OpenLLM-France/wikimedia huggingface dataset:
# Web Design/Create a simple mark-up language document to specification

This unit defines the competency required to design, create and save a simple mark-up language document to a given specification using a text editor rather than an authoring tool.
This competency can be viewed directly on the training.gov.au website:
The competency is outlined here together with ideas for demonstrating your competence as well as related modules where you can learn more skills relevant to this unit.

## Performance Criteria

Realistically, this unit is best undertaken together with ICAB4171A Develop cascading style sheets as some of the performance criteria below (regarding document formatting and positioning) are ideally achieved with Cascading Style Sheets. Together these two units form a good grounding for ICAB4137A Produce basic client side script for dynamic web pages.
The following performance criteria come from the National unit of competency.

## Elements
### Analyse specification

* Determine the uses and audience of the document
* Determine the appropriate mark-up language based on the document uses and audience
* Determine relevant document structure
* Determine appropriate browser-safe colours

### Create document structure to specification

* Create and assign the basic elements of the document, taking into account accessibility
* Add content text to the body of the document
* Save document using a descriptive name and an appropriate extension

### Format document to specification

* Apply a suitable format for the text
* Apply a suitable background colour
* Apply suitable positional elements
* Create lists

### Create tables, hyperlinks and graphics

* Create tables
* Create hyperlinks, anchors and image maps for internal and external navigation
* Define the colours for unvisited, visited and active links
* Create hyperlinks for sending email
* Attach images in a suitable format

### Validate documents

* Validate mark-up language document against specifications and record outcomes
* Validate mark-up language document in different browsers for compatibility and record outcomes

## Ideas for demonstrating competence

* A Small Website Project - A small website project (with some advanced options) will provide an opportunity to demonstrate most, if not all of the outcomes for this unit of competence.
* Other ideas? Edit and add your own ideas for demonstrating competence in this unit!

## Related Modules

* Learning Basic HTML and CSS
* Intermediate HTML and CSS

## External Links

ICAB4135B on NTISthis
# Web Design/Comments

Having conversations through comments is more convenient, if comment replies are structured as a subsidiary of a parent comment.
It is also strongly recommended to make comments referable through the URL.

## Case studies
### Twitter, Reddit

Ever since, Twitter and Reddit supported both structured threads and direct comment linking.

### Instagram

From its creation in 2010 to 2016-12-06, Instagram comments were sorted purely chronological.
There was a support for pinging user using the “@” sign, but no support for threaded, structured replies.
Additionally, as of 2019-10-12, there is still no way to refer to a specific comment using a comment Web Design/IDs in the URL.

### YouTube

YouTube comments have undergone many incremental technical changes over the years[which?], including AJAX comment loading instead of HTML preclusion, changes related to Google Plus, comment structung, comment ID formats and mentioning users, including distinctions from the new “Polymer” website layout/design and the legacy website layout that is accessible throuh the “disable_polymer=1” or “disable_polymer=true” URL parameter.
When YouTube introduced direct comment linking and comment searching circa 2010 or 2011, it was possible to link to comments by using only the comment ID in the video URL. Now, the parent video ID is also required.
The direct comment URL can be retreived by copying the hyperlink on the relative posting time indicator (e.g. 3 months ago)-
# Web Design/Contribute to personal skill development and learning

Web Design → Contribute to personal skill development and learning
This page is part of the Web Design project. :
This unit covers the skills and knowledge required to support own learning and skill development needs in the context of an organisation's goals and objectives.
This competency can be viewed directly on the Australian National Training Information Service website:
The competency is outlined here together with ideas for demonstrating your competence as well as related modules where you can learn more skills relevant to this unit.

## Performance Criteria

* Identify own learning needs for skill development
** Personal learning needs and skill gaps are self assessed
** Advice on learning needs is provided to relevant personnel
** Opportunities for undertaking personal skill development activities are identified and planned in liaison with work groups and relevant personnel
* Undertake personal skill development
** Appropriate opportunities provided by the workplace are identified
** Opportunities are identified to use appropriate new skills in workplace activities
** Coaching / mentoring advice is followed through in work activities
* Monitor learning effectiveness
** Feedback from individuals or colleagues is used to identify future learning opportunities
** Where a final assessment process is carried out, the outcomes are reviewed and further learning needs are identified.
** Suggestions for improving learning opportunities and assessment processes are provided to appropriate personnel

## Related Web Design Modules

* Using the Internet as a Learning Tool
# Units/Astronomy/Quiz

Units astronomy is a lecture that may be included in courses like principles of radiation astronomy. It is focused on units used to describe astronomical entities, sources, or objects, and astronomical equipment.
You are free to take this quiz at any time.
Once you’ve read and studied the lecture itself, the links contained within the lecture and listed under See also, External links, you should have adequate background to to get 100 %. The template {{radiation astronomy resources}} may also help with background knowledge.
Suggestion: Have the lecture available in a separate window.
Enjoy learning by doing!

## Hypotheses

* Units used in astronomy may have changed greatly since its beginnings.
# Vector space/Isomorphic iff equal dimension/Fact

Let $K$ denote a field and let $V$ and $W$ denote finite-dimensional $K$-vector spaces.
$V$ and $W$ are isomorphic to each other if and only if their dimension
In particular, an $n$-dimensional $K$-vector space is isomorphic to $K^{n}$.
# Vector space/Linear independence/Introduction/Section
## Definition

Let $K$ be a field, and let $V$ be a $K$-vector space. A family of vectors $v_{i}$, $i\in I$, (where $I$ denotes a finite index set) is called linearly independent, if an equation of the form
    $\sum _{i\in I}s_{i}v_{i}=0{\text{ with }}s_{i}\in K$
is only possible when $s_{i}=0$
$i$
If a family is not linear independent, then it is called linearly dependent. A linear combination $\sum _{i\in I}s_{i}v_{i}=0$ is called a representation of the null vector. It is called the trivial representation, if all coefficients $s_{i}$ equal $0$, and, if at least one coefficient is not $0$, a nontrivial representation of the null vector. A family of vectors is linearly independent, if and only if one can represent with it the null vector only in the trivial way. This is equivalent with the property that no vector of the family can be expressed as a linear combination by the others.

## Example

The standard vectors in $K^{n}$ are linearly independent. A representation
    $\sum _{i=1}^{n}s_{i}e_{i}=0\,$
just means
    $s_{1}{\begin{pmatrix}1\\0\\\vdots \\0\end{pmatrix}}+s_{2}{\begin{pmatrix}0\\1\\\vdots \\0\end{pmatrix}}+\cdots +s_{n}{\begin{pmatrix}0\\0\\\vdots \\1\end{pmatrix}}={\begin{pmatrix}0\\0\\\vdots \\0\end{pmatrix}}\,.$
The $i$-th row yields directly $s_{i}=0$.

## Example

The three vectors
    ${\begin{pmatrix}3\\3\\3\end{pmatrix}},\,\,{\begin{pmatrix}0\\4\\5\end{pmatrix}}\,{\text{ and }}\,{\begin{pmatrix}4\\8\\9\end{pmatrix}}$
are linearly dependent. The equation
    $4{\begin{pmatrix}3\\3\\3\end{pmatrix}}+3{\begin{pmatrix}0\\4\\5\end{pmatrix}}-3{\begin{pmatrix}4\\8\\9\end{pmatrix}}={\begin{pmatrix}0\\0\\0\end{pmatrix}}\,$
is a nontrivial representation of the null vector.

## Lemma

Let $K$ be a field, let $V$ be a $K$-vector space, and let $v_{i}$, $i\in I$,
$V$
* If the family is linearly independent, then for each subset $J\subseteq I$, also the family $v_{i}$ , $i\in J$, is linearly independent.
* The empty family is linearly independent.
* If the family contains the null vector, then it is not linearly independent.
* If a vector appears several times in the family, then the family is not linearly independent.
* A single vector $v$ is linearly independent if and only if $v\neq 0$.
* Two vectors $v$ and $u$ are linearly independent if and only if $u$ is not a scalar multiple of $v$ and vice versa.

### Proof

$\Box$

## Remark

The vectors $v_{1}={\begin{pmatrix}a_{11}\\\vdots \\a_{m1}\end{pmatrix}},\ldots ,v_{n}={\begin{pmatrix}a_{1n}\\\vdots \\a_{mn}\end{pmatrix}}\in K^{m}$ are linearly dependent, if and only if the homogeneous linear system
    ${\begin{matrix}a_{11}x_{1}+a_{12}x_{2}+\cdots +a_{1n}x_{n}&=&0\\a_{21}x_{1}+a_{22}x_{2}+\cdots +a_{2n}x_{n}&=&0\\\vdots &\vdots &\vdots \\a_{m1}x_{1}+a_{m2}x_{2}+\cdots +a_{mn}x_{n}&=&0\end{matrix}}$
has a nontrivial solution.
# Vector space/Introductory example/Mulled wine/Example/Exercise

Does there exist a solution $(a,b,c)\in \mathbb {Q} ^{3}$ for the system of linear equations
    $a{\begin{pmatrix}1\\2\\11\\2\end{pmatrix}}+b{\begin{pmatrix}2\\2\\12\\3\end{pmatrix}}+c{\begin{pmatrix}3\\1\\20\\7\end{pmatrix}}={\begin{pmatrix}1\\2\\20\\5\end{pmatrix}}\,$
from example?
# Vector space/Linear combination/Definition

Let $K$ be a field, and let $V$ be a $K$-vector space. Let $v_{1},\ldots ,v_{n}$ denote a family of vectors in $V$. Then the vector
    $s_{1}v_{1}+s_{2}v_{2}+\cdots +s_{n}v_{n}{\text{ with }}s_{i}\in K$
is called a linear combination of this vectors (for the coefficient tuple $(s_{1},\ldots ,s_{n})$).
# PlanetPhysics/Efimov States
## Efimov states

The Efimov states were initially proposed in 1970 as hypothetical, stable quantum states of coupled three-body systems such as three coupled bosons in ultracold `gedanken experiments'. A most interesting feature of such ultracold 3-boson systems was the presence of an infinite number of Efimov states when the boson coupling was weak but finite when the coupling became strong.
Subsequently, in 2006, there have been published claims of experiments indicating the presence of such "Efimov trimers".(See also the following references.)
# PlanetPhysics/Double Groupoid With Connection
### Introduction: Geometrically defined double groupoid with connection

In the setting of a geometrically defined double groupoid with connection, as in, (resp.), there is an appropriate notion of geometrically thin square. It was proven in, (theorem 5.2 (resp., proposition 4)), that in the cases there specified geometrically and algebraically \htmladdnormallink{thin squares {http://planetphysics.us/encyclopedia/Tree.html} coincide}.

### Basic definitions

A map $\Phi :|K|\longrightarrow |L|$ where $K$ and $L$ are (finite) simplicial complexes is PWL ({\it piecewise linear}) if there exist subdivisions of $K$ and $L$ relative to which $\Phi$ is simplicial.

### Remarks

We briefly recall here the related concepts involved: A square $u:I^{2}\longrightarrow X$ in a topological space $X$ is thin if there is a factorisation of $u$, $u:I^{2}{\stackrel {\Phi _{u}}{\longrightarrow }}J_{u}{\stackrel {p_{u}}{\longrightarrow }}X,$ where $J_{u}$ is a tree and $\Phi _{u}$ is piecewise linear (PWL, as defined next) on the boundary $\partial {I}^{2}$ of $I^{2}$.
A {\it tree}, is defined here as the underlying space $|K|$ of a finite $1$-connected $1$-dimensional simplicial complex $K$ boundary $\partial {I}^{2}$ of $I^{2}$.
# PlanetPhysics/Electric Charge

Electric charge is a property of the fundamental particles of the Universe. This property is easily observed and was known as far back as the ancient Greeks.
Petting a cat in a dry environment is an easy and fun way to test it out. If the conditions are correct after one full stroke you can deliver a small shock to the cat and as you continue to PET, it is easily reproduced. Lightning is another example that exists due to electric charge.
Although a lot of qualitative properties and experiments were done, it took the French Physicist Coulomb in the late 1700s to make the first quantitative measurements involving electric charge and he was able to come up with Coulomb's law showing the relationship between force and the distance between the charges.
Another great leap forward was provided by the American physicist Robert Millikan who in 1909 was the first person to measure the charge of the electron.
There are two types of charge observed
Positive Charge \newline Negative Charge \newline
An important property is that like charges repel and opposites attract.
# PlanetPhysics/Fourier Stieltjes Algebra of a Groupoid 2

The Fourier-Stieltjes algebra of a groupoid, $G_{l}$ . In ref.), A.L.T. Paterson defined the Fourier-Stieltjes algebra of a groupoid , $G_{l}$, as the space of coefficients $\phi =(\xi ,\eta )$, where $\xi ,\eta$ are $L^{\infty }$-sections for some measurable $G_{l}$ -Hilbert bundle $(\mu ,\Re ,L)$. Thus, for $x\in G_{l}$,
   $\phi (x)=L(x)\xi (s(x),\eta (r(x))).$
Therefore, $\phi$ belongs to $L^{\infty }{G_{l}}=L^{\infty }({G_{l}},\nu )$.
# PlanetPhysics/Free Encyclopedia From PM Books
## Free Encyclopedia in PM books

A Free Encyclopedia of PlanetMath entries up to 2006 is now available in P.D.F format for free downloads for private use in the books section of PlanetPhysics.org. The 2,000 page or 78 Mb P.D.F file contains useful mathematical and mathematical physics concepts generated at PM until the end of 2005; the one volume book has been edited by three PM editors and was enhanced with graphics, and also has available for downloads both the TEX and FEM files. Many of the concepts and other material presented in this Free Encyclopedia is also useful for physical and Computational Physics applications at PlanetPhysics.org, and elsewhere, in fields such as engineering and the industry. The two volume version, now also available in the book section of PlanetPhysics.org website, specifies the names of all PM contributors as well as those of the three Free Encyclopedia book editors who have generated and also copyrighted the two volumes under the GNUL terms. More than 300 entries have also been transferred to Wikipedia under the GNUL terms and the Wikipedia exchange project with PM.
A similar document, or Big Book could also be generated from the current contents of the PlanetPhysics.org Encyclopedia section of about 40 Mb, and additional books of documents totaling over 2 Gb could be "automatically" computer-generated from the Books, Papers and Exposition sections of PlanetPhysics.org. The Free Physics Encyclopedia alone is expected to run at over 1,000 pages based on the current contents of May 20, 2009.
# PlanetPhysics/Fully Faithful Functor 2

\newcommand{\sqdiagram}[9]{Failed to parse (unknown function "\diagram"): {\displaystyle \diagram #1 \rto^{#2} \dto_{#4}& \eqno{\mbox{#9}}} }
let $F:{\mathcal {A}}\to {\mathcal {B}}$ be a functor. $F$ is said to be a fully faithful functor if it is an isomorphism on every set $Hom(-,-)$ of morphisms, and that it is essentially surjective if for every object $X\in {\mathcal {B}}$, there is some $Y\in {\mathcal {A}}$ such that $X$ and $F(Y)$ are isomorphic.
# PlanetPhysics/Fresnel integrals

For any real value of the argument $x$, the Fresnel integrals $C(x)$ and $S(x)$ are defined as the integrals:
    $C(x)\;=\;\int _{0}^{x}\cos {t^{2}}\,dt,$ and
    $S(x)\;=\;\int _{0}^{x}\sin {t^{2}}\,dt.$

## The functions C and S

In optics, both of them express the intensity of diffracted light behind an illuminated edge.
Using the Taylor series expansions of cosine and sine, we get easily the expansions of the functions:
$C(z)\,=\,{\frac {z}{1}}\!-\!{\frac {z^{5}}{5\!\cdot \!2!}}\!+\!{\frac {z^{9}}{9\!\cdot \!4!}}\!-\!{\frac {z^{13}}{13\!\cdot \!6!}}\!+\!-\ldots$
$S(z)\,=\,{\frac {z^{3}}{3\cdot 1!}}\!-\!{\frac {z^{7}}{7\!\cdot \!3!}}\!+\!{\frac {z^{11}}{11\!\cdot \!5!}}\!-\!{\frac {z^{15}}{15\!\cdot \!7!}}\!+\!-\ldots$
    $S(z)=\int _{0}^{z}\sin(t^{2})\,\mathrm {d} t=\sum _{n=0}^{\infty }(-1)^{n}{\frac {z^{4n+3}}{(2n+1)!(4n+3)}}$
    $C(z)=\int _{0}^{z}\cos(t^{2})\,\mathrm {d} t=\sum _{n=0}^{\infty }(-1)^{n}{\frac {z^{4n+1}}{(2n)!(4n+1)}}$
These converge for all complex values $z$, and thus define entire transcendental functions.
The Fresnel integrals at infinity have the finite value $\lim _{x\to \infty }C(x)=\lim _{x\to \infty }S(x)={\frac {\sqrt {2\pi }}{4}}.$

## Clothoid

The parametric presentation
   ${\begin{matrix}x\,=\,C(t),\quad y=S(t)\end{matrix}}$
represents a curve called clothoid .
Since the equations both define odd functions, the clothoid has symmetry about the origin.
The curve has the shape of a "$\sim$" (see this diagram).
The arc length of the clothoid from the origin to the point ,$(C(t),\,S(t))$, is simply $\int _{0}^{t}{\sqrt {C'(u)^{2}+S'(u)^{2}}}\,du=\int _{0}^{t}{\sqrt {\cos ^{2}(u^{2})+\sin ^{2}(u^{2})}}\,du=\int _{0}^{t}du=t.$ Thus, the length of the whole curve to the point, $({\frac {\sqrt {2\pi }}{4}},\,{\frac {\sqrt {2\pi }}{4}})$ is infinite.
The curvature of the clothoid also is extremely simple, $\varkappa \,=\,2t,$ i.e. proportional to the arc lenth; thus in the origin only the curvature is zero.
Conversely, if the curvature of a plane curve varies proportionally to the arc length, the curve is a clothoid.
This property of the curvature of clothoid is utilised in way and railway construction, since the form of the clothoid is very efficient when a straight portion of way must be bent to a turn, the zero curvature of the line can be continuously raised to the wished curvature.
# PlanetPhysics/Frictionless Inclined Plane

The inclined plane is a common example of Newton's laws of motion. It was used in Galileo's experiment to calculate the acceleration due to gravity and has been used by students for centuries to explore the laws of motion. Here we will examine a block sliding down a frictionless inclined plane as shown below. The y axis is perpendicular to the incline and the x axis is parallel to incline.
   \vspace{20 pt} \includegraphics[scale=.85]{InclinePlane.eps} \vspace{20 pt}
   (1)
The first thing to do is draw a free body diagram to describe the external forces acting on our object and the coordinate system for the problem.
   \vspace{20 pt} \includegraphics[scale=.85]{FreeBodyDiagram.eps} \vspace{20 pt}
   (2)
Applying Newton's 2nd law to both x and y
$\sum {\vec {F}}=m{\vec {a}}$
{\mathbf y-dir} \\
First note that the block is stationary in the y direction, so we know that the acceleration is zero.
$\sum F_{y}=0$
The two forces in the y direction are due to the normal force applied by the incline and the force due to gravity.
$\sum F_{y}=N-mg\cos \theta =0$
{\mathbf x-dir} \\
With the block sliding down the frictionless incline, we get
$\sum F_{x}=mg\sin \theta =ma_{x}$
There are several quantities of interest, but let us start with the basics of acceleration, velocity and displacement. For acceleration we see that it is constant in the x direction
   $a_{x}=g\sin \theta$
Next, let us calculate the velocity at a given displacement. As usual, we integrate acceleration
${\frac {dv_{x}}{dt}}=g\sin \theta$ $\int _{0}^{v_{x}}dv_{x}=\int _{0}^{t}g\sin \theta dt$
and carrying out the integration gives us the velocity of the block as a function of time as it slides down the incline.
   $v_{x}(t)=g\,t\sin \theta$
Next, integrate again to get displacement down the incline.
${\frac {dx}{dt}}=g\,t\sin \theta$ $\int _{0}^{x}dx=\int _{0}^{t}g\,t\sin \theta dt$
Carrying out the integration gives us the displacement of the block as a function of time as it slides down the incline.
   $x(t)={\frac {1}{2}}g\,t^{2}\sin \theta$
Now we can focus on other interesting quantities such as the velocity as a function of displacement. To get this solve (3) for t and plug it into (2)
   $t={\sqrt {\frac {2x}{g\sin \theta }}}$
$v_{x}(x)=g\,{\sqrt {\frac {2x}{g\sin \theta }}}\sin \theta$
putting all the terms under the square root gives
   $v_{x}(x)={\sqrt {2\,g\,x\,\sin \theta }}$
A fun and easy experiment is to measure the acceleration of gravity by rolling objects down an incline. All you have to do is solve equation (4) for g
$g={\frac {2x}{t^{2}\sin \theta }}$
and then just measure $\theta$, $x$ and $t$. There is really nothing like carrying out experiments that helped shape physics, so go forth and measure.
{\mathbf equilibrium.}
We already saw that the forces perpindicular to the plane in the y direction are in equilibrium
$N=mgcos\theta .$
For the x direction parallel to the plane, one must apply a force $F_{a}$ in the opposite direction (up the plane) to counter the force due to gravity. This equilibrium condition would mean our forces in the x direction would cancel so
$F_{a}+mgsin\theta =0$ $F_{a}=-mgsin\theta .$
# Real function/Local extremum/Differentiable/Derivative zero/Fact

Let $D\subseteq \mathbb {R}$ denote an open subset and let
    $f\colon D\longrightarrow \mathbb {R}$
be a function, which attains in $a\in D$ a local extremum and is differentiable there.
    $f'(a)=0\,$
# Real function/Local extremum/Differentiable/Derivative zero/Fact/Proof

We may assume that $f$ attains a local maximum in $a$. This means that there exists an $\epsilon >0$, such that $f(x)\leq f(a)$ holds for all $x\in [a-\epsilon ,a+\epsilon ]$. Let ${\left(s_{n}\right)}_{n\in \mathbb {N} }$ be a sequence with $a-\epsilon \leq s_{n}<a$, tending to $a$ ("from below“). Then $s_{n}-a<0$, and so $f(s_{n})-f(a)\leq 0$, and therefore the difference quotient
    ${\frac {f(s_{n})-f(a)}{s_{n}-a}}\geq 0\,.$
Due to fact, this relation carries over to the limit, which is the derivative. Hence, $f'(a)\geq 0$. For another sequence ${\left(t_{n}\right)}_{n\in \mathbb {N} }$ with $a+\epsilon \geq t_{n}>a$, we get
    ${\frac {f(t_{n})-f(a)}{t_{n}-a}}\leq 0\,.$
Therefore, also $f'(a)\leq 0$ and thus $f'(a)=0$.
# Real function/Local maximum and minimum/Definition

Suppose that $D\subseteq \mathbb {R}$ is a subset and let
    $f\colon D\longrightarrow \mathbb {R}$
denote a function. We say that $f$ attains a local maximum in a point $x\in D$, if there exists some $\epsilon >0$, such that for all $x'\in D$ fulfilling $\vert {x-x'}\vert \leq \epsilon$, the estimate
    $f(x)\geq f(x')\,$
holds. We say that $f$ attains a local minimum in a point $x\in D$, if there exists some $\epsilon >0$, such that for all $x'\in D$ fulfilling $\vert {x-x'}\vert \leq \epsilon$, the estimate
    $f(x)\leq f(x')\,$
holds.
# Real function/Sine 1 over x/Sketch/Exercise

Sketch the function
    $g\colon \mathbb {R} _{+}\longrightarrow \mathbb {R} ,x\longmapsto \sin {\frac {1}{x}}.$
# Real function/Increasing and decreasing/Definition

Let $I\subseteq \mathbb {R}$ denote an interval and let
    $f\colon I\longrightarrow \mathbb {R}$
denote a function. Then $f$ is called increasing if
    $f(x')\geq f(x){\text{ holds for all }}x,x'\in I{\text{ with }}x'\geq x,$
strictly increasing if
    $f(x')>f(x){\text{ holds for all }}x,x'\in I{\text{ with }}x'>x,$
decreasing if
    $f(x')\leq f(x){\text{ holds for all }}x,x'\in I{\text{ with }}x'\geq x,$
strictly decreasing if
    $f(x')<f(x){\text{ holds for all }}x,x'\in I{\text{ with }}x'>x.$
# Real function/Increasing/Definition

Let $I\subseteq \mathbb {R}$ denote an interval and let
    $f\colon I\longrightarrow \mathbb {R}$
denote a function. Then $f$ is called increasing, if
    $f(x')\geq f(x){\text{ holds for all }}x,x'\in I{\text{ with }}x'\geq x.$