OpenLLM-France/wikimedia huggingface dataset:
# DESCRIPTION:

Returns TRUE for any-word values.
ANY-WORD? is an action value.

# ARGUMENTS

* value -- (Type: any-type)
# DESCRIPTION:

Appends a value to the tail of a series and returns the series head.
APPEND is a function value.

# ARGUMENTS

* series -- (Type: series port)
* value -- (Type: any)

# REFINEMENTS

* /only -- Appends a block value as a block
# DESCRIPTION:

Returns the trigonometric arccosine in degrees.
ARCCOSINE is a native value.

# ARGUMENTS

* value -- (Type: number)

# REFINEMENTS

* /radians -- Returns result in radians.
# DESCRIPTION:

Returns the trigonometric arcsine in degrees.
ARCSINE is a native value.

# ARGUMENTS

* value -- (Type: number)

# REFINEMENTS

* /radians -- Returns result in radians.
# DESCRIPTION:

Coerces any type of string into a binary! datatype without copying it.
AS-BINARY is a native value.

# ARGUMENTS

* string -- (Type: any-string)
# DESCRIPTION:

Combine X and Y values into a pair.
AS-PAIR is a function value.

# ARGUMENTS

* x -- (Type: number)
* y -- (Type: number)
# Rebol Programming/aqua

AQUA is a tuple of value: 40.100.130
# DESCRIPTION:

Returns the trigonometric arctangent in degrees.
ARCTANGENT is a native value.

# ARGUMENTS

* value -- (Type: number)

# REFINEMENTS

* /radians -- Returns result in radians.
# DESCRIPTION:

Apply a function to a reduced block of arguments.
APPLY is a function value.

# ARGUMENTS

* func -- Function value to apply (Type: any-function)
* block -- Block of args, reduced first (unless /only) (Type: block)

# REFINEMENTS

* /only -- Use arg values as-is, do not reduce the block

# (SPECIAL ATTRIBUTES)

* throw
# DESCRIPTION:

Makes and initializes a series of a given size.
ARRAY is a function value.

# ARGUMENTS

* size -- Size or block of sizes for each dimension (Type: integer block)

# REFINEMENTS

* /initial -- Specify an initial value for all elements
** value -- Initial value (will be called each time if a function) (Type: any)

# (SPECIAL ATTRIBUTES)

* catch
# String Theory/Introduction
## String Theory as a Theory of Everything

In the past couple of decades, only recently were alternative thoughts of past, present, and future dimension thought to exist. But as more relative physical and particle data are being discovered, more and more theories of extra dimensions, in which quantum mechanists believe alternatives live in.

## The History of String Theory
### The Second String Theory Revolution

In the early nineties when Edward Witten unified the five String Theories and Super Gravity into the framework of M-Theory.
# Supersymmetry

This chapter on supersymmetry intends to present it WITHOUT the use of Grassmann variables, preferring to use instead the formalism of Z$_2$ grading.
A Z$_2$-graded vector space is a vector space together with an assignment of an even (bosonic) (corresponding to 0 of Z$_2$) and an odd (fermionic) (corresponding to 1) subspace such that the vector space is the direct sum of the even and odd subspaces.
An even vector is an element of the even subspace and an odd vector is an element of the odd subspace. A pure vector is either an even or an odd vector. Any vector can be decomposed uniquely as the sum of an even and an odd vector.
The tensor product of two Z$_2$-graded vector spaces is another Z$_2$-graded vector space.
In fact, in this book, we will take the stronger point of view that it makes no physical sense to add even and odd vectors together. From this point of view, we might as well view a Z$_2$-graded vector space as an ordered pair <V$_0$,V$_1$> where V$_0$ is the even space and V$_1$ is the odd space.
Similarly, a Z$_2$-graded algebra is an algebra A with a direct sum decomposition into an even and an odd part such that the product of two pure elements obeys the Z$_2$ relations. Alternatively, we can think of it as <A$_0$,A$_1$>.
A Lie superalgebra is a Z$_2$-graded algebra whose product [·, ·], called the Lie superbracket or supercommutator, satisfies
    $[x,y]=-(-1)^{|x||y|}[y,x]$
and
    $(-1)^{|z||x|}[x,[y,z]]+(-1)^{|x||y|}[y,[z,x]]+(-1)^{|y||z|}[z,[x,y]]=0$
where x, y, and z are pure in the Z$_2$-grading. Here, |x| denotes the degree of x (either 0 or 1).
Lie superalgebras are a natural generalization of normal Lie algebras to include a Z$_2$-grading. Indeed, the above conditions on the superbracket are exactly those on the normal Lie bracket with modifications made for the grading. The last condition is sometimes called the super Jacobi identity.
Note that the even subalgebra of a Lie superalgebra forms a (normal) Lie algebra as all the funny signs disappear, and the superbracket becomes a normal Lie bracket.
One way of thinking about a Lie superalgebra—it's not the most symmetric way of looking at it—is to consider its even and odd parts, L$_0$ and L$_1$ separately. Then, L$_0$ is a Lie algebra, L$_1$ is a linear rep of L$_0$, and there exists a symmetric L$_0$-intertwiner $\{.,.\}:L_{1}\otimes L_{1}\rightarrow L_{0}$ such that for all x,y and z in L$_1$,
    $\left\{x,y\right\}[z]+\left\{y,z\right\}[x]+\left\{z,x\right\}[y]=0$
A supermanifold is a concept in noncommutative geometry. Recall that in noncommutative geometry, we don't look at point set spaces but instead, the algebra of functions over them. If M is a (differential) manifold and H is an (smooth) algebra bundle over M with a Grassmann algebra as the fiber, then the space of (smooth) sections of M forms a supercommutative algebra under pointwise multiplication. We say that this algebra defines the supermanifold (which isn't a point set space).
If M is a real manifold and we define an involution * over the fiber turning it into a * algebra, then the resulting algebra would define a real supermanifold.
# Stress-related Disorders/Clinical Stress

Stress as in Clinical Medicine

## Acute stress disorder

* Occurs in individuals without any other apparent psychiatric disorder, in response to exceptional physical/or psychological stress.
* While severe, such reactions usually subside within hours or days.
* The stress may be an overwhelming traumatic experience (e.g accident, battle, physical assault, rape) or unusually sudden change in social circumstances of the individual, such as multiple bereavement.
* Individual vulnerability and coping capacity play a role in the occurrence and severity of acute stress reactions, as evidenced by the fact that not all people exposed to exceptional stress develop symptoms.
* Symptoms show considerable variation but usually include:
** an initial state of DAZE with some constriction of the field of consciousness and narrowing of attention
** inability to comprehend stimuli
** disorientation.
* Followed either by further withdrawal from the surrounding situation to the extent of a dissociative stupor or by agitating and over activity.

### Autonomic signs of "Panic Anxiety"

* Tachycardia
* Sweating
* Hyperventilation
The symptoms usually appear within minutes of the impact of the stressful stimulus and disappear within 2-3 days.

## Post-traumatic disorders (PTSD)

This arises as a delayed and/or protracted response to a stressful event or situation of an exceptionally threatening nature and likely to cause pervasive distress in almost anyone.

### Causes of PTSD

* Natural or human disasters
* war
* serious accident
* witness of violent death of others
* being the victim of sexual abuse
* rape
* torture
* terrorism or hostage taking

### Predisposing factors

* Personality traits
* Previous history of Psychiatric illness

### Typical symptoms

* "Flashbacks" - the repeated reliving of the trauma in the form of intrusive memories or dreams.
* intense distress at exposure to events that symbolize or resemble an aspect of the traumatic event, including anniversaries of the trauma
* avoidance of activities and situations reminiscent of the trauma
* emotional blunting or "numbness"
* a sense of detachment from other people
* autonomic hyper-arousal with hyper-vigilance, an enhanced startle reaction and insomnia
* marked anxiety and depression and, occasionally, suicidal ideation

### Treatment

* Psychiatric consultation
** Exploration of memories of the traumatic event
** relief of associated symptoms
** counseling

### Prognosis

* The course is fluctuating but recovery can be expected in the majority of cases.
* Few people may show chronic course over many years and a transition to an enduring personality change

## Source

Kumar and Clark Clinical Medicine 4th Edition ISBN 0 7020 2458 9 page 1134
# Contents

* Introduction
* Supersymmetry
* Two-Dimensional Conformal Field Theory
* String Quantization
* The Free String
* String Interactions
* String Field Theory Compactifications
* Orbifolds and Orientifolds
* T-Duality
* T-Duality
* M-theory

# Notation

The metric has signature $(+,-,-,-,...)$.
Greek letters from the middle of the alphabet $(\mu ,\nu ,...)$ denote coordinates in spacetime. Roman letters taken from the beginning of the alphabet $(a,b,...)$ denote coordinates on the worldsheet.
The metric is denoted $g_{\mu \nu }$. In the case where there is a metric of spacetime and a metric of the worldsheet, the worldsheet metric is denoted $h_{ab}$
A lower-case $d$ is the number of dimensions. An upper-class $D$ represents the number of spacial dimensions.
# Stress-related Disorders/Relaxation Response

* Basic elements
** A quiet environment
** A comfortable posture
** A mental device
*** A mental device (a meaningful word or phrase)
** A passive attitude
* Instructions
** In a quiet environment
*** In a quiet environment, sit in a comfortable position.
* Close your eyes
** Deeply relax all your muscles
*** Deeply relax all your muscles, beginning at your feet and progressing up to your face (i.e., feet, calves, thighs, lower torso, chest, shoulders, neck, hand). Allow them to remain relaxed.
** Breathe through your nose
*** Become aware of your breathing. While breathing out, say silently to yourself the word "one" ("won") or some other word or short phrase that is meaningful to you (i.e., breathe in; breathe out, saying "won"; breathe in; breathe out, saying "won").
** Continue this way for 20 minutes
*** You may open your eyes periodically to check the time, but do not use an alarm. Do this once or twice daily and not within 2 hours after any meal.
** When you finish each 20-minute exercise
*** When you finish each 20-minute exercise, sit quietly for a few minutes, first with your eyes shut and then with them open.
** The goal is a passive attitude
*** Deep relaxation will not always occur, and distracting thoughts will come into your mind. When you become conscious of them, ignore them and sustain the breathing exercise.

### Source

Adapted from Benson H. The Relaxation Response. New York: Morrow, 1975; and Benson H, Beary JF, Carol MP. The relaxation response. Psychiatry 37:37-46, 1974.
# Stress-related Disorders/Anxiety Reduction

The Five Rs of Stress/Anxiety reduction
The five core concepts used in the reduction of anxiety or stress:
* Rcognition of the causes and sources of the threat or distress; education and consciousness raising.
* Relationships identified for support, help, reassurance
* Removal from (or of) the threat or stressor; managing the stimulus.
* Relaxation through techniques such as meditation, massage, breathing exercises, or imagery.
* Re-engagement through managed re-exposure and desensitization.
# Stress-related Disorders/Introduction
## Stress - Brief Introduction

Q. Differentiation between Anxious and Stress.
It is not very grammatically correct to write in patients chart- "Looks anxious" and referring them to psychiatric ward/PSY-consultation. Stress is not an anxiety (anxiety disorder), they are not synonymous.
A general concept/understanding in Human-psychology/Psychiatry is beneficial.
Q. When is stress experienced?
A person typically is stressed when they experiences positive or negative temporarily strain or overwhelm adaptive capacities.
In general - Stress can be physiological or pathological. A general concept/understanding in them is beneficial.
Q. Who can get Stress?
Stress is highly individualized and depends on variables such as the novelty, rate, intensity, duration, or personal interpretation of the input, and genetic or experiential factors.
For an example
* Panic attacks are more frequent when the predisposed person is exposed to stressors.
Q. What to do if you encounter stressed person in surgical ward?
Ultimate refer place is psychiatric consultation, But... pre-PSY-consultation, we can provide our little help.
Q. Which stress remedies are in fashion?
* Stress-reduction strategies can be helpful to many stressed/anxious patients/sufferer.
** Unfortunately, many stressed/anxious persons cannot concentrate enough to use such strategies effectively for acute relief.
** Most stress-reduction techniques have their greatest utility as elements of a prevention plan that attempts to raise one's threshold to anxiety-provoking experiences.

## Medical Disclaimer

Wikibooks contains books on many medical topics; however, no warranty whatsoever is made that any of the books are accurate. There is absolutely no assurance that any statement contained or cited in a book touching on medical matters is true, correct, precise, or up-to-date. The overwhelming majority of such books are written, in part or in whole, by nonprofessionals. Even if a statement made about medicine is accurate, it may not apply to you or your symptoms.
The medical information provided on Wikibooks is, at best, of a general nature and cannot substitute for the advice of a medical professional (for instance, a qualified doctor/physician, nurse, pharmacist/chemist, and so on). Wikibooks is not a doctor.
None of the individual contributors, system operators, developers, sponsors of Wikibooks nor anyone else connected to Wikibooks can take any responsibility for the results or consequences of any attempt to use or adopt any of the information presented on this web site.
Nothing on Wikibooks.org or included as part of any project of Wikimedia Foundation Inc., should be construed as an attempt to offer or render a medical opinion or otherwise engage in the practice of medicine.
# DESCRIPTION:

Load a block of stock image names. Return block of images.
LOAD-STOCK-BLOCK is a function value.

# ARGUMENTS:

* block -- (Type: any)
# DESCRIPTION:

Creates an OS-specific file requester
LOCAL-REQUEST-FILE is a native value.

# ARGUMENTS:

* parms -- Parameter block (Type: block)
# DESCRIPTION:

Returns the base-10 logarithm.
LOG-10 is a native value.

# ARGUMENTS:

* value -- (Type: number)
# DESCRIPTION:

Returns the base-E (natural number) logarithm.
LOG-E is a native value.

# ARGUMENTS:

* value -- (Type: number)
# DESCRIPTION:

Converts string of characters to lowercase.
LOWERCASE is a native value.

# ARGUMENTS:

* string -- (Type: any-string char)

# REFINEMENTS:

* /part -- Limits to a given length or position.
** range -- (Type: integer any-string)
# DESCRIPTION:

Load a net file from the disk cache.
LOAD-THRU is a function value.

# ARGUMENTS:

* url -- (Type: url file)

# REFINEMENTS:

* /update -- Force update from source site
* /binary -- Force binary mode, otherwise expects REBOL data or code.
* /to -- Specify local file target.
** local-file -- (Type: file none)
* /all -- Return block with REBOL script including unevaluated header (safe mode).
* /expand -- Auto-decompress after transfer.
* /check -- Update only if version, checksum/secure, or date/size do not match.
** info -- (Type: any)
# DESCRIPTION:

Returns TRUE for logic values.
LOGIC? is an action value.

# ARGUMENTS:

* value -- (Type: any-type)
# Rebol Programming/logo.gif

LOGO.GIF is an image of value:
# DESCRIPTION:

Return the base-2 logarithm.
LOG-2 is a native value.

# ARGUMENTS:

* value -- (Type: number)
# DESCRIPTION:

Evaluates a block a specified number of times.
LOOP is a native value.

# ARGUMENTS:

* count -- Number of repetitions (Type: integer)
* block -- Block to evaluate (Type: block)
# Supplementary mathematics/Pure mathematics

Pure mathematics is the study of mathematical concepts independent of any application outside of mathematics. These kinds of concepts may originate in real-world concerns, and the results obtained may later be highly useful for practical applications, but pure mathematicians are not primarily motivated by such applications. Instead, the attraction is attributed to the intellectual challenge and the aesthetic beauty of working to the logical consequences of underlying principles.
While pure mathematics as an activity has existed at least since ancient Greece and has made effective progress, of course, these concepts can be seen in ancient Iran, ancient Egypt, ancient Babylon,And even in the golden period of Islam, etc. This concept was carried out around 1900, after the introduction of theories with counterintuitive features (such as non-Euclidean geometries and the theory of infinite contour sets) and complex concepts of calculus, and the theory was explained. The discovery of apparent paradoxes (such as continuous functions that are nowhere differentiable and Russell's paradox) was also discussed as an example in the scientific field. It introduced the need to renew the concept of mathematical precision and rewrite all mathematics based on it, with the systematic use of axiomatic methods. This led many mathematicians to focus on complete mathematics for its own sake, i.e. pure mathematics.
It follows that, presently, the distinction between pure and applied mathematics is more a philosophical point of view or a mathematician's preference rather than a rigid subdivision of mathematics. In particular, it is not uncommon that some members of a department of applied mathematics describe themselves as pure mathematicians.
# Supplementary mathematics/Regular polygon

"Regular polygon" in Euclidean geometry is a polygon whose angles and sides are equal. Regular polygons can be cuboid or star-shaped. In the limiting case, a sequence of regular polygons with increasing number of sides becomes a circle if the perimeter remains constant and becomes an apeirogon if the length of the side remains constant.

## Perimeter and Area
### perimeter

The perimeter of a regular polygon is based on the multiplication of the number of sides of a regular polygon and the size of the sides of a regular polygon.
The perimeter of the area is obtained based on this relationship. $P=a_{1}+a_{2}+...+a_{n}=(n.a)=na$ Here n is equal to the number of sides of a regular polygon and a here is equal to the size of the sides of a regular polygon Is.

### Area

The area of a regular polygon is obtained based on trigonometric relationships. The area of a regular polygon is based on the fact that it is made of 1x1 squares and the number of its sides is n, and because it is based on the number pi, the number of sides expands trigonometrically based on the cotangent in the form of pi. It is obtained by dividing the number of sides of a regular polygon.
The area of a regular polygon is written accordingly:
$A={\frac {1}{4}}n.a^{2}\cot({\frac {\pi }{n}})$
Here, pi is in radians (equal to 180°).

#### The square area relationship by trigonometric method

Since the square is a regular polygon, its area can also be written as the area of a regular polygon which is obtained by trigonometric method, which is as follows: ${\frac {1}{4}}na^{2}\cot {\frac {\pi }{n}}=a^{2}\cot {\frac {\pi }{4}}=a^{2}.({\sqrt {1}})=1.a^{2}=a^{2}$ here:
${\frac {1}{4}}na^{2}={\frac {1}{4}}4a^{2}=a^{2}$
$\cot {\frac {\pi }{4}}=1$
Therefore, the area of a parallel square is equal to the square of its side.

#### Other other formula area

The area of an "n-" regular polygon with the size of the side a, the radius of the surrounding circle "R", the radius of the surrounding circle "r" and the perimeter "p" is obtained using the following relations:
(The angles are in radians.)
    $A={\tfrac {1}{2}}nar={\tfrac {1}{2}}pr={\tfrac {1}{4}}na^{2}\cot {\tfrac {\pi }{n}}=nr^{2}\tan {\tfrac {\pi }{n}}={\tfrac {1}{2}}nR^{2}\sin {\tfrac {2\pi }{n}}$
where R is equal to:
    $R={\frac {s}{2\sin \left({\frac {\pi }{n}}\right)}}={\frac {a}{\cos \left({\frac {\pi }{n}}\right)}}$
# Supplementary mathematics/Surface integral

In mathematics, a double integral or a surface integral is a type of dual-use 2D-3D integral that is used to add a group or data of values and intervals associated with points on a 2D and 3D surface. Calculating the surface integral is similar to calculating the surface area using the double integral except for the function inside the integral.
3D and 2D Cartesian, Cylindrical and Spherical coordinate fields in scalar continuous fields, algebraic, rational and numerical scalar value function and in 3D and 2D Heli fields, vector value function returns the vectors in coordinate or numerical form based on their dimensions. Like linear integrals, surface integrals are of two types:
1-Surface integral in scalar function (numerical function)
2-surface integral in vector function (coordinate function)
Surface integral or two-dimensional scalar function is also a simple generalization of double integral, while surface integral of vector functions plays an important role in the basic theorem of calculus.
# Supplementary mathematics/Taylor series

In mathematics, the Naylor series is an expression of a function, for example, f, in which all the derivatives of the order of magnitude of the order exist.
Σ ∞n = 0 f (n) (a) (z − a)n/n!
In this expression, sigma or Σ represents the sum of each element in the series, where n varies from zero (0) to infinity or (∞), f (n) represents the nth derivative of the function f and the expression n! The factorial function in the series is represented by the standard form. This series is named after Brooke Taylor, a mathematician and scientist from England.
# Supplementary mathematics/Theory of sets

Set theory is a fundamental branch of mathematics that deals with the study of sets, i.e. combinations of objects. All mathematics as commonly taught is formulated in the language of set theory and is built upon the axioms of set theory. Most mathematical objects that are treated in subareas such as algebra, analysis, geometry, stochastics or topology can be defined as sets. Measured against this, set theory is a fairly young science; only after overcoming the fundamentals crisis in mathematics in the early 20th century was set theory able to take its central and fundamental place in mathematics today.
# Supplementary mathematics/Real analysis

Real analysis or real-scientific analysis is a branch of mathematics analysis that studies and analyzes the behavior of real numbers, real sequences and series of real numbers and real functions.
Convergences, limits, continuity, smoothness, differentiability and integration are the characteristics of real-valued sequences and functions that are checked by real analysis. One of the applications of mathematical analysis is in integral and differential calculus and topology, of course. Its applications are analyzed and acted on based on real ideas. In a wide range of these applications and research, real-time analysis has become a vital tool for research and analysis for these ideas.
# Supplementary mathematics/References
## Book References

* calculus, James Stewart, published in 2008
* Calculus with Analytic Geometry, Richard A. Silverman, published in 2010
* Algebra and trigonometry, published by the authors of the college 2021.
* Fourier series,Fourier transform andTheir applications in mathematics andPhysics ,Springer Publishing.
* Proofbook, Richard Hammock, Virginia Commonwealth University, 2010
* advanced Modern engineering mathematics,Glyn James,2022

## Online References

* https://mathworld.wolfram.com
* https://www.britannica.com/
* www.en.m.Wikipedia.org
* https://fr.m.wikipedia.org
* https://de.m.wikipedia.org