OpenLLM-France/wikimedia huggingface dataset:
# PlanetPhysics/Clifford Algebra
### A Noncommutative Quantum Observable Algebra is a Clifford Algebra

Let us briefly define the notion of a Clifford algebra . Thus, let us consider first a pair $(V,Q)$, where $V$ denotes a real vector space and $Q$ is a quadratic form on $V$~. Then, the Clifford algebra associated to $V$ , is denoted here as ${\mbox{Cl}}(V)={\mbox{Cl}}(V,Q)$, is the algebra over Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle \bR} generated by $V$ , where for all $v,w\in V$, the relations: $v\cdot w+w\cdot v=-2Q(v,w)~,$ are satisfied; in particular, $v^{2}=-2Q(v,v)$~.
If $W$ is an algebra and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle c : V \lra W} is a linear map satisfying $c(w)c(v)+c(v)c(w)=-2Q(v,w)~,$ then there exists a unique algebra homomorphism Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle \phi : \mbox{Cl}(V) \lra W} such that the diagram
   Failed to parse (unknown function "\xymatrix"): {\displaystyle \xymatrix{&&\hspace*{-1mm}\mbox{Cl}(V)\ar[ddrr]^{\phi}&&\\&&&&\\ V \ar[uurr]^{\mbox{Cl}} \ar[rrrr]_&&&& W}}
commutes. (It is in this sense that Cl(V) is considered to be `universal').
# Motivation and emotion/Book/2013/Banner

Motivation and emotion: Improve your life (2013)
# Psycholinguistics/Development of Speech Production example
## Learning Exercise Example

Example: video 1
* In terms of phonology, this child is able to produce most sounds appropriately. She does produce a consonant cluster reduction (kechup - rather than ketchup).
* Her semantic development is good as she understands that ketchup refers to the sauce in the red bottle and mustard in the yellow bottle.
* Her syntactic speech production shows evidence of her still developing negative phrase structure. She says “I no like ketchup” which is an incorrect syntactic sentence. It should be “I don’t like ketchup”
video 2
* In this example, we see that this child may not yet understand the meaning of the word “gift” as her mother asked her if it’s a gift for her, and the girl replies “ no it’s a mirror”
video 3
* In this video, the child can combie multiple utterances, but seems to make some overregularization errors (morphological development). She says “it didn’t ate him” and it and he falled down”
# Nursery rhymes and songs/Twinkle, Twinkle, Little Star
## Lyrics and actions

Twinkle twinkle, little star, (Face palms outward, spread fingers wide, then make a fist; repeat to beat) How I wonder what you are, (Face palms upward, hold arms out to the side) Up above the world so high, (Point upwards) Like a diamond in the sky, (Make diamond shape with hands) Twinkle twinkle, little star, (Face palms outward, spread fingers wide, then make a fist; repeat to beat) How I wonder what you are, (Face palms upward, hold arms out to the side)

## Elsewhere in the Wikiverse

* "Twinkle, Twinkle, Little Star" on Wikipedia
* Sing free/Twinkle
# Nursery rhymes and songs/What Do You Do With a Drunken Sailor

What do you do with a drunken sailor is a sea shanty that can be fun to do with children. The original shanty is about a drunken sailor but there are some variants geared more towards children.

## Lyrics and Actions
### Tickle variant

What do we do with a sleepy [child's name], What do we do with a sleepy [child's name], What do we do with a sleepy [child's name], Early in the morning.
Take her and wake her and tickle her all over, (tickle child) Take her and wake her and tickle her all over, (tickle child) Take her and wake her and tickle her all over, (tickle child) Early in the morning.
Heave ho and up she rises, (lift child in the air) Heave ho and up she rises, (lift child in the air) Heave ho and up she rises, (lift child in the air) Early in the morning.

## Elsewhere on the Wikiverse

'Drunken Sailor' on Wikipedia
# Nursery rhymes and songs/Wind the Bobbin Up
## Lyrics and actions

Wind the bobbin up, (Create fists and circle hands around each other) Wind the bobbin up, (Continue circling fists) Pull, pull, (Put thumb, first and second fingers together with each hand and pull away from each other) Clap clap clap. (Clap with each word)
Wind it back again, (Circle fists in opposite direction) Wind it back again, (Continue circling fists) Pull, pull, (Put thumb, first and second fingers together with each hand and pull away from each other) Clap clap clap. (Clap with each word)
Point to the ceiling, (Point to the ceiling) Point to the floor, (Point to the floor) Point to the window, (Point to the window) Point to the door, (Point to the window) Put your hands together, (Put hands together) One, Two, Three (Clap with each number)

## Elsewhere in the Wikiverse

"Wind the Bobbin Up" on Wikipedia.
# Nursery rhymes and songs/Zoom, Zoom, Zoom, We're Going to the Moon

This nursery rhyme can be spoken or sung.

## Lyrics and actions

Zoom, zoom, zoom, we're going to the Moon. (point upwards) Zoom, zoom, zoom, we're leaving very soon. (point to wrist, as in a watch) 5... 4... 3... 2... 1... (use fingers to count down) Zoooooom! (lift child into the air)

## Other variants

* Zoom zoom zoom from King County Library System
# Nursery rhymes and songs/The Itsy Bitsy Spider
## Lyrics and actions
### American variant

The itsy bitsy spider climbed up the water spout,
Down came the rain and washed the spider out. Out came the sun and dried up all the rain, And the itsy bitsy spider climbed up the spout again.

### British variant

The incy wincy spider climbed up the water spout, (Touch left thumb to right forefinger, then left forefinger to right thumb, whilst moving hands upwards) Down came the rain and washed the spider out. (Wiggle fingers of both hands, palm out, whilst moving hands down; then make sweeping motion with both hands, center outwards) Out came the sun and dried up all the rain, (Lifting motion with both hands) And the incy wincy spider climbed up the spout again. (Touch left thumb to right forefinger, then left forefinger to right thumb, whilst moving hands upwards)

## Videos

* File:Itsy_Bitsy_Spider_-_La_Araña_Pequeñita.webmAmerican variant with American accent, followed by Spanish language version.
* File:Insey_winsey_spider_song_video.webmBritish variant, American accent

## Elsewhere in the Wikiverse

* 'Itsy Bitsy Spider' on Wikipedia
# Nursing Study Guide

This Nursing Study Guide is intended to be just that, a study guide for nursing. The intended content is for students pursuing becoming Registered Nurses (RN). Limiting contributions to that perspective should make it simpler for RN students to apply what they read here. Nursing students pursuing a different credential are encouraged to create a similar resource, and a link to and from this one might enhance the studies of each if that becomes the case.
This is intended to be a study guide, not an all-inclusive text.
Content is grouped so hopefully content will be easily accessible to students whether taking Fundamentals, or Med-Surge, or Pediatrics, or Maternal health.
# Nursery rhymes and songs/The Grand Old Duke of York
## Lyrics

Oh, the grand old Duke of York, He had ten thousand men; He marched them up to the top of the hill, And he marched them down again.
When they were up, they were up, And when they were down, they were down, And when they were only halfway up, They were neither up nor down.

## Actions

The core movements are often based upon the performers standing whenever a clear "up" is sung, reseating themselves whenever "down" is mentioned and briefly taking an abbreviated half-standing/crouching position for the "only half way up" phrase. A group of performers who, especially in an 'audience participation'-like situation, are originally seated (for example school children in an assembly, or the audience in a theatre - especially for a typical participative segment of a pantomime) will/should end the song back in their original positions.
The first verse is a rather gentle one to react to, with one clear standing and one clear seating action, and so other actions may be given. For example: a stiff salute for the "Duke of York", indicating "ten" by clearly displaying ten fingers (optionally emphasising this on the further syllables of "thou-sand men") and/or forming the hands/arms into a some form depicting a 'hill' summit.
The second verse becomes far more rapid, especially between the two pairs of "downs". The performer may make a bob, between the two, to emphasise the separate positions, rather than just stay up/down). Synchronisation is easily lost by those who are not as quick or able to change positions, or who are new to the 'game' and not as practiced. This activity does help group-bonding in young children and encourages the following the teacher/leader of the activity, but its use is often more as an easily controlled game that promotes physical activity.
# Nursery rhymes and songs/Trit Trot to Boston
## Lyrics and actions

(Bounce child on lap throughout) Trit trot to Boston, Trit trot to Lynn, Do be careful that you don't fall in! (Drop child between legs)
Trit trot to Boston, Trit trot to town, Do be careful that you don't fall down! (Drop child forward)
Trit trot to Boston, Trit trot to Dover, Do be careful that you don't over! (Drop child to the side)
# Nursing Skills Lab

Nursing Skills Lab - Faculty of Nursing - University of Manitoba NURS 2130 & 3280
This Wikiversity site was created for undergraduate nursing students to add their contributions on learning psychomotor skills. Each skill has specific components that need to be addressed. These include:
* Finding readings
* Create objectives
* Create case study for skill
* Develop principle-based evaluation criteria for the skill
* Create 5 multiple-choice questions for the skill
A sample of this has been provided to you. Please see the template for details.
All of the information will be posted on this wikiversity page with the exception of the test questions. Please submit these directly to your course instructor.
# Ohm's law
## Purpose

Understand Ohm's law in the context of electronics, and the meaning of Voltage, Current, and Resistance (Resistors) in the law.

## The Ohm's law

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points.
    $I\propto V$ then: ↑$V$ → ↑$I$ and ↓$V$ → ↓$I$
In the electrical circuit,there are three factors : current,denoted by I; potential difference, denoted by V; and resistance,denoted by R.
    $I={\frac {V}{R}}\;\;\;\;\;\;\;or\;\;\;\;\;\;\;V=I\cdot R$
Based on the work of Georg Simon Ohm, Ohm's law is one of three fundamental laws which begin the study of electronics, in partnership with Kirchhoff's Voltage Law and Kirchhoff's Current Law, laws. These three laws form the frame on which the rest of electronics is constructed. It's important to note that these laws don't apply everywhere, but definitely apply with great precision in wires, which are used to connect most electronic parts together in a circuit. Though individual parts may or may not be analysed by Ohm's law, their relationship to the circuit can be. Any student completing a course in electronics should be capable of quoting Ohm's law in his or her sleep. Not because they learn it once, but because it's used repeatedly in conjunction with almost every other task in electronics.
The actual statement of Ohm's Law is: The current flowing through a metallic conductor is proportional to the Electromotive force applied across its ends, provided the temperature and all other conditions remain constant.
Note there is no mention of resistance; that is simply the name given to the constant of proportionality involved.
Something important to take away from this definition is
* In a passive circuit, the current is a result of the voltage applied
and
* there are definite thermal effects on the resistance (or effective resistance) of conductors.
Ohm's law is linear and therefore assumes linearity in the electronic part. It's easy to think of the law in terms of the line equation $y=mx$ considering resistance to be the constant m, current as the independent variable x, and voltage as the dependent variable y. In this way a proportionate relationship between voltage and current is established. Of course, Ohm's law may be rearranged in three valid and easily derivable ways. It's important to be familiar with each of these and comfortable in recognizing and switching between them.
    $I={\frac {V}{R}}\;\;\;\;\;\;\;or\;\;\;\;\;\;\;V=I\cdot R\;\;\;\;\;\;\ or\;\;\;\;\;\;\;R={\frac {V}{I}}$
Example:
* If you have one amp (1A) of current flowing through a 2 ohm resistor, how much voltage will be across it?
| 2 volt Correct, I=1, R=2, I*R=V, 1*2=2 | 1 volts Try again, using ohm`s law | 1/2 a volt Try again, did you switch current and voltage? | 3 volts Try again, do not add them together, use I*R=V |

## External Links

* Ohm Law: Electronics for Beginners
# Olin College Student Courses/Introduction to 3D Art

Introduction to 3D Art will be taught at Olin College in Needham, MA in the Fall of 2009. The primary goal of this course is to teach basic sculpture techniques through two projects students will work on throughout the semester. Students will review each other's work throughout the process and learn to offer constructive criticism. Note: this is not ceramics.
# Real numbers/Heron's method/Convergence/Exercise

Let $a\in \mathbb {R}$ be a non-negative real number and $c\in \mathbb {R} _{+}$. Prove that the sequence defined recursively as $x_{0}=c$ and
    $x_{n+1}:={\frac {x_{n}+a/x_{n}}{2}}\,,$
converges to ${\sqrt {a}}$.
# Real numbers/Convergent sequences/Rules/Fact

Let ${\left(x_{n}\right)}_{n\in \mathbb {N} }$ and ${\left(y_{n}\right)}_{n\in \mathbb {N} }$ be convergent sequences. Then the following statements hold.
* The sequence ${\left(x_{n}+y_{n}\right)}_{n\in \mathbb {N} }$ is convergent, and holds.
    $\lim _{n\rightarrow \infty }{\left(x_{n}+y_{n}\right)}={\left(\lim _{n\rightarrow \infty }x_{n}\right)}+{\left(\lim _{n\rightarrow \infty }y_{n}\right)}\,$
* The sequence ${\left(x_{n}\cdot y_{n}\right)}_{n\in \mathbb {N} }$ is convergent, and holds.
    $\lim _{n\rightarrow \infty }{\left(x_{n}\cdot y_{n}\right)}={\left(\lim _{n\rightarrow \infty }x_{n}\right)}\cdot {\left(\lim _{n\rightarrow \infty }y_{n}\right)}\,$
* For $c\in \mathbb {R}$, we have
    $\lim _{n\rightarrow \infty }cx_{n}=c{\left(\lim _{n\rightarrow \infty }x_{n}\right)}\,.$
* Suppose that $\lim _{n\rightarrow \infty }x_{n}=x\neq 0$ and $x_{n}\neq 0$ for all $n\in \mathbb {N}$. Then $\left({\frac {1}{x_{n}}}\right)_{n\in \mathbb {N} }$ is also convergent, and holds.
    $\lim _{n\rightarrow \infty }{\frac {1}{x_{n}}}={\frac {1}{x}}\,$
* Suppose that $\lim _{n\rightarrow \infty }x_{n}=x\neq 0$ and that $x_{n}\neq 0$ for all $n\in \mathbb {N}$. Then $\left({\frac {y_{n}}{x_{n}}}\right)_{n\in \mathbb {N} }$ is also convergent, and holds.
    $\lim _{n\rightarrow \infty }{\frac {y_{n}}{x_{n}}}={\frac {\lim _{n\rightarrow \infty }y_{n}}{x}}\,$
# Real numbers/Convergent sequences/Rules/Fact/Proof

(1). Denote the limits of the sequences by $x$ and $y$, respectively. Let $\epsilon >0$ be given. Due to the convergence of the first sequence, there exists for
    $\epsilon '={\frac {\epsilon }{2}}\,$
some $n_{0}$ such that for all $n\geq n_{0}$ the estimate
    $\vert {x_{n}-x}\vert \leq \epsilon '\,$
holds. In the same way there exists due to the convergence of the second sequence for $\epsilon '={\frac {\epsilon }{2}}$ some $n_{0}'$ such that for all $n\geq n_{0}'$ the estimate
    $\vert {y_{n}-y}\vert \leq \epsilon '\,$
holds. Set
    $N={\max {\left(n_{0},n_{0}'\right)}}\,.$
Then for all $n\geq N$ the estimate
    ${\begin{aligned}\vert {x_{n}+y_{n}-(x+y)}\vert &=\vert {x_{n}+y_{n}-x-y}\vert \\&=\vert {x_{n}-x+y_{n}-y}\vert \\&\leq \vert {x_{n}-x}\vert +\vert {y_{n}-y}\vert \\&\leq \epsilon '+\epsilon '\\&=\epsilon \end{aligned}}$
holds.
(2). Let $\epsilon >0$ be given. The convergent sequence ${\left(x_{n}\right)}_{n\in \mathbb {N} }$ is bounded, due to fact, and therefore there exists a $D>0$ such that $\vert {x_{n}}\vert \leq D$ for all $n\in \mathbb {N}$. Set $x:=\lim _{n\rightarrow \infty }x_{n}$ and $y:=\lim _{n\rightarrow \infty }y_{n}$. We put $C:={\max {\left(D,\vert {y}\vert \right)}}$. Because of the convergence, there are natural numbers $N_{1}$ and $N_{2}$ such that
    $\vert {x_{n}-x}\vert \leq {\frac {\epsilon }{2C}}{\text{ for }}n\geq N_{1}{\text{ and }}\vert {y_{n}-y}\vert \leq {\frac {\epsilon }{2C}}{\text{ for }}n\geq N_{2}.$
These estimates hold also for all $n\geq N:={\max {\left(N_{1},N_{2}\right)}}$. For these numbers, the estimates
    ${\begin{aligned}\vert {x_{n}y_{n}-xy}\vert &=\vert {x_{n}y_{n}-x_{n}y+x_{n}y-xy}\vert \\&\leq \vert {x_{n}y_{n}-x_{n}y}\vert +\vert {x_{n}y-xy}\vert \\&=\vert {x_{n}}\vert \vert {y_{n}-y}\vert +\vert {y}\vert \vert {x_{n}-x}\vert \\&\leq C{\frac {\epsilon }{2C}}+C{\frac {\epsilon }{2C}}\\&=\epsilon \end{aligned}}$
hold.
For the other parts, see exercise, exercise and exercise.
# Real numbers/Geometric mean/Definition

For two nonnegative real numbers $x$ and $y$, we call
    ${\sqrt {x\cdot y}}$
their geometric mean.
# Real numbers/Floor/Definition

For a real number $x$, the floor $\left\lfloor x\right\rfloor$ is defined as
    $\left\lfloor x\right\rfloor =n,{\text{ if }}x\in [n,n+1[{\text{ and }}n\in \mathbb {Z} .$
# Real numbers/Convergent sequences/Rules/4/Fact/Proof/Exercise

Let ${\left(x_{n}\right)}_{n\in \mathbb {N} }$ be a real convergent sequence such that $x_{n}\neq 0$ for all $n\in \mathbb {N}$ and $\lim _{n\rightarrow \infty }x_{n}=x\neq 0$. Show that ${\left({\frac {1}{x_{n}}}\right)}_{n\in \mathbb {N} }$is also convergent and
    $\lim _{n\rightarrow \infty }{\frac {1}{x_{n}}}={\frac {1}{x}}\,$
holds.
# Real numbers/Convergent sequences/Rules/5/Fact/Proof/Exercise

Let ${\left(x_{n}\right)}_{n\in \mathbb {N} }$ and ${\left(y_{n}\right)}_{n\in \mathbb {N} }$ be real convergent sequences. Suppose that $\lim _{n\rightarrow \infty }x_{n}=x\neq 0$ and $x_{n}\neq 0$ for all $n\in \mathbb {N}$. Show that${\left({\frac {y_{n}}{x_{n}}}\right)}_{n\in \mathbb {N} }$is also convergent and that
    $\lim _{n\rightarrow \infty }{\frac {y_{n}}{x_{n}}}={\frac {\lim _{n\rightarrow \infty }y_{n}}{x}}\,$
holds.
# Real numbers/Different subsets/Boundedness/Exercise

Determine whether the following subsets $M\subseteq \mathbb {R}$ are bounded or not.
* $\mathbb {N}$,
* $\left\{{\frac {1}{2}},{\frac {-3}{7}},{\frac {-4}{9}},{\frac {5}{9}},{\frac {6}{13}},{\frac {-1}{3}},{\frac {1}{4}}\right\}$,
* $]{-5},2]$,
* ${\left\{{\frac {1}{n}}\mid n\in \mathbb {N} _{+}\right\}}$,
* ${\left\{{\frac {1}{n}}\mid n\in \mathbb {N} _{+}\right\}}\cup \{0\}$,
* $\mathbb {Q} _{-}$,
* ${\left\{x\in \mathbb {Q} \mid x^{2}\leq 2\right\}}$,
* ${\left\{x\in \mathbb {Q} \mid x^{2}\geq 4\right\}}$,
* ${\left\{x^{2}\mid x\in \mathbb {Z} \right\}}$.
# Real numbers/Convergent sequences/Rules/Exercise

Prove the statements (1), (3) and (5) of the rules.
# PlanetPhysics/Maxwell's Equations

Maxwell's equations are a set of four partial differential equations first combined by James Clerk Maxwell. Together, they completely describe classical electromagnetic phenomena, just as Newton's laws completely describe classical mechanical phenomena. All four are named after persons other than Maxwell, but Maxwell was the first to add the displacement current term to Amp\`ere's Law, which led to the association of electromagnetic waves with light and paved the way for the discovery of special relativity. All four equations can be written in both integral and differential forms, with both forms convenient for specific problems. Note that strictly speaking these are Maxwell's equation in vacuo, with different forms for interaction with matter.

### Notation

Throughout this article SI units are adopted for clarity, but the interesting mathematical aspects of the equations are independent of the constants $\mu _{0}$ and $\epsilon _{0}$, and indeed of the physical meaning of the equations.
   $\mathbf {E} ={\mbox{Electrical field strength, SI units Volt m}}^{-1}$
   $\mathbf {B} ={\mbox{Magnetic flux density, SI units Tesla}}$
   Failed to parse (syntax error): {\displaystyle \mathbf{J} = \mbox{Current density, SI units Amp\`ere m}^{-3} }
   $\mathbf {\epsilon _{0}} ={\mbox{Permittivity of free space}}\approx 8.85\times 10^{-12}{\mbox{m}}^{-1}$
   $\mathbf {\mu _{0}} ={\mbox{Permeability of free space}}=4\pi \times 10^{7}{\mbox{Henry m}}^{-1}$

### Gauss' Law of Electrostatics

Differential form
   $\nabla \cdot \mathbf {E} ={\frac {\rho }{\epsilon _{0}}}$
Integral form
   $\oint _{S}\mathbf {E} \cdot \mathrm {d} \mathbf {A} ={\frac {q}{\epsilon _{0}}}$
where $q$ is the charge enclosed in the volume bounded by the surface $S$.

### Gauss' Law of Magnetostatics

   $\nabla \cdot \mathbf {B} =0$
   $\oint _{S}\mathbf {B} \cdot \mathrm {d} \mathbf {S} =0$
This law can be interpreted as a statement of the non-existence of magnetic monopoles, a fact confirmed by all experiments to date.

### Faraday's Law

Differential form
   $\nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}$

### Amp\`ere's Law

Differential form
   $\nabla \times \mathbf {B} =-\mu _{0}\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}$
Integral form

### Properties of Maxwell's Equations

These four equations together have several interesting properties:
* Lorentz invariance
* Gauge invariance
* Invariance under the transformation Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle B \rightarrow \frac{E}} , $E\rightarrow Bc$