OpenLLM-France/wikimedia huggingface dataset:
# Notation and introduction

We will call two integers a and b congruent modulo a positive integer m, if a and b have the same (smallest nonnegative) remainder when dividing by m. The formal definition is as follows.

## Definition

Let a, b and m be integers where $m>0$. The numbers a and b are congruent modulo m, in symbols $a\equiv b{\pmod {m}}$, if m divides the difference $a-b$.

### Lemma

We have $a\equiv b{\pmod {m}}$ if and only if a and b have the same smallest nonnegative remainder when dividing by m.
Proof:
Let $a\equiv b{\pmod {m}}$. Then there exists an integer c such that $cm=a-b\,$. Let now $q,q',r,r'\,$ be those integers with
$a=qm+r,\quad 0\leq r<m$
and
$b=q'm+r',\quad 0\leq r'<m$.
It follows that
$cm=a-b=m(q-q')+(r-r')\,$
which yields $m|(r-r')\,$ or $m\ {\mbox{divides}}\ (r-r')\,$ and hence $r=r'\,$.
Suppose now that $r=r'\,$. Then, $a-b=m(q-q')\,$, which shows that $m|(a-b)\,$.

# Fundamental Properties

First, if $a\equiv b{\pmod {m}}$ and $c\equiv d{\pmod {m}}$, we get $ac\equiv bd{\pmod {m}}$, and $a+c\equiv b+d{\pmod {m}}$.
As a result, if $a\equiv b{\pmod {m}}$, then $a^{p}\equiv b^{p}{\pmod {m}}$
# Nuclear Physics/Molecules - an Analogy

A theoretical approach for estimating association free energies of -helices in nonpolar media has been developed. The parameters of energy functions have been derived from G values of mutants in water-soluble proteins and partitioning of organic solutes between water and nonpolar solvents. The proposed approach was verified successfully against three sets of published data: (1) dissociation constants of -helical oligomers formed by 27 hydrophobic peptides; (2) stabilities of 22 bacteriorhodopsin mutants, and (3) protein-ligand binding affinities in aqueous solution. It has been found that coalescence of helices is driven exclusively by van der Waals interactions and H-bonds, whereas the principal destabilizing contributions are represented by side-chain conformational entropy and transfer energy of atoms from a detergent or lipid to the protein interior. Electrostatic interactions of -helices were relatively weak but important for reproducing the experimental data. Immobilization free energy, which originates from restricting rotational and translational rigid-body movements of molecules during their association, was found to be less than 1 kcal/mole. The energetics of amino acid substitutions in bacteriorhodopsin was complicated by specific binding of lipid and water molecules to cavities created in certain mutants.
Keywords: binding; thermodynamics; potentials; solvation; membranes; micelles; -helix; entropy; peptides; bacteriorhodopsin; glycophorin A
Abbreviations: vdW, van der Waals interactions • ASA, accessible surface area • PDB, Protein Data Bank • SDS, sodium dodecylsulfate • DPC, N-dodecylphosphocholine • DDMAB, N-dodecyl-N,N-(dimethylammonio) butyrate • DMPC, 1,2 Dimytristoyl-sn-glycerol-3-phosphocholine • GpA, glycophorin A • MS1, QLLIAVLLLIAVNLILLIAVARLRYLVG • L7NL11, RARL7NL11GILIN • L19, RARL19GILIN • L16, KKGL7WL9KKA • Y16, KKGL7YL9KKA • L22, KKGL10WL12KKA • Y22, KKGL10YL12KK.
Article published online ahead of print. Article and publication date are at http://www.proteinscience.org/cgi/doi/10.1110/ps.04850804.
# Number Theory/Axioms
## Axioms of the Integers

Axioms are the foundation of the integers. They provide the fundamental basis for proving the theorems that you will see through the rest of the book.
Here is a mostly complete list:
For $a$, $b$, and $c$ integers:
Closure of $\times$ and $+$: $a\times b$ and $a+b$ are integers
Commutativity of $+$: $a+b=b+a$
Associativity of $+$: $(a+b)+c=a+(b+c)$
Commutativity of $\times$: $a\times b=b\times a$
Associativity of $\times$: $(a\times b)\times c=a\times (b\times c)$
Distributivity: $a\times (b+c)=a\times b+a\times c$
Trichotomy: Either $a<0$, $a=0$, or $a>0$.
Well-Ordered Principle: Every non-empty set of positive integers has a least element. (This is equivalent to induction.)
Non-Triviality: $0\neq 1$. *This is actually unnecessary to have as an axiom, since it can be easily be proven that $0\neq 1$.
Proof: Assume $0=1$. There exists a positive integer $a$ such that $a$ is a member of the positive integers. Then, $a\times 0=a\times 1$ Therefore, $0=a$ However, since trichotomy states that every integer is either equal to 0, positive, or negative, there is a contradiction such that $a$ is both 0 and a positive integer. Therefore, $0\neq 1$. This simple proof provides a more powerful system since less has to be assumed.
Existence: $1$ is an integer.
# Nuclear Physics/Radioactivity

Radioactivity is the conversion of one nuclear state to another. It is accompanied by the emission of particles or electromagnetic radiation. The nuclear state change can often involve a change in the atomic number of the atoms involved. The most well known forms of radiation emiited are alpha particles (helium nuclei - two protons bound with two neutrons), beta particles (energetic electrons) and gamma radiation (very high energy electromagnetic radiation). Another form of radioactivity is fission in which a nucleus splits into two smaller components.

## Natural Sources of Radiation

Most sources of natural, predictable radiation come from the decay of atomic nuclei, resulting in either alpha - $\alpha$ or beta - $\beta$ particles. In general, $\alpha$ decay is more common among the heavier elements, as it reduces the proton:neutron ratio, while $\beta$ decay is much more prominent among lighter elements, as it converts a neutron into a proton.
Two prominent examples of radioactive decay are:
${\boldsymbol {\alpha }}$ decay:
$U^{238}\longrightarrow Th^{234}+He^{4}(\alpha )$
This is the first decay in the famous Uranium decay. U-238 is essentially non-radioactive (especially compared to hyper-active U-235), and has a half-life of over four billion years.
${\boldsymbol {\beta }}$ decay:
$C^{14}\longrightarrow N^{14}+e(\beta )$
This is the decay that allows for carbon dating, and has a half-life of over 5000 years.
Gamma radiation is much more difficult to come by, as emitting a gamma ray does not allow an atomic nuclei to decay. The most famous source of high-energy gamma rays is what happens when an electron and a positron annihilate:
$e^{+}+e^{-}\longrightarrow \gamma +\gamma$
Since positrons are relatively rare, this is an interaction that is relatively hard to find. However there are fairly reliable sources of $\gamma$ radiation, including Cesium-137 and Cobalt-60. Both are useful for a wide variety of technical purposes, as well as for their utility in cancer treatment.

## See also

* Change of isotope composition of natural uranium
# Pinyin/Mercury

Mercury is the smallest planet in the solar system, nearest to the sun.
Shuiixing shih Taihyarngxih zuih xiaao d xirngxing, zuih kaohjihn Taihyarng.
# Pinyin/Mental

See also
# Pinyin/Mental disorder

See also
Mental disorders comprise a broad range of problems, with different symptoms. However, they are generally characterized by some combination of abnormal thoughts, emotions, behaviour and relationships with others. Examples are schizophrenia, depression, mental retardation and disorders due to drug abuse. Most of these disorders can be successfully treated.
Jīngshén zhàng'ài bāokuò fànwéi guǎngfàn hé zhèngzhuàng gèyì de yīxìliè wèntí. Dànshì, jīngshén zhàng'ài de yībān tèzhēng dōu shì cúnzài bù zhèngcháng sīwéi, qínggǎn, xíngwéi hé yǔ tārén guānxì de mǒuzhǒng zǔhé. Lìzi bāokuò jīngshén fēnlièzhèng, yìyùzhèng, jīngshén fāyù chíhuǎn hé lànyòng yàowù zàochéng de bìngzhèng. Zhèzhǒng zhàng'ài duōshù kě chénggōng de jìnxíng zhìliáo.
# Pinyin/Messenger

See also
# Rhetoric and Composition/Detailed TOC

What follows is a detailed table of contents.
# Rhetoric and Composition/Comma Splice
## What is a comma splice?

"Comma splice" is the term commonly used to describe two independent clauses (basically, clauses that express a complete thought and could stand on their own as full sentences) joined by a comma rather than other accepted punctuation approaches, such as a comma with a coordinating conjunction, a period, or a semi-colon. Like the run-on sentence, they may have a coordinating conjunction (and, or, nor, but, for, so yet) between them but not the comma that needs to accompany the coordinating conjunction when separating two independent clauses.

## Examples of comma spliced sentences

* Every day, millions of children go to daycare with millions of other kids, there is no guarantee that none of them are harboring infectious conditions.
* Many daycares have strict rules about sick children needing to stay away until they are no longer infectious, enforcing those rules can be very difficult.
* Daycare providers often undergo extreme pressure to accept a sick child "just this once," the parent has no other care options and cannot miss work.

## Fixing comma spliced sentences

Once you find a comma spliced sentence and notice where the two independent clauses are "spliced," you can then decide on how best to separate the clauses:
* You can make two complete sentences by inserting a period. This is the strongest level of separation.
* You can use a semicolon between the two clauses if they are of equal importance; this allows your your reader to consider the points together.
* You can use a semicolon with a transition word to indicate a specific relation between the two clauses;however, use this sparingly.
* You can use a coordinating conjunction following the comma, and this also will indicate a relationship.
* Or, you can add a word to one clause to make it dependent.

## Examples of fixed comma spliced sentences

Notice how the sentences above have been punctuated in the following examples.
* Every day, millions of children go to daycare with millions of other kids. There is no guarantee that none of them are harboring infectious conditions.
* Many daycares have strict rules about sick children needing to stay away until they are no longer infectious; however, enforcing those rules can be very difficult.
* Many daycares have strict rules about sick children needing to stay away until they are no longer infectious, but enforcing those rules can be very difficult.
* Daycare providers often undergo extreme pressure to accept a sick child "just this once" because the parent has no other care options and cannot miss work.
Learn more under "commas with two independent clauses" at Rhetoric and Composition/Commas.
# Rhetoric and Composition/Disruptive comma

Disruptive commas are simply those that aren't needed -- those that "disrupt" the flow of the sentence. Here are some guidelines about places where you don't need to use commas.

## Don't put a comma between a noun and the action it's doing, even when several words come between them.

    Most organic compounds , contain oxygen, nitrogen, and halogens.
    In the Islamic bayaa ceremony, prominent citizens , pledge allegiance to a newly elected leader.
    A visit to The City Museum's exhibit on the origins of photography , provided an inspiring start to the class.

## Don't put a comma before these words unless there is an independent clause on each side

    and, or, but, for, so, nor, yet.
    The town was first settled in 1865 , and incorporated in 1868.
    The study sample was the correct size , but insufficiently diversified.
    The Australian conductor Richard Bonynge was born in Sydney , and returned there after studying in London.

## Don't put a comma before a list.

    The neighborhood contains several examples of classic mid-century architecture, including , the Dean Martin, Frank Sinatra, and Kennedy homes.
    The recommended treatment focuses on changes in diet, such as , increased fiber, less fat, and fewer processed foods.
    The group of benefits considered standard is made up of , health insurance, disability insurance, and a retirement account.
# Pokémon/Pokédex/Orthworm
## Description

A wormlike pokémon.

## Base Statistics

A steel type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Orthworm: fire, fighting, ground Moves that deal 50% of their damage to Orthworm: normal, grass, ice, flying, psychic, bug, rock, dragon, steel, fairy Moves that deal 0% of their damage to Orthworm: poison

## Notes

Introduced in Pokémon Scarlet and Violet.
# Pokémon/Pokédex/Pawmi
## Description

A doglike pokémon.

## Base Statistics

A electric type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Pawmi: ground Moves that deal 50% of their damage to Pawmi: electric, flying, steel

## How to Evolve

Evolves into Pawmo.

## Notes

Introduced in Pokémon Scarlet and Violet.
# Pokémon/Pokédex/Pachirisu
## Description

A mouse-like pokémon.

## Base Statistics

A Electric type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Pachirisu: ground Moves that deal 50% of their damage to Pachirisu: electric, flying, steel
# Pokémon/Pokédex/Palossand
## Description

A sand castle Pokémon with a spinning shovel atop it's central mound.

## Base Statistics

A Ghost and Ground type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Palossand: ghost, dark, water, grass, ice Moves that deal 50% of their damage to Palossand: bug, rock Moves that deal 25% of their damage to Palossand: poison Moves that deal 0% of their damage to Palossand: normal, fighting, electric
# Pokémon/Pokédex/Oshawott
## Description

An otterlike pokémon.

## Base Statistics

A Water type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Oshawott: grass, electric Moves that deal 50% of their damage to Oshawott: fire, water, ice, steel
# Pokémon/Pokédex/Passimian
## Description

A monkey-like Pokémon.

## Base Statistics

A Fighting type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Passimian: flying, psychic, fairy Moves that deal 50% of their damage to Passimian: bug, rock, dark
# Pokémon/Pokédex/Overqwil
## Description

A pufferfish-like pokémon.

## Base Statistics

A Dark and Poison type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Overqwil: ground, psychic Moves that deal 50% of their damage to Overqwil: ghost, dark, grass Moves that deal 0% of their damage to Overqwil: psychic
# Saylor.org's Comparative Politics/Growth of the State System after the Second World War

Perhaps even more than the First World War, WWII discredited the idea of 'empire' once and for all. The destruction and worst crimes of the war were brought about by aggressive nations seeking expansion and empire: Nazi Germany in Eastern Europe, Fascist Italy in Northern Africa, and Japan in East Asia. Although British Prime Minister Winston Churchill would have liked to see the continuation of the British Empire and Soviet premier Josef Stalin ostensibly pushed for a Soviet empire in Eastern Europe, the post-war world was one decidedly based on nation-states and not empires. The number of independent states to have emerged since the end of the war is staggering. In 1945 there were only some 75 sovereign states, today the number hovers around 200. This explosion of sovereignty was largely due to the push for decolonization of the former British and French Empires, particularly in Africa. Central to the protection of state sovereignty in the Postwar world was the creation of the United Nations in 1945. Many believed that the aggression of the Axis Powers might have been prevented had the League of Nations had more authority, or participation from the United States.
# Saylor.org's Comparative Politics/Democratic States and Democratization

Unit 3 focuses exclusively on the concept of democracy. After defining the concept, this unit focuses on various attributes that characterize democratic states and differentiate them from authoritarian regimes. We then examine processes of democratization and the breakdown of democracy followed by the debate regarding the relationship between democracy and economic development. The unit concludes with a focus on the contemporary case of the Arab Spring.
As you work through unit 3, reflect on the following questions. What differentiates democracies from authoritative regimes? What conditions facilitate democratization and do contemporary trends in the early 21st century support or undermine democratic states? Finally, are those who argue that democracy improves economic outcomes correct in their analysis?
# Self Interest and Social Behavior

Self Interest and Social Behavior introduces you to decision theory and game theory by considering important applications throughout the social sciences.
Some sample questions we will ponder: GREED or ALTRUISM ?? When do people sacrifice for others? How about animals? Or is there really a payoff for them after all?
Social behavior, in general, involves actions taken by individuals that, at least when aggregated over a group, affect other individuals. We want to predict and explain this behavior. Viewing this as scientists, we would like to discover, in effect, any “natural laws” that determine this behavior, if not for all environments then for some. One candidate for such a law of social behavior, one that may offer the foundation for a paradigm for each of the social sciences, is that individuals behave to further their own self interest. These models are relatively simple, powerful in their predictions, and might apply to all social behavior. Self Interest and Social Behavior examines these models, builds up their mathematical infrastructure as necessary, and examines these models and their implications through important applications throughout the social sciences. These applications clearly come from economics, political science, psychology, and anthropology, but also biology and philosophy whenever they try to predict or explain social behavior. We intend to demonstrate that these models should, at a minimum, be considered seriously because of their simplicity, their power, and their potentially wide scope.
Models of individuals furthering their own self interest are formalized with either decision theory or game theory. Decision theory is the mathematics of optimizing behavior, where choices are made that further self interest against an environment that does not change in response to these choices. In decision theory, each individual’s choices can be considered independently of choices that any other individual makes. It can be the foundation of either rational choice models or of evolutionary models. Game theory, building upon the foundation of decision theory, is the mathematics of strategic decisions, decisions where the value of the outcome to each individual depends upon the actions that other individuals take as well as actions that the decision maker takes herself. The rival’s choices may be influenced by the first individual’s choices. In game theory, an individual’s choices are interdependent with other individual’s choices. These "choices" might actually be rational choices that individuals make, or they may be the implicit "choices" that natural selection or cultural selection make, in that other alternatives nearly vanish in later populations.

## Table of Contents

* Aims and Objectives
* Contributors

### Decision Theory

* Smart Choices and Models Based Upon Them
* Optimization in Markets
* Sincere Voters
* Natural Selection
* Cooperation with Kin Selection
* Cultural Evolution and Social Norms
* Decision Theory with Uncertainty
* Investments, Insurance, and Search
* Anomalies and Responses to Them
# Self-Replicating Automata/List
## List of Self Replicating Automata

This is a complete list of Self Replicating Automata analysed in the wikibook "Self-Replicating Automata". This is merely a source for cross referencing. To understand more completely the significance of these automata please follow the articles and the links in these pages.
* Elk Cloner
* Brain
* Lehigh
* Jerusalem
# Self-Replicating Automata/List/Lehigh
## Introduction

The Lehigh virus, a COMMAND.COM infector, appeared around 1987.
# Self-Replicating Automata/List/Brain
## Introduction

Like many of the earliest virus, it is evident from the code that Brain (brain.dos.x) does not utilise any inherent system vulnerabilities to spread. Its spreading is purely dependent on well documented function calls(interrupts).

## External link

* Story of the virus from Brain Limited - This link has the actual message of the virus, complete with the phone numbers, etc.
# Self-Replicating Automata/List/Elk Cloner
## Introduction

Elk Cloner is the first known computer virus to spread in the wild. It infected Apple II systems and was written by Richard Skrenta in 1982. It spread by infecting Apple II floppy disks. It did not cause any intentional harm to data, and displayed the message on every 50th booting.

## External link

* Skrenta's page on Elk Cloner
# Self Interest and Social Behavior/Contributors
## Authors

This will serve as a partial list of contributors to this book.

## Formatting Style

For information on the use of wikimedia formatting, see the Help Wikibook.

## License

This WikiBook is released under the GNU Free Documentation License, and may be edited, modified, copied or distributed according to the terms of that license.
# Self-Replicating Automata/List/Jerusalem
## Introduction

The Jerusalem family is very prolific in the number of variants . This is one of the variants of Jerusalem virus.
# Primary Mathematics/Metric system

The metric system, originating in France in 1791, is the current international standard for measurements. In common use, there are three units that are frequently used in the metric system:
* Meter (m) - a unit of length
* Gram (g) - a unit of mass
* Liter (L) - a unit of weight
The two tangible units, meter and gram, can be converted to larger and smaller representations simply by multiplying by 10.

## Meter

A meter is the standard unit of length; it is approximately equal to 39.37 inches (3.28 feet) in the US customary system.
A normal meter stick will have 10 divisions, each representing 1 decimeter (dm). This is further divided by 10 to give a total of 100 centimeters (cm), and then by ten again to give 1000 millimeters (mm).
1000 meters equals 1 kilometer (km).
In the UK a meter is known as a "metre".

## Gram

The gram is a unit of mass. It is commonly used to state weights as well.
There are 1000 grams in a kilogram (kg).
1000 kilograms is equal to 1 tonne (t).
A milligram (mg) is 1/1000th of a gram. Milligrams are often used in medicine and chemistry.

## Liter

The liter (L) is a unit of liquid volume, equal to a cube of water measuring 10cm * 10cm * 10cm. A milliliter (mL) is equal to one cubic centimeter.
# Primary Mathematics/Prime numbers

Prime numbers are positive numbers greater than one that cannot be divided evenly by any positive whole numbers other than one and themselves. For example, 7 is a prime number because the only numbers that divide it evenly are 1 and 7, but 8 is not a prime number because, in addition to 1 and 8, the numbers 2 and 4 also divide it. An equivalent definition is that a prime number is a number greater than one that cannot be written as the product of two smaller positive integers.
The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Numbers greater than one that are not prime are called composite numbers. Note that the number 1 is neither prime nor composite, but is instead classified as a unit.