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

At previous chapter, equations that govern dynamics of a particle in a field of forces where presented. In this chapter we introduce electromagnetic forces.
Electromagnetic interaction is described by the mean of electromagnetic field, which is solution of so-called Maxwell equations. But as Maxwell equations take into account positions of sources (charges and currents), we have typically coupled dynamics--field equations problem: fields act on charged particles and charge particles act on fields.
A first way to solve this problem is to study the static case. A second way is to assume that particles able to move have a negligible effect on the electromagnetic field distribution (assumed to be created by some "big" static sources). The last way is to tackle directly the coupled equations system (this is the usual way to treat plasma problems, see exercise exoplasmapert and reference ([#References|references])).
This chapter presents Maxwell equations as well as their applications to optics. Duality between representation by forces and by powers of electromagnetic interaction is also shown.
# Introduction to Mathematical Physics/Electromagnetism/Exercises

Exercice:
exoeqhelmoltz
Assume constitutive relations to be:
$D(r,t)=\epsilon (r,t)*E(r,t)$
where $*$ represents temporal convolution\index{convolution} (value of $D(r,t)$ field at time $t$ S depends on values of $E$ at preceeding times) and
$H={\frac {B}{\mu _{0}}}$
Show that in harmonical regime ($E(r,t)={\mathcal {E}}(r)e^{i\omega t}$) and without any charges ${\mathcal {E}}(r)$ field verifies Helmholtz equation :
$\Delta {\mathcal {E}}+k^{2}{\mathcal {E}}=0.$
Give the expression of $k^{2}$.
Exercice:
Show (see ([#References
Exercice:
Proove charge conservation equation eqconsdelacharge from Maxwell equations.
Exercice:
Give the expression of electrical potential created by quadripole $Q_{ij}$.
Exercice:
Show from the expression of magnetic energy that force acting on a point charge $q$ with velocity $v$ is:
$f=qv\wedge B$
# Introduction to Mathematical Physics/Energy in continuous media/Exercises

Exercice: Find the equation evolution for a rope clamped between two walls.
Exercice: {{{1}}}
Exercice: Give the expression of the deformation energy of a smectic (see section secristliquides for the description of smectic) whose i$^{t}h$ layer's state is described by surface $u_{i}(x,y)$,
Exercice: Consider a linear, homogeneous, isotrope material. Electric susceptibility $\epsilon$ introduced at section secchampdslamat allows for such materials to provide $D$ from $E$ by simple convolution:
eqexsusc
$D=\epsilon *E.$
where $*$ represents a temporal convolution. To obey to the causality principle distribution $\epsilon$ has to have a positive support. Indeed, $D$ can not depend on the future values of $E$. Knowing that the Fourier transform of function "sign of $t$" is $C.V_{p}(1/x)$ where $C$ is a normalization constant and $V_{p}(1/X)$ is the principal value of $1/x$ distribution, give the relations between the real part and imaginary part of the Fourier transform of $\epsilon$. These relations are known in optics as Krammers--Kr\"onig relations\index{Krammers--Kr\"onig relations}.
# Lambda Calculus

Lambda Calculus is a theory of computable functions, i.e. a formal system which formalize the abstract notion of computable functions. This calculus was developed by Alonzo Church in the 1930s at the same time which other researchers developed other models of computation which later were proved to be equivalent. S. C. Kleene developed recursive functions and Alan M. Turing a Universal abstract machine, later called Universal Turing Machine, among other formal systems. Recursive functions can be expressed in the lambda calculus, and vice versa, also an universal Turing machine can be defined in the lambda calculus and recursive functions and the lambda calculus in the universal Turing machine, the same with the other computation models not described here. The fact that every attempt to build a system to capture the notion of computation resulted in a theory equivalent to each other is a strong indication that no other "more powerful" system exists, that can not be proved, for that reason is known as the Churrch-Turing thesis. In other words it states that any compuable function is definable indistinctly in any of those systems. You may noticed that formal system, theory and model are used to refer to those formalisms, lets say what that means. A formal theory is a formal system which captures the notion of the abstract notion of computable functions.
The lambda calculus is one foundation for computer science, like infinitesimal calculus is a foundation for the Newtonian physics. Another foundation is the Von Neumann machine, which is a hardware realization of a Universal Turing Machine, of course as any physical implementation it has finite memory.
The lambda calculus served as the basis for functional programming languages in the same way that the von Neumann machine is the basis for the imperative programming languages.
An important subject in computer science the semantics of programming languages, i.e. how to state the meaning of a programming language. The lambda calculus is the basis for a denotational semantics, developed by Dana Scott.
There are different lambda theories studied in the lambda calculus. The untyped lambda calculus resulted in an inconsistent theory because there is a paradox equivalent to the Russell paradox in the naive set theory. that motivated the development of typed lambda theories.
The untyped lambda calculus formulas are induced from an infinite set of variables, $x,y,z,\ldots ,x_{0},y_{0},z_{0},\ldots$, abstractions with the form $\lambda v.M$ where $v$ is a variable and $M$ a formula of the lambda calculus also called lambda term, the last is called applications with the form $(MN)$ where $M$ and $N$ are also lambda terms and nothing else.
There are conversion rules, $\alpha ,\beta$ and $\eta$ defined as follows:

## Contents

* Syntax
* Equivalent formulas
# Lambda Calculus/Basic Definitions
## Axioms

The first concept is that of abstraction. It is analogous to defining a function.
    λx.M
This defines a function which takes an argument x and returns a term M. Functions in lambda calculus have no name.
The second concept is that of invocation. It is essentially a function call.
    M N
This binds the argument N to the term M

## Definitions
### Term

    A term in Lambda calculus is a defined function. A term may contain variables.

### Variable

    A variable, may represent any term. A term may contain free variables or bound variables

### Bound variables

    A bound variable is a variable which will be bound to some term passed as an argument. Eg, In λx.xy, x is a bound variable.

### Free variables

    A free variable is any variable in a term which is not bound to some other term. Eg, In λx.xy, y is a free variable.
# Laboratory Safety/Personal Responsibilities

Your are the person most responsible for your safety. You can prevent a dangerous or harmful situation more easily than can someone rescue you from your blunder. This being said the following points may shed some light on your responsibilities:
* Know the required PPE (Personal Protective Equipment) to use and use them properly.
* Never use unlabeled bottles or containers and always label Containers.
* Use Material safety data sheets to understand the chemicals you deal with (are they strongly acidic, alkaline, flammable, oxidizing, or capable of creating toxic fumes when they react with other materials) in addition with what their effects on your body are. These sheets will also inform you of what to do when exposed to such chemicals accidentally.
* Follow procedures. You are not the first person to have done the experiment.
* Never eat, drink, or smoke anything while in the laboratory. Never touch any chemical reagent.
* Never return unused material to reagent bottle. This may contaminate the entire bottle. Ask neighbors if they need it and throw away any leftovers in the proper waste container
* When getting any extra chemical reagent from the storage room, always make sure to have a secondary container in case of a spill.
* When the waste container is about 75 percent full, alert the TA to get a new waste container. Do not ever fill it up all the way.
* Locate emergency equipments before starting work (eye wash stations or fire extinguishers for example).
* Locate the safest routes to leave through the emergency exit doors.
Kennedy, Shelia, and John Palmer. Chemistry Lab Safety Manual. UCSD, 2010. eBook.
# Laboratory Safety/Protective Breathing Apparatus

Make sure you know where the respiratory aid kit is kept when working with chemicals.
# Laboratory Safety/Protective Equipment

Protective Equipments should be worn at all times in the lab even if you are done with your lab. There is no guarantee that someone else will not spill chemicals on you by accident
# Laboratory Safety/Personal Conduct

In general, use the acquired wisdom of others in doing any experiment, especially that of a teacher or whoever else is in charge. Make sure that before you do an experiment that you have read about it beforehand and know what you are doing. You are almost certainly not the first person to do an experiment, and someone already knows what is safe and what isn't. Always follow instructions, and neither do unplanned experiments nor modify the one planned -- even in doing the experiment on a larger scale. Recognize that fire, radioactive substances, hot or very cold objects, and all chemicals are potentially dangerous. Keep all equipment clean, and beware of broken glass that can be contaminated. Dispose of all hazardous substances properly.
You are the person most responsible for your safety. You can usually do far more to protect yourself from a bad incident than someone else can do to rescue you from a bad event. Report any known hazard that arises to the teacher or other person responsible for the laboratory.
# Laboratory Safety/Using Emergency Equipment

* Know where all the emergency equipments are located.
* To use the shower/eyewash, simply pull down the chain. For a special station designed only for eyewash, there is usually a foot petal you stand on to activate it. An uninjured neighbor should assist the person to the shower/eyewash.
* To use the fire blanket, completely cover the flames with the blanket until fire goes out. Obviously, the fire should be small enough to be covered by the blanket. Otherwise, use the fire extinguisher. Use the fire blanket to cover someone who just used the shower since their cloth would be wet and partially burned.
* Before using the fire extinguisher, you should know what class of fire extinguisher it is. There are three main classes with class A being suitable for regular combustible fires such as plastics or rubber, class B being suitable for oil based fires such as gasoline and
class C being suitable for electrical fires. DO NOT USE CLASS A EXTINGUISHER FOR ELECTRICAL FIRES.Class A extinguisher is made up of high pressure water so there is a risk of electrical shock. Pull off the metal safety pin and aim at the base of the fire, not at the flame itself. You should be trying to put out the source of the fire, which is much more effective.
Kennedy, Shelia, and John Palmer. Chemistry Lab Safety Manual. UCSD, 2010. eBook.
# Laboratory Safety/Waste Disposal Procedures

* Do not dump hazardous chemicals down the drain. Always use the waste container.
* Get a new waste container once it is about 75 percent full. This prevents spilling.
Kennedy, Shelia, and John Palmer. Chemistry Lab Safety Manual. UCSD, 2010. eBook.
# Laboratory Safety/Protective clothing

Always wear a lab coat and also when required contain long hairs using a hair net or in a ponytail. Wear gloves appropriate to the chemicals you are using. Wear safety glasses or goggles at all times to protect the eyes from chemical splashes.
It is important to notice that these PPE (personal protective equipment) needs to be chosen wisely and properly. This is due to the fact that in a laboratory there are many materials and hazards requiring different types of gloves (water samples need different gloves than those needed when dealing with acidic ones).
# Laboratory Safety/Protective eye wear

Always wear safety glasses.
These should be chosen to provide proper protection according to the task. The hazards may include chemical splashes or exposure to ultraviolet light and other things.
# Listen and Learn Science/Guide for Visually Impaired Students

Listen and Learn Science
* This is a Science book, designed for Visually impaired students.
* It Strives to make Science interesting, and related to day to day life.
* It is meant to be heard, with a screen reader.
* You can use the screen reader, native to your computer's OS.
* You can use NVDA , as a screen reader, if you wish.
* These modules do not have any diagrams, or visuals.
* It will not have notations, which are not comfortable for screen readers, example subscripts, and superscripts.
* Equations will be explicit. Example: Division will be stated as 'divided by'.
* Punctuation and some spellings are tweaked to enhance the audio experience.
* Sighted students and editors, may kindly be sensitive, to this.
* Completed modules are provided with links.
* 75% of listed pages are ready, and will be updated shortly.
* Other listed modules will be regularly added.
* The scope of the project, will also be continuously expanded.
# Listen and Learn Science/Elements
## Elements
### Alchemy

There is a very interesting history, to chemistry. In the old days, there was no clear difference between thinkers, philosophers, and scientists. Many philosophers in history, did scientific experiments. One of their favourite experiments, was to convert common metals, into gold. They experimented, with all kinds of chemicals, to do this. They were called, Alchemists. Today we might think that, they were foolish philosophers. But, you will be surprised, to know that the very famous, and distinguished scientist, Sir Isaac Newton, dabbled in Alchemy. They seriously believed that, they could somehow, convert other metals, to gold. The word chemistry, even the science of chemistry, came from the word Alchemy. Today, of course we know that, it is impossible to convert one element to another, in a chemical reaction although it can be done by nuclear physicists and it does happen naturally due to radioactive decay.

### Known Elements

An element is a pure substance, consisting of a single type of atom. An element is identified, by its atomic number. The atomic number is the number of protons in the nucleus of the atom. There are 118 known elements. For every atomic number, starting from 1, and going up to 118, there is a unique element. Out of the total number of known elements 80 of them occur naturally, and are stable. We will discuss some of the elements, which are commonly used.

### Nomenclature.

Every element from 1 to 118, has a unique name, like hydrogen, oxygen, copper and iron. Apart from the full name, each element has a unique symbol. These symbols are standardised and are either, one character, or two characters. For example, the symbol for hydrogen is "H"; oxygen is "O"; helium, is "He". In the same way all the 118 elements, have a unique name, and a unique symbol.

### Element Examples.
#### Hydrogen.
#### Silicon.

* Silicon's symbol is Si.
* It has an atomic number of 14.
* Most of sand and some rocks are made of silicon, and its compounds.
* Silicon dioxide, SiO$_2$ is called silicate.
* It is commonly on Earth and the other planets.
* Silicon is also present, in ceramics and porcelain.
* Highly purified silicon wafer, is widely used, in semi conductor electronics.
* It is the base material, in ICs (integrated circuits).
* Integrated circuits, also called as chips, is widely used, in all electronic equipment.
* Silicon wafers are used, in making solar cells.
* LCD (Liquid Crystal Display) screens, has silicon.

#### Phosphorus.

* Phosphorus's symbol is P.
* It has an atomic number of 15.
* Phosphorus is present in matches
* Phosphorus is used in the manufacture of fertilisers, and pesticides.
* In organic cells, phosphorus is present, in ATP, RNA, and DNA.
# Listen and Learn Science/Linear Motion
## Linear Motion.
### Motion Formulas.

Note : Names are are only pet names, used only in this module.
# Listen and Learn Science/Chemical Reactions
## Chemical Reactions.
### Chemical Reactions.

A chemical reaction, is a process that leads, to the transformation, of one set of substances, to another. In a chemical reaction, elements and compounds react, with each other, resulting in the formation, of other elements, and compounds. This reaction involves chemical bonding. This means, the elements get attached, to each other, at the atomic level. In nature, elements tend to have, an affinity to bond, with other elements. So, we will find most of the elements, in nature as compounds. There is an exception to this. Noble gases, and elements, do not combine, with other elements. Example, Neon.
Other elements have varying degrees, of affinity to combine, with other elements. This degree of affinity is related, to the atomic structure, of the element.Specifically it is related, to the number of electrons, in the outer most shell, of the atom. This gives a valence to an element.
# Introduction to Mathematical Physics/Quantum mechanics/Exercises

Exercice:
Study the binding between position operator $R_{x}$ and momentum operator $P_{x}$ with the infinitesimal generator of the translation group (see
Exercice:
Study the connection between kinetic moment operator $L$ and the infinitesimal generator of the rotations group (see
Exercice:
Study the linear response of a classical oscillator whose equation is:
${\frac {d^{2}x}{dt^{2}}}+\gamma {\frac {dx}{dt}}+\omega _{0}^{2}x=f(t)$
where $f(t)$ is the excitation. Compare with the results obtained at section secreplinmq.
# Introduction to Mathematical Physics/Quantum mechanics/Introduction

In the current state of scientific knowledge, quantum mechanics is the theory used to describe phenomena that occur at very small scale\footnote{ The way that quantum mechanics has been obtained is very different from the way other theories, relativity for instance, have been obtained. Relativity therory is based on geometric and invariance principles. Quantum mechanics is based on observation (operators are called observables).
Gravitational interaction is difficult to describe with the quantum mechanics tools. Einstein, even if he played an important role in the construct of quantum mechanics, was unsatisfied by this theory. His famous "God doesn't play dices" summerizes his point of view. Electromagnetic interaction can be described using quantum dynamics: this is the object of quantum electrodynamics (QED). This will not presented in this book, so the reader should refer to specialized books, for instance ([#References|references]).(atomic or subatomic). The goal of this chapter is to present the mathematical formalism of quantum mechanics. Applications of quantum mechanics will be seen at chapter chapproncorps. Quantum physics relies on a sequence of postulates that we present now. The reader is invited to refer to ([#References|references]) for physical justifications.
# Marijuana Cultivation/Introduction

* Marijuana Cultivation
* Introduction –
* Fundamentals –
* Seedlings –
* Vegetative Growth –
* Cloning –
* Sexing –
* Flowering –
* Harvesting –
* Curing –
* Producing Seeds –
* Pests and Pest Control –
* Common Plant Problems

# Marijuana Cultivation
## Purpose

This book is to provide instruction on the use and cultivation of marijuana, also known as cannabis or hemp. In this book you will find all the information needed to go from seed to a fully functioning garden.

## Disclaimer

The information contained in this book is intended for use only in jurisdictions where the activities contained therein are legal. No claim of the accuracy, safety, or the legality of following the instructions contained in this book is made and it is not recommended to follow them. You are responsible for your own actions if you do so. Nothing contained in this book should be construed to be legal or medical advice.

## How to Use

This book is not designed to be read straight through. Information is organized by topic, although you can certainly read everything through you can also jump right to the topic you are interested in.

## Copyright

   Copyright (C) 2009 Michael Fread
   This text is licensed under the open licensing terms of the Wikibooks project so long as this copyright notice remains intact. It has been donated for free and collaborative use for the benefit of all those who need, want, or enjoy this plant which is capable of industrial utility, medical potency, recreational happiness, and even supplying the complete nutritional needs of the hungry.
   Any part of this may be modified according to the terms of the aforementioned license but this section must remain intact.

## Table of Contents

* Fundamentals
* Seedlings
* Vegetative Growth
* Cloning
* Sexing
* Flowering
* Harvesting
* Curing
* Producing Seeds
* Pests and Pest Control
* Common Plant Problems
* Marijuana Cultivation
* Introduction –
* Fundamentals –
* Seedlings –
* Vegetative Growth –
* Cloning –
* Sexing –
* Flowering –
* Harvesting –
* Curing –
* Producing Seeds –
* Pests and Pest Control –
* Common Plant Problems
# Marijuana Cultivation/Fundamentals/Of Myths and Magic

* Marijuana Cultivation
* Introduction –
* Fundamentals –
* Seedlings –
* Vegetative Growth –
* Cloning –
* Sexing –
* Flowering –
* Harvesting –
* Curing –
* Producing Seeds –
* Pests and Pest Control –
* Common Plant Problems

### Of Myths and Magic

There is certainly as much myth and folklore spreading around about marijuana usage and cultivation as anything else. This book attempts to slash through those myths to actual proven and utilized techniques that have been put into practice. It is highly recommended that you consider the tested information in this book as a primary source of information and doubt conflicting third party information until it is proven to you.
Some common myths that are seen include the use of menstrual blood for flowering. The claim that baking soda and vinegar will kill plants if used to adjust PH. Some people claim that absolutely any light level whatsoever will destroy crops and others claim that a couple hours of light in the middle of the dark cycle will improve the size of flowers. If you want to know the truth about these claims just dive on in ahead. Everything you need to grow high quality, potent, and high yielding marijuana plants is contained in these pages.
* Marijuana Cultivation
* Introduction –
* Fundamentals –
* Seedlings –
* Vegetative Growth –
* Cloning –
* Sexing –
* Flowering –
* Harvesting –
* Curing –
* Producing Seeds –
* Pests and Pest Control –
* Common Plant Problems