OpenLLM-France/wikimedia huggingface dataset:
# Physics Formulae/Particle Physics Formulae

Lead Article: Tables of Physics Formulae
This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of particle physics.

## Atoms and Nuclei

| Fermi Energy | $E_{F}=(3/16{\sqrt {2}}\pi )^{2/3}h^{2}n^{2/3}m\,\!$ |
| Mass Number | $A=Z+N\,\!$ |
| Nuclear Radius | $r=r_{0}A^{1/3},r_{0}\approx 1.2fm\,\!$ |
| Mass Excess | $\Delta =M-A\,\!$ |
| Radioactive Decay | $N=N_{0}e^{-\lambda t}\,\!$ |
| Hubble Constant | $H=71.0km/s\,\!$ |
| Hubble's Law | $v=Hr\,\!$ |

## Quantum Numbers of Quark Flavuors

| Conservation of Lepton Number | $\,\!$ |
| Conservation of Baryon Number | $\,\!$ |
| Conservation of Strangeness | $\,\!$ |
| Eightfold Way | $\,\!$ |
| Weak Force | $\,\!$ |

## The Fundamental Forces

| Strong Force | ${\begin{aligned}{\mathcal {L}}_{\mathrm {QCD} }&={\bar {\psi }}_{i}\left(i\gamma ^{\mu }(D_{\mu })_{ij}-m\,\delta _{ij}\right)\psi _{j}-{\frac {1}{4}}G_{\mu \nu }^{a}G_{a}^{\mu \nu }\\&={\bar {\psi }}_{i}(i\gamma ^{\mu }\partial _{\mu }-m)\psi _{i}-gG_{\mu }^{a}{\bar {\psi }}_{i}\gamma ^{\mu }T_{ij}^{a}\psi _{j}-{\frac {1}{4}}G_{\mu \nu }^{a}G_{a}^{\mu \nu }\,,\\\end{aligned}}\,\!$ |
| Noether's Theorem | $\,\!$ |
| Electroweak Interaction | :${\mathcal {L}}_{EW}={\mathcal {L}}_{g}+{\mathcal {L}}_{f}+{\mathcal {L}}_{h}+{\mathcal {L}}_{y}.\,\!$ ${\mathcal {L}}_{g}=-{\frac {1}{4}}W_{a}^{\mu \nu }W_{\mu \nu }^{a}-{\frac {1}{4}}B^{\mu \nu }B_{\mu \nu }\,\!$ ${\mathcal {L}}_{f}={\overline {Q}}_{i}iD\!\!\!\!/\;Q_{i}+{\overline {u}}_{i}^{c}iD\!\!\!\!/\;u_{i}^{c}+{\overline {d}}_{i}^{c}iD\!\!\!\!/\;d_{i}^{c}+{\overline {L}}_{i}iD\!\!\!\!/\;L_{i}+{\overline {e}}_{i}^{c}iD\!\!\!\!/\;e_{i}^{c}\,\!$ ${\mathcal {L}}_{h}=|D_{\mu }h|^{2}-\lambda \left(|h|^{2}-{\frac {v^{2}}{2}}\right)^{2}\,\!$ ${\mathcal {L}}_{y}=-y_{u\,ij}\epsilon ^{ab}\,h_{b}^{\dagger }\,{\overline {Q}}_{ia}u_{j}^{c}-y_{d\,ij}\,h\,{\overline {Q}}_{i}d_{j}^{c}-y_{e\,ij}\,h\,{\overline {L}}_{i}e_{j}^{c}+h.c.\,\!$ |
| Quantum Electrodynamics | :${\mathcal {L}}={\bar {\psi }}(i\gamma ^{\mu }D_{\mu }-m)\psi -{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }\;,\,\!$ |
# Physics Formulae/Equations for Properties of Matter

Lead Article: Tables of Physics Formulae
This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Equations for Properties of Matter.

## Friction

| Normal Force | $f_{n}=\mathbf {f} \cdot \mathbf {n} \,\!$ |
| Static Friction, lies tangent to the surface | $f\leqslant \mu _{s}f_{n}\,\!$ |
| Kinetic Friction, lies tangent to the surface | $f=\mu _{k}f_{n}\,\!$ |
| Drag Force, tangent to the path | $f=\mu _{d}\rho av^{2}/2\,\!$ |
| Terminal Velocity | $v_{t}={\sqrt {\frac {2fg}{\mu _{d}\rho A}}}\,\!$ |
| Energy dissipation due to Friction (sound, heat etc) | $\Delta E=f_{k}d\,\!$ |

## Stress and strain

| Quantity (Common Name/s) | (Common) Symbol/s | Definining Equation | SI Units | Dimension |
| General Stress | $\sigma \,\!$ | $\sigma =F/A\,\!$ F may be any force applied to area A | Pa = N m$^{-2}$ | [M] [T] [L]$^{-1}$ |
| General Strain | $\epsilon \,\!$ | $\epsilon =\Delta D/D\,\!$ D = dimension (length, area, volume) $\Delta D\,\!$ = change in dimension | dimensionless | dimensionless |
| General Modulus of Elasticity | $E_{\mathrm {mod} }\,\!$ | $E_{\mathrm {mod} }=\sigma /\epsilon \,\!$ | Pa = N m$^{-2}$ | [M] [T] [L]$^{-1}$ |
| Yield Strength/ | $\,\!$ | | | |
| Ultimate Strength | $\,\!$ | | | |
| Young's Modulus | $E,Y\,\!$ | $Y={\frac {FL}{A\Delta L}}\,\!$ | Pa = N m$^{-2}$ | [M] [T] [L]$^{-1}$ |
| Shear Modulus | $G\,\!$ | $G={\frac {FL}{A\Delta x}}\,\!$ | Pa = N m$^{-2}$ | [M] [T] [L]$^{-1}$ |
| Bulk Modulus | $B\,\!$ | $B={\frac {P}{\Delta V/V}}\,\!$ | Pa = N m$^{-2}$ | [M] [T] [L]$^{-1}$ |

## Fluid Dynamics

| density | $\rho =\Delta m/\Delta V\,\!$ |
| pressure | $p=\Delta F/\Delta A\,\!$ |
| pressure difference | $\Delta p=\rho g\Delta y\,\!$ |
| pressure at depth | $p=p_{0}+\rho gh\,\!$ |
| barometer versus manometer | $$ |
| Pascal's principle | $$ |
| Archimedes' Principle | $$ |
| buoyant force | $F_{b}=m_{f}g\,\!$ |
| gravitational force when floating | $F_{g}=F_{b}\,\!$ |
| apparent weight | $weight_{app}=weight-F_{b}\,\!$ |
| ideal fluid | $$ |
| equation of continuity | $R_{V}=Av=\,\!$ constant |
| Bernoulli's Equation | $p+{\frac {\rho }{2}}v^{2}+\rho gh=\,\!$ constant |
# Principles of Public Health Practice/Subject intended learning outcomes

The assignments are used to assess the following Intended Learning Outcomes in this subject.

### Accurately describe the various concepts, values and strategies relating to public health practice.

Enabling Outcomes:
* Identify key aspects of public health philosophy and principles;
* Discuss critically the various determinants of health in terms of the environment, society and behaviour;
* Delineate the different types of interventions with regards to different understandings of public health activity.

### Adequately outline the often conflicting roles and interests held by the various stakeholders engaged in or affected by public health activities

Enabling Outcomes:
* Identify and discuss key aspects of the health system as they relate to public health policy;
* Outline the roles and interests of government, non-government, commercial and non-commercial stakeholders;
* Articulate the influence of various types of legislation (e.g., various Health, Safety, Sanitation and Food Acts) as they relate to public health, primary health care and health promotion.

### Critically articulate the applicability of various strategies engaged in by public health practitioners at various levels

Enabling Outcomes:
* Delineate the scope, importance and suitability of surveillance and monitoring strategies;
* Identify the commonalities and difference relating to health protection and preventative services;
* Compare and contrast the previous strategies with those relating to health promotion and primary health care.

### Define the limits of public health practice as a discipline with regards to work with ‘vulnerable’ communities within societies

Enabling Outcomes:
* Recognise the various value systems that historically inform the aspects of public health practice;
* Suggest reasons why certain ‘vulnerable’ groups might resist health promotion strategies and the potential consequences of this resistance;
* Demonstrate an understanding of how certain principles and practices might either hinder or enable ‘vulnerable’ groups to engage in the determinants of health in a culturally appropriate manner.
# Inverse function/Power series approach/sin x/0/Degree 4/Exercise

Determine the Taylor polynomial up to fourth order of the inverse of the sine function at the point $0$ with the power series approach described in an remark.
# Inverse matrix/Anti diagonal/Exercise

Determine the inverse matrix of
    ${\begin{pmatrix}0&0&\cdots &0&1\\0&0&\cdots &1&0\\\vdots &\vdots &1&\vdots &\vdots \\0&1&\cdots &0&0\\1&0&\cdots &0&0\end{pmatrix}}.$
# Inverse matrix/Field/Definition

Let $K$ denote a field. For an invertible matrix $M\in \operatorname {Mat} _{n}(K)$, the matrix $A\in \operatorname {Mat} _{n}(K)$ fulfilling
    $A\circ M=E_{n}=M\circ A\,,$
is called the inverse matrix of $M$. It is denoted by
    $M^{-1}.$
# Inverse trigonometric functions/Derivative/Fact/Proof

For example, for the arctangent, we have, due to fact,
    ${\begin{aligned}(\arctan x)^{\prime }&={\frac {1}{\frac {1}{\cos ^{2}(\arctan x)}}}\\&={\frac {1}{\frac {\cos ^{2}(\arctan x)+\sin ^{2}(\arctan x)}{\cos ^{2}(\arctan x)}}}\\&={\frac {1}{1+\tan ^{2}(\arctan x)}}\\&={\frac {1}{1+x^{2}}}.\end{aligned}}$
# Inverse trigonometric functions/Derivative/Fact

The inverse trigonometric functions have the following derivatives.
    ${\left(\arcsin x\right)}'={\frac {1}{\sqrt {1-x^{2}}}}\,.$
    ${\left(\arccos x\right)}'=-{\frac {1}{\sqrt {1-x^{2}}}}\,.$
    ${\left(\arctan x\right)}'={\frac {1}{1+x^{2}}}\,.$
    ${\left(\operatorname {arccot} x\right)}'=-{\frac {1}{1+x^{2}}}\,.$
# Maritime Health Research and Education-NET/Students Research Projects/Education for prevention of pre-diabetes and diabetes type 2 - evaluation of programs
## Prevention with education of pre-diabetes and diabetes type 2 among seafarers, fishermen and other workers – a description and evaluation of the program MyDESMOND platform

A. The basic task for the student is to describe and evaluate the program MyDESMOND platform: “The NewlyFoundation programme is group-based education which aims to support people with a diagnosis of Type 2 diabetes and work with them to self-manage their condition, through a structured education programme to target lifestyle modification and behaviour change which can be culturally adapted to suit your local population. A digital-version of the programme is available on our MyDESMOND platform”, click here to found out more
B. Supplemental tasks is to do literature reviews and respond to these questions:
* The prevalence of pre-diabetes and diabetes globally for seafarers and fishermen and other in some selected occupations over the latest ten years, truck drivers and other transport workers.
* Seafarers and fishermen have obligatory medical health examinations every 2 years globally, how do you think that can that be used to better prevent diabetes type 2?
* Some countries include measurements of diabetes by the use of blood tests as the early diagnostics, who is the benefit for the workers? In other countries diabetes urine sticks is used for diagnose of diabetes and pre diabetes at the health examinations what is the problems with that practice.
* What is the (scientific validity) problems by the use of urine sticks (literature exists)
* What is the health problems and work problems on the long sight for workers with diabetes Type 2?
* How is the knowledge, understanding and practice on prevention of diabetes type 2 among the seafarers, fishermen and other transport workers (ex truck drivers) ?
* How are the existing courses to improve the knowledge and practice used and evaluated, if they are evaluated?
* What could your contribution be to the world diabetes day ?
# Maritime Health Research and Education-NET/Students Research Projects/Students thesis supervision/MScPubHealth Thesis supervision VC

"Evaluating the relationship between musculoskeletal disorders and work environment among Panamanian port workers"

## 2. Study work

* Protocol
* Literature search and review writing
* Data analysis and thesis writing
* Thesis ready and defense
* Scientific publication, conference presentations
# Maritime Health Research and Education-NET/Students Research Projects/Students thesis supervision/MScPubHealth Thesis supervision - muskuloskeletal problems

"Evaluating the relationship between musculoskeletal disorders and work environment among Panamanian port workers"

## 2. Study work

* Protocol
* Literature search and review writing
* Data analysis and thesis writing
* Thesis ready and defense
* Scientific publication, conference presentations
# Maritime Health Research and Education-NET/Students Research Projects/Students thesis supervision/BScPubHealth Thesis supervision MZ&SMS
## 2. Study work

* Research questions and protocol
* Questionnaire Google Form - Thai
* Questionnaire Google Form - UMIP Feb 2022 new data
* Literature search and review writing
* Data analysis and thesis writing
* Thesis ready and defence
* Scientific publication, conference presentations
# Minecraft/Servers

A Minecraft server allows anyone to create a world that players around the world can connect to.

## Types
### Vanilla

Original/unmodified server that Mojang distributes, but not commonly used on public servers due to griefing.

### Bukkit

A previously very common server that no longer exists due to a DMCA takedown request.

### Spigot

As Spigot was based on Bukkit, it was also hit with a DMCA takedown. Spigot has been modified for newer versions of Minecraft, and no longer contains the code that caused the DMCA. It is the most common type of server used.

### Forge

Forge allows mods to be added to a server. Everyone who connects usually requires that mod to be installed.

#### Cauldron

Cauldron was a Forge server that allowed Bukkit plugins to be installed. It was hit with a DMCA takedown and no longer exists.

#### Sponge

Created in response to the DMCA takedowns of Bukkit, Spigot, and Cauldron, Sponge is a server that works on top of Forge, as it is a mod that is installed onto the Forge server. However, players who connect do not need the Sponge mod nor any mods that work with Sponge.
# Square root/2/Irrational/Fact

$2$
This means that the real number ${\sqrt {2}}$ is irrational.
# Square root of 5/Heron's method/Motivating example/R/Example

We would like to "compute“ the square root of a natural number, say of $5$. Such a number $x$ with the property $x^{2}=5$ does not exist within the rational numbers (this follows from unique prime factorization). If $x\in R$ is such an element, then also $-x$ has this property. Due to fact, there can not be more than two solutions.
Though there is no solution within the rational numbers for the equation $x^{2}=5$, there exist arbitrarily good approximations for it with rational numbers. Arbitrarily good means that the error (the deviation) can be made so small that it is below any given positive bound. The classical method to approximate a square root is Heron's method. This is an iterative method, i.e., the next approximation is computed from the preceding approximation. Let us start with $a:=x_{0}:=2$ as a first approximation. Because of
    $x_{0}^{2}=2^{2}=4<5\,$
we see that $x_{0}$ is to small, $x_{0}<x$. From $a^{2}<5$ ($a$ being positive) we get $5/a^{2}>1$ and therefore $(5/a)^{2}>5$, so $5/a>{\sqrt {5}}$. Hence we have the estimates
    $a<{\sqrt {5}}<5/a\,,$
where we get a rational number on the right hand side if $a$ is rational. Such an estimate provides a certain idea where ${\sqrt {5}}$ lies. The difference $5/a-a$ is a measure for how good the approximation is.
In particular, when we start with $2$, we get that the square root ${\sqrt {5}}$ is between $2$ and $5/2$. Then we take the arithmetic mean of the interval bounds, so
    $x_{1}:={\frac {2+{\frac {5}{2}}}{2}}={\frac {9}{4}}\,.$
Due to ${\left({\frac {9}{4}}\right)}^{2}={\frac {81}{16}}>5$, this value is too large and therefore ${\sqrt {5}}$ is in the interval $[5\cdot {\frac {4}{9}},{\frac {9}{4}}]$. Then, we take again the arithmetic mean of these interval bounds and we set
    $x_{2}:={\frac {5\cdot {\frac {4}{9}}+{\frac {9}{4}}}{2}}={\frac {161}{72}}\,$
to be the next approximation. Continuing like that, we get better and better approximations for ${\sqrt {5}}$.
# Staircase function/Sum/Exercise

Let
    $f,g\colon [a,b]\longrightarrow \mathbb {R}$
be two staircase functions. Prove that $f+g$ is also a staircase function.
# Staircase function/Sum product maximum minimum/Exercise

Let
    $f,g\colon [a,b]\longrightarrow \mathbb {R}$
be two staircase functions. Show that also
* $f+g$,
* $f\cdot g$,
* ${\max {\left(f,g\right)}}$,
* ${\min {\left(f,g\right)}}$,
are staircase function.
# Square root/Average value/1 to 4/Compare/Exercise

Determine the average value of the square root ${\sqrt {x}}$ for $x\in [1,4]$. Compare this value with the square root of the arithmetic mean of $1$ and $4$ and with the arithmetic mean of the square root of $1$ and of the square root of $4$.
# Square matrix/Trace/Definition

Let $K$ be a field and let $M={\left(a_{ij}\right)}_{ij}$ be an $n\times n$-matrix over $K$. Then
    $\operatorname {trace} {\left(M\right)}:=\sum _{i=1}^{n}a_{ii}\,$
is called the trace of $M$.
# Staircase integral/Explicite function/1/Exercise

Determine the Riemann sum over $[-3,+4]$ of the staircase function
    $f(t)={\begin{cases}5,{\text{ if }}-3\leq t\leq -2\,,\\-3,{\text{ if }}-2<t\leq -1\,,\\{\frac {3}{7}},{\text{ if }}-1<t<-{\frac {1}{2}}\,,\\13,{\text{ if }}t=-{\frac {1}{2}}\,,\\\pi ,{\text{ if }}-{\frac {1}{2}}<t<e\,,\\0,{\text{ if }}e\leq t\leq 3\,,\\1,{\text{ if }}3<t\leq 4\,.\end{cases}}\,$
# Square root/2/Irrational/Fact/Proof

We make the assumption that there exists some rational number whose square equals $2$, and we have to derive a contradiction from this. Our assumption means the existence of
    $x\in \mathbb {Q} \,$
fulfilling the property
    $x^{2}=2\,.$
A rational number can be written as a fraction, where numerator and denominator are integers. Hence, the rational number $x$ has the form
    $x={\frac {a}{b}}\,.$
Moreover, we can suppose that this fraction has been reduced to its lowest terms, so that the greatest common divisor of $a$ and $b$ is $1$. In fact it is enough to suppose that at least one of $a$ and $b$ are odd (if both are even we can divide both by $2$ until one gets odd). The property
    $x^{2}=2\,$
means then
    $x^{2}={\left({\frac {a}{b}}\right)}^{2}={\frac {a^{2}}{b^{2}}}=2\,.$
Multiplication by $b^{2}$ yields
    $2b^{2}=a^{2}\,$
(this is an equation in $\mathbb {Z}$ and even in $\mathbb {N}$). This equation means that $a^{2}$ is even, since $a^{2}$ is a multiple of $2$. This implies that $a$ itself is even, because the square of an odd number is again odd. Therefore, we can write
    $a=2c\,$
with an integer $c$. Putting this into the equation, we deduce
    $2b^{2}=(2c)^{2}=2^{2}c^{2}\,.$
Dividing both sides by $2$ we obtain
    $b^{2}=2c^{2}\,.$
Hence, also $b^{2}$ is even and so $b$ is even. But this is a contradiction, as $a$ and $b$ are not both even.
# Squat

Squat is a renowned element of many folk dances. In weightlifting and bodybuilding, as well as in other sports, squat is a physical exercise that strengthening the muscles of the thighs, hips and buttocks, as well as the bones, ligaments and insertion of the tendons throughout the lower body.
* Squatting on tips as a dance exercise
* Side split squat at a group calisthenics

## Health concerns

Although the squat is a basic element of weight training, it has been the subject of considerable controversy in recent years. Some trainers allege that squats are associated with injuries to the lumbar spine and knees. As a result, many trainers suggest that the standard barbell squat be modified in various ways. Others, however, reject all suggestions that the exercise be abandoned, continuing to advocate the squat.
# States and Capitals of the USA/West

The States in the Western USA region according to the National Census Bureau are:
* Alaska
* Arizona
* California
* Colorado
* Hawaii
* Idaho
* Montana
* Nevada
* New Mexico
* Oregon
* Utah
* Washington
* Wyoming
# States and Capitals of the USA/Southwest Capitals

| Texas | Austin |
| Oklahoma | Oklahoma City |
| Arizona | Phoenix |
| New Mexico | Santa Fe |
# States and Capitals of the USA/West Capitals

* Washington
* Olympia
* Montana
* Helena
# Static electricity/Charging & Discharging Human Body
## Problem

Mild charging of the human body may occur during a shower, walking around in the winter, during certain new age "healing" therapies, shock therapy to the brain and a defibrillator. The goal is to review the benefits to the human body of static electricity.
# Static electricity
## Problem

Electricity was confined to static demonstrations before the 1800's when Faraday began to experiment with moving energy through wires and creating magnetic fields. But magnetic fields are fragile, so studying fields in general starts with studying static electricity. The goal of these projects is to develop static demonstrations.

## Concept

Create demonstrations after completing a variety of projects in the static electricity areas including:
* Fly stick
* Static electricity safety
* Lightning
* Measuring high voltages
* Creating high voltages
* Dancing balls
* Static motors

## Design

After the Demonstrations project has created a format for demonstrations, then need to package each of the above projects into a demonstration.
Static electricity demos are so interesting because little modern technology uses static electricity. The secret is a source of electrons. Once this is made, then a tremendous number of demonstrations is possible. The goal of the project is to build the parts and develop a script for doing the demos.
# States and Capitals of the USA

* States and Capitals of the USA/Southwest
* States and Capitals of the USA/Northeast
* States and Capitals of the USA/Midwest
* States and Capitals of the USA/West
* States and Capitals of the USA/Southeast
# States and Capitals of the USA/Midwest

* Madison, Wisconsin
* St. Paul, Minnesota
* Lansing, Michigan
* Springfield, Illinois
* Indianapolis, Indiana
* Columbus, Ohio
* Des Moines, Iowa
* Jefferson City, Missouri
* Bismarck, North Dakota
* Pierre, South Dakota
* Lincoln, Nebraska
* Topeka, Kansas
# Survival Kit, software

This resource is to describe the usage of Survival Kit software package used for survival analysis (the paper). The focus will be on step by step description how to run the basic examples with fixed effects. The real advantage of the Survival Kit is its ability to handle very large databases (up to several million records) including random effects. This is however outside of scope of this beginner guide, while novice users should get familiar with the basic principles first. The description deals with Survival Kit v6.06 available online at boku.ac.at.
* Release notes
* 15. March 2010 - Wikiversity page has been created to assist Survival Kit v3.12 users.
* 02. November 2010 - Description on the page updated for SK v6.06, the program was uploaded to its non-official storage space.
* 08. November 2010 - The executable files updated on the [Mediafire storage space], but the link remained the same. Upload to the official BOKU site still pending.
* 23. November 2010 - The Survival Kit v6.06 is now reachable on its official website. See the World congress paper for more details. The temporary storage place was canceled.

### General description of the Survival Kit

The Survival Kit is intended for survival analysis using proportional hazards model with a single response time. These models describe the hazard function of each individual (i.e. its limiting probability of dying at time t, given it is still alive just prior to t) as the product of a baseline hazard function and a positive (exponential) function of explanatory covariates. The baseline hazard function can be parametric (Weibull model) or left unspecified (Cox model).
When the failure time variable is discrete (i.e. has very few values) and many observations with the same failure times, many ties occur between failure times. In such case, the Cox model is not valid any more, but the "grouped data" approach should be used.
The Survival Kit consists from 3 main programs:
* Prepare - for database preparation, internal recoding
* Cox - for non parametric Cox model
* Weibull - for grouped data or parametric Weibull models

### Prerequisites

The reader should be familiar with the basic concepts of survival analysis. Basic knowledge of computer usage is expected.

## Note

Users with practical experiences are encouraged to share them here. If something is not clear ask here or here.
# Survival Kit, software/Other possibilities

The reader should be aware of the fact that the Survival Kit is not the only software for survival analysis. The other choices are including (but not limited to) these programs

### coxph / coxme

These packages are available in R. Coxph is used for cox models, coxme for cox models including random variables. These are free programs.

### frailtypack

Again a free package available in R. The advantage of this is the ability to estimate two correlated random effects.

### SAS

Proc phreg and proc lifetest can be used in SAS after purchase of its license.
# Survey research and design in psychology/Web resources/Moodle

Moodle Moodle