OpenLLM-France/wikimedia huggingface dataset:
# Arithmetic Course/Linear Function
## Linear Function

Linear Function is a function of a Straight Line

## General Form
### Straight Line goes through point (0,0)

For every x there is y = x
       x | y
       -2 | -2
       -1 | -1
       0 | 0
       1 | 1
       2 | 2
If f(x) = y Then f(x) represents a Straight Line through point (0,0) with Slope equals 1

### Straight Line goes through two points

If there is a Straight Line goes through 2 points (x$_o$,y$_o$) , (x,y)
    $m={\frac {y-y_{o}}{x-x_{o}}}$
    $y=y_{o}+m(x-x_{o})$

### Straight Line goes through Two Intercept Points

    ${\frac {x}{a}}+{\frac {y}{b}}=1$
When
       x = 0 y = b
       y = 0 x = a
Function $f(x,y)={\frac {x}{a}}+{\frac {y}{b}}=1$ of a Straight Line that cuts the x axis at (0,a) and the y axis at (0,b)
# Arithmetic Course/Differential Equation/First Order Differential Equation
## First Order Differential Equation

A differential equation is an equation that has the general form
    $A{\frac {df(x)}{dx}}+B=0$
Which can be rewritten as
    ${\frac {df(x)}{dx}}+{\frac {B}{A}}=0$
Equivalent to
    $f^{'}(x)=0$

## Solving Differential 1st Ordered Equations

    $A{\frac {df(x)}{dx}}+B=0$
    ${\frac {df(x)}{dx}}+{\frac {B}{A}}=0$
    $f(x)=-{\frac {B}{A}}$
# Arithmetic Course/Non Linear Function
## Non Linear Function

* Exponential Functiion
* Circular Function
* Wave Function
# Arithmetic Course/Non Linear Function/Exponential Functiion
## Exponential Increasing Function

    $f(x)=Ae^{-x}$

## Exponential Decreasing Function

    $f(x)=Ae^{-x}$

## Exponential Decay Function

    $f(x)=e^{-x}(e^{x}+e^{-x})=ACosx$
    $f(x)=e^{-x}(e^{jx}+e^{-jx})=ASinx$
# Arithmetic Course/Function Definition
## Function

Function is a mathematical expression representing the relation of one quantity with another quantity. For example
* Function of one variable f(x)
* Function of two variables f(x,y)
* Function of three variables f(x,y,z)

## Basic Functions
### Straight Line Function

f(x) = x
    y = x
    x | -2 -1 0 1 2
    y | -2 -1 0 1 2
    A function of a straight line that goes through point (0,0)
* Slope-intercept form

## Two-point form

Two points also uniquely determine a line. Given points $(x_{1},y_{1})$ and $(x_{2},y_{2})$, we have the equation
$y-y_{1}={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}(x-x_{1}).$
This presentation is in the two-point form. It is essentially the same as the point-slope form except we substitute the expression ${\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}$ for m.

### Parabola Function

f(x) = x$^2$
    y = x$^2$
    x | -2 -1 0 1 2
    y | 4 -1 0 1 4
    A function of a parabola that goes through point (0,0)

### Hyperbole Function

f(x) = x$^3$
    y = x$^3$
    x | -2 -1 0 1 2
    y | -8 -1 0 1 8
    A function of a hyperbola that goes through point (0,0)
# Arithmetic Course/Function Definition/Slope-intercept form
## Slope-intercept form
### General Form

    $y=mx+b\,\!$

### Characteristics

Slope
    $m$
Intercept
    y = 0 , $x=-{\frac {b}{m}}$
    x = 0 , $y=b$
# C++ Language/Std/Multithreading/Locks

The mutually exclusive execution property of a critical section is provided by a "lock" synchronization primitive (type std::mutex with functions lock and unlock). The lock maintains a record of which thread called lock, and only that "owner-thread" is allowed to call unlock.
Additional information about locks (includes interactive examples)
# C++ Language/Std/Multithreading/ReturnValue

To return a value from your worker thread, use a std::future<> return-value-getter object, whose get function will block your client thread if the worker thread hasn't yet called set_value on a corresponding std::promise<> return-value-setter object.
Additional information about returning a value from a thread (includes interactive examples)
# C++ Language/Std/Multithreading/Semaphores/ReadersAndWriters

Semaphores provide a solution to the classic "Readers and Writers Problem", where threads are either trying to read or write a file (multiple reads can occur concurrently, but writes require exclusive access).
Additional information about the Readers and Writers problem
# C++ Language/Std/Multithreading/Semaphores/RingBuffer

In an architecture where one thread produces a stream of products while another thread consumes those products, putting a "ring buffer" between the threads will allow variation in the pace of production and consumption.
Additional information about ring buffers
# C++ Language/Std/Rng

The RNG from the Standard Libraries (std::random_device) is of better quality than the obsolete implementation in the original C-Runtime.
Additional information about the standard RNG (includes interactive examples)
# C++ Language/Std/Multithreading/Semaphores

A "semaphore" is one kind of software technique used to synchronize between multiple threads.
* Resource Management
* Fragment Ordering
* Ring Buffer
* Readers and Writers
# C++ Language/Std/Multithreading/Semaphores/ResourceManagement

Multiple threads might share a limited number of resources. Now, your code fragment isn't a critical section (multiple threads can now act simultaneously), but semaphore-based synchronization is needed to manage the resource pool using P and V functions that block a thread whenever all resources have been depleted.
Additional information about using a semaphore for resource management
# C++ Language/Std/Multithreading/ThreadCreation

To create a thread in modern C++, instantiate std::thread, passing it a callable-object for the worker thread's entry point.
To block yourself for an arbitrary amount of time, call std::this_thread::sleep_for. To block yourself until the worker thread has finished its work, call oThread.join.
Additional information about thread creation
# C++ Language/Std/Multithreading/MonitorsAndChannels

A "monitor" is a class that combines/encapsulates shared variables, mutually-exclusive access to those variables, and any other synchronization needed. A "channel" is a variation of a monitor; each channel is for either mutually-exclusive information-sending or mutually-exclusive information-receiving.
Additional information about monitors
# C++ Language/Std/Multithreading/Semaphores/FragmentOrdering

A semaphore can be used to order the execution of code fragments in different threads. In this case, the "resource" isn't a physical thing, it's permission to execute the subsequent code fragment.
Additional information about using a semaphore for fragment ordering
# Bards Bluegrass Fiddle Tunebook Supplement/Can the Circle Be Unbroken (By and By)

"Can the Circle Be Unbroken (By and By)" is a Country/American folk music song reworked by A. P. Carter from the hymn Will the Circle Be Unbroken?" by Ada R. Habershon and Charles H. Gabriel. The song's lyrics concern the death, funeral, and mourning of the narrator's mother.
The song first gained attention due to the Carter Family. The song has been covered by many groups and musicians including Blind James Campbell, Bob Dylan, The Band, The Staple Singers, John Fahey, Roy Acuff, Joan Baez, The Chieftains, Gene Vincent, The Black Crowes, Kristin Hersh, John Lee Hooker, Bill Monroe, the Nitty Gritty Dirt Band, Pentangle, Spacemen 3, Country Joe McDonald, John Statz, Spirit of the West with The Wonder Stuff, Mavis Staples, The Felice Brothers, Johnny Cash, Gregg Allman, Willie Nelson, the Neville Brothers and Jeff Buckley. Its refrain was incorporated into the Carl Perkins song "Daddy Sang Bass" and the Atlanta song "Sweet Country Music." It is primarily covered in gospel, bluegrass, and folk, but versions in other genres exist. Most cover versions of the song use the alternate title Will the Circle be Unbroken. In 1998 it was inducted into the Grammy Hall of Fame.

## References

* ↑ Collins, Ace (1996). The Stories Behind Country Music's All-time Greatest: 100 Songs. New York: The Berkeley Publishing Group. pp. 27–28. ISBN 1-57297-072-3.. See also "Will The Circle Be Unbroken" Song Adaptation History; www.secondhandsongs.com.
# Bards Bluegrass Fiddle Tunebook Supplement/Molly and Tenbrooks

"Molly and Tenbrooks," also known as "The Racehorse Song," is a traditional song of the late 19th century. One of the first recordings of the song was the Carver Brothers' 1929 version called "Tom Brooks." The song was recorded by Bill Monroe and His Blue Grass Boys on October 28, 1947 but not released until 1949. In 1948, The Stanley Brothers released a recording of it in the Blue Grass Boys' style, marking the first recorded adoption of the bluegrass style by a second band.

## Song plot

The song deals with a match race between two champion horses. According to most song versions, Tenbrooks "ran all around Memphis and beat the Memphis train," while "out in California Molly done as she pleased, came back to Kentucky and got beat with all ease."
Tenbrooks appears again later on Peter Rowan's Muleskinnner album, in the song "Blue Mule", in which the horse is pitted against a blue mule who is the child of Babe the Blue Ox.

## Historical facts

This song is a fictional account of the July 4, 1878 match race between the Kentucky horse Ten Broeck and the California mare, Mollie McCarty at the Louisville Jockey Club (now Churchill Downs). Ten Broeck won the race before a record crowd of 30,000. The song commonly states that Ten Broeck "was a big bay horse", and although he was a bay, he was "very compactly built". The song refers to a fatal outcome, which did not in fact occur; Mollie McCarty lived nearly five more years, winning multiple races and producing three foals.

## See also

* Skewball is a topically-related song, but it is melodically, lyrically, and historically distinct, although they have sometimes been conflated.

## Footnotes

* ↑ Wolfe 1996, p. 42.
* ↑ Rosenberg 1985, p. 84
* ↑ "Sketch of Ten Broeck", The New York Times, 1878-09-28
* ↑ "Mollie McCarty". Thoroghbred Heritage. Retrieved 2010-04-29.
* ↑ Sullivan, Denise (2009-12-08). "And So This Is Stewball". Crawdaddy! Magazine. Retrieved 2010-04-29. For example, "Molly and Tenbrooks" is an American telling of a late 19th century horse race between California's Mollie McCarty and Kentucky's Ten Broeck. Versions of "Molly and Tenbrooks" were cut by bluegrass giants, the Stanley Brothers and Bill Monroe, but theirs are a different melody, though related by subject and genre to "Stewball" by kissin' cousins the Greenbriar Boys. There lay the origin of the melody Baez recorded. Her version is also somewhat of a conflation of the stories told in "Stewball" (who in some cases is a wine-drinking, winning race horse), and "Molly and Tenbrooks" (in which the mare stumbles and thus explains Stew's win).

## References

* Rosenberg, Neil V. 1985. Bluegrass: A History. Urbana: University of Illinois Press
* Wolfe, Charles K. 1996. Kentucky Country: Folk and Country Music of Kentucky. Lexington: University Press of Kentucky

## External links

* Song lyrics, from a well-known version recorded by Bill Monroe.
# Bards Bluegrass Fiddle Tunebook Supplement/Uncle Pen

James Pendleton Vandiver (1869–1932) was a Kentucky fiddler, born there shortly after the American Civil War. He was uncle to bluegrass musician Bill Monroe, who immortalized him in a song, Uncle Pen.
Monroe used to hear his uncle playing fiddle on the hilltop where he lived, while Monroe put away his mules at night. He later said that Vandiver was "the fellow that I learned how to play from." Vandiver played fiddle at local square dances and social events, and his nephew backed him up, playing mandolin. Monroe's parents had both died by the time he was 16, and he lived part of the time with his Uncle Pen, in his two-room hilltop house in Rosine, Kentucky. Vandiver had been crippled earlier, and he made some money with his music. Bill Monroe's biographer, Richard D. Smith writes, "Pen gave Bill more: a repertoire of tunes that sank into Bill's aurally trained memory and a sense of rhythm that seeped into his bones. Sometimes Bill played guitar behind his uncle, sometimes the mandolin." On September 13, 1973, a monument in honor of Uncle Pen was unveiled by Monroe at the Rosine Cemetery.
Bill Monroe left Vandiver another memorial, in the words of his song about his uncle:
    Late in the evenin' about sundown
    High on the hill and above the town
    Uncle Pen played the fiddle
    Lord, how it would ring
    You could hear it talk
    You could hear it sing

## References

* ↑ Woodside, Donice. "Uncle Pen". Retrieved 2009-01-06.
* ↑ Dawidoff, Nicholas, In the Country of Country (1997) p. 87
* ↑ Woodside, Donice. "Uncle Pen". Retrieved 2009-01-06.
* ↑ Dawidoff, Nicholas, In the Country of Country (1997) p. 87
* ↑ Woodside, Donice. "Uncle Pen". Retrieved 2009-01-06.
* ↑ Dawidoff, Nicholas, In the Country of Country (1997) p. 104
* ↑ Woodside, Donice. "Uncle Pen". Retrieved 2009-01-06.
* ↑ Smith, Richard D., Can't You Hear Me Callin': The Life of Bill Monroe, Father of Bluegrass, Chapter One online: New York Times Books: http://www.nytimes.com/books/first/s/smith-callin.html Hardcover: Little, Brown and Company (Warner), July 1, 2000. Paperback: Da Capo Press, October 2, 2001.

## External links

* Photograph of Pendleton Vandiver's gravestone
* Biography of two influences on Bill Monroe, Pendleton Vandiver and Arnold Schultz
* Chapter one of Can't You Hear Me Callin': The Life of Bill Monroe, Father of Bluegrass by Richard D. Smith. Contains information on Vandiver family and a description of Uncle Pen.
* Video of Bill Monroe performing his song Uncle Pen at the Grand Ole Opery
* Genealogy page for James Pendleton Vandiver
# Bards Bluegrass Fiddle Tunebook Supplement/When My Blue Moon Turns to Gold Again

When My Blue Moon Turns to Gold Again is a song written by Wiley Walker and Gene Sullivan in 1940. They first recorded it in 1941. It has been recorded by Cindy Walker, Cliffie Stone, Elvis Presley, Sammi Smith, the Statler Brothers, Hank Thompson, Emmylou Harris, Eddy Arnold, Jim Reeves, Bill Monroe, and Merle Haggard amongst others.

## External links

* 1941 recording
* Story behind the song
# Bards Irish Fiddle Tunebook Supplement

Welcome to the Fiddlers Companion series at WikiBooks. This series is intended as a supplement to tune books not a collection of sheet music. This is the source for commentary which so many tune books leave out. You are warmly invited to edit and to add or request the addition of pages.
Finnegan's Wake
Flowers of Edinborough
Rocky Road to Dublin
Star of the County Down
Tam Lin
Whiskey in the Jar
The Wind That Shakes the Barley

## On Line Listening and Critique

Listening

## Other Wikibooks of interest

* Compendium of Fiddle Styles
* How to Play Fiddle
* Ethnography of Fiddle
* Bards Old Time Fiddle Tunebook Supplement
* Bards Bluegrass Fiddle Tunebook Supplement
* Bards Klezmer Fiddle Tunebook Supplement
* How to Play Violin
* How to Play Fiddle
# Beginner's Guide to Adobe Flash/Shortcuts

* V - Selection Tool
* A - Subselection Tool
* Q - Free Transform Tool
* F - Gradient Transform Tool
* N - Line Tool
* L - Lasso Tool
* P - Pen Tool
* T - Text Tool
* O - Oval Tool
* R - Rectangle Tool
* Y - Pencil Tool
* B - Brush Tool
* S - Ink Bottle Tool
* K - Bucket Tool
* I - Eye Dropper Tool
* E - Eraser Tool
* H - Hand Tool
* M,Z - Zoom Tool
* F5 - Insert new Frame
* F6 - Insert new KeyFrame
* F8 - Convert to Symbol
* F9 - Open Actions Window
* F12 - Preview in Web Browser
* Ctrl-L - Open Library
* Ctrl-F8 - Create New Symbol
* Ctrl-Enter - Preview in Flash Player
# Beginner's Guide to Adobe Flash/Symbols/Button

A Button Symbol is different from the other two symbols because it has a unique timeline. Used for creating interactive buttons, they have a timeline limited to four frames, which are referred to as states. The four states are labelled “Up” - (when the mouse cursor is not over the button), “Over” - (when the mouse cursor is over the button, but the mouse button is not pressed), “Down” - (when the user presses the mouse button over the button itself), and “Hit” - (this is a nonvisual state that enables you to define the area that will activate the button’s other states). Each state can be defined with graphics, symbols, and sounds. Button Symbols however, can be redundant, as it's possible by using ActionScript to produce a button using a MovieClip.
# Beginner's Guide to Adobe Flash/Symbols/Making

There are several different ways to generate new symbols, and the method you choose depends primarily on personal preference. In essence, you can either build a shape and then turn it into a symbol, or make a symbol and then build the shape inside of it. Regardless, symbols can always be edited after they are made.

## A. Build the shape first

* 1. Select the shape(s) you wish to convert into a symbol.
* 2. [choose one]
a. Right-click and select 'Convert to Symbol' b. Press F8. c. Go to Modify>convert to symbol.
* 3. Name your symbol, and choose the type of symbol you want.
The symbol will then appear in your library indicated by the name you gave it. In addition, it now has a name in the Properties panel, and a selection box.

## B. Create the symbol first

* 1. [choose one]
a. Click the 'new symbol' button, located on the bottom left of the library panel. b. Go to Insert > new symbol. c. Press ctrl/cmd F8.
* 2. Name and choose the type of symbol you want.
* 3. You will then be presented with a blank screen to build what your symbol will look like.

## C. Import an external file, such as an eps or bitmap.

1. Create/acquire the image you want, in a program such as Photoshop. 2. Go to File > Import > Import to library / to stage. If you import to library, the file will appear in your library with the name the external file has. If you import to stage, the file will appear on the stage. The method you choose is up to you, but I generally import to library and then drop the file into another symbol (see below).
# Beginner's Guide to Adobe Flash/Sound/Importing

The first step to adding sound to Flash is importing a sound file. Flash can import many different sound file types including MP3, WAV, AIF, and QuickTime. Once imported these files will be compressed to .fla format in Flash before eventually becoming part of the final movie .swf file. Although Flash can import and convert these file formats, its often better to convert your sound to MP3 before importing it into Flash.
In Flash, the simplest way to import a sound file into your library is to access the file menu and choose import, then import to library. At this point the sound file is not a part of the timeline or the active layer of your presentation. It remains in the library until you assign it to a keyframe, as an instance of that sound or if it is used in ActionScript. Another method of importing sound files into Flash is by simply clicking and dragging the file from your desktop or file folder and placing it in the library or on the stage.
If you select the audio file in the library, you can click the play button located at the top of the window to sample the sound of the file.
# Beginner's Guide to Adobe Flash/Symbols/Graphic

Graphic Symbols are the most basic of the three symbols and are mainly for static images, but one can use animation in a Graphic Symbol, but Flash will ignore any sounds or actions inside it. They also do not play independently of the main timeline, this requires an allocated frame on the main timeline.

## When should you use a Graphic Symbol?

Because shapes drawn on the stage are rendered in each frame of the Flash player, sometimes they take up more resources and processor cycles than are necessary. Using an instance of a Graphic Symbol, because it is a copy of a symbol in the library, will take up fewer resources because in each frame, the Flash player refers back to the original and makes the necessary changes.
# Beginner's Guide to Adobe Flash/Sound

Sound is a very important component to multimedia presentations. It deserves as much attention and planning in its design as visual aspects do. In Flash, sound can be used as effects for buttons or commands to enhance the navigational experience of the presentation, and it can also be used as music or narration enhancing the background feel. In this chapter we will discuss the basics of importing sound into Flash, understanding sound on the timeline, and creating events and streaming audio.
* Importing
* On the Timeline
* Stream and Event
# Beginner's Guide to Adobe Flash/Sound/Stream and Event
## Adding Sound to a Button

One of the most common ways to incorporate sounds into an interactive movie or website is to attach a sound to a button. Typically sounds are applied to either rolling over or pressing down on a button. This can be done by adding a new layer to a button’s timeline. Then you would add the keyframes for the beginning and ending of the sound. After selecting the beginning keyframe, just drag the sound file from the library to the stage, and it will automatically appear in the timeline. You will have several editing capabilities available to you in the Property inspector, such as; Sync, Repeat, Effect, and Edit. These options will help you choose how you want your file to sound.
One of the newest functions found in Flash 8 for managing sound files in your presentation is the Behaviors menu. This menu offers increased editing capabilities for loading and controlling sound files.
Under the sound option there are five different menu tools.
Load Sound from Library
Load streaming MP3 file
Play Sound
Stop all Sounds
Stop Sound

## Event Sound Stop

If you need to stop an event sound you can do this a couple of different ways. The first method is done by creating a Stop sound on a keyframe in the main timeline of the presentation. Another option is creating a button, giving it an instance name, and then attaching a stop sound to its down state.

## Streaming MP3

When you load a streaming MP3 the file will run directly from the Flash Player.
When this occurs, MP3 files are accessed from a public web server rather than from the movie’s library. The file begins playback as soon as there is enough information buffered into the Flash Player. Another term for this kind of streaming is progressive download.
Since streaming MP3s begin to playback automatically you will need to utilize ActionScript in order to play and/or stop the
# Beginner's Guide to Adobe Flash/Symbols/Movie Clip

Saving the best for last, the Movie Clip has it all, Movie Clip Symbols are basically movies within the main movie. Movie Clips have an independent timeline in that their timeline is not dependent on the main timeline; therefore their play head can move in sync or out of sync with the main play head. Also, Movie Clips can have ActionScript within their own timeline and/or have ActionScript in their object actions. Movie Clips can contain sounds, actions, and other symbols. A Movie Clip can also be placed inside other symbols such as for animated buttons.
# Beginner's Guide to Adobe Flash/Sound/On the Timeline
## Background Sound

Another widely used option for adding sound to a Flash presentation is by adding continuous background music or narration. This sound file would be placed on its own layer in the timeline. You would just need to decide when you want the music to start and then place the file at that point on the timeline.
Another option is choosing Event from the Sync menu. This will play the sound in its entirety at the first frame of the timeline. Once added, your sound will be visible on the timeline in waveform. (see figure)
If you need to stop an event sound you can do this by placing an instance of the sound at the specific keyframe in which the sound should stop and select the Stop Sync option for the keyframe. This will also stop all instances of that particular sound.
In a Flash movie, several sound layers can be played by the Flash Player at one time. Flash acts like a sound mixer by mixing the sound layers as separate channels. It is important to keep this in mind when adding multiple sound layers, as this may greatly increase your file’s size and slow down the performance of your computer.