are not. Therefore, some sub-lexical tasks are considered pre-ventral stream processing, and other more advanced aspects, forming full phonological representations are included. Here, the initial phonological-level processing is placed before the ventral stream, and includes the middle to posterior portions of the superior temporal sulcus bilaterally. This is the portion of the superior temporal sulcus that is used by both ventral and dorsal streams before they split. The mapping of the sensory or phonological representations is considered part of the ventral stream, and is the topic of interest when discussing phonological processing in the rest of the chapter. The ventral stream maps the phonological information onto conceptual and semantic representations. This means that the ventral system itself processes distinctive features of the sounds, phonemes, syllabic and phonological structures, and, grammatical and semantic information. Hickok and Poeppel propose that the ventral system also uses it’s own parallel computational pathways, that allows the system to be organized bilaterally, but asymmetrically.

Phonological Processing
In the study of phonological processing, Steven Petersen and colleagues conducted a study on the cortical anatomy of single-word processing using positron emission tomography. They found key auditory processing areas to be bilateral activation of the primary auditory cortex, and temporoparietal cortex, anterior superior temporal cortex, and inferior anterior cingulated cortex, all left lateralized. They hypothesized the temporoparietal region near the angular and supramarginal gyri areas as a good candidate for the phonological coding region. Then, in order to achieve proper lexical access the mapping of sound to a representation requires the integration of information on various time scales. In the study by Robert Zatorre and colleagues, they attempted to evaluate phonological processing in terms of these temporal, but also spectral changes in response to auditory stimuli. They found that there were distinct auditory cortex areas in each hemisphere, specific for each of these two parameters. The anterior auditory region in the right hemisphere showed greater cerebral blood flow to increasing spectral, rather then temporal, changes in stimuli. Whereas the same area on the left hemisphere showed the reverse pattern; a greater response to temporal changes in stimuli. The right superior temporal sulcus also showed increased response to spectral stimuli, but not to temporal parameters. Thus, the right auditory cortex appeared to respond less well to rapidly changing acoustic information characteristic of speech processing, where the left hemisphere was much better able to follow this stimuli. Thus, as explained in Hickok 2010, a critical portion of the superior temporal sulcus is involved in phonological processes, particularly in the area bounded anteriorly by the anterolateral aspect of Heschl’s gyrus and posteriorly by the posterior end of the sylvian fissure.

Lexical and Semantic Processing
Phonological processing yields phonological codes (or representations) which are then used in speech processing to reach higher-level lexicon representations that are essential for auditory speech comprehension. Strong empirical evidence shows the involvement of the posterior middle temporal lobe regions in accessing lexical and semantic information. Lesion studies of the posterior temporal lobe have also supported this evidence. Elizabeth Bates and her colleagues studied 101 left-hemisphere aphasic patients and found that lesions to the middle temporal gyrus (MTG) most accurately predicted auditory comprehension deficits, with a significant deficit also observed with dorsolateral prefrontal cortical lesions. Whereas, lesions to the insula and arcuate/superior longitudinal fasciculus affected verbal fluency the most. Functional magnetic resonance imaging studies (see Figure 3 for an example of an fMRI scan) have further implicated the posterior middle temporal lobe regions in semantic processing. In a semantic decision task in research conducted by Jeffrey Binder and colleagues, activations were found in both sides of the STS and almost all of the MTG in the left hemisphere. They also found that this activation spread ventrally across the inferior temporal gyrus (ITG). The authors found further activations in the angular gyrus, anterior and posterior cingulated gyrus, portions of the precuneus, retrosplenial cortex, and cinglulate isthmus in the left hemisphere; as well as subcortical activations in the anterior thalamus in the left hemisphere. . Many positron emission tomography (PET) studies (see Figure 4 for an example of a PET scan) examined the activated areas in response to semantic processing. They too found left lateralized non-STG temporparietal regions; including the MTG, inferior temporal gyrus (ITG), and the angular gyrus. Finally, Karalyn Patterson and her two colleagues, found using dementia patients that deficits can affect amodal semantic knowledge for objects, as opposed to mapping sound to meaning specifically. Meaning, that it is not restricted to auditory stimuli at all. Their dementia patients appeared to have deficits in conceptual knowledge of objects in auditory and in visual modalities. Therefore, they hypothesized that the posterior lateral and inferior temporal lobe is more involved in the access of semantic knowledge from auditory input. They labeled the anterior temporal lobe as performing more of an integrating function for certain semantic forms across modalities. .

Although significant information implicates the temporal lobe in semantic processing, frontal lobe activations were also observed in a significant amount of studies. The Jeffrey Binder research mentioned above found significant prefrontal cortex activation including much of the inferior and superior frontal gyri, aspects of the middle frontal gyrus, and anterior cingulate cortex. PET studies have found similar, but less extensive results showing left frontal activation as a result of language processing in the inferior frontal gyrus and into the posterior middle frontal gyrus. One hypothesis for the role of the frontal lobe areas in language processing is it’s role as a “language executive” proposed by Jeffrey Binder. His teams research hypothesized the frontal lobe's role in coordinating sensory and semantic processing, and accommodating momentary changing goals; but noted that after injury the role could be adopted by other areas. This hypothesis is supported by patients with left frontoparietal lesions, who experience global aphasias acutely after injury, only later for their symptoms to improve into an expressive aphasia.

Overall, the research suggests that the left STG plays an important role in the analysis of speech sounds for comprehension at a linguistic-semantic level. This converging evidence suggests that Wernicke’s area may not be the primary location for language comprehension. It also suggests that the left temporoparietal regions outside of Wernicke’s area, as well as the left frontal lobe, and these frontal areas extend beyond Broca’s area including the prefrontal cortex.

Dorsal Stream
While the ventral stream perception and recognition of speech is generally agreed upon, the dorsal stream holds less agreement. It is responsible for translating speech signals into articulatory representations in the frontal lobe, involving the posterior frontal lobe and posterior dorsal-temporal lobe and the parietal operculum. The dorsal processing stream is said to be the site for auditory-motor interaction according to Hickok and Poeppel who have suggested this circuit as crucial in speech development and that it provides the neural mechanisms for phonological short-term memory. They also suggest that the dorsal stream is strongly left lateralized, which would provide evidence toward the prominence of production deficits following lesions to dorsal temporal and frontal lobes. .

A study conducted by Price and colleagues evaluated the regions involved in auditory word perception and repetition. This is an example of how results and methods need to be read carefully as results can be interpreted in many ways. Activations of the left inferior frontal region (otherwise known as Broca's area, see Figure 5 for the location Broca's area and other important language centers) during auditory word processing were found during phonological judgement to auditory stimuli, word retrieval, and semantic judgements. These tasks all require the with holding of auditory stimuli in auditory-verbal short-term memory while making semantic or phonological judgements. We know that these short-term memory tasks with auditory stimuli increase the activation of Broca's area based on research from Paulesu and colleagues and therefore the role of Broca's area in these tasks may be as a result of phonological rehearsal. Whereas, Fiez et al. interprets the activation in the frontal operculum as phonological analysis, not required for listening to or identifying auditory stimuli. Remember back to the discussion on the ventral stream semantic processing, Binder and colleagues hypothesized similar frontal activation as a result of "language executive" functions. Thus, this frontal activation site has been interpreted in different ways, and requires additional research before a solid take on it's role in either the ventral or dorsal stream, or both, is reached.

Conclusion
In summary, currently the most appropriate way to characterize the neural aspect of speech perception is through the use of the dual stream model. The dual stream model proposes there are two streams for processing verbal auditory stimuli; the dorsal and ventral processing streams. The primarily bilateral ventral stream maps phonological information onto semantic representations. It uses a critical portion of the superior temporal sulcus for phonological processing. Lexical and semantic processing of the ventral stream makes use of the posterior middle temporal lobe, and left superior temporal lobe. The common activation in the superior temporal lobe for both phonological and semantic processing explains the double dissociation observed in lesion studies. The dorsal stream also utilizes the superior temporal lobe, this is the location for the early cortical stages for auditory processing bilaterally that occurs before the two processing streams diverge. Inferior frontal activations in studies have been explained as a result of language executive functions, and also as phonological rehearsal. Therefore, the traditional focus of Wernicke's area and Broca's area on their involvement in speech processing and production may be too confined when including all the current evidence. A much broader left temporoparietal region, and frontal lobe region are more likely involved then initially suspected.

Learning Exercises
Try to answer all the questions before resulting to the answer key. This will help to solidify your understanding. Note: Answer examples do not include portions of essay questions that are opinion based. These are designed to get you thinking for yourself, rather than just regurgitating your newly acquired information.

Part A) Language Processing 1. The use of passive listening to speech tasks in fMRI language studies failed to highlight the STG involvement as hoped, showing bilateral activations. Based on the information you’ve acquired reading the Phonological Processing section about manipulating auditory stimuli , hypothetically, what methodological factors may have resulted in this bilateral activation if they had been focusing on the early stages of speech perception? How could they have manipulated their stimuli to favour one of the two hemispheres?

2. What is the difference between the dorsal and ventral streams in the Dual-Stream model? Which hemisphere doe they reside in, or are they bilaterally organized?

3. Read through the following information provided and answer the subsequent questions: Broca’s area was traditionally understood as a frontal “expressive” area for planning and executing speech. An fMRI study by Binder and colleagues on lexical and semantic processing has shown significant and extensive inferior frontal activations. Other PET studies have found similar, but less extensive left frontal activations. Binder claimed the frontal area as a “language executive” in controlling sensory and semantic processes in accommodating moment-to-moment shifts in goals or strategies. Some researchers attributed similar activations to maintaining words in an active state, others that it is more the analysis of these active words.
 * What can account for the similarities and/or differences in these conclusions? Refer back to this question after completing the other questions. See if your response changes.

4. What aspects of phonological processing occur before the processing streams diverge? If a study revealed activations coinciding with this area, to musical stimuli, how might these language-processing activations be related to processing music?

5. Read through the following information provided and answer the subsequent questions: When looking through research it is important to read over the methods sections, and the results section. That way you know the methods that are used, and you can interpret the results accordingly. Authors also have their own biases, and so using your own interpretations will help you include the best information in your own research. For example, Price et al., 1995 conducted a PET study with subjects listening to words, and repeating words. Binder et al., 1997 conducted an fMRI study using a semantic decision task (that requires them to press a button if the aurally presented noun was an animal native to the United States). . Both of these articles state their methodology tests semantic processing, and thus their activations both show semantic related brain regions.
 * Why is it difficult to compare the results of these two studies if they both evaluate semantics?
 * Which of the two tasks is a better choice for evaluating semantic processes?
 * Can you think of another type of task that might better focus on semantic processing?
 * If you were to conduct a study using this type of task, what methods would you use, and would you expect a different result?

Part B) Neuroanatomy of Language 1. The temporal lobe is involved in which aspects of language?

2. The superior aspect of the temporal lobe is more heavily involved in which aspects of language specifically?

3. The middle aspect of the temporal lobe is believed to be more heavily involved in which aspects of language specifically?

4. Name the three parts of the inferior frontal gyrus, as well as its common name. Name the three different tasks that activated the inferior frontal gyrus in the textbook. What do these tasks all have in common that caused some researchers to attribute the activation to another part of speech processing? What part of speech processing was it?

5. What are the names of the two regions in the inferior parietal lobule that are said to be good candidates for the phonological coding region?

6. Read through the following information provided and answer the subsequent questions: Many researchers have termed the anterior temporal lobe (ATL) as the “semantic hub”. Input and output information from all different sensory and motor areas to from an amodal semantic representation is used to make appropriate generalizations based on the central semantic relationships in this hub. A meta-analysis on research examining the ATL in reference to semantics found that frequently PET studies would show activations, whereas fMRI would not. They pointed out that the fMRI signal from the ATL and orbito-frontal regions are known to produce artifacts because of magnetic susceptibilities in the area. This would explain the little amount ATL activation studies highlighted in the text.
 * Assuming these hypotheses as true, what would make the ATL region an appropriate location for extracting this conceptual information, particularly as it pertains to linguistic information?
 * Some researchers have said that the motor, sensory, and language aspects of conceptual knowledge are necessary, but not sufficient to form the entire neural basis of semantics as the semantic hub hypothesis implies. What is your position on this matter?

/Learning Exercises Answers/


text:
User talk:Rgulami

 Hello Rgulami, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twiter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! Erkan Yilmaz uses the Chat + Identi.ca 22:35, 22 January 2011 (UTC)

Hi
Hi, thanks for registering. I don't think I have your initial evaluation form from the first session. Perhaps you can give it to me on Friday

All the best, Leutha 11:05, 25 January 2011 (UTC)

Operation Beria
Hi, I've moved your game to SPIR608 Political Simulations and Gaming/2011/Operation Beria and added it to the Navigation bar. Looking forward tosee ing the cards!

What is the copyright of File:Condition Card1.jpg?
Hi! Thanks for uploading the file File:Condition Card1.jpg. Unfortunately, when you did so you didn't include information about the license, and the file will need a license or other copyright information in order to stay at Wikiversity.

You can easily fix this by adding on the page, and filling out who the owner is and the copying terms. In particular, we need to know who owns the rights to the file and what the terms of use are. In regard to the latter, Wikiversity accepts open content, public domain, and fair use works (see Wikiversity's Copyright policy). You can place a on the file page to signify the copyright terms. If you need any help, feel free to leave me a message, and I'll do what I can to assist.Bilby 06:58, 2 November 2011 (UTC)

 * Also in relation to the above, File:Iskorenim shpionov i diversantov.jpg will need licensing information. - Bilby 00:42, 4 November 2011 (UTC)

Files Missing License Information
Thank you for uploading files to Wikiversity. See Media for copyright and license requirements for Wikiversity files. All files must have copyright and/or license information added to the file.

Instructions for adding copyright and/or license information are available at License tags. Files must be updated within seven days or they may be removed without further notice. See Requests For Deletion for more information.

The following files are missing copyright and/or license information:
 * File:Iskorenim shpionov i diversantov.jpg
 * File:Media Headlines.pdf
 * File:Media Table.png
 * File:Table points.pdf
 * File:Table Points.png
 * File:Table.pdf

MaintenanceBot (discuss • contribs) 03:51, 11 November 2013 (UTC)

Files Missing Information
Thanks for uploading files to Wikiversity. All files must have source and license information to stay at Wikiversity. The following files are missing and/or License tags, and will be deleted if the missing information is not added. See Uploading files for more information.

 * File:Iskorenim shpionov i diversantov.jpg

MaintenanceBot (discuss • contribs) 15:30, 16 April 2016 (UTC)

title: User talk:Rgulami


text:
User:Egm6341.s11.team1.arm/HW1

Part (A)
Employ L'Hopital's Rule,

Define g and h as follows:

Therefore,

Problem 2
The Taylor series can be constructed from the well-known Taylor series for $$e^x$$ at $$ x = 0 $$ (Atkinson 1-1-4).

Subtracting one from this expression and dividing by $$x$$:

Therefore:

title: User:Egm6341.s11.team1.arm/HW1


text:
User:Eml5526.s11.team6.deshpande

Useful Links
Egm6341 Course Wiki

title: User:Eml5526.s11.team6.deshpande


text:
User:Egm6341.s11.team5.raghunathan

Solution
'''We solved this problem on our own. '''

The definition of the infinity norm is as follows: $$\left \| f(x) \right \|_{\infty }\ = max \left| f(x) \right|$$. Similarly, $$\left \| g(x) \right \|_{\infty }\ = max \left| g(x) \right|$$. Also, by definition: $$\left \| f - g\right \|_{\infty }\ = max\left| f(x) - g(x)\right| $$. 1. In the interval of $$ [0,1]$$, the norms are as follows: $$\left \| 3x + 5x^3 \right \|_{\infty }\ = 8$$ $$\left \| sinh x \right \|_{\infty }\ = 1.1752$$ $$\left \| f - g\right \|_{\infty }\ = 6.8248$$

title: User:Egm6341.s11.team5.raghunathan


text:
User:Eml5526.s11.team5.srv

HW 1
Home Work 1

HW 2
Home Work 2

HW 3
Home Work 3

HW 4
Home Work 4

HW 5
Home Work 5

HW 6
Home Work 6

HW 7
Home Work 7

title: User:Eml5526.s11.team5.srv


text: Template:Infobox Particle

title: Template:Infobox Particle


text:
User:Eml5526.s11.team4.simko/HW1

=Homework 1=

1.1 - Derive EOM and PDE
|Problem 1 - Charles Cook

Problem Statement:
Discuss the specific case where the elastic bar from homework problem 1.1 has a rectangular cross section. The cross section is defined as shown in the figure below, where the height 'h(x)' varies with axial position. The base 'b' is constant for the entire bar.

Solution:
Starting with Equation 1.4 which is in a general form,

the area term 'A(x)' can be modified for the more specific case of a rectangular cross section. The cross sectional area is given by:

Using the equation for the area of a trapezoid, the mass per unit length 'm(x)' can be written as:

where $$\rho$$ is the density. The mid-point of the differential element is used to approximate the density.

Given that:

It should be noted that the normal force terms 'N(x)' and 'N(x+dx)' contain an area dependence as shown previously in Equations 1.7-1.9. With this in mind, Equation 1.9 and Equation 2.2 can be substituted together into Equation 1.4 to produce:

which is the force balance for an elastic bar with a rectangular cross section.

Again taking the limit:

produces the following Equation 2.6. As noted previously in problem 1, dx changes from the finite difference to a differential difference.

Using Equation 1.7 and Equation 1.9, Equation 2.7 is produced.

A simple back substitution of Equation 2.1 into Equation 2.7 yields:

Where $$ A(x)\rho(x)=m(x)$$, Equation 1.1 has again been derived.

title: User:Eml5526.s11.team4.simko/HW1


text:
User:Techexplo/Case Study 2

Homework 3, Case 2
This is do by Jan. 29, 2011. Post homework below in the appropriate group

During class, we'll review the Functional Grid by Van Wyk. Each group will be responsible for finding a new technology in once cell and then posting below.
 * 1) Briefly explain the technology (do not copy directly from a source)
 * 2) Generate at least one idea on how to create a new business based on this technology, remeber to include business model
 * 3) Use the technology to solve a problem in an company you've worked in our organization you've studied at

Be prepared to present next Sunday --Techexplo 01:41, 23 January 2011 (UTC)

Group 1
Introduction

RFID (radio frequency identification), a technology similar in theory to bar code identification whit was innovated from radio wave. With RFID to exchange data between a reader and an electronic tag attached to an object. An RFID system consists of an antenna and a transceiver, which read the radio frequency and transfer the information to a processing device, and a transponder, or tag, which is an integrated circuit containing the RF circuitry and information to be transmitted. High frequency RFID systems (850 MHz to 950 MHz and 2.4 GHz to 2.5 GHz) offer transmission ranges of more than 90 feet. As we Small text know this Technology can be use in transportation, product tracking ,retail sales, animal and human identification as well as household benefit. When some stuffs disappear in the house ,people will get trouble in that so, this technology will be use by tracking the dust-size chip on each of product combined with mobile computing (reader). When people can not find something ,they can just only type the digit number in mobile, then the position of stuffs will be exactly shown.

Business Model

Manufacturer Model We will sell the package directly to customer which are consist with chips and software to install in Mobile phone. The program will be expire in 1 years, if they want to extend. They can used as a vector for mobile payment, has added security in that users would be required to enter a pass code or PIN before payment is authorized

Apply to career

I have been working in factory for 3 years, I found that some staffs lost their stuffs when they are working. It waste time to find out its. Furthermore, if they can not find it ,the company have to buy the new one so, every piece of stuffs effect the cost. If factory use this technology, they can know that where those stuffs are in. It will reduce time and cost, get more productivity as well as using in inventories system.

Narrow Down the Application in the Title

Radio-frequency identification (RFID) create by Leon Theremin in 19 80 is a technology that uses communication via radio waves to exchange data between a reader and an electronic tag attached to an object, for the purpose of identification and tracking. It is possible that by 2030, RFID technology will have inserted itself into our daily lives the way that bar code technology wrought unobtrusive but remarkable changes when it was new. RFID technology makes it possible to give each product in a grocery store its own unique identifying number. Compare that to the situation today, with bar codes, where it is only possible to identify the brand and type of package. Furthermore, RFID tags can be read if passed within close enough proximity to an RFID tag reader. It is not necessary to "show" them to it, as with a bar code. Some tags can be read from several meters away and beyond the line of sight of the reader. The application of bulk reading enables an almost-parallel reading of tags. The adventage of RFDI is 1. can contain mor information and identify the differentiate of the product. 2.RFDI is can read fast information 3.Very hard to copy 4. it is water resistance 5.can reuse

Scope : 3 to 5 years to Market

In 3 – 5 years time this machine will be use as a household accessory this will expand our target market. The material will decrease price that every middle class house hold can afford this item.

Alternative

RuBee which is being hailed as a cheaper alternative to RFID. Technically its termed as IEEE 1902.1 but the name RuBee is easier to use. Here low cost radio tags are used which can be read as far as fifty feet and below 450 kHz. RuBee scores over RFID since it can be survive in some of the most difficult conditions such as water and metal where RFID tends to under perform. Also it's quite easy to transfer the RuBee data to an internet database.

The RuBee radio tags have a good battery life and they can last for more than ten years with the costs of radio tags being low, can be fully programmed using four bit processors and are as thin as a credit card.

In terms of speed and accuracy RuBee is still behind RFID but it certainly scores in the cost arena and can be visualized as gap filler between RFID and personal area networks. Let me tell you that RuBee is being hailed as an alternative and not a replacement for RFID.

Briefly explain plan on acquiring the Technology

no license for RFID
 * purchase license

 * Develop yourselves

our team will do the aftersale sevice and development

 * outsource

Companies that supply Include

Chips AMI,

Charterate, Hitachi, IBM, Phillips, RFSaw, and TagSys

Inserts

Avery Dennison, International Paper, LabID, MeadWestvaco, Power Paper, Rafsec, SmartTag, and Texas Instruments

Printers

Alien Technology, Intermec, Printronix, Toshiba, and Zebra Technologies

Tags

Alien Technology, AmaTech, Avery Dennison, FlexChip, Flint Ink, Hitachi, Identec, Intermec, iPico, LabID, Matrics, MeadWestvaco, Omron, Phillips, PowerPaper, Rafsec, RFSaw, SAMSys Technologies, Savi Technology, Siemens, TagSys, Texas Instruments, Tyco, and WaveTrend

Antennae

Avery Dennison, EMS, Flint Ink, Moore, and Omron Readers Alien Technology, AmaTech, Check Point Software Technologies, Feig Electronic, Hitachi, Identec, InKode, Intermec, iPico, Matrics, Moba, Omron, Rafsec, SAMSys Technologies, Savi Technology, Siemens, Symbol Technologies, TagSys, Texas Instruments, Tyco, and WaveTrend

Data aggregation and filtering systems

ConnectTerra, IBM, and OATSystems

Middleware Accenture

Check Point Software Technologies, Genesta, IBM, Matrics, Microsoft, OATSystems, Oracle, SAP, Savi Technology, Sensormatic, Sun Microsystems, WhereNet

Directory services

Ember and VeriSign

 * Research Team

our speacila and programer will invent a new program and improve the privious ine

Charyanaan

Supasin

Group 2
Piyanut

Nannapad

 Homework 3, Case 2

1. Briefly explain the technology (do not copy directly from a source)

2. Generate at least one idea on how to create a new business based on this technology, remeber to include business model

3. Use the technology to solve a problem in an company you've worked in our organization you've studied at

3D Displays GPS Mapping

1.Introduction :

A 3D display is any display device capable of conveying a stereoscopic perception of 3-D depth to the viewer. The basic requirement is to present offset images that are displayed separately to the left and right eye. Both of these 2-D offset images are then combined in the brain to give the perception of 3-D depth. Although the term "3D" is ubiquitously used, it is important to note that the presentation of dual 2-D images is distinctly different from displaying an image in three full dimensions. The most notable difference is that the observer is lacking any freedom of head movement to increase information about the 3-dimensional objects being displayed. Holographic displays do not have this limitation, so the term "3D display" fits accurately for such technology.

An important question is what advantages does binocular vision provide in the real world? As a visual effect it clearly fascinates the majority of people when they see a 3D picture. Beyond the attractive nature of stereoscopic 3D images they provide the following beneﬁt over monocular vision:

 * Relative depth judgement. The spatial relationship of objects in depth from the viewer can be judged directly using binocular vision.
 * Spatial localisation. The brain is able to concentrate on objects placed at a certain depth and ignore those at other depths using binocular vision.
 * Breaking camouﬂage. The ability to pick out camouﬂaged objects in a scene is probably one of the key evolutionary reasons for having binocular vision.
 * Surface material perception. For example, lustre, sparkling gems and glittering metals are in part seen as such because of the dfferent specular reﬂections detected by the left and right eyes.
 * Judgement of surface curvature. Evidence suggests that curved surfaces can be interpreted more effectively with binocular vision.

2. Business Model (Merchant Model):

Nowadays GPS technology is the most popular, it makes more convenience when you drive. With the use of technology you can make your daily life easy. To find out something or any place that you need and want. When most people think of GPS devices with a “3D” display, what they picture is a view of the road ahead from the perspective of near-ground level. The width of the road ahead narrows to give the illusion of 3D. The area at the bottom of the GPS covers a shorter distance (more closely zoomed in) than the area at the top of the GPS furthest away from you. But we will use this technology to support our business that the customer can find our companies via 3D Displays GPS mapping.

3. Use the technology to solve a problem in a company:

A company will be used 3D Displays GPS mapping to solve a problem when we can not find the place between we drive. So the 3D Displays GPS mapping special full range of products using three-dimensional urban navigation system. Three-dimensional map of the city navigation system combined with two-dimensional map and more intuitive image. When the user first, before departure to check through the three-dimensional map of the specific building location to the destination, the destination ahead of familiar surroundings and reduce the strangeness. Advance by three-dimensional positioning of the buildings on the map location, can quickly find the building going to solve the navigation problems.

Short description of the technology :

 •  Narrow down the application in the title :

3D Displays GPS Mapping set the baseline standard for true 3D in dash visualization and are uniquely able to deliver real world views of not only the road network, but the entire surface of the earth. We’re excited to work with Intermap’s NEXTMap terrain data  (Intermap Technologies), which allows us to take navigation to the next level with a visually superior product set.

 •	Scope : 3 to 5 years to market :

How to planning on bringing this innovation to the market? First the company would assume that we are starting to talk about even bigger hard drives to handle the information. Then the customers will the thing be useful and easy to understand while they are driving the confusing streets of an unknown city. They will use 3D Displays GPS Mapping to solve a problem when they can not find the place between they drive. It makes more convenience when they drive. With the use of technology you can make their daily life easy.

3D Displays GPS Mapping plans on shipping 3D map data of large Asia cities by Scope: 3 to 5 years to market this is a pretty interesting innovation and it follows some of the Google Earth type applications that allow the customers to see a very real life view of a city as the customers are moving through it. So, 3D Displays GPS Mapping is planning on shipping these new maps to major Car companies like Honda, Toyota and Ford etc. 3D Displays GPS Mapping will start releasing this data to major Car companies. Following next plan will be more cities in Asia as well.

 •	Alternatives :

Some devices that are used primarily for purposes other than navigation, such as personal digital assistants (PDAs) and smart phones, may also offer navigational features that utilize GPS technology and 3D Displays GPS Mapping data. Multi-task devices such as these are recommended for the customers who prefer the convenience of an all-in-one solution. In addition, GPS-based systems powered by 3D Displays GPS Mapping, the customers can download or install application to smart phones as well.

Briefly explain plan on acquiring the technology :

 •  Purchase license :

Intermap Technologies will make an agreement with 3D Displays GPS Mapping. Under the terms of the agreement, Intermap will furnish uniform 3D elevation data derived from its 5-meter posted NEXTMap countrywide digital map database.

 • 	Develop yourself :

To help 3D Displays GPS Mapping develop devices and applications to utilize the new 3D data, 3D Displays GPS Mapping should has partnered with another 3D modeling companies and hardware companies to help 3D Displays GPS Mapping this data into their devices. 3D landmarks are already available of some cities in Thailand and there are already some devices on the market. Sometime next year 3D Displays GPS Mapping plans to deliver about 3D landmarks in the Thailand covering about 20 major cities.

 • 	Outsource :

Intermap Technologies.

 •	Research Team :

3D Displays GPS Mapping to facilitate the arrival of 3D city maps on navigation devices and applications, 3D Displays GPS Mapping also is collaborating with leading 3D modeling software companies, as well as leading hardware companies.

Group 3
Nanowire Battery

1. Introduction:

Good selection of technology and explaination'--Techexplo 01:15, 30 January 2011 (UTC)

A Nanowire Battery is new technology invented by Stanford University Team led by Dr. Yi Cui, Assistant Professor of Material Science and Engineering of Stanford University. In this technology silicon nanowires are used as the active lithium storage material for the battery electrode. Traditional graphite anode was replaced by a stainless steel anode covered in silicon nanowires. Silicon is an attractive anode material for lithium batteries because it has a low discharge potential and the highest known theoretical charge. This hi-performance lithium battery is rechargeable with higher energy capacity and longer cycle life for applications devices. This battery is the fastest in charging and discharging since ever.

According to Dr. Yi Cui, “Silicon can store a lot of lithium but the volume expansion is too high, by using nanowires solves the problem of volume expansion and can achieve extremely high capacity, lithium storage capacity with multiple cycles. This is 10 times more than the current technology. So the implication of this discovery is very, very exciting, it means having a better battery”.

This Nanowire Batteries are applicable to consumer electronic devices like cellular phones, PDAs, and notebooks. This all devices need strong batteries but small in size, the Nanowire batteries will be the best choice in coming days. Not only the small devices said above but also this battery can be used vehicles. It is well born in the human’s mind that the present energy sources are scare and it is needed to have an option to that. However this may serve several problems.

2. Business Model (Merchant Model)

Web Based Nanowire Battery Retailer:

''Business model is fine. I would like you to push to find a different and unique model. Retail model is very common.''--Techexplo 01:15, 30 January 2011 (UTC)

After the commercial launch of Nanowire Battery in the market it is nice to sell these batteries to the consumers directly through web. First of all buy the batteries to be used in cellphones, PDAs and laptops from the manufacturer and then sell them to consumers. When these batteries will be available in the market people will definitely replace their present batteries to the Nanowire batteries which will give longer battery life, cheap in price. This will be based in Thailand (Bangkok). We will sell all the products (batteries) manufactured using nanowire technology demanded by consumers.

In the future when electronic vehicle’s use and production will be popular batteries used in such vehicle will be sold. Or normal vehicle needs the batteries to start the engine; the Nanowire batteries for vehicles will be sold as well.

Infomediary Model

Advertising Networks:

Energy Generation has been great issue and there is lot of research going on to develop the technology to help with. Nanowire Battery is on it’s huge development and will come up global solution. However Nanowire Batteries will need to reach the consumer from the manufacturers. Which gives us opportunity of promoting the Products of Nanowire Batteries applicable to electronic devices like Laptop, Cameras, Audio-video players, game players, cars and trucks and even for medical equipments. The greatest task in promoting these products is to educate the audience, the consumers, to make them understand the utility of the Nanowire Batteries.

The global trend is towards the online shopping therefore we promote the products online using all the major two types of online advertising networks:

Blind Networks: There are companies offering good pricing for direct promotions in exchange for those marketers relinquishing control over where their ads will run, though some networks offer a "site opt out" method. These companies give good deal in context price.

Targeted Networks: this is also called “next generation” or “2.0” ad networks which focus on specific targeting technologies such as behavioral or contextual. Targeted networks specialize in using consumer clickstream data to enhance the value of the inventory they purchase. Like if the purchase the mobile the data will be collected and offer will be sent to them.

Blind Networks or Targeted Networks requires updating the technology which will be again expensive. Our part will be the third party advertising network promoting products of manufactures on these networks owned by other companies. However we will create creative ideas banners and all stuff like blogs to generate revenue.

3. Use of Nanowire Batteries:

I like this application of the technology.--Techexplo 01:15, 30 January 2011 (UTC)

I have worked in religious organization in India where I used teach in night especially in remote area where there was limited power supply. We had to use diesel power generator to get light and run projector. The generator was loud and noisy. Using Nanowire batteries we can have 230V power supply to get light and run projector. Nanowire batteries will be used in laptop computers where as we used to have desktop computer in the past which needed power supply of 230V.

Methinee

Anand

Group 4
Usanee

Apawan

Bacteria in agriculture and industry
Our group focuses on the use of bacteria in agriculture and industry. More particularly it focuses on how to market this technology including business model and how this technology will solve a business problem. It is concerned with the functionality of matter processing.

1.) Introduction

Increasingly bacteria will compete with traditional chemical processes. Bacteria have the technological advantage of being exo-thermic, i.e., they generate their own energy. In addition they work at room temperatures and ambient pressure. They usually require less space than conventional chemical processes. Finally, a vast potential exists for the genetic modification of bacteria to enhance their technological potency.

The Role of bacteria in agriculture and industry that this technology will solve a business problem will be such as;

•	Producing food and beverages •	Purifying water •	Ingesting toxins •	Fixing nitrogen •	Leaching metals •	Producing plastic

In this case, we will only focus on Producing Plastic from Bacteria.

Scientists at Genomatica Inc. recently announced that they have developed strains of bacteria that are able to produce plastic without the use of oil or natural gas. The sustainable process utilizes little more than sugar and water to produce butanediol (BDO), which can be manufactured into everything from plastics and fibers to pharmaceuticals. Genomatica estimates that within a year the energy-efficient process will cost less than current hydrocarbon-based processes - a revolutionary development since close to 3 billion pounds of BDO manufactured each year.

Currently BDO is made exclusively with oil and natural gas, and its production is very energy-intensive. Utilizing sugar and E. Coli to create the chemical allows the production process to be conducted under normal pressure and temperatures, which drastically cuts it energy use: “By using advanced computational modeling and evolution‐based methods to rapidly engineer living organisms, Genomatica can produce valuable chemicals from renewable feedstocks at low cost.

The bacteria-grown plastic can be produced in large fermentation tanks in a manner similar the way that algae is being used to produce biofuels, and the company plans on using sugars that are non-competitive with the food industry to steer clear of some of the conflicts that have been brought up with ethanol-based fuels.

2. Business Model

To be useful for the Public, Technology executives, Scientists and investment professionals should use business model to help for public this growing knowledge base of bacteria and their actions. For example,

- Infomediary Model: To Note and giving the data about bacteria and their actions; especially their characteristics for using in agriculture and industry. This will help to market this Technology to be known in the Public and creating for New innovation. In this Infomediary Model, we can create on the Web such as An Official web page, paper version on the Webpage, On-line database, Google Scholar, Blogs, Wikipedia etc. And also, publishing in Science Magazines and Journals.

3. Use the technology to solve a problem in a company:'

- Bacteria producing plastic can be solved the problem in a large company, it can reduce cost of and decrease the use of oil or natural gas. Moreover, Producing Plastic from Bacteria can help the Company to Low-cost and increase the innovation of food production system. Also, besides production aspect, the environmental advantage that can be attained from using Bacteria is enormous. No polluting agricultural machinery will need to be used with this system of the production. The company will be able to produce the product from animal origin (Bacteria) and replace with macrobiotics foods this will make the food and the products much more healthy and more safety.

Source: http://www.bacteriamuseum.org/homepageTW.shtml

Description of the Technology

Bacteria are the microscopic microorganisms. Their single cell does not contain a proper cell membrane and cell organelles. There are no mitochondria in it. They divide by binary fission, no mitosis or meiosis take place in them Bacteria are of so much importance in the biotechnology industry. Before the progress of biotechnology, it had been used in many domestic applications for example in the process of making yogurt. Bacteria are also of importance because they produce secondary metabolites. E.coli has special impotence because it is used in the cloning of many genes. Bacteria can also be used in agriculture.

Applications of Bacteria in Agriculture:-

There are certain bacteria which contain special properties which are beneficent for plants. These bacteria are present in soil and they affect the crops by fighting against the harmful bacteria and they are also the source of providing nutrition to the crops. Some bacteria like rhizobia and agrobacteria are used to release seed inoculants and are very useful for the plants. The bacteria like Azoarcus are of much importance for the plants that it fixes the endophyte of the grasses. This type of bacteria is mostly helpful for the crop of rice and they are very much environment friendly. When the seed is sown in the soil, bacteria play an important role in its germination. The bacteria grow in the seed ad seed in return get food from it. Bacteria increase the fertility of the soil and provide such nutrients to the soil which are useful for the plant growth. They also help in softening the food in the seed and this is the reason plants come out of the seeds. Though it is not certain what role bacteria play when the plants grow but they are of much importance in the early stages of plant development. Certain pesticides are developed using bacteria which give benefit to the crops. Bacillus thurengiensis is a gram positive bacterium used in agriculture.

Applications of Bacteria in Dairy Industry:-

It is a fact that from the beginning since the man has been used cattle for domestic use, bacteria played an impotent role in it. It is proved that milk does not contain any bacteria when it comes out of the glands of the animal, but after it is collected, all the changes which occur in the milk, they are all because of bacteria. Bacteria play their role in the making of yogurt. When milk along with some yogurt in it is kept for some hours, it will convert into yogurt. It is the bacteria which leads the whole process and changes the milk into yogurt. Similarly in making of beer and bread, bacteria are used.

Applications of Bacteria in Environment:-

Bacteria are very much of importance for the environment as they make the environment free from the pollutants. The pollutants which emerge from the industrial wastes, bacteria have the ability to digest them so that they can be recycled in the form of energy and nutrients and do not harm the environment. Bacteria also convert the trees into coal which are buried under the earth for millions and billions of years. This coal can be used for fuel, for producing electricity and various other useful purposes.

Narrow Down the Application in the Title : Producing Plastic from Bacteria

-  Scientists at Genomatica Inc. recently announced that they have developed strains of bacteria that are able to produce plastic without the use of oil or natural gas. The sustainable process utilizes little more than sugar and water to produce butanediol (BDO), which can be manufactured into everything from plastics and fibers to pharmaceuticals. Genomatica estimates that within a year the energy-efficient process will cost less than current hydrocarbon-based processes

Scope : 3 to 5 years to Market

- The economic importance of bacteria derives from the fact that bacteria are exploited by humans in a number of beneficial ways. Despite the fact that some bacteria play harmful roles, such as causing disease and spoiling food, the economic importance of bacteria includes both their useful and harmful aspects.

Alternatives

- In the Market todays, it is generally to use the Bacteria for business both Agriculture and Industry. There are several useful from Bacteria as follows; •	Fermentation processes, much as brewing, baking, cheese and butter manufacturing, Bacteria, often Lactobacillus in combination with yeasts and molds, have been used for thousands of years in the preparation of fermented foods such as cheese, pickles, soy sauce, sauerkraut, vinegar, wine, and yogurt. •	Chemical manufacturing such as ethanol, acetone, organic acid, enzymes, perfumes etc. In the chemical industry, bacteria are most important in the production of enantiomerically pure chemicals for use as pharmaceuticals or agrochemicals. •	Pharmaceuticals, such as antibiotics, vaccines and steroids. •	Microbial mining, which is the bacteria and other microorganisms are cultured in container and then used to bring these processes e.g., copper extraction.

Briefly explain plan on acquiring the Technology

- The National Institute of Health was the first federal agency to assume regulatory responsibility in the United States. The Recombinant DNA Advisory Committee of the NIH published guidelines for working with recombinant DNA and recombinant organisms in the laboratory. Nowadays, the agencies that are responsible for the biotechnology regulation are: US Department of Agriculture (USDA) that regulates plant pests and medical preparation from living organisms, Environmental Protection Agency (EPA) that regulates pesticides and herbicides, and the Food and Drug Administration (FDA) which ensures that the food and drug products are safe and effective

(http://en.wikipedia.org/wiki/Biotechnology#cite_note-Thieman-1)

Develop yourself : Education

In 1988, after prompting from the United States Congress, the National Institute of General Medical Sciences (National Institutes of Health) instituted a funding mechanism for biotechnology training. Universities nationwide compete for these funds to establish Biotechnology Training Programs (BTPs). Each successful application is generally funded for five years then must be competitively renewed. Graduate students in turn compete for acceptance into a BTP; if accepted then stipend, tuition and health insurance support is provided for two or three years during the course of their PhD thesis work. Nineteen institutions offer NIGMS supported BTPs. Biotechnology training is also offered at the undergraduate level and in community colleges. (http://en.wikipedia.org/wiki/Biotechnology#cite_note-Thieman-1)

Research Team :

Scientists at San Diego–based Genomatica, Inc., have announced success in manipulating the bacteria to directly produce butanediol (BDO), a chemical compound used to make everything from spandex to car bumpers, thereby providing a more energy-efficient way of making it without oil or natural gas.

(http://www.scientificamerican.com/article.cfm?id=turning-bacteria-into-plastic-factories-replacing-fossil-fuels)

title: User:Techexplo/Case Study 2


text:
User:Eml5526.s11.team4.simko/HW2

=Matrix Algebra=

Recall matrix algebra: (1) $$(\mathbf{A}\mathbf{B})^{T}=\boldsymbol{B}^{T}\boldsymbol{A}^{T}$$ (2) $$(\boldsymbol{A}^{-1})^{T}=(\boldsymbol{A}^{T})^{-1}=\boldsymbol{A}^{-T}$$ Given the matrices: $$ \boldsymbol{A}=\begin{bmatrix} 1 & 1 & 1\\ 2 & -1 & 3\\ 3 & 2 & 6 \end{bmatrix} $$ $$ \boldsymbol{B}=\begin{bmatrix} 1 & 3 & 5\\ 1 & -4 & 1\\ 2 & 5 & 8 \end{bmatrix} $$ {{1,1,1},{2,-1,3},{3,2,6}}*{{1,3,5},{1,-4,1},{2,5,8}}

http://www.wolframalpha.com/input/?i=matrix%20operations&lk=2 for matrix math

http://reference.wolfram.com/mathematica/ref/Transpose.html http://reference.wolfram.com/mathematica/tutorial/BasicMatrixOperations.html for transpose syntax

=Homework 2.2 (meeting 7)=

Problem Statement
Consider the family of vectors shown below in Equation 2.2-1.

These vectors exhibit properties such that

where $$\delta_{ij}$$ in Equation 2.2-2 is the Kronecker Delta defined as

The repeating index basis is given by Equation 2.2-4, where

The following two solution methods are observed in this problem set,

Complete the following tasks:

 * 1. Find $$ det[b_{jk}] $$

 * 2. Find $$ \mathbf{\Gamma(b_{1},b_{2},b_{3})}=\mathbf{K},\quad det(\mathbf{\Gamma}) $$

 * 3. Find $$ \mathbf{F}=\left\{F_{i}\right\}=\left\{\mathbf{b}_{i}\cdot \mathbf{v}\right\} $$

 * 4. Solve (2-4) for $$ \mathbf{d}=\left\{ v_{j} \right\} $$

 * 5. Use $$ \mathbf{w}_{i}\cdot \mathbf{\mathbb{P}(v)}=0 $$ to find (2-5). What is $$ \vec{\mathbf{K}} $$ and $$ \vec{\mathbf{F}}? \quad \mathbf{d}=\left\{ v_{j} \right\} $$

 * 6. Solve for $$ \mathbf{d} $$ ; Compare to $$ \mathbf{d} $$ in problem 4.

 * 7. Observe symmetry property of $$ \mathbf{K} $$ and $$ \vec{\mathbf{K}}. $$ Discuss pros and cons of 2 methods.(2-4 & 2-5)

1.) Find $$ det[b_{jk}] $$
In general the determinantof a 3X3 matrix is given by the following equation.

For the specific case of $$ [b_{jk}] $$ in Equation 2.2-4, the determinant is found to be equal to -8 ($$\textbf{Ans:} det[b_{jk}]=-8$$). This can also be calculated quickly using Matlab as shown below.  Matlab Code

 Result

2.) Find the Gram matrix $$ \mathbf{\Gamma(b_{1},b_{2},b_{3})}$$ and calculate the determinant.
From lecture slide 7-2,

The Gram matrix is given by $$ \mathbf{\Gamma(b_{1},b_{2},b_{3})}=\mathbf{K}_{ij}=\mathbf{[b_{i}]^{t}\cdot[b_{j}]}, \quad i,j=1,2,3 $$

where the stiffness matrix is given by,

with the vector components defined as

 * $$ \mathbf{b_{1}}=\begin{bmatrix}1 & 1 & 1\end{bmatrix}, \mathbf{b_{2}}=\begin{bmatrix}2 & -1 & 3\end{bmatrix}, \mathbf{b_{3}}=\begin{bmatrix}3 & 2 & 6\end{bmatrix} $$
 * }
 * }

Therefore,  Matlab Code

 Result  And the determinant of $$ \mathbf{\Gamma} $$ is 64.

title: User:Eml5526.s11.team4.simko/HW2


text:
User:Egm6341.s11.team3.Xia

= Numerical Methods =

Extra Solution
From Taylor series :

$$ e^x = 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \frac{x^4}{24} + \frac{x^5}{120} + ... $$

Then the original fuction could be expressed as:

$$ f(x) = 1 + \frac{x}{2} + \frac{x^2}{6} + \frac{x^3}{24} + \frac{x^4}{120} + ... $$

$$ \Rightarrow \lim_{x\to 0} f(x) = 1 + \frac{0}{2} + \frac{0^2}{6} + \frac{0^3}{24} + \frac{0^4}{120} + ... =1 $$

The original function is plotted from 0 to 1. For comparison, serie-form of f(x) of order 2nd and 3rd are also shown in the following plot.

Extra Solution
From Taylor series :

 * {| style="width:100%" border="0"

$$ e^x = 1 + \sum_{i=1}^n \frac{x^i}{i!} $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle
 * }

Then the original fuction could be expressed as:

 * {| style="width:100%" border="0"

$$ f(x) = \frac{e^{x}-1}{x} = \sum_{i=1}^n \frac{x^{i-1}}{i!} $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle
 * }

 * {| style="width:100%" border="0"

$$ \Rightarrow P_n(x) = \sum_{i=0}^{n} \frac{x^{i}}{(i+1)!} $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle (Eq. 2.12)
 * }

To find $$ R_n(x) $$, we need to solve for $$ f^{(n+1)}(x) $$ which is difficult. So, here we compute $$ R_n(x) $$ from the previous function $$ e^{x} $$. From (Eq. 2.7), we could write $$ e^{x} $$ as:

 * {| style="width:100%" border="0"

$$ e^{x} = 1+ \sum_{i=1}^{n+1} \frac{x^i}{i!} + \frac{x^{n+2}}{(n+2)!} e^\xi, \quad \xi \in [0, x] $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle $$
 * }

 * {| style="width:100%" border="0"

$$ \Rightarrow f(x) = \frac{e^{x}-1}{x} = \sum_{i=0}^{n} \frac{x^i}{(i+1)!} + \frac{x^{n+1}}{(n+2)!} e^\xi, \quad \xi \in [0, x] $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle (Eq. 2.13)

$$
 * }

Comparing (Eq. 2.12) and (Eq. 2.13) yields,

 * {| style="width:100%" border="0"

$$ R_n(x) = \frac{x^{n+1}}{(n+2)!} e^\xi, \quad \xi \in [0, x] $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle

$$
 * }

Problem
Given from lecture notes:

 * {| style="width:100%" border="0"

$$ p_2(x)=\sum_{i=0}^{n=2} l_{i,2}(x)f(x_i) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle (Eq. 11.1)
 * }
 * {| style="width:100%" border="0"

$$ l_{i,n}=\prod_{j=0,j \neq i}^{n} \frac{x-x_j}{x_i-x_j} $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle (Eq. 11.2)
 * }

Derive: Simple simpson's rule.

Solution
From definition:

 * {| style="width:100%" border="0"

$$ I_2(f) = \int_{a}^{b} f_2(x)dx = \sum_{i=0}^{2} \int_{a}^{b} l_{i,2}(x)dx f(x_i) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 11.3)
 * }

With

 * {| style="width:100%" border="0"

$$ x_0=a;x_1=\frac {a+b}{2};x_2=b. $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

from (Eq. 11.2), we can obtain:

 * {| style="width:100%" border="0"

$$ l_{0,2}(x) = \frac {(x-x_1)(x-x_2)}{(x_0-x_1)(x_0-x_2)} = \frac {2}{(a-b)^2} [x^2-\frac{a+3b}{2} x +\frac{(a+b)b}{2}] $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 11.4)
 * }

 * {| style="width:100%" border="0"

$$ l_{1,2}(x) = \frac {(x-x_0)(x-x_2)}{(x_1-x_0)(x_1-x_2)} = -\frac {4}{(a-b)^2} [x^2-(a+b) x +ab] $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 11.5)
 * }

 * {| style="width:100%" border="0"

$$ l_{2,2}(x) = \frac {(x-x_0)(x-x_1)}{(x_2-x_0)(x_2-x_1)} = \frac {2}{(b-a)^2} [x^2-\frac{3a+b}{2} x +\frac{(a+b)a}{2}] $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 11.6)
 * }

Integrate (Eq. 11.4)(Eq. 11.5)(Eq. 11.6), we can solve

 * {| style="width:100%" border="0"

$$ \int_{a}^{b}l_{0,2}(x) = \frac {2}{(b-a)^2} [-\frac{1}{12} (a-b)^3] = \frac{1}{6}(b-a) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 11.7)
 * }

 * {| style="width:100%" border="0"

$$ \int_{a}^{b}l_{1,2}(x) = \frac {4}{(a-b)^2} [-\frac{1}{6} (a-b)^3] = \frac{4}{6}(b-a) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 11.8)
 * }

 * {| style="width:100%" border="0"

$$ \int_{a}^{b}l_{2,2}(x) = \frac {2}{(b-a)^2} [-\frac{1}{12} (a-b)^3] = \frac{1}{6}(b-a) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 11.9)
 * }

With

 * {| style="width:100%" border="0"

$$ h=\frac {b-a}{2} $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

Plug (Eq. 11.7)(Eq. 11.8)(Eq. 11.9) into (Eq. 11.3), yields

 * {| style="width:100%" border="0"

$$ I_2(f) = \int_{a}^{b} l_{0,2}(x)dx f(x_0) + \int_{a}^{b} l_{1,2}(x)dx f(x_1) + \int_{a}^{b} l_{2,2}(x)dx f(x_2) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 11.10)
 * }

 * {| style="width:100%" border="0"

$$ \Rightarrow I_2(f) = \frac {h}{3} (f(x_0) + 4f(x_1) + f(x_2)) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

Which is right the simple simpson's rule.

Problem
Given:

 * {| style="width:100%" border="0"

$$ f(x)=\frac {e^x-1}{x} on [-1,1], x_0=-1,x_n=1 $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.1)
 * }

Find: 1) Construct $$ f_n(x) $$ by lagrange interpolation functions for $$ n=1,2,4,8,16 $$ and then plot $$ f(x) $$ and $$ f_n(x) $$. 2) Compute weight functions for $$ n=1,2,4,8,16 $$ and then form tables. 3) Compute $$ I_n(x) $$ for $$ n=1,2,4,8 $$ and compare to $$ I $$ that is solved using WolframAlpha with more digits. 4) For $$ n=5 $$, plot $$ l_0,l_1,l_2 $$ and then predict the shapes of $$ l_3,l_4,l_5 $$ based on those.

Solution
1) According to the problem, we construct the fuctions from following equations:

 * {| style="width:100%" border="0"

$$ f_n(x)=p_n(x)=\sum_{i=0}^{n} l_{i,n}(x)f(x_i) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.2)
 * }
 * {| style="width:100%" border="0"

$$ l_{i,n}=\prod_{j=0,j \neq i}^{n} \frac{x-x_j}{x_i-x_j} $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.3)
 * }

For n=1,

 * {| style="width:100%" border="0"

$$ x_0=-1,x_1=1 $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

 * {| style="width:100%" border="0"

$$ l_{0,1}(x) = \frac {x-x_1}{x_0-x_1} = -\frac{1}{2}(x-1) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.4)
 * }

 * {| style="width:100%" border="0"

$$ l_{1,1}(x) = \frac {x-x_0}{x_1-x_0} = \frac{1}{2}(x+1) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.5)
 * }

 * {| style="width:100%" border="0"

$$ f(x_0) = \frac {e^{x_0}-1}{x_0} = 1-e^{-1} \displaystyle $$ $$ f(x_1) = \frac {e^{x_1}-1}{x_1} = e-1 $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

 * {| style="width:100%" border="0"

$$ \Rightarrow f_1(x) = l_{0,1}(x)f(x_0) + l_{1,1}(x)f(x_1) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.6)
 * }

For n=2,

 * {| style="width:100%" border="0"

$$ x_0=-1,x_1=0,x_2=1 $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

 * {| style="width:100%" border="0"

$$ l_{0,2}(x) = \frac {(x-x_1)(x-x_2)}{(x_0-x_1)(x_0-x_2)} = \frac{1}{2}x(x-1) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.7)
 * }

 * {| style="width:100%" border="0"

$$ l_{1,2}(x) = \frac {(x-x_0)(x-x_2)}{(x_1-x_0)(x_1-x_2)} = -(x+1)(x-1) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.8)
 * }

 * {| style="width:100%" border="0"

$$ l_{1,2}(x) = \frac {(x-x_0)(x-x_1)}{(x_2-x_0)(x_2-x_1)} = \frac{1}{2}(x+1)x $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.9)
 * }

 * {| style="width:100%" border="0"

$$ f(x_0) = \frac {e^{x_0}-1}{x_0} = 1-e^{-1} $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

 * {| style="width:100%" border="0"

$$ f(x_1) = \frac {e^{x_1}-1}{x_1} = 1 $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

 * {| style="width:100%" border="0"

$$ f(x_2) = \frac {e^{x_2}-1}{x_2} = e-1 $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

 * {| style="width:100%" border="0"

$$ \Rightarrow f_2(x) = l_{0,2}(x)f(x_0) + l_{1,2}(x)f(x_1) +  l_{2,2}(x)f(x_2)$$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.10)
 * }

For n=4,8,16, we use matlab for plotting with (Eq. 12.2) and (Eq. 12.3). The code is attached below:

The plots are shown as following:

2) For n=1, integrate previous (Eq. 12.4) and (Eq. 12.5) from [-1,1], we get,

 * {| style="width:100%" border="0"

$$ w_{0,1} = \int_{-1}^{1} l_{0,1}(x)dx = 1 $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

 * {| style="width:100%" border="0"

$$ w_{1,1} = \int_{-1}^{1} l_{1,1}(x)dx = 1 $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

For n=2, integrate previous (Eq. 12.7), (Eq. 12.8) and (Eq. 12.9) from [-1,1], we get,

 * {| style="width:100%" border="0"

$$ w_{0,2} = \int_{-1}^{1} l_{0,2}(x)dx = \frac{1}{3} $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

 * {| style="width:100%" border="0"

$$ w_{1,2} = \int_{-1}^{1} l_{1,2}(x)dx = \frac{4}{3} $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

 * {| style="width:100%" border="0"

$$ w_{2,2} = \int_{-1}^{1} l_{2,2}(x)dx = \frac{1}{3} $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

For n=4,8,16, by apply LIET, we obtain the linear system equations:

 * {| style="width:100%" border="0"

$$ \sum_{i=0}^{n}w_{i,n}(x_i)^j = \frac{b^{j+1}-a^{j+1}}{j+1} $$ when $$ j=0,1,2,...,n $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.11)
 * }

Solving (Eq. 12.11) for n=4,8,16 by matlab and the code is attached below:

The results are shown in the following tables:

3) Integrate using Newton-Cotes Method, The integration could be expressed as:

 * {| style="width:100%" border="0"

$$ I_n(f) = \int_{a}^{b} f_n(x)dx = \sum_{i=0}^{n} w_{i,n}f(x_i) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.12)
 * }

With previously calculated value of weight functions, The results of the integrations are shown in the following table and compared with that obtained from WolframAlpha.

4) For n=5, the lagrange functions are computed from (Eq. 12.3) using matlab, the code is attached below:

The first three fuctions are plotted as follows:

Now, we will analyze the shapes of the lagrange functions. First it is obvious to identify:

 * {| style="width:100%" border="0"

$$ x_i = -x_{n-i} $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

From (Eq. 12.3), we could derive

 * {| style="width:100%" border="0"

$$ l_{n-i,n}(x) = \prod_{j=0,j \neq n-i}^{n} \frac{x-x_j}{x_{n-i}-x_j} = \prod_{j=0,j \neq n-i}^{n} \frac{x+x_{n-j}}{x_{n-i}+x_{n-j}} $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

 * {| style="width:100%" border="0"

$$ = \prod_{j=0,n-j \neq i}^{n} \frac{-x-x_{n-j}}{x_{i}-x_{n-j}} = \prod_{k=0,k \neq i}^{n} \frac{-x-x_{k}}{x_{i}-x_{k}} = l_{i,n}(-x) $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 12.13)
 * }

So from (Eq. 12.13), we can predict that $$ l_3 $$ and $$ l_2 $$, $$ l_4 $$ and $$ l_1 $$, $$ l_5 $$ and $$ l_0 $$ are axis-symmetric function pairs (With respect to y axis). We further plot $$ l_3 $$, $$ l_4 $$, $$ l_5 $$ in the following figure and the prediction is verified.

Plots
=References=

title: User:Egm6341.s11.team3.Xia


title: File:Nm1.s11.mtg10.djvu