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User:Egm6321.f11.team1/report5

= R*5.1 2nd Exactness Condition For n=2 Case of Nn-ODE (Method 2) =

Given
Equivalent form of 2nd Exactness Condition for N2-ODEs :

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

$$
 * $$g_0-\frac{dg_1}{dx}+\frac{d^2g_2}{dx^2}=0$$
 * $$\displaystyle (Equation\;4.7.1)
 * $$\displaystyle (Equation\;4.7.1)
 * }
 * }

Coefficient equalities, located in previous reference above.

 * $$\displaystyle g_0=f_yq+g_y$$

 * $$\displaystyle g_1=f_pq+g_p$$

 * $$\displaystyle g_2=f$$

Note also that $$\displaystyle p(x):=y'(x)$$ and $$\displaystyle q(x):=y''(x).$$

== Find ==

Show the following equality is true:

 * $$\displaystyle f_{xx}+2pf_{xy}+p^2f_{yy}-g_{xp}-pg_{yp}+g_y+\left( f_{xp}+pf_{yp}+2f_y-g_{pp}\right)q=0$$

Solution
Applying the chain rule to $$\frac{dg_1}{dx}$$ yields the following:

$$\frac{dg_1}{dx}=\frac{\partial g_1}{\partial x}+\frac{\partial g_1}{\partial y}\frac{dy}{dx}+\frac{\partial g_1}{\partial y^{(1)}}\frac{dy^{(1)}}{dx}$$

We know what $$\displaystyle g_1$$ is defined to be, we can substitute in $$\displaystyle p(x):=y'(x)$$ and $$\displaystyle q(x):=y''(x)$$ and carry out the derivatives:

$$\frac{dg_1}{dx}=\frac{\partial g_1}{\partial x}+\frac{\partial g_1}{\partial y}p+\frac{\partial g_1}{\partial p}q$$

$$\frac{dg_1}{dx}=\left(f_{xp}q+g_{xp}\right)+\left(f_{yp}q+g_{yp}\right)p+\left(f_{pp}+g_{pp}\right)q$$

We can apply the same approach to $$\frac{d^2g_2}{dx^2}$$ :

$$\frac{d^2g_2}{dx^2}=\frac{\partial^2 g_2}{\partial x^2}+\frac{\partial^2 g_2}{\partial y\partial x}\frac{dy}{dx}+\frac{\partial^2 g_2}{\partial x\partial y}\frac{dy}{dx}+\frac{\partial^2 g_2}{\partial x\partial y^{(1)}}\frac{dy^{(1)}}{dx}+\frac{\partial^2 g_2}{\partial y^{(1)}\partial x}\frac{dy^{(1)}}{dx}+\frac{\partial^2 g_2}{\partial^2 y}\frac{dy^2}{dx^2}$$

$$\frac{d^2g_2}{dx^2}=f_{xx}+f_{yx}p+f_{xy}p+f_{xp}q+f_{px}q+f_{yy}p^2$$

Adding $$\displaystyle g_0 $$, $$\displaystyle \frac{dg_1}{dx}$$ , and $$\displaystyle \frac{d^2g_2}{dx^2}$$ according to Equation 4.7.1 yields our final solution:

$$ g_0-\frac{dg_1}{dx}+\frac{d^2g_2}{dx^2}=\left(f_yq+g_y\right)-\left(f_{xp}q+g_{xp}+f_{yp}pq+g_{yp}p+g_{pp}q\right)+\left(f_{xx}+f_{yy}p^2+2f_{xy}p+2f_{xp}q\right)=0$$

= R*5.2 Exactness of Bessel, Legendre, and Hermite =

Given
Legendre L2-ODE-VC:
 * {| style="width:100%" border="0" align="left"

$$
 * $$\displaystyle G=(1-x^2)y''-2xy'+n(n+1)y=0$$
 * $$\displaystyle (Equation\;5.2.1)
 * $$\displaystyle (Equation\;5.2.1)
 * }
 * }

Bessel L2-ODE-VC:
 * {| style="width:100%" border="0" align="left"

$$
 * $$\displaystyle (1-x^2)y''-2xy'+(x^2-\nu^2)y=0$$
 * $$\displaystyle (Equation\;5.2.2)
 * $$\displaystyle (Equation\;5.2.2)
 * }
 * }

Hermite L2-ODE-VC:
 * {| style="width:100%" border="0" align="left"

$$
 * $$\displaystyle y''-2xy'+2ny=0$$
 * $$\displaystyle (Equation\;5.2.3)
 * $$\displaystyle (Equation\;5.2.3)
 * }
 * }

Exactness Conditions

 * $$\displaystyle ({Condition}\;1)\;\;G(x,y,y',y)=g(x,y,p)+f(x,y,p)y=0$$
 * where $$\displaystyle p=y'$$

 * $$\displaystyle (Condition\;2a)\;\;f_{xx}+2pf_{xy}+p^2f_{yy}=g_{xp}+pg_{yp}-g_y\;\mathbf{AND}\;f_{xp}+pf_{yp}+2f_y=g_{pp}$$

 * $$\displaystyle (Condition\;2b)\;\;g_0-\frac{dg_1}{dx}+\frac{d^2g_2}{dx^2}=0$$

 * $$\displaystyle g_0=f_yq+g_y$$
 * $$\displaystyle g_1=f_pq+g_p$$
 * $$\displaystyle g_2=f$$
 * where $$\displaystyle q=y''$$

== Find ==

(1) Verify the exactness conditions of Legendre, Bessel, and Hermite, using both methods for the 2nd exactness condition.

(2) If Equation 5.2.3 is not exact, check whether it is in power form, and see whether if it can be made exact using IFM with $$\displaystyle h(x,y)=x^my^n$$.

(3) Verify the following Hermite polynomials are homogenous solutions of Equation 5.2.3.

 * $$\displaystyle H_0(x)=1$$

 * $$\displaystyle H_1(x)=2x$$

 * $$\displaystyle H_2(x)=4x^2-2$$

Solution
Part (1)

Verify Exactness of Legendre L2-ODE-VC

Condition 1:

$$\displaystyle G(x,y,y',y)=\underbrace{n(n+1)y-2xy'}_{g(x,y,p)}+\underbrace{(1-x^2)}_{f(x,y,p)}y=0$$

Condition 2a:

$$\displaystyle f_{xx}+2pf_{xy}+p^2f_{yy}=-2+0+0=-2$$

$$\displaystyle g_{xp}+pg_{yp}-g_y=-2+0-n(n+1)$$

Letting

allows the first part of Condition 2a to be satisfied.

$$\displaystyle f_{xp}+pf_{yp}+2f_y=0+0+0$$

$$\displaystyle g_{pp}=0$$

$$\displaystyle 0=0$$

Thus Condition 2 (first method) is satisfied.

Condition 2b:

$$g_0-\frac{dg_1}{dx}+\frac{d^2g_2}{dx^2}=n(n+1)-\frac{d}{dx}\left(0-2x\right)+(-2)=0+2-2=0$$

Thus Condition 2a (second part) is satisfied.

Verify Exactness of Bessel L2-ODE-VC

Condition 1:

$$\displaystyle G(x,y,y',y)=\underbrace{(x^2-\nu^2)y-2xy'}_{g(x,y,p)}+\underbrace{(1-x^2)}_{f(x,y,p)}y=0$$

Condition 2a:

$$\displaystyle f_{xx}+2pf_{xy}+p^2f_{yy}=-2+0+0=-2$$

$$\displaystyle g_{xp}+pg_{yp}-g_y=-2+0-(x^2-\nu^2)$$

$$\displaystyle -2=-2-(x^2-\nu^2)$$

Thus the Bessel equation satisfies exactness only if we assume

$$\displaystyle f_{xp}+pf_{yp}+2f_y=0+0+0$$

$$\displaystyle g_{pp}=0$$

$$\displaystyle 0=0$$

Thus Condition 2a(second part) is satisfied.

Condition 2b:

$$g_0-\frac{dg_1}{dx}+\frac{d^2g_2}{dx^2}=(x^2-\nu^2)-\frac{d}{dx}\left(0-2x\right)+(-2)=0+2-2=0$$

Thus Condition 2a (second part) is satisfied.

Verify Exactness of Hermite L2-ODE-VC

Condition 1:

$$\displaystyle G(x,y,y',y)=\underbrace{2ny-2xy'}_{g(x,y,p)}+\underbrace{(1)}_{f(x,y,p)}y=0$$

Condition 2a:

$$\displaystyle f_{xx}+2pf_{xy}+p^2f_{yy}=0+0+0=0$$

$$\displaystyle g_{xp}+pg_{yp}-g_y=-2+0+2n$$

Letting

allows the first part of Condition 2a to be satisfied.

$$\displaystyle f_{xp}+pf_{yp}+2f_y=0+0+0$$

$$\displaystyle g_{pp}=0$$

$$\displaystyle 0=0$$

Thus Condition 2 (first method) is satisfied.

Condition 2b:

$$g_0-\frac{dg_1}{dx}+\frac{d^2g_2}{dx^2}=(2n)-\frac{d}{dx}\left(0-2x\right)+0=2-2+0=0$$

Thus Condition 2a (second part) is satisfied.

Part (2) Hermite differential equation $$\displaystyle y''-2xy'+2ny=0$$ is not exact if $$\displaystyle n\neq -1$$. And it is in the power form of L2-ODE-VC: $$\displaystyle \alpha x^ry''+\beta x^sy'+\gamma x^ty$$ with $$\displaystyle \alpha=1;\beta=-2;\gamma=2n.$$ $$\displaystyle r=0;s=1;t=0.$$ Assuming that we can find the integrating factor which is in power form, $$\displaystyle h(x,y)=x^my^n$$. Use the exactness condition to find $$m,n\in \mathbb{E}$$, such that the following N2-ODE is exact:
 * {| style="width:100%" border="0" align="left"

$$ Rewrite Equation(5,2,1) as $$\displaystyle G(x,y,y',y)=\underbrace{2\alpha x^m y^{n+1}-2x^{m+1}y^ny'}_{g(x,y,p)}+\underbrace{x^my^n}_{f(x,y,p)}y$$ Calculate the following terms in the exactness condition: $$\displaystyle f_x=mx^{m-1}y^n;\,f_{xx}=m(m-1)x^{m-2}y^n$$ $$\displaystyle f_{xy}=mnx^{m-1}y^{n-1};\,f_{xp}=0$$ $$\displaystyle f_y=nx^my^{n-1}$$ $$\displaystyle f_{yy}=n(n-1)x^my^{n-2};\,f_{yp}=0$$ $$\displaystyle g_x=2m\alpha x^{m-1}y^{n+1}-2(m+1)x^my^np;\,g_{xp}=-2(m+1)x^my^n$$ $$\displaystyle g_y=2\alpha (n+1)x^{m}y^{n-1}-2nx^{m+1}y^{n-1}p;\,g_{yp}=-2nx^{m+1}y^{n+1}$$ $$\displaystyle g_p=-2x^{m+1}y^n;\,g_{pp}=0$$ Recall the 2nd exactness condition for L2-ODE-VC:
 * $$\displaystyle x^m y^n(y''-2xy'+2\alpha y)=0$$
 * $$\displaystyle (Equation\;5.2.4)
 * $$\displaystyle (Equation\;5.2.4)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

$$
 * $$\displaystyle f_{xx}+2pf_{xy}+p^2f_{yy}=g_{xp}+pg_{yp}-g_y$$
 * $$\displaystyle (Equation\;5.2.5)
 * $$\displaystyle (Equation\;5.2.5)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

$$ Substituting those calculated terms into Equation(5,2,5) and Equation(5.2.6). The 1st exactness condition Equation(5,2,5) is $$\displaystyle m(m-1)x^{m-2}y^n+2p\cdot mnx^{m-1}y^{n-1}+p^2n(n-1)x^my^{n-2}=-2(m+1)x^my^n+p(-2nx^{m+1}y^{n-1})-2\alpha (n+1)x^my^n+2nx^{m+1}y^{n-1}p$$ The 2nd exactness conditionEquation(5.2.6) is $$\displaystyle 0+p\cdot 0+2nx^my^{n-1}=0$$ It is obvious that only if $$\displaystyle n=0$$, the 2nd exactness condition Equation(5.2.6) is satisfied. Substitute $$\displaystyle n=0$$ into Equation(5,2,5), we can obtain $$\displaystyle m(m-1)x^{m-2}=-2(m+1)x^m-2\alpha x^m$$ It means $$\displaystyle m(m-1)=0$$ and $$\displaystyle m+1+\alpha =0$$ We choose $$\displaystyle m=1,\alpha =-2 \,$$ to make the factor h(x,y) not zero.
 * $$\displaystyle f_{xp}+pf_{yp}+2f_y=g_{pp}$$
 * $$\displaystyle (Equation\;5.2.6)
 * $$\displaystyle (Equation\;5.2.6)
 * }
 * }

Part (3) Verify the first three terms of Hermite polynomials. Letting

$$\displaystyle y=H_0(x)=1$$ $$\displaystyle y'=H_0'(x)=0$$ $$\displaystyle y=H_0(x)=0$$ Substitute them into the Hermite differential equation Equation(5.2.3): $$\displaystyle 0-2x\cdot 0+0\cdot 1=0$$ Therefore, the first term of Hermite polynomial $$\displaystyle H_0(x)=1$$ is the homogeneous solution of the Hermite differential equation Equation (5.2.3).

Letting

$$\displaystyle y=H_1(x)=2x$$ $$\displaystyle y'=H_1'(x)=2$$ $$\displaystyle y=H_1(x)=0$$ Substitute them into the Hermite differential equation Equation(5.2.3): $$\displaystyle 0-2x\cdot 2+2\cdot 2x=0$$ Therefore, the second term of Hermite polynomial $$\displaystyle H_1(x)=2x$$ is the homogeneous solution of the Hermite differential equation Equation (5.2.3).

Letting $$\displaystyle y=H_2(x)=4x^2-2$$ $$\displaystyle y'=H_2'(x)=8x$$ $$\displaystyle y=H_2(x)=8$$ Substitute them into the Hermite differential equation Equation(5.2.3): $$\displaystyle 8-2x\cdot 8x+4\cdot (4x^2-2)=0$$ Therefore, the third term of Hermite polynomial $$\displaystyle H_2(x)=4x^2-2$$ is the homogeneous solution of the Hermite differential equation Equation (5.2.3).

= R*5.3 Find the expressions for X(x)in terms of $$\cos Kx,\ \sin Kx,\ \cosh Kx,\ \sinh Kx$$ =

Given
$$ \displaystyle X^{(4)}-K^4X=0 $$

$$ \displaystyle K:= \frac{\omega^2m}{EI} $$

Assume:

$$ \displaystyle X_{(x)}=e^{(rx)} $$

characteristic equation:

$$ \displaystyle r^4=K^4 $$

then:

$$ \displaystyle r_1=K,\ r_2=-K,\ r_3=iK,\ r_4=-iK,\ i:=\sqrt{-1} $$

Find
the expressions for $$X_{(x)}$$ in terms of:

$$ \displaystyle \cos Kx, \ \sin Kx,\ \cosh Kx,\ \sinh Kx $$

Solution

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

\displaystyle X_{(x)}=c_1e^{Kx}+c_2e^{-Kx}+c_3e^{iKx}+c_4e^{-iKx} $$ $$
 * $$\displaystyle (Equation\;5.3.1 )
 * }
 * }

$$ \displaystyle \begin{align} A_1: &=c_1e^{Kx}+c_2e^{-Kx}\ \in \mathbb{R} \\ &= c_1(\frac{e^{Kx}+e^{-Kx}}{2}+\frac{e^{Kx}-e^{-Kx}}{2}) + c_2(\frac{e^{Kx}+e^{-Kx}}{2}-\frac{e^{Kx}-e^{-Kx}}{2})\\ &= c_1(\cosh Kx+ \sinh Kx) + c_2(\cosh Kx- \sinh Kx)\\ &= (c_1+c_2)\cosh Kx + (c_1-c_2)\sinh Kx \end{align} $$

We can rewrite it to:
 * {| style="width:100%" border="0" align="left"

\displaystyle A_1=b_1\cosh Kx + b_2\sinh Kx $$ $$
 * $$\displaystyle (Equation\;5.3.2 )
 * }
 * }

$$ \displaystyle \begin{align} A_2: &=c_3e^{iKx}+c_4e^{-iKx} \\ &=c_3(\cos Kx +i\sin Kx)+c_4(\cos Kx -i\sin Kx) \\ &= (c_3+c_4)\cos Kx + (c_3-c_4)i\sin Kx \ \in \mathbb{R} \end{align} $$

We can rewrite it to:
 * {| style="width:100%" border="0" align="left"

\displaystyle A_2=b_3\cos Kx- b_4\sin Kx $$ $$
 *
$$\displaystyle (Equation\;5.3.3 )
 * }
 * }

So, add up the two terms from equation 5.3.2 and equation 5.3.3:
 * {| style="width:100%" border="0" align="left"

\displaystyle X_{x}=A_1+A_2=b_1\cosh Kx + b_2\sinh Kx + b_3\cos Kx- b_4\sin Kx $$ $$
 *
$$\displaystyle (Equation\;5.3.4 )
 * }
 * }

Where:

$$ \displaystyle b_1=c_1+c_2,\ b_2=c_1-c_2,\ b_3=c_3+c_4,\ b_4=-i(c_3-c_4) $$

= R*5.4 Find $$y_{xxxxx}$$ in terms of derivatives of y with respect to time= == Given == Transformation of variables: $$\displaystyle x=e^t$$. The derivatives of y with respect to x are: $$\displaystyle y_x=e^{-t} \, y_t$$ $$\displaystyle y_{xx}=e^{-2t} \, (y_{tt}-y_t)$$ $$\displaystyle y_{xxx}=e^{-3t} \, (y_{ttt}-3t_{tt}+2y_t)$$ $$\displaystyle y_{xxxx}=e^{-4t} \,(y_{tttt}-6y_{ttt}+11y_{tt}-6y_t)$$

Find
Find $$\displaystyle y_{xxxxx}$$ in terms of the derivatives of y with respect to t.

Solution
Recall that $$\displaystyle \frac{dt}{dx}=\left(\frac{dx}{dt}\right)^{-1}=e^{(-t)}$$ The derivative is
 * $$\displaystyle y_{xxxxx}=\frac{d}{dx}\,(y_{xxxx})=\frac{dy_{xxxx}}{dt}\cdot \frac{dt}{dx}$$
 * $$\displaystyle =\frac{d}{dt}\left[e^{(-4t)}\,(y_{tttt}-6y_{ttt}+11y_{tt}-6y_t)\right]\cdot e^{-t}$$
 * $$\displaystyle =e^{-t}\cdot\left[\frac{d}{dt}(e^{-4t}\cdot(y_{tttt}-6y_{ttt}+11y_{tt}-6y_t)+e^{-4t}\cdot \frac{d}{dt} (y_{tttt}-6y_{ttt}+11y_{tt}-6y_t)\right]$$
 * $$\displaystyle =e^{-t}\cdot[-4e^{-4t}\cdot (y_{tttt}-6y_{ttt}+11y_{tt}-6y_t)+e^{-4t}\cdot (y_{ttttt}-6y_{tttt}+11y_{ttt}-6y_{tt})$$

 * $$\displaystyle =e^{-5t}(y_{ttttt}-10y_{tttt}+35y_{ttt}-50y_{tt}+24y_t)$$
 * $$\displaystyle$$

= R*5.5 Solving Euler's 2nd-order differential equation using the method of trial solution =

Given
A second order linear ordinary differential equation with varying coefficients(L2-ODE-VC)

With Boundary Coditions,

Find
The solution using the method of trial solution

Solution
Using the given trial solution

where r is constant. Then

substituting (5.5.4) into (5.5.1)

this can be simplified to,

IN general a homogeneous solution takes the following form

Since we have two roots 5.5.7 is written as,

Using the given roots in 5.5.6 the general solution is

Using the boundary conditions given in 5.5.2, we get

These equations can be solved by simple substitution which yields c1=-11.5 and c2=7.5, therefore the solution of this BVP is

The plot of the homogeneous solution is shown below

= R5.6 Show that the trial solution in Method 2 is equivalent to the combined trial solutions in Method 1 =

Given
Show the equivalence of two methods using Euler L3-ODE-VC as an example:
 * {| style="width:100%" border="0" align="left"

\displaystyle a_3x^3y^{(3)}+a_2x^2y^{(2)}+a_1xy'+a_0y=0,\ y'=y^{(1)},\ y=y^{(0)} $$ $$
 *
$$\displaystyle (Equation\;5.6.1)
 * }
 * }

Find
That the trial solution in Method 2 is equivalent to the combined trial solutions in Method 1.

Solution
1.Method I Stage 1,

$$ \displaystyle x=e^t $$

and we have derived in class that:
 * {| style="width:100%" border="0" align="left"

\displaystyle y'=e^{-t}y_t $$ $$
 *
$$\displaystyle (Equation\; 5.6.2)
 * }
 * }

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

\displaystyle y^{(2)}=e^{-2t}(y_{tt}-y_t) $$ $$
 *
$$\displaystyle (Equation\; 5.6.3)
 * }
 * }

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

\displaystyle y^{(3)}=e^{-3t}(y_{ttt}-3y_{tt}+2y_t) $$ $$
 *
$$\displaystyle (Equation\; 5.6.4)
 * }
 * }

plug equations 2,3,4 into 1, we obtain:
 * {| style="width:100%" border="0" align="left"

\displaystyle a_3e^{3t}\cdot e^{-3t}(y_{ttt}-3y_{tt}+2y_t)+a_2e^{2t}\cdot e^{-2t}(y_{tt}-y_t)+a_1e^t\cdot e^{-t}y_t+a_0y=0 $$ $$
 *
$$\displaystyle (Equation\; 5.6.5)
 * }
 * }

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

\displaystyle a_3y_{ttt}+(a_2-3a_3)y_{tt}+(2a_3-a_2+a_1)y_t+a_0y=0 $$ $$
 *
$$\displaystyle (Equation\; 5.6.6)
 * }
 * }

Stage 2,

$$ \displaystyle y=e^{rt},\ r=constant $$

substitute into equation 5.6.6, we get:
 * {| style="width:100%" border="0" align="left"

\displaystyle a_3r^3e^{rt}+(a_2-3a_3)r^2e^{rt}+(a_1-a_2+2a_3)re^{rt}+a_0e^{rt}=0 $$ $$
 *
$$\displaystyle (Equation\; 5.6.7)
 * }
 * }

Finally:

2.Method II

$$ \displaystyle y=x^r,\ r=constant $$

substitute into equation 1:
 * {| style="width:100%" border="0" align="left"

\displaystyle a_3x^3r(r-1)(r-2)x^{r-3}+a_2x^2r(r-1)x^{r-2}+a_1xrx^{r-1}+a_0x^r=0 $$ $$
 *
$$\displaystyle (Equation\; 5.6.8)
 * }
 * }

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

\displaystyle a_3r(r-1)(r-2)x^r+a_2r(r-1)x^r+a_1rx^r+a_0x^r=0 $$ $$
 *
$$\displaystyle (Equation\; 5.6.9)
 * }
 * }

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

\displaystyle a_3(r^3-3r^2+2r)+a_2(r^2-r)+a_1r+a_0=0 $$ $$
 *
$$\displaystyle (Equation\; 5.6.10)
 * }
 * }

And, finally:

So, using whatever method I or method II, we can derive the exact same characteristic equation

thus, they are just the same.

= R*5.7 Euler L2-ODE With Multiple Roots =

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

$$
 * $$\displaystyle (r-\lambda)^2=0$$
 *
$$\displaystyle (Equation\;5.7.1)
 *
$$\displaystyle (Equation\;5.7.1)
 * }
 * }

Euler L2-ODE-VC
 * {| style="width:100%" border="0" align="left"

$$
 * $$\displaystyle a_2x^2y''+a_1xy'+a_0y=0$$
 *
$$\displaystyle (Equation\;5.7.2)
 *
$$\displaystyle (Equation\;5.7.2)
 * }
 * }

Euler L2-ODE-CC
 * {| style="width:100%" border="0" align="left"

$$
 * $$\displaystyle b_2y''+b_1y'+b_0y=0$$
 *
$$\displaystyle (Equation\;5.7.3)
 *
$$\displaystyle (Equation\;5.7.3)
 * }
 * }

== Find ==

(1.1) Find $$\displaystyle a_2,a_1,a_0$$ so that Equation 5.7.1 is a characteristic equation of Equation 5.7.2.

(1.2) Show the 1st homogenous solution is $$\displaystyle y_1(x)=x^\lambda$$.

(1.3) Find $$\displaystyle c(x)$$ such that $$\displaystyle y(x)=c(x)y_1(x)$$.

(1.4) Find the 2nd homogenous solution $$\displaystyle y_2(x)$$.

(2) Repeat steps 1.1 thru 1.4 for Equation 5.7.3.

Section 1
Solve for the coefficients using the trial solution method. We shall assume the solution is in the form $$\displaystyle y=e^r$$ where $$\displaystyle r$$ is a constant. The following derivatives are calculated:

$$\displaystyle y'=rx^{r-1}$$

$$\displaystyle y''=r(r-1)x^{r-2}$$

Substituting the above derivatives into Equation 5.7.2 yields the following:

$$\displaystyle a_2x^2r(r-1)x^{r-2}+a_1xrx^{r-1}+a_0x^r=0$$

$$\displaystyle a_2r^2x^r-a_2rx^r+a_1rx^r+a_0x^r=0$$

$$\displaystyle a_2r^2+(a_1-a_2)r+a_0=0$$

$$\displaystyle $$

Now we can compare the above result to the expanded characteristic equation:

$$\displaystyle r^2-2\lambda r+\lambda^2=0$$

A simple comparison of coefficients implies the following:

Section 2
We assumed a form of $$\displaystyle y=x^r$$ and the characteristic equation is $$\displaystyle (r-\lambda)^2=0$$, thus $$\displaystyle r$$ must equal $$\displaystyle \lambda$$ to satisfy the characteristic equation, and thus the first homogenous solution is

Section 3
The complete solution will be the form such that

$$\displaystyle y(x)=c(x)y_1(x)=c(x)x^\lambda$$

This $$\displaystyle y(x)$$ will be inserted into Equation 5.7.2, so lets calculate derivatives.

$$\displaystyle y'(x)=c'y_1+cy_1'$$

$$\displaystyle y(x)=cy_1+c'y_1'+c'y_1'+cy_1=cy_1+2c'y_1'+cy_1''$$

Entering these derivatives into Equation 5.7.2 yields:

$$a_2x^2\left[cy_1+2c'y_1'+cy_1\right]+a_1x\left[c'y_1+cy_1'\right]+a_0\left[cy_1\right]=0$$

Now group by $$\displaystyle c(x)$$:

$$\left[a_0x^2y_1\right]c+\left[2a_2x^2y_1'+a_1xy_1\right]c'+\left[a_2x^2y_1+a_1xy_1'+a_0y_1\right]c=0$$

Note the last set of terms will be zero by Equation 5.7.2. Then enter in the derivatives and constants and simplify.

$$c''(x)\left[x^{\lambda+2}\right]+c'(x)\left[2\lambda x^{\lambda+1}+\left(1-2\lambda\right)x^{\lambda+1}\right]=0$$

$$\displaystyle c''(x)x^{\lambda+2}+c'(x)x^{\lambda+1}=0$$

$$\displaystyle \left[c''(x)x+c'(x)\right]x^{\lambda+1}=0$$

$$\displaystyle c''(x)x+c'(x)=0$$

This is a fairly straighforward ODE:

$$\displaystyle c''x+c'=(c'x)'=0$$

$$\displaystyle c'x=k_1$$

$$\displaystyle c'=\frac{k_1}{x}$$

$$\displaystyle c(x)=k_1\ln(x)+k_2$$

Therefore it is clear that

Section 4
We have found the complete solution $$\displaystyle y(x)$$ in the previous section. We know this complete solution is equivalent to the linear combination of two homogeneous solutions:

$$\displaystyle y(x)=C_1y_1(x)+C_2y_2(x)$$

Thus it is a matter of comparing the two equations to extract the 2nd homogeneous solution $$\displaystyle y_2(x)$$. From Section 3 it is true that

$$\displaystyle y(x)=k_1\ln(x)x^\lambda+k_2x^\lambda$$

Knowing that $$\displaystyle y_1(x)=x^\lambda$$ it can be deduced that

Section 1
The coefficients of 5.7.3 can be found by using the trial solution method. The given trial solution for the Euler equation with constant coefficient is:

The derivatives are calculated:

Substituting the above derivatives into Equation 5.7.3 we get:

Now we can cancel out $$ {e}^{xr} $$

Comparing the above equation to the characteristic equation given in 5.7.3 we have:

By comparing the coefficients of both sides of the above equation we get:

Section 2
From the Part 2 Section 1, the characteristic equation of 5.7.3 is 5.7.1. There are two identical roots of equation 5.7.1 equal to $$ \begin{align}r=\lambda  \end{align}$$. The 1st homogeneous solution can be calculated by:

Section 3
The complete solution will be of the form such that:

This $$\displaystyle y(x)$$ will be inserted into Equation 5.7.3, so lets calculate derivatives.

Entering these derivatives into Equation 5.7.3 yields:

Now group by $$ c(x) $$ terms:

Note that the first term with $$ c(x) $$ will be zero by equation 5.7.3, then enter the derivatives and constants and simplify:

In order for this to be zero the following must be true:

Integrating both sides of the above we have:

Integrating the above we have c(x) as:

Finally, using the above equation and the 1st homogeneous solution from part 2 section 2 substituted into the form of the 2nd homogeneous solution stated above yields the 2nd homogeneous solution:

Section 4
The generalized homogeneous solution takes the following form:

Substituting the 1st and 2nd homogeneous solution into the general form above yields:

with $$\begin{align} C_3 = {{C}_{1}}+{{C}_{2}}{{k}_{2}} \end{align}$$

$$\begin{align} C_4 = {{C}_{2}}{{k}_{1}} \end{align}$$

Substituting these constants yields the generalized homogeneous solution:

= R*5.8 =

Question from meeting 32, page 32-2: Given: recall p. 12-2, R*2.17
$$y' + a_0(x)y = 0$$
$$\displaystyle (Equation\;5.8.1)$$

Find: use the same idea of variation of constants (parameters) to find the particular solution $$Y_P(x)$$ after knowing the homogeneous solution $$Y_H(x)$$, i.e., let y(x) = A(x)$$y_H(x)$$, with A(x) being the unknown to be found.

From lecture notes [[media:pea1.f11.mtg32.djvu|Mtg 32]]

Solution
The key is to start with equation (3) on p. 11-3 below.
$$\underbrace{\color{blue}{1}}_{\color{blue}{a_1(x)}} \cdot \underbrace{y'}_{\color{blue}{y^{(1)}}} + \underbrace{\frac{Q(x)}{P(x)}}_{\color{blue}{a_0(x)}}y^{\color{blue}{(0)}}=\underbrace{\frac{R(x)}{P(x)}}_{\color{blue}{b(x)}}$$
$$\displaystyle (Equation\;5.8.2)$$ The equation is an L1-ODE-VC. Note that the non-homogeneous equation above utilizes the following integration factor for the solution of y. But we must find the homogenous counterpart to this solution

$$y(x) = \frac{1}{h(x)} \left[\int^x h(s)b(s)ds + k_2 \right]$$
$$\displaystyle (Equation\;5.8.3)$$

The homogeneous solution of the L1-ODE-VC was derived in R2.17 by team 1. The solution summary is repeated for clarity. Note that team 1 has already submitted this solution for R2.17 back in Report 2. The steps are from a simple cross-reference used to define the homogeneous solution of 5.8.2

 $$\displaystyle \frac{y'}{y} = -{a}_{0} $$
$$\displaystyle (Eq 2.17.1) $$

Integration of both sides of this equation gives

 $$ \ln \left( y\right)= -\int^{x} {a}_{0} \left( s\right)ds + C$$
$$\displaystyle (Eq 2.17.2)$$

Solving for $$y$$ gives

$$ y_H= \exp\left[ -\int^{x} {a}_{0} \left( s\right)ds + C \right]= A\exp\left[ -\int^{x} {a}_{0} \left( s\right)ds\right]$$

Now, the homogenous solution is known from 2.17. The next step is to find the complete solution for the homogenous equation- $$y(x) = A(x)y_H(x)$$. The technique demonstrated in the lecture is to substitute the chosen form of y(x) into the original Euler equation to find the complete solution below. This is a classic application of the variation of parameters: (1) find homogenous solution, (2) find complete solution of Euler form - the L1-ODE-VC, and (3) find the particular solution by using (1) and (2).

$$y' + a_0(x)y = b(x) = 0$$
$$\displaystyle (Equation\;5.8.4)$$ The derivative simplifies the Euler equation. First, it must be derived.
$$y = A(x)y_H$$
$$y' = A_xy_H + Ay_{Hx}$$ The values can be substituted into the L1-ODE-VC to give the form below.
$$A_xy_H + Ay_{Hx} + a_0(x)Ay_H = 0$$ The equation can be rerranged to give a simple form for integration by natural logarithms and subsequent exponentiation for the complete solution of the L1-ODE-VC.
$$A_xy_H = -A(y_{Hx} + a_0(x)y_H$$
$$\frac{A_x}{A} = -\frac{y_{Hx} + a_0(x)y_H}{y_H} = -\frac{y_{Hx}}{y_H} + a_0(x)$$ The rearranged equation can be integrated by standard application of natural logarithms.
$$\int^x \frac{A_x}{A} = -\int^x \frac{y_{Hx}}{y_H} + \int^x a_0(s)ds$$

Use the identity for logarithms: $$\ln \frac{a}{b} = \ln{a} - \ln{b}$$, which gives $$\ln \frac{A(x)}{y_H} = \int^x a_0(s)ds$$. The equation then gives the next output form.
$$A(x) = y_H{\exp \int^x a_0(s)ds } = {y_H}^2$$
$$\displaystyle (Equation\;5.8.5)$$ The final complete solution is y(x) = A(x)$$y_H$$, which gives
$$y(x) = {y_H}^3$$
$$\displaystyle (Equation\;5.8.6)$$ The particular solution is simply found by substration the homogenous solution from the complete solution.
$$y_p = y(x) - y_H = {y_H}^3 - y_H$$
$$\displaystyle (Equation\;5.8.7)$$

Part 2
= References =

= Team Work Distribution =

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title: User:Egm6321.f11.team1/report5


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User:K.saunders/enes100/Sterling Engines

Link back to team 550_QSM page.

Give instructor top 3 project choice list
I was assigned to the Engines.

Write problem statement
How do you make a sterling engine and what are some techniques to getting one to work?

Assign Task1
In this week I will look up previous models that worked and how they were documented. I will also start finish my own sterling engine.

Compare actual work done to Task1
I started my own design before looking up past designs. This was beneficial and detrimental to the project.

Week1 Narrative
This week I really worked on getting my first prototype done. I immediately started constructing the engine from parts I found laying around my house.

Assign Task2
Correct mistakes made in my project and document how to correct them.

Compare actual work done to Task2
This week I tried less to build the model and get it done, and focused more on doing it right and completing the task at hand. I started my step by step instructions and they can be found here. I Also got advice from lots of people in the class about how I can improve my design and how to prevent possible problems from arising.

Week2 Narrative
Previous Design: Problems:
 * Poor displacer. The displacer's problem was that it wasn't close to half the volume of the piston. It needs to be able to move a larger volume of air.
 * Lack of precision. The displacer rod hole through the piston lid allowed the air pressure to escape.
 * Crank shaft is too big. The crank itself needs to be a 1/4 the height of the cylinder so the displacer makes a full motion

Solutions:
 * Add a piece of Styrofoam to the old displacer so that it is closer to half the volume of the displacer.
 * Add a sleeve of something to reduce the volume of the displacer rod hole.
 * Wait to make the crank until the majority of the cylinder is completed so that the crank reaches a full range of motion.

This week I worked on fixing the the displacer and the displacer rod hole. To increase the volume of the displacer I took a large chunk of Styrofoam and pushed it down till touched the soda can. I then took a marker and traced around the can. Because i wanted the Styrofoam to just fit inside the edge of the beer can I knew I had to remove all parts of Styrofoam that had marker on them. To evenly cut the Styrofoam I used the hot wire device and rotated the block about its center point. After shaving off all parts with marker on them the block of Styrofoam slid just inside the can. Once the block was in the can I set it next to the cylinder and cut it close to half the height of the cylinder.

I also worked on tightening the seal around the displacer rod. To do this I took a small blob of epoxy and worked it until it started stiffening up. I then scooped the ball on the lid and let gravity go to work. To make the drip even, centered, and straight I slowly turned the disc until the drip was even on all sides. Then I placed the lid upside down on the beer can and let it dry so that the drip stuck off the top of the lid. I then took my dial calipers and measured the diameter of my 16 gauge wire to be 1.29 mm.

Assign Task3
Assemble the engine and remake the crank. Test it!

Compare actual work done to Task3
This week me and Quifoor completed our first model of the Stirling engine. After analysis and group brainstorming we made a few modifications and tested our engine again. I also added on to my running how to page. This week I completed my second prototype engine after correcting previous flaws and still can not get enough power to continually turn the crank.

Week3 Narrative
This week after fully assembling the engine for the fist time we realized 2 mail flaws or places of friction:
 * The rod extending out of the power piston caused the piston to torque inside the cylinder and made the edges catch.
 * The displacer rod extending out of the cylinder lid was too long and caused the the displacer to do basically the same thing as the power piston.

Solutions:
 * To correct the power piston from twisting I set another piston that instead of a straight arm extruding outward, it hard a hook that could be loosely connected to a different crank arm.
 * Instead of having about 4 cm of displacer arm extend through the cylinder lid I cut it down to less than 1 cm so that less force would be applied horizontally.
 * Added more mass to the rotating disk to give a great rotational inertia.

After making these simple fixes and testing the engine, although I could get the engine to make about 3-4 cycles I could not get it to continuously rotate.

Problems:
 * Air pressure is lost around the new power piston and cylinder.
 * The disk might be too massive for the engine to turn.

Next step
My plan of action at this point is to use what I have learned about this engine and use it to make a new engine that harnesses the power of latex. Because such a high degree of precision is needed to correctly use a power piston I believe it is too hard to make one using simple everyday materials.

My plan: Follow my instructions from the beginning very similarly to my previous design. When it comes to making a new power piston I will instead make a cylinder and cover will latex/balloon. My challenges at this point is how am I going to attach a crank arm to latex since it is stretchy and tears very easily.

Assign Task4
Refine previous instructions to incorporate latex and make a time laps video of me making one.

Compare actual work done to Task4
This week I attempted correcting my flaws in the engine and made a poster board and made two presentations. One for the NSF STEM program and one in class.

Week4 Narrative
This week I decided to try and fix the pressure leak problems by covering the areas in concern with wax and seeing if it would harden so that less air could escape. I got this inspiration from the demo I did in the cafeteria. While using the candle to provide heat for the machine milled engine I noticed that once the wax melted off the candle and cooled on the the table, the cooled wax was actually quite hard and relatively smooth and slick. I then decided that if I could pour a small amount into the power piston that it would drip around the piston and make a better seal inside the cylinder. I then held the engine at a slant and poured melted max on top of the engine and worked it up the the displacer rod. I learned two things from doing this. 1) The wax is very hard to control when not contained (on the lid). 2) When it dried the wax had too high a coefficient of friction and rubbed too hard on the displacer shaft. However, pouring the wax into the cylinder the wax did a great job of sealing the piston. The down side to this was the wax sat on top of the previous piston so that when the piston was a its max height, the wax was entirely exposed breaking the seal inside of the cylinder. We got positive result from this because the engine now started showing signs of life and turned over occasionally. However once the wax extruded out of the cylinder the seal was broken and momentum was lost.

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


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User talk:Jessica Perkins/The Olympic Games as a Political Driver and its Impacts on the Australian Sports System

Hi, Jess. This article is really developing.

Jim Ferguson has a book too ... More than sunshine and vegemite. (http://www.ausport.gov.au/sportscoachmag/resource_reviews2/more_than_sunshine_and_vegemite_-_success_the_australian_way)

I wondered what you thought about sport as a bipartisan issue in Australia.

Postillion 06:00, 21 October 2011 (UTC)


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Highway

Highway is a road made for travel by the public between important places such as cities, towns and landmarks. Highways may come in different designs. They often include many lanes of traffic, a median (strip of lane or barrier) between lanes of opposing traffic, and access control (ramps and bridges). Highways can also be as simple as a two-lane road.

In many countries, these roads are numbered to easily tell them apart. These numbered highways are usually called routes. The United States includes a system called the Interstate Highway system, controlled by AASHTO, where major north/south routes are odd numbered and east/west are even numbered. In Canada, routes that are in the 400s are freeways. In China, types of routes are separated by the first letter of the route; "G" for national road, "S" for provincial road and "Y" for rural roads.

Highways are sometimes criticized because of the pollution cars make when driving highways. When too many cars travel along a highway, traffic slows down; this is known as a traffic jam. Public transportation (such as buses) and special lanes for those who have a given number of people in a car are used to help stop these problems.

title: Highway


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User:Beat Estermann

Hello everyone, welcome to my user page. I started to use this real name account in my (former) role as coordinator of the project TAO (Third Age Online) the goal of which is to highlight the ways in which the access of older adults to the opportunities offered by online communities can be facilitated.

For more information about my person see my User Page on the Outreach Wiki.

What are we up to on Wikiversity?
As part of the project TAO, we are planning to use Wikiversity as a support to:

 * Develop a handbook for online communities and operators of community platforms, containing effective strategies for an improved inclusion of older people in online communities and online social networks

 * Set up a community of practice with various stakeholders from different backgrounds around the topic "e-inclusion of older people in the web 2.0 era", with a special focus on online communities and online collaboration

If you want to see how we are doing and/or if you want to join in, please visit our working space here on Wikiversity: TAO.

title: User:Beat Estermann


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Wikiversity talk:Assembly/Full description

Thoughts while I read right now (not summarized, as they flow in; if they are already in that page, perhaps moving them somewhere else may be better?):
 * What other ways to seek consensus are there? Which ones are used (already) (un/successful) at WV?
 * example...
 * of usage of this Assembly concept somewhere else?
 * to a situation here at WV? Erkan Yilmaz uses the Chat + Identi.ca 10:30, 21 October 2011 (UTC)
 * this should be higher in the page: "It will issue reports, which will be signed by users who approve them" because I was asking so, what will be visible by this, Erkan Yilmaz uses the Chat + Identi.ca 10:32, 21 October 2011 (UTC)
 * clerks seem to have more "powers"
 * a picture showing the structures (roles/products) would help I think
 * another thought was: what happens when someone reverts on such a subpage or writes unwanted things?, Erkan Yilmaz uses the Chat + Identi.ca 10:38, 21 October 2011 (UTC)
 * I apparently missed this comment, it would have been my desire to respond promptly.
 * The Assembly concept arises out of study of standard deliberative process (such as Robert's Rules of Order, which requires a "chair") as it might be done on-wiki. It is normal for the person who calls an Assembly into existence to begin as chair, until an election is held.
 * Delegable proxy is a non-essential part of this proposal. It was designed to address and ameliorate the problem of "participation bias," which certainly afflict Wikipedia -- and other wikis. There is a form of delegable proxy, Asset voting, that was first proposed in about 1883 by Lewis Carroll, which disappeared from view until it was noticed in the early 2000s that certain proposals in the late 1990s on voting systems mailing lists ("Candidate proxy") were similar; and Asset Voting is similar to Delegable Proxy, except that Asset Voting, as generally proposed, uses secret ballot and can elect a fixed-size Assembly that is fully representative (or almost so) of the voting community, whereas Delegable Proxy doesn't create, by itself, a fixed Assembly. It has only been used once, in an election of a three-member steering committee, for the then-named Election Science Foundation (which became the Center for Election Science), with 17 voters and 5 candidates, and it worked spectacularly. The committee was elected with unanimous approval that it was fully representative; every voter either voted for a "winner" or for a candidate who transferred the vote to a winner. Would it work with larger groups? Probably. But we aren't using that, it hasn't been proposed yet. It is simply possible, once we start looking for ways to hybridize the wiki so that it becomes more stable and reliable.
 * Clerks have powers; the way the Assembly is structured, however, committee clerks only have special power on their committee pages, which are placed in their user space to fit with traditions about user control over their own user space. Essentially, clerks may blank material in their user space, and may ask users not to edit there.
 * However, if a clerk abuses that authority, anyone may form an independent committee, and clerk it. That will not cause harm. All it will do, if both committees actually function, is create multiple reports. Reports will be signed by those who approve them. Minority reports will be issued, and, indeed, there would be no way to stop it. However, consensus is powerful. A report that develops genuine consensus will naturally be more powerful than one that doesn't.
 * The Assembly page itself has a clerk. As the founder, that's me, but only by default. There should be at least one alternate. Any volunteers? The goal of the Assembly is consensus. If I run the Assembly, as clerk, unreasonably suppressing the participation of Wikiversity users, I'll be defeating the purpose. However, this is the safeguard: under the Assembly proposal and experiment, it is possible to have more than one Assembly page, with different clerks.
 * To see how this would work with a Wikversity resource, where otherwise there could have been revert warring and useless conflict, see a recent forking of Landmark Education. The top-level Assembly page would be rigorously neutral. Then there would be linked pages with responsible clerks. Suppose the two "Assemblies" each consider the same issue, but because of, say, some factional division of Wikiversity users, different users participate. Each faction generates a report. We may judge each reports in many ways: by the cogency of the arguments (and how the arguments are presented is a factor that cannot be neglected), by the users who supported each report, and, additionally, any interested person could analyze the support of each report in many ways: by the contribution history of participants, and, what's interesting, I think, by amalgamating this information using delegable proxy.
 * It is just information. But it would be information that could be used by a decider to guide the judgment of "consensus." Who is a decider?
 * This is a wiki. We all are. Key to the Delegable proxy concept, however is the consent to communication that exists between proxies and clients. If one ignores a genuine majority opinion, for example, one is risking alienating the actual community.
 * My understanding and belief and declaration is that most of us do want to see Wikiversity operating with genuine consensus, not an artificial consensus created by, say, driving away dissenting users. The Assembly is a process for making that more efficient. However, it will generally be slow, not "quick." It's long-term.
 * To complete the answers: clerks make ad hoc decisions about page content. We want to encourage and support clerks who do this, seeking consensus and clarity. The suggested process rules allow comment by any Wikiversity user on the attached talk pages, but only comment by registered members of the Assembly on actual committee pages. A clerk may exclude members from participation on the committee page, but not from commenting on Talk. Disruptive comments (i.e, uncivil, etc.) on all pages are subject to standard Wikiversity policy and practice.
 * A clerk may refactor content, but in so doing, should not be altering attributed comments in any way that implies the user wrote the refactored material. I.e., I might write that a specified user "discussed fair use issues" but if I quote the user, the quote should be accurate and not deceptive or cherry-picked, and should link to the original. Basic academic stuff, actually.
 * We have not seen a committee yet approach the report stage. Because there is a crying need to handle file licensing issues, that should change soon.
 * Thanks for asking, Erkan. --Abd (discuss • contribs) 01:15, 19 March 2014 (UTC)


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User:Bilby/Grounded Theory and Stargate Universe

Stargate Universe was a science fiction television series developed by MGM. Part of the larger Stargate franchise, it followed the success of Stargate SG1, Stargate Atlantis and the original Stargate movie. Given the success of the series that came before it, with the notable exception of the animated Stargate Infinity, it would have been reasonable to presume that Stargate Universe would go well. However, it appears to have performed worse than expected, having dropped from an initial high of 2.447 million US viewers to a low of just 0.814 million, and was cancelled prior to the end of the second season.

This raises the question as to why it failed. The aim of this research project is to explore how content and related issues affected the ratings figures, using a Grounded Theory-style approach. It will not employ a strict Grounded Theory methodology, as the aim is light enough to take a permit informal approach to the research, but it is hoped that there will be some valid findings and that they will prove interesting. If nothing else, it may point to future lines of research.

Limitations and data set
The initial data will be limited to material on the ratings, release dates, and information garnered from the episodes. Casting a wider net would be valuable, but also risks creating an unworkably large data set, so the aim at this point is to focus on possible correlations between show content and ratings. Some comparative data from other SF television shows may be sought, but given the potentially small sample size and the number of possible external factors outside the scope of the research, such data will be a rough guide at best.

As a result of these limitations, information such as the presence of other shows, changes in marketing methodologies, and the influence of events outside of the show's sphere of influence will not be taken into account.

Methodology
As is normal practice with Grounded Theory, the initial work will involve data collection and coding. There will be no attempt to analyse the data as it is collected, except for some visual representations, and the research will be conducted with as few prior preconceived ideas as possible. The data will be tagged using a faceted model, rather than made to fit into pre-calcualted categories, and stored on-wiki.

Initial data will be collected from Wikipedia, focusing on ratings and the dates on which each episode first aired. After that the two main sources will be the episodes themselves and the Stargate wiki. Those sources will be used to identify plot features and elements, characters, guest stars, and other possibly relevant components - there is not going to be a fixed list, as the intent is to be flexible enough to grow that list over time.

During collection the data will be coded using an open system. Once collected, if all goes well, patterns that warrant further consideration should emerge, and this may result in recoding using a more narrowly defined model.

Note that this is an open research project, and anyone is encouraged to take part.

Ethical concerns
None. Only publicly available quantitative data will be employed.

Initial data collection

 * Ratings figures


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Talk:Wikis

federated wiki:
 * videos
 * source code, Erkan Yilmaz uses the Chat + Identi.ca 16:21, 21 October 2011 (UTC)

title: Talk:Wikis


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User:Jobin RV

Welcome to Jobin's userpage This is Jobin, studying Information Technology in College of Engineering, Pune.

My hobbies are Wiki-ing, playing games on PC and playing cricket. I would love to hear from you in view of improving my User page.

All tips and suggestions are welcome!!! Hoping to listen from you, soon.

Languages
I don't understand languages other than English, Hindi, Marathi and Malayalam. So, an abuse in any other language shall be implied as a compliment.

E-Mail Address

 * jobin.rv@gmail.com

Important links

 * Maintenance
 * When is an article referred to as a stub

 * What not to say at Wikipedia
 * Referencing for beginners
 * Did you know!
 * Reverting

title: User:Jobin RV


text:
User talk:Jobin RV

Welcome!
Hello, this is my talk page. You may drop any suggestion regarding my user page or my talk page. All suggestions are welcome!!!

title: User talk:Jobin RV


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User talk:Dcaldero8983/enes100/eagles

I like your photos. It seems very interesting and keep working hard on arduino. Therefore, you will able to work any other program. Chaagii 0817 16:00, 21 October 2011 (UTC)

Write down the name of the software you were working with the arduino on. Good photos of the arduino though. Andyn6361 01:03, 22 October 2011 (UTC)

Hey D this is a very interesting topic to work on. Arduinos are not easy to work with and you are making good progress. Good enthusiasm and documentation. Dkromer1996 19:59, 23 October 2011 (UTC)

10/10/0 you should be polishing an arduino tutorial ... if you are brand new to the arduino .. otherwise, just a report .. no value added electronically ... if you are new to the arduino, should have lots and lots of pages written about all the details in your notebook. 204.126.132.241 13:54, 24 October 2011 (UTC)

I would like to learn more about arduino and your tutorial was helpful to me. If it is possible, try to upload video about arduino. Chaagii 0817 15:09, 28 October 2011 (UTC)

The uploaded videos were nice and the link to the tutorial is extremely helpful for anyone with no knowledge of arduinos including me. Keep up the good work! Andyn6361 14:00, 29 October 2011 (UTC)

Hey D good links for the project on your narrative. Very good progression on the arduino and the lights. Keep up the forward effort. Dkromer1996 16:45, 30 October 2011 (UTC)

10/5/50 ... good job ... did not commit to something over the weekend ... 1sfoerster 14:22, 31 October 2011 (UTC)

I saw the page. There was nothing on week 3. I hope you will do your personal page on time. By the way, I might need your help for next week. I want to learn arduino, so i can build the motors. Anyway Good Luck Chaagii 0817 14:32, 04 November 2011 (UTC)

Great in-depth description of your Week3 work. Keep it up! Andyn6361 15:36, 5 November 2011 (UTC)

Great page man. keep up the progression with the arduino.Dkromer1996 16:23, 6 November 2011 (UTC)

10/10/50 ... great job creating a tutorial page for the arduino .. notice I made some changes to it .. 1sfoerster 15:08, 7 November 2011 (UTC)

Hey. Can you do the "Story ,week 3, and week 4" for the team page?

Great links. You doing pretty good works with arduino keep working hard. Chaagii 0817 17:20, 11 November 2011 (UTC)

Good photos and work description. Keep working on that arduino man. Andyn6361 04:38, 12 November 2011 (UTC)

Good job with your overall page and good work with the arduino. dkromer1996 13:46, 13 Novemeber 2011 (UTC)

10/10/30 .. good work identifying a problem ... the problem is probably not the library, but where you are putting the library .. when you figure this out, please document ... 1sfoerster 15:17, 14 November 2011 (UTC)

title: User talk:Dcaldero8983/enes100/eagles


text:
User talk:Andyn6361/enes100/eagles

Try hard work on battery life, so we can make the tournament. Chaagii 0817 16:00, 21 October 2011 (UTC)

Hey you have some really good information on your page. Its really useful for our project. Keep up the good work and researching more information to find other alternatives that would best help us in flying the drone longer without consequences. Dcaldero8983 17:48, 23 October 2011

Hey i like the page so far. You put some very good background info about the parrot drone. Also, you documented good info on the drone apps. Dkromer1996 19:49, 23 October 2011

10/10/20 ... lots of stuff not clear here ... are you asking me to purchase the application? ... Need to provide references to the duty cycle (motors heating up) ... or links to testing you have done that documents this ... or maybe you were writing just possible theories ... if this is the case then work backwards and get a good problem statement ... what you wrote is fuzzy in my mind .. good work on identifying the battery problems in general ... 204.126.132.241 13:58, 24 October 2011 (UTC)

I saw the page. There was nothing on week 2 Chaagii 0817 14:20, 28 October 2011 (UTC)

Hey your week 2 looks good. Im interested in what you are doing with that lithuim battery. keep up the good work, your integration to the team has been really good. this definitively pushes the project to a new level. Dcaldero8983 1:23, 30 October 2011

Hey man i really liked your page and your part of this project. The narrative posts with the captions are very helpful to tell people about the battery. Dkromer1996 16:37, 30 October 2011 (UTC)

10/10/50 ... good job ... keep it up !!

I saw the page. There was nothing on week 3. I hope you will do your personal page on time. Good Luck  Chaagii 0817 14:25, 04 November 2011 (UTC)

Im impressed, every week you go farther and farther with your task. it looks good. you should present this information to the class during the week as part of the team presentation if we have one this week. Dcaldero8983 17:22, 6 Novemeber 2011

Hey man great project page. Very good ideas. Keep up the good work. Dkromer1996 16:20, 6 November 2011 (UTC)

10/10/30 .. keep up the work .. build a tutorial page like Calderon did for the arduino for the LogView software ... get real basic ... pictures of all the cables ... the harnesses (there should be two) ... what the icon looks like on the computer screen ... the software installation instructions ... 1sfoerster 15:11, 7 November 2011 (UTC)

Hey. Can you do the "Material List and Decision List" for the team page?

Nothing. Chaagii 0817 17:23, 11 November 2011 (UTC)

Nice work with your page. Try to get your parts of the team page done and we will also have to include our new page for our project 3 on the helicopter. Dcaldero8983 17:22, 12 Novemeber 2011

DONT FORGET TO ADD YOUR WEEKLY SUMMARIES TO THE TEAM PAGE. EVERYONE HAS TO DO THEIR OWN FOR THAT CATEGORY

Good job witht your page man. Good work with the battery for the drone. dkromer1996 13:48, 13 Novemeber 2011 (UTC)

10/10/100 ... great job with the battery charger ... need to add screen shots of actually charging/discharging/balancing battery ... screen shots of different batteries in the room, how many cells they have .. 1sfoerster 15:20, 14 November 2011 (UTC)

title: User talk:Andyn6361/enes100/eagles


text:
User talk:Dkromer1996/enes100/eagles

Keep working hard on Laptop, so we can control from Wii, Joystick, and Kinect. Chaagii 0817 16:05, 21 October 2011 (UTC)

Get your documentation online man. Make sure that work you have been doing doesn't go to waste. Andyn6361 01:12, 22 October 2011 (UTC)

I agree with Andy, try to get your page filled up with what you are doing so people can see your production. Dcaldero8983 17:30, 23 October 2011

10/10/10 .. not clear what you did ... no links to files you downloaded and unzipped ... did you install them? success? 1sfoerster 14:39, 24 October 2011 (UTC)

Try to finish your personal page, so we can see what you are doing. Chaagii 0817 15:15, 28 October 2011 (UTC)

Make sure you complete this page as soon as possible. Since it is a weekly report, try to fill it during the weekends. Andyn6361 15:36, 29 October 2011 (UTC)

I agree with the guys dean. try to add information so we can be knowledgeable. Dcaldero8983 1:23, 30 October 2011

10/10/15 ... this is a summary report ... it should be the easiest thing in the world to document what doesn't work ... without this nobody can pick up where you left off ... nobody can run their brain through what you have tried and suggest something else, nobody can provide some alternatives ... no discussion is possible ... Document everything you try, write ... 1sfoerster 14:27, 31 October 2011 (UTC)

I saw the page. There was nothing on week 3. Chaagii 0817 14:40, 04 November 2011 (UTC)

Complete the weekly report as soon as possible man. Andyn6361 15:51, 5 November 2011 (UTC)

yea try to see if you can get information on your page at least before sunday morning if possible that way we can evaluate your work. Dcaldero8983 17:22, 6 Novemeber 2011

10/10/0 ... nothing that pushes the project forward ... you would push the project forward if you would list links to the software you are trying to install, describe the exact error message you are getting on the screen, listing all the attempts you are trying to reinstall/remove/etc. Without that detail there is nothing to grade. 1sfoerster 15:13, 7 November 2011 (UTC)

Hey. Can you do the "Next Steps" for team page?

Nothing on this page. Chaagii 0817 17:28, 11 November 2011 (UTC)

Try to add some of your information for week 4 so we can view it. Also try to get your part of the team page done so we can have it finalized by Sunday night that way the professor can see it Monday all complete. Also create the new page for our third project and let us know so we can add ourselves to the team page. Dcaldero8983 17:22, 12 Novemeber 2011

DONT FORGET TO ADD YOUR WEEKLY SUMMARIES TO THE TEAM PAGE. EVERYONE HAS TO DO THEIR OWN FOR THAT CATEGORY

10/10/10 ... you posted the same link twice, you did not document your PC's error messages in a way that anyone could offer advice ... you again did not specify the success you had in class ... more failure details would result in more points here 1sfoerster 15:23, 14 November 2011 (UTC)

This was the userpage for last project being used for the current project. Don't edit this one like I did. Make a new userpage for Drones Andyn6361 14:57, 20 November 2011 (UTC)

Yea i agree with Andy, and also when you delete parts of the discussion page don't delete the last two comments cause they are for the new project we are currently working on. Good luck. Dcaldero8983 17:22, 20 Novemeber 2011

title: User talk:Dkromer1996/enes100/eagles


text:
Antifriction and Multi-Step Base Isolation

Antifriction and Multi-Step Base Isolation (AF&MS BI), also called Shock Evader, is relatively recent type of seismic vibration control. In spite of the fact that the first attempts to isolate buildings from potentially shaky ground were made thousands years ago, the modern concept of seismic isolation (flexible mounting + damping) is foreign for earthquake engineering: it has not been inherited, it has been borrowed from mechanical engineering.

Though the concept is working perfectly in all sorts of vehicles, in seismic isolation everything is not so smooth because the conditions in both cases are quite different. In a car, for instance, the working stresses in auto parts are far below their ultimate bearing capacity. Therefore, some overloads associated with heavy damping are of no practical importance here. Another matter is a building structure: during a strong earthquake, it is intended to perform at the near-to-collapse level and, therefore, any extras can become crucial for its safety.

However, there is an alternative to the contradictory damping mechanism of those base isolators. It can be found in the utmost lessening the damping and substituting its positive, mitigating quality with any sort of tuning-out mechanism which satisfies the following requirements:

 * Let the earth move its way.
 * Prevent resonant amplifications.
 * Restore the structure in its pre-earthquake position on the foundation.

It is not the building, it is the earth that should be vibrating if the building is supported on the ideal isolation system. Any attempt to reduce a relative displacement of the superstructure with respect to the base will inevitably result in additional transmission of earthquake energy into the building.

This new concept has been embodied in Shock Evader or, which is the same, in the Antifriction and Multi-Step Base Isolation (AF&MS BI) that incorporated the merits of the traditional flexible mounting but without its drawback - a compulsory damping mechanism.


text:
Building elevation control

Building elevation control is a valuable source of vibration control of seismic loading. Thus, pyramid-shaped skyscrapers, continue to attract attention of architects and engineers because such structures promise a better stability against earthquakes and winds.

Besides, the elevation configuration can prevent buildings' resonant amplifications due to the fact that a properly configured building disperses the shear wave energy between a wide range of frequencies.

Earthquake or wind quieting ability of the elevation configuration is provided by a specific pattern of multiple reflections and transmissions of vertically propagating shear waves, which are generated by breakdowns into homogeneity of story layers, and a taper. Any abrupt changes of the propagating waves velocity result in a considerable dispersion of the wave energy between a wide ranges of frequencies thus preventing the resonant displacement amplifications in the building.

Tapered profile of a building is not a compulsory feature of this method of structural control. A similar resonance preventing effect can be also obtained by a proper tapering of other characteristics of a building structure, namely, its mass and stiffness. As a result, the building elevation configuration techniques permit an architectural design that may be both attractive and functional.

title: Building elevation control


text:
Macedon (ancient kingdom)

Macedon, also known as Macedonia, was an ancient kingdom of the Macedonians bordered by Epirus to the west, Paeonia to the north, the region of Thrace to the east and Thessaly to the south. For a brief period, after the conquests of Alexander III of Macedonia (Alexander the Great), it became the most powerful state in the world, controlling a territory that included the former Persian empire, stretching as far as the Indus River.The ancient Macedonians lived in the southern area of present-day Macedonia since ancient time. The first Macedonian state occurs in VIII or early VII century BC under the leadership of the Argeadi dynasty, when the Macedonians had migrated there from western areas. The first king who has written sources was Perdiccas. At the time of King Alexander I, Macedonian territory began to spread in countries inhabited by Thracian tribes Eordaja , Botiaja , Pieria , Mygdonia and Almopija. Near the modern city of Edessa, Perdiccas I built the first capital of capital Vergina.

Early history
After a short period of Persian rule under King Darius I, the country regained its independence under King Alexander I ( 495 - BC 450 BC). Before the IV century BC, the kingdom covered a region size equal to the current area of Macedonia in Greece. Amyntas III (around 393 - 370 BC) was first centralized government in Macedonia, although the contrast between the lowland livestock region and isolated zadgrbnina was great. These are tied to the king by family ties. Clan communities in the barbarian invasions came out controlled the passes through which the Illyrian armies to attack the north and northwest Macedonia. Amyntas had three sons: the first two, Alexander II and Perdiccas III reigned only briefly. Premladiot son of Perdiccas III was replaced with the third son of Amyntas, Philip II of Macedon who proclaimed himself king and ushered Greece.

Decline of the Empire
Under the leadership of King Philip V ( 221 - 179 BC) and his son Perseus ( 179 - 168 BC) Macedonia faced the expansionism of the Roman republic. During the II century BC and I century BC Macedonia was in several wars with Rome. This resulted in the defeat of Macedonia Antigonid removal and dissolution of the Macedonian kingdom. Andrisk briefly managed to restore the monarchy in 149 BC but was defeated the next year and Macedonia fell under direct Roman rule as the Roman province of Macedonia.

title: Macedon (ancient kingdom)


text:
User talk:Chaagii 0817/enes100/eagles

Good Week1 narrative. I fixed a spelling error in Assign Task2, but that was the only problem.Andyn6361 00:59, 22 October 2011 (UTC)

Hey i really like the pictures you posted up. it gives us all an idea of how the game looks like. i wished i had your job it sounds really fun. keep up the good work.Dcaldero8983 18:48, 23 October 2011

Hey man you set up your documentation extremely well. I really like the apps and the gaming concept. Very great progress of the itouch/android market.Dkromer1996 19:49, 23 October 2011 (UTC)

10/10/30 ... good job with the game ... figure out where to purchase the stickers .. 204.126.132.241 13:51, 24 October 2011 (UTC)

Nice job on the pictures and links for the game. Lets just fix that dang connection Andyn6361 13:53, 29 October 2011 (UTC)

Looks good man. Do you think we actually need to buy those specific cones? maybe we can use regular cones and put the stickers on them and maybe they can work, its worth the try... and keep up the good work. it would be fun seeing those drones battling each other in competitional games. Dcaldero8983 15:42, 30 October 2011

Hey man, good work with your page. Keep up the good documentation with these screen shots. Definitely helpful to people learning about the drone. Dkromer1996 16:37, 30 October 2011 (UTC)

10/10/30 .. good review of the games .. now need to choose some and then begin practicing with them with the intent of forming a tourneyment.

Good description of your work and great pictures. I do think there are some grammatical errors but no worries on that. Andyn6361 15:30, 5 November 2011 (UTC)

Good presentation of your week 3. see if you can find a game that both android and apple can play simultaneously and against each other. there should be a game that both of these devices share the same. Dcaldero8983 15:42, 6, November 2011

Great page this week along with documentation. Keep up the good work. Looking forward to the drone fight game.Dkromer1996 16:20, 6 November 2011 (UTC)

10/10/30 .. you need to translate the game playing into the logistics of a tournament 1sfoerster 15:06, 7 November 2011 (UTC)

Put in some of the links of the batteries you have been researching on man. Some pictures would be nice too. Andyn6361 04:34, 12 November 2011 (UTC)

He does include pictures. And good page overall Chaagii. Try to look over the team's final page before monday to see if everything looks good to you or if you wanted to include something. Dcaldero8983 17:22, 12 Novemeber 2011

Good work with this project page overall. Very good narratives. dkromer1996 13:42, 13 Novemeber 2011 (UTC)

10/10/30 .. more points if you got wiki links, pictures working ... need more documentation .. we have 2100mAh 11.1 volt batteries .. do we need to order some more? ... what about connectors for the charger? 1sfoerster 15:14, 14 November 2011 (UTC)

title: User talk:Chaagii 0817/enes100/eagles


text:
User:Amcilrick

University of Canberra Student studying Business, Politics and Sport. Interests are any sports, especially athletics!

Assignments

 * /Rodeo in Australia - Welfare of Animals Used in Rodeo Events/

title: User:Amcilrick


text:
Dry-stone walls control

People of Inca civilization were masters of the polished dry-stone walls, called ashlar, where blocks of stone were cut to fit together tightly without any mortar. The Incas were among the best stone masons the world has ever seen, and many junctions in their masonry were so perfect that even blades of grass could not fit between the stones.

Peru is a highly seismic land, and for centuries the mortar-free construction proved to be apparently more earthquake-resistant than using mortar. The stones of the dry-stone walls built by the Incas could move slightly and resettle without the walls collapsing which should be recognized as an ingenious passive vibration control technique employing both the principle of energy dissipation and that of suppressing resonant amplifications.

title: Dry-stone walls control


text:
Wikiversity:Candidates for Custodianship/S Larctia (full custodian)

this page courtesy blanked per deletion request from the candidate, version before blanking.


text:
User talk:S Larctia

Deletion of file
Tough I provide licensing information, I can nto recover the following file dFile:Fluid Statics 4.png

Where is the problem?

 * The file is live, I edited your file name so it would display a link to the file. If you need help supplying the license information, ask me or a custodian. Neither S Larcita nor I are currently custodians. You can find custodians listed at WV:Staff --Abd 14:01, 25 November 2011 (UTC)
 * Ah! I see that User:Jtneill, who must have seen your request, restored the file, and notified you on your Talk page. It still has a template on it that will lead to deletion if you don't attend to the licensing issue.... Remove that template when you fix it. --Abd 16:58, 25 November 2011 (UTC)

Probationary custodianship
Thanks for your message. I'm not so well placed ATM for mentoring because summer break is nearing (once marking is completed). I'll be back around Feb 2012. Maybe nominate yourself and ask for a mentor? -- Jtneill - Talk - c 06:05, 28 November 2011 (UTC)

Template:CC-by-sa-3.0-dual
I've proposed that this template is deleted. Please see here. Thanks. Adambro 17:16, 1 January 2012 (UTC)

title: User talk:S Larctia


text:
Talk:Motivation and emotion/Book/2011/Sport participation

Comment
Hi there,

I'm wondering if you would like a pdf of a Motivation and Emotion Journal article? It is call Motivational clusters and performance in a real-life setting (2009). Short Abstract: The present research investigated whether assessing adolsecent elite athletes' motivational profiles at the beginning of the season would allow us to predict their subsequent performance over the course of a competition season. The article covers motivation, performance, cluster analysis and the self-determination theory.

If so, please let me know you email so I can send it to you (sorry I don't know of another way).

Regards --Flow 03:14, 22 October 2011 (UTC)

Hi, I was looking at your page, it seems kind of related to mine actually, and noticed that the references were all out of order. Hope you don't mind I just alphabetised them. But I was a bit confused by the Plant reference and the Plante reference, they have the same initials, is this a typo and supposed to be Plant instead of Plante or vice versa?? Hope I've helped EFA 06:22, 31 October 2011 (UTC)

Hi, Looks like you've got a good page going! You've done really well to incorporate theory and make it relevant/explain how it fits with your topic. The 'are you motivated' box is really cool too. Well done! Naomi 11:11, 5 November 2011 (UTC)

Great topic and presentation - very well done - Magnolia

Rfoster 05:43, 28 November 2011 (UTC)

-- Jtneill - Talk - c 03:36, 12 December 2011 (UTC)


text:
Action against heart diseases

Introduction to Heart Disease
The heart is like any other muscle, requiring oxygen and nutrient-rich blood for it to function. The coronary arteries that supply blood to the heart muscle spread across the surface of the heart, beginning at the base of the aorta and branching out to all areas of the heart muscle. The coronary arteries are at risk for narrowing as cholesterol deposits, called plaques, build up inside the artery. If the arteries narrow enough, blood supply to the heart muscle may be compromised (slowed down), and this slowing of blood flow to the heart causes pain, or angina. A heart attack or myocardial infarction occurs when a plaque ruptures, allowing a blood clot to form. This completely obstructs the artery, stopping all blood flow to part of the heart muscle, and that portion of muscle dies.

The great throbbing center of all human life and activity is the heart. No other organ carries so much responsibility for the rest of the body. Every part of the human system is entirely dependent upon the heart. The lungs enable us to breathe. The kidneys filter out the waste material from the blood. But the one great organ upon which all the others depend is the heart. Constantly, day and night,your wonderful heart continues to beat. When you are at rest, it beats quietly and slowly, conserving its great reserve powers for the time when they might be sorely needed. If an emergency should arise, your heart will immediately quicken its pace, speeding up the circulation of the blood to wherever it may be needed.

What are Heart Disease ?
Heart diseases are diseases of the heart and the blood vessel system within the heart. Many people are surprised to learn that there many different heart diseases. In fact, there are over 50 types of heart diseases, the most common being coronary artery disease. This confusion may stem from the fact that coronary artery disease is often referred to simply as "heart disease." Heart diseases fall within the broader category of cardiovascular diseases, which are conditions that not only affect the heart, but also the blood vessel system (arteries, capillaries, and veins) within a person's entire body, such as the brain, arms, legs, and lungs. "Cardio" refers to the heart "vascular" refers to the blood vessel system. Some people are born with heart diseases (such a disease is known as a congenital heart disease) others develop during a person's lifetime. Because there are so many types of heart diseases, it may be helpful to categorize them based on the areas of the heart or blood vessel system they affect, such as:
 * Arteries and veins
 * Electrical system
 * Heart chambers
 * Heart muscle itself
 * Heart valves
 * Heart lining

Keeping your Heart Healthy
When yout heart is strong and healthy, your whole body benefits. When it is sick, the whole body suffers. That is why it is so important for you to take care of your heart, for upon its condition will depend your ability to get the very best out of life. Now if you will place your hand on your chest toward the left side, you will feel the great throbbing center at work. That is your heart. Its function is to move the living stream of blood through all parts of your body, feeding all the cells and removing all the waste materials. If your heart should fail, your whole transportation system would breakdown. It is important for you to ask yourself whether you are giving your heart all the care that it deserves.

Circulation of blood through the heart
The heart is a large muscular organ which constantly pushes oxygen-rich blood to the brain and extremities and transports oxygen-poor blood from the brain and extremities to the lungs to gain oxygen. Blood comes into the right atrium from the body, moves into the right ventricle and is pushed into the pulmonary arteries in the lungs. After picking up oxygen, the blood travels back to the heart through the pulmonary veins into the left atrium, to the left ventricle and out to the body's tissues through the aorta.

How does the heart work ?
The heart is actually a muscle that works like a pump in distributing blood throughout the body. The heart has four chambers. The two at the top are the left and right atria and the two at the bottom are the left and right ventricles. Blood vessels lead in and out of these chambers. Oxygenated blood from the lungs flows into your heart and is then pumped out to the rest of your body. Once the blood has delivered the oxygen to the tissues of the body, it returns to your heart and gets pumped back out to the lungs where it will be re-oxygenated.

How does blood flow through the heart?
Your heart muscle is a very efficient pump that delivers blood, oxygen and nutrients to your body.

The heart has four chambers - two on the right and two on the left. Both sides of the heart work together. The right side pumps blood into the lungs and the left side pumps blood into the organs and tissues of your body.

After your blood flows through the body, its life-giving oxygen and nutrients have been depleted. To replenish the oxygen and revitalize the blood, it must pass through the heart and then into the lungs again.

Right side: First the oxygen-depleted blood enters the heart through two large veins, the inferior and superior vena cava and then flows into the right atrium. From the right atrium, it passes through the tricuspid valve and then into the right ventrical. The blood is then pumped through the pulmonary valve and into the lungs.

Once in the lungs, carbon dioxide is removed and oxygen is added to the blood.

Left side: The pulmonary vein empties oxygen-rich blood, from the lungs, into the left atrium. From here, the blood flows from your into your left ventricle through the open mitral valve and finally, it is pumped through the aortic valve into the aorta - the blood vessel that feeds all of the other parts of your body.

When the ventricles are full, the mitral and tricuspid valves close. This prevents blood from flowing backward into the atria while the ventricles contract or Pump. This pattern is repeated continuously throughout your life, causing blood to flow continuously to the heart, lungs and other parts of the body.

How does the heart beat?
The atria and ventricles work together by alternately contracting and relaxing to pump blood through your heart. The heartbeat is triggered by electrical impulses that travel down a special pathway through your heart. The electrical system of your heart is the power source that makes this beating possible.

What and where are the coronary arteries?
The heart requires oxygen to function properly. But the blood that is pumping through the heart does not supply oxygen to the heart muscle itself. Special blood vessels attached to the outside of the heart, called coronary arteries, supply the heart with oxygen and nutrients needs. Three major arteries and a number of smaller vessels are designed to perform this function.

title: Action against heart diseases


text:
Talk:Motivation and emotion/Book/Emotional development

Comments
Hi, the page structure is looking good. Just looked at some headings and thought if you wanted to include attachment theories under some emotional bonding and talk about trauma with children and how it may affect emotional development. This could provide more space at the end to provide strategies for carers/parents in more practical emotional appropriate ways of child rearing. (Benk 05:58, 22 October 2011 (UTC))

Nicole,

Good book chapter so far. You provide a good overview of the theoretical frameworks and the main areas of emotions. I like the way you are going to provide an example of one of the theories by providing further detail on the little Albert study. One suggestion though – maybe you could provide real life examples for either regulation of emotion, expression or recognising. I think it would help the reader relate it to themselves and the people around them.

Are there only three theories related to emotional development? You may be leaving them out due to room/word limit but perhaps consider two more theories.

Very interesting read to see what emotions are more prominent over certain time periods and particularly how people regulate their emotions!

(u3025302)

Heading casing
Rfoster 09:39, 11 December 2011 (UTC)

-- Jtneill - Talk - c 04:13, 11 December 2011 (UTC)


text:
User:Gmeijssen

 * translatewiki
 * meta
 * aka GerardM

I work for the Wikimedia Foundation as an Internationalization / Localization outreach consultant and am part of the Localisation team. I am a very frequent blogger. Thanks, Gmeijssen 12:42, 22 October 2011 (UTC)

title: User:Gmeijssen


text:
User:MehranVB

Messeage here.

title: User:MehranVB


title: File:CLTI.DiffEQ.1.A.20111022.pdf


title: File:DLTI.DiffEQ.1.A.20111022.pdf


text:
Foundation in construction

A foundation is a lower portion of building structure that transfers its gravity loads to the earth. Foundations are generally broken into two categories: shallow foundations and deep foundations. A tall building must have a strong foundation if it is to stand for a long time.

To make a foundation, we normally dig a trench in the ground, digging deeper and deeper until we come to subsoil, which is more solid than the topsoil that is used to grow plants and crops. When the trench is deep enough, we fill it with any strong, hard material we can find. Sometimes we pour in concrete into the trench, which we strengthen even more by first putting long thin round pieces of steel into the trench. When the concrete dries, the steel acts like the bones in our body to tie the foundation together. We call this reinforced concrete.

Once the foundation has been packed down tightly, or dried hard, we can begin to build the building superstructure.

title: Foundation in construction


text:
User talk:Cwoo4792/enes100/Robot Arm

10/10/50 .. good idea using the lego parts in this project ... keep working on it 1sfoerster 14:20, 25 October 2011 (UTC)

Week 1 Peer Review

 * I like how you have a link to the festo example of a robotic arm.
 * You may want to have some pictures next time for an even better page. User:TFrancis3580/enes100/Robotarm

Week 2 Peer Review

 * Great job on the picture of the robotic arm that is uploaded to Wikimedia commons
 * May I suggest that you upload some youtube videos for even more points if you can. User:TFrancis3580/enes100/Robotarm

0/0/0 .. don't see anything to grade 1sfoerster 20:08, 31 October 2011 (UTC)

Week 3 Peer Review

 * Great job utlizing the box for the robotic arm it looks great!!
 * You know if you contact me I can help put some youtube videos up for even more points. User:TFrancis3580/enes100/Robotarm

10/10/70 ... good job ... keep working 1sfoerster 15:58, 8 November 2011 (UTC)

Week 4 Peer Review

 * Great job with the component at the top of the robotic arm it makes it much easier to use.
 * You might want to try something different with the end effect perhaps we can discuss it. User:TFrancis3580/enes100/Robotarm

10/10/60 .. good job 1sfoerster 15:58, 15 November 2011 (UTC)

title: User talk:Cwoo4792/enes100/Robot Arm


text:
Elevated building foundation

Elevated building foundation (EBF) is a kind of seismic base isolation technology which is made a major part of a building superstructure. It is made to protect the building's superstructure against damage from the shaking caused by an earthquake.

This goal can be met with the right building materials, size, and setup of EBF for the building site and local soil conditions.

As a result of multiple wave reflections and diffractions, as well as energy dissipation of the seismic waves as they move up through the EBF, any movement of seismic wave energy into the building superstructure will be decreased, which will lower seismic loads and improve seismic performance of the structure.

In other words, the building does not shake as much because it is sitting on the elevated building foundation, and will probably take less damage from the earthquake.

title: Elevated building foundation


text: File:FPB testing.jpg

title: File:FPB testing.jpg


text:
User talk:Zchill/enes100/Speakers

Week 1 Review
You should post the work you completed for this project on your wiki page. I find it helpful to use what you wrote in your engineering notebook and organize everything onto this page. Baminnick 17:25, 22 October 2011 (UTC)

I agree with Ben you should put your work on wiki and some pictures, videos as well. over all we are doing very well...Ayapici 11:14pm, October 23 2011 (UTC)\

10/10/10 ... good description of what happened in class ... should have pictures, drawings showing how things were hooked up ... build a tutorial so don't have to wait for me next time ... 1sfoerster 14:34, 24 October 2011 (UTC)

you should show your work as much as you can on wiki that you can earn some points and we can see what you are doing from here. Ayapici 18:10, October 29 2011 (UTC)\

0/0/0 ... nothing to grade 1sfoerster 14:55, 31 October 2011 (UTC)

I think you have to start some work on wikiversity if you want some more points. try to use your notebook and stuff. Ayapici 10:45, November 6 2011 (UTC)\

10/5/30 ... comment on your team mates pages ... there is a toner cartridge in the room to take apart and try to get some toner out of it 1sfoerster 15:34, 7 November 2011 (UTC)

10/10/40 ... good job .. where is this going? 1sfoerster 15:58, 14 November 2011 (UTC)

title: User talk:Zchill/enes100/Speakers


text:
Friction pendulum bearing

Friction Pendulum Bearing (FPB) is another name of Friction Pendulum System (FPS). It is based on three pillars :
 * articulated friction slider;
 * spherical concave sliding surface;
 * enclosing cylinder for lateral displacement restraint.

Snapshot with the link to video clip of a shake-table testing of FPB system supporting a rigid building model is presented at the right.

title: Friction pendulum bearing


text:
File:Fluid viscous damper.jpg

Licensing
for school project

title: File:Fluid viscous damper.jpg


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Hysteretic damper

Hysteretic damper is intended to provide better and more reliable seismic performance than that of a conventional structure at the expense of the seismic load energy dissipation. There are four major groups of hysteretic dampers used for the purpose, namely:

 * Fluid viscous dampers (FVDs)

Viscous Dampers have the benefit of being a supplemental damping system. They have an oval hysteretic loop and the damping is velocity dependent. While some minor maintenance is potentially required, viscous dampers generally do not need to be replaced after an earthquake. While more expensive than other damping technologies they can be used for both seismic and wind loads and are the most commonly used hysteric damper.

 * Friction dampers (FDs)

Friction dampers tend to be available in two major types, linear and rotational and dissipate energy by heat. The damper operates on the principle of a coulomb damper. Depending on the design, friction dampers can experience stick-slip phenomenon and Cold welding. The main disadvantage being that friction surfaces can wear over time and for this reason they are not recommended for dissipating wind loads. When used in seismic applications wear is not a problem and there is no required maintenance. They have a rectangular hysteretic loop and as long as the building is sufficiently elastic they tend to settle back to their original positions after an earthquake.

 * Metallic yielding dampers (MYDs)

Metallic yielding dampers, as the name implies, yield in order to absorb the earthquake's energy. This type of damper absorbs a large amount of energy however they must be replaced after an earthquake and may prevent the building from settling back to its original position.

 * Viscoelastic dampers (VEDs)

Viscoelastic dampers are useful in that they can be used for both wind and seismic applications, they are usually limited to small displacements. There is some concern as to the reliability of the technology as some brands have been banned from use in buildings in the United States.

Each group of dampers has specific characteristics, advantages and disadvantages for structural applications.

title: Hysteretic damper


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Lead rubber bearing

Lead Rubber Bearing or LRB is a type of base isolation employing a heavy damping. It was invented by William Robinson, a New Zealander. Heavy damping mechanism incorporated in vibration control technologies and, particularly, in base isolation devices, is often considered a valuable source of suppressing vibrations thus enhancing a building's seismic performance. However, for the rather pliant systems such as base isolated structures, with a relatively low bearing stiffness but with a high damping, the so-called "damping force" may turn out the main pushing force at a strong earthquake. The video shows a Lead Rubber Bearing being tested at the UCSD Caltrans-SRMD facility. The bearing is made of rubber with a lead core. It was a uniaxial test in which the bearing was also under a full structure load. Many buildings and bridges, both in New Zealand and elsewhere, are protected with lead dampers and lead and rubber bearings.

title: Lead rubber bearing


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Tectonic hazards/Seismic performance analysis

Seismic performance analysis is an intellectual tool of earthquake engineering which breaks the complex topic into smaller parts to gain a better understanding of seismic performance of building and non-building structures. The technique as a formal concept is a relatively recent development. In general, seismic analysis is based on the methods of structural dynamics. For decades, the most prominent instrument of seismic analysis has been the earthquake response spectrum method which, also, contributed to the proposed building code's concept of today.

However, those response spectra are good, mostly, for single-degree-of-freedom structural systems. Numerical step-by-step integration, applied with the charts of seismic performance, proved to be a more effective method of performance analysis for the multi-degree-of-freedom structural systems with severe non-linearity and under a substantially transient process of earthquake type kinematic excitation or earthquake simulation.


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User talk:Baminnick/enes100/Speakers

Creating the oobleck documentation was awesome, just to get the feel for it I am going to try it tomorrow. Zchill 19:15, 22 October 2011 (UTC)\

What you have done was really impressive especially the documentation part, I have done the same thing my mixture was very thicker than your mixture that I have seen on the video you uploaded. Now, as a team we know how to make the corn starch ready...Ayapici 10:50, October 23 2011 (UTC)\

10/10/60 ... good job .. 1sfoerster 14:32, 24 October 2011 (UTC)

I have to say when I was watching your videos I was impressed by the amount of cornstarch, and most importantly how you could step on it.. I bet I was very messy.... Ayapici 18:08, October 29 2011 (UTC)\ 10/10/100 ... this is a good alternative to the huge tank ... we could do this in the spring 1sfoerster 14:53, 31 October 2011 (UTC)

Your task for this week is very interesting, I can't wait to find out more about it tomorrow, it seems to me we are the only two people working on here. Ayapici 10:45, November 6 2011 (UTC)\

10/10/80 1sfoerster 15:31, 7 November 2011 (UTC)\

Nice job with the experiment this week. Yours looked to be a bit more labor intensive than mine. My experiment didn't go quite as planned either. Zchill 15:17, 13 November 2011 (UTC)\

10/10/80 .. nice job 1sfoerster

title: User talk:Baminnick/enes100/Speakers


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Simple roller bearing

Simple roller bearing or Earthquake-protective building buffer  is a simplified version of a base isolation device called earthquake protector which is intended for protection of various building and non-building structures against potentially damaging lateral impacts of strong earthquakes.

The metallic bearing support shown on the right may be adapted, with certain precautions, as a seismic isolator to skyscrapers and buildings on soft ground. Recently, it has been employed for a housing complex (17 stories) in Tokyo, Japan.

title: Simple roller bearing


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File:Simple rollers BI.jpg

Housing complex mounted on Metallic Roller Bearings, see http://www.okumuragumi.co.jp/en/technology/building.html

title: File:Simple rollers BI.jpg