OpenLLM-France/wikimedia huggingface dataset:
# Control Systems/Modern Controls

| The Wikibook of: Control Systems and Control Engineering | Table of Contents | All Versions | PDF Version |
| The Wikibook of: Control Systems and Control Engineering | | | Glossary |

## Preface

This is the Modern Controls version of the Control Systems book. This book represents a subset of the larger parent book. Topics included here will include a basic introduction to systems theory, an introduction to and an explanation of basic state-space methods of control engineering, and design/analysis techniques used with the state-space methods.

### Warning

    This is a child version of the Control Systems parent book. The pages listed here constitute a suggested reading order of the material, and are not a stand-alone book. Do not edit these pages in a way that make them incompatable with the main narrative of the parent book. If you have questions, comments, or suggestions about this version, leave a message on the main book discussion page.
For a list of all child versions of this book, see All Versions.
# Control Systems/Nonlinear Systems

| The Wikibook of: Control Systems and Control Engineering | Table of Contents | All Versions | PDF Version |
| The Wikibook of: Control Systems and Control Engineering | ← State Machines | Common Nonlinearities → | Glossary |

## Nonlinear General Solution

A nonlinear system, in general, can be defined as follows:
    $x'(t)=f(t,t_{0},x,x_{0})$
    $x(t_{0})=x_{0}$
Where f is a nonlinear function of the time, the system state, and the initial conditions. If the initial conditions are known, we can simplify this as:
    $x'(t)=f(t,x)$
The general solution of this equation (or the most general form of a solution that we can state without knowing the form of f) is given by:
    $x(t)=x_{0}+\int _{t_{0}}^{t}f(\tau ,x)d\tau$
and we can prove that this is the general solution to the above equation because when we differentiate both sides we get the origin equation.

### Iteration Method

The general solution to a nonlinear system can be found through a method of infinite iteration. We will define x$_n$ as being an iterative family of indexed variables. We can define them recursively as such:
    $x_{n}(t)=x_{0}+\int _{t_{0}}^{t}f(\tau ,x_{n-1}(\tau ))d\tau$
    $x_{1}(t)=x_{0}$
We can show that the following relationship is true:
    $x(t)=\lim _{n\to \infty }x_{n}(t)$
The x$_n$ series of equations will converge on the solution to the equation as n approaches infinity.

### Types of Nonlinearities

Nonlinearities can be of two types:
* Intentional non-linearity: The non-linear elements that are added into a system. Eg: Relay
* Incidental non-linearity: The non-linear behavior that is already present in the system. Eg: Saturation

## Linearization

Nonlinear systems are difficult to analyze, and for that reason one of the best methods for analyzing those systems is to find a linear approximation to the system. Frequently, such approximations are only good for certain operating ranges, and are not valid beyond certain bounds. The process of finding a suitable linear approximation to a nonlinear system is known as linearization.
This image shows a linear approximation (dashed line) to a non-linear system response (solid line). This linear approximation, like most, is accurate within a certain range, but becomes more inaccurate outside that range. Notice how the curve and the linear approximation diverge towards the right of the graph.
| ← State Machines | Control Systems | Common Nonlinearities → |
# Chess Opening Theory/1. e4/1...e5/2. Nf3/2...Nc6/3. Bc4/3...h6
## Anti-Fried Liver Defence
### 3... h6

Black plays h6 to prepare for the move 4...Nf6. If Black played 3...Nf6 instead, White would respond with 4. Ng5 with the intention to take on f7, winning material and turning the game into a Fried Liver Attack. With 3...h6, 4. Ng5 would no longer be possible and Black can play 4... Nf6.
However, this move might be considered to lose tempo as White can utilize this slow play by playing 4. d4, striking back at the center. If Black insists with playing 4... Nf6? anyway, Black would be losing the e5 pawn.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. e4 e5 2. Nf3 Nc6 3. Bc4 h6
| | 4 |
| Anti-Fried Liver Defence | d4 exd4 |
When contributing to this Wikibook, please follow the Conventions for organization.
# Spanish Four Knights Game
## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation.
1. e4 e5 2. Nf3 Nc6 3. Nc3 Nf6 4. Bb5
| | 4 | 5 | 6 |
| Symmetrical Variation | Bb5 Bb4 | O-O O-O | d3 d6 | = |
| | ... Bc5 | O-O O-O | Nxe5 Nxe5 | = |
| Rubinstein Variation | ... Nd4 | Ba4 c6 | Nxe5 d5 | = |
When contributing to this Wikibook, please follow the Conventions for organization.

## References

* Modern Chess Openings 15th ed, 2008. Nick de Firmian. Random House, New York. ISBN 0-8129-3682-5.
* Nunn's Chess Openings. 1999. John Nunn (Editor), Graham Burgess, John Emms, Joe Gallagher. ISBN 1-8574-4221-0.
* This Chess related article is a stub. Please assist Wikibooks by expanding it.
# Rousseau Gambit Accepted

White accepts the gambit. This is usually a mistake, but White's position is still sound.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1.e4 e5 2.Nf3 Nc6 3.Bc4 f5 4.exf5
| | 4 | 5 | 6 |
| 1 | exf5 e4 | Nd4 Nf6 | Nxc6 dxc6 | = |
| 2 | ... ... | ... Nxd4? | Qh5+ - | +/- |
When contributing to this Wikibook, please follow the Conventions for organization.
# Four Knights Game, Italian Variation, 4...Nxe4

Black makes a temporary sacrifice of the knight, and if White plays 5.Nxe4, Black can play ...d5 with a fork which wins back the piece. This tactical trick does not win any material for Black, but knocking out the important White center pawn on e4 has secured Black a good foothold in the center.
Even so, 5.Nxe4, falling in with Black's plan is White's best move. 5.Bxf7+ looks good at first glance because Black's king gets slightly exposed, but White is not developed enough to sustain an attack. 5.O-O can cause problems for black if they are not careful.
The tactic employed by Black is called the "Fork Trick" and pops up in a number of openings, but it is particularly potent in the Four Knights.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. . 1. e4 e5 2. Nf3 Nc6 3. Nc3 Nf6 4.Bc4 Nxe4!
| . | 5 | 6 | 7 |
| 1 | Nxe4 d5 | Bd3 dxe4 | Bxe4 Bd6 | = |
| 2 | Bxf7+ Kxf7 | Nxe4 d5 | Neg5+ Kg8 | -/+ |
When contributing to this Wikibook, please follow the Conventions for organization.

## References

* Evans, Larry D. The Fork Trick. Published in two parts (April 2000 and May 2000) issues of Chess Life. Online facsimiles of the articles are available at chesscamp.net.
# Chess Opening Theory/1. e4/1...e5/2. Nf3/2...Nc6/3. Be2
## 3. Be2 - Tayler Opening

This opening is a bit passive and rare. The point of this move is to try and put Black off their comfort zone. But if Black is paying attention, they can get the upper hand. For these reasons, the Tayler Opening only gives white psychological advantage, just like in the Bongcloud or the Ware Opening.
1.e4 e5 2.Nf3 Nc6 3.Be2
# Three Knights Game

Black can copy White's moves with 3...Nf6, leading to a very quiet game.
Other alternatives include bishop moves:
    3...Bb4 is playable, but it may be too early because White can play 4. Nd5 (the knight is not pinned yet).
    3...Bc5 is dangerous because White can play 4. Nxe5; after 4...Nxe5, White can play 5.d4, winning back the material with a fork. However, it's not really a mistake, because Black will be able to take a pawn during the process. In this line, 4...Bxf2+ is playable and does not lose material.
It's also possible to play 3...g6. It may prepare f5. It may also transpose into Scotch Game as the d4 counterattack is often seen.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation.
1. e4 e5 2. Nf3 Nc6 3. Nc3
| | 3 | 4 | 5 |
| Four Knights Game | ... Nf6 | d4 exd4 | Nxd4 Bb4 | = |
| | ... Bb4 | Nd5 Ba5 | Bc4 | +/= |
| | ... Bc5 | Nxe5 Nxe5 | d4 Bd6 | +/= |
| | ... g6 | d4 exd4 | Nxd4 Bg7 | +/= |
| Winawer Defense | ... f5 | Bb5 fxe4 | Nxe4 Nf6 | +/= |
When contributing to this Wikibook, please follow the Conventions for organization.

## References

* Nunn's Chess Openings. 1999. John Nunn (Editor), Graham Burgess, John Emms, Joe Gallagher. ISBN 1-8574-4221-0.
* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.
# Four Knights Game

This is the classical Four Knights' Game. One of the beginning principles of the opening that the beginners learn is "Knights before bishops", and thus dogmatic followers of this principle stick to this system. All four knights have been developed (hence the name), leading to a symmetrical position. The classical players like Maroczy, Capablanca, Lasker, Tarrasch, and Rubinstein would play the Symmetrical Variation, 4. Bb5 Bb4 5. O-O O-O 6. d3 d6 7. Bg5, when Black should sever the symmetry with 7...Bxc3 (if 7...Bg4, then 8. Bxf6 Qxf6? (8...gxf6 is better, but leaves White with the better game because of Black's weakened kingside) 9. Nd5 Qd8 10. Bxc6 bxc6 11. Nxb4, when White is up a piece) 8. bxc3, with an even game. However, Rubinstein's 4...Nd4 and Marshall's 4...Bc5 are sharp alternatives. The Scotch Four Knights begins with 4.d4, and can lead to the enterprising Belgrade Gambit after 4...exd4 5.Nd5!?, a highly tactical system which often runs 4...exd4 5. Nd5 Nxe4 6. Bc4 Be7 7. Nxd4 O-O 8. Nb5 Bc5 9. O-O Nxf2 11. Qh5. Black is doing all right, but some careful play is required.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. . 1. e4 e5 2. Nf3 Nc6 3. Nc3 Nf6
| | 4 | 5 |
| Symmetrical Variation | Bb5 Bb4 | O-O O-O | = |
| Scotch Four Knights | d4 exd4 | Nxd4 Bb4 | = |
| Belgrade Gambit | ... ... | Nd5 Nxe4 | = |
| Italian Four Knights | Bc4 Nxe4 | Nxe4 d5 | = |
| Glek Variation | g3 d5 | exd5 Nxd5 | = |
| Halloween Gambit | Nxe5 Nxe5 | d4 Nc6 | =/+ |
When contributing to this Wikibook, please follow the Conventions for organization.

## References

de Firmian, Nick. Modern Chess Openings, 15th edition. New York, NY: Random House, 2008.
# Four Knights Game: Italian Variation

White's 4.Bc4 in here looks like a natural developing move, targeting f7 and getting ready to castle. There is however a tactical trick Black has (4...Nxe4!) which has made masters shun away from 4.Bc4. For some history, we might mention that Tarrasch played this against Lasker in the 1916 World Championship, and was crushed.
If Black wants to accept a normal game, there is nothing particularly wrong with a natural developing move like 4...Bc5, but 4...Nxe4! is the best move in the position, and White is then fighting for equality.
In fact, below the master level, this position crops up very often. One online chess database (365chess) says that 4.Bc4 is played in one out of every five games featuring the Four Knights, and since most amateur games never make it onto that database, the real figure is probably higher. Larry D. Evans (see references below) says that his students wind up in this line about once a tournament.
Since 4.Bc4 is played so often, learning the theory on 4...Nxe4 will let you get many good positions with Black after only a few moves. With best play, White should probably equalize (according to Pinski's book on the Four Knights), but has to work a bit for it.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. . 1. e4 e5 2. Nf3 Nc6 3. Nc3 Nf6 4.Bc4
| 4 | 5 | 6 |
| Bc4 Nxe4 | Bxf7+ Kxf7 | Nxe4 d5 | -/+ |
| ... Nxe4 | Nxe4 d5 | Bd3 dxe4 | = |
| ... Bc5 | | | = |
When contributing to this Wikibook, please follow the Conventions for organization.

## References

* Evans, Larry D. The Fork Trick. Published in two parts (April 2000 and May 2000) issues of Chess Life. Online facsimiles of the articles are available at chesscamp.net.
# Cell Biology/Genetic material

Cell Biology | Parts of the cell
* Prokaryotes
* Eukaryotes
* Nucleus
* Nuclear membrane
* Nucleolus
* Codons
* RNA polymerase
* Histones
# Cell Biology/Glossary By Lesson
## Glossary By Lesson

This glossary lists out technical words in each lesson

### What is living

* Homeostasis: the process by which a living thing reacts to the environment to maintain some constant conditions in its inner structure.
* Metabolism: the process by which a living thing takes energy and matters from the environment then converts it.
# Cell Biology/Introduction/Cell size
## Size of Cells

Although it is generally the case that biological cells are too small to be seen at all without a microscope, there are exceptions as well as considerable range in the sizes of various cell types. Eukaryotic cells are typically 10 times the size of prokaryotic cells (these cell types are discussed in the next Chapter). Plant cells are on average some of the largest cells, probably because in many plant cells the inside is mostly a water filled vacuole.
So, you ask, what are the relative sizes of biological molecules and cells? The following are all approximations:
What limits cell sizes?
* Prokaryotes — Limited by efficient metabolism
* Animal cells (eukaryotic) — Limited by surface area to volume ratio
* Plant cells (eukaryotic) — Have large sizes due to large central vacuole, which is responsible for their growth

## Related reading

* Some early history related to the development of an understanding of the existence and importance of cells. The importance of microscopy.
# Cell Biology/History
## Some History of the development of understanding of the Cell

The origin of the idea that living organisms are made of cells is often traced back to observations of thin slices of cork. In 1665 the book Micrographia: Some physiological descriptions of minute bodies made by magnifying glasses was published by Robert Hooke. He wrote:
    . . . I could exceedingly plainly perceive it to be all perforated and porous, much like a Honey-comb, but that the pores of it were not regular. . . . these pores, or cells, . . . were indeed the first microscopical pores I ever saw, and perhaps, that were ever seen, for I had not met with any Writer or Person, that had made any mention of them before this. . .
We now know that the "cells" Hooke observed were an indication of the cellular structure of multi-cellular organisms. During the 1670s, Antony van Leeuwenhoek used microscopes to observe sperm, red blood cells, and protozoa. While many cells are about 10 microns in diameter, some protozoa are visible to the naked eye, reaching over 1 millimeter in length. Leewenhoek is the inventor of the microscope. Thus, while it is true that the small size of most cells made it difficult to develop the theory that all living organisms are composed of cells, it was also difficult to recognize that living cells have certain functional components such as the nucleus and a surface membrane that allow cells to exist as the basic functional components of all living organisms. In 1833 Robert Brown published a report describing microscopic observations of plant cells in which he used first used the term "cell nucleus":
    In the compressed cells of the epidermis the nucleus is in a corresponding degree flattened; but in the internal tissue it is often nearly spherical, more or less firmly adhering to one of the walls, and projecting into the cavity of the cell.
Such observations of the microscopic cellular components of cells helped make it possible for Schleiden and Schwann to propose a cell theory specifying that nucleated cells are key structural and functional units in plants and animals (1832-1838). However, they did not understand cell reproduction. About this time microscopists such as the Belgian botanist Barthelemy C. Dumortier observed and reported the binary fission of cells. By 1879 the zoologist Walther Flemming was using chemical staining of "fixed" cells to allow clear visualization of chromosomes during cell division.
During the 1890s, Ernest Overton, developed a theory of lipid membrane structure and function, based largely on the osmotic properties of cells. Visualization of lipid bilayer membranes at the surface of cells had to wait until the development of electron microscopy.
<< | Size of cells
Cell Biology | Introduction
# Cell Biology/Introduction

* What is interesting about cell biology
* What is living
* What is a cell
* Size of cells
* Chemical elements necessary for life
Cell Biology | Introduction | Types of cells | Parts of the cell | Cell division | Gene expression and translation
# Cell Biology/Introduction/Cell biology's interest

What makes Cell Biology particularly interesting is that there is so much that is not fully understood. A cell is a complex system with thousands of molecular components working together in a coordinated way to produce the phenomenon we call "life". During the 20th century these molecular components were identified (for example, see Human Genome Project), but research continues on the details of cellular processes like the control of cell division and cell differentiation. Disruption of the normal control of cell division can cause abnormal cell behavior such as rapid tumor cell growth.
Cells have complex interactions with the surrounding environment. Whether it is the external world of a single celled organism or the other cells of a multicellular organism, a complex web of interactions is present. Study of the mechanisms by which cells respond appropriately to their environments is a major part of cell biology research and often such studies involve what is called signal transduction. For example, a hormone such as insulin interacting with the surface of a cell can result in the altered behavior of hundreds of molecular components inside the cells. This sort of complex and finely tuned cell response to an external signal is required for normal metabolism and to prevent metabolic disorders like Type II diabetes.
Most of the cells of a multi-cellular organism have the same genetic material in every cell; yet, there may be hundreds of different types of cells that make up the organism's body each with its own distinctive shape, size, and function. In any case, all of these cells were developed from one special cell, a zygote. The study of how the many cell types develop during embryonic development (Developmental Biology) is a branch of Biology that is heavily dependent on the use of microscopy. Much of the control of cell differentiation is at the level of the control of gene transcription, the control of which mRNAs are made. Muscle cells make muscle proteins and nerve cells make brain proteins. Geneticists, molecular biologists and cell biologists are working to discover the details of how cells specialize to accomplish hundreds of functions from muscle contraction to memory storage.

## Summary

* Complexity in:
** inter-relations between cells
** signal transduction pathways inside cells
** control of cell death and cell reproduction
** control of cell differentiation
** control of cell metabolism.
# Cell Biology/Introduction/Cells Under Microscopes
## Unit Conversion

1 μm = 10$^{-6}$m = 10$^{-3}$mm
1 nm = 10$^{-9}$m = 10$^{-3}$μm

## Light Microscope

One can use a light microscope to see living cells, its plasma membrane, nucleus and probably some most prominent organelles (with the help of a computer), as it can not see things smaller than 0.2 μm (due to light wavelength, not to the quality of lens).

## Electron Microscope

An electron microscope uses a beam of electrons to create an image with much finer resolution than a compound light microscope. Most organisms have to be killed before they can be observed in an electron microscope (the sole exception being a tick). Some transmission electron microscopes can have a resolution of better than 50 pm, and can magnify up to 10 000 000x. This is smaller than the wavelength of visible light, which is between 390 - 700 nm, so it cannot use light; thus, electrons are used rather than light. The two main types of electron microscopes are transmission electron microscopes (TEM) and scanning electron microscopes (SEM), and both of them usually need a partial vacuum in order to view the specimens, making them costly. However, they are much better for perceiving cell details than <2 000x magnification compound light microscopes.

## Naked eye

Some very large cells can be seen with the eye alone. An example of this is gromia sphaerica which has a maximum specimen size of 38 mm (millimeters).
# Cell Biology/Genes/Gene translation

The Translation Phase of Genetic Expression is divided into 2 Steps Transcription and Translation. During Transcription RNA Polymerase unzips the two halfs of the DNA where it needs to transcript. Then free RNA bases Attach to the DNA bases with the Polymerase starting at the promoter and ending at the Termination signal. From this the RNA can become mRNA, rRNA, or tRNA. The mRNA is a ribbon like strand that takes the genetic information from the nucleus of the cell to the ribosome. rRNA forms a globular ball that attaches to the rough E.R. to help make ribosomes. finally the tRNA forms a hair shaped landing base that reads the genetic information to make proteins. Translation happens when mRNA is pulled through a ribosome and tRNA reads the RNA bases on the mRNA to make anti-codons of 3 bases and brings amino-acids to form the protein. This starts with the condon AUG and ends at UAG. When done the protein forms the correct shape and does the task it was created for. This brings the genetic code from the nucleus, which it never leaves, to the cytoplasm of the cell where proteins are produced to upkeep the body.
# Cell Biology/How to edit this book
## How to edit this book

Each chapter includes the level of intended readers. One should not write too many advanced details in chapters for beginners.
You should create one 2nd level heading at the top of the lesson, so that others can edit.
# Dichotomous Key/Ensifera

Kingdom: Animalia Phylum: Arthropoda Class: Insecta Order:Orthoptera
# Dichotomous Key/Heteroptera
## 1

* Living under water
** Yes - Nepomorpha
** No - #2

## 2

* Living on water surface?
** Yes- Walking on water Gerromorpha
** No- #3

## 3

* Living near water on the shore?
** Yes - Dipsocoromorpha or Leptopodomorpha
** No - Can be found on or under the ground not necessary near water. #4

## 4

Cimicomorpha or Enicocephalomorpha or Pentatomomorpha
# Dichotomous Key/Hemiprocnidae
## Key to Hemiprocnidae

* 1: Two white stripes clearly present on each side of head, one going from bill to back of head and the other going from bill to neck or chest.
* 2: Two white stripes scarcely or not present on head.

## 1

* Hemiprocne comata: red patch present near eyes.
* Hemiprocne mystacea: red patch not present near eyes.

## 2

* Hemiprocne coronata: Patch of reddish color present near eyes.
* Hemiprocne longipennis: Patch of reddish color absent near eyes.