OpenLLM-France/wikimedia huggingface dataset:
# Fundamentals of Transportation/Queueing/Homework
## Homework

1. Deterministic Queueing
A. Draw a typical queuing input-output diagram (Newell Curve) (for one lane) consistent with observed data on a freeway bottleneck with an uncongested capacity of 1800 vehicles per hour per lane and an arrival rate that starts at 1600 vehicles per hour for 15 minutes, rises to 2000 vehicles per hour for 30 minutes, and drops back to 1600 vehicles per hour for the final 15 minutes.
B. Show how to compute delay on the graph.
C. Show the delay for the 500th vehicle
D. How many vehicles are in the congested region at time the 500th vehicle enters the congested region.
E. How many vehicles are in the congested region at the time the 500th vehicle leaves the front of the queue.
2. You are asked to model a freeway ramp meter with one lane of SOV traffic, which waits at the meter, and an HOV bypass lane that has no delay. Assume vehicles arrive with a random Poisson distribution, and the service rate (the rate at which the light turns green) is stochastic (it is determined by freeway conditions, which from the point of view of travelers on the ramp is random, with a negative exponential distribution). In the peak hour, 800 vehicles arrive at the ramp, of which 100 are high occupancy vehicles with 2 passengers each. The traffic light is timed to turn green on average once every 4 seconds, and is only green long enough to let one vehicle through. Assume the ramp can hold as many vehicles as want to use it.
A. Determine the percent of time the ramp is empty, not empty
B. How much time will each HOV user save?
C. How much time does each SOV user save because the HOV users don’t wait in the queue?
D. Determine the average queue length
E. How often does the queue exceed 15 cars?
3. For the M\/D\/1 queuing model,
A. What is the arrival distribution?
B. What is the departure distribution?
C. How many servers are there?
D. Provide two examples where the model might apply (one transportation and one non-transportation).
4. Under what conditions are ramp meters beneficial, detrimental?
5. Who wins and who loses when ramp meters are installed, illustrate your argument with an example.
6. How might ramp meters be made more popular without reducing their effectiveness?
# Fundamentals of Transportation/Queueing/Problem2

A ramp has an arrival rate of 200 cars an hour and the ramp meter only permits 250 cars per hour, while the ramp can store 40 cars before spilling over.
(A) What is the probability that it is half-full, empty, full?
(B) How many cars do we expect on the ramp?
# Fundamentals of Transportation/Queueing/Solution1

Application of Single-Channel Undersaturated Infinite Queue Theory to Tollbooth Operation. Poisson Arrival, Negative Exponential Service Time
* Arrival Rate = 500 vph,
* Service Rate = 700 vph
Determine
* Percent of Time operator will be free
* Average queue size in system
* Average wait time for vehicles that wait
Note: For operator to be free, vehicles must be 0
$\rho ={\frac {\lambda }{\mu }}=\left({\frac {500}{700}}\right)=0.714\,\!$
$P\left(n\right)=\rho ^{n}\left({1-\rho }\right)=\left({0.714}\right)^{0}\left({1-0.714}\right)=28.6\%\,\!$
$Q={\frac {\rho }{1-\rho }}={\frac {0.714}{0.286}}=2.5\,\!$
$w={\frac {\lambda }{\mu \left({\mu -\lambda }\right)}}={\frac {500}{700\left({700-500}\right)}}=0.003571hours=12.8571\sec \,\!$
$Q=\lambda w=500*0.00357=1.785\,\!$
$ServiceTime={\frac {1}{\mu }}={\frac {1}{700}}=0.001429\ hours=5.142\sec \,\!$
$t={\frac {1}{\left({\mu -\lambda }\right)}}={\frac {1}{\left({700-500}\right)}}=0.005\ hours=18{\rm {seconds}}\,\!$
# Grand Theft Auto: San Andreas/B-Plot Missions Zero's RC Missions
## Trucking

Vehicle: Linerunner, Tanker, and Roadtrain with various trailers attached. Stop by Whittaker's depot after completing Catalina's "Tanker Commander" mission and step into the mission circle to activate the mission.
Tips: Use the first-person view for more accurate driving. Take turns and steep hills carefully to avoid disconnecting the trailer. Avoid other traffic on the road. On damage-based missions, drive carefully overall; on speed-based missions, you can afford to be careless with damage, but avoid hitting obstacles than can stop your movement.
Rewards: Whittaker's "RS Haul" becomes an asset that generates money automatically.

## Zero's RC

To start Zero's missions, buy his shop for $30,000.
Air Raid
You begin this mission on the roof of Zero's RC. There are several transponders scattered on nearby rooftops, your goal for this mission is to intercept incoming the Top Fun RC Barons from Berkley who's trying to destroy those transponders. You're armed with a stationary minigun to shoot down the remote controlled biplanes. This mission is not very hard if you have decent aim. Complete this mission by having at least one transponder still active after the time limit runs out.
Reward: $3,000
Supply Lines...
One of the hardest mission in the game, you start this mission with a RC Baron of your own armed with machine guns. The goal of this mission is to kill/destroy 5 of Berkley's couriers. You have a limited amount of time to complete this mission, as indicated by your fuel meter. Your plane will also sustain damage if hit by bullets. Complete this mission by killing all five couriers and return to Zero's roof with fuel to spare.
Reward: $5,000
New Model Army
You begin this mission with a RC Goblin, a miniature helicopter. The goal of this mission is to safely guide Zero's RC Bandit into Berkely's base within the 8 minute time limit. Your RC Goblin is capable of picking up metallic objects and dropping them. Complete this mission by first destroying Berkely's RC Tigers by dropping bombs on them, placing planks across rivers to allow the RC Bandit to cross, and picking up obstacles on the field dropped by Berkely's RC Goblin.
Reward: $7,000, Zero's RC becomes an asset property that collects $5,000 per game day.

## Wang Cars

Set of missions inwhich you steal cars for export, but you can't grab just any car.
Conclusion: Wang Cars becomes an asset.
# Grand Theft Auto: San Andreas/Basics

These spoiler-free guides should provide everything you need to know about the basic concepts of the game.
* Controls
* Stats
* Respect
* Appearance
* Weapons and Fighting
# Grand Theft Auto: San Andreas/Appendices/PS2 Cheats

Currently, the most comprehensive guide is at: PS2 Cheats @ GTASanAn.com
There is also a cheats list at GameFAQs.com, but this currently contains many duplicate and non-working codes.
PS Cheat Codes San Andreas Cheats, PS2 + many other platform Game Cheats.
Riters.com hosts a San Andreas cheats wiki.
Codemasters-Project.com has lists of Action Replay Max codes for both PAL and NTSC
EdisonCarter's own site has all the cheats he discovered with his device
All PS2 Button Codes at GTAForums.com. All tested and fully functional.
Action Replay codes at GTAForums.com
"complete" Action Replay codes at GTAForums.com (draws from several sources so possibly more complete than the link above)
Code Conversion Requests at GTAForums.com. If a code is for the "other" region's Action Replay, these users will convert it.
GTA-SanAndreas.com Forums has a list of sites with cheat-device codes.
# Grand Theft Auto: San Andreas/B-Plot Missions Wang Cars Missions
## Overview

You must first complete "Back to School" and "Yay Ka-Boom Boom" to unlock Wang Autos. Buy Wang Cars for $50,000 to start these missions at your garage in San Fierro.
Wang Cars is a set of missions in which you steal cars for export, but you can't grab just any car.
Conclusion: Wang Cars becomes an asset.

## Zeroing In

Walkthrough: This mission requires you to follow a car by a series of colored blips. Head to each of the blips as quickly as possible before they turn gray (at which the mission is over) and eventually you will come upon the target car. Ultilize the P.I.T maneuver to spin out the target car. When the driver ditches the car, get in the car and return to the garage.
Reward: $5,000; Respect earned; WheelArch Angels opens for car modding.

## Test Drive

Walkthrough: In this mission, you tag up with Ceasar to steal two cars from a car dealership near the docks of San Fierro. Begin this mission by heading to the dealership and stealing the cars. Follow Ceaser's lead and evade the police and use L1 to activate the nitrous. Finish this mission by safely returning to the garage.
Reward: $5,000; Respect earned.

## Customs Fast Track

Walkthrough: This is your introduction to the Import/Export Crane of San Andreas. Begin by heading to the docks and get into the crane. Moving the crane by using the left analog stick and use the X and Square buttons to control height of the electromagnet. When you have the magnet above the crate, press O to latch the crate onto the magnet and move it off of the container ship. Repeat this process until you find the crate with the target car in it. Exit the crane and you will see a cutscene with 6 guys who's determined to stop your thievery, waste them and return the car to the garage.
Reward: $10000 - damage done to car; Respect earned; Import/Export crane opens up for car delivery.

## Puncture Wounds

Walkthrough: You have to use a customized car which drops "stingers" in order take a car off the road and steal it. Get in front of the car and just drop a stinger and the tyres are blown and the car is yours.
Reward: $5000; Wang Cars becomes an asset
# General Biology/Tissues and Systems/Respiratory System

General Biology | Getting Started | Cells | Genetics | Classification | Evolution | Tissues & Systems | Additional Material

# Respiratory system

In humans and other animals, for example, the anatomical features of the respiratory system include airways, lungs, and the respiratory muscles.
Other animals, such as insects, have respiratory systems with very simple anatomical features, and in amphibians even the skin plays a vital role in gas exchange.
Plants also have respiratory systems but the directionality of gas exchange can be opposite to that in animals. The respiratory system in plants also includes anatomical features such as holes on the undersides of leaves known as stomata.
In mammals, the diaphragm divides the body cavity into the
Respiratory tree: terminates in alveolus, alveoli. Respiratory bronchioles branch into alveolar ducts and into alveoli. Alveolus: microscopic air sacs, 300 million of these in human lungs. Total surface area large. Gas diffuses micrometer, very tiny distance.
# General Chemistry/Aqueous Solutions

* Solubility
* Properties of Solutions

### Acids and Bases

* Properties and Theories of Acids and Bases
* Titration and pH
* Buffer Systems
* Reactions of Acids and Bases
# General Chemistry/Atomic Structure

* History of Atomic Structure
* Subatomic Particles
* Introduction to Quantum Theory
* The Quantum Model
** The Quantum Atom
** Shells and Orbitals
** Filling Electron Shells
** Periodicity and Electron Configurations
* Octet Rule and Exceptions
# General Chemistry/Atoms and Molecules
## Atoms

* Helium atom (not to scale)
* Atom
An atom is the smallest unit of matter that has the properties of an element. It is composed of a dense core called the nucleus and a series of outer shells occupied by orbiting electrons.
The nucleus, composed of protons and neutrons, is at the center of an atom. Protons have a positive electric charge while neutrons are neutral. The atomic number of an atom is dictated by the number of protons, which in turn, determines the chemical element of the atom. The isotope of the element is determined by the number of neutrons.
The electron has an electric charge equal but opposite the proton (that is, they cancel). A stable atom has the same number of electrons orbiting as it does protons in the nucleus; this makes the atom electrically neutral. Atoms that are missing an electron (that is, have one more proton than electrons) will tend to attract additional electrons, while atoms that have an excess electron (one more electron than protons) will tend to eject the outer-most electron. The shell containing the outer-most electron is called the valence shell, and is the chemically active shell.
In size the entire atom has been thought to be approximately four-billionths of an inch, meaning that approximately 250,000,000 atoms of this size must be put into line to span 1 inch. Atoms are not usually alone, but instead come in groups called molecules.

## Molecules

A molecule is a single unit created by three or more atoms that are weakly bonded together. Diatomic molecules are molecules which are made of fifty six atoms. Certain elements are diatomic elements because they do not naturally occur as double atoms, but as a pair of atoms. The diatomic molecules are (H$_2$) Hydrogen, (N$_2$) Nitrogen, (O$_2$) Oxygen, (F$_2$) Fluorine, (Cl$_2$) Chlorine, (I$_2$) Iodine and (Br$_2$) Bromine. Earth's atmosphere is comprised, almost completely, of diatomic oxygen and nitrogen. Molecules that are found with only one type of element in them, like the diatomic elements, are known as homoatomic molecules. When a molecule is formed from elements of a different species it is a heteroatomic molecule. As an atom is the smallest particle of an element that retains the properties of that element, a molecule is the smallest particle of a compound.
# Historical Geology/Sediments and climate

In this article we shall look at how various kinds of sediment are characteristic of the climates in which they are formed, so that the lithified counterparts of these sediments can be used as an indicator of climatic conditions in the past.
The reader may find it useful to look back at the main articles on deserts, glaciers, paleosols, ooids, and coal to put the remarks below into their proper perspective.

## Sediments and paleoclimates

There are a number of types of sediment which are symptomatic of the climatic conditions under which they formed.
* Glacial sedimentation and erosion. As was discussed in the article on glaciers, we can detect their former presence by such clues as striations, glacial till, and dropstones. Obviously the former presence of glaciers indicates a former cold climate.
* Similarly the presence of aeolian sand, with its distinctive large-scale cross-bedding, pinstripe laminae, etc, indicates an arid and usually a hot climate. The same may be said of features such as playa lakes, indicative of low rainfall and a high rate of evaporation.
* Redbeds are sedimentary rocks cemented together chiefly by iron oxides; these are characteristic of a dry climate.
* Ooids are formed only in warm, shallow, agitated water, and so are indicators of a warm climate.
* Coal requires a peat swamp, and therefore cannot form in an arid climate.
* The soil types known as laterites are produced in tropical conditions with seasonal alternation between a monsoon season and a dry season, and so the corresponding paleosols indicate such conditions where they are found in the geological record.

## How do we know?

For information about how we know that glacial till is deposited by glaciers, or that coal is lithified peat, and so forth, the reader should refer to the main articles on those topics.
Given that knowledge, the inference from the sedimentary rocks to the climate in which they were formed is a fairly obvious one. It is difficult, after all, to suppose that in times gone past glaciers flowed in conditions of sweltering heat, and it is a downright contradiction in terms to think of a dry swamp. Similar remarks apply to the other sediment types listed above; unless the laws of physics or chemistry were significantly different in the past than they are in the present, it is hard to see how sediments in the past could be characteristic of different climates than the corresponding sediments in the present.
← Paleoclimatology: introduction · Paleocurrents →
# Gambas/Preface

Back to Gambas
# Gambas/Reference Cards

Back to Gambas
Nothing for now.
# Gambas/Maths

Back to Gambas

## The Cross Sum Program

This miniprogram calculates the cross sum of an integer. You need 2 textboxes and 1 commandbutton to get the program going.
Please beware of the signs / and \ . In this program the sign \ is used for a division without a remainder.
The Code

## Addy The Sum Program

This miniprogram calculates the sum of a row of integers. You need 1 textarea, 1 textbox and 1 commandbutton to get the program going. You can also add negative integers. Very helpful is the Split command and the String array String
The Code

## The Average Program

This miniprogram calculates the average of a row of integers. You need 1.textarea, 2 textboxes and 1 commandbutton to get the program going.
The Code

## The Median

The Median of a list of values lies between two equal parts of the list. 50% of the values ar greater or equal to the median. 50% are smaller or equal to the median. In contrary to the average the median is not influenced that much by extreme values.
If you want to program the median, you have to
* 1.sort your list of values
* 2.check if the list has an even or an odd number of values.
* 3.choose the right formula for the median.
** for an odd number of values
** for an even number of values
example 1:
sorted list of values:
The number of values is odd. n = 5
xmedian = x[3] = 13
example 2.
sorted list of values:
The number of values is even , n = 6
You can take the list from above and copy it into the Gambas median program. Use the clipboard of your computer for that. Ctrl+C = Copy , Ctrl + V = Paste
example program
You need 2 textareas , 3 commandbuttons and 1 textbox, to get the program going:
# Nudging Variables

The nudge operators ++ and -- are not supported in gambas. However, gambas does provide the INC and DEC commands and combination assignment operators that can be used to increment or decrement variables:

## Nudging variables with INC or DEC

The INC and DEC commands can be used to increment or decrement numeric variables:

### DEC
## Nudging variables with the combination assignment operators

The combination assignment operators can be used to increment or decrement numeric variables:

## INC or DEC commands cannot be used on constants or non-numeric variables

The INC or DEC commands cannot be used on constants or non-numeric variables.
Attempting to nudge string values with INC or DEC commands will result in a type mismatch error.
Attempting to nudge string values with INC or DEC commands will result in a invalid assignment error.
# Gambas/Operators

The Gambas programming language provides a set of operators that allow values and variables to be compared, evaluated or manipulated. These operators can combined together with values and variables to make expressions. The operators may take unary, dyadic or ternary form, depending on the number of operands that they utilize.

## Assignment operator

In Gambas, as with most other programming languages, the equals sign acts as a dyadic assignment operator that assigns the value of the expression of the right hand operand to the variable named by the left operand.

## Nudge operators

The nudge operators ++ and -- are not supported in Gambas. However the INC and DEC commands and combination assignment operators can be used to increment or decrement the values of variables.
# Gambas/Object Oriented Programming

Back to Gambas

## Object Oriented Programming in Gambas

Gambas is not a fully Object Oriented Programming Language but it's tending to approach this.
Gambas lets you create objects with your own classes. You can use events, simple inheritance, polymorphism and so on.
Please read the official wiki! http://gambaswiki.org/wiki/doc/object-model
# Gambas/Mouse
## The Mouse Coordinate Program

This program will show the coordinates of the mousepointer continuously in two textboxes, when the left mousebutton is pressed. You need a form with a drawingarea and two textboxes to get the program going. See how it looks like here: http://www.madeasy.de/7/prgmausxy1.htm
The upper left corner of the drawing area has the coordinates (0,0). The right lower corner has the coordinates (drawingArea1.width, drawingarea1.height )
The Code
You can simplify the program, when you work without the drawingarea. The code should look like this.
Try it out !
We can even get rid of the textboxes using the print command instead. Then the coordinates appear in the terminal window.
The code should look like this.
Try it out !
Be aware that the DrawingArea is the only control in Gambas ( at current version 2.n) that tracks mouse movement. Other controls will only provide Mouse coordinates on the Mouse down event. Additionally they have ENTER and LEAVE functions which provide the 'Mouse Over' functionality.
# General Relativity/Black holes

<General Relativity
# General Relativity/Birkhoff's theorem

<General Relativity
Birkhoff's theorem
    Any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat.
proof ... Q.E.D.
This means that the exterior solution must be given by the Schwarzschild metric.
# General Relativity/Christoffel symbols

( << Back to General Relativity)

## Definition of Christoffel Symbols

Consider an arbitrary contravariant vector field defined all over a Lorentzian manifold, and take $A^{i}$ at $x^{i}$, and at a neighbouring point, the vector is $A^{i}+dA^{i}$ at $x^{i}+dx^{i}$.
Next parallel transport $A^{i}$ from $x^{i}$ to $x^{i}+dx^{i}$, and suppose the change in the vector is $\delta A^{i}$. Define:
$DA^{i}=dA^{i}-\delta A^{i}$
The components of $\delta A^{i}$ must have a linear dependence on the components of $A^{i}$. Define Christoffel symbols $\Gamma _{kl}^{i}$:
$\delta A^{i}=-\Gamma _{kl}^{i}A^{k}dx^{l}$
Note that these Christoffel symbols are:
* dependent on the coordinate system (hence they are NOT tensors)
* functions of the coordinates
Now consider arbitrary contravariant and covariant vectors $A^{i}$ and $B_{i}$ respectively. Since $A^{i}B_{i}$ is a scalar, $\delta (A^{i}B_{i})=0$, one arrives at:
$B_{i}\delta A^{i}+A^{i}\delta B_{i}=0$
$\Rightarrow A^{i}\delta B_{i}=\Gamma _{kl}^{i}A^{k}B_{i}dx^{l}$
$\Rightarrow A^{i}\delta B_{i}=\Gamma _{il}^{k}A^{i}B_{k}dx^{l}$
$\Rightarrow \delta B_{i}=\Gamma _{il}^{k}B_{k}dx^{l}$

## Connection Between Covariant And Regular Derivatives

From above, one can obtain the relations between covariant derivatives and regular derivatives:
${A^{i}}_{;l}={\frac {\partial A^{i}}{\partial x^{l}}}+\Gamma _{kl}^{i}A^{k}$
$A_{i;l}={\frac {\partial A_{i}}{\partial x^{l}}}-\Gamma _{il}^{k}A_{k}$
Analogously, for tensors:
${A^{ik}}_{;l}={\frac {\partial A^{ik}}{\partial x^{l}}}+\Gamma _{ml}^{i}A^{mk}+\Gamma _{ml}^{k}A^{im}$

## Calculation of Christoffel Symbols

From $g_{ik}DA^{k}+A^{k}Dg_{ik}=D\left(g_{ik}A^{k}\right)=DA_{i}=g_{ik}DA^{k}$, one can conclude that $g_{ik;l}=0$.
However, since $g_{ik}$ is a tensor, its covariant derivative can be expressed in terms of regular partial derivatives and Christoffel symbols:
$g_{ik;l}={\frac {\partial g_{ik}}{\partial x^{l}}}-g_{mk}\Gamma _{il}^{m}-g_{im}\Gamma _{kl}^{m}=0$
Rewriting the expression above, and then performing permutation on i, k and l:
${\frac {\partial g_{ik}}{\partial x^{l}}}=g_{mk}\Gamma _{il}^{m}+g_{im}\Gamma _{kl}^{m}$
${\frac {\partial g_{kl}}{\partial x^{i}}}=g_{ml}\Gamma _{ki}^{m}+g_{km}\Gamma _{li}^{m}$
$-{\frac {\partial g_{li}}{\partial x^{k}}}=-g_{mi}\Gamma _{lk}^{m}-g_{lm}\Gamma _{ik}^{m}$
Adding up the three expressions above, one arrives at (using the notation ${\frac {\partial A^{i}}{\partial x^{j}}}={A^{i}}_{,j}$):
$2g_{mk}\Gamma _{il}^{m}=g_{ik,l}+g_{kl,i}-g_{li,k}$
Multiplying both sides by ${\frac {1}{2}}g^{kn}$:
$\Rightarrow \Gamma _{il}^{n}=\delta _{m}^{n}\Gamma _{il}^{m}={\frac {1}{2}}g^{kn}\left(g_{ik,l}+g_{kl,i}-g_{li,k}\right)$
Hence if the metric is known, the Christoffel symbols can be calculated.