text:
University of Florida/Egm4313/s12.team5.R5

Question
Find $$ R_c $$ for the following series: 1. $$ r(x)=\sum_{k=0}^\infty(k+1)kx^k $$ 2. $$ r(x)=\sum_{k=0}^\infty \frac{(-1)^k}{\gamma^k}x^{2k} $$ $$ \gamma= \text{constant} $$ Use (2)-(3)p.7-31 to find $$ R_c $$ for the Taylor series of 3. $$ sinx   $$ at $$  \hat x=0 $$ 4. $$ log(1+x)  $$ at  $$ \hat x=0 $$ 5. $$ log(1+x)  $$ at  $$ \hat x=1 $$

Solution
1. $$ r(x)=\sum_{k=0}^\infty(k+1)kx^k = 0 + 2x + 6x^2... $$ Using L'Hospital's rule and (2)p.7-31, and setting $$ d_k=(k+1)k $$: $$ R_c = \left [\lim_{k \to \infty } \left|\frac{(k+2)(k+1)}{(k+1)k}\right|\right]^{-1} = \left [\lim_{k \to \infty } \left|\frac{k+2}{k}\right|\right]^{-1} = \left [\lim_{k \to \infty } \left|\frac{1}{1}\right|\right]^{-1} = 1 $$

2.$$ r(x)=\sum_{k=0}^\infty \frac{(-1)^k}{\gamma^k}x^{2k} = 1 - \frac{1}{\gamma}x^2 + \frac{1}{\gamma^2}x^4... $$ Using (3)p.7-31 and setting $$ d_k=\frac{(-1)^k}{\gamma^k} $$: $$ R_c= \lim_{k \to \infty} \left[ \sqrt[k] {\left|\frac{(-1)^k}{\gamma^k} \right|} \right]^{-1}=\lim_{k \to \infty} \frac{\sqrt[k]{|\gamma^k}|}{\sqrt[k]{|(-1)^k|}} = \lim_{k \to \infty} \frac{\sqrt{|\gamma|}}{\sqrt{|-1|}} = \sqrt{|\gamma|}$$

3. Taylor series about $$ \hat x = 0 $$: $$ sinx = x + \frac{1}{6}x^3 + \frac{1}{120}x^5... \Rightarrow \sum_{k=0}^\infty \frac{(-1)^k}{(2k+1)!}x^{2k+1} $$ Using (2)p.7-31 and setting $$ d_k=\frac{(-1)^k}{(2k+1)!} $$: $$ R_c=\left [\lim_{k \to \infty } \left|\frac{\frac{(-1)^{k+1}}{(2(k+1)+1)!}}{\frac{(-1)^k}{(2k+1)!}}\right|\right]^{-1} = \left[\lim_{k \to \infty}\left |\frac{-1}{(2k+3)(2k+2)} \right|\right]^{-1} = \infty $$

4. Taylor series about $$ \hat x = 0 $$: $$log(1+x)= 0 + x - \frac{x^2}{2} + \frac{x^3}{3}... \Rightarrow \sum_{n = 0}^{\infty }\frac{(-1)^k (x)^{k+1} }{(k+1)} $$ Using L'Hospital's rule and (2)p.7-31, and setting $$ d_k=\frac{(-1)^k}{(k+1)} $$: $$ R_c=\left [\lim_{k \to \infty } \left| \frac{\frac{(-1)^{k+1}}{(k+2)}}{\frac{(-1)^k}{(k+1)}} \right|\right]^{-1} = \left [\lim_{k \to \infty } \left| \frac{(-1)(k+1)}{(k+2)} \right|\right]^{-1} = \left [\lim_{k \to \infty } \left| \frac{-1}{1} \right|\right]^{-1} = 1 $$

5. Taylor series about $$ \hat x=1 $$: $$ log (1+x)=log(2) + \frac{(x-1)}{2} - \frac{(x-1)^2}{8} + \frac{(x-1)^3}{24}... \Rightarrow log(2) + \sum_{n = 0}^{\infty } \frac{(-1)^{k+1}(x-1)^k }{k2^k} $$ Using L'Hospital's rule and (2)p.7-31, and setting $$ d_k=\frac{(-1)^{k+1}}{k2^k} $$: $$ R_c=\left [\lim_{k \to \infty } \left| \frac{\frac{(-1)^{k+2}}{(k+1)2^{k+1}}}{\frac{(-1)^{k+1}}{k2^k}} \right|\right]^{-1} = \left [\lim_{k \to \infty } \left| \frac{-1k}{2(k+1)} \right|\right]^{-1} = \left [\lim_{k \to \infty } \left| \frac{-1}{2} \right| \right]^{-1} = 2 $$

Author
This problem is solved and uploaded by Radina Dikova

Question
Determine whether the following pairs of functions are linearly independent:

$$ \displaystyle \ 1. f(x) = x^2, g(x) = x^4\ $$

$$ \displaystyle \ 2. f(x) = \cos(x), g(x) = \sin(3x)\ $$

First use the Wronskian method, then use the Gramian method.

Solution
The Wronskian is defined as: $$ \displaystyle \ W(f,g) := \det \begin{bmatrix} f &g \\ f' & g' \end{bmatrix} = fg' -gf'\ $$

If $$ \displaystyle \ W(f,g) \neq 0\ $$, then the functions f and g are linearly independent.

The Gramian is defined as: $$ \displaystyle \ \Gamma (f,g) : = \det \begin{bmatrix}  & \\ &  \end{bmatrix}\ $$

Where $$ \displaystyle \  := \int_{a}^{b} f(x)g(x)dx\ $$

If $$ \displaystyle \ \Gamma(f,g) \neq 0\ $$, then the functions f and g are linearly independent.

1. Using Wronskian.

$$ \displaystyle \ W(f,g) = fg' - gf' = x^2 (4x^3) - x^4 (2x) = 4x^5 - 2x^5 = 2x^5 \neq 0 $$

Therefore, f and g are linearly independent.

2. Using Wronskian.

$$ \displaystyle \ W(f,g) = fg' - gf' = \cos(x) (3\cos(3x)) - \sin(3x) (-\sin(x)) \neq 0 $$

Therefore, f and g are linearly independent.

1. Using Gramian with an interval of [-1,1]

$$ \displaystyle \  = \int_{-1}^{1} x^2(x^2)dx = \frac{1}{5} x^5 \mid_{-1}^{1} = \frac{2}{5}\ $$

$$ \displaystyle \  =  = \int_{-1}^{1} x^2(x^4)dx = \frac{1}{7} x^7 \mid_{-1}^{1} = \frac{2}{7}\ $$

$$ \displaystyle \  = \int_{-1}^{1} x^4(x^4)dx = \frac{1}{9} x^9 \mid_{-1}^{1} = \frac{2}{9}\ $$

$$ \displaystyle \ \Gamma (f,g) =   -   = \frac{2}{5} (\frac{2}{9}) - \frac{2}{7} (\frac{2}{7}) = \frac{4}{45} - \frac{4}{49} \neq 0\ $$

Therefore, f and g are linearly independent.

2. Using Gramian with an interval of [-1,1]

$$ \displaystyle \  = \int_{-1}^{1} \cos(x) (\cos(x)) dx = \int_{-1}^{1} \cos^2(x) dx = \frac{1}{2} \int_{-1}^{1} 1 + \cos(2x) dx = \frac {1}{2} (x + \frac{1}{2} \sin(2x)) \mid_{-1}^{1} = 1.4546\ $$

$$ \displaystyle  =  = \int_{-1}^{1} \sin(3x) \cos(x) dx = 0\ $$

$$ \displaystyle <g,g> = <g,g> = \int_{-1}^{1} \sin^2(3x) dx = \frac{1}{2} \int_{-1}^{1} 1-cos(6x) dx = \frac{1}{2} (x - \frac{1}{6} \sin(6x)) \mid_{-1}{1} = 1.04657\ $$

$$ \displaystyle \ \Gamma(f,g) = <f,f> <g,g> - <f,g> <g,f> = 1.4546 (1.04657 ) - 0(0) \neq 0\ $$

Therefore, f and g are linearly independent.

Author
This problem was solved and uploaded by David Herrick.

Question
Verify that $$b_1$$ and $$b_2$$ in (1)-(2) p.7-34 are linearly independent using the Gramian

Solution
The given Grammian:

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

$$  \displaystyle \Gamma (b_1,b_2) = \begin{bmatrix} \left \langle b_1,b_1 \right \rangle \left \langle b_1,b_2 \right \rangle \\ \left \langle b_2,b_1 \right \rangle \left \langle b_2,b_2 \right \rangle \end{bmatrix} $$
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 * }

In reference to to (3) on p.8-9

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$$  \displaystyle \left \langle b_1,b_1 \right \rangle = (b_1 \cdot b_2) $$
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 * style="width:95%" |

 * }

Calculating the dot products yields:

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$$  \displaystyle \left \langle b_1,b_1 \right \rangle = 4 + 49 = 53 $$
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 *

 * }

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$$  \displaystyle \left \langle b_1,b_2 \right \rangle = 3 + 21 = 24 $$
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 *

 * }

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

$$  \displaystyle \left \langle b_2,b_1 \right \rangle = 3 + 21 = 24 $$
 * style="width:95%" |
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 *

 * }

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

$$  \displaystyle \left \langle b_2,b_2 \right \rangle = 2.25 + 9 = 11.25 $$
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 * }

Plugging the dot products into the Grammian yields:

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

$$  \displaystyle
 * style="width:95%" |
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\Gamma = 596.25 - 576 = 20.25 \ne 0

$$

 * }

Therefore, b1 and b2 are linearly independent.

Author
Solved and uploaded by Derik Bell

Question
Show that: $$ y_p (x) = \sum_{i=0}^{n} (y_{p,i} (x)) $$ is the particular solution to: $$ y' ' + p(x) y' + q(x) y = r(x) $$ Discuss the choice of particular solutions in the table on p8-3. In other words, for r(x) = kcos(wx), why would you need to have both cos(wx) and sin(wx) in the particular solution?

Solution
For a single excitation that satisfies $$ r_i (x) $$, $$ y_{p,i} ' ' + p(x) y_{p,i} ' + q(x) y_{p,i} = r_i (x) $$ for example: $$ y_{p0} ' ' + p(x) y_{p0} ' + q(x) y_{p0} = r_0 (x) $$ $$ y_{p1} ' ' + p(x) y_{p1} ' + q(x) y_{p1} = r_1 (x) $$ $$ y_{p2} ' ' + p(x) y_{p2} ' + q(x) y_{p2} = r_2 (x) $$ and so on until... $$ y_{p,n} ' ' + p(x) y_{p,n} ' + q(x) y_{p,n} = r_n (x) $$ where by linearity: $$ r(x) = \sum_{i=0}^n r_i (x) $$ Since $$ y_{p,i} $$ is the solution to a single iteration of r(x) and $$ r(x) = \sum_{i=1}^n r_i (x) $$, then by linearity, the solution to r(x) is: $$ y_p (x) = \sum_{i=1}^n y_{p,i} $$ Part 2: kcos(wx) is a periodic function. As shown by (3) on p8-2, any periodic function can be broken down into a fourier trigonometric series: $$ r(x) = a_0 + \sum_{n=1}^\infty [a_n cos(nwx) + b_n sin(nwx)] $$ r(x) can be further broken down as the sum of: $$ r_a=a_0 $$ $$ r_b = \sum_{n=1}^\infty a_n cos(nwx) $$ $$ r_c = \sum_{n=1}^\infty b_n sin(nwx) $$ Where $$ r(x) = r_a + r_b + r_c $$ Since r(x) is expressed in terms of cos(x) and sin(x) the particular solution, which is also a sum of the individual particular solutions for each iteration of $$ r_a $$, $$ r_b $$, and $$ r_c $$, needs to be in terms of sin(x) and cos(x) as well. That applies to all periodic functions as shown on p8-2, which sin(x) is as well. Therefore that justifies why the particular solutions for kcos(wx), ksin(wx), $$ ke^{\alpha x} \cos{wx} $$, and $$ ke^{\alpha x} \sin{wx} $$ must all include both cos(x) and sin(x).

Author
This problem was solved and uploaded by John North.

Question

 * 1. Show that cos(7x) and sin(7x) are linearly independent using the Wronskian and the Gramian (integrate over 1 period)
 * 2. Find 2 equations for the two unknowns M,N and solve for M,N
 * 3. Find the overall solution y(x) that corresponds to the initial condition y(0)=1, y'(0)=0. Plot the solution over 3 periods.

Solution
(1)

First, using Wronskian:

 * For 2 functions, f and g, the Wrosnkian is defined as $$\displaystyle W(f,g):=det\begin{bmatrix}

f &g \\ f'&g' \end{bmatrix}=fg'-gf' $$

 * Where f and g are linearly independent if $$\displaystyle W(f,g)\neq 0 $$

 * For $$\displaystyle f=cos(7x), g=sin(7x),f'=-7sin(7x),g'=7cos(7x) $$

 * Then, $$\displaystyle W(f,g):=det\begin{bmatrix}

cos(7x) &sin(7x) \\ -7sin(7x)&7cos(7x) \end{bmatrix}=7cos^{2}(7x)+7sin^{2}(7x)\neq 0 $$

Therefore, f and g are linearly independent

Second, using Gramian:

 * Consider two functions, f and g, where the scalar product is defined as

 * $$\displaystyle <f,g>:=\int_{a}^{b}f(x)g(x)dx $$

 * And the Gramian defined as

 * $$\displaystyle \Gamma (f,g):=det\begin{bmatrix}

<f,f> &<f,g> \\ <g,f> &<g,g> \end{bmatrix} $$

 * Then f and g are linearly indepdent if $$\displaystyle \Gamma (f,g)\neq 0 $$

 * For f=cos(7x) and g=sin(7x) and integrating over one period ($$\displaystyle \frac{2\pi }{7} $$)

 * $$\displaystyle <f,f>=\int_{0}^{\frac{2\pi }7{}}cos^{2}(7x)dx $$

 * Letting $$\displaystyle u=7x, du=7dx $$ and changing limits of integration by plugging in old limits into "u" equation

 * $$\displaystyle <f,f>=\frac{1}{7}\int_{0}^{2\pi }cos^{2}(u)du=\frac{1}{7}[\frac{u}{2}+\frac{1}{4}sin2u\mathbf{\mid} _{0}^{2\pi } ]=\frac{\pi }{7} $$

 * $$\displaystyle <g,g>=\int_{0}^{\frac{2\pi }{7}}sin^{2}(7x)dx $$

 * Letting $$\displaystyle u=7x,du=7dx $$ and changing the limits of integration by plugging in old limits into "u" equations

 * $$\displaystyle <g,g>=\frac{1}{7}\int_{0}^{2\pi }sin^{2}(u)du=\frac{1}{7}[\frac{u}{2}-\frac{1}{4}sin2u\mid _{0}^{2\pi }]=\frac{\pi }{7} $$

 * $$\displaystyle <f,g>=<g,f>=\int_{0}^{\frac{2\pi }{7}}cos(7x)sin(7x)dx $$

 * From Kreyszig p.479, it is apparent that sin and cos are orthogonal to each other, so the above integration will equal zero

 * $$\displaystyle <f,g>=<g,f>=\int_{0}^{\frac{2\pi }{7}}cos(7x)sin(7x)dx=0 $$

 * Plugging in the results of each integral into the Gramian

 * $$\displaystyle \boldsymbol{\Gamma }(f,g)=det\begin{bmatrix}

<f,f> &<f,g> \\ <g,f> &<g,g> \end{bmatrix}=det\begin{bmatrix} \frac{\pi }{7} &0 \\ 0& \frac{\pi }{7} \end{bmatrix}=\frac{\pi ^{2}}{49}\neq 0 $$

Therefore, f and g are linearly independent

(2)

 * Given $$\displaystyle y''-3y'-10y=3cos(7x) $$

 * And particular solutions of the form $$\displaystyle y_{p}(x)=Mcos(7x)+Nsin(7x),y'_{p}(x)=-M7sin(7x)+N7cos(7x),y''_{p}(x)=-M49cos(7x)-N49sin(7x) $$

 * Plug particular solutions back into original ODE and collect like terms

 * $$\displaystyle -M49cos(7x)-N49sin(7x)+M21sin(7x)-N21cos(7x)-M10cos(7x)-N10sin(7x)=3cos(7x) $$

 * $$\displaystyle -59Mcos(7x)-59Nsin(7x)+21Msin(7x)-21Ncos(7x)=3cos(7x) $$

 * Equating coefficients

 * $$\displaystyle -59M=3\rightarrow M=-\frac{3}{59} $$
 * $$\displaystyle -21N=3\rightarrow N=-\frac{1}{7} $$

$$\displaystyle M=-\frac{3}{59},N=-\frac{1}{7} $$

(3)

The overall solution $$\displaystyle y(x)=y_{p}(x)+y_{h}(x) $$ consists of the particular solution and homogeneous soloution

 * Homogeneous solotuion

 * $$\displaystyle y''-3y'-10y=0 $$

 * $$\displaystyle a^{2}-4b=3^{2}-4(10)=49>0 $$ so we have distinct real roots

 * $$\displaystyle \lambda _{1,2}=\frac{1}{2}[-a\pm \sqrt{a^{2}-4b}]=\frac{1}{2}[3\pm7 ]=5,-2 $$

 * $$\displaystyle y_{h}(x)=c_{1}e^{5x}+c_{2}e^{-2x} $$

 * Using initial conditions $$\displaystyle y(0)=1,y'(0)=1 $$ and $$\displaystyle y'_{h}(x)=5c_{1}e^{5x}-2c_{2}e^{-2x} $$

 * $$\displaystyle 5c_{1}-2c_{2}=0 $$
 * $$\displaystyle c_{1}+c_{2}=1 $$

 * Solving the two equations for the two unknowns yields $$\displaystyle c_{1}=\frac{2}{7},c_{2}=\frac{5}{7} $$

 * $$\displaystyle y_{h}(x)=\frac{2}{7}e^{5x}+\frac{5}{7}e^{-2x} $$

 * Particular solution

 * $$\displaystyle y_{p}(x)=Kcos(\omega x)+Msin(\omega x) $$ where $$\displaystyle \omega =7, K=M=-\frac{3}{59},M=N=-\frac{1}{7} $$

 * $$\displaystyle y_{p}(x)=-\frac{3}{59}cos(7x)-\frac{1}{7}sin(7x) $$

 * Giving us an overall solution of

$$\displaystyle y(x)=y_{h}(x)+y_{p}(x)=\frac{2}{7}e^{5x}+\frac{5}{7}e^{-2x}-\frac{3}{59}cos(7x)-\frac{1}{7}sin(7x) $$

 * Plotting the solution over three periods $$\displaystyle P=\frac{2\pi }{7} \Rightarrow 3P=\frac{6\pi }{7} $$

Matlabcode EDU>> x=0:0.001:(6*pi)/7; EDU>> y=(2/7).*exp(5.*x)+(5/7).*exp(-2.*x)-(3/59).*cos(7.*x)-(1/7).*sin(7.*x); EDU>> plot(x,y)

Author
Solved and uploaded by Joshua House

Question
Find the solution to the following initial condition problem, and plot it over 3 periods. $$ \displaystyle y'' + 4y' + 13y = 2e^{-2x}cos(3x) $$ $$ \displaystyle y_h(x) = e^{-2x}(Acos(3x)+Bsin(3x)) $$ $$ \displaystyle y_p(x) = xe^{-2x}(Mcos(3x)+Nsin(3x)) $$ $$ \displaystyle y(0) = 1, y'(0) = 0 $$

Solution
First, we take the first and second derivative of the particular solution: $$ \displaystyle y'_p(x) = e^{-2x}(-3Msin(3x)-2Mcos(3x)+3Ncos(3x)-2Nsin(3x)) = e^{-2x}[(-3M-2N)sin(3x)+(-2M+3N)cos(3x)] $$ $$ \displaystyle y''_p(x) = e^{-2x}(-9Mcos(3x)+6Msin(3x)-9Nsin(3x)-6Ncos(3x))-2e^{-2x}(-3Msin(3x)-2Mcos(3x)+3Ncos(3x)-2Nsin(3x)) $$ $$ \displaystyle = 2e^{-2x}[(12M-5N)sin(3x)+(13M-12N)cos(3x)]$$ Now, we plug the particular solution derivatives into the initial equation: $$ \displaystyle y'' + 4y' + 13y = 2e^{-2x}cos(3x)$$ $$ \displaystyle 2e^{-2x}[(12M-5N)sin(3x)+(13M-12N)cos(3x)] + 4[e^{-2x}[(-3M-2Nsin(3x)+(-2M+3N)cos(3x)]]$$ $$ \displaystyle + 13[e^{-2x}[Mcos(3x)+Nsin(3x)]] = 2e^{-2x}cos(3x) $$ $$ \displaystyle e^{-2x}[(24M-10N)sin(3x)+(26M-24N)cos(3x)+(-12M-8N)sin(3x)+(-8M+12N)cos(3x)+13Mcos(3x)+13Nsin(3x)] $$ $$ \displaystyle = 2e^{-2x}cos(3x) $$  $$ \displaystyle (12M-5N)sin(3x) + (31M-12N)cos(3x) = 2cos(3x) $$  Now, we equate the coefficients of sin(3x) and cos(3x) to determine the unknown coefficients M and N:  $$ \displaystyle 12M-5N = 0 $$ $$ \displaystyle 31M-12N = 2 $$ $$ \displaystyle N = \frac{24}{11}, M = \frac{10}{11} $$  Therefore, the particular solution is:  $$ \displaystyle y_p(x) = e^{-2x}[ \frac{10}{11}cos(3x) + \frac{24}{11}sin(3x)] $$  Now, we focus on the homogeneous part of the solution. It is given to us as:  $$ \displaystyle y_h(x) = e^{-2x}[Acos(3x)+Bsin(3x)] $$  As you can see, this is identical to the particular solution, except that M is now A and N is now B. Therefore, the first derivative of the homogenous solution will be in the same form as the first derivative of the particular solution: $$ \displaystyle y'_h(x) = e^{-2x}(-3Asin(3x)-2Acos(3x)+3Bcos(3x)-2Bsin(3x)) = e^{-2x}[(-3A-2B)sin(3x)+(-2A+3B)cos(3x)] $$ Remembering the two initial conditions, y(0) = 1 and y'(0) = 0, we apply these to the homogenous equations: $$ \displaystyle y_h(0) = e^{-2x}[Acos(3x)+Bsin(3x)] = 1 $$ $$ \displaystyle y'_h(x) = e^{-2x}[(-3A-2B)sin(3x)+(-2A+3B)cos(3x)] = 0 $$ This yields two equations that we can use to solve for the coefficients A and B: $$ \displaystyle A = 1 $$ $$ \displaystyle -2A+3B = 0 \Rightarrow 3B=2 \Rightarrow B = \frac{3}{2} $$ Therefore, the homoegenous solution is: $$ \displaystyle y_h(x) = e^{-2x}[cos(3x) + \frac{3}{2}sin(3x)] $$ We find the final solution, y(x), by adding the homogenous and particular solutions as seen below: $$ \displaystyle y(x) = y_h(x) + y_p(x) = e^{-2x}[cos(3x) + \frac{3}{2}sin(3x)] + e^{-2x}[ \frac{10}{11}cos(3x) + \frac{24}{11}sin(3x)] $$ $$ \displaystyle y(x) = e^{-2x}[ \frac{21}{11}cos(3x) + \frac{81}{22}sin(3x)] $$

Matlab Code: x= 0:0.001:(2*pi/3);

y = exp(-2.*x)*(21/11).*cos(3.*x) + exp(-2.*x)*(81/22).*sin(3.*x);

plot(x,y)

Author
This problem was solved and uploaded by Will Knapper

Question
$$ v=4e_1+2e_2=c_1b_1+c_2b_2 $$ The oblique basis vectors are: $$ b_1=2e_1+7e_2 $$ $$ b_2=1.5e_1+3e_2 $$ 1. Find the components $$ c_1, c_2 $$ using the Gram matrix as in (1)p.8-11. 2. Verify the results by using (1)-(2)p.7c-34 in (2)p8-11, and rely on the non-zero determinant of the matrix of components of $$ b_1, b_2 $$ relative to the basis $$ e_1 , e_2 $$, as discussed on p.7c-34.

Solution
1. Using Gram matrix as in (1) p.8-10: $$ \begin{bmatrix} <b_1,b_1> & <b_1,b_2> \\ <b_2,b_1> & <b_2,b_2> \end{bmatrix} $$ $$ \begin{Bmatrix} c_1 \\ c_2 \end{Bmatrix} $$ = $$ \begin{Bmatrix} <b_1, v> \\ <c_2, v> \end{Bmatrix} $$ From (3)p.8-9 we know that $$ <b_i, b_j>=b_i \cdot b_j $$. Solving the various components we get: $$ \begin{bmatrix} 53 & 24 \\ 24 & 11.25 \end{bmatrix} $$ $$ \begin{Bmatrix} c_1 \\ c_2 \end{Bmatrix} $$ = $$ \begin{Bmatrix} 22 \\ 12 \end{Bmatrix} $$ In order to solve for $$ c_1, c_2 $$ we need to calculate the inverse of $$ \begin{bmatrix} 53 & 24 \\ 24 & 11.25 \end{bmatrix} $$. This gives is the Gram matrix as used in (1)p.8-11: $$ c= \Gamma^{-1}d $$ $$ \begin{bmatrix} 0.55556 & -1.18519 \\ -1.18519 & 2.61728 \end{bmatrix} $$ $$ \begin{Bmatrix} 22 \\ 12 \end{Bmatrix} $$ = $$ \begin{Bmatrix} c_1 \\ c_2 \end{Bmatrix} $$ Thus: $$ c_1= -2 ; c_2= 5.333= \frac{16}{3} $$

2. Plugging in $$ b_1, b_2 $$ into $$ v $$ we get: $$ c_1(2e_1+7e_2)+c_2(1.5e_1+3e_2)=4e_1+2e_2 $$ $$ 2c_1e_1+7c_1e_2+1.5c_2e_1+3c_2e_2=4e_1+2e_2 $$ $$ e_1(2c_1+1.5c_2)+e_2(7c_1+3c_2)=4e_1+2e_2 $$ Separating into components: $$ 2c_1+1.5c_2=4 $$ and $$ 7c_1+3c_2=2 $$ Solving the two linearly independent equations we get: $$ \ $$ $$ c_1= -2 ; c_2= \frac{16}{3} $$

Author
This problem was solved and uploaded by Radina Dikova

Question
Find the integral (see R5.9)

$$ \displaystyle \ \int x^nlog(1+x)dx\ $$

using integration by parts and then with the help of General binomial theorem.

$$ \displaystyle \ (x + y)^n = \sum_{k=0}^{n} \binom{n}{k}   x^{n-k}y^k \ $$

$$ \ \binom{n}{k} = \frac{n!}{k!(n-k)!} = \frac{n(n-1)...(n-k+1)}{k!} \ $$

Solution
The indefinite integral of $$ \ x^n \ $$ is

$$ \ \frac{x^{n+1}}{n+1} + C \ $$

For n = 0, we get $$ \ \int x^0 = x \ $$

For n = 1, we get $$ \ \int x^1 = \frac{x^2}{2} \ $$

And the indefinite integral of $$ \ log(1+x) \ $$ is

$$ \ (x+1)log(1+x) - x + C \ $$

Integration by parts

- For n = 0 $$ \ \int x^0log(1+x)dx = log(1+x)[x+1] - x \ $$

- For n = 1 $$ \ \int x^1log(1+x)dx = \frac{1}{2}*[(x - log(1+x))+ x^2log(1+x)- \frac{x^2}{2}] \ $$

Author
Solved and uploaded by Mike Wallace

Question
Consider the L2-ODE-CC(5)p.7b-7 with log(1+x) as excitation:

$$ \ y'' - 3y'+ 2y = r(x) \ $$

$$ \ r(x) = log(1+x) \ $$

and the initial conditions

$$ \ y(-\frac{3}{4}) = 1, y'(-\frac{3}{4}) = 0 \ $$

Part One
Project the excitation r(x) on the polynomial basis $$ \ [b_j(x) = x^j, j = 0, 1,...,n] \ $$

i.e., find $$ \ d_j \ $$ such that

r(x) ≈ $$ \ r_n(x) = \sum_{j = 0}^{n} d_jx^j \ $$

for x in $$ \ [- \frac{3}{4}, 3 ], \ $$ and for n = 3, 6, 9

Plot $$ \ r(x), r_n(x) \ $$ to show uniform approximation and convergence

Part Two
In a separate series of plots, compare the approximation of the function log(1+x) by 2 methods:

A. Projection on polynomial basis (1) p.8-17

B. Taylor series expansion about x = 0

Observe and discuss the pros and cons of each method

Find $$ \ y_n(x) \ $$ such that:

$$ \ y_n'' + ay_n' + by_n = r_n(x) \ $$

with the same initial conditions (2) p.7c-28

Plot $$ \ y_n(x) \ $$ for n = 3, 6, 9, for x in $$ \ [- \frac{3}{4}, 3]. \ $$

In a series of separate plots, compare the results obtained with the projected excitation on polynomial basis to those with truncated Taylor series of the excitation. Plot also the numerical solution as a baseline for comparison.

Solution
Using $$ \ y'' - 3y'+ 2y = log(1+x) \ $$

For n = 0

$$ \ {b_0} = {x^0} \ $$

$$ \ r = log(1+x) = C_0x^0 \ $$

$$ \ d_0 = <x^0, log(1+x)>  = \int_{-\frac{3}{4}}^3 log(1+x)dx = 2.14175 \ $$

$$ \ <x^0, x^0> = \int_{-\frac{3}{4}}^3 x^0x^0dx = x|_{-\frac{3}{4}}^3 = \frac{15}{4} \ $$

$$ \ d_0 = C_0<x^0, x^0> = C_0(\frac{15}{4}) = 2.14175 \ $$

$$ \ C_0 = 0.57113 \ $$

--

$$ \ Y = Y_h + Y_p = C_1e^{2x} + C_2e^x + 0.57113 \ $$

$$ \ Y' = 2C_1e^{2x} + C_2e^x \ $$

$$ \ y(\frac{3}{4}) = C_1e^{\frac{6}{4}} + C_2e^{\frac{3}{4}} + 0.57113 = 1 \ $$

$$ \ y'(-\frac{3}{4}) = -\frac{6}{4}C_1e^{-\frac{6}{4}} + C_2e^{-\frac{3}{4}} = 0 \ $$

Subtracting Y from Y' in order to find the coefficients

$$ \ C_1e^{-\frac{6}{4}} - 0.57113 = -1 \ $$

$$ \ C_1 = - -1.92205 \ $$

$$ \ C_2 = 1.81582 \ $$

For n = 0 the final solution will be

$$ \ Y = -1.92205e^{2x} + 1.81582e^x + 0.57113 \ $$

--

For n = 1

$$ \ C_0 = -.09399, C_1 = 0.591217 \ $$

We need to find the homogeneous Y

$$ \ \lambda^2 - 3\lambda + 2 = 0 => (\lambda-2)(\lambda-1) = 0 \ $$

$$ \ \lambda_{1,2} = 2, 1 \ $$

$$ \ Y_h = C_1e^{2x} + C_2e^x \ $$

$$ \ Y = Y_h + Y_p = C_1e^{2x} + C_2e^x - 0.09399 + 0.591217x \ $$

Solving for the initial conditions

$$ \ y(\frac{3}{4}) = C_1e^{\frac{6}{4}} + C_2e^{\frac{3}{4}} - 0.09399 + 0.591217(\frac{3}{4}) = 1 \ $$

$$ \ Y' = = 2C_1e^{2x} + C_2e^x + 0.591217 \ $$

$$ \ y'(-\frac{3}{4}) = -\frac{6}{4}C_1e^{-\frac{6}{4}} + C_2e^{-\frac{3}{4}} + 0.591217 = 0 \ $$

This gives coefficients of:

$$ \ C_1 = -9.5398, C_2 = 7.761 \ $$

-- For n = 1 the final solution will be;

$$ \ Y = -9.5398e^{2x} + 7.761e^x + 0.591217x - 0.09399 \ $$

Author
This problem was solved and uploaded by Mike Wallace

Contribution Summary
Problem 2 was solved and Problem 5 was proofread by David Herrick

Problem 5 was solved and uploaded by Joshua House

Problems 1 and 7 were solved and uploaded by Radina Dikova

Problem 3 was solved and uploaded by Derik Bell

Problem 4 was solved and uploaded by John North

Problem 8 and 9 were solved and uploaded by Mike Wallace

Problem 6 was solved and uploaded by William Knapper


text:
3D Scan/Kinect Makerbot/Howard Community College/Spring2012/P1501msn/Yawcam Tutorial

Tutorial on how to set up Yawcam and use as motion detector.
 * 1. Download and install software from http://www.yawcam.com
 * 2. After install, run program Yawcam.
 * 3. Go to setting tab on the top, then go to device and choose the webcam that you want to use.
 * 4. Next go to the window tab next to the setting tab on the top.
 * 5. Click on motion detection, this will open a new window with three new tabs at the top. Setting, Actions, and Motion Events
 * 6. Click on Settings tab to change the defined area of motion detection. Clicking on the "Define area..." button will open a new screen.
 * 7. From this screen create a box around the live video to the area where you want the program to monitor for detection.
 * 8. Close that screen and click on the Actions tab.
 * 9. Click on "settings..." the button next to save file.
 * 10. Click on "Info..." button to get the codes for a time stamp for saved files.
 * 11. In this window change the save location to the same one used in Picasa and use the code in step 10.
 * 12. Under image array change settings to 5 images with interval of 500ms.
 * 13. Under flood control, deactivate. Close file settings window.
 * 14. Go Motion Events and click the enable button to run motion detection.

15. If setup properly with Picasa, photos will automatically be added to the Picasa library with the time stamp from Yawcam.

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


text:
Talk:Radiation astronomy/Positrons

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title: Talk:Radiation astronomy/Positrons


text:
User talk:Ranji.psj

What can we do with wikiversity?

title: User talk:Ranji.psj


text:
User:Ranji.psj

Hi i am ranji

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text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/Cadmium

Background
Cadmium is a chemical element (symbol Cd) with an atomic number of of 48. It is extracted for industrial purposes from lead ore. It was discovered in 1817.

Its uses include:-
 * battery manufacture;
 * as a pigment;
 * solar panels;
 * electroplating;
 * nuclear fission.

Cadmium does not have a known role in human metabolism and is not therefore associated with any deficiency diseases.

Exposure to excessive cadmium can induce renal failure, initially in metal fume fever, chemical pneumonitis and pulmonary oedema. These conditions can be fatal. Post-menopausal women seem particularly susceptible to cadmium toxicity.

Research
1997

Okuda et al describe the case of a 64 year old man, who experienced Parkinsonism following acute exposure to cadmium.

2011

Tvermoes et al evaluated the effects of cadmium on under non-cytotoxic and cytotoxic conditions. They observed that Cadmium affects the expression of hundreds of functionally unrelated genes, by activating multiple signal transduction pathways, but it may also influence the gene expression of second messengers, such as calcium.


text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/Copper

Background
Copper is a metallic element (symbol Cu) with an atomic number of 29.

It is an essential trace element in humans and the recommended adult daily intake is 0.97 mg/day It is  found in whole grain cereals, vegetables, oysters, offal (particularly liver), cherries, dark chocolate, fruits, leafy green vegetables, nuts, poultry, prunes, and soybeans products such as tofu.

Copper deficiency produces anaemia, bone marrow failure and ultimately a form of leukaemia.

If copper accumulates abnormally in the body it causes Wilson's Disease.  This produces the familiar symptoms of Parkinson's Disease - cogwheel rigidity, bradykinesia, lack of balance, hand tremor, masked facial expressions, slurred speech, ataxia (lack of coordination) or dystonia (twisting and repetitive movements of part of the body). Other symptoms are seizures and migraine and cognitive deficits. Wilson's Disease is generally characterised by distinctive rings around the iris of the eyes.

Research
1987

Pall et al and measured the copper concentrations in the cererbrospinal fluid of 24 PD patients and compared them with 39 controls. The PD patients had significantly higher levels of copper.

2007

Gibney describes a Polish study into the effects of raised copper levels on dopaminergic neurons.

"“To examine the precise role of copper in alpha-synuclein aggregation, the Polish team studied how copper(II) ions interact with fragments of a mutant form of alpha-synuclein that is particularly prone to aggregation. They found that the ions bind to the peptide fragments primarily through histidine, methionine and lysine residues. Copper binding makes these residues more susceptible to reaction"

2012

Rasia et al demonstrated that copper accelerated the aggregation of alpha synuclein, which is one of the pathological hallmarks of PD.

" By using numerous spectroscopic techniques (absorption, CD, EPR, and NMR), we have located the primary binding for Cu(II) to a specific site in the N terminus, involving His-50 as the anchoring residue and other nitrogen/oxygen donor atoms in a square planar or distorted tetragonal geometry. "


text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/Manganese

Evidence
The first person to link manganese (Mn) toxicity to the onset of Parkinson’s Disease symptoms was Couper (1837). .

He described the effects of exposure to manganese oxide on workers at the chemical factory of Charles Tennant and Co.(staggering, drooling, impassive expression and low audibility}.

These observations were confirmed by subsequent researchers, who added that, in contrast to other PD cases, manganese toxicity was marked by a lack of a resting tremor and a poor repose to L-dopa therapy. The condition has also been named manganism and has been extensively evaluated by Guilarte (2010). It is believed that manganese induces Parkinsonism by inhibiting the production of tyrosine hydroxylation, which is an essential metabolic step in the formation of dopamine.

2007

Santamaria et al reviwed the neurological risks associated with welding and concluded;-

"Existing exposure data indicate that, in general, Mn exposures in welders are less than those associated with the reports of clinical neurotoxicity (e.g., 'manganism') in miners and smelter workers. It was also found that although manganism was observed in highly exposed workers, the scant exposure-response data available for welders do not support a conclusion that welding is associated with clinical neurotoxicity."

2012

Butterworth decribes a form of Parkinsonism arising from cirrhosis of the liver.

"Acquired hepatolenticular degeneration, also known as 'Parkinsonism in cirrhosis' is characterized by extrapyramidal symptoms including hypokinesia, dystonia and rigidity that are rapidly progressive and may be independent of the severity of cognitive dysfunction..... The cause of Parkinsonism in cirrhosis has been attributed to manganese deposition in basal ganglia structures, leading to the dysfunction of the dopaminergic neurotransmitter system. "

Ephedrone
Several reports from Eastern Europe have recorded MnPD arising from the intravenous injection of a homemade psychostimulant drug called “ephedrone” or “Russian cocktail,” a drug in which ephedrine is oxidized using potassium permanganate and acetic acid

(2007)

Sanotsky et al. Normal Mn concentrations in whole blood are ≤ 10–12 μg/L, but the blood Mn concentrations in ephodrone addicts have been measured at levels as high as 2,000–3,000 μg/L.

MnPD has not been observed among ephedrone users in North America. Here, however, chromate is used as the oxidizing agent rather than potassium permanganate.

Liver Disease
Patients with chronic liver disease excrete manganese into their bile and this too can lead to MnPD. Welders are prone to MnPD from the inhalation of manganese fumes and, atypically, show a positive response to L-dopa therapy.

There is scope for more research into the natural occurrence of manganese compounds in the environment and its production as a by-product of industrial processes.


text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/Maneb

Background
Maneb is a member of the ethylene bisdithiocarbamate (EBDC) group of fungicides, which includes the related active ingredients mancozeb and metiram. Its full name is Manganese ethylene-1,2-bisdithiocarbamate, polymer. It was first registered in the United States in 1962 for use on food and ornamental crops. It is designed to protect crops from fungi both during their growing and storage stages. In 1977 the registration body – the Environmental Protection Agency (EPA)– initiated a review based on reports that the product contained a contaminant, and in 1982 issued a Final Determination requiring the implementation of risk reduction measures.Further reports were issued in 1985, 1989 and 1992.

A second Final Determination was issued in 1987 warning against the use of the product in connection with the growing of apricots, carrots, celery, collards, mustard greens, nectarines, peaches, rhubarb, spinach, succulent beans, and turnips. There is no mention of potential neurological damage in the EPA Fact Sheet dated August 1985.

The product was implicated as a toxic precursor to Parkinson’s Disease as the result of a series of experiments carried out on mice by Thiruchelvam et al (2000). . Corroboration came from a similar study carried out in California in 2009 by Beate Ritz and Sadie Costello of UCLA and another by Zhonghua (2011).

Maneb was included in a biocide ban proposed by the Swedish Chemicals Agency and approved by the European Parliament on January 13, 2009.

Research
2000

Mona Thiruchelvam, PhD and Gail Zeevalk of the Robert Wood Johnson Medical School, New Jersey have made the observation that hormone replacement therapy can reduce the risk of PD in postmenopausal women. Studies in animal models of PD have shown a difference in susceptibility between genders, with males more vulnerable to dopaminergic neurotoxicants such as Paraquat and Maneb. This appears to be due to the protective effect of increased levels of oestrogen. They are evaluating the possibility of producing non-feminizing analogues of oestrogen as a form of vaccination against PD. Warning See Below

2010

Ahmad et al demonstrated the effect of Maneb and Paraquat on rat livers.

2011

Roede et al found that Maneb and Paraquat used in combination were particularly toxic.

Grosicka et al demonstrated that N-acet-L-cysteine offered protection against the toxic effects of Maneb (in Chinese hamster cells).

Singhal et al demonstrated that silymarin and melatonin offer nigrostriatal dopaminergic neuroprotection against Maneb and Paraquat-induced PD  (in rats) by the modulation of oxidative stress and apoptotic machinery.

2012

Mona Thiruchelvam, PhD committed research misconduct by fabricating data, according to an investigation by the university and the Department of Health and Human Services Office of Research Integrity (ORI). The ORI, which announced its findings on Thursday (June 28), determined that Mona Thiruchelvam falsified cell count data published in two papers in 2009 in Environmental Health Perspectives and Journal of Biological Chemistry, both of which she has agreed to retract. One of the papers slated for retraction investigated the neurological response to the combined pesticides paraquat and maneb. The false data were used to create several summary bar graphs, which Thiruchelvam modified to support the hypothesis that proteasomal dysfunction is higher in males than females with PD, and that exposure to paraquat and maneb enhances this effect.


text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/Mercury

"The Phrase 'Mad as a Hatter' is a reference to Mad Hatter Disease which is a form of Parkinsonism that traditionally afflicted milliners, who were exposed to continual inhalation of Mercury vapour, used in felting when making hats. "

Background
Mercury is a chemical element (Symbol Hg) with an atomic number of 80.

It is used in lighting, in thermometers, as as an amalgam for filling teeth and in cosmetics such as mascara.

Research
1989

Ngim & Devasthasan carried out an epidemiologucal study on 54 idiopathic PD patients in Singapore and established a statistical link between mercury levels in the body and the occurrence of PD.

2003

Miller et al gives a detailed description of a case of mercury exposure.

2004

Bates et al evaluated a cohort of 20,000 people to see whether they had incurred an increased disease risk (including PD) from mercury amalgam fillings. Their results state,” Results were generally reassuring, and provide only limited evidence of an association between amalgam and disease.”

2006

Dantzig  set out to test the hypothesis that there might be a link between the onset of Parkinson’s Disease, Grover’s Disease and blood mercury levels is the body. Grover’s Disease manifests itself as itchy red bumps on the chest and back. He (she?) formed a cohort of 14 randomly selected PD patients an 14 matching controls.

Of the 14 patients with Parkinson's Disease, 13 had Grover's Disease and detectable blood mercury. None of the patients in the control group had a cutaneous eruption and only 2 of the 14 had detectable blood mercury. This extraordinary finding, which will set most PD patients into scratching their chests, appeared in a peer-reviewed journal and has not, so far, been corroborated elsewhere.


text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/n-Hexane

Background
The Chemical formula of n-Hexane is CH3CH2CH2CH2CH2CH3 and its alternative name is Hexyl Hydride.

It is used as a solvent in the extraction of oils from seeds, and in the manufacture and processing of paint, glues and petroleum products. Industrially it is used in the manufacture of shoes, tungsten carbide and press-proofing. Artists and painters of all descriptions are exposed to it and it has been found at waste sites, in the air surrounding fuel storage tanks and in some water supplies.

1995

Pezzoli et al studied a single case of n-Hexane induced PD. Their conclusions stated:-

"“Positron emission tomography studies demonstrated regional striatal abnormalities of the nigrostriatal dopaminergic system and of glucose metabolism that were different from those found in idiopathic Parkinson's disease.'"

1996

Pezzoli et al described the case of a PD patient, who had experienced a prolonged exposure to n-Hexane. Their conclusions state:-

" “The patient developed a rapid-course disease that progressed even after withdrawal from the toxic exposure. Pathological examination and immunohistochemical analysis of the brain revealed severe and widespread dopaminergic neuronal loss, associated with severe gliosis, in the substantia nigra, and almost complete loss of tyrosine hydroxylase immunostaining in the striatum. No Lewy bodies were detected. Neuronal loss was also observed in the periaqueductal gray matter, locus ceruleus, and pedunculopontine nucleus. These changes, combined with the moderate anemia due to marrow suppression, and the mild axonal neuropathy observed in vivo, are suggestive of a hydrocarbon toxic insult.”"

2003

Canesi et al record the results of a two-part experiment. Their conclusions state:-

"“In the first part, in order to assess whether age and PD may affect the catabolism of the hydrocarbon n-hexane the urinary levels of its main metabolites, 2,5-hexanedione and 2,5-dimethylpyrroles, were measured in 108 PD patients and 108 healthy controls, matched by age and sex. Metabolite urinary excretion was significantly reduced in PD patients as compared with controls and was inversely related to age in both groups. In the second part the same comparison was made between 24 non-smoking and 10 smoking patients, matched to controls, after smoking of a hydrocarbon-rich cigarette. In these subjects also n-hexane and 2,5-hexanedione blood levels were measured. There was no appreciable difference in n-hexane blood levels between patients and controls in non-smokers, whereas there was a significant increase in patients over controls in smokers (p < 0.01). 2,5-hexanedione blood levels were significantly lower in patients than in healthy controls, both in non-smokers and in smokers, but the reduction was more pronounced in smokers (-46.3 % versus -10.7 %). The same was true for 2,5-hexanedione and 2,5-dimethylpyrrole urinary levels. This study suggests that aging and PD may be associated with a reduction in the capacity to eliminate the hydrocarbon n-hexane. This metabolic alteration may play a role in the pathogenesis of PD.”"

2009

Vanacore et al evaluated at length the case of a PD patient with 17 years’ exposure to n-Hexane and established a causal link.


text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/Paraquat

Background
Paraquat was first synthesised in 1882 and was marketed as a herbicide in 1961 by ICI (now Zeneca). Its formula is N,N′-dimethyl-4,4′-bipyridinium dichloride. It has a similar molecular structure to MPTP. The Zeneca factory in Huddersfield,UK makes some 8,000 tonnes a year, most of which is exported. It is a very effective weedkiller if used properly, and is sold under a variety of tradenames including Weedol Pathclear, Crisquat; Dexuron; Esgram; Gramuron; Para-col; Pillarxone; Tota-col; Toxer Total; PP148; Cyclone; Gramixel; Gramoxone; and AH 501.r.  It kills plants by inhibiting photosynthesis, but becomes biologically inactive upon contact with the soil. Its uses include land clearance, defoliation and as a desiccant.

In its undiluted state it is very toxic. Death by heart, kidney and respiratory failure occurs within 30 days of ingesting half a teaspoonful and there is no antidote. For this reason it was banned by Finland, Sweden, Austria, Norway and Hungary, and its use is restricted in the USA, but this did not stop America from spraying Mexican marijuana fields with it in the 1970s. The European Union approved the use of paraquat in 2004, but annulled the directive authorizing its use in 2007 following court action by Sweden, Denmark, Austria, and Finland.

One of its uses in Third World countries is committing suicide (76% of suicides in Trinidad in 1990/91). Taking a single swig of undiluted Paraquat and spitting it out immediately is fatal.

2007

Miller published a detailed refutation of the PD case against paraquat. One of his main arguments was that because of the fierce nature of Paraquat toxicity most researchers induced PD in laboratory animals by direct injection of Paraquat into the substantia nigra. Miller argued that this negated the efficacy of the blood brain barrier in keeping out the toxin. He also observed that any inflammatory substance injected in this manner would have the same effect.

2009

His case was supported by the findings of Bartlett et al who attempted to induce PD through the application of Paraquat to Macaque Rhesus monkeys. Their conclusion was:-

"'This acute exposure study found that paraquat is excluded from the brain by the blood brain barrier and thus does not readily support the causative role of paraquat exposure in idiopathic Parkinson's disease.'"

2011

Tanner et al made a positive association between Parkinson’s Disease and Paraquat (and Rotenone) by cluster analysis.

Roede et al found that Maneb and Paraquat used in combination were particularly toxic.

Singhal et al demonstrated that silymarin and melatonin offer nigrostriatal dopaminergic neuroprotection against Maneb and Paraquat-induced PD (in rats) by the modulation of oxidative stress and apoptotic machinery.

Research
2011

Littlejohn et al found that male mice were much more susceptible to Paraquat induced PD than female mice.

Mangano et al found that the application of granulocyte macrophage colony stimulating factor (GM-CSF) inhibited the neurodegenerative effects of Paraquat.

Yin et al exposed different varieties of recombinant inbred mice to Paraquat injection and measured the rate and extent of the onset of dopamine neuron loss in the substantia nigra. They found that there were marked and consistent variations according the genetic make-up of the mice. Their conclusions state:-

"“This is the first study to report genetically-based differences in susceptibility to PQ neurotoxicity and to understanding individual differences in vulnerability to PQ neurotoxicity and its relation to PD in humans.”"

Kwon et al found that DJ-1 null gene cells resisted Paraquat toxicity. Their conclusions state:-

"“DJ-1 null cells showed reduced complex I activity, which was partially rescued by ectopic DJ-I expression. In summary, our results suggest that DJ-1 is critical to maintain mitochondrial complex I and complex I could be a key target in interaction of paraquat toxicity and DJ-1 for giving rise to PD.”"

2012

Lee, Pei-Chen et al enrolled 357 incident idiopathic PD cases and 754 population controls from 2001 to 2011 in central California. Participants were asked to report all head injuries with loss of consciousness for >5 minutes. Paraquat exposure was assessed via a validated geographic information system (GIS) based on records of pesticide applications to agricultural crops in California since 1974 and ambient pesticide exposure within 500 m of residences and workplaces were recorded.

They observed a 2-fold increase in risk of PD for subjects who reported a Traumatic Brain Injury (TBI),  and a weaker association for paraquat exposures. However, the risk of developing PD was 3-fold higher in study participants with a TBI and exposure to paraquat than those exposed to neither risk factor.


text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/Rotenone

General
Emmanuel Geoffroy was a French botanist and explorer, who travelled to French Guiana in the late 19th century. The object of his search was to find latex bearing trees but he became distracted by the practices of the forest Indians who made an extract from the roots of the Robinia nicou plant (now called Lonchocarpus nicou) and put it in water to catch fish by poisoning them. Geoffroy named the poison nicouline. It is now known as Rotenone and has been discovered in a wide variety of other plants. It was subsequently developed commercially as a piscicide, insecticide and pesticide and is also known as Tubatoxin and Praderil. Its chemical name is hexahydro-2-isopropenyl-8,9-dimethoxychromeno[3,4-b]furo(2,3-h)chromen-6-one. The formula is C23H22O8

It is currently sold as a universal pest killer in gardens and for ridding chickens of parasites and is commonly called Derris Dust.

Bristol University has produced a good clear language description of the product.

There is some evidence that Rotenone can induce Parkinson's Disease in humans, but it is not high on the list of potential environmental toxins as it decomposes rapidly naturally and the human metabolism has defensive screens, which inhibit its progression to the substantia nigra. It is one of the few pesticides approved for use by organic farmers.

What is exciting about Rotenone is that, when it is administered in quantities to laboratory rats, it produces a form of Parkinson's Disease which very closely models that found in humans. This has been described by Canon et al (2009) and Telford (2010). (see separate topic - Rotenone Model)

Research
Tain et al (2009) have initiated PD in fruit flies with PINK1 and PARK2 by the application of Rotenone. They then treated these models with Rapamycin.  This had the effect of reversing the PD symptoms.

All published sources on Rotenone and Parkinson's Disease (including some that are quoted here) are unanimous about the way in which the toxin works. It inhibits the production of NADH Dehydrogenase, also known as Complex 1. This is one of a chain of enzyme molecules involved in the metabolism of oxygen into ATP by mitochondria. It has an important role, since ATP is the fuel that drives all animal cells.

However this hypothesis has recently been the subject of study by Choi et al (2011)

They started by knocking out an essential component of Complex 1 called Ndufs4 in the mitochondria of healthy mice. In theory the mice should have experienced dopaminergic cell death and begin to exhibit PD symptoms. Instead they remained stubbornly healthy. If Rotenone was administered subsequently, only then did PD symptoms develop. The team then tried another Complex 1 inhibitor, piericidin A, with the same result. The inference was that Rotenone was killing neurons in some other way.

Research then concentrated on another property of Rotenone, its ability to destroy microtubules. Microtubules are molecular ‘railway tracks’ that run the length of a neuron’s axons. These can be over a metre long in adult humans. Normally there is continual traffic up and down the microtubule. Specially adapted molecules haul mitochondria, neurotransmitters. Proteins and waste products from around the cell's nucleus to the synapses and back again. When Rotenone destroys the tracks, untransported cargoes pile up around the cell’s nucleus (Lewy bodies?) and the cell cease to function. The team then treated mouse neurons with colchizine, an unrelated microtubular destructive agent and it produced the same effect as Rotenone. Finally they treated neurons with a microtubule stabilising drug called taxol. This had the effect of insulating them against the effect of Rotenone.

The work may have identified a new therapeutic target for Rotenone-induced PD and may have significance for other forms of PD.

Taxol is a compound which was isolated from the bark of the Pacific yew tree Taxus brevifolia in 1971 by Monroe E. Wall and Mansukh C. Wani and found to have microtubule protective properties. It was developed commercially by Bristol-Myers Squibb (BMS) and the generic name was changed to paclitaxel. The BMS compound is sold under the trademark TAXOL. In this formulation, paclitaxel is dissolved in Cremophor EL and ethanol, as a delivery agent. A newer formulation, in which paclitaxel is bound to albumin, is sold under the trademark Abraxane.

Paclitaxel is now used to treat patients with lung, ovarian, breast cancer, head and neck cancer, and advanced forms of Kaposi's sarcoma. Paclitaxel is also used for the prevention of restenosis.


text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/MPTP

"An American student named Barry Kidston was unwittingly responsible for a major advance in PD research when he accidentally manufactured MPTP and gave himself PD. This paved the way for the reproduction of PD in laboratory animals."

Background
In 1947 a North American pharmaceutical company named Hoffmann La Roche set about finding painkiller compounds that were less addictive than heroin. One of these was a derivative of a synthetic opiate called Demerol. A researcher named Albert Ziering developed a new compound called 1-methyl-4-phenyl-4-propionoxy-piperidine (MPPP), which proved to be no better than Demerol, and it was never marketed. In 1977 a 23 year old Maryland chemistry graduate named Barry Kidston read a paper by Ziering on this research and decide to explore MPPP’s potential as a recreational drug. He manufactured a quantity of it in his parent’s garage. However an error in the processing meant that he actually produced a subtly different compound called 1-methyl-4-phenylpyridinium or MPTP

Kidston experimentally injected the drug into himself and within three days had developed chronic and irreversible Parkinson’s Disease. Once MPTP was in his brain it was metabolized by the enzyme MAO-B of glial cells, and went on to interfere with Complex_1 of the electron transport chain, a component of mitochondrial metabolism leading to dopaminergic cell death and the buildup of free radicals, toxic molecules that contributed further to cell destruction.

The National Institute of Mental Health became involved and reproduced Kidston’s experiment. They tested the substance on rats, but due to the rodents' tolerance for this type of neurotoxin nothing was observed. Subsequently MPTP was successfully used to engender PD in squirrel monkeys and later on in laboratory mice.

Kidston's parkinsonism was successfully treated with levodopa but he died 18 months later from a (possibly deliberate) cocaine overdose. A post mortem was carried out and the havoc which MPTP had wrought to the dopaminergic neurons in his substantia nigra was revealed.

History repeated itself in 1982 when seven people in Santa Clara County, California were diagnosed with Parkinsonism after having used MPPP contaminated with MPTP. The neurologist J. William Langston in collaboration with NIH tracked down MPTP as the cause. Eventually the motor symptoms of two of the seven patients were successfully treated at Lund University Hospital in Sweden with neural grafts of foetal tissue.

Kidston unwittingly advanced the course of medical science by providing researchers with a drug which could induce PD in laboratory animals, thus opening a path for the closer study of the pathogenesis of the disease and the development of new therapies. There is speculation that MPTP might occur as a trace compound naturally and be the prime causative agent of P.D., but this hypothesis awaits proof.

Research
2011

Kidd and Schneider have shown that valproic acid protects against the effects of MPTP. Their conclusions state,

"'VPA was able to partially prevent striatal dopamine depletion and almost completely protect against substantia nigra DAergic cell loss. These results suggest that VPA may be a potential disease-modifying therapy for PD.'"

Acuña-Castroviejo, D. et al tested the effect of four synthetic kynurenines in the MPTP model of PD in mice. Their conclusions state:-

"“The results suggest that the kynurenines here reported represent a family of synthetic compounds with neuroprotective properties against PD, and that they can serve as templates for the design of new drugs able to target the mitochondria.'"

Archer and Fredriksson have shown that excercise reduces the effects of MPTP. Their conclusions state:-

"'Physical exercise markedly attenuated the hypokinesic effect of MPTP in the exercise condition, MPTP-exercise, but not in the non-exercise conditions, MPTP-Cage and MPTP-Wheel, for both spontaneous motor activity and L: -dopa-induced activity. MPTP-induced loss of DA was also attenuated by exercise.'"

Lim et al have rescued dopaminergic neurons from cell death in an MPTP induced mouse-model by the application of Lanosterol. Their conclusions state;-

"' Collectively, our results highlight a novel sterol-based neuroprotective mechanism with direct relevance to PD.Cell Death and Differentiation.'"

Li and Pu  have demonstrated a dramatic reversal of the effects of MPTP induced PD in a mouse model by the application of kaempferol. Their conclusions state:-

"' Immunohistochemical studies using anti-tyrosine hydroxylase (TH) antibody showed that medication of kaempferol could prevent the loss of TH-positive neurons induced by MPTP. Taken together, we propose that kaempferol has shown anti-parkinsonian properties in our studies. More work is needed to explore detailed mechanisms of action.'"

Hansard et al reversed PD motor symptom in MPTP-induced marmosets by treatment with buproprion.  Their conclusions state:-

"“The data suggest that the S,S-enantiomer of hydroxybupropion may possess potential antiparkinsonian activity.”"

Patel et al  have treated MPTP-induced mice with an angiogenic inhibitor, cyclic RGDfV, and reversed the Parkinsonin symptoms. Their conclusions include the statement:-

"“These data suggest that cyRGDfV, and perhaps other anti-angiogenic drugs, are neuroprotective following acute MPTP treatment and may suggest that compensatory angiogenesis and BBB dysfunction may contribute to inflammation and DA neuron loss.”"

Masilamoni et al  have carried out experiments with MPTP-induced Parkinsonian monkeys and concluded that:-

"“Our data demonstrate that chronic treatment with the metabotropic glutamate receptor 5 antagonist, 3-[(2-methyl-1,3-thiazol-4-yl) ethynyl] pyridine, significantly reduces 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine toxicity towards dopaminergic and noradrenergic cell groups in non-human primates. This suggests that the use of metabotropic glutamate receptor 5 antagonists may be a useful strategy to reduce degeneration of catecholaminergic neurons in Parkinson's disease.”"

Liu et al have treated mice with MPTP-induced PD with rapamycin and demonstrated a reversal of symptoms. Their conclusions state:-

" “ These results demonstrate that treatment with rapamycin is able to rescue dopaminergic neurons and ameliorate the loss of DOPAC following MPTP treatment, likely via activation of autophagy/lysosome pathways. The use of rapamycin may therefore be a promising therapeutic agent for the treatment of PD.”"


text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/Toluene

Background
Toluene is a benzene derivative with the chemical formula C6H5CH3. It is used in the manufacture of solvents, paint thinners, lacquers, sealants, printing inks, fuel additives and adhesives. It is a colourless liquid with a distinctive smell. It is the subject of solvent abuse as repeated inhalation induces a euphoric, dissociative state.

Research
1999

Hageman et al presented the results of an evaluation of 3 patients who had had sustained exposure to solvents including toluene. They had developed Parkinson symptoms but were unresponsive to levodopa.

2002

Aydin et al carried out MRI scans of 41 patients who had chronically abused solvents – including toluene. They noted significant permanent damage to parts of the brain including the basal ganglia. Some of the patients were showing signs of Parkinson’s Disease.

2003

Pals et al (2003) examined the records of 423 Belgian P.D. patients and found clusters corresponding to their degree of exposure to zinc and toluene.


text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/Trichloroethylene

Background
Trichloroethylene (C2HCl3) is a chlorinated hydrocarbon commonly used as an industrial solvent. It is a clear, non-flammable liquid with a sweet smell.

It is also known as TCE, 1,1,2-Trichloroethene, 1,1-Dichloro-2-Chloroethylene, 1-Chloro-2,2-Dichloroethylene, Acetylene Trichloride, TCE, Trethylene, Triclene, Tri, Trimarand Trilene.

It was introduced by the UK Company Imperial Chemical Industries (ICI) in the 1920s as an anaesthetic and was widely used as an analgesic in childbirth, but was phased out owing to doubts about its toxicity.

Other uses for the product are:-
 * extracting vegetable oils from plants such as coconuts, palms and soy;
 * coffee decaffeination;
 * a dry cleaning solvent;
 * cleaning machines in the film industry;
 * preparation of flavouring extracts;
 * degreasing metals;
 * cleaning rocket engines;
 * the manufacture of hydrocarbon refrigerants.
 * cleaning military weapons during the Gulf War.

Among the toxic effects noted on humans are:-
 * anaesthesia (dizziness);
 * tachypnea (rapid breathing);
 * irregular heartbeat;
 * headaches;
 * cranial nerve dysfunction;
 * facial numbness;
 * hepatoxicity (liver damage);
 * renal failure (kidneys);

Considerable concern has been expressed in the United States about the contamination of well water by TCE.

Research
1992

Bringmann et al  postulated that the hypnotic chloral reacts chemically with tryptamine and tryptophan in the human body under physiological conditions to form TCE.

1999

Bringmann et al, established that TCE formed endogenously in humans after administration of the hypnotic chloral hydrate

Guehl et al describe the case of a 47 year old woman, who contracted PD after 7 years’ exposure to TCE.   The researchers were able to reproduce the condition in laboratory mice, and concluded,

"“The environmental trichlorethylene pollution, as well as other unspecific neurotoxic solvents, could potentially contribute to the genesis of some cases of Parkinson's disease.'"

2003

Kochen et al examined the possible causative links between Volatile Organic Solvents (VOS) and neurodegenerative diseases. Their conclusions state,

"“The onset of Parkinson's disease in three chronic TRI-exposed individuals during the postexposure period could be associated with the presence of TaClo [TCE] in ng-range. Consequently, determination of TaClo and its derivatives in blood of humans exposed to chlorinated VOSs may serve as a marker of risk indicating either causative or supportive processes of neurodegeneration that may lead to manifestation of PD after many years.”"

2004

Akundi et al evaluated TCE.  Their conclusions state,

"“Earlier studies have revealed the relative permeability of the molecule through the blood-brain barrier and its ability to induce Parkinson-like symptoms in rats. In this study, we report that TaClo induces an apoptotic pathway in the human neuroblastoma cell line, SK-N-SH, involving the translocation of mitochondrial cytochrome c to the cytosol and activation of caspase 3. TaClo-induced apoptosis shows considerable differences from that mediated by other Parkinson-inducing agents such as MPTP, rotenone and manganese.”"

2008

Gash et al studied the job histories of 99 pairs of twins, where one had contracted PD and the other had not. This was done to try to eliminate genetic factors from the investigation. They found that individuals who had the greater exposure to trichloroethylene were six times more likely to contract Parkinson’s Disease.

2011

Zaheer & Slevin  evaluated the evidence linking TCE to the incidence of PD. The indication was that TCE induced mitochondrial failure in nigral neurons.

Goldman et al carried out extensive lifestyle and case history interviews on 99 pairs of twins, where one sibling had contracted PD and the other had not. They concluded that people with a history of exposure to TCE were 6 times more likely than normal to contract PD. The chemical is prevalent in groundwater in parts of the USA. They also found evidence implicating Perchloroethylene -PERC and Carbon tetrachloride - CCl(4) in the spread of the disease.


text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/Ziram

Background
Ziram is an organic zinc salt used as a fungicide. It has been in use since 1949. The formula is C6H12N2S4Zn and the name is derived from Zinc dithiocarbamate. It is marketed under a variety of names and is used primarily on almonds and stone fruits.

Research
2008

Chou et al examined the effect of Ziram on dopaminergic cells in vitro and concluded:-

"“These results demonstrate that ziram causes selective dopaminergic cell damage in vitro by inhibiting an important degradative pathway implicated in the etiology of PD. Chronic exposure to widely used dithiocarbamate fungicides may contribute to the development of PD, and elucidation of its mechanism would identify a new potential therapeutic target.”"

2011

Wang et al examined the relationship between the incidence of PD and exposure to toxins in the Central Valley of California and concluded:-

"“Those exposed to ziram, maneb, and paraquat together experienced the greatest increase in PD risk. Our results suggest that pesticides affecting different mechanisms that contribute to dopaminergic neuron death may act together to increase the risk of PD considerably.”"


text:
Progress and Prospects in Parkinson's Research/Causes/Toxins/Dieldrin

Background
Dieldrin is an insecticide which was invented in the 1940s. However once it is used it is persistent and seems to gain in toxicity as it passes up through the food chain. It has been linked to a number of diseases in humans and, as a result, it has been banned in many countries.

Research
2001

Uversky et al showed that pesticides including Dieldrin were responsible for the formation of alpha-synuclein fibrils in dopaminergic neurons.

2005

Kanthasamy et al produced evidence linking Dieldrin to the onset of Parkinson’s Disease.

2006

Richardson et al  established the toxicity of Dieldrin to dopaminergic neurons. Their conclusions state:-

"'These data suggest that developmental exposure to dieldrin leads to persistent alterations of the developing dopaminergic system and that these alterations induce a 'silent' state of dopamine dysfunction, thereby rendering dopamine neurons more vulnerable later in life.'"

2007

Hatcher et al demonstrated that dopaminergic neurons (in mice) were severely damaged by Dieldrin.


text:
Mindfulness

Introduction to Mindfulness

This is a training resource on mindfulness

Developed as part of a university assignment for the course Group Work at University of Canberra.

This page can be accessed at: http://tinyurl.com/introtomindfulness

What is Mindfulness?
Mindfulness is the psychological state of paying attention on a moment-to-moment basis. In this state, a person is both aware and accepting of each thought and sensory perception that may arise.

History of Mindfulness
Coming soon...please see mindfulness for more information

Mindfulness Meditation
Place some examples of mindfulness meditation sessions.

With some sort of physicals example say, I can ensue threw being in a sort of metaphysical, /( mind and thought pattern)-induced or, an out of mind minimal brain function wave sensory field, then in a heightened hierarchy and  in this, the practice of purposely bringing one's attention to the present-moment experience without evaluation.

Clinical psychology and psychiatry since the 1970s have developed a number of therapeutic applications based on mindfulness for helping people experiencing a variety of psychological conditions. Mindfulness practice has been employed to reduce depression, stress, anxiety, and in the treatment of drug addiction, as well as sever cases of minute deflection from ones perception or ones self and the world around them in the sense of a whole.

Resources

 * Group Work Course/Developmental Notes (Blondlox Blog)

title: Mindfulness


text:
User:Ot

more: http://de.wikipedia.org/wiki/Benutzer:Ot

title: User:Ot


text:
User talk:Learnerwp

I started something up, but I'm basing it on Yale university's course on the Old Testament (Hebrew bible).

Before I get too far along, I'd like to get feedback on whether my idea is do-able. I don't mind contributing to Wkiversity, but I don't want to have to write an entire course myself. I need a framework, and resources to make the course usable.

http://en.wikiversity.org/w/index.php?title=Introduction_to_the_Old_Testament_(Hebrew_Bible)&action=edit

Anyone have any suggestions?

Learnerwp (talk) 16:01, 18 March 2012 (UTC)

title: User talk:Learnerwp


text:
User:Pjmarsden/enes100/My Work 2nd 4 week cycle

''This is designed for a person working on a project for 4 weeks as part of a 3 credit class. Please copy this form to your user page. Then delete everything in italics when filling out this form.''

Write problem/project Goal
I want to build a full scale working wind turbine to generate and store electricity. I have already worked with many prototypes and I am ready to move forward.

My First Task
My first task will be to find a suitable wind gernerator that will generate high voltage at a low RPM.

Summary of actual work over first weekend
How is what you did different than what you planned?

Week1 Narrative
Tell a detailed story describing what you did for your team over the weekend.

My Second Task
Record what you are planning on doing for the team during the second weekend.

Summary of actual work over second weekend
In the second week I planned on coming up with a way to produce more power. To do this I needed a bigger generator so I found ceiling fan motors in the lab that i thought would fit the bill. So I spent the whole week trouble shooting them.

Week2 Narrative
In week two I begun to dissect a ceiling fan motor to determine how to harness its power

This is a picture of what I was working with

The first thing I did was start to hook up to various wires to test the continuity There was a pair of wires that worked and a pair that didn't work so I was assuming there were 2 coils inside the motor and one must have not been working.

So next I wanted to see if the 2 wires that were working would produce a voltage. So i disassembled all the wires except for the two that were still working. below is all the wires I removed.

These 2 wires were not working so i decided to open the motor up to take a closer look. So as you can see my prediction about there being two coils was correct now I just needed to determine what coil was working and what one was not.

Next I separated all the wires so I could tell where they went and which coil was working After testing the wires out again I found the outside coil was not working. So I wanted to find out why because the inside coil was to far from the magnet to be able to generate a voltage.

After examination I found that one of the coils in the outside coil had a major break in it. So after I determined that this would not work I needed to find something else that would work. The one good thing I took out of this was getting a good understanding of how a ceiling fan works.

My Third task
Record what you are planning on doing for the team during the third weekend.

Summary of actual work over third weekend
How is what you did different than what you planned?

Week3 Narrative
Tell a detailed story describing what you did for your team over the weekend.

My Fourth task
Record what you are planning on doing for the team during the final weekend of project work.

Summary of actual work over fourth weekend
I week 4 I planned on integrating the LED voltage gauge to the wind turbine assembly.

Week4 Narrative
The first thing to do before adding the circuit into the pole of the wind turbine was to hard wire it outside of a breadboard.

This is a diagram of the circuit to be constructed.

To compleate this task I had to solder many connections. Here is a link to a tutorial on how to soldier an LED to a wire how to soilder and LED

After soldering all of the connections to the circuit this was this is what it looked like

Next I drilled holes in the pole to mount the LEDs to.

Then I glued the LEDs in the holes.

To connect the circuit to the motor I got the wiring harness that came with the motor and soldered them together.

Here is the wiring harness.

Now I was mounting the motor back to the pole, but i encountered a problem because the motor body was pinching the wires.

So I cut a slit in the pole to fit the wires.

After all this work here is a video of the final product of the LED gauge. LED power gauge

Complete Team Page
Fill out the Team Form (should have already copied the form, created the team page, linked to it and started filling it out).


text:
User:MundaneUser/enes100/My Work 2nd 4 week cycle

Wind Turbine II

Write problem/project Goal
To design and construct a full scale functioning wind turbine capable of articulating its movement to maximize efficiency

My First Task
Continuing my previous work on the Wind Turbine, I am going to gather data about my LED Voltage Detector circuit in order to maximize its efficiency. The problem, as it stands, is that R2 is getting hot and both LED1 and LED2 are having too much voltage applied. To solve this problem, I have to test voltage drops within my circuit and determine the relationships between the parallel resistors and the amount of voltage dropped. If I am able, I also want to solder a hard-wired LED voltage detector on to a wire harness and connect it to the wind turbine generator (a radiator fan motor).

Summary of actual work over first weekend
I had originally planned on gathering data from my circuit and understanding the electrical movement and use that information to change resistance values to reduce heat and wear on the Resistors and LEDs. I encountered a very interesting problem using a breadboard to build my circuit, which I will go into detail about below. Additionally, this complication also prevented me from hard wiring my circuit before it is optimized.

Week1 Narrative
During my initial test, when I turned on the variable power supply it caused the LEDs to burn out. A word of advice to anyone trying to replicate this process, always check that your power supply is not on max and if it is, make sure to turn the voltage and current to minimum.
 * Next, I measured the total circuit current by connecting the positive Ammeter lead directly to the positive lead coming off the power supply. Then I attached the negative lead off of my ammeter to the incoming lead on the resistor. Following these steps, I measured: 155.5mA Max Current.

 * Following my Max Current measurement, I measured maximum circuit voltage. To do this, I attached the positive lead of the Voltmeter to a pin in the breadboard before the resistor in the circuit and the negative lead in the pin next to the positive lead. The distinction that must be made is that to measure Amps you must break the circuit and measure through, to measure the Voltage you measure across the circuit (or components).

Next, I attempted to measure the voltage drop across R1. During the measurement, the voltmeter did not display any voltage passing through the resistor. I did not understand why I was not getting a voltage readout and so I figured that the Resistor must be getting bypassed (if the circuit is functioning but the resistor has not current passing through it). Another indication that the resistor was getting bypassed is when I measured the total circuit current it equaled 155.5mA but when the circuit was not being measured through the Ammeter the power supply was allowing 141mA to flow. Because I am using a breadboard, the components in series are all sharing a trace, as a result the resistor was in parallel with the circuit and electricity follows the path of least resistance and thus, bypassing R1. I spent a long time analyzing the situation to conclude that the resistor was being bypassed, leaving me with little time to hard-wire the circuit or experiment with resistance values. Despite the complication during the test phase, I pressed on and measured the drops across each component, following the same process as I did to measure R1.
 * Results (All measurements taken while R1 is bypassed):

 * {| class="wikitable"

! Component !! R2 !! R3 !! R4 !! R5 !! LED1 !! LED2 !! LED3 !! LED4
 * Voltage Drop (Volts) || 7.05v || 4.48v || 2.08v || .19v || 3.02v || 2.55v || 2.4v || 1.89v
 * }
 * }

After a quick analysis of the results I noticed a very interesting relationship between each parallel leg and its preceding Resistor.

 * Voltage dropped across R2 = 7.05V equaled the Voltage dropped across R3 + LED2 (~4.48v + ~2.55v = 7.03)
 * Voltage dropped across R3 = 4.48V equaled the Voltage dropped across R4 + LED3 (~2.08v + 2.4v = 4.48v)
 * Voltage dropped across R4 = 2.08V equaled the Voltage dropped across R5 + LED4 (~0.19v + 1.89v = 2.08v)

I also must add that the Voltage dropped across R2 and LED1 (7.05 + 3.02 = 10.07) was equivalent to the total circuit voltage.

My Second Task
My next goal is to rewire the circuit, now that I understand how to correctly wire R1 so that it is not bypassed. Next, to re-take all test measurements, including Voltage dropped across R1 and total circuit current. Thirdly, to determine relationships between Resistance and Voltage drops and use that information to optimize my circuit as not to over-current the LEDs. Lastly, to hard-wire the Voltage Detector and mount it on the turbine.

Summary of actual work over second weekend
Spent the whole week testing and optimizing the LED Voltage Detector. I was not able to hard-wire the circuit or mount it on the turbine.

Week2 Narrative
During this week, I've continued trying to optimize my circuit so that the voltage drops across each LED are not greater than the optimal range. I've utilized the same testing process as the previous week, I am measure voltage drops across the components of my circuit and changing resistor values. This weeks data:
 * Test #1 (Original Circuit):
 * {| class="wikitable"

! Component !! R1 !! R2 !! R3 !! R4 !! R5 !! LED1 !! LED2 !! LED3 !! LED4 Test #2 (Changed R2 value from 100 Ohm to 1K Ohm):
 * Voltage Dropped (Volts) || 2.02v || 6.92v || 4.34v || 1.96v || 0.10v || 3.01v || 2.54v || 2.38v || 1.87v
 * }
 * }
 * {| class="wikitable"

! Component !! R1 !! R2 !! R3 !! R4 !! R5 !! LED1 !! LED2 !! LED3 !! LED4
 * Voltage Dropped (Volts) || 1.4v || 7.99v || 5.15v || 2.57v || 0.59v || 2.65v || 2.74v || 2.55v || 2.01v
 * }
 * }
 * Test #3 (Changed R2 and R3 values to 1K Ohm):
 * {| class="wikitable"

! Component !! R1 !! R2 !! R3 !! R4 !! R5 !! LED1 !! LED2 !! LED3 !! LED4
 * Voltage Dropped (Volts) || 0.95v || 8.7v || 6.24v || 3.48v || 1.3v || 2.43v || 2.43v || 2.74v || 2.17v
 * }
 * }
 * Test #4 (Changed R2,3,4 vlaues to 1K Ohm):
 * {| class="wikitable"

! Component !! R1 !! R2 !! R3 !! R4 !! R5 !! LED1 !! LED2 !! LED3 !! LED4
 * Voltage Dropped (Volts) || 0.63v || 9.2v || 6.97v || 4.51v || 2.13v || 2.26v || 2.22v || 2.46v || 2.35v
 * }
 * }
 * Test #5 (Changed R2,3,4,5 vlaues to 1K Ohm):
 * {| class="wikitable"

! Component !! R1 !! R2 !! R3 !! R4 !! R5 !! LED1 !! LED2 !! LED3 !! LED4 Now I have all my LEDs operating in their optimal voltage range (between ~1.8V and 2.2V).
 * Voltage Dropped (Volts) || 0.39v || 9.57v || 7.48v || 5.38v || 3.42v || 2.14v || 2.05v || 2.10v || 1.95v
 * }
 * }

My Third task
Download and utilize CircuitMaker to simulate my circuit, gather data on resistance changes, and fully understand the theory behind my circuit. I will also design the circuit and how I will mount it on to the wind turbine.

Summary of actual work over third weekend
How is what you did different than what you planned?

Week3 Narrative
Tell a detailed story describing what you did for your team over the weekend.

My Fourth task
Hard wire LED Voltage Detector (Voltage Divider Circuit) and mount on to Wind Turbine.

Summary of actual work over fourth weekend
Completed planned task with minor difficulty. I had not planned on testing components after each connection and additional parallel leg.

Week4 Narrative
First, I had to reuse the wire harness from the previous turbine prototype. I removed the previous circuit that was attached to the wire harness using wire cutters. I made two cuts just after the solder that was on the harness leads.

Before connecting the positive and negative leads of my LED Voltage Detector, I had to test the polarity of the wire harness leads. I plugged the harness back in to the motor, attached my positive voltmeter clip to the left lead (when looking at the harness from behind) then attached the negative clip to the right lead. I mounted the fan blades onto the motor and spun them in the direction corresponding to the shape of the blades. When turning the fan blades clockwise with the clips attached in the order specified earlier, the motor produces a positive voltage.

I began hard wiring my circuit so that I may mount it inside of the turbine shaft: I used a 3 inch wire (Red, to indicate the positive terminal of my circuit) stripped the insulation one half inch on both sides and soldered it directly to R1. Next, I used a 7 inch black wire, same gauge as the positive lead, stripped it in five places. I stripped a half inch off the end where it will be soldered to the harness and removed four small areas corresponding to the spacing of the parallel resistors. Step 1) Soldered LED1 directly to the lead off of R1 and attached R2 directly to LED1's cathode. Step 2) Soldered R2 to the exposed part of the return wire.

Step 3) Solder LED2 directly to R2

Step 4) Solder R3 to LED2 and return wire

Step 5) Solder LED3 directly to R3

Step 6) Solder R4 to LED3 and return wire

Step 7) Solder LED4 directly to R4

Step 8) Solder R5 to LED4 and return wire

Following the completion of the circuit, I attached the positive and negative leads to a variable power supply and tested the circuit to ensure that all connections are correct. During the test, I realized that I had wired LEDs 3 and 4 backwards and so I had to break the connections at R2, R3, R4, and R5, and re-solder the diodes in the correct arrangement. After the correction was made, the circuit functioned as it had on the breadboard. I conclude that the circuit is not malfunctioning in any way and moved on to mounting

Next, I soldered the positive and negative leads of my circuit on to the corresponding leads of the wire harness and attached it to the motor. After attempting to mount the circuit inside of the turbine, I realized that the exposed wire may cause the circuit to short. I decided to coat the circuit in epoxy to insulate the exposed wire. To test that the circuit was entirely insulated, I attached the harness to the motor and set the circuit inside of the hollow turbine shaft. I used a leaf blower to spin the turbine blades and power my circuit. The circuit functions inside of the turbine and does not short. Although I had doubted the effectiveness of the epoxy as an insulator, it seems to have been the easiest solution. Another solution I had devised was to use duct tape to line the inside of the shaft.

Complete Team Page
Fill out the Team Form (should have already copied the form, created the team page, linked to it and started filling it out).


text:
User:Mbaig5753/enes100/Bridge: My Work

Bridges

Write problem/project Goal
What is your wording of the overall problem/project goal?

To create a spaghetti arch that will support as much weight as possible.

My First Task
What are you going to do for the team this first weekend?

Look into construction techniques that is used in the real life to have arches support various loads. Also look at other previous arch designs and analyze where they went wrong and where they succeeded.

Summary of actual work over first weekend
This weekend I was assigned to look at real life arches and how they are designed to hold a large force. I did this plus look into ways on how to manipulate pasta to hold large amounts of weight, and the best glue to use.

Week1 Narrative
Tell a detailed story describing what you did for your team over the weekend. I looked at actual arch structures that are used in real life and noticed most arches use a design that incorporates two force members attached at a 45 degree angle. For example this design right here This is also the design used by the spagetti arch winner as you can see here from the top and side view. What I did over this weekend was since we already know the best design possible was to see in a constructive point of view how we can manipulate pasta to take this form and hold the most amount of weight. I noticed that having thin flattened pasta be essentially strung through the pasta that was cylindrical would give the structure more support and allow to to be flexible.

The epoxy that was also used wasn't the greatest so I did research and found that the best epoxy to use to dry on pasta is JB Weld epoxy epoxy. I learned this from discussions regarding this subject manner online discussion

My Second Task
I plan on having a working build of the arch ready and analyze it to see where the weak points are.

Summary of actual work over second weekend
I wasn't able to get a working arch together because there is stil not epoxy available to use in the workshop. I actually completed the arch and held it in place using duck-tape.

Week2 Narrative
What was done over the weekend was that I built a lot of pasta arches in sections because I knew that in testing they would break and I would have to make repairs and patches. I also looked back at the work I had did and analyze the work such as the pasta that we glued together. Heres a pic of what the section looks like.
 * Photo_1.JPG

As you can see from here I laced the hollow pasta with flat spegghatii inside it, gives it strength but also weighs the arch down. Which is a potential pitfall. Here is another photo of the pasta
 * Photo_2.JPG

The arch that we used earlier with the epoxy wasn't working well either what I learned from that is the epoxy didnt dry well. My group and I didnt do a good 50/50 split when making the compound. So when the new epoxy arrives we need to make sure we mix it properly. With the very little glue i had at home I did manage to put together some arches but I noticed that the glue I had at home added to much weight and collapsed on them self.

 * My instructor did tell us to try using wire that we can use to loop the slanted shaped pasta into. I did try that but i dont have the correct epoxy right now to use to put it all together. What I do like about the wire is that it can be easily removed and doesnt weigh the arch down like having flat shaped spegghetti running through it. It is a light, efficient and works well. I just need to get the epoxy that the Instructor is going to order.

My Third task
Meet with my group and built arches and test them with weight.

Summary of actual work over third weekend
I planned on making physical arches over this weekend, one arch was made, and tested. I then worked off of the results of the first arch. See my narrative for details.

Week3 Narrative
This weekend I met with my team members and we finished our construction of the arch. We let it sit and dry and made sure it was ready so we could add weight. From lifting it off the wooden frame we have been using it felt very fragile. I had a bad feeling about the strength of it. We tested .5 pound shoe on there and it broke the arch. Seeing this a realization came that the design was not efficient in holding weight. The design was later rebuilt using wire that was threaded through the entire arch, and then my team member Nathan bought epoxy something which has been missing from our designs because there was none in class. The slanted pasta was strung on the wire and then glued onto our wooden semi circle. As shown here

Once we applied epoxy and let the glue settle we began to take of the tape as shown in the picture. The tape is used to hold the pasta in place over the arch. Once that dried we took the tape of and began to lift the arch up. What we noticed was that firstly the epoxy wasn't strong enough the arch was starting to cave in on itself at certain points. I doubt this error was on our part in terms of mixing the epoxy because this epoxy we bought has two tubes that once squeezed pour at once. I put the blame on the epoxy not being strong enough. Also that we couldn't get the epoxy to cover all of the pasta. This is because the tape only allowed us to glue on side and not rotate. This arch was not successful it broke on itself. Our next idea was to lace the wire with wax paper because we believed the glue was sticking to the wire and having wire coated with wax paper would prevent this. From the attached picture you could see our attempt at this. It wasnt successful because of the fact that the wax paper with the wire was to hard to string through the narrow hole in the pasta.

My Fourth task
Hopefully the glue that Forester orders is stronger we plan on using that glue and making the arch in a way that arch can be glues 360 degrees, and our team member is making an assembly that can sand the pasta at a perfect angle so it glues better.

Summary of actual work over fourth weekend
I helped in the process of making the assembly for the grinding box, and built an arch again using a different construction technique.

Week4 Narrative
First all I helped my teammate Nathan with assisting him and prepping the wood for the grinding box so we could grind the noodles at the perfect angle. Moreover though this week I worked on making another arch using a design of wire running through the pasta but instead of only gluing one side of the pasta that was exposed. We would glue the top side that fit completely over the wooden frame then let it dry and flip the pasta and glue the other side of the pasta. This gave the arch added strength. We used the previous method of taping the cross sections where the pasta didn't meet each other, also utilizing wax paper. The most time extensive part of this has to to be the gluing of the noodles together because epoxy dries fast and a lot of care is involved in handling it. Making sure the pasta was held securely together and there was no slack was also tough.

The arch again wasn't very effective again we ran into issues with the glue it wasnt holding the pasta together strong enough.

Complete Team Page
Fill out the Team Form (should have already copied the form, created the team page, linked to it and started filling it out).

title: User:Mbaig5753/enes100/Bridge: My Work


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CIVICS/Quantitative Research Methods

Stefan Schwarze

University of Goettingen, Department of Agricultural Economics and Rural Development, Goettingen, Germany

Spring School - Integrative Conservation Planning in the South Caucasus - Tbilisi, March 05-10, 2012

Why do we need economic data for conservation planning?

 * Vast expansion of human activity during the last century
 * widespread conversion of natural habitat
 * many species are at risk of extinction

 * Large-scale anthropogenic threats to biodiversity, but only limited resources devoted to conservation.

 * Where to use the limited resources for conservation?
 * Maximize the conservation return on investment

Two domains for socio-economic assessments in conservation planning:

 * Understand the threat to biodiverstiy
 * Why do people change their land use?

 * Assess the costs of conservation
 * Which costs occur?

Costs of conservation

Acquisition and transaction costs: Costs involved buying the land

Management costs: Costs for managing the park (staff, vehicles, offices, etc.)

Damage costs: Damages of crops and livestock due to wild animals

Opportunity costs: Potential economic benefits from using the park area for economic activities instead of protecting it

CIVICS

title: CIVICS/Quantitative Research Methods


text:
User:Garcia123/ENES100/My Work 2

Write problem/project Goal
pick a car hack try to repeat it and build on it.

My First Task
pick a hack/starting point and follow through it. Stop looking for other hacks and pick a hack that i already looked into and build on it.

Summary of actual work over first weekend
Nothing different. I decided to go with the MPGuino project

Week1 Narrative
I was looking into all the projects me and my group researched since the project is very broad. The projects I looked at were: improving the gas mileage, turning a car into a sports car, hacking the tire pressure sensor systems in cars, MPGunio, and many more. I decided I wanted a project that is hands on instead of researching codes and how to use the codes so I decided to pick the MPGuiino project.

My Second Task
Take apart a piece of a printer and do some soldering so I can get the LCD screen part out the way of the project.

Summary of actual work over second weekend
Took apart the printer component and introduced myself to soldering

Week2 Narrative
I looked for a screw driver or anything I can use to unscrew the screws off the printer component. I couldn’t find anything to use. I only found screwdrivers for bigger screws. The screws on the component are small so I wasn’t able to use them. I then made my way to my friend’s house to see if he had any screwdrivers that can unscrew the small screws on the component. Luckily he had a couple of them I can borrow. I used the screwdrivers to unscrew the screws, taking apart the component. I then searched how to solder and watched YouTube videos on how to solder.

My Third task
Get the LCD screen to work.

Summary of actual work over third weekend
How is what you did different than what you planned?

Week3 Narrative
Tell a detailed story describing what you did for your team over the weekend.

My Fourth task
''Record what you are planning on doing for the team during the final weekend of project work. ''

Summary of actual work over fourth weekend
Nothing different. Soldered wires to the LCD screen. Connected wires to the Arduino and tried to get the screen to work.

Week4 Narrative
I watched more videos on how to solder. After I collected all the materials I needed to solder such as: Solder, newspaper, soldering iron, and wires. I then readied my workplace, clearing the table and placing newspaper on it. I then plugged in the soldering iron and soaked the sponge. Once the soldering iron was hot enough, I unplugged it. Then I soldered 5 wires onto the component. I melted solder on the soldering iron and using the melted solder, I connected 5 wires to the component. Some of the wires kept falling off when I moved it around so I had to keep re-soldering them. I then tried to follow the diagram, connecting the wires to the Arduino. I noticed one of the wires was too short and that I was missing wires. The diagram was confusing to me so I tried to follow it as best as I could. Next, I went on the Arduino website to download the software I need to use the Arduino. I then plugged the USB to the Arduino and to the laptop. Arduino worked but I was not able to use the Arduino to get the LCD screen to work.

Complete Team Page
Car Hack 2

title: User:Garcia123/ENES100/My Work 2


text:
Engineering Projects/Robot end effector/Howard Community College/Spring2012/p1501mjj2

Problem Statement
Need to make a robot arm that will pick up objects.

Team Members

 * Michael Hicks
 * Jon Fourney
 * Jonathan Sunday

Summary
Over over second four week section on this project a lot of progress was made. We took from the foundations we previously built and pushed the project much further forward using new designs for our coffee grind hand to create a larger amount of suction. Found out that we may have been losing suction between the PVC and the balloon, so we added a little plastic PVC piece to create a better seal. The coffee gripper was finished and there was a lot of software understanding gained with getting the dc motor to go forward and backwards, also figuring out how to run twp stepper motors on one motor shield. With a lot of the physical pieces done there is less than half of the project that must be completed and hopefully it will be done soon.

Poster
Project Overview

Story
Again we all took to our own separate ways in hopes of gaining knowledge and products that could soon be put together for a final functioning result. Jon Fourney stuck with his coffee grind hand and practically finished it. He was having trouble with suction in the hand so he used a coupler inside of the drain to create a much more effective seal. He also discovered that putting a compressor to the balloon prior to the vacuum for picking up is much better. It inflates the balloon partially and allows it to conform to the desired object much easier. He cut it down to make it much more weight efficient. The to make the connection he simply used two threaded couplers, one of which connected to the makerbot wires and the other to the hand. This way it can be screwed in and out allowing for a quick change to the fin ray. Mike Hicks approach the product on the front of the motors and their function. First of all he built the mounts to hold the motors. In the stands the makerbot wire runs up through them and allows the motor to pull the wires up or push down and move as desired with the rotation of the stepper motors. Second he figured out the software issue. He found out how to make a motor work going up and down on a desired circuit so that we can control everything it does very easily. The only trouble he ran into was powering all of the motors at once on a single arduino. There was a problem or two with the motor shield but he should have this worked out shortly by using an external power source. Jonathan Sunday worked toward advancing his fin ray claw powered by a worm drive motor. The main source of his frustration was figuring out how to make the worm drive go in two directions. Making the hand close was very simple, but he could not figure out how to make it retract. After several days of extensive research and development he accomplished his goal. he can now make the motor go in both directions using the arduino with no problems whatsoever. All in all the project has taken large steps forward and it is going great.

Decision List
Using the direct connection of the hose from the vacuum to the balloon may have been the best suction, but it would tip the balloon. Using the original design was not suctioning that well and only able to pick up light weight items, but wasn't ripping or stretching the balloon. Attaching the coupling was out best option, created the best seal to have a stronger suction in order to pick up heavier items and was putting no wear and tare on the balloon.

Material List

 * 1. 2 Stepper motors
 * 2. scrap wood
 * 3. Sheet metal
 * 4. external power supply
 * 5. 12" shrink wrap
 * 6. Metal rod
 * 7. 2 rubber wheels
 * 8. 2 Motor shields
 * 9. 2 Hose clamps, $2
 * 10. Male Threaded Coupling, $3
 * 11. Female Threaded Coupling, $3
 * 12. Maker Bot Wire
 * 13. 2" Coupling, $2
 * 14. PVC Glue, $6

Future Materials Needed

 * 1. 1 arduino/motor shield
 * 2. metal enclosure
 * 3. wire
 * 4. Sheet metal

Software List

 * Arduino software to control the dc motor and the tree stepping motors.
 * 123d to design the coffee grind hand
 * Auto cad to design the coffee grind hand

Time
31 total hours

Tutorials

 * Sand hand diagram 1
 * Sand hand diagram 2
 * Connection System 1
 * Connection System 2

Next Steps
The next steps of the project are more of the difficult ones. A lot of kinks need to be worked out as far as powering multiple stepper motors on one arduino. Also we still need a completed finray claw to complete the end effector. After this a final installation must occur. Not yet have all the pieces each member has made been put together on the table. these pieces include mainly the motor mounts. Because these are the only part that is physically attached to the table permanently. After this most everything is interchangeable.