OpenLLM-France/wikimedia huggingface dataset:
# New Zealand Law/Criminal/Theft
## Definition

Dishonestly, or without claim of right:
    (a) taking any property with intention to deprive an owner permanently of that property or any interest in that property;
    (b) using or dealing with property with the intention to deprived any owner of that property or any interest in that property after obtaining possession of, or control over, the property in whatever manner.

## Owner of Stolen Property

A person is regarded as the owner at the time of a theft if the person:
    (a) is in possession or control of the property
    (b) any interest in the property
    (c) the right to take possession or control of the property (ie. has a present vested right).

## Cases
### R v Crooks

* Facts
* P gave D stolen money and alcohol.
* D said he assumed stuff stolen, intended to seek legal advice.
* Held
* Criminal knowledge to same as common definition which implies certainty.
* If person but doesn’t suspect because knows answer, actual belief = knowledge.

### Dronjak v Police

* Facts
* Store clerk rung up wrong price.
* Def realised mistake.
* Held
* Obtaining by false pretences - keeping quiet was a representation.
* No theft because title passed.

### R v Wilkinson

* Facts
* Asked bank to lend money on machinery.
* Forged documents to show partnership owned machinery.
* Convicted of obtaining by false pretences but statute required thing to be capable of being stolen. The thing in this case wasn't pty but a right of demand.
* Held
    Movable means physical, does not incl intangible.

### R v Morunga

I like eggs
# PlanetPhysics/Vector Identities

It is difficult to get anywhere in physics without a firm understanding of vectors and their common operations. Here, we will give vector identities as a reference. Basic terminology to keep straight.
| {\mathbf Operation} | {\mathbf Symbol} Gradient |
| Laplacian | $\nabla ^{2}$ |
| divergence | $\nabla \cdot$ |
| curl | $\nabla \times$ |
{\mathbf Vector Magnitude
$A=\left|\mathbf {A} \right|={\sqrt {{A_{x}}^{2}+{A_{y}}^{2}+{A_{z}}^{2}}}$\\ $A={\sqrt {\mathbf {A} \cdot \mathbf {A} }}$
{\mathbf scalar product (Dot Product)}
$\mathbf {A} \cdot \mathbf {B} =A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z}$ \\ $\mathbf {A} \cdot \mathbf {B} =\left|\mathbf {A} \right|\left|\mathbf {B} \right|\cos \theta$
{\mathbf vector product (Cross Product)}
$\mathbf {A} \times \mathbf {B} =\left(A_{y}B_{z}-A_{z}B_{y}\right)\mathbf {\hat {i}} +\left(A_{z}B_{x}-A_{x}B_{z}\right)\mathbf {\hat {j}} +\left(A_{x}B_{y}-A_{y}B_{x}\right)\mathbf {\hat {k}}$
It can be easier to remember with determinant formulation
</math> \mathbf{A} \times \mathbf{B} = \left| \begin{matrix} \mathbf{\hat{i}} & \mathbf{\hat{j}} & \mathbf{\hat{k}} \\ A_x & A_y & A_z \\ B_x & B_y & B_z \end{matrix}\right| = \left ( A_y B_z - A_z B_y \right ) \mathbf{\hat{i}} + \left ( A_z B_x - A_x B_z \right ) \mathbf{\hat{j}} + \left ( A_x B_y - A_y B_x \right ) \mathbf{\hat{k}}${\mathbf { [../BACKCAB/|VectorTripleProduct]],aka.BACCAB}<math>\mathbf {A} \times \left(\mathbf {B} \times \mathbf {C} \right)=\mathbf {B} \left(\mathbf {A} \cdot \mathbf {C} \right)-\mathbf {C} \left(\mathbf {A} \cdot \mathbf {B} \right)$
{\mathbf scalar Triple Product}
$\mathbf {A} \cdot \left(\mathbf {B} \times \mathbf {C} \right)=\mathbf {B} \cdot \left(\mathbf {C} \times \mathbf {A} \right)=\mathbf {C} \cdot \left(\mathbf {A} \times \mathbf {B} \right)$
{\mathbf Gradient}
$\nabla f={\frac {\partial f}{\partial x}}\mathbf {\hat {i}} +{\frac {\partial f}{\partial y}}\mathbf {\hat {j}} +{\frac {\partial f}{\partial z}}\mathbf {\hat {k}}$
{\mathbf Gradient identities}
$\nabla \left(f+g\right)=\nabla f+\nabla g$ \\ $\nabla \left(\alpha f\right)=\alpha \nabla f$ \\ $\nabla \left(f\,g\right)=f\nabla g+g\nabla f$ \\ $\nabla \left(f/g\right)={\frac {\left(g\nabla f-f\nabla g\right)}{g^{2}}}$ \\
{\mathbf Divergence}
</math> \nabla \cdot \mathbf{A} = \frac{\partial A_x}{\partial x} + \frac{\partial A_y}{\partial y} +\frac{\partial A_z}{\partial z} ${\mathbf {D} ivergenceofthecrossproduct}<math>\nabla \cdot \left(\mathbf {A} \times \mathbf {B} \right)=\mathbf {B} \cdot \left(\nabla \times \mathbf {A} \right)-\mathbf {A} \cdot \left(\nabla \times \mathbf {B} \right)$
{\mathbf Divergence of the curl}
$\nabla \cdot \left(\nabla \times \mathbf {A} \right)=0$
{\mathbf Laplacian Identities}
$\nabla \times \left(\nabla \times \mathbf {A} \right)=\nabla \left(\nabla \cdot \mathbf {A} \right)-\nabla ^{2}\mathbf {A}$
# PlanetPhysics/Vector Functions

A vector function of position in space is a function
${\mathbf {V} }(x,y,z)$
which associates with each point $x,y,z$ in space a definite vector. The function may be broken up into its three components
${\mathbf {V} }(x,y,z)=V_{1}(x,y,z){\mathbf {\hat {i}} }+V_{2}(x,y,z){\mathbf {\hat {j}} }+V_{3}(x,y,z){\mathbf {\hat {k}} }$
Examples of vector functions are very numerous in physics. Already the function $\nabla {V}$ has occurred. At each point of space $\nabla {V}$ has in general a definite vector value. In mechanics of rigid bodies the velocity of each point of the body is a vector function of the position of the point. Fluxes of heat, electricity, magnetic force, fluids, etc., are all vector functions of position in space.
The scalar operator ${\mathbf {a} }\cdot \nabla$ may be applied to a vector function ${\mathbf {V} }$ to yield another vector function.
Let
${\mathbf {V} }=V_{1}(x,y,z){\mathbf {\hat {i}} }+V_{2}(x,y,z){\mathbf {\hat {j}} }+V_{3}(x,y,z){\mathbf {\hat {k}} }$
and
${\mathbf {a} }=a_{1}{\mathbf {\hat {i}} }+a_{2}{\mathbf {\hat {j}} }+a_{3}{\mathbf {\hat {k}} }$
Then
${\mathbf {a} }\cdot \nabla =a_{1}{\frac {\partial }{\partial x}}+a_{2}{\frac {\partial }{\partial y}}+a_{3}{\frac {\partial }{\partial z}}$
$\left({\mathbf {a} }\cdot \nabla \right){\mathbf {V} }=\left({\mathbf {a} }\cdot \nabla \right)V_{1}{\mathbf {\hat {i}} }+\left({\mathbf {a} }\cdot \nabla \right)V_{2}{\mathbf {\hat {j}} }+\left({\mathbf {a} }\cdot \nabla \right)V_{3}{\mathbf {\hat {k}} }$
and
$\left({\mathbf {a} }\cdot \nabla \right){\mathbf {V} }=\left(a_{1}{\frac {\partial V_{1}}{\partial x}}+a_{2}{\frac {\partial V_{1}}{\partial y}}+a_{3}{\frac {\partial V_{1}}{\partial z}}\right){\mathbf {\hat {i}} }+\left(a_{1}{\frac {\partial V_{2}}{\partial x}}+a_{2}{\frac {\partial V_{2}}{\partial y}}+a_{3}{\frac {\partial V_{2}}{\partial z}}\right){\mathbf {\hat {j}} }+\left(a_{1}{\frac {\partial V_{3}}{\partial x}}+a_{2}{\frac {\partial V_{3}}{\partial y}}+a_{3}{\frac {\partial V_{3}}{\partial z}}\right){\mathbf {\hat {k}} }$
more to come..
This is from the public domain text by Gibbs.
# PlanetPhysics/Variable Network Topology

A variable network topology is defined by an indexed family or class of networks of one-dimensional $CW$-complexes $[CW_{i}]$ with $i\in I$ in the category Top of topological spaces with additional homology (or cohomology) axioms, rules, or properties of the underlying $CW$-complexes, that specify the transformation maps as a sequence of homotopoy maps.
# PlanetPhysics/Variable Category

A variable category is defined as an indexed family or class of either categories and, or functor categories Failed to parse (unknown function "\G"): {\displaystyle [\G_i]} with $i\in I$ in the functor category Failed to parse (unknown function "\F"): {\displaystyle \F_{ct}} of categories and functors with additional axioms, rules, or properties of the underlying categories, that specify for example how such categories can be 'freely generated'.
# PlanetPhysics/Variable Groupoid

A variable groupoid is defined as a family of groupoids $\{{\mathsf {G}}_{\lambda }\}$ indexed by a parameter $\lambda \in T$ , with $T$ being either an index set or a class (which may be a time parameter, for time-dependent or \htmladdnormallink{dynamic {http://planetphysics.us/encyclopedia/NewtonianMechanics.html} groupoids}). If $\lambda$ belongs to a set $M$, then we may consider simply a projection Failed to parse (unknown function "\lra"): {\displaystyle \mathsf{G} \times M \lra M} , which is an example of a trivial fibration. More generally, one can consider a fibration of groupoids Failed to parse (unknown function "\lra"): {\displaystyle \mathsf{G} \hookrightarrow Z \lra M} (Higgins and Mackenzie, 1990) as defining a non-trivial variable groupoid .
Remarks An indexed family or class of topological groupoids Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle [\grp_i]} with $i\in I$ in the category Grpd of groupoids with additional axioms, rules, or properties of the underlying topological groupoids, that specify an indexed family of topological groupoid homomorphisms for each variable groupoid structure.
Besides systems modelled in terms of a fibration of groupoids , one may consider a multiple groupoid defined as a set of $N$ groupoid structures, any distinct pair of which satisfy an {\it interchange law} which can be formulated as follows. There exists a unique expression with the following content:
   Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle \begin{bmatrix} x&y \\z&w \end{bmatrix}\quad \directs{j}{i}, }
where $i$ and $j$ must be distinct for this concept to be well defined. This uniqueness can also be represented by the equation
   $(x\circ _{j}y)\circ _{i}(z\circ _{j}w)=(x\circ _{i}z)\circ _{j}(y\circ _{i}w).$
Remarks This illustrates the principle that a 2-dimensional formula may be more comprehensible than a linear one.
Brown and Higgins, 1981a, showed that certain multiple groupoids equipped with an extra structure called connections were equivalent to another structure called a crossed complex which had already occurred in homotopy theory. such as double, or multiple groupoids (Brown, 2004; 2005). For example, the notion of an atlas of structures should, in principle, apply to a lot of interesting, topological and/or algebraic, structures: groupoids, multiple groupoids, Heyting algebras, $n$-valued logic algebras and $C^{*}$-convolution -algebras. Such examples occur frequently in higher dimensional algebra (HDA).
# PlanetPhysics/Vector Potential

Let\, ${\vec {U}}={\vec {U}}(x,\,y,\,z)$\, be a vector field in $\mathbb {R} ^{3}$ with continuous partial derivatives.\, Then the following three conditions are equivalent:
* The surface integrals of ${\vec {U}}$ over all contractible closed surfaces $S$ vanish: $\oint _{S}{\vec {U}}\cdot d{\vec {S}}=0$
* The divergence of ${\vec {U}}$ vanishes everywhere in the field: $\nabla \!\cdot \!{\vec {U}}=0$
* There exists the vector potential \, ${\vec {A}}={\vec {A}}(x,\,y,\,z)$\, of ${\vec {U}}$: $\nabla \!\times \!{\vec {A}}={\vec {U}}$
Under those conditions, the vector field ${\vec {U}}$ is called solenoidal .
# Nonlinear finite elements/Buckling of beams
## Nonlinear post-buckling

* Buckling of beams.

## Newton-Raphson

Standard Newton-Raphon methods perform poorly for bucking problems.
* Predicting buckling with Newton_Raphson.

## Arc length method

* Also called Modified Riks Method.
* Control the size of the load step using a parameter $\lambda$.
* Solve for both $\lambda$ and $\Delta u$ in each Newton iteration.
Assume $F$ = independent of geometry. Then
    $F=\lambda ~{\bar {F}}$
$\lambda$ can be thought of as a normalized load parameter.
    ${\text{Residual}}~=r(u,\lambda )=K(u)~u-\lambda ~{\bar {F}}$
* Arc-length method
The load increment is computed using
    $\lambda =\pm {\sqrt {\Delta s^{2}-\Delta u_{n}^{2}}}$
The reference arc length
    $\Delta s_{0}={\cfrac {F}{n_{\text{loadstep}}}}$
# Nonlinear finite elements/Bubnov Galerkin method
## (Bubnov)-Galerkin Method for Problem 2

The Bubnov-Galerkin method is the most widely used weighted average method. This method is the basis of most finite element methods.
The finite-dimensional Galerkin form of the problem statement of our second order ODE is :
Since the basis functions ($N_{i}$) are known and linearly independent, the approximate solution $u_{h}$ is completely determined once the constants ($a_{i}$) are known.
The Galerkin method provides a great way of constructing solutions. But the question is: how do we choose $N_{i}$ so that these functions are not only linearly independent but arbitrary? Since the solution is expressed as a sum of these functions, the accuracy of our result depends strongly on the choice of $N_{i}$.
Let the trial solution take the form,
    $u_{h}(x)=\sum _{i=1}^{n}a_{i}N_{i}(x)~.$
According to the Bubnov-Galerkin approach, the weighting function also takes a similar form
    $w_{h}(x)=\sum _{j=1}^{n}b_{j}N_{j}(x)~.$
Plug these values into the weak form to get
    $\int _{0}^{1}\left[\left(\sum _{i=1}^{n}a_{i}{\cfrac {dN_{i}}{dx}}\right)\left(\sum _{j=1}^{n}b_{j}{\cfrac {dN_{j}}{dx}}\right)+\left(\sum _{i=1}^{n}a_{i}N_{i}\right)\left(\sum _{j=1}^{n}b_{j}N_{j}\right)-x\left(\sum _{j=1}^{n}b_{j}N_{j}\right)\right]~dx=0$
or
    $\int _{0}^{1}\left[\sum _{j=1}^{n}b_{j}\left({\cfrac {dN_{j}}{dx}}\sum _{i=1}^{n}a_{i}{\cfrac {dN_{i}}{dx}}+N_{j}\sum _{i=1}^{n}a_{i}N_{i}-x~N_{j}\right)\right]~dx=0$
or
    $\int _{0}^{1}\left[\sum _{j=1}^{n}b_{j}\left(\sum _{i=1}^{n}\left(a_{i}{\cfrac {dN_{j}}{dx}}{\cfrac {dN_{i}}{dx}}+a_{i}N_{j}N_{i}\right)-x~N_{j}\right)\right]~dx=0~.$
Taking the sums and constants outside the integrals and rearranging, we get
    $\sum _{j=1}^{n}b_{j}\left[\sum _{i=1}^{n}a_{i}\int _{0}^{1}\left({\cfrac {dN_{i}}{dx}}{\cfrac {dN_{j}}{dx}}+N_{i}N_{j}\right)~dx-\int _{0}^{1}x~N_{j}~dx\right]=0~.$
Since the $b_{j}$s are arbitrary, the quantity inside the square brackets must be zero. That is
    ${\text{(21)}}\qquad {\sum _{i=1}^{n}a_{i}\int _{0}^{1}\left({\cfrac {dN_{i}}{dx}}{\cfrac {dN_{j}}{dx}}+N_{i}N_{j}\right)~dx-\int _{0}^{1}x~N_{j}~dx=0\qquad j=1\dots n~.}$
Let us define
    ${\text{(22)}}\qquad {K_{ji}:=\int _{0}^{1}\left({\cfrac {dN_{i}}{dx}}{\cfrac {dN_{j}}{dx}}+N_{i}N_{j}\right)~dx\qquad {\text{and}}\qquad f_{j}:=\int _{0}^{1}x~N_{j}~dx~.}$
Then we get a set of simultaneous linear equations
    ${\text{(23)}}\qquad {\sum _{i=1}^{n}K_{ji}a_{i}=f_{j}~.}$
In matrix form,
    ${\mathbf {K} \mathbf {a} =\mathbf {f} ~.}$
# Nonlinear finite elements/Axially loaded bar
## An axially loaded bar

Let us consider the simplest solid mechanics problem that we can think of - the axial loading of a bar (see Figure 1).
* Figure 1. Axial loading of a bar.
Given:
The bar is of length $L\,$ and has an area of cross-section $A\,$. The Young's modulus of the material is $E\,$.
Find:
We want to find the stresses and deformations in the bar due to the concentrated axial load $\mathbf {R}$ at the end.
Assumptions:
* The cross-section of the bar does not change after loading.
* The material is linear elastic, isotropic, and homogeneous.
* The load is centric.
* End-effects are not of interest to us.

### Strength of Materials Approach

From the free-body diagram of the bar, a balance of forces gives
    $\mathbf {f} _{\text{wall}}=\mathbf {R} =\mathbf {f} (\mathbf {x} )~.$
The stress in the bar is given by
    ${\boldsymbol {\sigma }}(\mathbf {x} ):={\cfrac {\mathbf {f} (\mathbf {x} )}{A}}\qquad \implies \qquad {{\boldsymbol {\sigma }}(\mathbf {x} )={\cfrac {\mathbf {R} }{A}}}~.$
The constitutive model for the bar is given by Hooke's law (${\boldsymbol {\sigma }}=E{\boldsymbol {\varepsilon }}$). Therefore, the strain in the bar is
    ${\boldsymbol {\varepsilon }}(\mathbf {x} )={\cfrac {{\boldsymbol {\sigma }}(\mathbf {x} )}{E}}\qquad \implies \qquad {{\boldsymbol {\varepsilon }}(\mathbf {x} )={\cfrac {\mathbf {R} }{AE}}}~.$
To get the deformation of the bar, we use the strain-displacement relations
    ${\boldsymbol {\varepsilon }}:={\cfrac {\Delta l}{l}}={\cfrac {\delta _{(\mathbf {x} =L)}}{L}}\qquad \implies \qquad {\delta _{(\mathbf {x} =L)}={\cfrac {\mathbf {R} L}{AE}}}~.$
We can get the deformation of any point in the bar in a similar manner:
    ${\boldsymbol {\varepsilon }}(\mathbf {x} )={\cfrac {\delta (\mathbf {x} )}{\mathbf {x} }}\qquad \implies \qquad {\delta (\mathbf {x} )={\cfrac {\mathbf {R} \mathbf {x} }{AE}}}~.$

## A more complicated axial load

Now, suppose that we have a linear distributed axial load $\mathbf {q} (\mathbf {x} )=a\mathbf {x}$ in addition to the load $\mathbf {R}$ (see Figure 2(a)). This load has units of force per unit length and is also called a body load. Examples are gravity and inertial forces due to rotation around the $y$ axis.
* Figure 2(a). Distributed axial load
* Figure 2(b). Free body diagram for distributed axial load
Once again, we want to calculate stresses and displacements. Note that stresses are no longer constant along the length of the bar.

### Strength of Materials Approach

From the free body diagram of the bar, a balance of forces gives
    $\mathbf {f} _{\text{wall}}=\mathbf {R} +\int _{0}^{L}\mathbf {q} (\mathbf {x} )~dx\qquad \implies \qquad {\mathbf {f} _{\text{wall}}=\mathbf {R} +{\cfrac {aL^{2}}{2}}}~.$
So we know the reaction force at the wall. But we want to know the stress and displacement at any point along the bar.
To do this, we can make a cut at any point along the length and use the free body diagram to compute a reaction force $\mathbf {f} (\mathbf {x} )$ (see Figure 2(b)). But this is tedious since we have to repeat the process for every point in the bar.
# Nonlinear finite elements/Balance of mass
## Statement of the balance of mass

The balance of mass can be expressed as:
where $\rho (\mathbf {x} ,t)$ is the current mass density, ${\dot {\rho }}$ is the material time derivative of $\rho$, and $\mathbf {v} (\mathbf {x} ,t)$ is the velocity of physical particles in the body $\Omega$ bounded by the surface $\partial {\Omega }$.

## Proof

We can show how this relation is derived by recalling that the general equation for the balance of a physical quantity $f(\mathbf {x} ,t)$ is given by
    ${\cfrac {d}{dt}}\left[\int _{\Omega }f(\mathbf {x} ,t)~{\text{dV}}\right]=\int _{\partial {\Omega }}f(\mathbf {x} ,t)[u_{n}(\mathbf {x} ,t)-\mathbf {v} (\mathbf {x} ,t)\cdot \mathbf {n} (\mathbf {x} ,t)]~{\text{dA}}+\int _{\partial {\Omega }}g(\mathbf {x} ,t)~{\text{dA}}+\int _{\Omega }h(\mathbf {x} ,t)~{\text{dV}}~.$
To derive the equation for the balance of mass, we assume that the physical quantity of interest is the mass density $\rho (\mathbf {x} ,t)$. Since mass is neither created or destroyed, the surface and interior sources are zero, i.e., $g(\mathbf {x} ,t)=h(\mathbf {x} ,t)=0$. Therefore, we have
    ${\cfrac {d}{dt}}\left[\int _{\Omega }\rho (\mathbf {x} ,t)~{\text{dV}}\right]=\int _{\partial {\Omega }}\rho (\mathbf {x} ,t)[u_{n}(\mathbf {x} ,t)-\mathbf {v} (\mathbf {x} ,t)\cdot \mathbf {n} (\mathbf {x} ,t)]~{\text{dA}}~.$
Let us assume that the volume $\Omega$ is a control volume (i.e., it does not change with time). Then the surface $\partial {\Omega }$ has a zero velocity ($u_{n}=0$) and we get
    $\int _{\Omega }{\frac {\partial \rho }{\partial t}}~{\text{dV}}=-\int _{\partial {\Omega }}\rho ~(\mathbf {v} \cdot \mathbf {n} )~{\text{dA}}~.$
Using the divergence theorem
    $\int _{\Omega }{\boldsymbol {\nabla }}\bullet \mathbf {v} ~{\text{dV}}=\int _{\partial {\Omega }}\mathbf {v} \cdot \mathbf {n} ~{\text{dA}}$
we get
    $\int _{\Omega }{\frac {\partial \rho }{\partial t}}~{\text{dV}}=-\int _{\Omega }{\boldsymbol {\nabla }}\bullet (\rho ~\mathbf {v} )~{\text{dV}}.$
or,
    $\int _{\Omega }\left[{\frac {\partial \rho }{\partial t}}+{\boldsymbol {\nabla }}\bullet (\rho ~\mathbf {v} )\right]~{\text{dV}}=0~.$
Since $\Omega$ is arbitrary, we must have
    ${\frac {\partial \rho }{\partial t}}+{\boldsymbol {\nabla }}\bullet (\rho ~\mathbf {v} )=0~.$
Using the identity
    ${\boldsymbol {\nabla }}\bullet (\varphi ~\mathbf {v} )=\varphi ~{\boldsymbol {\nabla }}\bullet \mathbf {v} +{\boldsymbol {\nabla }}\varphi \cdot \mathbf {v}$
we have
    ${\frac {\partial \rho }{\partial t}}+\rho ~{\boldsymbol {\nabla }}\bullet \mathbf {v} +{\boldsymbol {\nabla }}\rho \cdot \mathbf {v} =0~.$
Now, the material time derivative of $\rho$ is defined as
    ${\dot {\rho }}={\frac {\partial \rho }{\partial t}}+{\boldsymbol {\nabla }}\rho \cdot \mathbf {v} ~.$
Therefore,
    ${{\dot {\rho }}+\rho ~{\boldsymbol {\nabla }}\bullet \mathbf {v} =0~.}$
# OpenMP programming in plain view
## Introduction

* Overview (pdf)
* Functions (pdf)
* Directives (pdf)
* Environment Variables (pdf)
* Clause (pdf)
* Synchronization (pdf)

## Parallel Constructs and Clauses

* 1. Parallel Construct (pdf)
* 2. Parallelize Loop Construct (pdf)
* 3. Collapse clause (pdf)
* 4. Private clauses (pdf)
* 5. Reduction Clause (pdf)
* 6. Task construct (pdf)
* 7. Taskloop construct (pdf)
* 8. Taskgroup construct (pdf)
* 9. Sections Construct (pdf)
* 10. Critical Construct (pdf)
* 11. Atomic Construct (pdf)
* 12. Flush Construct
* 13. Ordered Construct
* 14. Single construct (pdf)
* 15. SIMD construct
* 16. Barrier

## Example Codes

* Hello (pdf)
* Loop (pdf)
* Task

## Computing Parallel Prefix Sum

* OpenMP (pdf)
* CUDA (pdf)
go to [ Electrical_&_Computer_Engineering_Studies ]
# OpenSCAD Designs

Wikibooks: OpenSCAD User Manual

## Doughnut shape

rotate_extrude(convexity=10,$fn=100)
translate([2,0,0])
circle(r=1,$fn=100);

## Sample Bridge

difference {
cube(size =[12,21,2],center=true);
translate ([0,0,1])
cube(size =[10,21,2],center=true);
union{
translate ([4.5,9,-3.5])
cylinder(h=5, r=1, center=true, $fn=100);
translate ([-4.5,9,-3.5])
cylinder(h=5, r=1, center=true, $fn=100);
translate ([-5.5,9,-2])
rotate ([90,0,90]) cylinder (r=1, h=11,$fn=100);
union{
translate ([4.5,-9,-3.5])
cylinder(h=5, r=1, center=true, $fn=100);
translate ([-4.5,-9,-3.5])
cylinder(h=5, r=1, center=true, $fn=100);
translate ([-5.5,-9,-2])
rotate ([90,0,90]) cylinder (r=1, h=11,$fn=100);
# OpenNMS

OpenNMS Wireshark is a free and open source network monitoring and network management platform. These activities will show you how to use OpenNMS to monitor and manage a network.

## Readings

* Wikipedia: OpenNMS

## Activities

* Use OpenNMS to monitor a network.
# OpenSSH/Configure OpenSSH to allow Public-key authentication

Create file touch ~/.ssh/authorized_keys and add public key of client to provide access.
Limit connecting host and command: It is also possible also to lock access to only be able to run a specific command, or use it only from a specific host. See man ssh.
Example syntax::cat ~/.ssh/authorized_keys
    from="10.22.33.45",command="/path/to/executable argument" ssh-rsa key name
# OpenKollab/tent

This is tent by tav from http://github.com/tav/scripts/blob/master/tentbot.py

## Top matter

Python - Here's the setup:
So we see that tent is some sort of IRC bot $_{Bots}$ written in python

## Setting up classes

Hmmm. classes..
# OpenNMS/Demo

OpenNMS Wireshark is a free and open source network monitoring and network management platform. These activities will show you how to use the OpenNMS Demo web site to monitor a network.

## Preparation

To prepare for this activity:
* Start Windows.
* Log in if necessary.

## Activity 1 - Access the OpenNMS Demo Web Site

To access the OpenNMS web site:
* Open a web browser.
* Navigate to http://www.opennms.org.
* Select Live Demo or See a Live Demo.
* Follow the instructions to log in to the demo web site.

## Activity 2 - Use OpenNMS to Monitor a Network

To use OpenNMS to monitor a network:
* Observe the OpenNMS Home page and network availability.
* Select Node List to view the network nodes currently being monitored.
* Select one of the nodes on the list to view detailed information about that node.
* Select Outages and then Current Outages or All Outages to view outage information.
* Select Path Outages to view network path outages.
* Select Events and then All Events to view event information.
* Select Assets and then All nodes with asset info to view asset information.
* Select Charts to view a chart summary of monitoring information.
* Select Support and then the OpenNMS.com support page for information on how OpenNMS is supported.
* Close the web browser to complete this activity.
# Real numbers/Convergence/Root of it/Exercise

Let $x_{n}\in \mathbb {R} _{\geq 0}$ be a convergent sequence with limit $x$. Show that the sequence ${\sqrt {x_{n}}}$ converges to ${\sqrt {x}}$.