OpenLLM-France/wikimedia huggingface dataset:
# Pharmacology/Cough Suppressants
## Pharmacology of Nasal Decongestants

Nasal decongestants work by narrowing the blood vessels that are present in the nose. By doing this, it reduces the amount of blood that flows through the nasal cavity so that the swollen tissues shrink in order to allow more air to pass through this area. The majority of decongestants function by increasing the amount of norepinephrine and epinephrine. This is done by stimulating the alpha-adrenergic receptors, which is a class of G protein-couple receptors that are targeted by catecholamines. By doing this, the blood vessels in the nose, throat, and sinuses vasoconstrict and reduces the swelling of the tissues and mucus in these areas. The main ingredients used in decongestants are pseudoephedrine or phenylephrine. Because these ingredients cause vasoconstriction of the blood, people with high blood pressure are not recommended to take this medicine. Other side effects of these chemicals include anxiety, drowsiness, nervousness, and excitability. Common names found in over-the-counter drug stores for decongestants include Sudafed, Afrin, Mucinex, Zicam, and Claritin.

## References

Johnson DA. The Pharmacology of alpha-adrenergic decongestants. 1993, Pharmacotherapy. p. 110s-115s.
# XForms/Inline Repeats
## Motivation

Most computer displays are wider than they are high. So to take advantage of this you sometimes want to grow form data to the right, not down. To do this you must add CSS instructions to use an "inline" display for items within a repeat.

## Method

CSS has two "display" options:
* display:block adds new elements vertically so the left edge is aligned.
* display:inline is horizontal placement where new divs gets added to the right just like new text is added to an input field.
The new elements get added to the current row. By default XForms used a block repeat. But this can be easily changed with a two stylesheet command.
In FireFox the class to modify the attributes of the repeated item is .xf-repeat-item. Other XForms players may use a different CSS element.

## Executable XForms Application

Load XForms Application

## Discussion

In the example above we note that the widths of each cell is determined by the size of the label. Each cell can have a different label. Note that we create a wrapper for each cell using a div. Both the cell wrapper and the .xf-fepeat-item must be set to be display:inline.

## Adding Two Dimensional Nesting

You can nest repeat groups to create grids of cells. Just make the outer repeat have class attribute to adjust the line height.

## CSS

The following CSS will be needed to display a each row on a new line:

## Scoreboard Example

The following example shows how you can put text in before and after the inner repeat.

## Repeats into CSS display tables

Get the table to align using CSS.
Here is an example:
# The Seven Wonders of the World/The Pharos

The Seven Wonders of the World
The Pharos, also known as the lighthouse of Alexandria was a large lighthouse that served as a navigational aide for ships entering the city. The precise height of the lighthouse is not known, but it is estimated by scientists and archeologists to have been between 115 meters and 180 meters tall. The top end of that estimate would have the lighthouse being taller than the great pyramid and therefore the tallest building in the ancient world. The lower end of the estimation, 115 meters, would have been the third largest building in the world, after the great pyramid and the pyramid of Khafra.
The Lighthouse was built on a small island known as Pharos off the coast of Alexandria. The island was connected to the mainland by a man-made connector that formed one side of the Alexandrian harbor. Because the egyptian coast line was so flat and featureless, the lighthouse was an important navigational aide for sailors.
The structure was originally designed as being simply a tall tower to serve as a marker, but fire and mirrors were added to make it a true lighthouse in the first century BCE.
Earthquakes in 1303 and 1323 CE turned the lighthouse into a ruin. In 1480 Qaitbay the sultan of Egypt built a medieval fort on the former location of the building, using some of the fallen stone. The remnants of the Pharos that were incorporated into the walls of Fort Qaitbey are clearly visible due to their excessive size in comparison to surrounding masonry.
# Artificial Neural Networks/Committee of Machines

Artificial neural networks can have very different properties depending on how they are constructed and how they are trained. Even in the case where two networks are trained on the same set of input data, different training algorithms can produce different systems with different characteristics. By combining multiple ANN into a single system, a committee of machines is formed. The result of a committee system is a combination of the results of the various component systems. For instance, the most common answer among a discrete set of answers in the committee can be taken as the overall answer, or the average answer can be taken.
Committee of machines (COM) systems tend to be more robust than the individual component systems, but they can also lose some of the “expertise” of the individual systems when answers are averaged out.
# Analog and Digital Conversion/Delta Modulation
## Delta Modulation

The sample values of analog waveforms of real world processes are very often predictable—i.e. the average change from sample to sample is very small. Hence we can make "educated guess" of what the next sample value depending on the current sample value. Though there is error, it is much less than peak to peak signal range. This concept is used in Predictive coded modulation, where instead of sending the signal, it transmits just the prediction errors. Delta Modulation employs Predictive coded modulation to simplify hardware
Delta Modulation is strange in the fact that it attempts to represent an analog signal with a resolution of 1 bit. This is accomplished by successive steps, either up or down, by a preset step size. In delta modulation, we have the stepsize (Δ) that is defined for each sampler, and we have the following rules for output:
* If the input signal is higher than the current reference signal, increase the reference by Δ, and output a 1.
* If the input signal is lower than the current reference signal, decrease the reference by Δ, and output a 0.
Some benefits of delta modulation are as follows:
* 1 bit of resolution, and therefore requires very little bandwidth and very little hardware.
* No preset upper or lower bounds, so Delta modulation can (theoretically) be used to modulate unbounded signals.
These benefits are countered by the problems of Slope Overload, and Granular Noise, which play an important role when designing a Delta Modulated system.

## Slope Overload

If the input signal is rising or falling with a slope larger than Δ/T, where T is the sampling time, we say that the sampler is suffering from Slope Overload. In essence, this means that in a Delta Modulation scheme, we can never have slopes larger than a certain upper limit, and functions that rise or fall at a faster rate, are going to be severely distorted. If the slope of m(n Ts) is greater than the slope of m(n Ts- Ts), then Slope Overload distortion occurs.

## Granular Noise

A problem with delta modulation is that the output signal must always either increase by a step, or decrease by a step, and cannot stay at a single value. This means that if the input signal is level, the output signal could potentially be oscillatory. That is, the output signal would appear to be a wave, because it would go up and down regularly. This phenomena is called Granular Noise.
When used in ADCs (Analog to Digital Converters), this problem can be solved by internally adding additional bit(s) of resolution that correspond to the value of Δ. This way, the LSBs (Least significant bits) that were added can be ignored in the final conversion result.

## Delta-Sigma Modulation

A delta-sigma ADC—also called a sigma-delta ADC—use the delta modulation technique internally.

## Further reading

* Continuously-Variable Slope Delta Modulation
# AQA A-Level Physics/Particles and Anti-particles/Creation and annihilation

All particles have a corresponding anti-particle, which has equal mass and opposite charge. For example the positron, the anti particle of an electron, is exactly the same as an electron but with a positive charge. A particle and its corresponding anti particle are created through pair production and destroyed through annihilation. This theory comes from Einstein's 'Special theory of Relativity' through which mass can turn into energy and energy into mass. The equation is E=MC$^2$.

## Pair Production

Pair production is a process which happens when a gamma ray photon splits into a particle and an antiparticle, this will only happen if the photon has enough energy to produce the mass of the two particles, the equation used to determine whether the photon pair has the energy required to form different particles is E=mc² (this being discovered by Einstein). Along with this, if the energy transferred is greater than the rest mass of the particle been created, then this spare energy is transferred in to kinetic energy. This usually occurs near a nucleus, which helps to conserve the momentum of the gamma ray photon. Electron-Positron pairs are produced more often than any other pairs as they have relatively low masses.

## Annihilation

The opposite of Pair Production is Annihilation. When a particle meets its equivalent anti particle (eg. an electron colliding with a positron) the two, having exact opposite charges are automatically destroyed. All the mass that has been destroyed in this process is changed into energy in the form of two or more gamma ray photons.
# French/Lessons/Rêveries du promeneur solitaire

* Slavery under Napoleon
* Algerian War of Independence
* Candide, (ou l'Optimisme)
* Rêveries du promeneur solitaire
* Boule de Suif
* Les Fleurs du Mal
* Demain, dès l'aube
* Agreement of past participles with avoir
Lessons · Vocabulary · Grammar · Appendices · Texts
Vous retrouverez le texte entier des Rêveries du promeneur solitaire sur Wikisource.
Me voici donc seul sur la terre, n'ayant plus de frère, de prochain, d'ami, de société que moi-même. Le plus sociable et le plus aimant des humains en a été proscrit. Par un accord unanime ils ont cherché dans les raffinements de leur haine quel tourment pouvait être le plus cruel à mon âme sensible, et ils ont brisé violemment tous les liens qui m'attachaient à eux. J'aurais aimé les hommes en dépit d'eux-mêmes. Ils n'ont pu qu'en cessant de l'être se dérober à mon affection. Les voilà donc étrangers, inconnus, nuls enfin pour moi puisqu'ils l'ont voulu. Mais moi, détaché d'eux et de tout, que suis-je moi-même ? Voilà ce qui me reste à chercher. Malheureusement cette recherche doit être précédée d'un coup d'œil sur ma position. C'est une idée par laquelle il faut nécessairement que je passe pour arriver d'eux à moi.
← Candide ·  Level four lessons  · Boule de Suif →
Slavery under Napoleon · Algerian War of Independence · Candide, (ou l'Optimisme) · Rêveries du promeneur solitaire · Boule de Suif · Les Fleurs du Mal · Demain, dès l'aube · Agreement of past participles with avoir
Lessons :
Introductory · Level one · Level two · Level three · Level four
French :
Lessons · Vocabulary · Grammar · Appendices · Texts
# Algebra/Chapter 17/Hyperbolas

Hyperbolas can be thought of as the "opposite" of ellipses - instead of the sum of distances from two foci, the difference is used. This leads to two curves that point in opposite directions. The major axis is 2a units long, and the transverse axis is 2b units long. When a$^2$ + b$^2$ = c$^2$, eccentricity is again c/a. The foci are at either side of the major axis, c units away from the center.
An "east-west" hyperbola is written as:
    ${\frac {\left(x-h\right)^{2}}{a^{2}}}-{\frac {\left(y-k\right)^{2}}{b^{2}}}=1$
while a "north-south" one is written as:
    ${\frac {\left(y-k\right)^{2}}{a^{2}}}-{\frac {\left(x-h\right)^{2}}{b^{2}}}=1$
For rectangular hyperbolas with the coordinate axes parallel to their asymptotes:
As the curve progresses, it gets closer and closer to two lines called asymptotes. In the second image, the asymptotes are y = ±x. The length of each latus rectum is (..?)
# Algebra/Chapter 5/Exercises

A set of exercises related to concepts from Chapter 5.
This set contains 8 exercises (including the Conceptual Questions)

## Exercises
### Section 5.1

5.1 (Identifying Quadrants) Look at the diagram below, and identify the quadrant each point is located on.
5.2 (Determining Quadrants) Determine the quadrant that each point is located on.
1. (-95, 200)
5.3 (Plotting Coordinates) Draw a coordinate plane, and then graph the following points.

### Section 5.4

5.4 (Using Bar Graphs) Look at the diagram below, and use it to answer the following questions.
5.5 (Using Multibar Graphs) Look at the diagram below, and use it to answer the following questions.
5.6 (Using Line Graphs) Look at the diagram below, and use it to answer the following questions.
5.7 (Creating a Bar Graph) Look at the table below, and use it to create a bar graph.
5.8 (Sky High) The table below shows the altitude each of the cloud types are found at. Graph the numbers on the vertical number line below.
# Algebra/Chapter 15/Geometric Progression (GP)

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2.
Example 1:
A classical example of geometric progression (GP) is population growth. Say the population doubles every 15 years. If the population is 7 billion in 2012, the population in 2027 will be 14 billion.
Since we know that the population doubles ever 15 years, this means from 7 billion in 2012 to 2027 (15 years later) is 14 billion because: $7\cdot 2=14.$
So what will be the population in 2042? If you said 28 billion, you are correct. So how did you get 28? You multiplied 14 by common ratio of 2 to get 28. So to get next term of GP you always multiply the common ratio to current term, and to get previous term you always divide the current term by common ratio.
A more general formula to get the ‘n’th term of a GP is: $a_{n}=a_{1}r^{n-1}$
Where $a_{1}$ is the first term and r is the common ratio of the GP.
So the general terms of GP are:
$a_{1},\;a_{1}r,\;a_{1}r^{2},\;\dots \;a_{1}r^{n-1}$

### Finding the sum of ‘n’ terms of an geometric sequence

When needed to find the sum of ‘n’ terms of a GP whose first term is $a_{1}$, you use:
If |r| < 1 then use: $s_{n}=a_{1}{\frac {(1-r^{n})}{(1-r)}}$
If |r| > 1 then use: $s_{n}=a_{1}{\frac {(r^{n}-1)}{(r-1)}}$

## Notes

* The sum of infinite geometric sequence with |r| > 1, is essentially infinite.
* The sum of infinite geometric sequence with |r| < 1, is $s_{n}={\frac {a_{1}}{(1-r)}}$
# Algebra/Chapter 16/Probability

Probability is the chance that something will occur. For example, what are the chances that two dice rolled will equal 7? To solve this, a chart can be made of all the pairs of the integers {1, 2, 3, 4, 5, 6} that add up to 7.
* 1 + 6
* 2 + 5
* 3 + 4
* 4 + 3
* 5 + 2
* 6 + 1
note that the first three seem to be the same as the second three. This is because there are two dice, so when the first die gets number X and the second gets Y, it's a different outcome than the first being Y and the second X.
Next, we find out how many possibilities there are in total.
6 possibilities for the first die * 6 possibilities for the second = 36 combinations.
Since 6 out of the 36 combinations add up to 7, the answer is 1/6 or 16.6666666...% or 0.166666666... Usually, probabilities are measured in the first or second way.

## Ratios

Quite often, ratios are used to show the probability of an event occurring compared to another event. Be careful! The ratio of heads to tails is 1:1 or 1/1, but the probability of heads is 1:2 or 1/2. Don't confuse these two ways of writing the same thing.
# Algebra/Chapter 17/Circles
## Building a Circle

A circle is defined as the set of points that are a fixed distance from a center point. This definition is expressed in the way we draw circles. We pick a point as the center and then use some mechanical means to rotate a drawing utensil around that point. Of course our drawings are always approximations of the shape we think of as a circle. Drawings are only as accurate as the hardness and thickness of our tools will allow. For instance if you blow the drawing below up large enough on your computer screen you might see it is composed of adjacent colored squares and rectangles on your screen. If you used software that maintained the scale of the points as you magnified the circle then eventually it would start to look like a line. This is the reason that we perceive roads as being straight even though we know the Earth is round.
Still using this drawing We know that the equation for distance is $d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}$. To make the calculations easy let's let point $(x_{1},y_{1})=(0,0)$.
As you likely have learned before, a circle is defined as any set of points that is a fixed distance (the radius) from a fixed point (the center). To find a formula for this, suppose that the center is the point (a,b). According to the distance formula, the distance c from the point (a,b) to any other point (x, y) is:
$c^{2}=(x-a)^{2}+(y-b)^{2}$
By definition, a circle is the set of all points for a given value of c. We call this r and come up with the following equation for a circle:
$\left(x-a\right)^{2}+\left(y-b\right)^{2}=r^{2}.$
# Algebra/Chapter 17/Ellipses

An ellipse is the collection of points that are equidistant from two points, called foci (singular focus).
The foci are found on the major axis, which has a length of 2a. The minor axis is 2b, and is smaller.
The "roundness" or "longness" of an ellipse can be measured by eccentricity. If c is the distance from the center to a focus, then e = c / a.
The latus rectum is a line parallel to the minor axis that crosses through a focus. Its length is b$^2$ / a.
"Long" ellipses are generally written as
    ${\frac {(x-h)^{2}}{a^{2}}}+{\frac {(y-k)^{2}}{b^{2}}}=1$
where (h,k) is the center, while "tall" ellipses are written as
    ${\frac {(y-k)^{2}}{a^{2}}}+{\frac {(x-h)^{2}}{b^{2}}}=1$
# Algebra/Chapter 7/Graphing Systems of Inequalities

$^{Superscripttext}$

## Inequalities in 2 variables

Linear inequalities in 2 variables are typically in the form of $y<mx+b\!\$, where m is the slope of the line and b is the y-intercept.
Graphing an inequality is easy. First, graph the inequality as if it were an equation. If the sign is ≤ or ≥, graph a normal line. If it is > or <, then use a dotted or dashed line. Then, shade either above or below the line, depending on if y is greater or less than mx + b.

## Example: Highway and City Gas Mileage

* The gas mileage sticker on cars gives two numbers: one for city driving, and one for highway driving. If a sticker says the car gets 25 mpg in the city and 32 mpg on the highway how far can you drive?
* The abbreviation mpg stands for miles per gallon. The sticker on our car predicts that we get between 25 and 32 mpg, but when we drive our car we estimate how far we are going and how much gas we have in our tank. When we graph we need to change our inequality to a function where x is the number of gallons of gas in our tank.
* 25x < f(x) < 32x.
* The picture on the left has two lines one for y=25x and one for y = 32x. The yellow portion of the picture represents how far we may be able to drive when we have x gallons of gas. The vertical line at 10 shows us that we can drive between 250 and 320 miles on 10 gallons of gas. The difference between these two numbers is 70. If we drew a line at 1 gallon of gas we would see that we could drive between 25 and 32 miles, and the difference would be 7.
* What this graph shows us is the predicted range of miles we can drive on a given amount of gas. The more gas we have, the more likely our actual mileage is going to be different from what the sticker on our car predicted. If our actual mileage falls outside of this range than we may want to take our car to a mechanic to make sure everything is running correctly on our car. If your mileage is too high the odometer on your car may be broken. If your mileage is too low your car might need a tune up.
# Algebra/Bibliography

* Alexander, Daniel; Koeberlein, Geralyn (1999) "Elementary Geometry for College Students, 2nd Edition", Houghton Mifflin Company
* Carson, Tom (2006) PreAlgebra, Cengage Learning.
* Chrystal, George (1886) Algebra: An Elementary Text-book for the Higher Classes of Secondary Schools and for Colleges
* Courant, Richard; Robbins, Herbert (1978), What is Mathematics?, Oxford University Press.
* Cummings, Jay (2021) Proofs: A Long-Form Mathematics Textbook
* Gonick, Larry (2015) The Cartoon Guide to Algebra
* Liu, Andy (2015) Arithmetical Wonderland, MAA Press.
* Lockhart, Paul (2017) Arithmetic, Harvard University Press.
* Millier, Julie (2011) PreAagebra, McGraw Hill.
* Monahan, Chris (2020) Must Know High School Pre-Calculus, McGraw Hill.
* Patrick, David; Rusczyk, Richard (2011) Prealgebra, Art of Problem Solving (AoPS)
* Swokowski, Earl; Cole Jeffery (1997) ' Algebra and Trigonometry with Analytic Geometry, Ninth Edition, Brooks/Cole Publishing Company
* Tussy, Alan S. (2006) PreAlgebra, Cengage Learning.
# Algebra/Chapter 10/Graphing Polynomials

The graph of an equation represents all the points for which that equation are valid. The points where the different graphs intersect show the points that are valid for more than one equation in a system.
For instance figure 1 shows a graph for the parabola $y=-x^{2}+9$.
Table for various values of x and y :
| x | y | x | y |
| -4 | -7 | 4 | -7 |
| -3 | 0 | 3 | 0 |
| -2 | 5 | 2 | 5 |
| 0 | 9 | | |
# Algebra/Chapter 6/Standard Form and Solving Slope
## Standard Form

Standard form is another way to write slope-intercept form (as opposed to y=mx+b). It is written as Ax+By=C where A, B, C are all integers. You can also change slope-intercept form to standard form like this: Y=-3/2x+3. Next, you isolate the y-intercept(in this case it is 3) like this: Add 3/2x to each side of the equation to get this: 3/2x+y=3. You can not have a fraction in standard form so you solve this. 2(3/2x+y)=3(2). To get: 3x+2y= 6. Now you have a standard form equation! However, there are some rules for standard form. A, B, C are integers (positive or negative whole numbers) No fractions nor decimals in standard form. "Ax" term is positive. If these are not followed, it is not standard form. i.e. -1/3x+1/4y=4 is NOT standard form

## Solving Slope
### Solving Standard Form

Slope intercept equations (y=mx+b) are the easiest to graph. So if you encounter an equation in standard form that you are required to graph, you must convert it to slope intercept form. To do this you must take the equation and solve for Y.
Example:
$9x+7y=-3$
$9x-9x+7y=-3-9x$
$7y=-3-9x$
${\frac {7y}{7}}={\frac {-3-9x}{7}}$
$y={\frac {-3}{7}}-{\frac {9}{7}}x$
That is technically slope intercept form, but if you want to make it true (y=mx+b) simply follow the rule of negatives (a - b = a + -b):
$y={\frac {-9}{7}}x+{\frac {-3}{7}}$
Solving an equation in slope-intercept form- how?
If you come upon an equation in slope-intercept form and require it to be in standard form, simply solve for m (c).
Example:
$y=10x+9$
$y-10x=9+10x-10x$
$y-10x=9$
Standard form cannot have fractions. If they are in a fraction, you must multiply each side to get rid of it.
Example:
${\frac {9}{10}}x+9y=5$
$10[{\frac {9}{10}}x+9y]=10[5]$
$9x+90y=50$