text:
User:Egm6321.f10.team2.zou/HW2

= Problem 5: =

Given

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$$ \displaystyle M(x,y)+N(x,y)f(y')=0$$ (Eq 5.1)
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Find
Find $$\displaystyle f(y')$$ so that there is no analytical solution to $$\displaystyle f(y')=-\frac{M}{N}$$. (i.e., such ODE cannot be exact.)

Solution
If we were to create the following parts of such an equation that is described in Eq 5.1, we can get the following functions out of an infinite possibilities pool.

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$$ \displaystyle
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M(x,y)=5xy$$

(Eq 5.2)
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$$ \displaystyle N(x,y)={{x}^{2}}{{y}^{3}}$$ (Eq 5.3)
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$$ \displaystyle f(y')=10y'{{e}^{y'}}$$ (Eq 5.4)
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Then plugging in all of the equations into Eq 5.1 will get us the following:

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$$ \displaystyle 5xy+{{x}^{2}}{{y}^{3}}(10y'{{e}^{y'}})=0$$ (Eq 5.5)
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Reorganizing the equation to solve for y’ will yield

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$$ \displaystyle 5xy+{{x}^{2}}{{y}^{3}}(10y'{{e}^{y'}})=0$$ (Eq 5.6)
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$$ \displaystyle {{x}^{2}}{{y}^{3}}(10y'{{e}^{y'}})=-5xy$$ (Eq 5.7)
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$$ \displaystyle y'{{e}^{y'}}=-\frac{5xy}{10{{x}^{2}}{{y}^{3}}}=-\frac{1}{2xy}$$ (Eq 5.8)
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Finally taking the natural logarithms of both sides will yield

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$$ \displaystyle \ln (y')+y'=\ln (-\frac{1}{2xy})$$ (Eq 5.9)
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Therefore, it can be concluded that $$\displaystyle f(y')=10y'{{e}^{y'}}$$ will not yield an exact equation for the given $$\displaystyle M(x,y)$$ & $$\displaystyle N(x,y)$$.

= Problem 6: =

Given

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$$ \displaystyle y(x)={{\sin }^{-1}}(k-15{{x}^{5}})$$, (Eq 6.1)
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$$ \displaystyle M(x,y)+N(x,y)y'=0$$, (Eq 6.2)
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where $$\displaystyle \left\{ \begin{align} & M(x,y)=75{{x}^{4}} \\ & N(x,y)=\cos y \\ \end{align} \right.$$.

Find
Verify that Eq 6.1 satisfies Eq 6.2.

Step 1
When we plug in the given $$\displaystyle M(x,y)$$ & $$\displaystyle N(x,y)$$ values into Eq 6.2, we get:

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$$ \displaystyle 75{{x}^{4}}+(\cos y)y'=0$$. (Eq 6.3)
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Step 2
So now let’s look at Eq 6.1 and rewrite it in a different from such that

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$$ \displaystyle y(x)={{\sin }^{-1}}(k-15{{x}^{5}})\Rightarrow \sin y=(k-15{{x}^{5}})$$. (Eq 6.4)
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Step 3
Taking the derivative of both sides of the new form we get the following:

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$$ \displaystyle (\sin y)'=(k-15{{x}^{5}})'$$, (Eq 6.5)
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$$ \displaystyle (\cos y)y'=-75{{x}^{4}}$$. (Eq 6.6)
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Step 4
Rearranging the result from Step 3 will give us $$\displaystyle 75{{x}^{4}}+(\cos y)y'=0$$; thereby, proof is complete.

= Problem 7: Solving General Non-Homogeneous Linear First Order Ordinary Differential Equations =

Given

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$$ \displaystyle {y}'+xy=2x+3$$, (Eq 7.1)
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$$ \displaystyle {y}'+\frac{{{a}_{0}}(x)}{{{a}_{1}}(x)}y=\frac{b(x)}{{{a}_{1}}(x)}$$, (Eq 7.2)
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where we assume that for any $$\displaystyle x $$, $$\displaystyle {{a}_{1}}(x)\ne 0 $$.

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$$ \displaystyle ({{x}^{2}}+1){y}'+xy=2x$$. (Eq 7.3)
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Find
Solutions regarding Eq 7.1 ~ Eq 7.3.

Solution
Before we get started, we should find the method of deriving solutions of non-homogeneous 1st order ODEs.

Method by King et al.
Consider a general non-homogeneous 1st order ODE like:

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$$ \displaystyle {{a}_{1}}(x){y}'+{{a}_{0}}(x)y=b(x)$$, (Eq 7.4)
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If for any $$\displaystyle x $$, $$\displaystyle {{a}_{1}}(x)\ne 0 $$, then we get another form of $$Eq 7.4 $$,

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$$ \displaystyle {y}'+P(x)y=Q(x)$$, (Eq 7.5)
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where $$P(x)=\frac{{{a}_{0}}(x)}{{{a}_{1}}(x)}$$ and $$Q(x)=\frac{b(x)}{{{a}_{1}}(x)}$$.

If we let factor $$\displaystyle \exp \left\{ \int_ – ^{x}{P(s)ds} \right\}$$ times each sides of Eq 7.5, we derive,

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$$ \displaystyle \exp \left\{ \int_ – ^{x}{P(s)ds} \right\}\frac{dy}{dx}+\exp \left\{ \int_ – ^{x}{P(s)ds} \right\}P(x)y=Q(x)\exp \left\{ \int_ – ^{x}{P(s)ds} \right\}$$. (Eq 7.6)
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We can see that the left side of the equation can be simplified, thus,

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$$ \displaystyle {{h}^{1}}\frac{dy}{dx}+y\frac{d{{h}^{1}}}{dx}=Q{{h}^{1}}$$, (Eq 7.7)
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By integrating Eq 7.7 we have the solution,

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$$ \displaystyle y(x)=\frac{1}{{{h}^{1}}(x)}\int_ – ^{x}{{{h}^{1}}(s)Q(s)}ds$$, (Eq 7.8)
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where $$\displaystyle {{h}^{^{1}}}(x)=\exp \left\{ \int_ – ^{x}{P(s)ds} \right\} $$.

Method by finding exact total differential
We can also get the solution fully under the idea of using exact total differential to eliminate the $$\displaystyle {{y}'} $$ and utility of line integral. By doing this, Eq 7.5 can be also be written as,

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$$ \displaystyle \left[ P(x)y-Q(x) \right]dx+dy=0$$. (Eq 7.9)
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If we find a function $$\displaystyle \mu (x,y)$$ whose total differential is same as the left side of Eq 7.9, then we will have,

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$$ \displaystyle \mu (x,y)=C$$, (Eq 7.10)
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where $$\displaystyle C$$ is some constant, then we get the implicit or explicit solution from Eq 7.10.

However the prerequisite of existence of such $$\displaystyle \mu (x,y)$$ is not assured, so we need a factor multipled to the Eq 7.9 to make it satisfy the second condition of exactness. Let's call this factor $$\displaystyle {{h}^{2}}$$ and assume it a function only of $$\displaystyle x$$. We have,

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$$ \displaystyle {{h}^{2}}(x)\left[ P(x)y-Q(x) \right]dx+{{h}^{2}}(x)dy=0$$. (Eq 7.11)
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Eq 7.11 must satisfy the second condition of exactness, hencce we obtain,

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$$ \displaystyle \frac{\partial \left\{ {{h}^{2}}(x)\left[ P(x)y-Q(x) \right] \right\}}{\partial y}=\frac{\partial {{h}^{2}}(x)}{\partial x}$$ (Eq 7.12)
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$$ \displaystyle \Rightarrow {{h}^{2}}(x)=\exp \int_ – ^{x}{P(s)}ds$$ (Eq 7.13)
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We can see that the assumption "$$\displaystyle {{h}^{2}}(x)$$ is a function only of $$\displaystyle x$$" is automatically satisfied and $$\displaystyle {{h}^{2}}(x)$$ is actually equal to $$\displaystyle {{h}^{1}}(x)$$.

Now we can concentrate on getting the critical important function: $$\displaystyle \mu (x,y)$$.

Theorem 7-1
Let $$\displaystyle I(x,y)$$ and $$\displaystyle J(x,y)$$ be both smooth functions in its domain and such relationship is satisfied:

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$$ \displaystyle \frac{\partial I}{\partial y}=\frac{\partial J}{\partial x}$$. (Eq 7.14)
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Then the total differential of function $$\displaystyle u(x,y)=\int_{({{x}_{0}},{{y}_{0}})}^{(x,y)}{I(x,y)dx+J(x,y)dy}$$ equals $$\displaystyle I(x,y)dx+J(x,y)dy$$ in which the $$\displaystyle u(x,y)$$ is a line integral and $$\displaystyle ({{x}_{0}},{{y}_{0}})$$ is an arbitrary point.

Verification:

To illustrate this theorem, we just need to prove relationships below:

 * $$\displaystyle \frac{\partial u}{\partial x}=I(x,y)$$, $$\displaystyle \frac{\partial u}{\partial y}=J(x,y)$$

Then we have,

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$$ \displaystyle \frac{\partial u}{\partial x}=\underset{\Delta x\to 0}{\mathop{\lim }}\,\frac{u(x+\Delta x,y)-u(x,y)}{\Delta x}$$ (Eq 7.15)
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The Eq 7.14 satisfied the condition of path independence of line integrals(please see Green's theorem), therefore, line integral $$\displaystyle u(x+\Delta x,y)=\int_{({{x}_{0}},{{y}_{0}})}^{(x+\Delta x,y)}{I(x,y)dx+J(x,y)dy}$$ can be designated onto 2 line segments:

 * $$\displaystyle ({{x}_{0}},{{y}_{0}})\to (x,y)\to (x+\Delta x,y)$$. We obtain,

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$$ \displaystyle u(x+\Delta x,y)=u(x,y)+\int_{(x,y)}^{(x+\Delta x,y)}{I(x,y)dx+J(x,y)dy}$$, (Eq 7.16)
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$$ \displaystyle \Rightarrow u(x+\Delta x,y)-u(x,y)=\int_{x}^{x+\Delta x}{I(x,y)dx}$$, (Eq 7.17)
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$$ \displaystyle \Rightarrow u(x+\Delta x,y)-u(x,y)=I(x+\omega *\Delta x,y)\Delta x$$, (Eq 7.18)
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where $$\displaystyle 0\le \omega \le 1$$(please see Intermediate value problem).

Then we substituting Eq 7.18 back to Eq 7.15, we derive,

 * $$\frac{\partial u}{\partial x}=I(x,y)$$.

Similarly we have,

 * $$\frac{\partial u}{\partial y}=J(x,y)$$.

Thus the whole theorem is proved.

Now we go back to the Eq 6.11. Because Eq 6.12 meets the prerequisite of Eq 7.14, we can apply Theorem 7-1 on Eq 7.11, we have,

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$$ \displaystyle \begin{align} u(x,y) & =\int_{({{x}_{0}},{{y}_{0}})}^{(x,y)}{\left\{ {{h}^{2}}(x)\left[ P(x)y-Q(x) \right]dx+{{h}^{2}}(x)dy \right\}} \\ & =\int_{({{x}_{0}},{{y}_{0}})}^{(x,{{y}_{0}})}{\left\{ {{h}^{2}}(x)\left[ P(x)y-Q(x) \right] \right\}dx}+\int_{(x,{{y}_{0}})}^{(x,y)}{{{h}^{2}}(x)dy} \end{align}$$, (Eq 7.19)
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where $$\displaystyle ({{x}_{0}},{{y}_{0}})$$ is an arbitrary point. And if combined with Eq 7.10, we are able to get the solution from the equation below:

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$$ \displaystyle \int_{({{x}_{0}},{{y}_{0}})}^{(x,{{y}_{0}})}{\left\{ {{h}^{2}}(x)\left[ P(x)y-Q(x) \right] \right\}dx}+\int_{(x,{{y}_{0}})}^{(x,y)}{{{h}^{2}}(x)dy}=C$$, (Eq 7.20)
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where $$\displaystyle C$$ is some constant.

Solution for Eq 7.1
We use the first method.

From Eq 7.1 we know,

$$\displaystyle P(x)=x$$, $$\displaystyle Q(x)=2x+3$$.

The integrating factor is,

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$$ \displaystyle \begin{align} h= & \exp \int_ – ^{x}{sds} \\ & ={{e}^{\tfrac{2}}} \end{align}$$. (Eq 7.21)
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So,

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$$ \displaystyle \begin{align} y & =\frac{1}{h(x)}\int_ – ^{s}{h(s)Q(s)ds} \\ & ={{e}^{-\frac{2}}}\int_ – ^{x}(2s+3)ds \\ & ={{e}^{-\frac{2}}}\left( 2\int_ – ^{x}{{{e}^{\frac{2}}}d\frac{2}+3\int_ – ^{x}{{{e}^{\frac{{{s}^{2}}}{2}}}ds}} \right) \\ & =2+{{e}^{-\frac{2}}}*3\int_ – ^{x}{{{e}^{\frac{{{s}^{2}}}{2}}}ds} \\ & =2+\frac{3\sqrt{\pi }}{2}{{e}^{-\frac{2}}}*erfi(x) \end{align}$$, (Eq 7.22)
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The term $$\displaystyle \int_ – ^{x}{{{e}^{\frac{{{s}^{2}}}{2}}}ds}$$ is unable to be described by the combination of elementary functions and their integrals (please see Lists of integrals). But it can be described by imaginary error function(the term $$\displaystyle erfi(x)$$ in Eq 7.22), see also Error Function.

Solution for Eq 7.2
From Eq 7.2 we know,

$$P(x)=\frac{{{a}_{0}}(x)}{{{a}_{1}}(x)}$$ and $$Q(x)=\frac{b(x)}{{{a}_{1}}(x)}$$.

Substituting these two into Eq 7.8, we dereive,

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$$ \displaystyle y(x)=\frac{1}{\exp \left\{ \int_ – ^{x}{\frac{{{a}_{0}}(s)}{{{a}_{1}}(s)}ds} \right\}}\int_ – ^{x}{\exp \left\{ \int_ – ^{x}{\frac{{{a}_{0}}(s)}{{{a}_{1}}(s)}ds} \right\}\frac{b(s)}{{{a}_{1}}(s)}ds}$$ (Eq 7.23)
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Solution for Eq 7.3
We use second method.

As $$\displaystyle {{a}_{1}}=({{x}^{2}}+1)\ne 0$$, Eq 7.3 can de written as:

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$$ \displaystyle {y}'+\frac{x}{{{x}^{2}}+1}y=\frac{2x}{{{x}^{2}}+1}$$ (Eq 7.24)
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The integation factor is,

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$$ \displaystyle h=\exp \int_ – ^{x}{\frac{s}{{{s}^{2}}+1}ds}={{\left( {{x}^{2}}+1 \right)}^{\frac{1}{2}}}$$ (Eq 7.25)
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Hence Eq 7.24 can be written as,

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$$ \displaystyle \frac{\left( y-2 \right)x}{\sqrt{{{x}^{2}}+1}}dx+\sqrt{{{x}^{2}}+1}dy=0$$ (Eq 7.26)
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Integrate Eq 7.26, we have,

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$$ \displaystyle \begin{align} & \int_{(0,0)}^{(x,y)}{\left\{ \frac{\left( y-2 \right)x}{\sqrt{{{x}^{2}}+1}}dx+\sqrt{{{x}^{2}}+1}dy \right\}=0} \\ & \Rightarrow \int_{(0,0)}^{(x,0)}{\frac{\left( y-2 \right)x}{\sqrt{{{x}^{2}}+1}}dx}+\int_{(x,0)}^{(x,y)}{\sqrt{{{x}^{2}}+1}dy}=0 \\ & \Rightarrow -2\sqrt{{{x}^{2}}+1}+\sqrt{{{x}^{2}}+1}*y=C \\ & \Rightarrow y=\frac{C}{\sqrt[{}]{{{x}^{2}}+1}}+2 \\ & \\ \end{align}$$ (Eq 7.27)
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where $$\displaystyle C$$ is some constant.

title: User:Egm6321.f10.team2.zou/HW2


text:
3-ary Boolean functions

There are $$2^{2^{3}}$$ = 256 3-ary Boolean functions, like set operations or logical connectives.

This Venn diagram, representing the intersection of 3 sets, or the conjunction of 3 statements respectively, gives an example of a 3-ary Boolean function.

Equivalence classes

 * See: Equivalence classes of Boolean functions

The set of 256 functions can be parted into various equivalence classes. The most basic way to do that are the 46 small equivalence classes (secs). Functions belong to the same sec, when they can be expressed by each other by negating arguments. There are 3 arguments that can be negated, so there can be up to $$2^{3}$$ = 8 different functions in a sec.

When binarily colored cubes can be transformed into each other by mirroring and rotation, they are essentially the same. The corresponding Boolean functions are often called equivalent and belong to the same big equivalence class (bec).

The following sequences show the number of secs and becs by weight: weight  =   0   1   2   3   4   5   6   7   8 secs: A054724(3, 0..8)  =   1   1   7   7  14   7   7   1   1 becs: A039754(3, 0..8)  =   1   1   3   3   6   3   3   1   1

The following sequences show the number of secs and becs by number of functions in each sec: 1   2    4    8  secs: A227725(3, 0..3)   =   2    7   14   23 becs:                       2    3    6   11

Permutations of functions in a bec
Theoretically a bec could have 3! * 23 = 6 * 8 = 48 functions, but the largest becs have only 24. (There are some becs of 4-ary functions with the highest possible number of functions, e.g. this one.)

Nonlinearity
The nonlinearity of a function is the smallest Hamming distance it has from one of the 16 linear functions, i.e. from a row of the binary Walsh matrix or its complement. The functions in wec E0 are the linear functions, i.e. those with nonlinearity 0. The functions in wec O have nonlinearity 1, and all others have nonlinearity 2. There are no 3-ary bent functions.

Walsh spectrum

The Walsh spectrum of a Boolean function is the product of its binary string (as a row vector) with a Walsh matrix. The first entry of the Walsh spectrum is the functions digit sum, and all entries have the same parity.

In the following chapter Walsh spectra are shown in the "by ggbec" sections. Walsh spectra of the same sec (which differ only in the signs of their entries) are always shown in the same file.

The Walsh spectra of complements sum up to $$\scriptstyle (8,0,0,0,0,0,0,0,)$$.

Further the binary Walsh spectra are always shown by the red squares in the background. They are always rows of a binary Walsh matrix - or, in other terms, exclusive disjunctions of unnegated arguments.

The functions with odd digit sum, which make up wec O, have each binary Walsh spectrum one time in every sec.

The functions with even digit sum, which make up the other four wecs, have always the same binary Walsh spectrum in the same sec:

Functions with the same binary Walsh spectrum
In the diagrams in this section the even functions are shown in red, and the odd ones (i.e. those in wec O) in yellow. Each odd function differs in the lowest bit (numerically: by 1) from an even function with the same binary Walsh spectrum. So in the octeract graphs each red vertex is connected to a yellow vertex by an edge of the direction corresponding to the lowest bit (like the edge connecting vertices 0 and 1). The pattern of the red vertices is always symmetrical to the main axes. Surprisingly the yellow vertices are also symmetrical, but to axes tilted to the left or to the right (indicated by \ or / in the table).

Overview

The matrix on the right shows the 256 functions arranged in a way similar to the Hasse diagram, which is an octeract graph. The colors indicate the five wecs, as shown in the table below.

The two following matrices are examples of a gbec and a ggsec. Both contain the sec 26. Files like these are in the collapsible boxes below in boxes labeled Positions.

These matrices are symmetric to the main diagonal, because they contain complete secs. They are also symmetric to the antidiagonal, because they contain all the complements, and complements are symmetric about the center of the matrix. The ggsec matrices are also symmetric about the central axes, because they contain all the half-complements. Left half-complements are vertically, and right ones are horizontally symmetric to each other.

The tables above show how the equivalence classes are nested in each other. Each table shows the equivalence classes in a wec. The vertical axes show ggsecs, gsecs and secs, and the horizontal ones show ggbecs, gbecs and becs. The entries in the matrices show which secs belong to which becs. The numbers in these fields show how many functions are in each sec. A dark red background tells that the sec contains a monotonic function.

Monotonic functions
The right Hasse diagram in the file on the right shows the 20 monotonic 3-ary Boolean functions.

If a sec has a monotonic function, all the secs in the gbec and gsec it belongs to also have one. So one can call secs, gbecs and gsecs monotonic, when they contain monotonic functions. There are 6 gbecs and 12 gsecs that are monotonic in this sense. Their collapsible boxes are marked with Tudor roses.

In the above tables that show the nesting of the equivalence classes the monotonic secs have a dark red instead of a black background.

All wecs except E2 contain monotonic functions.

Subgroups of nimber addition

 * See: Subgroups of nimber addition#Z23

16 secs with in all 8 + 7*4 + 7*2 + 1 = 51 functions are related to subgroups of nimber addition:

In each sec matrix its leading function appears in a sona pattern. This pattern is 0 in N(0) iff the sec contains 8 different functions. All the other different sona patterns appear only in the sec matrices of the actual sonas between 1 and 15 and their Boolean complements. Each gbec is marked in green with its sona-bec, and each gsec is marked with its sona-sec.

Complements in secs
There are two kinds of secs that are their own complements (i.e. complete gsecs): Those with sona rank 2, marked as N(2, ...), and the following seven secs containing 8 functions each:

Gbecs by similarity to 4-ary sec matrix
In the octeract matrices of the gbecs it can be seen, that they belong together in a way that is independent of ggbecs and wecs. Their pattern is part of a sec matrix of one of the five 4-ary exact-value functions. On the left the functions in these gbecs are shown in the Hasse diagram.

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

title: 3-ary Boolean functions


text:
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title: User talk:Schibeci~enwikiversity


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User talk:Charuldip

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User talk:Prammod

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User talk:PRASHANSU

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title: User talk:PRASHANSU


text:
User:Sucheera

Homework2:

IPhone4

- CPU & speed

ARM Cortex-A8 Apple A4

Maximum clockspeed of 1 GHz and commonly runs around 750 MHz to 800 MHz

- Bus speed

- Cache size

variable (L1+L2)

L1 Instruction Cache 32 Kbytes

L1 Data Cache 32 Kbytes

L2 Cache 256 Kbytes

- Storage: type and amount

512 MB eDRAM

Flash memory, 16 and 32 GB

As we look at the spec of the 3 models which are Iphone4, Ipad and Acer Aspire One, we conclude that Acer Aspire One has more advance technology than Iphone4 and Ipad which they use the same type of CPU.

Acer Aspire One's cpu speed is 1.6GHz while Ipad and Iphone is only 1 GHz.

Also, the cache size (L2) of Acer is bigger which is 512 Kbytes while Iphone4 is only 256 Kbytes.

Homework1: http://www.youtube.com/watch?v=QksITBCDu0s By Sucheera Seenumpetch ID: 5180419

Name: Sucheera Seenumpetch

Nickname: Oil

Birthday: 21 June 1990

E-mail: oillleyton@hotmail.com

Facebook: http://facebook.com/oilliverpool

title: User:Sucheera


text:
User:EGM6321.f10.team6.yoshioka/HW2

Required
Find the function of $$f\left( y' \right)$$ such that there is no analytical solution to $$f\left( y' \right)=-\frac{M\left( x,y \right)}{N\left( x,y \right)}$$.

Solution
The solution of the problem is equivalent to find a N1_ODE that does not satisfy the 1st condition of exactness. In order to a N1_ODE to be exact, it must be in the form of:

The function chosen to test the first condition of exactness is:

From Equation 5.3 we can identify the functions, $$M\left( x,y \right)$$, $$N\left( x,y \right)$$ and $$f\left( y' \right)$$ as:

If we can rearrange Equation 5.3 to fit in the form of the Equation 5.2, than the 1st condition of exactness, if not we found Non-Exact N1_ODE.

Doing some algebra with Equation 5.3 to arrange in the fashion of $$f\left( y' \right)=-\frac{M\left( x,y \right)}{N\left( x,y \right)}$$:

Equation 5.7 does not fit in the same arrangement of Equation 5.2, since we got $$y'+\cos y'$$ on the right hand side of the equation instead of only $$y'$$. Therefore there is no analytical solution to the function chosen and also proves that Equation 5.3 is a Non Exact N1_ODE.

Given
The Euler Integrating Factor Method may be applied to homogeneous differential equations when the equations meet the first condition of exactness, but do not meet the second condition of exactness. That is to say, those equations that can me made to fit the form shown in equation 7.1, but do not meet the criteria shown in equation 7.2 can be made exact using the Euler method. One of the benefits of the Integrating Factor Method is that it can be applied to solve non-homogenous differential equations.

Required
(i) Solve the following non-homogeneous differential equation using the Integrating Factor Method:

(ii) Assume that $${{a}_{1\left( x \right)}}\ne 0$$ for any $$x$$ and find an expression for $${{y}_{\left( x \right)}}$$ in terms of $${{a}_{0}}$$, $${{a}_{1}}$$, $${b}$$ for the following form:

(iii) Apply the integrating factor method to the following equation:

Explanation of Process
The Integrating Factor Method assumes that some function $${{h}_{\left( x,y \right)}}$$ can be found to make a differential equation exact when it meets the first criterion of exactness (equation 7.1) but not the second (equation 7.2). This factor is multiplied by the original equation to yield equation 7.6.

Applying the second condition of exactness and using the product rule to differentiate each term we obtain:

If we assume that the partial derivative of h with respect to y is zero, then h becomes a function of x only and we are left with the following:

Which can be rearranged to obtain:

Dividing by h and rearranging terms we obtain:

Integrating both sides with respect to x we obtain the following function we can use to obtain h:

If we return to our original non-exact equation given in equation 7.1 we can apply the integrating factor to obtain the following equation:

If we recall that $$h\left( {y}'+{{a}_{0}}y \right)=hb$$, we can rearrange the above to obtain the following:

The reader might recognize that the left side of equation 7.13 is really nothing more than $${{\left( hy \right)}^{\prime }}$$. Substituting into 7.13 we obtain:

After integrating we are left with the solution to y.

Solution to Part I
From equation 7.3 we obtain the following:

Substituting into equation 7.11 we obtain an expression for h:

Combing the result from equation 7.17 with equation 7.15 we obtain the solution to y.

Rearranging the terms:

Solving the first Integral

Using the substitution method

Substituting in the Euqation 7.? we get

And here I hit the wall, I have no idea how to solve the second integral...

Solution to Part II
From equation 7.3 we obtain the following:

Substituting into equation 7.11 we obtain an expression for h:

Combing the result from equation 7.20 with equation 7.15 we obtain the solution to y.

Solution to Part III
First we need to rearranging Equation 7.5 to be in the form of:

Rearranging Equation 7.5 we get:

Calculating $${{M}_{y}}$$, $$N$$ and $${{N}_{x}}$$:

Substituting into equation 7.11 we obtain an expression for h:

From equation 7.21 we have a general solution in terms of $${{a}_{0}}$$, $${{a}_{1}}$$, $${b}$$. Substituting the terms given in the problem statement in equation 7.5 we obtain:

Using the substitution method to solve the integral

Substituting Equation 7.24 into 7.15:

Using the substitution method to solve the integral

From Equation 7.27 we get the final answer for $$y(x)$$

title: User:EGM6321.f10.team6.yoshioka/HW2


text:
Fluid mechanics for MAP

Objectives
This is an introductory course of fluid mechanics. This course is given within the Master Degree Program in Advanced Materials and Processes (MAP) at FAU Erlangen-Nuremberg.

By the end of this course, the students, who has no background in fluid mechanics, are expected

1. To get acquainted with the following fluid flow phenomena.

 * Newtonian and non-Newtonian fluids
 * fluid statics
 * laminar and turbulent flows
 * separated flows
 * multi-phase flows
 * Cavitation
 * etc.

2. To have theoretical understanding of fluid flow. This will be achieved by giving the the mathematical fundamentals of integral and differential modeling of fluid flows for the conservation laws of mass, momentum and energy.

3. To classify different types of fluid flow phenomena and derive the necessary non-dimensional parameters.

4. To apply fluid mechanics knowledge on real life problems by simplifying the the governing equations for peculiar flows and solving them.

Moreover, students have the chance to see the direct application of the content in the research and development work conducted at the Institute of Fluid Mechanics-Erlangen (LSTM-Erlangen).

Motivation of studying fluid mechanics as a MAP student
Fluid mechanics is a fundamental subject of many disciplines of engineering and natural sciences. It is involved, for example, in chemical engineering, aerospace engineering, biomedical engineering and, also, in material sciences. As a matter of fact, it is a field where multiple physical effects can be met. Extrusion of polymers, crystal growth, die casting and production of micro and nano structures are example fields related material science, where fluid mechanics plays a very important role. Fluid mechanics knowledge is necessary to understand the nature of flowing medium. This knowledge certainly helps us to develop new materials and processes with which we can feasibly produce these new materials. Furthermore, application of the systematics of fluid mechanics in other research subjects might be beneficial.

Fact check
{ 1.click the true statement. - Fluid mechanics doesn't have applications in wide range of disciplines + Fluid mechanics have applications in wide range of disciplines - we can't use this knowledge to create new materials - production of micro and nano structures is not an example field related to fluid mechanics application in material science
 * type=""}

Basic components of the course
This course is dominnatly a theoretical one. However, examples are provided in the form of visual media and laboratory experiments. Exercises are made and homeworks are given so that students get acquainted to the theoretical systematic in fluid mechanics. In the last part of the course, relevant examples of research work, which are conducted at LSTM-Erlangen, are provided.

Chapters

 * Chapter 1. Introduction
 * Chapter 2. Scalar, Vectors and Tensors
 * Chapter 3. Fluid Statics
 * Chapter 4. Fluid Dynamics
 * Chapter 5. Differential Analysis of Fluid Flow
 * Chapter 6. Analytical solutions of internal and external flows
 * Chapter 7. Dimensional Analysis
 * Chapter 8. Energy Considerations

Important Links

 * Institute of Fluid Mechanics, Erlangen (LSTM-Erlangen)
 * List of fluid mechanics sources in wikipedia
 * Yet another list of fluid mechanics sources in wikipedia
 * Visual flow courses filmed in 1960’s by very renowned scientists, which were made publicly available by M.I.T.
 * Gallery of fluid motion by Physics of Fluids (don’t forget to visit the archive)
 * Numerical fluid mechanics sources prepared by computational fluid dynamics community

Literature

 * Munson, B.R., Young, D.F., and Okiishi,T.H., Huebsch, W.W., “Fundamentals of Fluid Mechanics”, John Willey and Sons.
 * Fox, R.W. and McDonald, A.T., “Introduction to Fluid Mechanics”, John Willey and Sons.
 * Spurk, J. and Aksel, N., “Strömungslehre: Einführung in die Theorie der Strömungen“, Springer.
 * Spurk, J., “Fluid Mechanics“, Springer.
 * Durst, F., “Grundlagen der Strömungsmechanik: Eine Einführung in die Theorie der Strömung von Fluiden“, Springer.
 * Durst, F., "Fluid Mechanics: An Introduction to the Theory of Fluid Flows", Springer.
 * White, F., “Fluid Mechanics“, McGraw Hill.
 * Pozrikidis, C., "Fluid Dynamics: Theory, Computation and Numerical Simulation", Springer, 2009.
 * Fay james., introduction to fluid mechanics, PHI.

title: Fluid mechanics for MAP


text:
Fluid Mechanics for MAP/Introduction

>back to Chapters

Definition of Fluid
Fluid Mechanics is the study of fluids at rest (fluid statics) and in motion (fluid dynamics).

A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. Whereas a solid can resist an applied force by static deformation.

Liquids, gases, plasmas and, to some extent, plastic solids are accepted to be fluids. A perfect fluid offers no internal resistance to change in shape and, consequently, they take on the shape of their containers. Liquids form a free surface (that is, a surface not created by their container) whereas gases and plasmas do not, but, instead, they expand and occupy the entire volume of the container.

Deborah number
A transition from a more resistant (elastic) to a less resistant behavior (viscous) has a relevant characteristic time scale: the relaxation time of the material. Correspondingly, the ratio of the relaxation time of a material to the timescale of a deformation is called Deborah number :

$$ \displaystyle \displaystyle De = \frac{\text{characteristic relaxation time of material}} {\text{time scale of deformation}} $$

Small Deborah numbers correspond to situations where the material has time to relax (and behaves in a viscous manner), while high Deborah numbers  correspond to situations where the material behaves rather elastically. Water can show elastic behavior when the time scale of deformation becomes very short. For example, when one tries to jump to water from a height more than 100 meters, water feels like a solid ground at the instant of collision ( do not try). Corn starch and water mixture (suspension) is a good example with which low and high De number effects can be shown.

Rheological Material
Fluids can be classified according to the relation between stress $$ \displaystyle \tau$$ and deformation rate $$ \displaystyle du/dy$$. The Newtonian fluids show a linear relation $$ \displaystyle \tau = \mu\frac{du}{dy}\Rightarrow \mu=\mu(T,P)$$

Fluids which do not follow the linear law between stress an the deformation rate are called non-newtonian and they are the subject of rheology. A dilatant (shear-thickening) fluid increases resistance with increasing applied stress. Alternately, a pseudoplastic (shear-thinning) fluid decreases resistance with increasing stress. If the thinning effect is very strong, the fluid is termed plastic. The limiting case of a plastic substance is one which requires a finite yield stress before it begins to flow. The linear-flow Bingham plastic idealization is shown in the figure, but the flow behavior after yield may also be nonlinear. Examples of a yielding fluid are toothpaste and ketchup, which will not flow out of the tube until a finite stress is applied by squeezing.

Some fluids show decreasing (thixotropic) or  increasing resistance (rheopectic) in time for the same deformation rate. For example, pudding is a rheopectic fluid and some paints are thixotropic.

Pressure in a fluid
Pressure is force per unit area and is a scalar quantity.

$$ \displaystyle p=\frac{F}{A}\left[Pa\right]\ ; \left(1 bar = 10^{5} Pa\right) $$

In a fluid at rest,  the tangential viscous forces are  absent and the only force between adjacent surfaces is normal to the surface. In a resting fluid there is only a normal stress (pressure). In other words, force caused by the pressure on a surface is normal to that surface.

Balance in x-direction:

$$ \displaystyle \left(p_{1}\ ds\right)\ sin\theta - p_{3}\ dz = 0$$

$$ \displaystyle dz=ds\sin\theta\longrightarrow p_{1} = p_{3}$$

Balance in z-direction:

$$ \displaystyle -\left(p_{1}\ ds\right)\ cos\theta + p_{2}\ dx - \frac{1}{2}\rho g\ dx\ dz = 0$$

$$ \displaystyle ds\ cos\theta = dx\longrightarrow p_{2} - p_{1} - \frac{1}{2}\rho g\ dz = 0$$

For an infinitesimal prism, effect of gravity can be neglected.

$$ \displaystyle \rightarrow p_{1} = p_{2} = p_{3}$$

Interface phenomena and surface tension
If the interface is curved, a mechanical balance shows that there is a pressure difference across the interface, the pressure being higher on the concave side, $$ \displaystyle \Delta\ p=\sigma\left(\frac{1}{R_{1}}+\frac{1}{R_{2}}\right) $$

where $$ \displaystyle \sigma\left[\frac{N}{m}\right]$$ is the surface tension coefficient. Surface tension coefficient is not a property of the liquid alone, but a property of the liquid's interface with another medium.

According to the above equation, in the soap bubble or in the droplet, inner pressure is higher than outer pressure. This can also be shown by a force balance. In the droplet, the force balance in the vertical direction reads

$$ \displaystyle F_{net}=\sigma2\pi\!R - \left(p_{i} - p_{0}\right)\pi\!R^{2}=0$$

$$ \displaystyle \Delta\ p=\sigma\frac{2}{R}$$

Similarly, in the soap bubble the force balance becomes $$ \displaystyle \Delta\ p=\sigma\left(\frac{1}{R}+\frac{1}{R}\right)=\sigma\frac{2}{R}$$

$$ \displaystyle F_{net}=2\sigma2\pi\!R - \left(p_{i}-p_{0}\right)\pi\!R^{2}=0$$

$$ \displaystyle \Delta\ p=\sigma\frac{4}{R}$$

Note that owing to the two interfaces in the soap bubble force due to surface tension is as double as that in the droplet.

The contact angle is the angle between the liquid-solid and gas-liquid interfaces. It is calculated such that angle remains in the liquid. It is dependent on the adhesion forces between the liquid molecules and the solid wall. These forces are sensitive to the actual physicochemical conditions of the solid-liquid interface.

Compressibility
Ideal Gas law (Equation of State)

$$\displaystyle p = \rho RT $$ : Where R is the gas constant and T is the universal temperature.

$$R_{air} = 286,9 \left[\frac{J}{kg}K\right]$$

title: Fluid Mechanics for MAP/Introduction


text:
User:Kittiphum4980587

HW1: Introduction

My name is Kittiphum Sringammuang. I'm a student at MUIC (Mahidol University International College), majoring in Social Science. My favorite sites are Toms Hardware, Overclockzone, Crack, mrpalm, BBC and Al Jazeera. My favorite magazine is Stuff magazine which provides different news and review of all kind of technology, especially gadgets. My new hobby is overclocking CPU and GPU. I brunt the CPU for on first trial :D.

ps. I hate Intel, I'm a fan of AMD.

HW2: Short Clip introducing MUIC MUIC

http://www.youtube.com/watch?v=USgfsrCtXPs

HW3: Hardware specification, I choose iPad and compare with other tablets.

Apple iPad (3G model) OS: iOS4 CPU: A4 Clock speed: 1GHz Bus speed: Unknown Cache size: L1 cache contains 64KB (32KB for instruction and 32KB for data), L2 cache contains 640KB Storage: Flash memory 16 32 64GB

WeTab (3G model) OS: Linux CPU: Intel Atom N450 Clock speed: 1.66GHz Bus speed: Unknown (Intel Atom's Bus Speed is at the range of 400 MHz to 667 MHz) Cache size: L2 512 KB Storage: Flash memory of 16 or 32 GB (Can expand another 32GB by using SDHC Card)

Samsung Galaxy Tab OS: Android 2.2(Codename: Froyo) CPU: ARM Cortex A8 processor Clock speed: 1GHz Bus speed: Unknown Cache size: L2 512 KB Storage: Flash memory of 16 or 32 GB (Can expand another 32GB by using SDHC Card)

Conclusion: Tablet is not a new technology these 3 tablets have different pros and cons. Apple iPad is the snappiest because the OS and not many applications can run on the background which it can help to off load the ram. One of the cons that make iPad unpopular among the users is it has to sync with iTune only which it's not very user friendly, it would be real nice if we can perform drag and drop to transfer file into the device. WeTab on the other hand comes with more powerful CPU and an open source OS which could bring the new applications for the device. The only thing that make the WeTab unique from other tablets in the market is its extension ports. It comes with the USB ports and HDMI port which is a new technology for the tablet. However, the battery is not long comparing to iPad and Galaxy Tab The only thing that I choose Galaxy Tab to compare with the other 2 tablets is its OS. I have to mention that Galaxy Tab is not 100% tablet because it can be a phone but other than that it pretty much like iPad but use different OS and has smaller screen.

If I have to choose one among these 3, I'll go for iPad. I don't see the necessity by having USB or HDMI ports because tablet is not a computer and it suited for lighty use. I don't choose Samsung because the OS and number of applications. iOS is one of the snappiest mobile OS in the market and there are 100,000+ of application available for iPad even though the android market is expanding over 2 years, the bottle neck is still; the OS.

title: User:Kittiphum4980587


title: File:Problem3-plot.png


text:
User:Chilover30

ASU Graduate Student

title: User:Chilover30


text:
User talk:Bpennington

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Self-introduction
Hello, My name's Saniya. Im 18 years old, and i'm currently studying in Mahidol Univesity International College. I decided to major in T.I.M, concentrating on hotel management, and will soon apply for a minor in psychology. I don't know much about computers, as i am not a very techinical person. However, i am aware of the basics that benefit me academically on a daily basis. All said and done, i am willing to learn more about computers and hopefully will get to apply what i am about to learn, in the future.

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User talk:Kittiphum4980587

 Hello Kittiphum4980587, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:Kittiphum4980587


text:
User talk:Borami kim

저작권법 역사

title: User talk:Borami kim


text:
User:Pp mall

Sup guys!
My name is Poomphun and my nick name is Mall. I am 19 years old. I am single and I have no girl friend yet. I have to craate an account here because my teacher command me to do so. And i cannot reject any of his orders because he is like a god. He is the one who decide whether i would achieve or fail the course. I wish I would get an A and i hope everyone does.

Love you all. (fake)

Welcome to MUIC
http://www.youtube.com/watch?v=EW41pnuGG-w

Enjoy

ipad Specification
CPU speed: 1GHZ Apple A4

Bus speed: 133Mhz

Cache speed size: L1 32Kb,L2 640Kb Storage: 16, 32,and 64 (flash drive)

Ram: 256Mb 2 layers 128*2

Net Book
Acer Aspire One

CPU: Intel Atom N270, 1.6GHz

RAM: 512MB (1GB optional) DDR2 533 MHz

L2 Cache: 512/ KB

Storage: NAND Flash (8GB) or HDD (120GB)

Conclusion
Net Book is more efficient because CPU is faster and more cache. Also, HDD is larger. However, it still depends on different purpose of the user.

title: User:Pp mall


text:
Comparative law and justice/Luxembourg

Part of the Comparative law and justice Wikiversity Project

Basic Information
Population
 * The total population in Luxembourg is 491,775 as of July 2010. The population is broken down into 46,918 male and 44,052 females, between the ages of 0-14, who make up 18.5% of the population.66.7% of the population is made up of 165,342 males and 162,681 females between the ages of 15 to 64 years old. 29,839 males and 42,943 females make up the rest of the population consists of 14.8% of people who are age 65 and older.

Geographic Information
 * Luxembourg is located in Western Europe between the countries of France and Germany. France, Germany, and the country of Belgium boarder the country of Luxembourg. The total Land mass in Luxembourg is 2,586 sq km. Usually the climate in Luxembourg consists of mild winters and cool summers. The city of Luxembourg is the largest in the country making up 78,800 of the country’s population.

Religion
 * The country of Luxembourg does not have an official Religion even though the country is mainly broken down into 87% of people who practice the Catholic Religion. The remaining 13% of the population choose to practice other religions such as; Protestant, Jewish, and Islamic.

Ethnicity
 * The majority of the ethnic groups that live in Luxembourg, and are not native born, come from other European countries. The native born Luxembourger make up 63.1% of the population. The rest of the ethnic groups found in this country are 13.3% Portuguese, 4.5% French, 4.3% Italian, 2.3% Germans,7.3% other EU countries and, 5.2% of the rest of the population come from other countries.

Language
 * Luxembourgish is the Nation language of the country. Languages like French and German, are also spoken in the country by it citizens.

Economic development'
 * GDP per capital
 * In Luxembourg the GDP per capita is an estimated $79,600.

 * GDP-

 * Key industry
 * the key Industries in Luxembourg consists of banking and financial services, iron and steel, information technology, telecommunications, cargo transportation, food processing, chemicals, metal products, engineering, tires, glass, aluminum, and tourism.

 * Exports
 * The Country of Luxembourg export chemicals, rubber products, glass, machinery and equipment. Netherlands, Italy, Belgium, Germany, France, and the UK are all export partners with Luxembourg. The country make about 14.18billion dollars in exports.

 * Imports
 * The Imports of Luxembourg consists of minerals, food products, quality consumer goods and metals. The Netherlands, China, France, Germany and Belgium are partners with Luxembourg.

Health and Education
 * The infant mortality rate is 4.56 deaths per 1,000 live births.
 * The Life expectancies rate in the Country of Luxembourg is 79.33 years of the total population. Males in the country live to about an average age of 76.07, and the females live to about 82.81 years of age.
 * The Literacy rate in Luxembourg is about 100%. In the country the people are exposed to a first- rate education system and the people of the country are required to stay in school until the age of 16, similar to the United States School System.

https://www.cia.gov/library/publications/the-world-factbook/geos/lu.html http://www.infoplease.com/ipa/A0107734.html?pageno=2

Brief History
In 1815 the Congress of Vienna made Luxembourg a Grand Duchy. Before this date Luxembourg was dominated by a lot of different European countries. It had been part of Charlimeagnes Empire, after being made a Grand Duchy the country was given to King William I in 1838. The country of Luxembourg became independent in 1835, but it was not until the year 1867 when Luxembourg was given the guarantee of perpetual neutrality, and recognized for their independence. In 1949 Luxembourg became a charter member of the North Atlantic Treaty Organization (NATO) and gave up their Neutrality. During World War I, the country was used as an area where the German soldiers used to stay, even though the country of Luxembourg decided to remain neutral during the war. The same thing happened in World War II and the Germans once again took over the country of Luxembourg, during the war 5,259 of the citizens of Luxembourg lost their lives.

Governance
The Luxembourg Government is set up like a Constitutional Monarchy. Luxembourg received its independence in 1839 from and adopted a constitution in 1868. Like the United States the Luxembourg government is broken down into three branches. The Executive Branch consists of the Grand Duke, who is the head of state, and is used only for ceremonial purposes. The Prime minister is also in this category and he is considered to be the head of state. The other branch of government is the legislative branch which is set up as a unicameral parliament; it has a chamber of deputies with council of state who serve as consultative body. The third branch of the Luxembourg Government is the Judicial Branch this is where the superior court is found.

Law Enforcement
The nation Police of Luxembourg is known as the “Police Grand-Ducale”. This name was adopted after January 2000. Before this date the Police system was made up into a dual system, the national police known as “corps de la police” and the Gendarmerie. The police work under the supervision of the Minister of Justice.

A general directorate, central units and regional divisions, are all part of the Police system in Luxembourg. The General Directorate is divided into five different Branches and it has the overreaching authority.

The Secretary General- Watches over the five branches, buys the items for the different units and advices the new projects before the director General has time to make his decision.

Human services department is in charge of the recruitment, retirements, payroll, internal transfers and the training in foreign countries The Operational department organizes big events. This department also takes care of the security intelligence, and deals with the function of the national emergency unit.

Budget and Equipment department handles the budget accounting, barracking and logistics covering the management of the fleet, arming, etc. Information technology department assures the access and information of judicial documents, establishes criminal statistics, and runs the offices of international co-operation and the internal computer and telephone system.

Organization and Methodology department is where the creation and development of new procedures are sometimes created to replace the existing ones, it also has the responsibility of updating police documents.

The central Units is where the Criminal Investigation Department is Located. This department is organized based on the different types of crimes. The sub departments located in the Criminal Investigation Department include: Protection of Minors, Police Records, Crime Analysis General Crime, Organized Crime, Drugs, Financial and Economic Crimes. The Criminal Investigation Department also has the responsibility of preserving evidence and conserving crime scenes.

The Regional division is in charge of preventing crimes and misdemeanors.

Crime Rates and Public Opinion
Luxembourg is known to be a safe place. Violent crimes are not a common thing in this country. Theft on the other hand has slowly become a problem .Residential burglary happens in the country usually by people who spend a lot of time watching their victims every move in order to find the perfect opportunity to invade their home and steal their belongings. In public areas such as the hotel lobbies, train stations, bus stations and air ports, pick pocketing often occurs. The most common non Violent Crime in Luxembourg is car theft. Lately there has been a new drug epidemic and the country is trying their best to try and cope with the situation. West African immigrants have been the ones eliciting the drugs to the youth who in return are committing petty crimes in order to support their habits. The country has been trying different things in order to deal with the problem. Outreach programs in the schools have proven to be effective so far.

title: Comparative law and justice/Luxembourg


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Comparative law and justice/Belarus

Part of the Comparative law and justice Wikiversity Project

<!when you have set up your page, delete this line and replace it with four ~!>

Basic Information
Demographic Information:

Source: Downloaded from http://commons.wikimedia.org/wiki/File:Flag_of_Belarus.svg

Total Population:

9,648,533

Age Breakdown:

(0-14 yrs.) 14.3% (15-64 yrs.) 71.3% (65+) 14.5%

Gender: (0-14) Male 707,550        Female 667,560 (15-64) Male 3,337,253     Female 3,540,916 (65+) Male 446,746         Female 948,508

Ethnic Make Up: Belarusian 81.2%, Russian 11.4%, Polish 3.9%, Ukrainian 2.4%, other 1.1%

Religion: Eastern Orthodox 80%, other (Including Roman Catholic Protestant, Jewish and Muslim) 20%

Official Languages: Belarusian 36.7%, Russian 62.8%

Unofficial Languages: Polish/Ukrainian 0.5%

Region: Eastern Europe

Continent: Europe

Total Landmass: 207,600 square kilometers

Avg. Climate: Cold Winters, humid summers

Bordering Countries: Latvia, Lithuania, Poland, Russia, Ukraine

Terrain: Flat, created by glacial carving

Brief History
Belarus became its own independent country from the USSR in 1991. Apart from any other former USSR countries, Belarus developed the strongest political and economic ties to Russia. Regardless of the two-state treaty signed between Russia and Belarus on December 8, 1999 there has been no serious intergration of the political and economic relationship between the two countries. Freedoms such as speech and press, religion, and peaceful assembly are not enjoyed yet by the Belarus popuation. President Lukashenko (elected in 1994) has gained power through an authoritarian approach.

Economic Development, Health, and Education
The GDP of Belarus is 120.7 billion dollars per year. In 2008 there was a projected growth of 10% for the year however with the recession in 2009 it turned out to be a negative 0.2%. GDP capita is 12,500 per year. With an unemployment rate of 27.1% it appears that there is some growth to happen before the 10% improvement rate is reached. The key industries in Belarus include metal cutting machine tools, tractors, trucks, earth movers, motorcycles, televisions, synthetic fibers, fertilizers, radios and refridgerators. Exports of Belarus include machinery and equipment, mineral products, chemicals, metals, foodstuffs, and textiles.

Concerning health, the infant mortality rate is currently 6.43 per 1,000 live births. The male life expectancy rate is 64.95 years and the female life expectancy rate is 76.64 years.

As far as education goes, more than a good majority of the population can read and write at the total rate of 99.6%. The males barely win with 99.6% over the females with 99.4%. The females do attend one year more of school on average with 15 years of attendance, making the male attendance 14 years.

Elections
The official title of the country is The Republic of Belarus. Belarus is a Civil Law country based on the fact that the written Constitution is regarded as supreme law. As it stands the country is a dictatorship in reality. Belarus has been through a number of different hand-offs of power and governmental structure since the country began. After the USSR let go of the country in 1994 it took it's current type of government drafting the Constitution that is still in use and considered supreme law today.

The law making power rests on the President who is issues Decrees, Edicts, and Orders needing only the consent of Parliament to finalize these proposals. Parliament and the President are the only two componants of the law making process that matter leaving citizen input out of the picture.

The government is comprise of two parts, the House of Representatives comprised of 110 deputies and the Council of the Republic totaling 56 members.

In terms of elections the Belarus Official City Website states that all elections are held for and by the people of Belarus. The Belarus website states that all people have the right to vote but since Aleksandar Lukashenko took office the elections have been fixed and completely disregard what the citizens desires.

The elections since Aleksandar Lukashenko had been nominated prove that violence against opposition parties, peaceful protestors, and human rights activists are the preferred route that the electoral process now follows.

Judicial Review
In regards to judicial review there is none. Belarus governmental authorities hold a tight grasp on what the Belarus courts do. Serious violations of the legal system are happening despite what the UN and other countries are asking Belarus to do.

The courts are manipulations of the President as seen in recent events of December. Many peaceful protestors and human rights activists were arrested and sent to trail without defense councils and condemned as the president saw fit.

Punishment
Belarus has a lack of information on the actual punishment of it's convicted criminals.

What little is mentioned is in regards to the death penalty. Belarus is the only European country at this point to still have a death penalty. Just recently this past year two prisoners were executed minutes after they were notified. A mother of one prisoner was informed of the execution a day after it happened although it might take many more months for her to get an official notification by the government.

The execution rates are hard to know for sure since a lot of them happen secretly. As far as the style for execution, the prisoners can be told minutes before they are killed and it is by a single shooter with a gun to the back of the prisoners head. Amnesty International estimates approximately 400 executions since 1991.

One journalist had been thrown in jail for 3 years for re-printing a Muhummod cartoon. The trial took place behind closed doors. Afterwards the Belarusian-Muslim community was issued an apology by the government they felt that the punishment did not correspond with the actions.

A lot of Belarusian punishments are not mentioned online most likely because of the lock-down that the government has on the people and information that comes out of the country.

Legal Personnel
Belarus uses three branches of courts. General courts, economic courts, and constitutional courts. The general courts consist of four different branches, the Supreme court of the Republic of Belarus, religious courts, MInsk City County, Regional Courts, Military Courts, and Town Courts. The economic courts consist of The Supreme Economic Court of the Republic of Belarus, the Regional Economic Courts, and the Minsk City Economic Courts. The Constitutional Courts are made up of people with two standards, people under the age 70 and people qualified to a degree level.

The actual purpose of each court is unclear. In recent events President Lukashenko was elected again by a landslide and this lead to the prosecution of opposition candidates and many other people. Each trial lasted no longer than 15 minutes a piece and it was clear that the government was pressuring the lawyers to get to these results. The government also ensured that the people who were detained did not receive any legal representation in the form of defense lawyers. The court system is comprised of puppets for the government so they can condemn and punish anyone that they want.

Law Enforcement
Belarus is a Martial Law style country. Information about the Belarusian law enforcemnt group tends to be hard to find. There are not very many mentions of the through the internet however there are mentions of what the government is providing the police force with. In the 90's there were a few training excerises that the American government helped with. These included a customs training course, a financial inverstigative course, security upgrades at the nuclear facility, and a legal reform course. In a section from the World Police Encyclopedia the law enforcement make up is comprised of the Committee for State Security, the Ministry of Interior, the Presidential Guard, the Emergency Ministry, the State Customs committee, and the Border-Security forces.

Although the information about what the Police are doing is unavailable there is some information to show what the Belarusian police are not doing. The police and justice forces are not fully complying with the minimum standards to prevent human trafficking and are currently attempting to make a positive change in that regard

Crime Rates and Public Opinion
The information on Belarus shows that theft and smaller degrees of crime are the most committed. Most recently in 2008 the crime rate had been recorded at 902.9 per capita (100,000) while the theft count broke 100,000 incidents the previous three years. For the most part these crimes are committed around tourist locations and involve some degree of discretion, utilizing dark areas. Even when it comes to crime involving cars, actual stealing of the cars is uncommon, stripping parts and vandalism is favored. A few years ago there was a 9.3% decrease in crimes of this nature as stated by President Alexander Lukashenko. Lukashenko then publicly demanded more coordination between the law enforcement agents and the General Persecutors Office.

In regards to more extreme crimes, murder is something that doesn't happen too often which has a standing crime rate of 5.6 per capita (2008). Belarus also houses a certain level of organized crime both at the local and transnational level. Regardless of this element being present there is little to no violence influenced by organized crime, including street level. As far as sexual assaults are concerned, it is a more common instance than not. It appears as though the assaults are on the decline, however, with the count of 797 in 2007 to 613 in 2008. Per capita the number decreased from 8.2 to 6.3.

Prevelent crime exists in the form of cyber-crime. Belarus has a good hold on ID theft, hacking and blackmail schemes, and purchasing merchandise with fraudulent credit cards. Visitors and tourists are cautioned to use debit/credit cards only at atms inside major banks. Although there is usually no violence towards the tourists during street atm robberies, there has been known violence in the case of resistance.

Along with cyber-crime Belarus has been looked at for money-laundering. With the known local and transnational organized crime it became of notice in 2008 when the "know-your-customer" requirement was greatly decreased from the anti-money-laundering legislation. Belarus has been very lax about investigating and persocuting money laundering situations.

After searching everywhere it appears that there are no opinions on public crime polls and statistics taking. From a UNODC Metadata report the statistics that are provided for the world survey are provided after investigations are closed.

Family Law
The constitution of Belarus states in article 32 that all citizens of Belarus are allowed to get married after they reach the legal age of consent. Both the woman and the man are allowed to chose for themselfs who they will be married to. In regards to getting married to a non-citizen of Belarus a number of different documents must be submitted from both America and Belarus. The only way that a marriage will be legally acknowledged is if the marriage takes place at a registrar's office called ZAGS (Office for matrimonal acts registration).

In the constitution there are no laws about the dissolution of marriage. In regards to inheritance the only mention found online regarded inheriting property. January 2009 brought about a new Land Code making it possible for foreigners to be able to inheret land. Before the change the property of the deceased was to be rented to the intended inheretors. The inhereted land can then be either sold to Belarus citizens and authorities or given away to anyone.

Belarus did not let a lot of information out about the rights of women in the country or their legal privilidges. A NGO by the title of HOPE is a women's rights movement that started in the 19th century. This group fights for the equality of women in the working world as well as stopping domestic violence, improving legislation and over all inclusion in the decision making processes. Looking at the situation from the outside, it appears that women have little to no rights in the country regardless of whether the law states it or not.

The person who makes the decision process is presumably the husband. The constitution states that the parents are the ones who should provide a healthy living environment, education, and well being so that the children can take care of their parents when they reach the age to do so.

Social Inequality
It appears that the government and President are only out for themselves. The heath care and hospitals are horrible. Corruption and greed in government authorities demand high prices for education and other governmental services.

Living conditions are awful and there's almost nothing that the people can do about it because of the vast control that the government has.

Human Rights
Belarus has been a concern of the United Nations as well as Amnesty International in regards to human rights. Since Aleksander Lukashenko was declared President in 1994 the importance of human rights has deteriorated.

On top of the lack of Amnesty International the election of President Lukashenko brought a crack down on social and civil rights organizations, opposing political parties and religious groups. The Amnesty International group is concerned about this country in regards to the currently active death penalty, 'disappearances', oppression of freedom of expression and right to assembly and other human rights concerns Belarus has opposed functioning NGO groups, opposing acitivists, and journalists with interest in political opposition movements

In 2007 the United Nations flat out denied Belarus a seat on the Human Rights Watch due to it's abuse of this cause .On top of blatant disregard for these basic human rights, Belarus has been in the habit of denying any cooperation with the United Nations which is another reason to give Belarus a big red light. The denial of this seat created hope that Belarus would renounce it's ways and start becoming a more constructive country.

title: Comparative law and justice/Belarus


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User talk:Lluangsouphom

 Hello Lluangsouphom, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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User talk:Wgoodkind

 Hello Wgoodkind, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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User talk:Carrie Vaz

 Hello Carrie Vaz, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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User talk:Nflstar212

 Hello Nflstar212, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:Nflstar212