OpenLLM-France/wikimedia huggingface dataset:
# Statics/Force Vectors

Many quanities in mechanics are vectors. A vector is a quantity that has a magnitude and a direction. Velocity is a vector. To solve a problem, it is not enough to know the speed a vehicle is travelling, but one must also know the direction in which the vehicle is travelling at that speed. Likewise, Force is a vector quantity. It has a magnitude (the amount of force in Newtons) and the direction in which the force is being applied.

## Graphical Representation

Vectors are usually denoted in boldface, as a. Other conventions include ${\vec {a}}$ or a, especially in handwriting. Alternately, some use a tilde (~) or a wavy underline drawn beneath the symbol, which is a convention for indicating boldface type.
Vectors are usually shown in graphs or other diagrams as arrows, as illustrated below:
Here the point A is called the tail, base, start, or origin; point B is called the head, tip, endpoint, or destination. The length of the arrow represents the vector's magnitude, while the direction in which the arrow points represents the vector's direction.
In the figure above, the arrow can also be written as ${\overrightarrow {AB}}$ or AB.
On a two-dimensional diagram, sometimes a vector perpendicular to the plane of the diagram is desired. These vectors are commonly shown as small circles. A circle with a dot at its centre indicates a vector pointing out of the front of the diagram, towards the viewer. A circle with a cross inscribed in it indicates a vector pointing into and behind the diagram. These can be thought of as viewing the tip an arrow front on and viewing the vanes of an arrow from the back.

## Dot Product

The dot product of two vectors a = [a$_1$, a$_2$, … , a$_n$] and b = [b$_1$, b$_2$, … , b$_n$] is defined as:
    $\mathbf {a} \cdot \mathbf {b} =\sum _{i=1}^{n}a_{i}b_{i}=a_{1}b_{1}+a_{2}b_{2}+\cdots +a_{n}b_{n}$
where Σ denotes summation notation and n is the dimension of the vectors.

## Scalars

Magnitudes without directions are referred to as scalars. These are not vectors but only single numbers.
scalar have only magnitude
# Stata/Publication Quality Ouput

Stata
* Basics
** Introduction
** Settings
** Documentation
** Probability Function
** Random Number Generation
** Data Management
** Graphics
** Programming
** Mata
** Natural Language Processing
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Bayesian Methods
** Bootstrap
** Non Parametric
** Matching
** Quantile Regression
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Count Data Models
** Tobit and Selection Models
** Duration Analysis
** Multilevel Modeling
** Time Series
** Spatial Econometrics
** Factor Analysis
* Problems

## Weaving

Weaving is an integration of statistical program with a publishing software. You have in the same file your code and your text. Weaving is intended to improve reproducibility standards (see Roger Koenker's webpage).
* Ben Jann's texdoc provides weaving capabilities for Stata and LaTeX

## Export to LaTeX

* eststo, esttab, estadd and estout are the best solution to print and export to latex the estimation results.
** eststo is a prefix command which stores estimation results.
** estout prints the results. It includes many options and is difficult to use.
** esttab is a wrapper for estout which includes less options and is easier to use.
** estadd allows to store more statistics.
* outreg
* outreg2
* modl :
* outtex
* sutex
* tabout
* latab
* latabstat
* listtex

## Export to a spreadsheet (Excel)

* outreg
* outsheet

## Export to a text format

* outsheet

## References

* ↑ Visit the website http://repec.org/bocode/e/estout/
# Statics
## Objective

By the end of this course, you should understand the fundamentals of forces and moments, and be able to solve equilibrium problems for rigid (non-deformable) bodies in both two and three dimensions.

## What You Should Already Know

In order to completely comprehend the material in this course, you should have a firm understanding of all math leading up to Calculus I. Also, an understanding of basic physics, as well as technical sketching is useful.

## Table of Contents
### Introduction

* Introduction to Statics
* Measurement and Units
* Vector Math

### Forces

* Newton's Laws and Equilibrium
* Forces As Vectors
* Resultants of Force Systems

### Equilibrium For Points and Rigid Bodies

* Rigid Body Equilibrium
* Two-Dimensional Equilibrium
* Three-Dimensional Equilibrium

### Structural Analysis

* Trusses
* Method of Joints
* Method of Sections
* Multiforce Members

### Internal Forces

* Internal Forces

### Moments of Inertia

* Moment of Inertia

### Center of Gravity and Centroids

* Center of Gravity and Centroid
* Center of Gravity Problems

### Quizzes and Tests

* Quizzes
* Tests

### References

* Equations of Statics
* Geometric Properties of Lines and Areas
* Geometric Properties of Solids

### Acknowledgement and Further Reading

Acknowledgements and Further Reading

## Printable Version

There is a printable version of this book.
# Statics/Acknowledgements

Beer, Ferdinand P. and E Russell Johnston, Jr. "Vector Mechanics For Engineers, Statics" 3rd edition, McGraw Hill c 1977.
# Stata/Time Series

Stata
* Basics
** Introduction
** Settings
** Documentation
** Probability Function
** Random Number Generation
** Data Management
** Graphics
** Programming
** Mata
** Natural Language Processing
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Bayesian Methods
** Bootstrap
** Non Parametric
** Matching
** Quantile Regression
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Count Data Models
** Tobit and Selection Models
** Duration Analysis
** Multilevel Modeling
** Time Series
** Spatial Econometrics
** Factor Analysis
* Problems
* ts is the prefix for time series command
* tsset declares data as time series
# Stata/Tobit and Selection Models

Stata
* Basics
** Introduction
** Settings
** Documentation
** Probability Function
** Random Number Generation
** Data Management
** Graphics
** Programming
** Mata
** Natural Language Processing
** Publication Quality Output
** Descriptive Statistics
* Methods
** Maximum Likelihood
** Bayesian Methods
** Bootstrap
** Non Parametric
** Matching
** Quantile Regression
* Topics
** Linear Models
** Binomial Outcome Models
** Multinomial Models
** Count Data Models
** Tobit and Selection Models
** Duration Analysis
** Multilevel Modeling
** Time Series
** Spatial Econometrics
** Factor Analysis
* Problems

## Censoring

We observe the full marginal distribution of x but we only observe the distribution of y above or below a given threshold.
Estimation :
We can also have a two limit tobit model :

## Truncation

We only observe the distribution of x and y if y is above or below a given threshold.

## Selection Models

heckman estimates the Heckman selection model.
# Statics/Center of Gravity and Centroid (contents)

To discuss the concept of the center of gravity, center of mass, and the centroid
To show how to determine the location of the center of gravity and centroid for a system of discrete particles and a body of arbitrary shape
To use the theorems of Pappas and Guldinus for finding the area and volume for a surface of revolution
To present a method for finding the resultant of a general distributed loading and show how it applies to finding the resultant of a fluid
9.1 - Center of Gravity and Center of Mass for a System of Particles
Center of Gravity The center of gravity G is a point which locates the resultant weight of a system of particles, if a body is in gravitational field; if not, center of gravity is a center of inertia of the body (= a system of particles). To show how to determine this point consider the system of n particles fixed within a region of space. The weights of a particle comprise a system of parallel forces which can be replaced by a single (equivalent) resultant weight having the defined point G of application.
The resultant weight must be equal to the total weight of all n particles; that is:
W$_R$=ΣW
# Condition Of Equilibrium

When forces are in equilibrium, that is, there is no net force and the summation of the particle's moment, taken at any point, is equal to 0.
$\sum F_{x}=0$
$\sum F_{y}=0$
$\sum F_{z}=0$
$\sum M_{o}=0$

# Newton's Second Law of Motion

$F=ma$

# Trigonometry
## Sine Law

${a \over sinA}={b \over sinB}={c \over sinC}$

## Cosine Law

$a^{2}=b^{2}+c^{2}-2bc\cos A\$
$b^{2}=a^{2}+c^{2}-2ac\cos B\$
$c^{2}=a^{2}+b^{2}-2ab\cos C\$

# Vector Relations
## Dot Product

${\vec {a}}\bullet {\vec {b}}=ab\cos \theta$

## Cross Product

    ${\vec {a}}\times {\vec {b}}={\begin{pmatrix}a_{1}\\a_{2}\\a_{3}\end{pmatrix}}\times {\begin{pmatrix}b_{1}\\b_{2}\\b_{3}\end{pmatrix}}={\begin{pmatrix}a_{2}b_{3}-a_{3}b_{2}\\a_{3}b_{1}-a_{1}b_{3}\\a_{1}b_{2}-a_{2}b_{1}\end{pmatrix}}=\left|{\vec {a}}\right|\left|{\vec {b}}\right|\sin(\theta )\cdot {\vec {e}}$
# Scouting/BSA/Law Merit Badge
## Requirement 1

Define "law." Tell some of its sources. Describe functions it serves.

## Requirement 2

Discuss TWO of the following:
    A. Justinian’s Code, The Code of Hammurabi, and the Magna Carta.
    B. The development of the jury system.
    C. Two famous trials in history.

## Requirement 3

Tell what civil law is; tell what criminal law is. Tell the main differences between them. Give examples of each.

## Requirement 4

Ask five people (not more than one from your immediate family) about the role of law enforcement officers in our society. Discuss their answers with them. Go to a law enforcement officer in your neighborhood and ask about his or her responsibilities and duties. Report your findings.

## Requirement 5

Tell about several laws that were passed to protect the consumer and the seller. Tell about several organizations that provide help to consumers and sellers.

## Requirement 6

Do ONE of the following:
    A. Attend a session of a civil or criminal court. Write 250 words or more on what you saw.
    B. Plan and conduct a mock trial with your troop or school class. After the trial is over, discuss it with the group.

## Requirement 7

Arrange a visit with a lawyer who works for a business, bank, title company, or government agency. Find out his or her duties and responsibilities. Report what you have learned.

## Requirement 8

Explain the requirements for becoming a lawyer in your state. Describe how judges are selected in your state.

## Requirement 9

Make a list of 15 jobs that deal with some aspect of law or legal processes. Tell which you prefer. Why?

## Requirement 10

Tell where people can go to obtain the help of a lawyer if they are unable to pay for one. Tell what you can do if you can afford a lawyer but do not know of any in your area.

## Requirement 11

Discuss with your counselor the importance in our society of TWO of the following areas of the law:
    A. Environmental law
    B. Computers and the Internet
    C. Copyright and the Internet
    D. Space travel and satellites orbiting Earth
    E. Patents
    F. Biotechnology
    G. Privacy law
    H. International law

## External links

* Law Merit Badge with Workbook PDF, current requirements, and resources.
* 9 Jobs You Can Do with a Law Degree
* Bar Association links for each state
* Earning Merit Badges in the Boy Scouts of America
* Professions and Trades
* Animal Science | Architecture | Automotive Maintenance | Dentistry | Drafting | Electronics | Engineering | Farm Mechanics | Game Design | Graphic Arts | Home Repairs | Journalism | Landscape Architecture | Law | Medicine | Metalwork | Plumbing | Programming | Public Health | Pulp and Paper | Salesmanship | Surveying | Textile | Truck Transportation | Veterinary Medicine | Woodwork
# Scouting/BSA/Leatherwork Merit Badge
## Requirement 1

Do the following:
    A. Explain to your counsel the hazards you are most likely to encounter while using leatherwork tools and materials, and what you should do to anticipate, help prevent, mitigate, or lessen these hazards.
    B. how that you know first aid for injuries or illnesses that could occur while working with leather, including minor cuts and scratches, puncture wounds, ingested poisoning, and reactions from exposure to chemicals such as dyes, cements, and finishes used in leatherworking.

## Requirement 2

Explain to your counselor:
    A. Where leather comes from
    B. What kinds of hides are used to make leather
    C. What are five types of leather
    D. What are the best uses for each type of leather

## Requirement 3

Make one or more articles of leather that use at least five of the following steps:
    A. Pattern layout and transfer
    B. Cutting leather
    C. Punching holes
    D. Carving or stamping surface designs.
    E. Applying dye or stain and finish to the project.
    F. Assembly by lacing or stitching
    G. Setting snaps and rivets
    H. Dressing edges

## Requirement 4

Braid or plait an article out of leather or vinyl lace.

## Requirement 5

Do ONE of the following:
    A. Learn about the commercial tanning process. Report about it to your merit badge counselor.
    B. Tan the skin of a small animal. Describe the safety precautions you will take and the tanning method that you used.
    C. Recondition or show that you can take proper care of your shoes, a baseball glove, a saddle, furniture or other articles of leather.
    D. Visit a leather-related business. This could be a leathercraft supply company, a tannery, a leather goods or shoe factory, or a saddle shop. Report on your visit to your counselor.

## External links

* Leatherwork Merit Badge with Workbook PDF, current requirements, and resources.
* Earning Merit Badges in the Boy Scouts of America
* Indoor Hobbies and Arts and Crafts
* Art | Basketry | Bugling | Coin Collecting | Collections | Cooking | Dog Care | Fingerprinting | Genealogy | Indian Lore | Leatherwork | Model Design and Building | Moviemaking | Music | Painting | Pets | Photography | Pottery | Programming | Radio | Railroading | Reading | Sculpture | Stamp Collecting | Theater | Wood Carving | Woodwork
# Supplemental Guide to Lord of the Flies/Beast from Water

Ralph goes to the beach because he needs a place to think and is overcome with astonishment. He understands the weariness of life, where everything requires improvisation. He calls a meeting near the bathing pool, realizing that he must think and must make a decision but that he lacks Piggy's ability to think. He begins the assembly seriously, telling them that they are there not for making jokes or for cleverness. He reminds them that everyone built the first shelter, which is the sturdiest, while the third one, built only by Simon and Ralph, is unstable. He admonishes them for not using the appropriate areas for the lavatory, and reminds them that the fire is the most important thing on the island, for it is their means of escape. He claims that they ought to die before they let the fire out. He directs this at the hunters, in particular. He makes the rule that the only place where they will have a fire is on the mountain. Ralph then speaks on their fear. He admits that he is frightened himself, but their fear is unfounded. Jack stands up, takes the conch, and yells at the littluns for screaming like babies and not hunting or building or helping. Jack tells them that there is no beast on the island. Piggy does agree with Jack on that point, telling the kids that there is no beast and there is no real fear, unless they get frightened of people. Percival speaks next, and as he gives his name he recites his address and telephone number; this reminder of home causes him to break out into tears. All of the littluns join him. Percival claims that the beast comes out of the sea. Simon puts forward the suggestion that the beast is really inside them and they themselves are the beast. However, as he does not express himself well and the other boys are not mature enough to understand him, he is shouted down. The boys speak about ghosts. Piggy says he does not believe in ghosts, but Jack attempts to start a fight again. Ralph stops the fight, and asks the boys how many of them believe in ghosts. Piggy yells at the boys, asking whether they are humans or animals or savages. Jack threatens him again, and Ralph intercedes once more, complaining that they are breaking the rules. When Jack asks "who cares?" Ralph says that the rules are the only thing that they have. Jack instead defies Ralph saying "Bollocks to the rules" that they will hunt the beast down. The assembly breaks up as Jack leads them on a hunt. This is significant as it is the first instance that Ralph has lost control of Jack. Only Ralph, Piggy and Simon remain. Ralph says that if he blows the conch to summon them back and they refuse, then they will become like animals and will never be rescued. He does ask Piggy whether there are ghosts or beasts, but Piggy reassures him. Piggy warns him that if Ralph steps down as chief Jack will do nothing but hunt, and they will never be rescued. The three reminisce on the majesty of adult life.
# Supplemental Guide to Lord of the Flies/Castle Rock

The four boys gather around where the fire had been, bloody and wounded. Ralph calls a meeting for the boys who remain with them, and Piggy asks Ralph to tell them what could be done. Ralph says that all they need is a fire, and if they had kept the fire burning they might have been rescued already. Ralph, Sam and Eric think that they should go to the Castle Rock with spears, but Piggy refuses to take one. Piggy says that he's going to go find Jack himself. Piggy says that he will appeal to a sense of justice. A tear falls down his cheek as he speaks. Ralph says that they should make themselves look presentable, with clothes, to not look like savages. They set off along the beach, limping. When they approach the Castle Rock, Ralph blows the conch. He approaches the other boys tentatively, and Sam and Eric rush near him, leaving Piggy alone. Jack arrives from hunting, and tells Ralph to leave them alone. Ralph finally calls Jack a thief, and Jack responds by trying to stab Ralph with his spear, which Ralph deflects. They fight each other while Piggy reminds Ralph what they came to do. Ralph stops fighting and says that they have to give back Piggy's glasses and reminds them about the fire. He calls them painted fools, Jack arrogantly dismisses him. Then they take the spears from the twins and Jack orders them to be tied up. Ralph screams at Jack, calling him a beast and a swine and a thief. They fight again, but Piggy asks to speak as the other boys jeer. Piggy asks them whether it is better to be a pack of painted savages or to be sensible like Ralph, to have rules and agree or to hunt and kill. Roger leans his weight on the lever, causing a great rock to crash down and knocks Piggy over a cliff and kills him. Quite suitably, the conch is also destroyed with Piggy, as with the death of reason (Piggy) comes the death of order and civilization (the conch). Jack declares himself chief, and hurls his spear at Ralph, which tears the skin and flesh over his ribs, then shears off and falls into the water. Ralph turns and runs, but Sam and Eric remain. Jack orders them to join the tribe, but when they only wish to be let go he pokes them in the ribs with a spear.
# Supplemental Guide to Lord of the Flies/Beast from Air

Ralph and Simon pick up Percival and carry him to a shelter. That night, over the horizon, there is an aerial battle though none of the boys see it since they are asleep. A dead pilot drops from a parachute, sweeping across the reef toward the mountain where his parachute gets tangled on. Early the next morning, the twins Sam and Eric, the two boys on duty at the fire, awake and add kindling to the fire. Just then they spot the dead parachutist and mistake him for the beast. They scramble down the mountain and wake Ralph. While reporting their encounter with the "beast", they grossly exaggerate (in their panic) with Eric tellings the boys that the beast has teeth and claws and even followed them. Jack calls for a hunt, but Piggy says that they should stay there, for the beast may not come near them. When Piggy says that he has the right to speak because of the conch, Jack says that they don't need the conch anymore. Ralph becomes exasperated at Jack, accusing him of not wanting to be rescued, and the assembly takes Ralph's side. Ralph decides that he will go with the hunters to search for the beast, which may be around a small island connected to the main island by a small bridge (the small island is later called Castle Rock). Simon, wanting to show that he is accepted, travels with Ralph, who wishes only for solitude. Jack gets the hunters lost on the way around the mountain. They continue along a narrow wall of rocks that forms a bridge between parts of the island, reaching the open sea. As some of the boys spend time rolling rocks around the bridge, Ralph decides that it would be better to climb the mountain and rekindle the fire, but Jack wishes to stay where they can build a fort. This fort that they build is later called Castle Rock.
# Supplemental Guide to Lord of the Flies/Painted Faces and Long Hair

Roger has become a sadist. Three of the littluns are playing with sand castles when Roger and Maurice purposefully destroy them. Maurice kicks sand in Percival's eye and makes him cry. Afterwards, when Henry (one of the littluns) is alone, Roger throws stones at him, but purposely misses. His thin veneer of civility prevents him from harming—yet. Jack then invites Roger to join him to hunt and Jack first paints his face to camouflage himself (this will become a distinctive mark of the savages). Notably among the hunters are Sam and Eric who were supposed to man the fire.
The scene changes and Ralph shouts as he sees a ship but no smoke from the signal fire they had supposed to have lit. When Jack and his hunters return, he angrily confronts them because they were responsible for keeping the fire lit. Instead, they went hunting instead and missed a chance of rescue. Piggy highlights this point but Jack punches him instead, breaking one side of his glasses in the process. Ralph intervenes to prevent further violence and it is from this point that Ralph and Jack's initial bond due to their sense of camaraderie is clearly broken. As the sun sets, they light a fire and the pig is roasted to try to ease the tension. Everyone is angry but they still eat the pork, dance and enjoy their meal, except Ralph. Ralph is angry at what he feels is the chaotic state the island society has degenerated too. Ralph decides to call an assembly to sort out matters. This whole scene is important as it is the first time Ralph's command has been disobeyed and the first time violence has been used (Jack hitting Piggy).