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User:Egm6341.s10.team3.heejun/HW3

= (2) Error bound for Composite Simpson's Rule=

Problem Statement
$$ \displaystyle Show\, the\, error\, for\, Composite\, Simpson's\, Rule,\, $$ $$ \displaystyle \left| {E}_{n}^{2} \right| \leq \frac{(b-a)^{5}}{2880 n^{4}} M_{4} = \frac{(b-a)h^{4}}{2880} M_{4} $$ $$ \displaystyle Where\,\, M_{4} := max \left| f^{4}(\xi) \right| \,\, and \,\, \xi \in [a,b]$$

Ref: Lecture Notes [[media:Egm6341.s10.mtg17.djvu|p.17-2]]

Solution
Ref: Lecture Notes [[media:Egm6341.s10.mtg16.pdf|p.16-2&3]]

$$ \begin{align} \displaystyle E_{n}^{2} &:= I - I_{n} \\ &=\int_{a}^{b}f(x)dx - \frac{h}{3}[f(x_{0})+4f(x_{1})+2f(x_{2})+...+2f(x_{n-2})+4f(x_{n-1})+f(x_{n})] \\ &=\sum_{i=1}^{n} [ \int_{x_{i-1}}^{x_{i}}f(x)dx - \frac{h}{3}[f(x_{i-1}) + 4f(\frac{(x_{i-1}+x_{i})}{2}) + f(x_{i})] \\\end{align}\ $$

$$ \left| E_{n}^{2} \right| \leq \left| \frac{h^{5}}{90} \underbrace {\sum_{n}^{i=1}max\left(F^{(4)}(\xi )\right)}_{Call \bar{M}_{4}} \right| $$ $$ \displaystyle \xi \in [x_{i-1},x_{i}] $$

Ref: Lecture Notes [[media:Egm6341.s10.mtg14.pdf|p.14-1]]

$$ \Rightarrow M_{4} := max \left| f^{(4)}(\xi)\right| $$ $$ \displaystyle \xi \in [a,b] $$

$$ \bar{M}_{4} \leq n \times M_{4} $$

$$ \Rightarrow \left| E_{n}^{2} \right| \leq \left| \frac{(b-a)^{5}}{2880n^{5}}nM_{4} \right| = \left| \frac{(b-a)(b-a)^{4}}{2880n^{4}} \right| = \frac{(b-a)h^{4}}{2880}M_{4} $$ where $$ \displaystyle h= \frac{(b-a)}{n} $$

Therefore,
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$$\displaystyle \displaystyle \left| {E}_{n}^{2} \right| \leq \frac{(b-a)^{5}}{2880 n^{4}} M_{4} = \frac{(b-a)h^{4}}{2880} M_{4} $$
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--Heejun Chung 18:14, 17 February 2010 (UTC)

Problem Statement
$$ \displaystyle I=\int_{0}^{\pi}e^{x}cos(x)dx,\,\, $$ $$\displaystyle Evaluate\, I_{n}, E_{n}, Ratio \,\, and \,\, \bar{E}_{n}\, by\, Trapezoidal\, rule.\,\,\, where\,\,\, n=1,2...,9 \,$$

Ref: Lecture Notes [[media:Egm6341.s10.mtg17.djvu|p.17-3]]

Solution
=Matlab Code for Trapezoidal Rule= MATLAB Code

Results: Trapezoidal Rule

Formula a) Comp. Trap. rule $$ \int_{a}^{b}f(x)dx=\frac{b-a}{2n}*[f(x_{0})+2f(x_{1})+2f(x_{2})+.........+2f(x_{n-1})+f(x_{n})] $$

b) Corrected Trap. rule $$ \int_{a}^{b}f(x)dx=\frac{b-a}{2n}*[f(x_{0})+2f(x_{1})+2f(x_{2})+.........+2f(x_{n-1})+f(x_{n})]-\frac{h^2}{12}*[f^{'}(b)-f^{'}(a)] $$

c) Asymptotic error $$ \bar{E}_{n} \equiv -\frac{h^{2}}{12}[f^{'}(b)-f^{'}(a)] $$

--Heejun Chung 01:31, 17 February 2010 (UTC)

title: User:Egm6341.s10.team3.heejun/HW3


text:
University of Florida/Egm6341/s10.Team2/HW3

Problem Statement
-Pg. 17-1

 * Derive the tighter error bound of the simple Simpson's rule on pg.14-2 for the following two cases by changing the function:

$$ G\left ( t \right ):= e\left ( t \right )-t^{4} \; e\left ( 1 \right )$$ $$ G\left ( t \right ):= e\left ( t \right )-t^{6} \; e\left ( 1 \right )$$

Point out where the proof breaks down.

 * $$ G\left ( t \right ):= e\left ( t \right )-t^{5} \; e\left ( 1 \right )$$ Find if $$ G^{\left (3 \right )}\left ( 0 \right )= 0$$ and follow the same steps as in the proof to see what happens.

Derivation of Tighter Error Bound of Simple Simpson's Rule
$$\begin{align} E_{2} & = \frac{(b-a)^5}{2880}f^{(4)}(\xi )\\ & = \frac{h^5}{2880}f^{(4)}(\xi )\\ \end{align}$$

$$ \mbox{where, }\quad h=\frac{(b-a)}{2}$$

Shift origin of x axis to point at $$x_1\!$$

$$x(t)=x_1+ht\! \qquad \mbox{where, } t\epsilon [-1,1]\!$$

$$\begin{cases} t=0 &, x= x(0) = x_1\\ t=+1 &, x= x(1) = x_1+h = x_2\\ t=-1 &, x= x(-1)= x_0\\ \end{cases}$$

$$E_2= I - I_2 = \frac{(b-a)}{2} e(1) = h\;e(1)$$

Therefore, $$\;\;-\frac{h^5}{90}f^{(4)}(\xi)= h\;e(1)$$

$$e(1)=\frac{h^4}{90}f^{(4)}(\xi)$$

$$e(t)=\int_{-t}^{+t}F(t)dt-\frac{t}{3}[F(-t)+4F(0)+F(t)] \qquad \mbox{where, } f(x(t))=F(t)$$

By Definition: $$\quad G^{(3)}(\xi_3)=0$$

 * $$ G\left ( t \right ):= e\left ( t \right )-t^{4} \; e\left ( 1 \right )$$

$$G^{(3)}(t)=e^{(3)}(t)-\frac{t^7}{210}\;e(1)$$

$$G^{(3)}(\xi_3)= 0 = e^{(3)}(\xi _3)-\frac{{\xi_{3}}^{7}}{210}\;e(1)$$

$$\begin{align} 0      & = e^{(3)}(\xi _3)-\frac{{\xi_{3}}^{7}}{210}\;e(1)\\ e(1)   & =e^{(3)}(\xi_3)\;\frac{210}{{\xi_{3}}^{7}}\\ \end{align}$$

Proof breaks down here. Neglects to properly integrate $$t^5\;e(1)$$

 * $$ G\left ( t \right ):= e\left ( t \right )-t^{6} \; e\left ( 1 \right )$$

$$G^{(3)}(t)=e^{(3)}(t)-\frac{t^9}{504}\;e(1)$$

$$G^{(3)}(\xi_3)= 0 = e^{(3)}(\xi _3)-\frac{{\xi_{3}}^{9}}{504}\;e(1)$$

$$\begin{align} 0      & = e^{(3)}(\xi _3)-\frac{{\xi_{3}}^{9}}{504}\;e(1)\\ e(1)   & =e^{(3)}(\xi_3)\;\frac{504}{{\xi_{3}}^{9}}\\ \end{align}$$

Proof breaks down here. Neglects to properly integrate $$t^5\;e(1)$$

Solution of Tighter Error Bound Function at t=0
$$ G\left ( t \right ):= e\left ( t \right )-t^{5} \; e\left ( 1 \right )$$

$$G^{(3)}(t)=e^{(3)}(t)-\frac{t^8}{336}\;e(1)$$

$$G^{(3)}(0)=e^{(3)}(0)-\frac{0^8}{336}\;e(1)$$

$$ G^{(3)}(0)= -\frac{2(0)^2}{3}\;[F^{(4)}(0)+90\;e(1)]$$

$$G^{(3)}(0) =0\!$$

Solution for problem 1:Egm6341.s10.team2.patodon 10:05, 17 February 2010 (UTC)

Proofread problem 1:

Problem Statement
Pg. 17-2 Show that the error of the Composite Simpson's Rule is:

$$ \left| E_{n}^{2} \right| \leq \frac{(b-a)^{5}}{2880 \; n^{4}}M_{4} = \frac{(b-a)h^{4}}{2880}M_{4} $$

where $$ \; M_{4} $$ is the maximum of  $$ \quad \left| F^{4}(\zeta) \right| \quad and \quad \zeta \epsilon \left[a,b \right] $$

Problem Solution
The error for the Simpson's Composite rule, can be expressed as follows:

$$ \; E_{n}^{2} = I - I_{n} $$

This error can be rewritten as follows:

$$ E_{n}^{2} =  \int_{a}^{b} f(x)dx - \frac{h}{3}\left[f_{0} + 4f_{1} + 2f_{2} +4f_{3} + 2 f_{4} ... + 2f_{n-2} + 4f_{n-1} + f_{n} \right] $$

This can be expressed by using the Composite Simpson's rule and dividing the interval 'a' to 'b' into smaller intervals, the error can be expressed as follows:

$$ E_{n}^{2} = \int_{x_{i}-1}^{x_{i}} f(x)dx - \frac{h}{3} \left[f(x_{i-1}) + f(x_{i}) \right] $$

In this manner the error for simple Simpson's rule can be used to describe the error as follows:

$$ \left|E_{n}^{2} \right| \leq \left| \frac{h^{5}}{90} \underbrace{\sum_{i=1}^{n} max F^{(4)}(\zeta)}_{\bar{M_{4}}} \right| $$

$$ \bar{M_{4}} \leq n \cdot M_{4} $$

Using this expression the error can then be expressed as follows:

$$ \left|E_{n}^{2} \right| \leq \left| \frac{(b-a)^{5}}{2880 \; n^{5}}n \; M_{4} \right| = \frac{(b-a)^{5}}{2880\; n^{4}}M_{4} $$

$$ \left|E_{n}^{2} \right| \leq \left| \frac{(b-a)(b-a)^{4}}{2880 \; n^{4}}M_{4} \right| = \frac{(b-a)h^{4}}{2880}M_{4} $$

Solution for problem 2: Guillermo Varela

Proofread problem 2: Srikanth Madala 05:22, 18 February 2010 (UTC)

Problem Statement
Pg. 17-2

See also HW1-problem 8HW1-problem8
 * 1) Using the error estimates of Taylor Series ,Composite Trapezoidal rule and Composite Simpson's rule estimate $$\boldsymbol{n}$$ such that $$\boldsymbol{E_n=I-I_n=O(10^{-6})}$$ and compare against numerical results of HW1.
 * 2) Numerically find the power of the step size h in the error i.e Plot the error vs h on semilog and fit a straight line and measure the slope.

Note: This problem is a logical continuation of problem 8 in HW1. In HW1 it was attempted by iteration to find the value of n. In this problem it is done analytically.All numerical data can be found on the HW1 page linked above and also the corresponding MATLAB codes.

Solution: Taylor series
Error is defined as
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$$  \displaystyle E_n=I-I_n =\int_{a}^{b}[f(x)-f_n(x)]dx $$
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For the Taylor series, from the discussion on p6-4, we know that the error is nothing but the remainder of the Taylor series integrated over the given interval i.e
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$$  \displaystyle \int_{a}^{b}R_{n+1}(x)= \int_{a}^{b}\left [\frac{(x-x_0)^{n+1}}{(n+1)!}f^{(n+1)}(\xi ) \right ] $$ where $$\xi \varepsilon [a,b] $$    (1 p2-3)
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For the given function the error is
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$$  \displaystyle E_n=\int_{0}^{1}\underbrace{\frac{x^n}{(n+1)!}}_{w(x)}\underbrace{e^{\xi (x)}}_{g(x)}dx $$    (2)
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Using the Integral Mean Value Theorem, we have
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$$  \displaystyle E_n=e^{\xi (x=\alpha)} \int_{0}^{1}\frac{x^n}{(n+1)!}dx $$    (3)
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integrating we get,
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$$  \displaystyle E_n=e^{\xi (x=\alpha)} \frac{1}{(n+1)!(n+1)} $$    (4)
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This function has a minimum when $$\; \alpha=0$$ and maximum when $$\; \alpha=1$$ thus we have
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$$  \displaystyle \frac{1}{(n+1)!(n+1)}\leq E_n\leq \frac{e}{(n+1)!(n+1)} $$    (5) Setting the upper bound of the error to $$\; 10^{-6}$$ we have
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$$  \displaystyle \ E_n\leq \frac{e}{(n+1)!(n+1)}=10^{-6} $$    (6) Solving this equation for $$\; n$$ we get
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$$  \displaystyle (n+1)!(n+1)=e*10^6 \Rightarrow n\approx 7.92 = 8 $$     (A)
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In the numerical analysis in problem 8 of HW1 it was seen that the Error for n = 8 was -3.848E-07

Solution:Composite Trapezoidal rule
From the discussion on page 16-3 we have

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$$  \displaystyle \left | E_n^1 \right |\leq \frac{(b-a)}{12n^2}M_2 $$    (1)
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where $$\; M_2 = max \left | f^{(2)} (\zeta )\right |$$ for $$\; \zeta \varepsilon [a,b]$$

For the given function $$\; f(x)= \frac{e^x - 1}{x}$$, we have

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$$  \displaystyle f^{(2)}(x)= \frac{e^x [x^2-2x+2]-2}{x^3} $$     (2)
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Evaluating over the given interval it is seen that the function $$\; f^{(2)}(x)$$ has maximum value at $$\; x=1$$

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$$  \displaystyle M_2= f^{(2)}(x=1)=\frac{e[1+2-2]-2}{1}=0.718282 $$    (3)
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Setting the error to the $$\; 10^{-6}$$ and solving for $$\; n$$ we get

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$$  \displaystyle \frac{(1-0)^3}{12n^2}(0.718282)=10^{-6}\Rightarrow n\approx 244.657= 245 $$     (B)
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In the numerical analysis the value of n =245 was found to be 5.872E-07

Solution :Composite Simpson's Rule
We have from p 17-2, the error estimate of the Composite Simpson's rule as
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$$  \displaystyle \left | E_n^2 \right |\leq \frac{(b-a)^5}{2880n^4}M_4 $$    (1)
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where $$M_4 = max \left | f^{(4)} (\zeta )\right |$$ for $$\zeta \varepsilon [a,b]$$

For the given function $$f(x)= \frac{e^x - 1}{x}$$, we have

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$$  \displaystyle f^{(4)}(x)= \frac{e^x [x^4-4x^3+12x^2-24x]-24}{x^5} $$     (2)
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Evaluating over the given interval it is seen that the function $$\; f^{(2)}(x)$$ has maximum value at $$\; x=1$$
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$$  \displaystyle M_4= f^{(4)}(x=1)=\frac{e[1-4+12-24+24]-24}{1}=9(e)-24=0.464536
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$$    (3)
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Setting the error to the $$\; 10^{-6}$$ and solving for $$\; n$$ we get

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$$  \displaystyle \frac{(1-0)^5}{2880n^4}(0.464536)=10^{-6}\Rightarrow n\approx 3.35735= 4 $$     (c)

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In the numerical analysis the error for n= 4 was 6.717E-06

Part 2:Numerical determination of power of h
In order to verify the power of $$\boldsymbol {h}$$ in the error, data from Problem 8 of HW1 is used.

In the case of a Semilog plot [log(y) vs x], a straight line has an equation of the form

$$\boldsymbol{log(Y)=a X+b}$$

such that $$\boldsymbol{Y= e^{(aX+b)}=e^b (e^{aX})=ke^{aX}}$$.From the above equation it is seen that if the plot on a semilog graph is a straight line then the relationship between the two variables is exponential.

A log-log plot(log(y) vs log(x)) is a similar plot, for which the equation is of the form

$$\boldsymbol{log(Y)=a [log(X)]+b}$$

such that, $$\boldsymbol{Y= kx^a;k=e^b}$$.It is readily seen that the slope of the line in the log-log graph is the power of the x variable. Further reference on the theory of semilog and log plots and methods to fit curves is given below:
 * 1) Semilog plot [w:Semi-log_graph]
 * 2) Log-Log plot [w:Log-log_graph]
 * 3) Methods of fitting curves in MATLAB for power and exponential series []

This discussion is used in the interpretation of the graphs given below.

Composite trapezoidal Rule
Given below is the data from the numerical evaluation of the given function using Composite Trapezoidal Rule.[Egm6341.s10.Team2/HW1] First we plot a semilog graph for the data. The graph is shown below:

The graph is not a straight line which implies that the relationship between $$\boldsymbol{h}$$ and $$\boldsymbol{log(error)}$$ is not exponential. Hence we plot a log-log graph as below:

This is seen to be linear. A straight line if fitted to the data the equation of which is given above. From the discussion above, we see that the slope of line is 2.1447 which is very close to the analytical value of 2.

Composite Simpson's Rule
Given below is the data obtained from HW1 for the Composite Simpsons Rule.[Egm6341.s10.Team2/HW1]

Plotting a semilog graph of $$\boldsymbol{log(error)}$$ against $$\boldsymbol{h}$$ we see that it is non-linear as in the case of the Composite Trapezoidal Rule.

Thus, plotting the log-log graph as below,

we see that the slope of the line is 4.0881 which is very close to the analytically determined value of 4.

Taylor Series
Given below is the data for the Taylor series method.$$\boldsymbol{h}$$ can be defined for the taylor series as $$(b-a)/n$$ but since $$\boldsymbol{h}$$ is not used explicitly in the Taylor series method,it might be of interest to observe how error depends on $$\boldsymbol{n}$$,the number of terms of the series. Given below are the plots.Semilog plots and log-log plots can be made of error vs h much like the ones given above, but no linearity is shown in both.

From this plot it is clearly seen that minimizing the error does not require an infinite series.The error curve is asymptotic and it can be seen that 8 terms gives a very low error.

Solution for problem 3: Niki Nachapa

Proofread problem 3: Guillermo Varela

Problem Statement
Pg. 17-3 and 18-1

a] Replicate the table 5.1, page 255, Atkinson text book using the composite Trapezoidal rule.

$$I=\int_{0}^{\pi} e^{x} \cos \left ( x \right )\cdot dx$$

b] Replicate the table 5.3, page 258, Atkinson text book using the composite Simpson's rule.

$$I=\int_{0}^{\pi} e^{x} \cos \left ( x \right )\cdot dx$$

c] Replicate the table 5.4, page 261, Atkinson text book

$$I=\int_{0}^{1} x^{3} \sqrt{x} \cdot dx$$

d] Replicate the table 5.5, page 262, Atkinson text book

$$I=\int_{0}^{5} \frac{1}{1+\left ( x-\pi \right )^{2}} \cdot dx$$

e] Replicate the table 5.6, page 262, Atkinson text book

$$I=\int_{0}^{1} \sqrt{x} \cdot dx$$

f] Replicate the table 5.7, page 263, Atkinson text book

$$I=\int_{0}^{2\pi} e^{\cos \left ( x \right )} \cdot dx$$

Problem Solution
 Solution for Part (a):  Here our given Integral is: $$I=\int_{0}^{\pi} e^{x} \cos \left ( x \right )\cdot dx$$ where $$f\left ( x \right )=e^{x} \cos \left ( x \right )$$ is the integrand and $$\;x\in \left [ 0,\pi \right ]$$. We use composite Trapezoidal rule to obtain the following tabulated results:

 MATLAB Code:

 Solution for Part (b):  Here our given Integral is: $$I=\int_{0}^{\pi} e^{x} \cos \left ( x \right )\cdot dx$$ where $$f\left ( x \right )=e^{x} \cos \left ( x \right )$$ is the integrand and $$\;x\in \left [ 0,\pi \right ]$$. We use composite Simpson's rule to obtain the following tabulated results:

 MATLAB Code:

 Solution for Part (c):  Here our given Integral is: $$I=\int_{0}^{1} x^{3} \sqrt{x} \cdot dx$$ where $$f\left ( x \right )=x^{3} \sqrt{x}$$ is the integrand and $$\;x\in \left [ 0,1 \right ]$$. We use both composite Trapezoidal and Simpson's rules to obtain the following tabulated results:

 MATLAB Code:

 Solution for Part (d):  Here our given Integral is: $$I=\int_{0}^{5} \frac{1}{1+\left ( x-\pi \right )^{2}} \cdot dx$$ where $$f\left ( x \right )=\frac{1}{1+\left ( x-\pi \right )^{2}}$$ is the integrand and $$\;x\in \left [ 0,5 \right ]$$. We use both composite Trapezoidal and Simpson's rules to obtain the following tabulated results:

 MATLAB Code:

 Solution for Part (e):  Here our given Integral is: $$I=\int_{0}^{1} \sqrt{x} \cdot dx$$ where $$f\left ( x \right )=\sqrt{x}$$ is the integrand and $$\;x\in \left [ 0,1 \right ]$$. We use both composite Trapezoidal and Simpson's rules to obtain the following tabulated results:

 MATLAB Code:

 Solution for Part (f):  Here our given Integral is: $$I=\int_{0}^{2\pi} e^{\cos \left ( x \right )} \cdot dx$$ where $$f\left ( x \right )=e^{\cos \left ( x \right )}$$ is the integrand and $$\;x\in \left [ 0,2\pi \right ]$$. We use both composite Trapezoidal and Simpson's rules to obtain the following tabulated results:

 MATLAB Code:

Solution for problem 4: Srikanth Madala 05:22, 18 February 2010 (UTC)

Proofread problem 4:

Problem Statement
Pg. 19-2 (cont'd on Pg. 6-5)

a) Modify the code to make the computation of T(2^j) efficient;

b) Add Romber Table and compare with previous results.

Problem Solution
a) Modified code

function [I1,I2,T1] = trapzoid(f,a,b,n) h=(b-a)/n; x=linspace(a,b,n+1); fx=feval(f,x); I1=h*(fx(1)/2+sum(fx(2:1:n))+fx(n+1)/2); n=2*n; h=(b-a)/n; x=linspace(a,b,n+1); fx=feval(f,x); I2=I1/2+h*sum(fx(2:2:n)); T1=(2^2*I2-I1)/(2^2-1);

%call function %I1=To(4),I2=To(8), and T1=T1(4) format long [I1,I2,T1]=trapzoid(@(x) (exp(x)-1)./x,eps,1,4)

b) Romberg Table

Convergence is achieved much faster than the composite trapezoidal rule.

Solution for problem 5:

Proofread problem 5:

Contributing Authors
Problem 1 Solution --Patrick O'Donoughue 10:07, 17 February 2010 (UTC)

Problem 2 solution --Guillermo Varela 19:16, 17 February 2010 (UTC)

Problem 3 solution --Niki Nachappa 15:31, 17 February 2010 (UTC)

Problem 4 solution and proof-read problem 2 -- Srikanth Madala 05:22, 18 February 2010 (UTC)

Problem 5 solution -- PENGXIANG JIANG 19:00, 17 February 2010 (UTC)

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


text:
Strokes and screening information

Background
Cardiovascular disease, which includes both heart attack and stroke, is the leading cause of death among all racial and ethnic groups, and for both sexes in the United States and Missouri. When examined along, heart disease is the leading cause of death, with stroke the third leading cause of death. The effects of cardiovascular disease also have an economic impact. Cardiovascular diseases cost Missourians roughly $3.5 billion dollars in direct hospital charges each year1. Cardiovascular disease is one of the most preventable diseases. Major risk factors for strokes are lifestyle related and can be controlled. These risk factors include tobacco use, physical activity, diet and maintaining a health weight. You are also at a greater risk of stroke if you have diabetes, hypertension (high blood pressure), or have suffered a stroke in the past2.

What is a Stroke?
Strokes are characterized into two different types, ischemic or hemorrhagic. Ischemic strokes occur as the result of a lack of oxygen, usually caused by a blood clot. As a result, the area of the brain affected is unable to function. The second type of stroke, which is less common than ischemic stroke, occurs due to a rupture vessel in the brain. The signs and symptoms of stroke typically start suddenly, over second to minutes, and in most cases do not progress further. In both types, there may be an inability to move limbs on one side of the body, inability to understand or create speech, or the inability to see one side of the visual field. Blood carries oxygen and nutrients to the brain. When blood flow to part of the brain stops, that part of the brain starts to die within minutes. The dying cells then release chemicals that can damage other cells. The symptoms depend on the area of the brain affected. If the brain is extensively affected, more functions are likely to be lost.

Transient Ischemic Attacks (TIAs) are related to strokes, sometimes called “ministrokes”. These ministrokes are caused by short interruptions of blood flow to the brain. The effect is only temporary, lasting as long as 24 hours. TIAs can be an important warning sign. As may as 1 out of 3 individuals who suffer a TIA will have a stroke in the future3.

How to Recognize a Stroke
According to the American Stroke Association, one of the easiest and most effective ways to increase recognition of stroke is the F.A.S.T. system. F.A.S.T. stands for Face, Arm, Speech, and Time4. The most warning signs include:
 * •	sudden numbness or weakness of the face, arms, or legs, especially on only one side of the body
 * •	sudden confusion, trouble speaking or understanding

 * •	sudden trouble seeing in one or both eyes
 * •	sudden trouble walking, dizziness, loss of balance or coordination
 * •	sudden severe headache with no known cause

Taking Action
It should be noted that not all warning signs occur in every stroke. Also, do not ignore signs if they happen to go away. Immediately call 9-11 or your local Emergency Medical Service (EMS) number so that an ambulance can quickly be sent to you.

How Can You Prevent a Stroke?

 * •	Don’t smoke
 * •	Keep your blood pressure under control

 * •	If you have diabetes, treat and monitor it

 * •	Eat a healthy diet consisting mostly of fruits, vegetables, and whole grains

 * •	Maintain a healthy weight
 * •	Stay active

 * •	Keep your blood cholesterol under control5

Stroke Screenings
Because up to 80 percent of strokes are preventable, being screened is important. Patients who have already suffered a stroke are at an increased risk and should have ultrasounds done on the carotid arteries, the abdominal aorta, and the peripheral arteries in the lower legs. These ultrasounds can detect harmful blood clots that may eventually lead to stroke or heart attack6.

title: Strokes and screening information


text:
User:Jel3728/Psychopharmacology

Antipsychotic drugs decrease psychotic, paranoid and disorganized thinking, alter bizarre behavior, decrease dangerous hyperactivty, increase activity levels in severly withdrawn patients.

Action: Blocks postsynaptic dopamine receptors in basal ganglia,limbic system, brainstem, and medulla.

Treatment for schizophrenia, manic bipolar, and organic brain syndromes.

Ex: Chlorpromazine (Thorazine) Thioridazine (Mellaril) Fluphenazine (Prolixin) Thiothixene (Navane) Haloperidol (Haldol) Clozapine   (Clozaril) Risperidone (Risperdal)

SE: Anticholinergic effects sedation wt gain extrapyramidal effects Tardive dskinesia

Neuroleptic Malignant Syndrome (FATAL)

title: User:Jel3728/Psychopharmacology


text:
User:Egm6341.s10.team3.Min/HW3

= (1)Proof the error bound for Simple Simpson' Rule = Ref: Lecture Notes [[media:Egm6341.s10.mtg17.djvu|p.17-1]]

Problem Statement
 Part 1  Replicate the proof of tighter error bound for Simple Simpson for two cases:
 * {| style="width:100%" border="0" align="left"

a) G(t) = e(t) - t^{4}e(1) $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

b) G(t) = e(t) - t^{6}e(1) $$ Point out where proof breaks down  Part 2  $$ \displaystyle G(t) = e(t) - t^{6}e(1) $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

Find $$ \displaystyle G^{(3)}(0) $$ and follow same steps in proof and see what happens

Solution
 Part 1

a) For case 1
 * {| style="width:100%" border="0" align="left"

G(t) = e(t) - t^{4}e(1) $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

From (3) in lecture[[media:Egm6341.s10.mtg14.pdf|p.14-2]]we have
 * {| style="width:100%" border="0" align="left"

e(t) = \int_{+t}^{-t}F(t)\, dt-\frac{t}{3}[F(-t)+4f(0)+F(t)] $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

e(0)= \int_{0}^{0}f(x)\, dx -\frac{0}{3}[F(-0)+4f(0)+F(0)]=0 $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

G(0) = e(0) - 0^{4}e(1)=0 $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

G(1) = e(1) - 1^{4}e(1)= 0 $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

According to Rolle' thm,
 * {| style="width:100%" border="0" align="left"

\exists  \zeta _1 \ni ]0,1[,  G^{(1)}(\zeta _1) = 0   $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

G^{(1)}(t) = e^{(1)}(t) - 4t^{3}e(1) $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

e^{(1)}(t)& = F(-t)+F(t)- \frac{1}{3}[F(-t)+4F(0)+F(t)]-\frac{t}{3}[-F^{(1)}(-t)+F^{(1)}(t)]\\ & = \frac{2}{3}[F(-t)+F(t)] - \frac{4}{3}F(0)-\frac{t}{3}[-F^{(1)}(-t)+F^{(1)}(t)]\\ \end{align} $$
 * $$ \displaystyle \begin{align}
 * $$ \displaystyle \begin{align}
 * }
 * }

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

e^{(1)}(0) &= \frac{2}{3}[F(0)+F(0)] - \frac{4}{3}F(0)-\frac{0}{3}[-F^{(1)}(-0)+F^{(1)}(0)]\\ &=\frac{4}{3}-\frac{4}{3}F(0)-0\\ &=0\\ \end{align} $$
 * $$ \displaystyle \begin{align}
 * $$ \displaystyle \begin{align}
 * }
 * }

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

G^{(1)}(0) = e^{(1)}(0) - 4(0^{3})e(1)= 0 $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

G^{(1)}(\zeta _1) = 0  $$ Thus According to Rolle' thm,
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

\exists  \zeta _2 \ni ]0,\zeta _1[,  G^{(2)}(\zeta _2) = 0   $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

G^{(2)}(t) = e^{(2)}(t) - 12t^{2}e(1) $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

G^{(2)}(0) = e^{(2)}(0) - 12(0^{2})e(1) = e^{(2)}(0)  $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

e^{(2)}(t) &= \frac{2}{3}[-F^{(1)}(-t)+F^{(1)}(t)] - \frac{1}{3}[-F^{(1)}(-t)+F^{(1)}(t)]-\frac{1}{3}[F^{(2)}(-t)+F^{(2)}(t)]\\ &=\frac{1}{3}[-F^{(1)}(-t)+F^{(1)}(t)]-\frac{t}{3}[F^{(2)}(-t)+F^{(2)}(t)]\\ \end{align} $$
 * $$ \displaystyle \begin{align}
 * $$ \displaystyle \begin{align}
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

e^{(2)}(0) = \frac{1}{3}[-F^{(1)}(-0)+F^{(1)}(0)]-\frac{0}{3}[F^{(2)}(-0)+F^{(2)}(0)]=0 $$ Thus
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * }
 * {| style="width:100%" border="0" align="left"

G^{(2)}(0) = e^{(2)}(0)=0   $$ Recall
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

G^{(2)}(\zeta _2) = 0  $$ Thus According to Rolle' thm,
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

\exists  \zeta _3 \ni ]0,\zeta _2[,  G^{(3)}(\zeta _3) = 0   $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

G^{(3)}(t) = e^{(3)}(t) - 24te(1) $$ Where
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

e^{(3)}(t) = -\frac{t}{3}[F^{(3)}(t)+F^{(3)}(-t)] $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * }

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

G^{(3)}(\zeta_3) & = -\frac{\zeta_3}{3}\underbrace{[F^{(3)}(\zeta_3)+F^{(3)}(-zeta_3)]}_{use DMVT}- 24\zeta_3e(1)\\ &=-\frac{\zeta_3}{3}[2\zeta_3F^{(4)}(\zeta_4)]- 24\zeta_3e(1)\\ &=0 \end{align} $$
 * $$ \displaystyle \begin{align}
 * $$ \displaystyle \begin{align}

$$
 * $$\displaystyle (Eq. 1)
 * }
 * }

Where $$\zeta _{4} \in [-\zeta _{3}, \zeta _{3}]$$ Since $$\zeta _{3} \neq 0, $$

Solve for

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

$$\displaystyle e(1)= -\frac{\zeta_3}{36}F^{(4)}(\zeta_4) $$
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style = |
 * }
 * }

From the relation ship between $$\zeta_4 and \xi $$ See HW2, No 15 for details

$$ \displaystyle F(t)=f(x(t)) $$

$$ \displaystyle x(t)=x_{1}+ht $$

$$ \displaystyle F^{(4)}(t) = \frac{d\left(F(t)^{(3)}\right)}{dt} = \frac{d\left(h^{3}f(x)^{(3)}\right)}{dx}\frac{dx}{dt} = h^{3}f^{(4)}(x) \times h = h^{4}f^{(4)}(x) $$

Let

$$ \displaystyle \xi = x_{1}+h \zeta_{4} $$

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

$$\displaystyle e(1)= -\frac{\zeta_3}{36}h^{4}f^{(4)}(\xi )=-\frac{\zeta_3(b-a)^{4}}{576}f^{(4)}(\xi )
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style="width:10%; padding:10px; border:2px solid #8888aa" |

$$ We know the Error for Simple Simpson's rule from lecture[[media:Egm6341.s10.mtg14.pdf|p.14-2]] $$ \displaystyle
 * style = |
 * }
 * }

E_{2} = I - I_2 = \frac{b-a}{2}e(1) = h e(1) $$

Thus the error is
 * {| style="width:100%" border="0" align="left"

$$\displaystyle E_{2} = h e(1)=-\frac{\zeta_3(b-a)^{5}}{1152}f^{(4)}(\xi )
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style="width:10%; padding:10px; border:2px solid #8888aa" |

$$
 * style = |
 * }
 * }

Sum: the proof breaks though at Eq 1, where we can not cancel $${\zeta_3}^2$$, because the third derivative of G(t) at $$\zeta_3$$ gives $$\zeta_3 e(1)$$ instead of $${\zeta_3}^2 e(1)$$

b) For case 2
 * {| style="width:100%" border="0" align="left"

G(t) = e(t) - t^{6}e(1) $$ The proof procedure is similar to case 1 <\br> From (3) in lecture[[media:Egm6341.s10.mtg14.pdf|p.14-2]]we have
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

e(t) = \int_{+t}^{-t}F(t)\, dt-\frac{t}{3}[F(-t)+4f(0)+F(t)] $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

e(0)= \int_{0}^{0}f(x)\, dx -\frac{0}{3}[F(-0)+4f(0)+F(0)]=0 $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

G(0) = e(0) - 0^{6}e(1)=0 $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

G(1) = e(1) - 1^{6}e(1)= 0 $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

According to Rolle' thm,
 * {| style="width:100%" border="0" align="left"

\exists  \zeta _1 \ni ]0,1[,  G^{(1)}(\zeta _1) = 0   $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

G^{(1)}(t) = e^{(1)}(t) - 6t^{5}e(1) $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

e^{(1)}(t)& = F(-t)+F(t)- \frac{1}{3}[F(-t)+4F(0)+F(t)]-\frac{t}{3}[-F^{(1)}(-t)+F^{(1)}(t)]\\ & = \frac{2}{3}[F(-t)+F(t)] - \frac{4}{3}F(0)-\frac{t}{3}[-F^{(1)}(-t)+F^{(1)}(t)]\\ \end{align} $$
 * $$ \displaystyle \begin{align}
 * $$ \displaystyle \begin{align}
 * }
 * }

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

e^{(1)}(0) &= \frac{2}{3}[F(0)+F(0)] - \frac{4}{3}F(0)-\frac{0}{3}[-F^{(1)}(-0)+F^{(1)}(0)]\\ &=\frac{4}{3}-\frac{4}{3}F(0)-0\\ &=0\\ \end{align} $$
 * $$ \displaystyle \begin{align}
 * $$ \displaystyle \begin{align}
 * }
 * }

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

G^{(1)}(0) = e^{(1)}(0) - 6(0^{5})e(1)= 0 $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

G^{(1)}(\zeta _1) = 0  $$ Thus According to Rolle' thm,
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

\exists  \zeta _2 \ni ]0,\zeta _1[,  G^{(2)}(\zeta _2) = 0   $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

G^{(2)}(t) = e^{(2)}(t) - 30t^{3}e(1) $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

G^{(2)}(0) = e^{(2)}(0) - 30(0^{4})e(1) = e^{(2)}(0)  $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

e^{(2)}(t) &= \frac{2}{3}[-F^{(1)}(-t)+F^{(1)}(t)] - \frac{1}{3}[-F^{(1)}(-t)+F^{(1)}(t)]-\frac{1}{3}[F^{(2)}(-t)+F^{(2)}(t)]\\ &=\frac{1}{3}[-F^{(1)}(-t)+F^{(1)}(t)]-\frac{t}{3}[F^{(2)}(-t)+F^{(2)}(t)]\\ \end{align} $$
 * $$ \displaystyle \begin{align}
 * $$ \displaystyle \begin{align}
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

e^{(2)}(0) = \frac{1}{3}[-F^{(1)}(-0)+F^{(1)}(0)]-\frac{0}{3}[F^{(2)}(-0)+F^{(2)}(0)]=0 $$ Thus
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * }
 * {| style="width:100%" border="0" align="left"

G^{(2)}(0) = e^{(2)}(0)=0   $$ Recall
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

G^{(2)}(\zeta _2) = 0  $$ Thus According to Rolle' thm,
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

\exists  \zeta _3 \ni ]0,\zeta _2[,  G^{(3)}(\zeta _3) = 0   $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

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

G^{(3)}(t) = e^{(3)}(t) - 120t^{3}e(1) $$ Where
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

e^{(3)}(t) = -\frac{t}{3}[F^{(3)}(t)+F^{(3)}(-t)] $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * }

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

G^{(3)}(\zeta_3) & = -\frac{\zeta_3}{3}\underbrace{[F^{(3)}(\zeta_3)+F^{(3)}(-\zeta_3)]}_{use DMVT}- 120{\zeta_3}^{3}e(1)\\ &=-\frac{\zeta_3}{3}[2\zeta_3F^{(4)}(\zeta_4)]- 120{\zeta_3}^{3}e(1)\\ &=0 \end{align} $$
 * $$ \displaystyle \begin{align}
 * $$ \displaystyle \begin{align}

$$
 * $$\displaystyle (Eq. 2)
 * }
 * }

Where $$\zeta _{4} \in [-\zeta _{3}, \zeta _{3}]$$ Since $$\zeta _{3} \neq 0, $$

Solve for

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

$$\displaystyle e(1)= -\frac{1}{180\zeta_3}F^{(4)}(\zeta_4) $$
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style = |
 * }
 * }

From the relation ship between $$\zeta_4 and \xi $$ See HW2, No 15 for details

$$ \displaystyle F(t)=f(x(t)) $$

$$ \displaystyle x(t)=x_{1}+ht $$

$$ \displaystyle F^{(4)}(t) = \frac{d\left(F(t)^{(3)}\right)}{dt} = \frac{d\left(h^{3}f(x)^{(3)}\right)}{dx}\frac{dx}{dt} = h^{3}f^{(4)}(x) \times h = h^{4}f^{(4)}(x) $$

Let

$$ \displaystyle \xi = x_{1}+h \zeta_{4} $$

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

$$\displaystyle e(1)= -\frac{1}{180\zeta_3}h^4F^{(4)}(\xi)= -\frac{(b-a)^4}{2880\zeta_3}F^{(4)}(\xi)
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style="width:10%; padding:10px; border:2px solid #8888aa" |

$$
 * style = |
 * }
 * }

We know the Error for Simple Simpson's rule from lecture[[media:Egm6341.s10.mtg14.pdf|p.14-2]] $$ \displaystyle

E_{2} = I - I_2 = \frac{b-a}{2}e(1) = h e(1) $$

Thus the error is
 * {| style="width:100%" border="0" align="left"

$$\displaystyle E_{2} = h e(1)= -\frac{(b-a)^4}{2880\zeta_3}hF^{(4)}(\xi)=-\frac{(b-a)^5}{5760\zeta_3}F^{(4)}(\xi)
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style="width:10%; padding:10px; border:2px solid #8888aa" |

$$
 * style = |
 * }
 * }

Sum: the proof breaks though at Eq 2, where we can not cancel $${\zeta_3}^2$$, but the third derivative of G(t) at $$\zeta_3$$ gives $${\zeta_3}^2 e(1)$$ instead of $${\zeta_3}^2 e(1)$$

 Part 2  Continue the proof from lecture [[media:Egm6341.s10.mtg15.djvu|Lecture p.15-2]] where we have
 * {| style="width:100%" border="0" align="left"

G^{(3)}(t) = e^{(3)}(t) - 60t^{2}e(1) $$
 * $$ \displaystyle
 * $$ \displaystyle

$$
 * $$\displaystyle (Eq. 3)
 * }
 * }

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

G^{(3)}(\zeta _3)=0 $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

e^{(3)}= \frac{t}{3}[F^{(3)}(t)-F^{(3)}(-t)] $$ $$
 * $$ \displaystyle
 * $$ \displaystyle
 * $$\displaystyle (Eq. 4)
 * }
 * }

From Eq 3. and Eq 4, we have

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

G^{(3)}(t) = \frac{t}{3}[F^{(3)}(t)-F^{(3)}(-t)] - 60t^{2}e(1) $$ Thus
 * $$ \displaystyle
 * $$ \displaystyle
 * }
 * {| style="width:100%" border="0" align="left"

$$\displaystyle G^{(3)}(0) = \frac{0}{3}[F^{(3)}(0)-F^{(3)}(-0)] - 60(0)^{2}e(1) = 0 $$
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style = |
 * }
 * }

Again, according to Rolle's thm,
 * {| style="width:100%" border="0" align="left"

\exists  \zeta _4 \ni ]0,\zeta _3[,  G^{(4)}(\zeta _4) = 0   $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

Next is to find the 4th derivative of G(t), we calculate the 4th derivative of e(t) first
 * {| style="width:100%" border="0" align="left"

e^{(4)}= -\frac{1}{3}[F^{(3)}(t)-F^{(3)}(-t)]-\frac{t}{3}[F^{(4)}(t)+F^{(4)}(-t)] $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

The 4th derivative of G(t) is given as:
 * {| style="width:100%" border="0" align="left"

G^{(4)}(t) & = e^{(4)}(t) - 120te(1) \\ & = -\frac{1}{3}[F^{(3)}(t)-F^{(3)}(-t)]-\frac{t}{3}[F^{(4)}(t)+F^{(4)}(-t)] - 120te(1)\\ \end{align} $$
 * $$ \displaystyle \begin{align}
 * $$ \displaystyle \begin{align}
 * }
 * }

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

G^{(4)}(\zeta _{4}) &= -\frac{1}{3}\underbrace{[F^{(3)}(\zeta _{4})-F^{(3)}(-\zeta _{4})]}_{use DMVT}-\frac{\zeta _{4}}{3}[F^{(4)}(\xi_4)+F^{(4)}(-\xi_4)] - 120\xi_4e(1)\\ &=-\frac{1}{3}[2\zeta _{4}F^{(4)}(\xi_5)]-\frac{\zeta _{4}}{3}[F^{(4)}(\xi_4)+F^{(4)}(-\xi_4)]-120\zeta _{4}e(1)\\ &=0 \end{align}$$ Where $$\zeta _{5} \in [-\zeta _{4}, \zeta _{4}]$$ Since $$\zeta _{4} \neq 0, $$
 * $$ \displaystyle \begin{align}
 * $$ \displaystyle \begin{align}
 * }
 * }

Solve for

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

$$\displaystyle e(1)= -\frac{1}{360}[2F^{(4)}(\zeta _{5})+F^{(4)}(\zeta _{4})+F^{(4)}(-\zeta _{4})] $$
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style = |
 * }
 * }

Since

$$ \displaystyle F(t)=f(x(t)) $$

$$ \displaystyle x(t)=x_{1}+ht $$

$$ \displaystyle F^{(4)}(t) = \frac{d\left(F(t)^{(3)}\right)}{dt} = \frac{d\left(h^{3}f(x)^{(3)}\right)}{dx}\frac{dx}{dt} = h^{3}f^{(4)}(x) \times h = h^{4}f^{(4)}(x) $$

See HW2, No 15 for details

Let

$$ \displaystyle \xi_1 = x_{1}+h \zeta_{4} $$

$$ \displaystyle \xi_2 = x_{1}+h \zeta_{5} $$

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

$$\displaystyle e(1)= -\frac{1}{360}[2h^{4}f^{(4)}(\xi_2 )+h^{4}f^{(4)}(\xi_1 )+h^{4}f^{(4)}(-\xi_1 )] =-\frac{(b-a)^4}{5760}[2f^{(4)}(\xi_2 )+f^{(4)}(\xi_1 )+f^{(4)}(-\xi_1 )] $$
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style = |
 * }
 * }

We know the Error for Simple Simpson's rule from lecture[[media:Egm6341.s10.mtg14.pdf|p.14-2]] $$ \displaystyle

E_{2} = I - I_2 = \frac{b-a}{2}e(1) = h e(1) $$

Thus the error is
 * {| style="width:100%" border="0" align="left"

$$\displaystyle E_{2} = h e(1)= -\frac{(b-a)^5}{11520}[2f^{(4)}(\xi_2 )+f^{(4)}(\xi_1 )+f^{(4)}(-\xi_1 )]
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style="width:10%; padding:10px; border:2px solid #8888aa" |

$$
 * style = |
 * }
 * }

Sum: Simple simpson is exact for poly deg less than 3. Because $$f ^4(t) = 0$$, thus $$ E_{2} = 0 $$

-- By Min Zhong 12:00, 17 February 2010 (UTC)

title: User:Egm6341.s10.team3.Min/HW3


text:
User:Michelism

Michelism is young and lovely who chooses to learn at a sight of the slightest chance available.I love reading articles,experiences and appreciates educative plus creative works. Am a kind of an African who appreciate Africa,her tradition and the rich culture that trail her people.To be precise,am a Nigeria.A country rich with human resources but have to live with one natural disaster,Corrupt Leaders. I love to make and see people happy,expecially the challenged people.Am 26 yrs this year not yet in university.My main priority is to gain admission this year and have a good year too. Am from a family of nine.I love them all and wishes to make a mark in their lives.Thank you!

title: User:Michelism


text:
University of Florida/Egm6341/s10.team2.niki/HW3

Problem Statement
Pg. 17-2

See also HW1-problem 8[] Using the error estimates of estimate $$\boldsymbol{n}$$ such that $$\boldsymbol{E_n=I-I_n=O(10^{-6})}$$
 * Taylor Series
 * Composite Trapezoidal rule
 * Composite Simpson's rule

Solution: Taylor series
Error is defined as
 * {| style="width:100%" border="0"

$$  \displaystyle E_n=I-I_n =\int_{a}^{b}[f(x)-f_n(x)]dx $$
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

For the Taylor series, from the discussion on p6-4, we know that the error is nothing but the remainder of the Taylor series integrated over the given interval i.e
 * {| style="width:100%" border="0"

$$  \displaystyle \int_{a}^{b}R_{n+1}(x)=\int_{a}^{b}[\frac{(x-x_0)^{n+1}}{(n+1)!}f^{(n+1)}(\xi )]$$ where $$\xi \varepsilon [a,b] $$    (1 p2-3)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

For the given function the error is
 * {| style="width:100%" border="0"

$$  \displaystyle E_n=\int_{0}^{1}\underbrace{\frac{x^n}{(n+1)!}}_{w(x)}\underbrace{e^{\xi (x)}}_{g(x)}dx $$    (2)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Using the Integral Mean Value Theorem, we have
 * {| style="width:100%" border="0"

$$  \displaystyle E_n=e^{\xi (x=\alpha)} \int_{0}^{1}\frac{x^n}{(n+1)!}dx $$    (3)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

integrating we get,
 * {| style="width:100%" border="0"

$$  \displaystyle E_n=e^{\xi (x=\alpha)} \frac{1}{(n+1)!(n+1)} $$    (4)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

This function has a minimum when $$\alpha=0$$ and maximum when $$\alpha=1$$ thus we have
 * {| style="width:100%" border="0"

$$  \displaystyle \frac{1}{(n+1)!(n+1)}\leq E_n\leq \frac{e}{(n+1)!(n+1)} $$    (5) Setting the upper bound of the error to $$10^{-6}$$ we have
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * {| style="width:100%" border="0"

$$  \displaystyle \ E_n\leq \frac{e}{(n+1)!(n+1)}=10^{-6} $$    (6) Solving this equation for n we get
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle (n+1)!(n+1)=e*10^6 \Rightarrow n\approx 7.92 = 7 $$     (A)
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 *
 * }

Solution:Composite Trapezoidal rule
From the discussion on page 16-3 we have

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

$$  \displaystyle \left | E_n^1 \right |\leq \frac{(b-a)}{12n^2}M_2 $$    (1)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

where $$M_2 = max \left | f^{(2)} (\zeta )\right |$$ for $$\zeta \varepsilon [a,b]$$

For the given function $$f(x)= \frac{e^x - 1}{x}$$, we have

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

$$  \displaystyle f^{(2)}(x)= \frac{e^x [x^2-2x+2]-2}{x^3} $$     (2)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Evaluating over the given interval it is seen that the function $$f^{(2)}(x)$$ has maximum value at $$x=1$$

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

$$  \displaystyle M_2= f^{(2)}(x=1)=\frac{e[1+2-2]-2}{1}=0.718282 $$    (3)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Setting the error to the $$10^{-6}$$ and solving for $$n$$ we get

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

$$  \displaystyle \frac{(1-0)^3}{12n^2}(0.718282)=10^{-6}\Rightarrow n\approx 244.657= 245 $$     (B)
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 *
 * }

Solution :Composite Simpson's Rule
We have from p 17-2, the error estimate of the Composite Simpson's rule as
 * {| style="width:100%" border="0"

$$  \displaystyle \left | E_n^2 \right |\leq \frac{(b-a)^5}{2880n^4}M_4 $$    (1)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

where $$M_4 = max \left | f^{(4)} (\zeta )\right |$$ for $$\zeta \varepsilon [a,b]$$

For the given function $$f(x)= \frac{e^x - 1}{x}$$, we have

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

$$  \displaystyle f^{(4)}(x)= \frac{e^x [x^4-4x^3+12x^2-24x]-24}{x^5} $$     (2)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Evaluating over the given interval it is seen that the function $$f^{(2)}(x)$$ has maximum value at $$x=1$$
 * {| style="width:100%" border="0"

$$  \displaystyle M_4= f^{(4)}(x=1)=\frac{e[1-4+12-24+24]-24}{1}=9(e)-24=0.464536
 * style="width:95%" |
 * style="width:95%" |

$$    (3)
 *
 * }

Setting the error to the $$10^{-6}$$ and solving for $$n$$ we get

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

$$  \displaystyle \frac{(1-0)^5}{2880n^4}(0.464536)=10^{-6}\Rightarrow n\approx 3.35735= 3 $$     (c)
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 *
 * }

Part 2:Numerical determination of power of h
In order to verify the power of $$\boldsymbol {h}$$ in the error, data from Problem 8 of HW1 is used.

In the case of a Semilog plot (log(y) vs x), an equation of the form

$$\boldsymbol{log(Y)=a X+b}$$

such that

$$\boldsymbol{Y= e^{(aX+b)}=e^b (e^{aX})=ke^{aX}}$$

From the above equation it is seen that if the plot on a semilog graph is a straight line then the relationship between the two variables is exponential.

A log-log plot(log(y) vs log(x)) is a similar plot, for which the equation is of the form

$$\boldsymbol{log(Y)=a [log(X)]+b}$$

such that, $$\boldsymbol{Y= kx^a;k=e^b}$$

This discussion is used in the interpretation of the graphs given below.

It is readily seen that the slope of the line in the log-log graph is the power of the x variable.

Composite trapezoidal Rule
Given below is the data from the numerical evaluation of the given function using Composite Trapezoidal Rule. First we plot a semilog graph for the data. The graph is shown below:

The graph is not a straight line which implies that the relationship between $$\boldsymbol{h}$$ and $$\boldsymbol{log(error)}$$ is not exponential. Hence we plot a log-log graph as below:

This is seen to be linear. A straight line if fitted to the data the equation of which is given above. From the discussion above, we see that the slope of line is 2.1447 which is very close to the analytical value of 2.

Composite Simpson's Rule
Given below is the data obtained from HW1 for the COmposite Simpsons Rule.

Plotting a semilog graph of $$\boldsymbol{log(error)}$$ against $$\boldsymbol{h}$$ we see that it is non-linear as in the case of the Composite Trapezoidal Rule.

Thus, plotting the log-log graph as below,

we see that the slope of the line is 4.0881 which is very close to the analytically determined value of 4.

Taylor Series
Given below is the data for the Taylor series method. Eventhough $$\boldsymbol{h}$$ is not used in the Taylor series method,defining $$\boldsymbol{h}$$ based on the number of terms of the series, it is seen that the error and h are not related exponentially or by a power relation i.e. both semilog and log log plots are not linear.

--Egm6341.s10.team2.niki 08:10, 17 February 2010 (UTC)


text: User:Zollerriia

title: User:Zollerriia


text:
User talk:Gaby nicolas habis

 Hello Gaby nicolas habis, 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. To get started, you may

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Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 16 February 2010 (UTC)

title: User talk:Gaby nicolas habis


text:
User talk:Sleiner

 Hello Sleiner, 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. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Mu301Bot 08:18, 16 February 2010 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 16 February 2010 (UTC)

title: User talk:Sleiner


text:
User talk:Lnunez 7403

 Hello Lnunez 7403, 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. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Mu301Bot 08:18, 16 February 2010 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 16 February 2010 (UTC)

title: User talk:Lnunez 7403


text:
Value chains and new media/Detail of the topics

08.02.2010	Concepts of Media, Media studies

15.02.2010	Media economics field and its subfields

22.02.2010	Participatory economy I: advertising and revenue sharing model

01.03.2010	Participatory economy II: Freemium and virtual production & commerce (topic 1)

08.03.2010	Participatory economy III: virtual production & commerce (topic 2)

15.03.2010	Long Tail and Media I

22.03.2010	Long Tail and Media II

29.03.2010	Web 2.0 rhetoric 5.03.2010      Social media and value chains I

12.03.2010     Social media and value chains II

19.03.2010     Produsage and recent developments in the field of new media

Topics and their order may be subject to changes


text: File:PK Case1.pdf

title: File:PK Case1.pdf


text:
User:Hotbuffy

My own personal university for learning about the things I'm interested in.

title: User:Hotbuffy


text: File:HW3 Q5 PK Case1.jpg

title: File:HW3 Q5 PK Case1.jpg


text: File:HW3 Q5 PK Case2.JPG

title: File:HW3 Q5 PK Case2.JPG


text: File:HW3 Q5 PK Case3.JPG

title: File:HW3 Q5 PK Case3.JPG


text: File:PK Case4.JPG

title: File:PK Case4.JPG


text:
User:Ernie03

Personal background:

I was born up north and raised in Miami, but had been trying to leave Florida for most of my life. After many years, I was finally able to leave. I have been in North Carolina for 16ish years.

I have been married for 24+ years and although I am child-free, I have had numerous pets. I currently have one outdoor cat that is most likely someone else's....

Professional/Academic background:

I graduated from a high school in Miami in 1977 and stranglely decided to pay out of state tuition for college. In 1981, I graduated from East Carolina University with a degree in Chemistry. After the first four years, I attended the University of Florida and graduated in 1985 from the College of Dentistry.

My first 6 years of my career, I worked in public health providing dental services to those that could not afford it. While working in this setting, I was slowly introduced into the world of education. I have been in education full-time for 18+ years.

In 1994, I accepted a position as the dental director at GTCC where I oversee the dental assisting and dental hygiene programs.

Information/Technology background:

I am mainly self-taught with regards to the technology aspect of life. I use a lot of different software to get the things done that I want to do. It probably also help with my ADHD and allows me to bounce from thing to thing.

I am not sure as to what I consider my knowledge level to be at, but I tend to play with Toolbook, Powerpoint, Photoshop, SoftChalk, TurningPoint, Audacity, Sony Vegas and now Dreamweaver.

title: User:Ernie03


text:
User:House.thomas

Thomas House

 * Attended Appalachian State University in Boone, Graduating in 1991 with a degree in Community and Regional Planning with a concentration in Geographic Information Systems and a minor in Geography
 * Later attended UNC - Asheville for a Post Baccalaureate Teaching Certification
 * Later attended East Carolina University Greeneville, NC Llcensure for instructional technology specialist computers (077 license)
 * Currently enrolled in the New Media and Global Studies program at Appalachian State University

title: User:House.thomas


text:
Data recovery

This resource is intended to be sort of a guideline what to do in order to rescue the data in case of operating system failure, accidental deletion, or file system corruption. The main focus will be on the Microsoft Windows, but applicable to the other operating systems as well.

Before anything happens
There are quite a few things you can do to ensure the relative safety of your data before anything even happens.

Backup
This is the number one rule! You are writing a thesis? A computer program? Creating resources offline for Wikiversity? In all of these cases you are dealing with small and portable files, but you put a lot of your time into them.

Data loss can have a multitude of causes, such as hardware failure of a data storage device, power outage during write access, software bugs, poor software design, malware, or even human error such as deleting the wrong directory, or formatting or writing a disk image to the wrong drive or partition.

At the end of each day you should backup these to a USB flash drive, memory card, or to your email inbox or Cloud storage in case you have access to the Internet. For larger files use external hard disk or a bigger USB flash drive. If the available space for backup is limited, consider data compression (i.e. to zip, rar, or 7z). Compression algorithms are particularly efficient on files with human-readable content.

If you use a flash drive on the go with data and tools you need regularly, mirror it to a hard drive at home regularly. You may also occasionally (e.g. monthly) check flash storages' data integrity by benchmarking its sequential read transfer rate from into a line graph, where downspikes may indicate error correction attempts by its memory controller, while a stable and constant speed signifies good storage health. Make sure your software benchmarks the whole space from beginning to end, not only few samples ("quick benchmark"), as results of whole benchmarks are more telling.

Support for some file formats for both user data and backups, such as Acronis backup, may be limited on different systems, or only readable through paid software. Such proprietary file formats restrict data portability through vendor lock-in and thus should only be used with caution.

Those currently lacking space storage may wish to create an image of the beginning (around 100 MB) of a data storage and/or partition, which contains crucial file system information. In case of file system corruption, an earlier state of the file system can be reinstated by applying back the image. The simplest way to create such a minimal image using existing software is to cancel the creation of a full disk image after few seconds.

Verify the backup
If you are about to delete files you think are already copied somewhere else, verify the copy.

Misconfigured file permissions might have prevented the files from being transfered in first place.

Create a file list
If you currently lack the storage to back up large amounts of data, a recursive file list should be created. Such a list has a marginial file size compared to a disk, making it very portable.

A list of files and the directory structure among file size information and date/time attributes can facilitate the guesswork that would be necessary to recover data after a file system corruption, as well as prevent loss of date/time information when not stored in files' internal metadata such as EXIF

Such a file list can be created using these example commands:

 * Windows:  – Creates a recursive file list of your user directory with sizes and last modified time stamps of minutely accuracy by default. The ,  , and   options allow specifically showing the creation, last access, and last modification times respectively.   redirects the output to a specified file. Only one   should only be used with caution, as it clobbers (overwrites) any existing file with the given name rather than appending to it.
 * Linux:
 * produces a similar output.  is the user's home directory variable. Any other path may be used.
 * produces a plain recursive list with full paths and file names, and can be used to back up the directory structure.  with no arguments outputs paths relative to the current working directory, and the   makes it only output folder names, no file names.
 * produces a detailed list of entries in the current working directory, with all time attribute types in full accuracy. However, the command lacks support for recursion, which means it can not scan through subfolders automatically.
 * The cross-platform  command produces an eye-candy text-based tree-style representation of the directory naming structure, optionally with file names.
 * On Windows, the  option includes files, rather than only folders, and   outputs only basic ASCII characters to represent the lines of the tree.

Check for damage
Tools such as  for Linux and HDD Scan for Windows allow scanning an entire disk for unreadable sectors.

For hard disk drives, an analysis using so-called S.M.A.R.T. (self-monitoring analysis and reporting tool) approximates the health by diagnosing disk parameters such as the number of spin-ups and hours in operation.

As this is just a rough approximation, a drive that appears healthy should still be backed up.

Optical media is not tied to a specific storage controller and is more predictable, as software such as QPx Tool and Nero DiscSpeed are able to scan the media and count the correctable errors, represented in a graph.

Minor errors are correctable to some extent, but a too high density of minor errors might render sectors of data uncorrectable.

Divide your HDD?
Dividing your hard drive into 2 partitions, one for backup and one for the operating system was a cheap way to help protect your data if your operating system becomes corrupt. The problem is though, if your hard drive crashes you can still lose everything. But now that prices have dropped on hard drives, backing up all important data on an external hard drive is the obvious, easy solution. Furthermore, even if your operating system becomes corrupt, there are ways to recover your data.

Use the Recycle bin
Enable the "Recycle bin" in Windows to save files before final deletion. This may take a little more time, but you can easily bring them back if you change your mind, or in case of accidental deletions.

Trustable data storage
Data storages from questionable and unreputable brands should be avoided, as they might be of low quality, not retain data well, and even overreport their capacity to the computer, leading to data loss upon writing to sectors that physically do no exist.

Storage with fraudulent capacity can be detected using tools such as f3probe for Linux and h2testW for Windows.

Online forms
For online forms, using a form recovery browser extension (or add-on) such as Textarea Cache should be considered, which automatically backs up online forms against potential losses and browser crashes.

If a form submission failed and the content is lost, it might still be recoverable by performing a text string search through a RAM dump generated using the task manager (in Windows) or GCore in Linux. In Linux, the precluded  tool is able to perform regular expression searches.

Develop the habit of copying larger text posts into your clipboard before hitting (or similar), or even save it locally to a text file into a dump folder. As a rule of thumb, do it for any text addition of more than 1000 characters, and/or anything that took over five minutes to write.

I have a problem...
Sooner or later you might face a situation, that your computer goes down and you are not able to access your data. Depends on the circumstances there are several possibilities to make things right, or at least rescue what could be rescued. Some of the scenarios are listed below.

Recovering data after physical damage
If your hard disk drive (HDD) was physically damaged or exposed to a magnetic field, then often your only choice is to send it to a recovery lab if need be. Such labs have clean rooms where they can open the case, remove the platter(s) and then try to recover what they can. Expect such services to cost far beyond the price of any new computer system, with no guarantee of success. Data Recovery on Wikipedia

Accidental deletion or format
For this section we start with some background information: If you delete something in Windows or format a hard disk with the "quick" format (the one which takes a few seconds) your data are not completely gone. The operating system just lets some other data to be written on the same place. In fact this replacement causes the final data loss.

Quick formatting overwrites the previous file system, but file contents themselves still exist as orphaned file fragments on the disk. Those need to be puzzled together.

So if you deleted something, but it is not rewritten yet, you can get these "lost" data back with help of special data recovery programs. You will have to search the web for these. In general you have better chance to retrieve smaller files compared to big ones. This is because if only a part of a big file is rewritten with something else it may cause the loss of the whole file.

If you are trying to rescue data from a formatted operating system partition ( drive in Windows), it is not the best sollution to install the operating system and then try to rescue (undelete) files with a program. This is because during the installation procedure you can rewrite the data you want to rescue. If you have the possibility, better connect the HDD to another computer and do the recovery process from there. If you wish to do continue using the source hard drive, first create a full disk image on a different hard drive. The disk image file is as large as the source disk itself, and contains all data that would have been recoverable. Data recovery software usually allows scanning disk image files.

Sidenote: Although this resource is about data rescue rather than data destruction, please note that there are programs for secure data erease. These rewrite (usually some sensitive or confidental) data with random bits of information, so they can't be recovered afterwards.

These methods do not work with smartphones' internal memory, as files on it are only accessed through the abstraction layer of the media transfer protocol (MTP).

Note that on solid state drives, an accidental deletion or formatting might have triggered a TRIM command, which would make existing data inaccessible to the computer, as the flash memory controller makes them appear empty to facilitate the internal so-called garbage collection process.

System failure (best case)
Your Windows system went down. First thing you should check if you can restore it with a few moves. When restarting your PC press F8 (at least for Windows XP). There you can try to start "Last good configuration". If this doesn't work, try to boot up the "Safe mode" and correct the potential error there whatever it is. You can use the safe mode to rescue your data as well.

If you have successfully entered safe mode, copy or move any data you do not wish to lose onto an intact external storage device immediately.

System failure (still good)
Your Windows system went down. You can't restore it via "Last good configuration" nor "Safe mode". Next thing what you can try is reinstall the corrupt or missing system files via a Windows installation CD.

For this insert the CD and restart your computer. Bring up the boot menu (usually F11 or F12) and boot it up. Select the "Repair" option and follow the steps there. Please note, that for this procedure you will most probably need the "administrator password" that you set, when you installed Windows last time.

System failure (bad, but not hopeless)
Your Windows system went down. You can't restore it via "Last good configuration" nor "Safe mode". The "Repair" procedure failed. You know, that you will have to reinstall the operating system, but you still have important data on the C drive. Remember: All files on the Windows desktop are on the C drive!

Before reinstalling the whole system and the eventual danger of rewriting important files (as mentioned earlier) you can use some Linux distributions to access your data. These are called "Live" versions, which means that you don't have to install them to your machine, but you can run them from a CD/DVD/USB directly. These are available for free, so you can just download and burn them. You can pick any Live distribution you want. The original author of this resource suggests SLAX, because it is small and very user friendly even for the non-experienced Linux users. (In fact the initial version of this resource was written on a crashed Windows machine with SLAX's KWrite. Thank you guys for this, whoever you are!)

Re-installation procedure
If you still have some data on the C drive you want, you can try to reinstall Windows without formatting the hard disk. In this case the Windows installation overwrites or renames the previous version, so the rest of the HDD could be saved.

However, for the duration of the installation, it is still recommended to have a backup of the partition. On some setups, the operating system partition is smaller than the secondary partition, which saves time on the backup.

To the end
On this page you can find some, but surely not every possibility for data rescue or good practice in order to keep your files as safe as possible. If you know about some other way, tell us!

title: Data recovery


text:
18th century European scholarly societies and academies/Century Club

Summary
Name of Society: Century Club

Country: England

City: London

Active Dates: 1865-1881

Mainly a political club with a Liberal outlook consisting of gentlemen of high intelligence from Oxford and Cambridge Universities who devoted themselves primarily to humanitarian causes. One of the founding causes for the club was the reform of Oxford and Cambridge Universities from a church based education system to a non-secular scholarly system of higher education.


text:
User:EinarKramer~enwikiversity

Man, living in Sandnes, ROgaland, Norway

Einar Kramer website

Kramer's Woden

title: User:EinarKramer~enwikiversity


text:
Comparative law and justice/Greece

Part of the Comparative law and justice Wikiversity Project

Basic Information
"Geography Area: 131,957 sq. km. (51,146 sq. mi.; roughly the size of Alabama). Major cities: Capital--Athens. Greater Athens (pop. 3,566,060), municipality of Athens (772,072), Thessaloniki (749,048), Piraeus (182,671), Greater Piraeus (880,529), Patras (170,452), Larissa (113,090), Iraklion (132,117). Terrain: Mountainous interior with coastal plains; 1,400-plus islands. Climate: Mediterranean; mild, wet winter and hot, dry summer. People Population (March 2001 est.): 10,939,771 million. Growth rate: 0.21%. Languages: Greek 99% (official); English. Religions: Greek Orthodox 98%, Muslim 1.3%, other .7%. Education: Years compulsory--9. Literacy--95%. All levels are free. Health: Infant mortality rate--6/1,000. Life expectancy--male 76 years, female 81 years. Work force: 4.32 million."

"MONETARY UNIT : "The euro replaced the drachma as official currency in 2002. The euro is divided into 100 cents. There are coins in denominations of 1, 2, 5, 10, 20, and 50 cents and 1 euro and 2 euros. There are notes of 5, 10, 20, 50, 100, 200, and 500 euros. As of May 2003, €1 = $1.0977 (or $1 = €0.911)". The metric system is the legal system."

"Approximately 98% of the population is Greek. Minority groups consist of Turks, Slavs, Albanians, Armenians, Bulgarians, Jews, and Vlachs. Under League of Nations supervision in 1923, more than 1 million Greek residents of Asia Minor were repatriated, and some 800,000 Turks left Greece. During the German occupation (1941–44) and the civil war (1944–49), there was a general movement of people from the islands, the Peloponnesus, and the northern border regions into the urban areas, especially the Athens metropolitan area, including Piraiévs. Between 1955 and 1971 about 1,500,000 peasants left their farms—about 600,000 going to the cities, the rest abroad. According to the 1981 census, 813,490 Greeks had migrated since 1975 to urban areas, and 165,770 had moved to rural areas. The growth rate of the Athens, Thessaloniki, Pátrai, Iráklion, and Vólos metropolitan areas during 1971–81 far exceeded the population growth rate for the nation as a whole. Modern Greek is the most popular language spoken in Greece. Approximately 99% of the population speaks Greek. English and French are spoken often in Greece, but are not taught in the school systems."

"The conservative government that came to power in 1990 adopted a 1991–93 "adjustment program" that called for reduction of price and wage increases and a reduction in the public-sector deficit from 13% to 3% of GDP. Twenty-eight industrial companies were to be privatized. In 2000, agriculture (with forestry and fishing) generated about 9% of the GDP but employed about 20% of the labor force. Agricultural exports include tobacco, cotton, wheat, raisins, currants, fresh fruits, tomato products, olive oil, and olives. In 2000, industry and construction accounted for about 22% of the GDP and 21% of the labor force. Wholesale and retail trade and other services provided some 70% of the GDP. Next to food processing, textile manufacturing used to be the most important industry, but chemicals and metals and machinery have outstripped it in recent years."

"At present, 100% of the population has access to safe water. In 1999, Greece immunized children up to one year of age against diphtheria, pertussis, and tetanus, 88%, and measles, 88%. In 2000, the infant mortality rate was 5 per 1,000 live births. The total fertility rate in 1980 (2.2) has dropped to 1.3 as of 2000. The sharp birth rate decline since World War II has been attributed to the legalization of abortion. In 2000, life expectancy averaged 78 years. As of 2002, the overall mortality rate was estimated at 9.8 per 1,000 people. The birthrate was an estimated 9.8 per 1,000 people. A large percentage of Greek men (54%) and women (13%) smoked between 1986 and 1994. As of 1999, the number of people living with HIV/AIDS was estimated at 8,000 and deaths from AIDS that year were estimated at fewer than 100. HIV prevalence was 0.2 per 100 adults."

"For the year 2000, adult illiteracy was estimated at 2.8% (males,1.4%; females, 4.0%). Education is free and compulsory for nine years beginning at age six, and primary education lasts for six years. Secondary education is comprised of two steps: first three years, followed by an additional three years of college preparation. The central and local governments pay the cost of state schools, and private schools are state-regulated."

"Greek History - The Dark Age of Greece - 1100-600 B.C., The collapse of the Mycenaean civilisation at the end of the Bronze Age disrupted life in the Aegean and resulted in the depopulation of the area. It is unclear what caused this but the result was that the Aegean became relatively isolated. The beginning of this period is sometimes known as the Dark Age as it saw the loss of many arts and crafts, including the art of writing. Recovery was patchy, and some areas flourished again as early as the 11th century BC. From around 800 BC recovery became more widespread. Trade picked up, wealth increased and technical and artistic skills were revived. Pottery was increasingly decorated with human figures and scenes from myths. Around this time writing was reintroduced using an alphabet adapted from that of the Phoenicians. The Greeks developed the political structure known as the city-state and began to establish colonies to both the east and west. The period from about 700 BC, known as the Orientalising Period, was a time when the Aegean re-entered the wider world of the eastern Mediterranean. Exotic Near Eastern animals, monsters and other motifs were increasingly used in Greek art. One example is the ‘Mistress of the Animals’ plaque from Rhodes."

Governance
The government of Greece is a parliamentary democracy. The power is basically put into the hands of the parliament. The administration is run by 151 political party members in the parliament. There is a president and a Prime minister in this form of government. The Prime Minister is basically the leader of the parliament. The Minister then goes on to appoint cabinet members, similar to what the President does in our country. The Parliament deputies elect the president rather than the public, and he/ or she serves for 5 year terms.

Greece has a constitution similar to that of the United States, and it gives rights and obligations to the citizens of Greece.

The Criminal law system is very simlar to that of the United States. You are allowed the right to a jury. There is a judicial branch and a supreme court. The judges are choosen by the president. You are allowed hearrings when requested.

Elections
Greek elections only require voters to be Greek citizens that are 18 yeard of age or older. There are 300 active members in the legislative branch, whom are elected by the public to serve four terms for their country. Judges have to be choosen by the president, and then accepted by a judicial council to receive their jobs. Once made into a judge, they are able to serve as a judge for the rest of their lives. You have to be a Greek citizen to vote, but it is not manditory to vote.

Judicial Review
Greece does have a role for judicial review. "The accused will meet with the Chair and Advisor to review their rights, review the charges and outline the judicial process. The organization is notified of the date, time and location for the hearing."

Courts and Criminal Law
The Greek courts are divided into an aministrative branch, a criminal branch and a civil branch, each dealing with different types of crimes. The Judicial Law enforcement consists of judges, clerks, and prosecutors. The district court judges are in charge of all private and criminal law cases. Juries do not participate in non-serious crimes such as civil crimes, and they only have a small amount of power in contributing to the outcome in serious criminal and federal crimes.You are innocent until proven guilty. The judges are choosen by judicial lawyers, who have at least two years of experience under their belts.

The Supreme court in Greece is located in Athens. In these cases fifty six judges listen to both sides of the case, and it takes twenty eight votes in one favor for a decision to be made. This court deals with questions of law as opposed to questions of fact.

After graduating from law school, graduates must work as apprentices in law firms for a year and a half before they are allowed to take a bar exam and fufill their carrers. As an apprentice, they are not allowed to participate in current law cases. Once this is completed, they take a series of written and oral exams, testing their knowledge of Criminal law, Commercial law, and the all around basis of the legal system. Once they pass the exam they can participate in local District Court cases. After four years of experience they can hen particpate in cases in the local Court of Appeals, and eventually with more experience appear in the Supreme Court

Punishment
"In Greece, possession of weapons is strictly prohibited, and unless one obtains a licence such as for hunting purposes, owning firearms is forbidden. Possessing, importing, and selling weapons carries severe penalty in Greece, including life imprisonment. In the past, people who committed gun crimes because of insult to their families were not punished. This old idea drew many critics from the Greek citizens, and the Greek government has since been less lenient to those who commit this type of crime."

"The Criminal Code punishes those who encourage prostitution of minors with imprisonment for up to ten years and a fine of €10,000 to €50,000. The punishment is more severe if the crime involves a minor under the age of fifteen or is committed by parents or step-parents, relatives, guardians, custodians, or teachers."

"The importance of the rule of law in the organization of the state is generally evident. Articles 4 to 25 of the Greek Constitution provide for the protection of human rights including the free development of one’s personality (Art. 5) and recognize the value of human dignity (Art. 2). Every act of the state must be in conformity with the law and it must also be provided for by a law. The Constitution divides state authority into the three functions of executive, legislative, and judicial (Art. 26). It grants the Judiciary independence from the other functions and the power to control and even annul acts of the public administration and to examine the constitutionality of acts of Parliament and refuse to apply statutes if they are found to be unconstitutional. The Constitution also grants to all citizens the right to seek judicial protection whenever their rights are infringed (Art. 20).

"One who by physical force or threat of serious and immediate danger forces another into extra-marital intercourse or attempts an indecent act, is punished with confinement.If the act of rape is committed by two or more perpetrators who were acting jointly, the persons are punished with confinement of at least 10 years.If the act of rape causes the death of the victim, confinement of at least ten years or life-imprisonment is imposed."

"Greece consists of one large mainland and more than 1,400 islands, including Crete and Rhodes, with a combined population of about 5.5 million people. Greece also is home to between 500,000 and one million illegal aliens. Most of the illegal immigrants are economic refugees who began arriving from Albania, Egypt, Palestine, Poland, Russia and Ukraine after 1990. Prior to that time, 99 percent of the country's residents spoke Greek as their first language and 98 percent were of the Greek Orthodox Adj. 1. Greek Orthodox - of or relating to or characteristic of the Eastern Orthodox Church Eastern Orthodox, Russian Orthodox, OrthodoxPolice officers and other law enforcement officers are authorized by federal, state, and local lawmakers to arrest and confine persons suspected of crimes. The judicial system is authorized to confine persons convicted of crimes.Rates in Europe (35 people incarcerated per 100,000). However, the influx of illegal immigrants and the diversification of the formerly homogeneous society has led to a current incarceration rate of nearly 72 per 100,000."

The death penalty was abolished in Greece in 1993 for all ordinary crimes. Later, in 2004, the death penalty was abolished in Greece for all crimes.

"The new law results from the work of the Greek Network for the Prevention and Combating of Corporal Punishment of Children, a committee of government and non-government bodies established in October 2005 specifically to draft legislation which would prohibit all corporal punishment."

"The Greek juvenile justice system has been traditionally characterized by the principle of education, protection, support and integration of the minor. Particularly, the new law (Act 3189/2003 ‘Reform of Criminal Legislation on Minors and Other Provisions’, in force since 21 October 2003) aims at strengthening not only the principle of education but also the rule of law (‘due process of law’) and care for crime victims in the way that the juveniles’ (re)integration into society can be achieved. The modernization of the juvenile justice system came through the adoption of a large variety of non-custodial educational measures which consider the deprivation of liberty as a measure of last resort, the development of non-custodial therapeutic measures, the consideration of the victim’s interests, the abolition of indeterminate sentences."

"The United Nations' top anti-torture envoy says conditions in Greek prison and police station detention facilities are often "appalling," with severe overcrowding and limited access to health care.Manfred Nowak described Greek detention facilities as being "in a situation of crisis," with some holding three times more people than they have capacity for."

Law Enforcement
The police academy in Greece consists of An Officers` School, which is a university-level institution, A Police Constable School, a national security school, and a school for continuting education. The director of the police academy, is a senior-level officer and is responsible for supervising and coordinating these separate faculties.Instructors are comprised of distinguished university professors, experts and experienced officers from the Force. The curriculum includes university-level courses, specialized vocational courses and field training.

"The Hellenic (Greek) Police assumed its present structure in 1984 when the Gendarmerie (Chorofylaki) and the Urban Police Forces (Astynomia Poleon) were merged (Law 1481/1-10-1984, Government Gazette 152 A). Hellenic Police (Elliniki Astynomia) is a Law Enforcement Agency according to the Law nr. 2800/2000 and its mission is to: Ensure peace and order as well as citizens` unhindered social development, a mission that includes general policing duties and traffic safety, and prevent and interdict crime as well as to protect the State and the democratic form of government within the framework of constitutional order, a mission that also includes the implementation of public and state security policy"

"Drug prevention in Greece is mostly implemented by the nationwide network of 71 Prevention Centres established by ΟΚΑΝΑ, local authorities, by the Ministry of Education, as well as by other governmental and non-governmental drug-specialised or health services, etc., which among other tasks are active in the field of prevention."

Greece is number 46 on the list for most police corruption in the world.

"The purpose of CEPOL's Common Curricula is to provide recommendations about police training on specific subjects with a European dimension. Member States can then use the recommendations within their national police training programmes according to their individual needs. The Common Curricula also provides the basic ideas and elements for CEPOL's courses and seminars. The subjects of the Common Curricula are determined by the Governing Board and are in line with the priorities outlined at a European level Terrorism is a global problem that shows no respect for international boundaries. It is appropriate when dealing with this threat that law enforcement activities are not constrained by international or jurisdictional boundaries. To achieve this, senior police officers should have a common understanding of contemporary techniques available and the inter-personal skills for them to be better able to plan for, prevent and react to terrorist threats in whatever forms it may arise.The Common Curriculum on Police Cooperation and Europol (CC05/C) aims to support the CEPOL partners to establish and develop national and international training about Europol and its role in the international law enforcement cooperation. Training is on a high professional level."

"19-45 years of age for compulsory military service; during wartime the law allows for recruitment beginning January of the year of inductee's 18th birthday, thus including 17 year olds; 17 years of age for volunteers; conscript service obligation - 1 year for all services; women are eligible for voluntary military service."

Military branches include Hellenic Army (Ellinikos Stratos, ES), Hellenic Navy (Ellinikos Polemiko Navtiko, EPN), Hellenic Air Force (Elliniki Polimiki Aeroporia, EPA).

Crime Rates and Public Opinion
"Assaults 3,322  [42nd of 49]  Burglaries  15,899  [30th of 38]  Car thefts  8,486  [29th of 46]  Corruption > % of managers surveyed ranking this as a major business constraint  9.8 %    [29th of 39]  Drug offences  33.3 per 100,000 people  [25th of 46]  Frauds  391  [55th of 48]  Illicit drugs a gateway to Europe for traffickers smuggling cannabis and heroin from the Middle East and Southwest Asia to the West and precursor chemicals to the East; some South American cocaine transits or is consumed in Greece; money laundering related to drug trafficking and organized crime  Manslaughters  19  [36th of 42]  Murders  81  [49th of 49]  Murders committed by youths  25  [54th of 73]  Murders committed by youths per capita  0.9  [53rd of 57]  Prisoners  8,841 prisoners  [67th of 168]  Prisoners > Female  4.9%  [48th of 134]  Prisoners > Foreign prisoners  42.4%  [9th of 86]  Prisoners > Per capita  83 per 100,000 people  [103rd of 164] Rapes 114  [49th of 50] Robberies 833  [52nd of 47] Software piracy rate 58%  [60th of 107] Total crimes 102,783  [36th of 50] Unpaid diplomatic parking fines 0"

The types of problems that can occur with statistics like these is that not all crimes that are committed are reported. Not even close.

"The 1950s in Greece were marked by a rash of «honour crimes» and by an extensive public debate on their penal management. The public interventions revolved around the emotions of the perpetrators and the jurors and had two aspects. One concerned the legal structure of honour as an emotion, described as intervening at the moment of the criminal act, and its assessment by the jury as a mitigating circumstance. The second referred to the emotions expressed by the jurors through their verdicts and explored to what degree these registered the existence of a cultural value system shared by the perpetrators and the jurors judging them. The much-discussed leniency which was systematically attributed to the jurors trying «honour crimes» gradually led, in the 1960s, to the contestation of the jury system of penal justice."

"The Greek legal system is a member of the family of European laws and is especially influenced by German and French law. For the most part, Greek law is codified and, unlike Anglo-American common law, only enacted laws either in the form of codes or other statutes are the sources of law in addition to custom and international law (Civil Code, Art. 1). The importance of custom, however, is minimal."

Greek law classifies any person between seven and seventeen years of age as a juvenile. The crime rate among juveniles in Greece is rather low compared with those in other Western countries. It is confined mainly to petty theft and property damage.

Rights
"Section 1 Respect for the Integrity of the Person, Including Freedom From: a. Arbitrary or Unlawful Deprivation of Life There were no reports that the government or its agents committed any politically motivated killings during the year; however, immigrant activists alleged that police officers killed one person in a scuffle. In December 2008 authorities arrested two police officers for the December 2008 killing of 15-year-old Alexandros Grigoropoulos and charged them with intentional homicide and complicity in homicide. The killing set off weeks of riots and demonstrations by youths and self-styled anarchists in cities across the country. The trial was pending at year's end. On January 8, the European Court of Human Rights (ECHR), in the case Leonidis vs. Greece, determined that the country had violated the right to life of an 18-year-old-youth who was accidentally killed by a police officer in 2000 during an arrest. According to media and immigrant NGOs, on January 3, a Bangladeshi man died when he fell into a ravine after an alleged scuffle with police. His death followed the death of a Pakistani man in October 2008 at the same spot. Police denied any involvement in the incidents, which took place close to immigration headquarters where hundreds of immigrants gathered every week to submit applications for asylum. Some nongovernmental organizations (NGOs) representing Muslim and immigrant groups criticized the police for brutality and poor organization of asylum processing procedures. In October the media reported that the new minister for citizen's protection held an unprecedented meeting with Pakistani community leaders to discuss ways to prevent future incidents. The trial in the 2007 case of a border guard, who shot and killed an Albanian immigrant attempting to illegally cross the Greek-Albanian border, remained pending at year's end. On February 4, the Council of Europe's Commissioner for Human Rights reported that, since 1995, at least 108 persons attempting to cross the border had been killed and another 187 persons were severely injured by marked minefields in the Evros area along the Greek-Turkish border. No minefield-related deaths were reported during the year. b. Disappearance There were no reports of politically motivated disappearances. c. Torture and Other Cruel, Inhuman, or Degrading Treatment or Punishment The law prohibits such practices and provides safeguards for criminal suspects and illegal immigrants in detention. However, during the year several international organizations and NGOs reported abuse by police personnel and the coast guard, particularly of undocumented immigrants, asylum seekers, and Roma." "2009 Human Rights Report: Greece."

Family Law
Marriage lisences take about a week to be issued, after an application is sent in, and is credible for half a year. A wedding or ceremony can legal be performed anywhere in Greece, as long as an application is sent to whomever is in power of that community, regarding the place that they will be married. That person in power is then responsible for setting the date of the ceremony. There needs to be at least two witnesses, (whom can be choosen by those getting married), one serving as an interpreter, and these witnesses must have proof with them, that they are Greek citizens.

"Divorce requires a court decision that is no longer open to appeal. Proceedings are of two kinds: (a) In a divorce by consent, the spouses agree to dissolve the marriage between them, and make a joint petition to the single-judge court of first instance of the place. There is no litigation, the procedure being that followed in non-contentious cases. The couple must have been married one year or longer. (b) In a contested divorce, one of the spouses brings an action seeking dissolution of the marriage, on stated grounds, before the multi-member court of first instance of the place, or both spouses bring such actions separately."

"Adults between the ages of 30 and 60, and who are at least 18 years older than the person to be adopted (this holds for adult adoption as well, however the adopting parent must be at least 40 years of age, and there is no upper age limit). Adopting parents may be married or single. If married, both parties must adopt jointly except in the case of stepparent adoption (rare exceptions may be allowed). If single, only one person may adopt. Co-parent adoption by unrelated single persons is not permitted."

"Greek Inheritance Law provides the bequest of the deceased's property to his legal heirs in two ways: by virtue of a will or in intestacy. In case that the deceased has left a Greek will, the bequest of the inherited property, i.e. the transfer of the property under the names of his heirs, appointed by the deceased, and to what property parts they are entitled to, is arranged according to the provisions of the Greek will. The law provides three types of Greek wills: • The holographic will; written entirely by the hand of the testator, who writes the date of the Will, and signs same, verifying its content. • The public will, which consists of the testator's last will and testament and is executed before a Notary  Public under the presence of three witnesses. • The secret will. The testator delivers the document to the Notary Public, stating that the document  consists of his last Will and testament, under the presence of three witnesses"

"According to Greek Family Law (Civil Code), during the marriage both parents have joint custody of the child. Custody includes care of the child's person, management of his/her property and the representation of the child in any matter, legal transaction or Court action relating to the child's person and/or to the child's property as well as decision making regarding the child's educational needs, place of residence etc. In case of a divorce, both parents continue to have the legal custody of the minor child; however, there is a need for a regulation of physical custody. According to Article 1513 of the Civil Code, in the case of a divorce physical custody in Greece is regulated by the Court. The most common solution that Greek Courts order for the regulation of physical custody is to assign it to one of the parents, whom the Court considers most appropriate to exercise it. If the parents agree to continue to share physical custody after the divorce, the Court may decide that both parents can continue to exercise the custody, provided that they also agree regarding the place of residence of the child. Moreover, the Court may divide the physical custody between the parents."

"The Greek juvenile justice system has been traditionally characterized by the principle of education, protection, support and integration of the minor. Particularly, the new law (Act 3189/2003 ‘Reform of Criminal Legislation on Minors and Other Provisions’, in force since 21 October 2003) aims at strengthening not only the principle of education but also the rule of law (‘due process of law’) and care for crime victims in the way that the juveniles’ (re)integration into society can be achieved. The modernization of the juvenile justice system came through the adoption of a large variety of non-custodial educational measures which consider the deprivation of liberty as a measure of last resort, the development of non-custodial therapeutic measures, the consideration of the victim’s interests, the abolition of indeterminate sentences, the introduction of diversion at the prosecutorial stage and the extension of the scope of the right to appeal to a higher judicial body."

Elders are treated no different than those over the age of 18, and women do have citizenship rights.

http://eng.atlants.lv/summaries-notes/the-basic-information-about-greece/429889/

title: Comparative law and justice/Greece


text:
18th century European scholarly societies and academies/Aberdeen Philosophical Society

Summary
Name of Society: Aberdeen Philosophical Society

Alternate Name(s): Wise Club

Country: Scotland

City: Aberdeen

Active Dates: 1758-1773

The society was made up of intellectuals from the two nearby colleges, King's and Marischal. A tightly knit group whose discussions centered on the Enlightenment thought of the 18th century. The original members were Thomas Reid, John Gregory, David Skene, George Campbell, John Stewart, Robert Traill and James Olgivie, Lord Deskford.


text:
18th century European scholarly societies and academies/Cosmopolitan Club

Summary
Name of Society: Cosmopolitan Club

Country: England

City: London

Active Dates: 1852–1902

A exclusive social club where lively conversation was encouraged. The club was limited to 150 members but encouraged members to bring guests, especially those from foreign lands and its main topic of discussion was politics on any given day. The club had a strong artistic representations including, Anthony Trollope.


text:
User:M\reyesjr05

M Reyes Jr

title: User:M\reyesjr05


title: File:Egm6341.niki.test.jpg