OpenLLM-France/wikimedia huggingface dataset:
# Pokémon/Pokédex/Arcanine

| Basic: Growlithe | Stage 1: Arcanine |

## Basic Statistics

* National Index: 59
* Johto Index: 128
* Hoenn Index: 246
* Stage: Stage 1
* Height: 1.9 meters (6.2 ft)
* Weight: 155 kilograms (340 lb)
* Gender Distribution: 75% Male
* Ability: Intimidate/Flash Fire
* Type: Fire
* Species: Legendary
* Egg Group: Ground
* Hatch Steps: 5120
* Catch Rate: 75
* Base Experience: 213
* Max Experience: 1250000
| | HP | Attack | Defense | Speed | Special Attack | Special Defense |
| Base Stats (RB/Y) | 90 | 110 | 80 | 95 | 80 | 80 |
| Base Stats (GS/C) | 90 | 110 | 80 | 95 | 100 | 80 |
| Base Stats (RS/FL/E) | 90 | 110 | 80 | 95 | 100 | 80 |
| Base Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Base Stats (BW/B2W2) | – | – | – | – | – | – |
| Base Stats (XY/ORAS) | – | – | – | – | – | – |
| Base Stats (SM/USUM) | – | – | – | – | – | – |
| Base Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Max Stats (RB/Y) | 383 | 318 | 258 | 288 | 258 | 258 |
| Max Stats (GS/C) | 383 | 318 | 258 | 288 | 298 | 258 |
| Max Stats (RS/FL/E) | 384 | 350 | 284 | 317 | 328 | 284 |
| Max Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Max Stats (B/W/B2W2) | – | – | – | – | – | – |
| Max Stats (X/Y/ORAS) | – | – | – | – | – | – |
| Max Stats (SM/USUM) | – | – | – | – | – | – |
| Max Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Effort Points (Sword/Shield/BDSP) | – | – | – | – | – | – |

## Type Matching

Move types which are good on Arcanine: Ground, Rock, Water Move types which are bad on Arcanine: Bug, Fire, Grass, Ice², Steel²
All other move types are normal effectiveness on Arcanine.
¹ – Red/Blue/Yellow only ² – All other Pokemon games

## Moveset

| Level | Red / Blue | Yellow | Gold / Silver | Crystal | Ruby / Sapphire Emerald XD / Colosseum | Fire Red / Leaf Green |
| Start | Roar Ember Leer Take Down | Roar Ember Leer Take Down | Roar Leer Take Down Flame Wheel | Roar Leer Take Down Flame Wheel | Bite Roar Ember Odor Sleuth | Bite Roar Ember Odor Sleuth |
| 49 | - | - | - | - | Extremespeed | Extremespeed |
| 50 | - | - | Extremespeed | Extremespeed | - | - |

### TM/HM

* RB/Y/GS/C/RS/FL: Dig, Double Team, Fire Blast, Hyper Beam, Rest, Toxic
* RB/Y/GS/C: Swift
* GS/C/RS/FL: Attract, Frustration, Hidden Power, Iron Tail, Protect, Return, Roar, Rock Smash, Sunny Day
* C/RS/FL: Flamethrower
* RB/Y: Bide, Body Slam, Double-Edge, Dragon Rage, Mimic, Rage, Reflect, Skull Bash, Substitute, Take Down, Teleport
* GS/C: Curse, Dragonbreath, Endure, Headbutt, Sleep Talk, Snore, Swagger
* RS/FL: Aerial Ace, Facade, Overheat, Secret Power, Strength, Thief

### Evolution

* GS/C/RS/FL: Body Slam, Crunch, Fire Spin, Safeguard, Thrash
* RS/FL: Heat Wave, Howl

## Trading Cards

* Base Set #23 - Arcanine
* Gym Challenge #1 - Blaine's Arcanine
* Neo Destiny #12 - Light Arcanine
* Aquapolis #H2 - Arcanine
* Aquapolis #2 - Arcanine
* Skyridge #H2 - Arcanine
* Skyridge #3 - Arcanine
* EX Sandstorm #15 - Arcanine
* EX FireRed and LeafGreen #18 - Arcanine
# Pokémon/Pokédex/Ariados
## Basic Statistics

* National Index: 168
* Johto Index: 33
* Hoenn Index: 323
* Stage: Stage 1
* Height: 1.1m/3'7"
* Weight: 33.5kg/74.0lb
* Gender Distribution: 50% Male
* Ability: Swarm/Insomnia
* Type: Bug/Poison
* Species: Long Leg
* Egg Group: Bug
* Hatch Steps: 3840
* Catch Rate: 90
* Base Experience: 134
* Max Experience: 800000
| | HP | Attack | Defense | Speed | Special Attack | Special Defense |
| Base Stats (RB/Y) | - | - | - | - | - | - |
| Base Stats (GS/C) | 70 | 90 | 70 | 40 | 60 | 60 |
| Base Stats (RS/FL/E) | 70 | 90 | 70 | 40 | 60 | 60 |
| Base Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Base Stats (BW/B2W2) | – | – | – | – | – | – |
| Base Stats (XY/ORAS) | – | – | – | – | – | – |
| Base Stats (SM/USUM) | – | – | – | – | – | – |
| Base Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Max Stats (RB/Y) | - | - | - | - | - | - |
| Max Stats (GS/C) | 343 | 278 | 238 | 178 | 218 | 218 |
| Max Stats (RS/FL/E) | 344 | 306 | 262 | 196 | 240 | 240 |
| Max Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Max Stats (B/W/B2W2) | – | – | – | – | – | – |
| Max Stats (X/Y/ORAS) | – | – | – | – | – | – |
| Max Stats (SM/USUM) | – | – | – | – | – | – |
| Max Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Effort Points (Sword/Shield/BDSP) | – | – | – | – | – | – |

## Type Matching

Move types which are good on Ariados: Fire, Flying,Psychic, Rock Move types which are bad on Ariados: Bug, Poison Move types which are very bad on Ariados: Fighting, Grass
All other move types are normal effectiveness on Ariados.

## Moveset

| Level | Gold / Silver | Crystal | Ruby / Sapphire Emerald XD / Colosseum | Fire Red / Leaf Green |
| Start | Poison Sting String Shot Scary Face Constrict | Poison Sting String Shot Scary Face Constrict | Poison Sting String Shot Scary Face Constrict | Poison Sting String Shot Scary Face Constrict |
| 6 | Scary Face | Scary Face | Scary Face | Scary Face |
| 11 | Constrict | Constrict | Constrict | Constrict |
| 17 | Night Shade | Night Shade | Night Shade | Night Shade |
| 25 | Leech Life | Leech Life | Leech Life | Leech Life |
| 34 | Fury Swipes | Fury Swipes | Fury Swipes | Fury Swipes |
| 43 | Spider Web | Spider Web | Spider Web | Spider Web |
| 53 | Screech | Agility | Agility | Agility |
| 63 | Psychic | Psychic | Psychic | Psychic |

### TM/HM

* GS/C/RS/FL: Attract, Dig, Double Team, Flash, Frustration, Giga Drain, Hidden Power, Hyper Beam, Protect, Psychic, Rest, Return, Sludge Bomb, Solarbeam, Sunny Day, Thief, Toxic
* GS/C: Curse, Endure, Sleep Talk, Snore, Swagger
* RS/FL: Facade, Secret Power

### Evolution

* GS/C/RS/FL: Baton Pass, Disable, Psybeam, Pursuit, Sonicboom
* RS/FL: Signal Beam

## Trading Cards

* Neo Genesis # 27 - Ariados
* Neo Discovery # 17 - Dark Ariados
* Aquapolis #H3 - Ariados
* Aquapolis #3 - Ariados
* EX Team Rocket Returns #30 - Dark Ariados
| Basic: Spinarak | Stage 1: Ariados | (No Stage 2) |
# Pokémon/Pokédex/Archaludon
## Description

An Architecture inspired pokémon, appearing similar to a skyscraper when standing, or a bridge when laying down or attacking.

## Base Statistics

A Steel and Dragon type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Archaludon: fighting, ground Moves that deal 50% of their damage to Archaludon: normal, flying, psychic, bug, rock, steel, water, electric Moves that deal 25% of their damage to Archaludon: grass Moves that deal 0% of their damage to Archaludon: poison

## How to Evolve

Evolves from Duraladon when given an alloy item.

## Notes

Introduced in the DLC for Pokémon Scarlet and Violet.
# Pinyin/Mosque

See also
# Pinyin/Mother

Search mother
Mother is a female parent.
muuqin shih nvvxihng d fuhmuu.
# Pinyin/More than

more than: used before a number or amount for saying that the actual number or amount is larger than this
chaoguoh: yohngyur shuhzih zhiqiarn, biaaoshih shirjih shuhzih gehng dah
# Pinyin/Mother's Day

Search Pinyin mother
Search Pinyin day
Mother's Day is a celebration honoring mothers. Many countries celebrate it on the second Sunday of May, but it is also celebrated on other days. Mother's Day complements Father's Day, a celebration honoring fathers.
Muuqinjier shih gaanxieh muuqin d jierrih. heenduo guorjia zaih Wuuyueh d dih-2'g Xingqirih qihngzhuh, yee yoou zaih qirta rih'zi qihngzhuh. torng Muuqinjier duihyihng gaanxieh fuhqin d shih Fuhqinjier.
# Pinyin/Morphology

Special:search/morphology prefix:Pinyin/
Morphology is a part of linguistics. It studies the method of word formation using morphemes. A morpheme is the smallest part of a word that has meaning. Different languages have different morphemes, and have different rules for morpheme combination.
gouhcirfaa shì yǔyánxué d yībùfèn. Tā yánjiū yǔsù gòuchéng cí d fāngfǎ. Yǔsù shì jùyǒu yìyì d, cí d zuìxiǎo bùfèn. Bùtóng d yǔyán yǒu bùtóng d yǔsù, bìngqiě yǒu bùtóng d yǔsù zǔhé guīzé.
# Pinyin/Mostly

See also
# Pinyin/Mother's love

Search mother
《Mother's love》
《Mǔqīn de ài》
Mother, is like an umbrella.
Mǔqīn, jiù xiàng yī-bǎ yǔsǎn.
In rainy days, it protects us, but itself is wetted.
Zài xiàyǔ shí, wèi wǒmen dǎngyǔ, zìjǐ què línshī le.
A mother's love, is irreplaceable.
Mǔqīn de ài, shì wúkě tìdài de.
Honor mother, everyone should do.
Xiàojìng mǔqīn, shì měigèrén dōu yīnggāi zuòdào de.
# Pinyin/Most

most: the largest in number or amount
zuih: shuhzih huoh shuh`er zuih dah
# Polish/List of words

These are words without pronunciation. Practice Polish alphabet and words.

### Miesiące (months)

* styczeń - January
* luty - February
* marzec - March
* kwiecień - April
* maj - May
* czerwiec - June
* lipiec - July
* sierpień - August
* wrzesień - September
* październik - October
* listopad - November
* grudzień - December

### Kolory (colors)

* biały - white
* różowy - pink
* czerwony - red
* pomarańczowy - orange
* brązowy - brown
* żółty - yellow
* szary - grey
* zielony - green
* błękitny - cyan
* niebieski - blue
* czarny - black
* fioletowy - violet, purple

### Dni tygodnia (days of week)

* poniedziałek - Monday
* wtorek - Tuesday
* środa - Wednesday
* czwartek - Thursday
* piątek - Friday
* sobota - Saturday
* niedziela - Sunday

### Liczby (numbers)

* 1 - jeden;
* 2 - dwa;
* 3 - trzy;
* 4 - cztery;
* 5 - pięć;
* 6 - sześć;
* 7 - siedem;
* 8 - osiem;
* 9 - dziewięć;
* 10 - dziesięć;
* 11 - jedenaście;
* 12 - dwanaście;
* 13 - trzynaście;
* 14 - czternaście;
* 15 - piętnaście;
* 16 - szesnaście;
* 17 - siedemnaście;
* 18 - osiemnaście;
* 19 - dziewiętnaście;
* 20 - dwadzieścia;
* 21 - dwadzieścia jeden;
* 30 - trzydzieści;
* 40 - czterdzieści;
* 50 - pięćdziesiąt;
* 60 - sześćdziesiąt;
* 70 - siedemdziesiąt;
* 80 - osiemdziesiąt;
* 90 - dziewięćdziesiąt;
* 100 - sto;
* 101 - sto jeden;
* 110 - sto dziesięć;
* 200 - dwieście;
* 300 - trzysta;
* 400 - czterysta;
* 500 - pięćset;
* 600 - sześćset;
* 700 - siedemset;
* 800 - osiemset;
* 900 - dziewięćset;
* 1000 - tysiąc;
* 1001 - tysiąc jeden;
* 1234 - tysiąc dwieście trzydzieści cztery;
* 2000 - dwa tysiące;
* 3000 - trzy tysiące;
* 4000 - cztery tysiące;
* 5000 - pięć tysięcy;
* 6000 - sześć tysięcy;
* 7000 - siedem tysięcy;
* 8000 - osiem tysięcy;
* 9000 - dziewięć tysięcy;
* 10 000 - dziesięć tysięcy;
* 11 000 - jedenaście tysięcy;
* 12 000 - dwanaście tysięcy;
* 30 000 - trzydzieści tysięcy;
* 31 000 - trzydzieści jeden tysięcy;
* 32 000 - trzydzieści dwa tysiące;
* 35 000 - trzydzieści pięć tysięcy;
* 301 000 - trzysta jeden tysięcy;
* 302 025 - trzysta dwa tysiące dwadzieścia pięć;
* 312 003 - trzysta dwanaście tysięcy trzy;
* 1 000 000 - milion;
* 2 000 000 - dwa miliony;
* 3 000 000 - trzy miliony;
* 4 000 000 - cztery miliony;
* 5 000 000 - pięć milionów;
* 6 000 000 - sześć milionów;
* 1 000 000 000 - miliard;
* 2 000 000 000 - dwa miliardy;
* 5 000 000 000 - pięć miliardów;
* 1 000 000 000 000 - bilion;
* 2 000 000 000 000 - dwa biliony;
* 5 000 000 000 000 - pięć bilionów;
* 1 000 000 000 000 000 - biliard;
* 2 000 000 000 000 000 - dwa biliardy;
* 5 000 000 000 000 000 - pięć biliardów;
1st - male singular: pierwszy, female s: pierwsza, neutral s: pierwsze, male-personal(men) plural: pierwsi, not-male-personal(women and others) plural: pierwsze;
2nd - m s: drugi, f s: druga, n s: drugie, m-p p: drudzy, n-m-p p: drugie;
3rd - m s: trzeci, f s: trzecia, n s: trzecie, m-p p: trzeci, n-m-p p: trzecie;
4th - m s: czwarty, f s: czwarta, n s: czwarte, m-p p: czwarci, n-m-p p: czwarte;
5th - m s: piąty, f s: piąta, n s: piąte
# Neuter noun declension

The neuter gender in Polish is least common. Many neuter words end in "-o" and their declension is somewhat similar to inanimate-masculine.
| | Beer | Beer | Cake | Cake | Chair | Chair | Eye | Eye | Ear | Ear |
| | Singular | Plural | Singular | Plural | Singular | Plural | Singular | Plural | Singular | Plural |
| Nom./Acc./Voc. | Piwo | Piwa | Ciastko | Ciastka | Krzesło | Krzesła | Oko | Oczy | Ucho | Uszy |
| Genitive | Piwa | Piw | Ciastka | Ciastek | Krzesła | Krzeseł | Oka | Oczu | Ucha | Uszu |
| Dative | Piwu | Piwom | Ciastku | Ciastkom | Krzesłu | Krzesłom | Oku | Oczom | Uchu | Uszom |
| Locative | Piwie | Piwach | Ciastku | Ciastkach | Krześle | Krzesłach | Oku | Oczach | Uchu | Uszach |
| Instrumental | Piwem | Piwami | Ciastkiem | Ciastkami | Krzesłem | Krzesłami | Okiem | Oczami/ archaic Oczyma | Uchem | Uszami |
The archaic instrumental oczyma doesn't have much to do with the neuter gender - it was the Indoeuropean dual number (for a pair of things), which disappeared in almost all modern Indo-European languages. You can still find it in some expressions.
In the singular locative "krześle" you can see how softening works on a group of consonants – all consonants are softened, in that case "s" changes to "ś" and "ł" to "l".
As with other declensions, "e" may appear between two final consonants if there is no vowel after them ("null" ending).
The plural instrumental is "-ami"/"-iami" in almost all nouns, and "-imi"/"-ymi" in almost all adjectives. Here you can see one of the exceptions. For some historical reasons "a" disappeared and we have "-ćmi" instead of the expected "-ciami".
In the case of "dziecko", "oko" and "ucho" you can see that a slightly different form is used as the base for the singular and plural forms. This is also quite archaic.
If you find some neuter noun, try to decline it rather like "piwo", "krzesło" and "ciastko" rather than like "dziecko", "oko" or "ucho".
Examples:
* Dziecko je ciastka - child eats cakes (cake in accusative)
* Dzieci nie piją piwa - children don't drink beer (beer in genitive)
* Oczy Piotra są zielone - Piotr's eyes are green (eyes in nominative, Piotr in genitive, green in nominative)
* Kot jest na krześle - cat is on chair (chair in locative)
* zielone - plural neuter form of adjective "green"

## Neuter nouns ending in "-e" or "-ę"

The most common template is:
| | Meeting | Meeting |
| | Singular | Plural |
| Nom./Acc./Voc. | Spotkanie | Spotkania |
| Genitive | Spotkania | Spotkań |
| Dative | Spotkaniu | Spotkaniom |
| Instrumental | Spotkaniem | Spotkaniami |
| Locative | Spotkaniu | Spotkaniach |
Other templates are:
| | Given name/First name | Given name/First name | Baby | Baby |
| | Singular | Plural | Singular | Plural |
| Nom./Acc./Voc. | Imię | Imiona | Niemowlę | Niemowlęta |
| Genitive | Imienia | Imion | Niemowlęcia | Niemowląt |
| Dative | Imieniu | Imionom | Niemowlęciu | Niemowlętom |
| Instrumental | Imieniem | Imionami | Niemowlęciem | Niemowlętami |
| Locative | Imieniu | Imionach | Niemowlęciu | Niemowlętach |
# Polish/Na kursie

Classroom vocabulary.
kreda (f) [krɛda] - chalk
tablica (f) [tablit͡sa] - blackboard, whiteboard gąbka (f) [gɔ̃pka] - sponge papier (m) [papʲɛr] - paper stół (m) [stuː] - table komputer (m) [kɔmputer] - computer odtwarzacz CD (m) [ɔttvaʐ̠at͡ʂ̠ si di] - CD player
lampa (f) [lampa] - lamp podręcznik (m) [pɔdrɛ̃t͡ʂɲ] - textbook
# Polish/Introductions

^ Polish ^
When introducing themselves, most Poles simply shake hands and pronounce their names. However, there are two types of questions that you, as a foreigner, need to know in order to respond properly if a curious Pole wants to know your name.
* imię /eemye/ – first name
* nazwisko /nazveesko/ – last name
1. Jak się nazywasz? /yak she nazivash/ – "what's your name"; usually implies both first and last name, although it is used colloquially to ask about the last name
Conjugation:
| | Singular | Plural |
| 1. | (ja) nazywam się | (my) nazywamy się |
| 2. | (ty) nazywasz się | (wy) nazywacie się |
| 3. | (on/ona/ono) nazywa się | (oni/one) nazywają się |
For example:
In a formal setting, the question will be:
2. a. Jak masz na imię? /yak mash na eemye?/ – literally "what have you got as a name?"- asks specifically about the first name
b. Jak Ci na imię? /yak chy na eemye/ – literally "what your name?"-paradoxally, sounds even more eloquent than the other two types above, even though there is no verb...
Conjugation:
| | Singular | Plural |
| 1. | (ja) mam | (my) mamy |
| 2. | (ty) masz /mash/ | (wy) macie /mache/ |
| 3. | (on/ona/ono) ma | (oni/one) mają /majõ/ |
For example:
< Polish pronunciation < ^ Polish ^
# Polish/List of Words

Fruits
    apple - jabłko
    banana - banan
    pear - gruszka
    grapes - winogrona
    strawberry - truskawka
    orange - pomarańcza
    cherries - wiśnie
    raspberry - malina
# Nuclear Energy/Introduction

Nuclear energy is one of the most widely used forms of knowledge for the production of other energies such as electricity, heat, light, material production, etc. Of course, nuclear energy is unfortunately used in the ways of atomic and hydrogen bombs, whose use causes the extinction of the human race. (for example: Hiroshima and Nagasaki incident)
In this book, we describe the advantages and disadvantages as well as the application of nuclear energy.
# Nuclear Energy/Nuclear technology

Nuclear technology refers to the ability to convert naturally occurring uranium into enriched uranium, which is obtained through the fission of atoms, which has a lot of energy. By fissioning the nucleus or the uranium atom, nuclear energy is released in the form of heat and thermal energy, which can be used to generate water vapor and turn electricity generating turbines. Uranium is one of the dense radioactive metals that exist in nature. This metal exists in most areas such as: rocks, soil, deep sea and oceans, so that its presence and distribution is more than gold, silver or mercury. This metal exists in the form of oxide or mixed salts in minerals such as uranite or caronite, and in terms of color; It is silvery white and flexible.
History of nuclear technology About three centuries BC, Democritus, a Greek scientist, after studying things, realized that things are composed of very small and decomposable particles in addition to their appearance. He named these particles "atom" which means "unbreakable". Centuries after this discovery, in 1700 AD, John Dalton, an English scientist, also discovered that atoms can be broken down. But this result remained at the limit of theory. Until in 1927, Albert Einstein, a German American scientist, proved the theory of atomic disintegration in a practical way. After this discovery, the first nuclear test was carried out in the Nevada desert by the United States, and at the end of World War II, it was used to rain bombs on Japanese cities. After the United States, in 1949, the Soviet Union was able to acquire nuclear weapons and put them into action. With the increase in the demand for the production of nuclear weapons by powerful countries such as France and China, the leaders of the countries thought of controlling the production of this destructive weapon and suggested the use of destructive energy for peace. For this purpose, in 1954, US President Eisenhower proposed the "Atoms for Peace" program. Following this proposal, from 1954 to 1956, the organization's statutes were drafted and after that the "Nuclear Energy Agency" was formed. In 1968, the Nuclear Energy Agency approved the "Non Proliferation of Nuclear Weapons Treaty" (Non Proliferation of Nuclear Weapons Treaty) by the United Nations General Assembly and it became effective in 1970. Currently, 189 countries are members of this treaty.
# Nuclear Fusion Physics and Technology/Atomic Physics summary
#### Definition: Linear Harmonic Oscillator Hamiltonian

Linear Harmonic Oscillator Hamiltonian ${\hat {H}}_{LHO}:\mathbb {V} \rightarrow \mathbb {V}$ of a particle $p\in {\mathfrak {ParticleSet}}$is defined as ${\hat {H}}(|n>)={\frac {{\hat {p}}^{2}(|n>)}{2m}}+{\frac {1}{2}}m\omega {\hat {x}}^{2}(|n>)$ where operators ${\hat {x}}(|n>),{\hat {p}}(|n>):\mathbb {V} \rightarrow \mathbb {V}$

#### Definition: Anihilation Operator

Anihilation Operator ${\hat {a}}:\mathbb {V} \rightarrow \mathbb {V}$ is defined as
${\hat {a}}(|n>)={\sqrt {\frac {m\omega }{2\hbar }}}{\hat {x}}+i{\sqrt {\frac {1}{2\hbar m\omega }}}{\hat {p}}$

#### Definition: Creation Operator

Creation Operator ${\hat {a}}^{+}:\mathbb {V} \rightarrow \mathbb {V}$ is defined as
${\hat {a}}^{+}(|n>)={\sqrt {\frac {m\omega }{2\hbar }}}{\hat {x}}-i{\sqrt {\frac {1}{2\hbar m\omega }}}{\hat {p}}$

#### Theorem: a, a+ compound expressions

Lets assume Linear Harmonic Oscillator Hamiltonian. Then
${\hat {a}}[{\hat {a}}^{+}(|n>)]={\frac {{\hat {H}}(|n>)}{\hbar \omega }}+{\frac {{\hat {1}}(|n>)}{2}},\qquad {\hat {a}}^{+}[{\hat {a}}(|n>)]={\frac {{\hat {H}}(|n>)}{\hbar \omega }}-{\frac {{\hat {1}}(|n>)}{2}},$
Proof: Directly form a, a+ definitions with respect to LHO Hamiltonian definition and [x,p] commutator
$a[a^{+}(|n>)]{\overset {def\,a,a^{+}}{=}}\left({\sqrt {\frac {m\omega }{2\hbar }}}{\hat {x}}+i{\sqrt {\frac {1}{2\hbar m\omega }}}{\hat {p}}\right)\left({\sqrt {\frac {m\omega }{2\hbar }}}{\hat {x}}-i{\sqrt {\frac {1}{2\hbar m\omega }}}{\hat {p}}\right)=$ $={\frac {m\omega }{2\hbar }}{\hat {x}}^{2}(|n>)-i^{2}{\frac {1}{2\hbar m\omega }}{\hat {p}}^{2}(|n>)-i{\sqrt {\frac {m\omega }{2\hbar }}}{\sqrt {\frac {1}{2\hbar m\omega }}}{\hat {x}}[{\hat {p}}(|n>)]+i{\sqrt {\frac {m\omega }{2\hbar }}}{\sqrt {\frac {1}{2\hbar m\omega }}}{\hat {p}}[{\hat {x}}(|n>)]=$ $=|{\hat {H}}={\frac {{\hat {p}}^{2}|n>}{m}}+{\frac {1}{2}}m\omega {\hat {x}}^{2}|n>|={\frac {\hat {H}}{2\hbar \omega }}-i{\sqrt {\frac {m\omega }{2\hbar }}}{\sqrt {\frac {1}{2\hbar m\omega }}}({\hat {x}}{\hat {p}}|n>-{\hat {p}}{\hat {x}}|n>)=$ $={\frac {\hat {H}}{2\hbar \omega }}-{\frac {i}{2\hbar }}[{\hat {x}},{\hat {p}}]|n>={\frac {\hat {H}}{2\hbar \omega }}-{\frac {i}{2\hbar }}(i\hbar {\hat {1}})|n>={\frac {{\hat {H}}|n>}{2\hbar \omega }}+{\frac {{\hat {1}}|n>}{2}}$

#### Theorem: H,a,a+ commutators

Lets assume Linear Harmonic Oscillator Hamiltonian. Then
$[{\hat {a}},{\hat {a}}^{+}](|n>)={\hat {1}}(|n>),\qquad [{\hat {H}},{\hat {a}}^{+}](|n>)=\hbar \omega {\hat {a}}^{+}(|n>)\qquad [{\hat {H}},{\hat {a}}](|n>)=-\hbar \omega {\hat {a}}(|n>)$
Proof: The first expression may be evaluated from commutator definition directly from a, a+ compound expression theorem
$[{\hat {a}},{\hat {a}}^{+}]={\hat {a}}{\hat {a}}^{+}-{\hat {a}}^{+}{\hat {a}}{\overset {theorem}{=}}{\frac {{\hat {H}}|n>}{2\hbar \omega }}+{\frac {{\hat {1}}|n>}{2}}-{\frac {{\hat {H}}|n>}{2\hbar \omega }}-{\frac {{\hat {1}}|n>}{2}}={\hat {1}}|n>$
The second and the third expressions needs ${\hat {H}}={\hat {H}}({\hat {a}},{\hat {a}}^{+})$ first, which can be obtained from a,a+ compound expression theorem again:
# Nuclear Energy/Atom components

An atom is the smallest constituent particle of an element, which itself consists of the following particles:
* Proton
* Neutron
* Electron
Protons and neutrons form the nucleus, and the mass of each atom goes back to its nucleus The space around the nucleus is surrounded by electrons, and the chemical behavior of each atom is related to its electrons.
# Nuclear Fusion Physics and Technology/Algebra summary
#### Definition: Cartesian multiplication

Cartesian multiplication of two sets A, B with |a>,|b> elements is defined as $A\times B=\{(|a>,|b>):|a>\in A\wedge |b>\in B\}$

#### Definition: Projection

Projection f from set A to set B is AxB subset defined as $f=\{(|a>,|b>)\in A\times B:\forall |a>\in A\exists _{1}|b>\in B\}$ and notation $f(|a>)=|b>$ is used.

#### Definition: Body of numbers

Body of numbers T is defined as $T=\{c\in \mathbb {C} :(\exists c_{1},c_{2})(c_{1}\neq c_{2})\wedge (\forall c_{1},c_{2})(\exists c_{3}=c_{1}+c_{2}\wedge \exists c_{4}=c_{1}.c_{2}\wedge \exists c_{5}=-c_{1}\wedge \exists 0\neq c_{6}=c_{1}^{-1})\}$

#### Definition: Vector space

Vector space V is defined as $\mathbb {V} =\{(V,T,f_{1},f_{2}):(\forall |a>,|b>\in V)(f_{1}(|a>,|b>)=f_{1}(|b>,|a>))(...)\}$

#### Definition: Function

Function is a projection $f:\mathbb {C} \rightarrow \mathbb {C}$, which meets
$(\forall x\in D_{f})(\exists _{1}y\in H_{f})(f(x)=y)$

#### Definition: Functional

Functional is a projection $f:\mathbb {V} \rightarrow \mathbb {C}$, which meets
$(\forall x\in D_{f})(\exists _{1}y\in H_{f})(f(x)=y)$

#### Definition: Operator

Operator is a projection $f:\mathbb {V} \rightarrow \mathbb {V}$, which meets
$(\forall x\in D_{f})(\exists _{1}y\in H_{f})(f(x)=y)$