OpenLLM-France/wikimedia huggingface dataset:
# PlanetPhysics/Sources and Sinks of Vector Field

Let the vector field ${\vec {U}}$ of $\mathbb {R} ^{3}$ be interpreted, as in the remark of the parent entry, as the velocity field of a stationary flow of a liquid.\, Then the flux
   $\oint _{a}{\vec {U}}\cdot d{\vec {a}}$
of ${\vec {U}}$ through a closed surface $a$ expresses how much more liquid per time-unit it comes from inside of $a$ to outside than contrarily.\, Since for a usual incompressible liquid, the outwards flow and the inwards flow are equal, we must think in the case that the flux differs from 0 either that the flowing liquid is suitably compressible or that there are inside the surface some sources creating liquid and sinks annihilating liquid.\, Ordinarily, one uses the latter idea.\, Both the sources and the sinks may be called sources, when the sinks are negative sources .\, The flux of the vector ${\vec {U}}$ through $a$ is called the productivity or the strength of the sources inside $a$.
For example, the sources and sinks of an Electric Field (${\vec {E}}$) are the locations containing positive and negative charges, respectively.\, The Gravitational Field has only sinks, which are the locations containing mass.\\
The expression
   ${\frac {1}{\Delta v}}\oint _{\partial \Delta v}{\vec {U}}\cdot d{\vec {a}},$
where $\Delta v$ means a region in the vector field and also its volume, is the productivity of the sources in $\Delta v$ per a volume-unit.\, When we let $\Delta v$ to shrink towards a point $P$ in it, to an infinitesimal volume-element $dv$, we get the limiting value
   ${\begin{matrix}\varrho \;:=\;{\frac {1}{dv}}\oint _{\partial dv}{\vec {U}}\cdot d{\vec {a}},\end{matrix}}$
called the source density in $P$.\, Thus the productivity of the source in $P$ is $\varrho \,dv$.\, If\, $\varrho =0$, there is in $P$ neither a source, nor a sink.\\
The Gauss's theorem
   $\int _{v}\nabla \cdot {\vec {U}}\,dv\;=\;\oint _{a}{\vec {U}}\cdot d{\vec {a}}$
applied to $dv$ says that
   ${\begin{matrix}\nabla \cdot {\vec {U}}\;=\;{\frac {1}{dv}}\oint _{\partial dv}{\vec {U}}\cdot d{\vec {a}}.\end{matrix}}$
Accordingly,
   ${\begin{matrix}\varrho \;=\;\nabla \cdot {\vec {U}}\end{matrix}}$
and
   ${\begin{matrix}\oint _{a}{\vec {U}}\cdot d{\vec {a}}\;=\;\int _{v}\varrho \,dv.\end{matrix}}$
This last formula can be read that\, the flux of the vector through a closed surface equals to the total productivity of the sources inside the surface. \, For example, if ${\vec {U}}$ is the electric flux density ${\vec {D}}$, (4) means that the electric flux through a closed surface equals to the total charge inside.
# PlanetPhysics/Spectroscopy Areas
## Spectroscopy Areas

* Atomic spectroscopy
* Emission spectroscopy
* Electron spectroscopy, including Auger spectroscopy
* Electron spin resonance
* \htmladdnormallink{Fourier transform {http://planetphysics.us/encyclopedia/FourierTransforms.html} spectroscopy and imaging}
* Fluorescence spectroscopy , including Fluorescence correlation spectroscopy (FCS) and fluorescence cross-correlation spectroscopy (FCCS)
* Gamma spectroscopy
* Infrared spectroscopy (IR)
* Laser induced breakdown spectroscopy
* mass spectrometry (MS)
* microspectroscopy: including fluorescence/FLIM, IR and NIR microspectroscopy
* Nanospectroscopy
* $M{\ddot {o}}ssbauer$ spectroscopy
* Near Infrared spectroscopy (NIR)
* Hyperspectral, or Chemical NIR (IR) Imaging
* Nuclear magnetic resonance spectroscopy, including FT-NMR, 2D-FT NMR and NMR Imaging
* positron annihilation spectroscopy and imaging (PET scanning)
* Raman spectroscopy
* Resonance enhanced multiphoton ionization
* Rotational microwave spectroscopy
* Terahertz spectroscopy
* Ultraviolet-visible spectroscopy vibrational spectroscopy X-ray spectroscopy
# PlanetPhysics/Spacetime Interval Is Invariant for a Lorentz Transformation

The spacetime interval between two events $E_{1}(x_{1},y_{1},z_{1},t_{1})$ and $E_{2}(x_{2},y_{2},z_{2},t_{2})$ is defined as
$(\triangle s)^{2}=c^{2}\triangle t^{2}-(\triangle x)^{2}-(\triangle y)^{2}-(\triangle z)^{2}.$
If $\triangle s$ is in reference frame $S$, then $\triangle s'$ is in reference frame $S'$ moving at a velocity $u$ along the x-axis. Therefore, to show that the spacetime interval is invariant under a Lorentz transformation we must show
$(\triangle s)^{2}=(\triangle s')^{2}$
with the reference frames related by The Lorentz transformation $x'={\frac {x-ut}{\sqrt {1-u^{2}/c^{2}}}}$ $y'=y$ $z'=z$ $t'={\frac {t-ux/c^{2}}{\sqrt {1-u^{2}/c^{2}}}}.$
The change in coordinates between events in the $S'$ frame is then given by
$\triangle x'=\left({\frac {x_{2}-ut_{2}}{\sqrt {1-u^{2}/c^{2}}}}\right)-\left({\frac {x_{1}-ut_{1}}{\sqrt {1-u^{2}/c^{2}}}}\right)={\frac {\triangle x-u\triangle t}{\sqrt {1-u^{2}/c^{2}}}}$
$\triangle y'=y_{2}-y_{1}=\triangle y$
$\triangle z'=z_{2}-z_{1}=\triangle z$
$\triangle t'=\left({\frac {t_{2}-ux_{2}/c^{2}}{\sqrt {1-u^{2}/c^{2}}}}\right)-\left({\frac {t_{1}-ux_{1}/c^{2}}{\sqrt {1-u^{2}/c^{2}}}}\right)={\frac {\triangle t-u\triangle t}{\sqrt {1-u^{2}/c^{2}}}}.$
Squaring the terms yield
$(\triangle x')^{2}=\left({\frac {\triangle x-u\triangle t}{\sqrt {1-u^{2}/c^{2}}}}\right)\left({\frac {\triangle x-u\triangle t}{\sqrt {1-u^{2}/c^{2}}}}\right)={\frac {(\triangle x)^{2}-2u\triangle x\triangle t+u^{2}(\triangle t)^{2}}{1-u^{2}/c^{2}}}$
$(\triangle y')^{2}=(\triangle y)^{2}$
$(\triangle z')^{2}=(\triangle z)^{2}$
$(\triangle t')^{2}=\left({\frac {\triangle t-u\triangle t}{\sqrt {1-u^{2}/c^{2}}}}\right)\left({\frac {\triangle t-u\triangle t}{\sqrt {1-u^{2}/c^{2}}}}\right)={\frac {(\triangle t)^{2}-2u\triangle x\triangle t/c^{2}+u^{2}(\triangle x)^{2}/c^{4}}{1-u^{2}/c^{2}}}.$
Substituting these terms into the spacetime interval gives
$(\triangle s')^{2}={\frac {c^{2}((\triangle t)^{2}-2u\triangle x\triangle t/c^{2}+u^{2}(\triangle x)^{2}/c^{4})}{1-u^{2}/c^{2}}}-{\frac {((\triangle x)^{2}-2u\triangle x\triangle t+u^{2}(\triangle t)^{2})}{1-u^{2}/c^{2}}}-(\triangle y)^{2}-(\triangle z)^{2}.$
Adding the first two terms with common denominators together yields
$(\triangle s')^{2}={\frac {c^{2}(\triangle t^{2})-(\triangle x)^{2}-u^{2}(\triangle t)^{2}+u^{2}(\triangle x)^{2}/c^{2}}{1-u^{2}/c^{2}}}-(\triangle y)^{2}-(\triangle z)^{2}.$
Pulling out a $-u^{2}/c^{2}$
$(\triangle s')^{2}={\frac {c^{2}(\triangle t^{2})-(\triangle x)^{2}-u^{2}/c^{2}(c^{2}(\triangle t)^{2}+(\triangle x)^{2})}{1-u^{2}/c^{2}}}-(\triangle y)^{2}-(\triangle z)^{2}.$
Factoring out a $c^{2}(\triangle t)^{2}-(\triangle x)^{2}$ in the numerator
$(\triangle s')^{2}={\frac {(c^{2}(\triangle t^{2})-(\triangle x)^{2})(1-u^{2}/c^{2})}{1-u^{2}/c^{2}}}-(\triangle y)^{2}-(\triangle z)^{2}.$
Finally, canceling terms gives
$(\triangle s')^{2}=c^{2}(\triangle t^{2})-(\triangle x)^{2}-(\triangle y)^{2}-(\triangle z)^{2}=(\triangle s)^{2}.$
Hence, the spacetime interval is invariant under a Lorentz transformation.
# PlanetPhysics/Spectroscopy Topics

Spectroscopy is broadly described as a field in physics concerned with recording of spectra, ranging from gamma to X-rays, neutrons, UV, visible, NIR, IR, microwaves, radio frequency, ultrasound, acoustic waves, gravitational, etc.
This is a contributed topic on spectroscopy themes and underlying concepts and theories.
* Electrical fields
* magnetic fields
* Electromagnetic fields and waves
* Biot-Savart equations
* Maxwell's equations
* vector calculus in electrostatics
* Vector and scalar potentials
* Kramers-Kronig relations
* Stokes theorem
* Laplace equation
* Poisson equation
* Einstein's GR equations
* Planck's equation
* Polarization
* Polarizability
* Poynting vector
* Reflection spectroscopy (NIR, vis, electron, etc.)
* Transmission spectroscopy (vis/UV, NIR/IR, etc.)
* Polarized IR and Polarized NIR
* Vibrational Circular Dichroism (VCD )
* Absorption spectroscopy (vis/UV, NIR/IR, NMR, EPR/ESR, FMR etc.)
* Spectroscopy and spectrophotometry
* Coherent spectroscopy of atoms and molecules
* Electron spectroscopy (x-ray photoelectron (XPS), Auger electron spectroscopy (AES), and so on)
* EXAFS and X-ray spectroscopy
* Neutron spectroscopy
* M\"ossbauer spectroscopy
* Infrared and Raman spectroscopy
* Hyperspectral (NIR, IR, UV/vis) imaging
* Microspectroscopy
* Fluorescence Correlation Spectroscopy (FCS )
* Fresnel equations
* Diffraction equations
* Electric dipoles
* Dipole-dipole interactions
* dipole-induced dipole interactions
* Ion-dipole interactions
* London dispersion forces
* Yang-Mills equations
* Yang-Baxter equations
* Quantum Yang-Baxter equations
* Total intermolecular pair potentials
* Optical constants
* Extinction coefficient
* Refraction and reflection coefficients
* Total internal reflection
* Derivation of the Kramers-Kronig relations
* Lorentz model
* AC and DC conductivity
* Displacement
* Skin depth
# Projection/Idempotent/Definition

Let $K$ be a field and $V$ a $K$-vector space. A linear mapping
    $\varphi \colon V\longrightarrow V$
is called a projection, if
    $\varphi ^{2}=\varphi \,$
holds.
# Project management/Transfer results

Wikiversity:Main Page → Practical Arts and Sciences → School of Project Management → Project Management based on Mindmaps
# Projection/Linear subspace/Idempotent/Fact/Proof

Let $\pi _{U}$ be the projection onto $U$. Write $v=u+u'$ with $u\in U,\,u'\in U'$. Then we have
    $\pi _{U}(\pi _{U}(u+u'))=\pi _{U}(u)=u=\pi _{U}(u+u')\,,$
and hence
    $\pi _{U}^{2}=\pi _{U}\,.$
Suppose now that
    $\varphi \colon V\longrightarrow V$
is an endomorphism with
    $\varphi ^{2}=\varphi \,.$
Let $x\in \operatorname {kern} \varphi \cap \operatorname {Im} \varphi$. Then there exists some $y\in V$ such that
    $\varphi (y)=x\,.$
Then
    $x=\varphi (y)=\varphi (\varphi (y))=\varphi (x)=0\,.$
This means that the intersection of these linear subspaces is the zero space. For an arbitrary $v\in V$, we write
    $v=\varphi (v)+(v-\varphi (v))\,.$
Here, the first summand belongs to the image and, because of
    $\varphi (v-\varphi (v))=\varphi (v)-\varphi (\varphi (v))=\varphi (v)-\varphi (v)=0\,,$
the second summand belongs to the kernel. Therefore, we have a direct sum decomposition.
# Programming Fundamentals/Variables/Pseudocode
## See Also

* Pseudocode
* Gaddis Pseudocode
# Programming Fundamentals/Variables/Go
## Try It

Copy and paste the code above into one of the following free online development environments or use your own Go compiler / interpreter / IDE.
* CodeChef
* Ideone
* GoLang.org
* paiza.IO
* repl.it
* TutorialsPoint

## See Also

* GoLang.org: Documentation
# Programming Fundamentals/Variables/Input-Process-Output Model

The input–process–output (IPO) model is a widely used approach in systems analysis and software engineering for describing the structure of an information processing program or other process. This activity introduces the IPO model using a simple calculation. This activity will help you understand how to design a simple program.

## Objectives

* Understand the input-process-output model.
* Create a simple program using a visual programming environment.

## Prerequisites

* Review Creating Flowcharts.
* Review MathsIsFun: Temperature Conversion.
* The formulas for temperature conversion are:
** C = (F - 32) * 5 / 9
** F = C * 9 / 5 + 32
* An operator is a character or symbol used to perform an arithmetic, logical, or bitwise operation on one or more operands.
* String concatenation is the joining of character strings end-to-end.
* An assignment statement sets and/or re-sets the value stored in the storage location(s) denoted by a variable name; in other words, it copies a value into the variable.

## Introduction

Review the flowchart example on the right.

### Questions

* What flowcharting symbol is used to indicate the beginning and ending of a program?
* What flowcharting symbol is used to indicate annotations or comments?
* What flowcharting symbol is used to indicate variable declaration?
* What flowcharting symbol is used to indicate input and output?
* What flowcharting symbol is used to indicate a process or calculation?
* What operator is used for addition, subtraction, multiplication, and division?
* What operator is used for assignment?
* What operator is used for string concatenation?

## Activity

With a partner, perform the following:
* Using a visual programming language, create a program matching the flowchart on the right.
* Save the program.
* Test the program with known Fahrenheit-Celsius temperature pairs to make sure it works correctly.
* Trade places, so that both partners have an opportunity to "drive" the visual programming environment.
* Copy the program and change it so that it performs the opposite calculation, converting Celsius temperatures to Fahrenheit.
* Save the program.
* Test the program with known Celsius-Fahrenheit temperature pairs to make sure it works correctly.

## Applications

* Identify specific steps which must be followed when creating a program using the Input-Process-Output model.
* Discuss your activity experience with your classmates. What surprised you? What have you learned that you can apply to your own school or work environment?
# Programming Fundamentals/Variables/PowerShell
## Try It

Copy and paste the code above into one of the following free online development environments or use your own PowerShell compiler / interpreter / IDE.

### Online

* There are some options, but none are fully functional at this time.

### Windows

* Microsoft:Starting Windows PowerShell

### macOS / Linux

* HowToGeek: How to Install Microsoft PowerShell on Linux or OS X

## See Also

* PowerShell
# Programming Fundamentals/Variables/Java
## Try It

Copy and paste the code above into one of the following free online development environments or use your own Java compiler / interpreter / IDE.
* CodeChef
* GDB Online
* Ideone
* InterviewBit
* paiza.IO
* PythonTutor
* repl.it
* TutorialsPoint

## See Also

* Wikibooks: Java Programming
# Programming Fundamentals/Variables/JavaScript
## Try It

Copy and paste the code above into one of the following free online development environments or use your own JavaScript compiler / interpreter / IDE.
* Chapman.edu: Online JavaScript Interpreter
* CodeChef
* GDB Online
* Ideone
* JS.do
* paiza.IO
* PythonTutor
* repl.it

## See Also

* Wikibooks: JavaScript
# Programming Fundamentals/Variables/PHP
## Try It

Copy and paste the code above into one of the following free online development environments or use your own PHP compiler / interpreter / IDE.
* CodeChef
* GDB Online
* Ideone
* Online PHP
* paiza.IO
* repl.it
* W3Schools

## See Also

* Wikibooks: PHP Programming
# Programming Fundamentals/Variables/Fortran
## Try It

Copy and paste the code above into one of the following free online development environments or use your own Fortran compiler / interpreter / IDE.
* CodeChef
* GDB Online
* Ideone
* RexTester
* TutorialsPoint

## See Also

* TutorialsPoint: Fortran
* Fortran90.org: Best Practices
# Programming Fundamentals/Variables/Lua
## Try It

Copy and paste the code above into one of the following free online development environments or use your own Lua compiler / interpreter / IDE.
* CodeChef
* Ideone
* repl.it
* TutorialsPoint

## See Also

* Lua.org: Reference Manual
# Programming Fundamentals/Variables/Perl
## Try It

Copy and paste the code above into one of the following free online development environments or use your own Perl compiler / interpreter / IDE.
* CodeChef
* Ideone
* paiza.IO
* TutorialsPoint

## See Also

* Wikibooks: Perl Programming
# Motivation and emotion/Book/2015/Emotion as motivation
## Emotion as motivation

* Extreme Emotion
* The continuum of emotion and motivation
* Theory three
# Motivation and emotion/Book/2015/Emotional Freedom Techniques/Practice EFT now: Click here for your own step-by-step guide

* Practice EFT now: A step-by-step guide
* Step 1. Begin by sitting in a comfortable, quiet position. Take a deep breath and evoke the memory or event causing you distress, noticing the emotions you are experiencing. Establish where the feelings exist in your body, and rate them on a Subjective Units of Distress (SUDS) scale, with 0 being no effect and 10 being maximum intensity. If you have noticed any pain, you can also rate this using the same scale. This is your starting number and will provide a standard to assess progress after each round.
* Step 2.
* Next, verbally express the negative cognitions with an opposing, positive state of self-acceptance. This is known as the ‘setup statement’.
* For example “Even though I [insert problem statement], I deeply and completely accept myself anyway.”
* You are now ready to complete the tapping component of the technique (see Figure ? for tapping points).
* Step 3.
* Repeat the 'setup statement' aloud three times while rubbing on your Sore Spot located or tapping on the Karate Chop Point (point 12) using your index finger and middle finger. You might find it easiest to use your dominant hand to tap on your non-dominant hand.
* Step 4.
* Complete the rest of the tapping sequence as labelled in the figure, starting at point one and continuing through to point 12.
* Tap about seven times on each point, repeating the 'reminder phrase' the whole time. The 'reminder phrase' describes the problem in a short phrase or single word and is there to remind you what you are working on throughout the sequence.
* It doesn't matter if you swap tapping sides during the round, for example, you can tap about your left eye and under your right arm.
* Step 5.
* After completing the sequence of tapping points, take another deep breath. Re-assess and rate your level of distress out of 10 again.
* If the emotional intensity is getting worse, consider changing the phrasing to be more specific to the problem, and be sure to say it with conviction each time.
* If the intensity is lessening, continue the rounds until you reach zero or close to it.
* For each subsequent round, adjust the setup statement to “Even though I still feel [problem statement]” “Even though I still have this [problem statement]"
* (Craig, 2011).
* Figure 4. EFT tapping points.
# Motivation and emotion/Book/2015/Emotional Freedom Techniques/Would you like to practice EFT now? Click here for your very own step-by-step guide!

* Practice EFT now
* Step one. Begin by sitting in a comfortable, quiet position. Take a deep breath and evoke the memory or event causing you distress and notice any emotions that arise. Establish where the feelings exist in your body and rate them on a Subjective Units of Distress (SUDS) scale, with zero being no effect and 10 being maximum intensity. You can also rate any pain using the same scale. This is your starting number and will provide a standard to assess your progress after each round.
* Step two. Verbally express your negative cognitions with an opposing, positive statement of self-acceptance. This is known as the ‘setup statement’. For example “Even though I [insert problem statement], I deeply and completely accept myself.” After you have developed your setup statement, you are ready to complete the tapping component of the technique. Please see the figure below for each of the tapping points.
* Step three. Repeat the 'setup statement' aloud three times while rubbing on your sore spot or tapping on the karate chop point (point 12) using your index finger and middle finger. You might find it easiest to use your dominant hand to tap on your non-dominant hand.
* Step four. Complete the rest of the tapping sequence as labelled in the figure, starting at point one and continuing through to point 12. Tap about seven times on each point, repeating the 'reminder phrase' the whole time. The 'reminder phrase' describes the problem in a short phrase or single word and is there to prompt you throughout the sequence.
* Step five. After completing the sequence of tapping points, take another deep breath and re-assess your level of distress out of 10. If the emotional intensity is getting worse, consider changing the phrasing to be more specific to the problem. If the intensity is lessening, continue the rounds until you reach zero. For each subsequent round, adjust the setup statement to “Even though I still feel [problem statement]” or “Even though I still have this [problem statement]".
* (Craig, 2011).
* Figure 4. EFT tapping points.
# Solar System, interactive/Earth/Solar System overview/Mars

Mars
Mars is sometimes called the "Red Planet". Mars has two tiny moons which orbit very close to the surface. Their names are Phobos and Deimos.
# Solar System, interactive/Earth/Solar System overview/Moon

Moon
The Moon is a natural object that moves round the Earth. It is a satellite. Its path is called its orbit. It has four phases:
* New moon
* First Quarter
* Full Moon (above)
* Last Quarter
# Solar System, interactive/Earth/Solar System overview/Pluto

Pluto
# Solar System, interactive/Earth/Solar System overview/SSQ

Questions to go
Before leaving to the open space, you should answer some questions:
1. How many planets has our Solar system?
# Solar System, interactive/Earth/Solar System overview/Saturn

Saturn
# Solar System, interactive/Earth/Solar System overview/Sun

The Sun - everything orbits around the Sun in our solar system
The Sun is a flaming ball, a star situated in the center of Our Solar System. Planets, such as The Earth, Mars, Venus or Jupiter are flying around it on their orbits. There are also orbits of asteroids, comets and dust. The Sun consists of hydrogen, helium and other elements. Most of them are gases. In the center of the Sun, hydrogen is slowly changed into the helium. During this proces a lot of light energy is emited. This light energy makes day on the Earth and also enable the life on the Earth. Clicking on the Sun, you can get more information about this star.
# Solar System, interactive/Earth/Solar System overview/Uranus

Uranus
# Solar System, interactive/Earth/Solar System overview/Mercury

Mercury
Mercury is the smallest planet in our solar system and it also is the closest planet to the sun.
# Solar System, interactive/Earth/Solar System overview/Neptune

Neptune
# Solar System, interactive/Earth/Solar System overview/Venus

Venus
Venus is the hottest planet in the solar system. Venus is the brightest planet in the
whole solar system and it is also known as the morning and the evening star.
# Motivation and emotion/Book/2022/Banner

* Motivation and emotion:
* Understanding and improving our motivational and emotional lives using psychological science (2022)
* Key
* best chapter
* high quality chapter
* low quality chapter
* best presentation
* high quality presentation
# Server-Side Scripting/Strings and Files/Go
## Try It

See Server-Side Scripting/Routes and Templates/Go to create a test environment.
# Server-Side Scripting/SQL Databases/Node.js (Express)
## Try It

See Server-Side Scripting/Routes and Templates/Node.js (Express) to create a test environment.
# Server-Side Scripting/SQL Databases/Python (FastAPI)
## Try It

See Server-Side Scripting/Routes and Templates/Python (FastAPI) to create a test environment.

## See Also

* FastAPI
* SQLite
# Server-Side Scripting/SQL Databases/Node.js (Express MySQL)
## Try It

See Server-Side Scripting/Routes and Templates/Node.js (Express) to create a test environment.
# Server-Side Scripting/SQL Databases/PHP
## Try It

Copy and paste the code above into the following free online development environment or use your own PHP compiler / interpreter / IDE.
* PHPFiddle
# Server-Side Scripting/SQL Databases/Python (Flask)
## Try It

Copy and paste the code above into the following free online development environment or use your own Python (Flask) compiler / interpreter / IDE.
* Repl.it

## See Also

* Flask
# Server-Side Scripting/Strings and Files/Node.js (Express)
## Try It

Copy and paste the code above into the following free online development environment or use your own Node.js (Express) compiler / interpreter / IDE.
* Repl.it
# Server-Side Scripting/SQL Databases/Go MySQL
## Try It

See Server-Side Scripting/Routes and Templates/Go to create a test environment.