OpenLLM-France/wikimedia huggingface dataset:
# PlanetPhysics/Determination of Fourier Coefficients

Suppose that the real function $f$ may be presented as sum of the Fourier series:
   ${\begin{matrix}f(x)\;=\;{\frac {a_{0}}{2}}+\sum _{m=0}^{\infty }(a_{m}\cos {mx}+b_{m}\sin {mx})\end{matrix}}$
Therefore, $f$ is periodic with period $2\pi$.\, For expressing the Fourier coefficients $a_{m}$ and $b_{m}$ with the function itself, we first multiply the series (1) by $\cos {nx}$ ($n\in \mathbb {Z}$) and integrate from $-\pi$ to $\pi$.\, Supposing that we can integrate termwise, we may write
   ${\begin{matrix}\int _{-\pi }^{\pi }\!f(x)\cos {nx}\,dx\,=\,{\frac {a_{0}}{2}}\!\int _{-\pi }^{\pi }\!\cos {nx}\,dx+\!\sum _{m=0}^{\infty }\!\left(a_{m}\!\int _{-\pi }^{\pi }\!\cos {mx}\cos {nx}\,dx+b_{m}\!\int _{-\pi }^{\pi }\!\sin {mx}\cos {nx}\,dx\right)\!.\end{matrix}}$
When\, $n=0$,\, the equation (2) reads
   ${\begin{matrix}\int _{-\pi }^{\pi }f(x)\,dx={\frac {a_{0}}{2}}\cdot 2\pi =\pi a_{0},\end{matrix}}$
since in the sum of the right hand side, only the first addend is distinct from zero.
When $n$ is a positive integer, we use the product formulas of the trigonometric identities, getting $\int _{-\pi }^{\pi }\cos {mx}\cos {nx}\,dx={\frac {1}{2}}\int _{-\pi }^{\pi }[\cos(m-n)x+\cos(m+n)x]\,dx,$ $\int _{-\pi }^{\pi }\sin {mx}\cos {nx}\,dx={\frac {1}{2}}\int _{-\pi }^{\pi }[\sin(m-n)x+\sin(m+n)x]\,dx.$ The latter expression vanishes always, since the sine is an odd function.\, If\, $m\neq n$,\, the former equals zero because the antiderivative consists of sine terms which vanish at multiples of $\pi$; only in the case\, $m=n$\, we obtain from it a non-zero result $\pi$.\, Then (2) reads
   ${\begin{matrix}\int _{-\pi }^{\pi }f(x)\cos {nx}\,dx=\pi a_{n}\end{matrix}}$
to which we can include as a special case the equation (3).
By multiplying (1) by $\sin {nx}$ and integrating termwise, one obtains similarly
   ${\begin{matrix}\int _{-\pi }^{\pi }f(x)\sin {nx}\,dx=\pi b_{n}.\end{matrix}}$
The equations (4) and (5) imply the formulas $a_{n}\;=\;{\frac {1}{\pi }}\int _{-\pi }^{\pi }f(x)\cos {nx}\,dx\quad (n=0,\,1,\,2,\,\ldots )$ and $b_{n}\;=\;{\frac {1}{\pi }}\int _{-\pi }^{\pi }f(x)\sin {nx}\,dx\quad (n=1,\,2,\,3,\,\ldots )$ for finding the values of the Fourier coefficients of $f$.
# PlanetPhysics/Differential Equation of the Family of Parabolas

To find the differential equation of the family of parabolas
$y=ax+bx^{2}$
we differentiate twice to obtain
$y^{\prime }=a+2bx$ $y^{\prime \prime }=2b$
The last equation is solved for $b$, and the result is substituted into the previous equation. This equation is solved for $a$, and the expressions for $a$ and $b$ are substituted into $y=ax+bx^{2}$. The result is the differential equation $y=xy^{\prime }-{\frac {1}{2}}x^{2}y^{\prime \prime }$
The elimination of the constants $a$ and $b$ can also be obtained by considering the equations
$xa+x^{2}b+(-y)1=0$ $a+2xb+(-y^{\prime })1=0$ $2b+(-y^{\prime \prime })1=0$
as a system of homogeneous linear equations in $a$,$b$,$1$. The solution $(a,b,1)$ is nontrivial, and hence the determinant of the coefficients vanishes.
$\left|{\begin{matrix}x&x^{2}&-y\\1&2x&-y^{\prime }\\0&2&-y^{\prime \prime }\end{matrix}}\right|=0$
Expansion about the third column yields the result above.
# PlanetPhysics/Developments of Relativity Theories

This is a contributed topic on further developments of relativity theories.

## Recent Developments of Relativity Theories
### Quantum Riemannian geometry (QRG)

QRG represents a new approach to quantum gravity in terms of `deformed' Riemannian, quantum geometry.

### Globally covariant GR theories (GC-GR)
#### ECE

(ECE is presented at the AIAS website).
# Spanish 1/Countries
## Spanish-speaking countries

Before learning Spanish, it is important to know the names of the countries where the language is spoken:

### Norteamérica (North America)

* México - Mexico
* (los) Estados Unidos - (the) United States

### El Caribe (The Caribbean)

* Cuba - Cuba
* República Dominicana - Dominican Republic
* Puerto Rico - Puerto Rico

### América Central (Central America)

* El Salvador - El Salvador
* Guatemala - Guatemala
* Honduras - Honduras
* Nicaragua - Nicaragua
* Costa Rica - Costa Rica
* Panamá - Panama

### América del Sur (South America)

* Colombia - Colombia
* Venezuela - Venezuela
* Ecuador - Ecuador
* Perú - Peru
* Bolivia - Bolivia
* Chile - Chile
* Paraguay - Paraguay
* Argentina - Argentina
* Uruguay - Uruguay

### Europa (Europe)

* España - Spain

### África (Africa)

* Guinea Ecuatorial - Equatorial Guinea
# Main theorem of calculus/Riemann/Newton-Leibniz-formula/Fact

Let $I$ denote a real interval, and let
    $f\colon I\longrightarrow \mathbb {R}$
denote a continuous function. Suppose that $F$ is a primitive function for $f$.
$a,b\in I$, the identity
    $\int _{a}^{b}f(t)\,dt=F(b)-F(a)\,$
# Main theorem of calculus/Riemann/Newton-Leibniz-formula/Fact/Proof

Due to fact, the integral exists. With the integral function
    $G(x):=\int _{a}^{x}f(t)\,dt\,,$
we have the relation
    $\int _{a}^{b}f(t)\,dt=G(b)=G(b)-G(a)\,.$
Because of fact, the function $G$ is differentiable and
    $G'(x)=f(x)\,$
holds. Hence $G$ is a primitive function for $f$. Due to fact, we have $F(x)=G(x)+c$. Therefore,
    $\int _{a}^{b}f(t)\,dt=G(b)-G(a)=F(b)-c-F(a)+c=F(b)-F(a)\,.$
# Make Listening Safe Workstream
## Introduction

To address the risks of hearing damage caused by unsafe listening practices, the World Health Organization (WHO) launched the "Make Listening Safe" initiative in 2015. This initiative aims to create a world where people of all ages can enjoy recreational listening without endangering their hearing.
To achieve this overarching goal, the World Hearing Forum was created to foster a robust and cohesive partnership among community-at-large members. The World Hearing Forum operates through five key workstreams, each contributing to the promotion of high-quality Ear and Hearing Care for everyone. These workstreams are: Make Listening Safe, World Hearing Day, External Relations, Membership Engagement, and Changemakers.
The primary goal of the Make Listening Safe workstream is to "ensure that no one's hearing is endangered by unsafe listening." To accomplish this, the workstream is structured with four main objectives, nine subgroups, and 15 coordinators, all working together to promote safe listening habits worldwide.

## Make Listening Safe Initiative

The World Health Organization (WHO) launched the Make Listening Safe (MLS) initiative as part of the World Hearing Day celebrations on March 3, 2015. The main goal of this initiative is to ensure that people of all ages can enjoy music and other audio media in ways that do not pose a risk to their hearing.
MLS partnership activities among members of the World Hearing Forum are being coordinated by the Make Listening Safe Workstream, chaired by Katya Freire and Lidia Best.

## Objectives

The four main objectives of the initiative are:
* Raise awareness about the risks of exposure to high sound levels in recreational settings and through the use of personal audio devices.
* Develop and implement public health policies that emphasize the importance of safe listening.
* Strengthen partnerships between governments, civil society, and industry to promote safe listening practices.
* Empower users and health professionals with knowledge about the risks of sound exposure and strategies for preventing hearing loss.

## Materials and Newsletter

Materials related to this initiative and its goals, including a presentation, can be accessed through Wikimedia Commons. These materials are available on the following page Make Listening Safe Workstream.
The Make Listening Safe Workstream Newsletter is now available on Wikimedia Commons. Do you want to be in the next newsletters? Send your actions to mlsworkstream@gmail.com.
# Maintain website performance

Web Design → Maintain website performance
This page is part of the Web Design project. :
From the official document:
    "This unit defines the competency required to ensure that a website maintains its performance levels during peak traffic times and during full utilisation access."
Basically, that means ... (translate above into plain english)
You can read more about this unit on the National Training Information Systems Official document for ICAS4191A.
This unit is part of the following qualifications:
This unit has now been superseded by new units: ICAWEB406A Create website testing procedures and ICAWEB407A Conduct operational acceptance tests of websites You can find out more details about these and other units at Training Australia website

## How this unit will help you

After learning and applying the skills required by this unit you'll be able to demonstrate your skills in:
| ELEMENT | PERFORMANCE CRITERIA |
| 1. Benchmark website performance | Review client performance expectations from specifications and business requirements |
| 2. Track website performance | Measure actual website performance against performance benchmarks in key areas and record outcomes |
| 3. Tune performance | Compare actual website performance against benchmarks over an appropriate period and make changes based on inconsistencies |
| 4. Initiate and monitor performance improvement | Establish a mechanism for capturing client initiatives to assist in identifying maintenance or administration process performance problems |
* translate the above elements and performance criteria into plain english and summarise here...

## Ideas for demonstrating this unit

The best way to demonstrate these skills is ...

## Grading

If you are demonstrating this unit as part of a formal course, you might find that the unit is graded (meaning you can not only demonstrate your competence, but can also gain a credit or distinction). Your facilitator may already have set criteria that your college uses. If not, here are some ideas for possible credit/distinction activities that you can discuss with your facilitator:
# MakerBot
## Introduction

The Makerbot Replicator 2 is a 3D printer that extrudes a biodegradable thermoplastic (PLA) to create parts. This is the older and smaller of two Makerbot 3D printers at HCC, but it prints faster than the newer (5th Gen) model.

## Warnings

* Printing gun parts violates US Federal Law
* Printing trademarked or actively patented stuff could result in a legal problems
* The school can not support printing personal stuff including personal inventions
* Focus printing on things that are related to engineering projects.

## Quick Start Guide

* Find or create a 3D model of a part.
** Find an existing 3D model (pre-drawn STL files) at the Smithsonian, thingiverse, and traceparts. 3Dwarehouse and Archive3D models do not convert to STL files consistently without problems. Makerbot needs STL or OBJ files to print from. MakerWare saves files in its own format called THING which can also be printed from.
** Create your own 3D model using a CAD program. For example:Autodesk Inventor,Solid Edge,123D, 3Dtin, Sculptris, tinkercad, openscad, wings3d, pov-ray, Heeks-cad, art of illusion, processing model building library, Google Sketchup.
* convert CAD file to STL:
for inventor: - click on "I" icon in top left corner -click on export - click on CAD format - select STL from the save as type drop down menu
** Clean up/Repair STL file with Microsoft netfabb
* Use MakerWare software to convert 3D model (STL file) into X3G file.
* Use Makerbot Replicator 2 to print part.
* Carefully remove the part from the build platform.
If you have a problem and don't know what to do, STOP and ask an instructor or lab aide for help.

## Detailed Information

* Replacing the Tape
* clogged printhead
* Makerware Troubleshooting Page
* Replicator 2 Troubleshooting Page

## Quiz

quiz - Take this after reading through the tutorial, and before taking the Canvas quiz.

## Old pages

Replicator 2 MakerBot page
* Printing Instructions
* prints blob
* curling pla
* clean gear mechanism
* assembly of iris box
* How To: Find Or Create A Printable STL File
* stuff to print
* installing Export STL
* clogged printhead
Original MakerBot Cupcake Tutorial Page
* Set Up & Run The MakerBot
* Filament Changing/Troubleshooting
* How to Change the Wire of the Makerbot
* How to Download 3D programs to build STL files
* How to print STL files with letters or Numbers in it
* Tutorial on Blender
* Kinect
* Scanning An Object Using The Kinect: Full 360 Degree View
* Cleaning Up Point Cloud Meshes in Meshlab For 3D Printing
* How to download 123D
* How to format SD card for MakerBot
# The Idea Incubator/Crowdsourcing Weather Stations

Weather forecasting accuracy can be improved by obtaining accurate weather observations from more locations more frequently. Developing a compact, inexpensive, accurate, and easy to use personal weather station can benefit regional, national, and global weather forecasting and provide the homeowner or building manager important weather, environmental, and home maintenance information.
Indoor air quality monitors that measure temperature, humidity, carbon dioxide (CO2) levels, volatile organic compound (VOC) levels, and fine particulate (PM2.5) levels are now commonly available. The Awair Element is one example. These affordable and compact units connect via Wi-Fi to smartphone apps that report and record air quality conditions.
A similar unit adapted for outdoor use that measures temperature, humidity, barometric pressure, windspeed, and perhaps wind direction could also report data frequently to the national weather service or similar agency. Adding air quality measures to the device would allow monitoring and reporting of air pollution, pollen counts, and airborne chemical toxins. Registration of the device with an agency would establish the location and accuracy of each device. These additional frequent weather observations can be used to increase the weather forecast accuracy.
Projects such as Purple Air, Ambient Weather Network, Weather Underground, and the Citizen Weather Observer program provide prototype examples.
In addition to improving weather forecast accuracy, paring an outdoor weather monitoring device with an indoor air quality monitor can provide the homeowner several benefits. These benefits include accurate temperature, humidity, barometric pressure, and windspeed data reporting and recording at the home location. Also, comparison of outdoor measurements to indoor conditions allows the homeowner or building manager to monitor, manage, maintain, and improve HVAC system efficiency and effectiveness.
Data from external and internal air monitors could be integrated with detailed electrical energy monitors (such as sense) to provide continuous HVAC efficiency monitoring and predictive maintenance alerts.
# The Human Body

* Circulatory system: Blood circulations with heart and blood vessels.
* Digestive system: Processing food with mouth, stomach and intestines.
* Endocrine system: Communicating within the body using hormones.
* Immune system: Defending against disease-causing agents.
* Integumentary system: Skin, hair and nails.
* Lymphatic system: Structures involved in the transfer of lymph between tissues and the blood stream.
* Muscular system: Moving the body.
* Nervous system: Collecting, transferring and processing information with brain and nerves.
* Reproductive system: The sex organs.
* Respiratory system: The organs used for breathing, the lungs.
* Skeletal system: Structural support and protection through bones.
* Urinary system: The kidneys and associated structures involved in the production and excretion of urine.

## Links to Related Fields of Study

* Category:Biology
* Category:Anatomy
* Category:Physiology
* Category:Anatomy stubs
Extraordinary care must be taken while studying human body for the purpose of treatment or education, etc. There are many extraordinarily yet importantly sophisticated natural systems which make up the whole human body. A few examples are the skeletal system, the muscular system, respiratory system, the reproductive system, the digestive system, the nervous system, the blood circulatory system, the urinary system, etc. The various systems consist of different organs and/or limbs which have specific functions. For example digestive system consists of hands, mouth, tongue, teeth, inner throat, stomach, small intestine, large intestine, etc. There are many parts of human body, namely: head, neck, shoulders, chest, arms, back, abdomin, buttock, legs, feet, etc. Health of every organ, limb or system is important. However, the health of some organs is vital for survival as that of heart, brain, liver, lungs, etc. Physical, psychological, mental and spiritual healths are inter-related and interdependant.
# The Idea Incubator/Blood Type Certification

Blood type remains stable throughout the lifetime of any individual human. None-the-less, it is not unusual for blood to be drawn and typed prior to certain medical procedures. This proposal is to establish a reliable system of a blood test and trusted certificate that will attest to the blood type of the patient. This certification can be used instead of procedures to draw blood and test for subsequent medical procedures.
# The Idea Incubator/Blockchain-Secured Power of Attorney

While it is important and customary to grant power of attorney (POA) to be exercised when the principal (grantor) is incapacitated, the possibility for abuse is always present. Two primary POA-related goals typically conflict. It is often important that POA be exercised quickly. It is always important that the POA be exercised responsibly.
This conflict can be resolved by securing the Power of Attorney with a Blockchain-secured record of the transactions performed each time the power of attorney was exercised by the agent. The POA authorization letter would include a notice that it is blockchain secured, and include a unique identifier, perhaps represented by a barcode or QR code. When the POA letter is used by the agent to authorize some transaction, the institution granting access would scan the code into an application that would create a blockchain record of the transaction. This record includes the time and date, identification of the agent, the identifiers of the institution and accounts accessed, a description of the transaction, and the transaction amounts.
This blockchain record of transactions could be accessed by the principle, other trusted individuals authorized by the principle, and potentially by courts. This record can then be used to monitor POA activity and resolve disputes.
# UTPA STEM/CBI Courses Organized by STEM Category/Engineering and Computer Science/Mechanical Engineering/Statics

Topics
Force Equilibrium
Truss Bridge
# UTPA STEM/CBI Courses Organized by STEM Category/Mathematics
## Courses

Algebra
Business Math
Calculus
Contemporary Mathematics
Geometry
Graduate Seminar in Applied Mathematics
Graduate Seminar in Applied Mathematics
Mathematics Teaching and Learning
Probability and Statistics

## Topics

Mathematics of Apportionments, The
# UTPA STEM/CBI Courses Organized by STEM Category/Mathematics/Business Math

Courses
Business Algebra
Business Calculus
Topics
Compound Interest and Annuities
# UTPA STEM/CBI Courses Organized by STEM Category/Engineering and Computer Science/Mechanical Engineering/Thermal Systems Design and Optimization

Topics
Economics
# UTPA STEM/CBI Courses Organized by STEM Category/Engineering and Computer Science/Mechanical Engineering/Thermodynamics

Topics
The First Law for Closed Systems
The First Law for Open Systems
# UTPA STEM/CBI Courses Organized by STEM Category/Mathematics/Business Math/Business Algebra

Topics
Financial Models
Future Value of an Annuity - Sinking Funds
Linear Programming
# UTPA STEM/CBI Courses Organized by STEM Category/Mathematics/Business Math/Business Calculus

Topics
Limits with Application to Business and Economics
Optimization Applications
# UTPA STEM/CBI Courses Organized by STEM Category/Environmental Science

Courses
Environmental Impact Assessment
# UTPA STEM/CBI Courses Organized by STEM Category/Environmental Science/Environmental Impact Assessment

Topics
Nutrient Transport, Cycling and Storage (in plants)
Map, Compass, and GPS Skills
# UTPA STEM/CBI Courses Organized by STEM Category/Mathematics/Algebra

Courses
Exponential Growth Regression
Financial Models
Motion Problems
Right Triangle Problems
Slope and Linear Functions
Work Problems
# PlanetPhysics/Magnetostatics

Magnetostatics is the study of static magnetic fields. In electrostatics the charges were stationary but in magnetostatics the currents are steady. As it turns out magnetostatics is a good approximation even when the currents are not steady as long as the currents do not alternate "too fast".
If all currents in a system are known (i.e. if a complete description of {\mathbf J} is available) then the magnetic field can be determined from the currents by the Biot-Savart law:
${\mathbf {B} }={\frac {\mu _{0}}{4\pi }}\int {\frac {I{\mathbf {d} l}\times {\mathbf {\hat {r}} }}{r^{2}}}$
This technique works well for problems where the medium is a vacuum, air or some similar material with a relative permeability of 1. This includes Air core inductors and Air core transformers. One advantage of this technique is that a complex coil geometry can be integrated in sections, or for a very difficult geometry numerical integration may be used. Since this equation is primarily used to solve linear problems, the complete answer will be a sum of the integral of each component section.
One pitfall in using the Biot-Savart law is that it does not implicitly enforce Gauss's Law for magnetism so it is possible to come up with an answer that includes magnetic monopoles. This will occur if some section of the current path has not been included in the integral (implying that electrons are being continuously created in one place and destroyed in another).
Using the Biot-Savart law in the presence of Ferromagnetic, Ferrimagnetic or Paramagnetic materials is difficult because the external current induces a surface current in the magnetic material which in turn must be included in the integral. The value of the surface current depends on the magnetic field which was what you were trying to calculate in the first place. For these problems, using Ampere's law (usually in integral form) is a better choice. For problems where the dominant magnetic material is a highly permeable magnetic core with relatively small air gaps, a magnetic circuit approach is useful. When the air gaps are large in comparison to the magnetic circuit length, fringing becomes significant and usually requires a finite element calculation. The finite element calculation uses a modified form of the magnetostatic equations above in order to calculate magnetic potential. The value of {\mathbf B} can be found from the magnetic potential.
This entry is a derivative of the Magnetostatics article from Wikipedia, the Free Encyclopedia. Authors of the orginial article include: Shantavira, Tradnor and Pearle. History page of the original is here