OpenLLM-France/wikimedia huggingface dataset:
# Ordinary Differential Equations:Cheat Sheet/Second Order Homogeneous Ordinary Differential Equations
## With Constant Coefficients
### General Form

$ay''+by'+cy=0$ or $p(D)y=0$, where
    $p(D)=aD^{2}+bD+c$ is called the polynomial differential operator with constant coefficients.

### Solution

* Solve the auxiliary equation, $p(m)=0$, to get $m=\lambda _{1},\lambda _{2}$
* If $\lambda _{1},\lambda _{2}$ are
** Real and distinct, then $y(x)=Ae^{\lambda _{1}x}+Be^{\lambda _{2}x}$
** Real and equal, then $y(x)=(Ax+B)e^{\lambda _{1}x}$
** Imaginary, $\lambda _{i}=a\pm bi$, then $y(x)=(A\cos {bx}+B\sin {bx})e^{ax}$

## Euler-Cauchy Equations
### General Form

$ax^{2}y''+bxy'+cy=0$ or $p(D)y=0$ where
    $p(D)=ax^{2}D^{2}+bxD+c$ is called the polynomial differential operator.

### Solution

Solving $ax^{2}y''+bxy'+cy=0$ is equivalent to solving $ay''+(b-a)y'+cy=0$

## General Homogenous ODE with Variable Coefficients
### If one particular solution is known

If one solution of a homogeneous linear second order equation is known, $y_{1}(x)\neq 0$, original equation can be converted to a linear first order equation using substitutions $y_{2}=y_{2}(x)z(x)$ and subsequent replacement $z^{'}(x)=u$.

#### Abel's identity

For the homogeneous linear ODE $y''+p(x)y'+q(x)y=0$, Wronskian of its two solutions is given by $W_{y_{1},y_{2})(x)=W(x_{0})e^{-\int _{x_{0}}^{x}p(x)dx}$

##### Solution with Abel's identity

Given a homogenous linear ODE and a solution of ODE, $y_{1}(x)$, find Wronskian using Abel’s identity and by definition of Wronskian, equate and solve for $y_{2}(x)$.

##### Few Useful Notes

* If $y_{1},y_{2}$ are linearly dependent, $W(x)=0,\forall x$
* If $W(x)=0$, for some $x$, then $W(x)=0,\forall x$.
← First Order Ordinary Differential Equations · Second Order Inhomogeneous Ordinary Differential Equations →
# Organ

Welcome! This is a book devoted to the organ, the largest of musical instruments. It is designed to give you an understanding of how the instrument works, its history, and the basics of how to play it.
Note: This book is still a work in progress and is not complete. If you have experience playing this instrument and/or wish to help expand it, please post a comment on Talk:Organ or jump right in and expand/improve the existing material.

## Contents

* Getting Started
   * Introduction
   * History of the Organ
   * How the Organ Works
   * Types of Organs
* Technique
   * Posture
   * Playing the Manuals
   * Playing the Pedals
   * Operating the Console
* Sounds and Registrations
   * Pipe pitches
   * Types of Pipes
   * Using Tasteful Registrations
   * Short Glossary of Common Pipe Names
# Outdoor Survival/Fire

Start the fire first with tinder, then add small twigs (wire size), then pencil size twigs, then thumb size twigs. Keep the fire small so that you aren't wasting valuable energy gathering firewood all the time. However if gathering wood is easy big fires attract attention. Burn whole logs without cutting them by just sliding them into the fire as they burn (the whole log will not catch fire).
Don't fear rain. Rainwater is just on the outside, and this does not mean that wood is sodden through. Green wood and young branches are "wet," and won't ignite readily, but any kind of wood will eventually burn on a hot enough fire. If it looks like a heavy downpour is coming, build a roof over your fire using one or two big logs about a foot (30cm) above the coals.
* Paper, cardboard, or unneeded cloth can be easy to start on fire
* Use small twigs from under the main canopy of the tree as tinder. (If they don't break off easily, they are still green.)
* Dry pine needles work great to start fires and give off lots of smoke.
* Rubbing bark between your hands until it is fluffy also makes excellent tinder
* Cattails easily catch on fire.
* If stranded in a vehicle, siphon out some gas or oil.
If you don't have matches:
* The old "fire-bow" trick is very hard work even under the best circumstances
* Fire can be started with a glass lens from a magnifying glass, mirror, binoculars, and the polished bottom of a soda can. (Most eyeglasses will not work.)
* The reflector of a (broken) car headlight can be used to concentrate sunlight and start a fire. Place tinder where the filament is and point the lamp at the sun. Same with a flashlight reflector.
* Flint and steel works but you must practice with it first.
Lately many new products have become available:
* Two-part chemical fire starters work fairly well and work even in the rain
* Magnesium fire starters work well but practice with them first
Some other ideas
* a tealight candle works wonders.
* If you have a 9 volt battery and a bit of steel wool, hold the steel wool against the battery's terminals and it will spark and start the steel wool burning.
* Just for fun ( be careful with frost bite for this one) but you can actually start a fire by melting a piece of ice with your hands into a lens and using it to start a fire. However Mythbusters showed this does not work.
* Be creative
To coax a struggling fire into a healthy blaze, fan it or blow on the coals. A flap of cardboard makes an ideal fan. Be careful not to blow it out.
# Outdoor Survival/Quinzhee

A quinzhee is a type of snow shelter made by making a pile of snow, waiting for it to settle together, then hollowing out the inside. In contrast, an igloo is made by carefully stacking cut blocks of snow.

## Design principles

It is not difficult to make a quinzhee, though it will be warmer and stronger if certain techniques are carefully followed and on that note, make sure you live in an area with snow, or this will have little use to you, a stupid wikibook, right?. For strength, the quinzhee needs to be a dome and the lower walls must not need to support too much weight. The walls should be very thick at the base and get slightly thinner towards to the top of the dome.
For warmth, the entrance of the quinzhee should be a tunnel with an upward sloping floor such that the floor is slightly higher than the top of the entrance. Be careful not to increase the height of the door by hitting it with your back each time you enter! And DO NOT bring a heater in with you, or the structure might melt on you.

## How to build a quinzhee

To make a quinzhee, make a large dome of snow. When making the pile, consider the inside shape that you want. A quinzhee to sleep two should have an oval footprint. Remember to make it high enough so that the floor can be elevated. Placing it on a hill can help with this. The length needs to be the wall thickness plus the length of your sleeping bag.
Once the pile is done, insert sticks straight in to a depth of 30 cm. As you dig it out, these sticks will tell you when you are near the outside so that you won't dig through. Wait for an hour or two for the snow to settle. The snow will re-form into a hard material that will not fall in when it is dug out.
Dig out the quinzhee with a small shovel. The fastest way is to cut blocks and push those towards the door. Cut the blocks left, right, top, and bottom. Don't pry too much as this can create cracks in the wall. As you get further in, it will be helpful to have a person outside moving the snow out of the tunnel and away. Eventually, two people will be able to fit inside and the digging goes much faster.

## See also

Outdoor Survival
# Outdoor Survival/Preparedness

You should be prepared for going into the outdoors even if is for less than a day.
* Make sure you know the area you are going to ahead of time even if it is just looking at maps.
* Check the weather.
* Tell some one you trust where you are going and for how long. If you are going some where with a park service tell them too.
* Make sure the people going with you are prepared.
* Know some first aid and read this wikibook.
* Talk to some one who has been where you are going or has more experience, better yet invite them along.
* Make sure you keep your car in good condition for car trips.
* Bring a survival kit.
* Go with at least one person if you can.
* Practice survival skills. Practicing them can be lots of fun.
If an emergency happens relax, prioritize, and be creative with what you have.
# Outdoor Survival/Signals

Bigger is better. Just don't burn down any forests.
# Rugby Union/Prop

Props are usually the some of the biggest players on the field. They are part of the scrum. There are 2 props on the field per team.

## Responsibilities
### In the Scrum

* Support the hooker
* Push back the other team
* Hold the front row together

### In Open Play

* Follow the ball, in order to support the runner
* Mark and tackle the other team's big players
* Be active in the ruck
* Be ready to run the ball into the other team's defense

### In Lineouts

* Lift the lock into the air
* Be ready to stop the other team if they steal the throw-in
# Rugby Union/Positions

There are ten different positions in rugby. Each team has fifteen players on the field at one time. The positions are:

## Forwards

* Prop (2 people)
* Hooker
* Lock (2 people)
* Flanker (2 people)
* 8-man

## Backs

* Scrum Half
* Fly Half
* Centre (2 people)
* Wing (2 people)
* Fullback
# Russian/Appendix/Signs
## Signs in Russian

Russian language has two unusual letters. They are called hard sign and soft sign (твёрдый знак and мягкий знак in Russian). The hard sign looks like a ъ, and the soft sign looks like a ь.

##### The hard sign

The hard sign designates a [j] sound (the letter й in Russian), though most people think that it doesn't designate this sound. They think that it only separates the first part of the word from the second. This letter always comes after letters е, ё, ю, я and always after consonants. In Russian words it stands between the root and the prefix. For example, the word подъезд (entrance). The transcription of this word is [podjézd]. If there was no hard sign, it would be подезд [podézd]. As can be seen, there is a difference. Later on, we will return once more to the hard sign.

##### The soft sign

The soft sign softens the preceding consonant and by itself doesn't designate the sound. But sometimes it combines its pronunciation and the hard sign's pronunciation. For example, the word семья (family). The transcription of this word is [sem'já]. If there wasn't the soft sign, it would be семя [sem'á] - seed. If it combines its pronunciation and hard sign's pronunciation it is called separating. If it doesn't combine, it is called softening.

##### Other pronunciation of the hard sign

In words that came to Russian language from foreign languages the hard sign's pronunciation is the same as the separating soft sign. For example, the word адъютант [ad'jutánt] - adjutant. In this word the hard sign doesn't stand between the root and the prefix.
# Russian/Answers/Lesson 1

(approximate translation - idiomatic and should give you the basic ideas)
    Sasha: Hi! My name is Sasha. What is your name?
    Katya: Hi, Sasha. My name is Katya. How are you?
    Sasha: I'm feeling good. And yourself?
    Katya: Also good.
    Sasha: I'm a student. Are you?
    Katya: Yes, I'm a student.
    Sasha: Neat! Well, see you!
# Russian/Appendix

Russian language · Русский язык :
| Lessons | Introduction · Alphabet · Lesson 1 · Lesson 2 · Lesson 3 · Lesson 4 · Lesson 5 | (view) |
| Reference | Numbers · Cases (Nom. · Gen. · Dat. · Acc. · Inst. · Prep.) · Adjectives · Prepositions · Verbs (Aspect · Past · Future) · Pronouns (Personal · Possessive · Interrogative) · Cursive | |
| Appendices | Appendix · Alphabet · Internet · Cheat Sheet | |
The appendix is a place for things you would normally find at the end of a language textbook: conjugation of verbs, cardinal and ordinal numbers, charts of cases, and the like.
* Internet Resources
* Noun declensions
* Verbs
* Signs
# Rugby Union/Lock

There are 2 locks on the field at one time. They are in the second row of the scrum. They also get lifted in lineouts.

## Responsibilities
### In the Scrum

* Keep the front row stable by backing up the props
* Guide the ball to the 8-man with their feet
* Provide a handhold for the flankers

### In General Play

* Follow the ball, providing support for the runner
* Be active in the ruck
* Be ready to run the ball into the other team's defense
* Be ready to tackle the other team's big players

### In the Lineout

* Responsible for getting the ball from the throw-in
* Try to take the other team's throw-in
* Is lifted into the air by props
# Saylor.org's Ancient Civilizations of the World/Medieval Society and Culture

In this section, we will examine the social hierarchies and culture that emerged from the Medieval Era. Central to this topic is an understanding to the medieval philosophical/religious conception of how the universe was ordered.

## The Great Chain of Being

One of the most important ideas that governed medieval society was that of the "Great Chain of Being". The Great Chain of being held that all life (as medievals thought of it, although you will see some things in the chain were not 'alive' according to modern science) in the world was structured in an elaborate hierarchy of authority. At the top ruled God followed by the different classes of angels, demons (fallen/renegade angels), stars, the moon, kings, princes, nobles, men, wild animals, domesticated animals, trees, other plants, precious stones, precious metals, and other minerals.
God, and beneath him, the angels, both existing wholly in spirit form, sit at the top of the chain. Earthly flesh is fallible and ever-changing: mutable. Spirit, however, is unchanging and permanent. This sense of permanence is crucial to understanding this conception of reality. It is generally impossible to change the position of an object in the hierarchy. (One exception might be in the realm of alchemy, where alchemists attempted to transmute base elements, such as lead, into higher elements, either silver, or, more often, gold—- the highest element.)
In the natural order, earth (rock) is at the bottom of the chain: this element possesses only the attribute of existence. Each link succeeding upward contains the positive attributes of the previous link and adds (at least) one other. Rocks, as above, possess only existence; the next link up, plants, possess life and existence. Animals add not only motion, but appetite as well.
Man is both mortal flesh, as those below him, and also spirit as those above. In this dichotomy, the struggle between flesh and spirit becomes a moral one. The way of the spirit is higher, more noble; it brings one closer to God. The desires of the flesh move one away from God. The Christian fall of Lucifer is thought of as especially terrible, as angels are wholly spirit, yet Lucifer defied God, the ultimate perfection.

## Attribution

"The Great Chain of Being" (Wikipedia) http://en.wikipedia.org/wiki/Great_chain_of_being
# Saylor.org's Ancient Civilizations of the World/Neolithic Revolution and the Birth of Civilization

Civilizations are societies that rely on sedentary agriculture, develop social stratification and economic specialization, and create populations that are sufficient to support urban life. However, such civilizations have only existed for the last 9,000 years—a tiny fraction of the time that the human species has inhabited the earth.
In this unit, we will begin by defining what civilization means and by understanding the early stages of civilization that emerged during the Paleolithic Era (2.5 million years ago). Secondly, we will examine the transition from hunter-gatherer groups to sedentary agricultural communities during the Neolithic Age—one of the first great transformations of human society.
# Saylor.org's Ancient Civilizations of the World/Peoples of the Americas

Civilizations in the Americas emerged separately from other major civilizations in the world. The indigenous people of the Americas are believed to have been immigrants from Asia, who crossed over to America during the Ice Age, approximately 20,000 years ago. These new immigrants quickly spread throughout the Americas, in small and culturally distinct groups. The development of agriculture in the Americas five thousand years ago led to the flourish of new culturally advanced societies and innovations. Pre-Columbian American civilizations, such as the Mayas, Aztecs, Incas, and Olmecs were socially stratified and technologically advanced.
In this unit, we will see that civilizations developed in two main regions of the Americas: Mesoamerica and the Peruvian highlands. In fact, we will see that the entire area that stretched from central Mexico to Chile formed a continuous chain of developing civilizations.
# Pathology/Preface

This book, as based of a translation of the German Wikibook, aims to cover subjects and matters of pathology, and it is intended for reference and educational puposes, not medical advices.
# Pathology/Mediastinum

Navigation
* Main Page | Introduction in Pathology | Adjustment Reactions | Cell and Tissue Damage | Exogenic Noxa
* Cardiovascular System: Heart | Vessels | Mediastinum
* Respiratory System: Upper Airway Tract | Lower Airway Tract and Lungs | Pleura
* Gastrointestinal System: Mouth and Oral Glands | Esophagus | Stomach | Intestine | Liver | Biliary Tract - Pancreas
* Urogenital System: Kidneys | Urinary Tract Collection System | Mammary Gland | Ovary | Uterus and Cervix | Vagina and Vulva | Gestation | Testes | Prostate
* Endocrine System: Endocrine Glands
* Neuropathology: Central Nervous System | Neoplasms of the Nervous System | Vertebral Column and Spinal Cord | Peripheral Nervous System | Muscle
* Locomotive System: Joints | Bone | Neoplasms of the Cartilage and Bone | Tendon Sheaths, Fasciae, and Connective Tissue
* Integument: Skin and Adnexal Structures | Hereditary Skin Diseases | Autoimmune Skin Diseases with Blisters | Non-Heritable Connective Tissue Disorders of the Skin | Microbial Skin Diseases | Neoplasms of the Skin | Cutaneous Symptoms in Internal Diseases
* Blood, Bone Marrow, and Immune System: Hämatopoetic System | Lymphatic System | Hematology
* Metabolism: Metabolic Disorders
* Procedures of Tissue Preparation | Glossary | Resources

## Mediastinitis

Inflammation of the Mediastinum.
Ät.: Bacterial

## Tumours

* Morbus Hodgkin - Tumour of the lymphatic tissue
* NHL - Tumours of the lymphatic tissue
* Thymoma - Assoziated with Myasthenia gravis
* Thymuscarcinoma
* Teratoma - germ cell tumour
* Seminoma - germ cell tumour
Navigation
* Main Page | Introduction in Pathology | Adjustment Reactions | Cell and Tissue Damage | Exogenic Noxa
* Cardiovascular System: Heart | Vessels | Mediastinum
* Respiratory System: Upper Airway Tract | Lower Airway Tract and Lungs | Pleura
* Gastrointestinal System: Mouth and Oral Glands | Esophagus | Stomach | Intestine | Liver | Biliary Tract - Pancreas
* Urogenital System: Kidneys | Urinary Tract Collection System | Mammary Gland | Ovary | Uterus and Cervix | Vagina and Vulva | Gestation | Testes | Prostate
* Endocrine System: Endocrine Glands
* Neuropathology: Central Nervous System | Neoplasms of the Nervous System | Vertebral Column and Spinal Cord | Peripheral Nervous System | Muscle
* Locomotive System: Joints | Bone | Neoplasms of the Cartilage and Bone | Tendon Sheaths, Fasciae, and Connective Tissue
* Integument: Skin and Adnexal Structures | Hereditary Skin Diseases | Autoimmune Skin Diseases with Blisters | Non-Heritable Connective Tissue Disorders of the Skin | Microbial Skin Diseases | Neoplasms of the Skin | Cutaneous Symptoms in Internal Diseases
* Blood, Bone Marrow, and Immune System: Hämatopoetic System | Lymphatic System | Hematology
* Metabolism: Metabolic Disorders
* Procedures of Tissue Preparation | Glossary | Resources
# Pathology

Comprisal of Human Pathology
This book is intended as a translation and continuation of the german Wikibook Pathologie. You are invited to help (it is fortunately not complicated, the technical terms and the facts are the same in English as in German. Exact translation is not necessary, write your own text, if you want).
Please upload new images not here but at Wikimedia Commons.
* Preface
* Introduction: Pathology
* General Pathology
* Adjustment Reactions
* Cell and Tissue Damage
* Exogenic Noxa
* Systemic Pathology
* Cardiovascular System
* Heart - Vessels - Mediastinum
* Respiratory System
* Upper Airway Tract - Lower Airway Tract and Lungs - Pleura
* Gastrointestinal System
* Mouth and Oral Glands - Esophagus - Stomach - Intestine - Liver - Biliary Tract - Pancreas
* Urogenital System
* Kidneys - Ureters - Bladder - Urethra
* Mammary Gland - Ovary - Uterus and Cervix - Vagina and Vulva - Gestation
* Testes and Epididymis - Prostate - Penis
* Endocrine System
* Endocrine Glands
* Neuropathology
* Central Nervous System - Neoplasms of the Nervous System - Vertebral Column and Spinal Cord - Peripheral Nervous System - Muscle
* Locomotive System
* Joints - Bone - Neoplasms of the Cartilage and Bone - Tendon Sheaths, Fasciae, and Connective Tissue
* Integument
* Skin and Adnexal Structures - Hereditary Skin Diseases - Autoimmune Skin Diseases with Blisters - Non-Heritable Connective Tissue Disorders of the Skin - Microbial Skin Diseases - Neoplasms of the Skin - Cutaneous Symptoms in Internal Diseases
* Blood, Bone Marrow and Immune System
* Hämatopoetic System - Lymphatic System - Hematology
* Metabolism
* Metabolic Disorders
* Appendices
* Procedures of Tissue Preparation
* Glossary
* Resources
* Print version
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.
# Pinyin/Gene

Genes are forms of DNA. DNA is a collection of chemical information that carries the instructions for making all the proteins a cell will ever need. Each gene contains a single set of instructions. These instructions usually code for a particular protein. Half of a person's genes come from the mother. The other half come from the father.
Jīyīn yóu DNA zǔchéng. DNA shì yī zǔ xiédài zhǐlìng de huàxué xìnxī, yòngyǐ zhìzào xìbāo bùduàn xūyào de suǒyǒu dànbáizhì. Měi gè jīyīn hányǒu dānyī de zhǐlìng zǔ. Zhèxiē zhǐlìng tōngcháng yòngyú tèdìng dànbáizhì de biānmǎ. Rén de jīyīn yībàn láizì mǔqīn, lìngyībàn láizì fùqīn.
# Pinyin/Generally

See also
# Pinyin/General name

See also
# Pinyin/Gamma-ray burst

Gamma-ray bursts (GRBs) are flashes of gamma rays from extremely energetic explosions. They have been seen in distant galaxies. They are the most luminous electromagnetic waves known to occur in the universe.
Gamma shèxiàn bàofā (GRB) shì láizì jídà néngliàng bàozhà de gamma shèxiàn de shǎnguāng, láizì yáoyuǎn de xīngxì, shì yǐzhī fāshēng zài yǔzhòu zuì guāngliàng de diàncíbō.
# Pinyin/Gate

See also
# Pinyin/Genetic disorder

See also
Hereditary diseases, are diseases with genes as the main cause. According to causes are divided into: single gene defect hereditary diseases, chromosome mutation hereditary diseases, hereditary diseases caused by the simultaneous effects of multiple genes, and diseases caused by changes in mitochondrial DNA. Of which genetic diseases caused by single gene defect are called Mendelian diseases. In most clinics through genetic testings and genetic screenings to help with diagnosis.
Yíchuánbìng, shì jīyīn wéi zhǔyào bìngyīn de jíbìng. Yījù chéngyīn fēnwéi: Dānyī jīyīn quēxiàn de yíchuánbìng, rǎnsètǐ biànyì yíchuánbìng, yóu duōchóng jīyīn gòngtóng yǐngxiǎng suǒ zàochéng de yíchuánbìng, hé lìxiàntǐ jīyīn biànyì suǒ yǐnqǐ de jíbìng. Qízhōng yóuyú dānyī jīyīn quēxiàn ér yǐnqǐ de yíchuánbìng chēngwéi Mendel-bìng. Línchuáng shàng dàduō tòuguò jīyīn jiǎncè hé jīyīn shāijiǎn lái fǔzhù zhěnduàn.
# Pinyin/Gang

See also