OpenLLM-France/wikimedia huggingface dataset:
# Chinese Medicinal Formulas/Prescriptions for Inducing Resuscitation with Cold Herbs
## Prescriptions

* Angong Niuhuang Wan
* Zixue Dan
* Zhibao Dan
# Chinese Medicinal Formulas/Prescriptions for Clearing away Heat
## Introduction

Prescriptions for clearing away heat are used for clearing heat, purging fire, cooling blood and removing toxins from the body.

## Types of Formulas

* Prescriptions for Clearing away Heat from Yingfen and Blood
* Prescriptions for Clearing away Heat and Toxins
* Prescriptions for Removing Heat from Zang-fu Organs
* Prescriptions for Clearing away Heat of Deficiency Type
* Prescriptions for Clearing away Summer-heat
# Chinese Medicinal Formulas/Prescriptions for Regulating the Flow of Qi
## Types of Formulas

* Prescriptions for Promoting the Flow of Qi
* Prescriptions for Suppressing upward Adverse Flow of Qi
# Biochemistry/Authors
## Authors of this book

* Magnus Manske : Started this book
* Cyclop : Began the work on Proteins section
* Brandon : Lipids and membranes chapter
* Justin : Filled in a few gaps
# Biochemistry
## Contents

* Introduction
** The Cell
** Thermodynamics
** Catalysis
** Metabolism and energy
** pKa values
* Proteins
** Introduction
** The chemistry of proteins
** Protein structure and folding
** Types of Protein
* Carbohydrates
** Regulation of Glucose Transporter Translocator in Health and Diabetes
* Membranes and Lipids
* Lipids And The Plasma Membrane
* Complex Lipid Metabolism and Cholesterol
* Enzymes
* Metabolism
** Glycolysis
** Gluconeogenesis
** Regulation of glycolysis and gluconeogenesis
** Glycogenolysis and glycogenesis
** Conversion of pyruvate to acetyl CoA
** Tricarboxylic Acid (TCA) Cycle
** Electron Transport Chain
* DNA and RNA
** Micro RNA(miRNA)
* Respiratory Pigments
* Cell Signaling Pathways
* Bioinformatics
    Authors
# Biochemistry/Catalytic Strategies/Acid Base reactions
## Introduction to acid base catalysis reactions

This type of catalysis involves proton donors or acceptors other than water. There is then a nucleophilic or electrophilic attack. Finally, the enzyme is then restored.
The donation or acceptance of protons is generally to stabilize the transition state. A corollary to this is metal ion catalysis which involves a metal ion that stabilizes the transition state with its positive charge. Some acid base catalysis reactions also use metal ions. One common amino acid present in most enzymes that acts as an acid or a base is histidine, since its pKa is close to that of the surrounding pH. Thus, it can act as either an acid or a base.
One example is with carbonic anhydrase that breaks down carbonic acid into a proton and a bicarbonate ion.
H$_2$CO$_3$ <-(with carbonic anhydrase)-> H$^+$ HCO$_3$$^-$
There is a part at the active site of carbonic anhydrase that contains a Zinc ion (Zn$^{2+}$) that is coordinated to a few histidine R groups. The Zinc also coordinates with the oxygen of a water molecule. When Zinc is coordinated with a water molecule, the pKa reduces from 15.7 to about 7. Thus, this means that at the physiological pH, the water molecule readily deprotonates. Now this Oxygen atom acts as a nucleophile, attacking the carbon of a carbon dioxide. This creates a complex coordination compound attached to the Zinc ion, resembling the bicarbonate ion. In the final step, another water molecule replaces the biocarbonate ion, and the enzyme is reformed, ready to react again.
# Breton/Introductory lessons/Breton Basics

* Introduction to Breton Breton Basics
Your first steps in Breton
Here are the very first sentences of Breton in this course :
Who is it ?
Piv eo ?
Who is ?
It's John
Yann eo
John is
What does John do?
Petra a ra Yann ?
What does John ?
John reads Bremañ (insisting upon the subject : John)
Yann a lenn Bremañ
John reads Bremañ
John reads Bremañ (insisting upon the verb : To read)
Lenn a ra Yann Bremañ
To read does Yann Bremañ
First Breton words
Breton
English
IPA notation
Piv
Who
piu
Eo
Is
eo
Yann
John
yañn
Petra
What
petra
Lenn
To read
len
Bremañ
Now (Breton newspaper)
bremañ :
* Verbal group
* In the preceding sentences, we have several verbal groups :
* "eo" : the verb "to be" is used alone in a personal form
* "a ra" : the verb "to do" is used in a personal form with a verb particle "a" (other verb particles exist "e", "o", etc.)
* "a lenn" : the verb "to read" is used in a personal form with a verb particle "a" as above
* "lenn a ra" : the verb "to read" is used in an impersonal form with an auxiliary verb which is in a personal form "a ra"
# Breton/Introductory lessons/Breton Dialects

* Introduction to Breton Breton Dialects
* The dialects of Breton as identified by ethnologists are Leoneg, Tregerieg, Gwenedeg, and Kerneveg (in French, respectively: léonard, trégorrois, vannetais, and cornouaillais). There are no clear borders between those dialect areas because the language varies slightly from one village to the next. Compared to the other dialects, the Gwenedeg dialect is somewhat more distinct due several pronunciation specificities.
* The following table shows common and local expressions :
Example of Gwenedeg
Me zo ganet é kreiz er mor
Tèr lèu ér méz;
Un tiig gwenn duhont em-es,
Er benal 'gresk étal en nor
Hag el lann en hol en anvez.
Me zo ganet é kreiz er mor,
E bro Arvor.
Excerpt from "Ar en deulin" from Yann-Ber Calloc'h
Example of Gwenedeg
GwenedegPeurunvanEnglish meaning
Me zo ganet é kreiz er mor
Me 'zo ganet e-kreiz ar mor
I was born in (the middle of) the sea
Tèr lèu ér méz;
Teir lev er maez;
Three leagues outside;
Un tiig gwenn duhont em-es,
Un tiig gwenn du-hont am eus,
A small white house I have over there,
Er benal 'gresk étal en nor
Ar banal a gresk e-tal an nor
Broom grows in front of the door
Hag el lann en hol en anvez.
Hag al lann en holl an anavez.
And heather all around.
Me zo ganet é kreiz er mor
Me zo ganet e-kreiz ar mor
I was born in (the middle of) the sea
E bro Arvor.
E bro Arvor.
In the country of Arvor. :
Example of Leoneg
Digeri a reas he divreh d'he muia-karet heb en em renta kont. Pokad a reent dibaouez an eil d'egile, o muzellou o tañva evid ar wech kenta mel dous ar garantez.
Excerpt from "Ar Vastardez" from Yann-Vadezour Lagadeg.
Example of Leoneg
LeonegPeurunvanEnglish meaning
Digeri a reas he divreh d'he muia-karet heb en em renta kont.
Digeriñ a reas he divrec'h d'he muiañ-karet heb en em rentañ kont.
She opened her arms to her beloved boyfriend without realizing.
Pokad a reent dibaouez an eil d'egile,
Pokad a reent dibaouez an eil d'egile,
They kissed each other without end,
o muzellou o tañva evid ar wech kenta mel dous ar garantez.
o muzellou o tañvañ evid ar wech kentañ mel dous ar garantez.
their lips tasting for the first time the sweet honey of love. :
* Breton spellings
* After several attempts at unifying the spelling, two main spellings exist : the "peurunvan" ("completely unified" spelling) and the "skolveurieg" ("university" spelling).
* This course uses "peurunvan" as it is today the most commonly used.
* "Peurunvan" accommodates for dialectal differences. Most notably, the notation "zh" - used in the name "Breizh" ("Brittany") - must be interpreted according to the dialect spoken.
* In Leon, it will be most often interpreted as "z" (therefore Breizh is pronounced Breiz).
* In Gwened (and some part of Kerne), it will often be interpreted as "h" (therefore Breizh is pronounced Breih).
* The transcription of "C'h" is also subject to confusion or criticism as pronunciation may widely vary according to the regions.
# C++ Programming/STL/Algorithms
### Algorithms

The STL also provides several useful algorithms, in the form of template functions, that are provided to, with the help of the iterator concept, manipulate the STL containers (or derivations).
The STL algorithms aren't restricted to STL containers, for instance:

#### The _copy suffix

* Non-modifying algorithms
* Modifying algorithms
* Removing algorithms
* Mutating algorithms
* Sorting algorithms
* Sorted range algorithms
* Numeric algorithms

#### Sorting and related operations
##### sort
##### Minimum and maximum

The standard library provides function templates min and max, which return the minimum and maximum of their two arguments respectively. Each has an overload available that allows you to customize the way the values are compared.
An example of how to use the Compare type parameter :
# C++ Programming/Programming Languages/Paradigms/Polymorphism
##### Polymorphism

Polymorphism allows a single name to be reused for several related but different purposes. The purpose of polymorphism is to allow one name to be used for a general class. Depending on the type of data, a specific instance of the general case is executed.
The concept of polymorphism is wider. Polymorphism exists every time we use two functions that have the same name, but differ in the implementation. They may also differ in their interface, e.g., by taking different arguments. In that case the choice of which function to make is via overload resolution, and is performed at compile time, so we refer to this as static polymorphism.
Dynamic polymorphism will be covered deeply in the Classes Section where we will address its use on redefining the method in the derived class.
# C++ Programming/Programming Languages/Paradigms/Encapsulation
### Encapsulation

Encapsulation (also known as information hiding) is a concept commonly used on large software projects to allow for extensibility. The principal behind encapsulation is to hide the inner workings of a class from the code that uses the class, only exposing the essentials.

#### Why Bother?

Team development projects often split up tasks. Designing clean, easy to understand interfaces makes code easier to understand. If a data member of a class written by Team A is used by Team B, and the class changes a way the data member works, it can break compatibility with Team B's code. Not only is maintaining data members of a class very difficult, it can also be quite confusing to clients. The interface of an encapsulated class is like a contract to clients, stating what it is capable of doing. The client shouldn't care how it is done, in fact it can be upgraded in the future, as long as it complies with the same interface.

#### Implementation

To completely encapsulate a class, all data members of the class must be private. In designing the class, it must be determined what data must be accessible, and what can be kept completely hidden. The data to be made public will require "accessor functions," which can allow data to be read or stored in private data members.
# C++ Programming/Programming Languages/Paradigms/Inheritance
##### Inheritance

Inheritance describes a relationship between two (or more) types, or classes, of objects in which one is said to be a "subtype" or "child" of the other; as a result, the "child" object is said to inherit features of the parent, allowing for shared functionality. This lets programmers re-use or reduce code and simplifies the development and maintenance of software.
Inheritance is also commonly held to include subtyping, whereby one type of object is defined to be a more specialized version of another type (see Liskov substitution principle), though non sub-typing inheritance is also possible.
Inheritance is typically expressed by describing classes of objects arranged in an inheritance hierarchy (also referred to as inheritance chain), a tree-like structure created by their inheritance relationships.
For example, one might create a variable class "Mammal" with features such as eating, reproducing, etc.; then define a subtype "Cat" that inherits those features without having to explicitly program them, while adding new features like "chasing mice". This allows commonalities among different kinds of objects to be expressed once and reused multiple times.
In C++ we can then have classes that are related to other classes (a class can be defined by means of an older, pre-existing, class ). This leads to a situation in which a new class has all the functionality of the older class, and additionally introduces its own specific functionality. Instead of composition, where a given class contains another class, we mean here derivation, where a given class is another class.
This OOP property will be explained further when we talk about Classes (and Structures) inheritance in the Classes Inheritance Section of the book.
If one wants to use more than one totally orthogonal hierarchy simultaneously, such as allowing "Cat" to inherit from "Cartoon character" and "Pet" as well as "Mammal" we are using multiple inheritance.
# C++ Programming/Programming Languages/Paradigms/Inheritance/Multiple Inheritance
###### Multiple inheritance

Multiple inheritance is the process by which one class can inherit the properties of two or more classes (variously known as its base classes, parent classes, ancestor classes, or super-classes).
This is shown in more detail in the C++ Classes Inheritance Section of the book.
# Cellular Automata/Equivalence Classes
## Introduction

Stephen Wolfram was one of the first to focus on the complete set of CA rules. He observed all the rules that can be created using binary cells $k=2$ and a three cell neighborhood $m=2$. There are $k^{k^{m}}=2^{2^{3}}=256$ such rules. The number of rules grows exponentially with the number of cell states and even faster with the neighbourhood size. This vast number of rules is a limiting factor when observing the whole set of rules.

## Definiton of equivalence

In this definition a more formal name for rule is used, the local definition function.
The local definition function $f_{1}$ is equal to the local definition function $f_{2}$, if and ony if there exists a homomorfism $g$ of global CA states that
    $f_{1}f_{2}$

## Clustering rules

or different symmetries
* input complement
* output complement
* reflection symmetry
* rotation smetry (2D) ?can be produced by reflection no it can not
* equivalence class

### Equivalence classes
## References

* Mirek Wojtowicz, Cellular Automata rules lexicon
* Global Dynamics
* http://en.wikipedia.org/wiki/Symmetries
* http://en.wikipedia.org/wiki/Equivalence_class
* http://en.wikipedia.org/wiki/Euclidean_plane_isometry
* about xlcau21 (22) http://groups.google.com/group/comp.theory.cell-automata/browse_frm/thread/b4596943ee04f3d6/9fffa47e715ffb7e?q=symmetry&rnum=6&hl=en#9fffa47e715ffb7e

### mix

* http://groups.google.com/group/comp.theory.cell-automata/browse_thread/thread/eedd3e963691fda2/41f376c8b51455b2?q=clusters&rnum=5&hl=en#41f376c8b51455b2
* http://groups.google.com/group/comp.theory.cell-automata/browse_frm/thread/2375d42de9f86ee1?tvc=1&q=clusters&hl=en
* http://groups.google.com/group/comp.theory.cell-automata/browse_frm/thread/86b9db28b67edf1/c5aac90b816f8f32?q=symmetry&rnum=21&hl=en#c5aac90b816f8f32
* http://groups.google.com/group/comp.theory.cell-automata/browse_frm/thread/3a24112941446717/1e809a7956a95529?q=symmetry&rnum=9&hl=en#1e809a7956a95529
* http://en.wikipedia.org/wiki/Natural_isomorphism
* http://www.mathematics21.org/formulas-theory.html
* http://en.wikibooks.org/wiki/Abstract_algebra
# Cellular Automata/Fluid Dynamics

The basic idea of simulating fluid dynamics with cellular automata is implementing particle dynamics as cellular automata rules and fluid dynamics would emerge as mean properties of

## Differential equation model for incompressible fluids

We are interested in the flow velocity $u$ that is defined by two differential equations

### Navier-Stokes equation

    ${\frac {\partial u}{\partial t}}+(u\nabla )u=-\nabla P+\nu \nabla ^{2}u$

### continuity equation

    $\nabla \cdot u=0$
$P=p/\rho _{0}$ is the kinematic pressure, $p$ is the pressure, $\rho _{0}$ constant mass density and $\nu$ is the kinematic share viscosity.

## References

* Dieter A. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models An Introduction, Springer 2000
# Cellular Automata/Examples

This section is a collection of examples used by the theorethical sections.
# Cellular Automata/Formalization

Formalization sometimes seems an unneeded burden when learning something new, yet it is the main tool to pass scientific knowledge to others. An informal introduction into CA was already presented, now is time for a detailed formalization that will allow us to dig further into the theory of CA.

# Overview

This book tries to mix rigorous mathematical formulae with self explanatory graphical representations of the same equations.
The formalization chapter is composed of the following sections:
* The mathematical model focuses on a general definition of one-dimensional cellular automata. At the end, it generalizes the theory to more than one dimension and functions that look more than one step into history.
* A neighborhood can be defined with general equations or can be described with a less general graphical definition. This chapter focuses on the last approach to describe the most common CA.
* A rule is a common way to define transition functions, some common ways to define a rule are described here.
* A pattern is used to describe a part of the content of a cellular automaton. Since some CA have been studied in detail, some patterns have been observed frequently as well. This section describes common methods for describing patterns.

# Common nomenclature

A common nomenclature lookup table is provided here.

#### Abbreviations:

| CA | cellular automata |

#### Basic symbols:

| $S$ | set of cell states |
| $k$ | number of cell states in S ($k=|S|$) |
| $c$ | cell state (value) ($c\in S$) |
| $\alpha$, $\beta$ | strings of cell values |
| $C$ | configuration (might be finite or infinite) |
| $N$ | finite configuration length |
| $x$ | position index |
| $A$ | neighborhood definition as a set of neighbors |
| $r$ | neighborhood radius |
| $n$ | neighborhood specific value or link in the preimage network |
| $o$ | overlap specific value or node in the preimage network |
| $f$ | local transition function |
| $F$ | global transition function |
| $t$ | time index or identifies the present |

#### Preimage model related symbols:

| $D$ | preimage matrix |
| $d$ | elements of $D$ |
| $b$ | preimage vector |
| $b_{\mathrm {L} }$ | left boundary vector |
| $b_{\mathrm {R} }$ | right boundary vector |
| $b_{\mathrm {u} }$ | unrestricted boundary vector |
| $p$ | number of preimages |
| $w_{n}$ | link (neighborhood) weight |
| $w_{o}$ | node (overlap) weight |
# Engineering Acoustics/Transverse vibrations of strings
## Introduction

This section deals with the wave nature of vibrations constrained to one dimension. Examples of this type of wave motion are found in objects such a pipes and tubes with a small diameter (no transverse motion of fluid) or in a string stretched on a musical instrument.
Stretched strings can be used to produce sound (e.g. music instruments like guitars). The stretched string constitutes a mechanical system that will be studied in this chapter. Later, the characteristics of this system will be used to help to understand by analogies acoustical systems.

## What is a wave equation?

There are various types of waves (i.e. electromagnetic, mechanical, etc.) that act all around us. It is important to use wave equations to describe the time-space behavior of the variables of interest in such waves. Wave equations solve the fundamental equations of motion in a way that eliminates all variables but one. Waves can propagate longitudinal or parallel to the propagation direction or perpendicular (transverse) to the direction of propagation. To visualize the motion of such waves click here (Acoustics animations provided by Dr. Dan Russell,Kettering University)

## One dimensional Case

Assumptions :
- the string is uniform in size and density
- stiffness of string is negligible for small deformations
- effects of gravity neglected
- no dissipative forces like frictions
- string deforms in a plane
- motion of the string can be described by using one single spatial coordinate
Spatial representation of the string in vibration:
File:1Dwave graph1.png
The following is the free-body diagram of a string in motion in a spatial coordinate system:
File:String dwg.jpg
From the diagram above, it can be observed that the tensions in each side of the string will be the same as follows:
File:Equations1.jpg
Using Taylor series to expand we obtain:
File:Equations2.jpg

## Characterization of the mechanical system

A one dimensional wave can be described by the following equation (called the wave equation):
$\left({\frac {\partial ^{2}y}{\partial x^{2}}}\right)=\left({\frac {1}{c^{2}}}\right)\left({\frac {\partial ^{2}y}{\partial t^{2}}}\right)$
where,
$y(x,t)=f(\xi )+g(\eta )\,$ is a solution,
With $\xi =ct-x\,$ and $\eta =ct+x\,$
This is the D'Alambert solution, for more information see:
Another way to solve this equation is the Method of separation of variables. This is useful for modal analysis. This assumes the solution is of the form:
$y(x,t)=f(x)g(t)\$
The result is the same as above, but in a form that is more convenient for modal analysis.
For more information on this approach see: Eric W. Weisstein et al. "Separation of Variables." From MathWorld—A Wolfram Web Resource.
Please see Wave Properties for information on variable c, along with other important properties.
For more information on wave equations see: Eric W. Weisstein. "Wave Equation." From MathWorld—A Wolfram Web Resource.
Example with the function $f(\xi )$ :
Example: Java String simulation
This show a simple simulation of a plucked string with fixed ends.
Back to Main page
# Engineering Analysis
## Preface

This book is about the topic of mathematical analysis, particularly in the field of engineering. It attempts to be a companion piece to high-level engineering texts that will rely on a certain fundamental mathematical background among readers.
This will build on topics covered in Probability, Algebra, Linear Algebra, Calculus, and Ordinary Differential Equations. Readers of this book are expected to have background knowledge in all those topics. Topics covered will be inter-disciplinary engineering topics, and will be highly mathematical. However, overlap between this book and other mathematics books, except where necessary, will be minimized.
This book is intended to accompany a graduate course of study in engineering analysis.

## Table of Contents
### Linear Algebra

* Vector Spaces
* Vector Basics
* Linear Independence and Basis
* Linear Transformations
* Minimization
* Projections
* Linear Spaces
* Matrices
* Matrix Forms
* Quadratic Forms
* Eigenvalues and Eigenvectors
* Diagonalization
* Spectral Decomposition
* Error Estimation

### Matrix Calculus

* Matrix Functions
* Cayley-Hamilton Theorem
* Matrix Exponentials
* Lyapunov Equation
* Function Spaces
* L$_2$ Space
* Banach and Hilbert Spaces
* Fourier Series
* Arbitrary Basis Expansion
* Bessel Equation and Parseval Theorem
* Multi-Dimensional Fourier Series

### Algorithms Design And Analysis

* Wavelets
* Wavelet Transforms

### Stochastic Processes

* Random Variables
* Probability Functions
* Distributions
* Expectation and Entropy
* SISO Transformations
* MISO Transformations
* Correlation
* Random Vectors

### Analysis

* Leibnitz' Rule
* Differential Operator Theory
** Linear Operators
* Complex Analysis

### Optimization and Minimization

* Optimization
* Unconstrained Optimizations
* Constrained Optimizations

## Appendices

* Resources
# Engineering Acoustics/Time-Domain Solutions
## d'Alembert Solutions

In 1747, Jean Le Rond d'Alembert published a solution to the one-dimensional wave equation.
The general solution, now known as the d'Alembert method, can be found by introducing two new variables:
$\xi =ct-x\,$ and $\eta =ct+x\,$
and then applying the chain rule to the general form of the wave equation.
From this, the solution can be written in the form:
$y(\xi ,\eta )=f(\xi )+g(\eta )\,=f(x+ct)+g(x-ct)$
where f and g are arbitrary functions, that represent two waves traveling in opposing directions.
A more detailed look into the proof of the d'Alembert solution can be found here.

## Example of Time Domain Solution

If f(ct-x) is plotted vs. x for two instants in time, the two waves are the same shape but the second displaced by a distance of c(t2-t1) to the right.
The two arbitrary functions could be determined from initial conditions or boundary values.
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