OpenLLM-France/wikimedia huggingface dataset:
# Introduction to Mathematical Physics/Authors

The author of this book is Alex Madon.
Alex holds a PhD in Plasma Physics from the University of Provence (France).
# Introduction to Mathematical Physics/Continuous approximation/Conservation laws
## Integral form of conservation laws

A conservation law\index{conservation law} is a balance that can be applied to every connex domain strictly interior to the considered system and that is followed in its movement. such a law can be written:
eqcon
${\frac {d}{dt}}\int _{D}A_{i}dv+\int _{\partial D}\alpha _{ij}n_{j}d\sigma =\int _{D}a_{i}dv$
Symbol ${\frac {d}{dt}}$ represents the particular derivative (see appendix chapretour). $A_{i}$ is a scalar or tensorial\footnote{ $A_{i}$ is the volumic density of quantity ${\mathcal {A}}$ (mass, momentum, energy ...). The subscript $i$ symbolically designs all the subscripts of the considered tensor. } function of eulerian variables $x$ and $t$. $a_{i}$ is volumic density rate provided by the exterior to the system. $\alpha _{ij}$ is the surfacic density rate of what is lost by the system through surface bording $D$.

## Local form of conservation laws

Equation eqcon represents the integral form of a conservation law. To this integral form is associated a local form that is presented now. As recalled in appendix chapretour, we have the following relation:
${\frac {d}{dt}}\int _{D}A_{i}dv=\int _{D}{\frac {d}{dt}}A_{i}dv$
It is also known that:
${\frac {dA_{i}}{dt}}={\frac {\partial A_{i}}{\partial t}}+(A_{i}u_{j})_{,j}$
Green formula allows to go from the surface integral to the volume integral:
$\int _{\partial D}\alpha _{ij}n_{j}d\sigma =\int _{D}\alpha _{ij,j}dv$
Final equation is thus:
${\frac {\partial A_{i}}{\partial t}}+(A_{i}u_{j}+\alpha _{ij})_{,j}=a_{i}$
Let us now introduce various conservation laws.
# Introduction to Art/Painting II/Brushes

The two main types of brush for watercolour are sable and synthetic. They come in shapes of round or flat brushes.
Others brushes include the rigger brush, chisel brush, mop brush, and fan brush.

## Tips:

If you can, buy the best quality of brushes. The hairs of the cheaper brushes tend to fall out quicker. Don't leave your brush in the water for a long time.
# Introduction to Art/References

Books on contemporary art, theory, and its predecessors:
Relational Aesthetics by Nicolas Bourriaud
The Return of the Real: Art and Theory at the End of the Century (October Books) by Hal Foster
Six Years: The Dematerialization of the Art Object from 1966 to 1972 : A Cross-Reference Book of Information on Some Esthetic Boundaries : Consisting of a biblio by Lucy R. Lippard
Theory in Contemporary Art since 1985 Edited By: ZOYA KOCUR, New York University SIMON LEUNG, University of California, Irvine
# Introduction to Art/Painting II

Medium in painting is very important, as each one will act very different from each other. The focus of this page is based on watercolours. Of course clean up and tinting can be done with water not thinner, as with oils. The base or binder is called gum arabic and mixes with the pigment to create watercolour. It can be used from a dry cake with water or from small tubes. If mixed with a lot of water it can become very light and make a sort of stain on the paper. It can also be used thicker and will sit more on top of the paper with a flatter look that does not let the paper show through, more like a gouache or acrylic look. Because of this versatility watercolour can have many different looks or styles, though it is difficult to cover with layers like oils or acrylics. We are creating an art site to educate the public in many areas of the arts, from art history to technique. Take a look: Impressionism

## Table of Contents

* Colours
* Brushes
* Paper
* Techniques
# Introduction to Art/Sculpture I
## Sculpture I

Sculpture I usually serves as the introductory course that allows the student to become familiar with three-dimensional forms. A general knowledge of basic tools and concepts is introduced, setting the foundation for more advanced work.

## Tools

There are a variety of sculpting tools that sculptors use to help define and form their figures.
* Loop Tool/Rake Tool - This tool consists of a metal loop attached to a rod of wood. The metal loop is designed in such a way that the artist can easily "rake" across the surface of clay, plaster, and other materials to smooth and better define the form. This tool comes in a variety of sizes, suitable for all applications.
* Pin Tool - A small, sharp metal point attached to a rod of wood. This tool is designed for making sharp, pen-like impressions into surfaces, primarily clay. Many prefer to use this tool to "sketch" onto the surface of their subject when in the development stage.
* Hands - Often disregarded as a tool, this is actually the most important tool of them all. Never substitute your hands for another tool just because the other tool is specifically suggested for the application. Sometimes your hands can do the best work.
Please understand though that the artist is not limited by these tools alone. Many artists use whatever is available; as long as the intentions of the artist are portrayed in the sculpture, it doesn't matter what tools you use. There are an almost infinite amount of tools, with many different variations, which could be substituted for by any simple object.

## Materials

Unlike drawing in which you're restricted to pencils, pastels, and other concrete mediums, Sculptures can consist of any material you can obtain, making it a very free and expansive art form. Sculptures have been erected of aluminum foil, chicken wire, packaging tape, and even plants! The beginning sculptor, however, will want to become familiar with the most readily-available and common sculpting materials.
* Clay -
* Plaster -
Other materials and their uses will be covered in the following sculpture Wikibooks.
# Introduction to Art/Painting I

Painting can be done in a variety of media. For example, Oils, Watercolour, Acrylics, Gouache and Tempera.
Paints are made from a pigment, and a binder. Binder is relatively cheap, while pigment is much more expensive. Pigments are a colored powder, made from organic or inorganic materials. (This is different than a colorant, which dyes or stains a color.)
All paints use the same basic pigments, but the binder changes. The binder for acrylics dries quickly and the paint is more like a plastic than oils which have an oil based binder and dry slowly. Oil Paints are often built up in layers or glazes. The other paints---Watercolour, Acrylics, Gouache, and Tempera---are water-based, meaning the paint can be diluted with water and clean-up can be done with soap and water. Oil paints, on the other hand, require paint thinner to clean brushes. The number and variety of painting techniques is endless.
Besides quality of paint, factors affecting color quality include: paint opacity, glossiness of painting surface, lighting, transparency, and texture.
# Introduction to Art/Painting II/Colours

There are commonly two main commercial grades of watercolour paint, one is called "Artists" and the other is called "Students". Although Artists quality paint is more expensive, the pigment is much stronger and it is easier to obtain satisfactory results. Also, Artists quality paints are available in a larger range of colours.
The paint is supplied in either tubes or cakes which are called pans, either whole or half pans.
There are many colours to choose from, but a typical palette of twelve colours would look like this.
Greens can be made from mixing the blues and yellows.
Purples can be made from mixing the blues and reds.
Greys can be made from browns and blues.
Black can be made from a rich mix of Burnt Umber and Ultramarine Blue.
Left click onto the colours to see them full size.
# Lombard/Past Perfect Indicative

* The reference orthography for this page of Lombard course is New Lombard orthography
It is built like this:
       Indicative imperfect of the auxiliary verb + past participle
             The auxiliary verb is vesser (coniugation) for reflexive verbs and for most of intransitive verbs, havé ( coniugation) for transitive verbs.
Example:
# Lombard/Phonology
## Summary

* Accent
* Orthography and pronunciation rules
** Milanese dialect
** Laghee dialect
** Bergamasque dialect
** Pavese dialect
# Lombard/Phrasal verbs

* The reference orthography for this page of Lombard course is New Lombard orthography
Some verbs change their meaning when they are succeeded by a preposition or by some adverbs, an example list is presented here(the Lombard-language Wiktionary has a special category for phrasal verbs):
# Lombard/Present Conditional

* The reference orthography for this page of Lombard course is New Lombard orthography
Here are the endings to be added to verbs to conjugate the regular verbs. The verb "varda" for the first conjugation is shown as an example (the second and the third conjugations are like the first in future indicative in Milanese dialect),"finì" for the fourth incoative conjugation, "dormì" for the fourth non-incoative conjugation.

## Milanese dialect

| | I II, III conjugation | IV incoative conjugation | IV non-incoative conjugation |
| Mi | vardariss / vardaria | finissaria | dormariss / dormaria |
| Ti | vardarisset / vardariet | finissariet | dormarisset / dormariet |
| Lù el Lee la | vardariss / vardaria | finissaria | dormariss / dormaria |
| Num | vardarissom / vardariom | finissariom | dormarissom / dormariom |
| Vialter | vardarissov / vardariov | finissariov | dormarissov / dormariov |
| Lor (i) Lore (i) | vardarissen / vardarien | finissarien | dormarissen / dormarien |

## Other dialects

See the appendices to the wiktionary in Lombardy:

### Western Lombard

→First conjugation →Second conjugation →Third conjugation →Forth non-incoative conjugation →Forth incoative conjugation

### Eastern Lombard

→First conjugation →Third conjugation →Forth conjugation
# Lombard/Present Imperative

* The reference orthography for this page of Lombard course is New Lombard orthography
Here are the endings to be added to verbs to conjugate the regular verbs. The verb "vardà" for the first conjugation, "vedé" for the second one (the third conjugation is like the second one, in the imperfect indicative), "finì" for the fourth incoative one, "dormì" for the foeuth non-incoative one are shown as examples.

## Milanese dialect

| | I conjugation | II-III conjugation | IV incoative conjugation | 'IV non-incoative conjugation |
| | varda | ved | finiss | dorma | ti |
| che 'l/che la | varda | veda | finissa | dorma | lu lee |
| | vardèm | vedèm | finissèm / finèm | dormèm | num |
| | vardé | vedì | finì | dormì | vialter |
| che (i) | varden | veden | finissen | dormen | lor lore |
* ↑ there is the final a just when followed by a consonant and/or the root ends in two consonants

## Other dialects

See the appendices to the wiktionary in Lombardy:

### Western Lombard

→First conjugation →Second conjugation →Third conjugation →Forth non-incoative conjugation →Forth incoative conjugation

### Eastern lombard

→Firstconjugation →Third conjugation →Forth conjugation
# Lombard/Possessive pronouns

* The reference orthography for this page of Lombard course is New Lombard orthography
The possessive pronouns are obtained by putting the article to the corresponding possessive adjective.
    Examples:
* El mè (in dialect Milanese)
* El tò (in dialect Milanese)
       and so on
| | English | Lombard (milanese dialect) |
| 1 | mine | el mè |
| 2 | yours | el tò "m" la toa "f" |
| 3 (of him) | his | el sò (de lu) "m" la soa (de lu) "f" |
| 3 (of her) | her | el sò (de lee) "m" la soa (de lee) "f" |
| 4 | ours | el nost "m" la nosta "f" |
| 5 | yours | el vost "m"" la vosta "f" |
| 6 (...) | theirs | el sò (de lor) "m" la soa (de lor) "f" |
| 6 (...) | theirs | el sò (de lore) "m" la soa (de lore) "f" |
Note
# Lombard/Present Subjunctive

* The reference orthography for this page of Lombard course is New Lombard orthography
Here are the endings to add to the verbs to conjugate the regular verbs. The verb "vardà" for the first conjugation, "creder" for the third one (in present subjuntive the second one is conjugated like the third one) , "finì" for the forth incoative one and dormì for the forth inon incoative are shown as examples.

## Milanese dialect

| | I conjugation | II e III conjugation | IV incoative conjugation | IV non-incoative conjugation |
| Mi | vardi | creda | finissa | dorma |
| Ti | vardet | credet | finisset | dormet |
| Lu el Lee la | varda | cred | finissa | dorma |
| Num | vardom | credom | finissom | dormom |
| Vialter | vardii | credii / credov | finissov | dormii / dormov |
| Lor (i) Lore (i) | varden | creden | finissen | dormen |

## Other dialects

Please refer to the appendices of the Lombard-language Wiktionary:

### Western Lombard

→Prima conjugation →Seconda conjugation →Terza conjugation →Quarta conjugation non incoativa →Quarta conjugation incoativa

### Eastern Lombard

→Prima conjugation →Terza conjugation →Quarta conjugation
# Lombard/Present Indicative

* The reference orthography for this page of Lombard course is New Lombard orthography
Here are the endings to be added to verbs to conjugate the regular verbs. As an example, the verb "vardà" for the first conjugation, "creder" for the second conjugation (in the present indicative the third conjugation is like the second one) "finì" for the fourth incoative conjugation, "dormì" for the forth non-incoative conjugation are shown.

## Milanese dialect

| | I conjugation | II e III conjugation | IV incoative conjugation | IV non-incoative conjugation |
| Mi | vardi | credi | finissi | dormi |
| Ti | vardet | credet | finisset | dormet |
| Lu el Lee la | varda | cred | finiss | dorma |
| Num | vardom | credom | finissom | dormom |
| Vialter | vardii/vardee | credii | finii | dormii |
| Lor (i) Lore (i) | varden | creden | finissen | dormen |
* ↑ the suffix is not added -i when the root of the verb ends in "i"

## Other dialects

See the appendices to the wiktionary in Lombard:

### Western Lombard

→First conjugation →Second conjugation →Third conjugation →Forth conjugation not incoative →Forth conjugation incoative

### Eastern Lombard

→First conjugation →Third conjugation →Forth conjugation
# Isoba/Case

In the Morphosyntactic Alignment section, six cases were identified:
* Ergative
* Direct
* Accusative
* Locative
* Instrumental
* Dative
The table in the aforementioned section provided a basic overview of how nouns declined for these cases. This section provides examples for and further information about each case.

## Ergative Case

Uninflected nouns are identical in form to their ergative case counterparts; the first syllable of the root morpheme takes a high tone. For the sake of simplicity, uninflected nouns be treated as if they were truly in the ergative case.
The ergative case is used for the following purposes:
* Identifying the agent of a transitive verb or the sole argument of an intransitive verb while implying but not emphasizing volition. This was covered in the Morphosyntactic Alignment section.
* Addressing or pointing out entities.
** “Giu” means cat. To address a cat, one can say, “Giu!” (“Cat!”) or “Ei giu!” (“Hey, cat!”)
** Pointing out a cat means to utter “cat” to imply its presence, during a walk in the park, for instance. It would be appropriate to say “Giu” to point out the cat. This is nearly equivalent to saying “La gyu” which means “there is a cat.” In this construction, the accusative case is used.
* Using a single noun phrase as the answer to a question, even when that noun would be in a different case were the answer a complete sentence.
** “Lé xyn” means “What do you see?” An acceptable answer is “Giu,” though the accusative form “Gyu” is also acceptable.
* Equating arguments with the copula “hi,” which means “to be.”
    Higiu=∅duxa=∅. Be.3cat.SG=ERGanimal.SG=ERG
    The cat is an animal.
Note that “duxa” is not in its accusative form, “duxaa.” Also, note that this statement is in reference to a specific cat because the general statement “Cats are animals” would have to use the plural forms of both “giu” and “duxa,” “giur” and “doxa,” respectively. More on the verb “hi” can be found in the Verbs section.
# Isoba/Consonants and Vowels

Isoba has 7 monophthongs (basic vowels), 13 diphthongs (two-vowel combinations), 24 consonants, and 1 pharyngealization phoneme that interacts with nearby phonemes to produce different phonetic results. This page will introduce all 20 vowels and the 24 consonants.
All pronunciation tips in the following table are based on General American English (GenAm) unless otherwise specified.

## Vowels

Monophthongs :
| Vowel | Pronunciation | Phoneme | Notes | Pronunciation Tip |
| a | [a] | /a/ | a in father is too far back. | No GenAm equivalent; a in Spanish casa |
| o | [o̞] | /o/ | Can also be [o̞u̯] | ol in cold |
| u | [u] | /u/ | Can be [ʊ] in indeliberate speech | oo in pool without the offglide |
| e | [ɨ̞] | /ɨ/ | Can be [ə] in indeliberate speech | e in chicken but more open, though not as open as ir in Australian English bird |
| i | [i] | /i/ | Can be [ɪ] in indeliberate speech | ee in seed |
| ö | [ɵ] | /ɵ/ | ö in German schön is too far forward | No GenAm equivalent; ir in New Zealand English bird |
| eu | [y] | /y/ | Can be [ʉ̞] in indeliberate speech | No GenAm equivalent; ü in German über |
Diphthongs :
| Vowel | Pronunciation | Diaphoneme | Notes | Pronunciation Tip |
| au | [ɑu̯] | /au/ | Can be [ɑʊ̯] in indeliberate speech; [ɑ] is an allophone of /a/. | No GenAm equivalent; ao in Mandarin Pinyin |
| ai | [ai̯] | /ai/ | Can be [aɪ̯] in indeliberate speech | ie in lie |
| oi | [o̞i̯] | /oi/ | | oy in boy |
| ua | [wa] | /wa/ | | No GenAm equivalent; hua in Spanish marihuana |
| uo | [wo̞] | /wo/ | | No GenAm equivalent; like uo in Mandarin Pinyin |
| ui | [wi] | /wi/ | Can be [wɪ] in indeliberate speech | we |
| ei | [e̞i̯] | /ei/ | Can be [e] in indeliberate speech | ey in hey |
| ia | [ja] | /ja/ | | No GenAm equivalent; Russian я |
| iu | [ju] | /ju/ | | No GenAm equivalent; Ju in German Julia |
| ie | [je̞] | /je/ | | No GenAm equivalent; ie in Mandarin Pinyin |
| iö | [jɵ] | /jɵ/ | | No GenAM equivalent; like ё in Russian её |
| öu | [ɵy̯] | /ɵy/ | Not equivalent to Finnish öy, which is rather [ø̞y̯]; Isoba öu starts more closed and farther back. | No GenAM equivalent; pronounce [ɵ], then [y] immediately, emphasizing the former over the latter. |
| ue | [ɥe̞] | /ɥe/ | | No GenAm equivalent; üe in Mandarin Pinyin |
Tone →
# Isoba/Dictionary

This is an Isoba-English dictionary. The following sections are arranged in Isoba alphabetical order, which is as followsː
    a o u e i ö eu m b p f fh n d t s z l r ll g k h ch j c x sj zs q gh

## eu
### eu

    num. one; a; an
    Must be used with appropriate classifier, like "se," to quantify a noun.
    eusegiu oneCLcat.SG=ERG
    one cat
# Graphic Design/Authors

This book was started by Karl Wick, a graduate of the acclaimed University of Cincinnati College of Design, Architecture, Art and Planning (DAAP).

## Note from the author

There are not many textbooks published on the discipline of graphic design. Perhaps this is due in part to the abstract, subjective nature of many of its aspects, and the fact that there are few universally-agreed-upon rules like there are for mathematics or the hard sciences.
This book is an attempt to formalize some of the concepts that were taught to me while in design school. The material was difficult and sometimes even overwhelming for me at the time. I did not graduate at the top of my class. However DAAP is a widely respected school and I did receive the vigorous training that characterizes its graphic design department. In this book I will try to break down in a simple and understandable way the basics of what I learned.
# Graph Theory/Trees

A tree is a type of connected graph. An directed graph is a tree if it is connected, has no cycles and all vertices have at most one parent. An undirected graph is considered a tree if it is connected, has $|V|-1$ edges and is acyclic (a graph that satisfies any two of these properties satisfies all three).
* Exercise: Equivalent Definitions
* Show that the following are equivalent definitions for a tree:
* A graph with a minimal number of edges which is connected.
* A graph with maximal number of edges without a cycle.
* A graph with no cycle in which adding any edge creates a cycle.
* A graph with n nodes and n-1 edges that is connected.
* A graph in which any two nodes are connected by a unique path (path edges may only be traversed once).
* Hint: To keep the total proof short, put the definitions in a suitable order, and then prove A=>B=>C=>D=>E=>A. Take particular care over graphs with zero and one node.
* Additionally,
* A graph is connected and each edge is a bridge.

## $tree$

Acyclic and connected $graph$. $forest$ is acyclic graph. So, $tree\subseteq forest$

## �Significance

* tree : minimum size connected graph
* cycle : minimum size 2-connected graph
# Form and function

Just like in architecture, one of the fundamental debates in graphic design is between form and function.
Form is defined as the shape or visual quality of something. It refers to aesthetics, how a piece looks. Much of graphic design centers on how to make a work appealing (or unappealing, or any other quality depending on the project goals).
Function relates to getting the job done. Function is pragmatic and business-oriented. Printing newspaper on glossy magazine paper is too expensive, and printing it on tissue paper would fall apart. An artistic photograph of a mountain may not convey a message appropriate to an Arctic cruise.
# Graph Theory/Weighted graphs and algorithms

Algorithm (Dijkstra's algorithm):
Let $G=(E,V)$ be a finite digraph with weight $c:E\to \mathbb {R}$. Fix a node $x\in V$. Then the following algorithm computes a shortest path from any node other than $x$ to $x$:
In C, the graph $G$ and the function $c:E\to \mathbb {R}$ shall be given by the nodes $0,\ldots ,n-1$ (where $n=|V|$ and $x=0$) and a weight function double long weight(int source, int target) which is $-1$ whenever source and target are not incident.