OpenLLM-France/wikimedia huggingface dataset:
# Principles of Economics/Liquidity trap

Normally, monetary policy works because a change in the money supply changes interest rates, which then goes on to change most other things in the economy. However, there is a possibility that in certain situations, most often during financial crises (especially banking crises), an economy may enter a liquidity trap, in which an increase in the money supply does not further lower the interest rate. The demand for money is so responsive, or elastic, that it completely consumes all the additional money, without helping to boost the economy. In this situation, monetary policy is futile (unless it is practiced at a point above (to the left of) the liquidity trap, which would be even worse for the economy).
Beyond a certain point (the liquidity trap line), L(r,y), the money demand, becomes perfectly horizontal. Shifts in (M/P)S, the money supply, in this area have no effect on interest rate r. This is what the diagram shows.
# Principles of Economics/Money
## Definitions of Money

Economists use multiple definitions of money. By far the most important are:
* Monetary base (MB)
** "high-powered money"
** stricter definition of money
** consists of all currency (C) and reserves (R)
** note that this is the actual extant money
* Money type 1 (M1)
** "money in the economy"
** consists of all currency (C) and deposits (D)
** standard definition of money
** note that this is the amount of money that influences the well-being of the economy
These definitions of money are very confusing.
When customers deposit money in banks, the banks keep a certain small portion as reserves (R) and hold onto it for when customers withdraw. The remaining deposited money is then lent out to others, who, upon having that money, deposit into banks, who lend a fraction of that, and so on. Eventually, this cycle involves infinitesimally small amounts of money, so the cycle actually does come to an end, based on the basic geometric series rule:
    $(r)^{1}+(r)^{2}+(r)^{3}+...={\frac {1}{1-r}}$
where
* r is the portion of money that banks lend out
The result is that the economy is working with more money than really exists, because firms and individuals can still work with abstract money such as loaned money. This is the principal way in which banks "make money".

## Equations

Monetary Base = Non Borrowed Monetary Base + Discount Loans
Monetary Base (MB) * Money base money multiplier (m) = M1
Monetary Base = "High-powered money" = Currency (C) + Reserves (R) = Currency (C) + (Deposits (D) * Required Reserve Ratio (r))
(Contrast with M1, which is Currency + Deposits)
# Principles of Economics/Labor Production
## Marginal product of labor

In firms, people start off rather productive, but as more people are added, specialization occurs, with the result that the marginal product of labor (the next worker's labor productivity) increases. After the critical point at which this has reached its maximum, the MPL begins to decline as additional workers become less productive. In the short run this is most acute, where a constant amount of available capital limits productivity. After a certain point, adding workers begins to reduce overall (total) productivity; this is reflected by a negative MPL.

## Firms' production frontier

The gold line is the typical firm's production frontier. It is the sum of each worker's marginal productivity (taking the integral of MPL from 0 to L). At first the production frontier increases faster, then it increases slower, then it stops increasing, before beginning a decline (which should never happen if the firm is money-conscious).

## Isoprofit lines set

Isoprofit lines are lines composed of amounts of labor and its total output that yield the same amount of profit for the firm. There are an infinite number of isoprofit lines, one above another, similarly to how there are an infinite number of indifference curves. The isoprofit line that is tangent to the production frontier is also the highest isoprofit line that the firm can reach.

## Isoprofit lines part 2

There are a variety of isoprofit lines that may be drawn. Realistically, their slopes will be flatter than the ones shown here, and their y axis will be higher.
The slope is equal to wage divided by price of output.
The y intercept is profit divided by price of output.
# Principles of Economics/Labor Supply

This supply curve shows how the change in real wage rates affects the number of hours worked by employees.
Referring to the graph, if real wages were to increase from W1 to W2 then the worker will obtain a greater utility, due to their higher income. Therefore, they would be willing to increase their hours worked from L1 to L2. Note that this may be hours worked per day, month, year or even lifetime. Over this section of the curve the substitution effect is positive while the income effect is negative. However, the substitution effect is greater than the income effect. Therefore, the increase in the real wage rate will cause an increase in the number of hours worked.
However, if the real wage increased from W2 to W3, then the number of hours worked per year would fall from L2 to L3. This is because the income effect has now become greater than the substitution effect. This is because utility gained from an extra hour of leisure is greater than the utility gained from the income earned working. Beyond this point, workers have reduced incentives to work because they are already being paid enough to sustain their current lifestyle without having to work more hours, therefore creating the backwards bend in the curve.
# Principles of Economics/List Of Contributors

* Endless melee
* Yunzhong Hou
* BU Rob13
# Principles of Economics/Monetary Policy

There are four major components to Monetary policy, the decision of how much money is to be made available to the economy. All of them are controlled in part by the Central Bank:

## Setting the required reserve ratio

Banks can only lend out a (albeit large) portion of the deposits consumers make to them. A few percentage points are generally required to be held on hand so that consumers making withdrawals will be able to get their money and to prevent infinite money multipliers perpetuated by unscrupulous and risky banking procedures. The Required Reserve Ratio (r) limits the amount of money available in the economy by preventing banks from creating more money than the Central Bank desires.

## Setting the discount window lending rate

The Discount Window Lending Rate is the rate at which the Central Bank makes loans exclusively to other registered banks in times of financial and banking instability. Use of the discount window is generally frowned down upon by the general populace and any banks using it (without the backing of moral suasion, see below) will suddenly find stock shares plummeting due to a greatly reduced confidence due to a historical savings-and-loans crisis involving weak banks using the discount window. The discount window's rate is determined by the Central Bank; an announcement of an increase in the rate would mean fewer banks obtaining money through that means, less money for the economy, and shrinkage, while an announcement of a decrease in the rate would pump more money into the economy.

## Open market operations

The Central Bank may also buy and sell securities to and from the public and banks in what is known as Open market operations. If it buys securities, its money is entered into the economy, hence allowing for more transactions to be made. If it sells securities, it takes money out of the economy, slowing it down.

## Moral suasion

This method involves encouraging people to take certain actions that have certain effects on the economy. This is generally the one with the least determinate effect and is heavily laden sociologically.
# Principles of Economics/Money Supply
## Money

The money system is a significant improvement over the barter (item for item) system because while the former allowed trading between anyone who cared for money, the latter could only take place between parties with nearly equivalent marginal benefits of all traded goods (or otherwise, one side would be unwilling to make the trade). Money serves several purposes:
* Medium of exchange - as an object that is generally accepted as a form of payment, thereby increasing market flexibility
* Unit of account - a means of keeping track of how much something is worth (in barter systems, it becomes difficult to see how much a traded item is being traded for in terms of worth)
* Store of value - can be held and exchanged later for goods and services, at an approximate (though slowly changing) value
Money is in two forms:
* Currency C - circulating money
* Deposits D - placed in banks and other depository institutions
** Reserves R - the fraction of deposits that banks are required to hold on to

## Money Supply

The money supply is the amount of M1 in the economy (the effective money). The supply of money is determined by the Central Bank through 'monetary policy; the economy then has to make do with that set amount of money. Since the economy does not influence the quantity of money, money supply is considered perfectly vertical (on models).

### Consequences of changing the Money Supply

* Since increasing the money supply can affect AD, then ceteris paribus (cp.) inflation in prices will result at the same time as an increase in output, as can be shown on any supply and demand diagram. A central bank must decide whether the benefits of demand-side economic growth outweigh the costs of potential demand-pull inflation.
* This resultant inflation could cause the currency to depreciate against others, as fewer goods and services can be bought for the same nominal amount of money. This means that the exchange rate is lower, increasing the price of imports and increasing the competitiveness of exports with their associated effects on the economy!

## Money Circulation

The equation MV = PY can be roughly translated as money supply times how fast it cycles through the economy (in a given time period) equals the output of the economy (in a given time period) times the price index. Both sides of the equation reflect the amount of money being used over the course of a period of time. An increase in the money supply (M) means that there will be more money being used by the economy; an increase in the velocity of money (V) means that this money goes through the economy faster (recycles into different hands faster), thereby seeming to increase the money supply. The output (Y) is the amount of goods produced in the economy over the period of time; multiply this by the price index (P) and one obtains the total price of all goods produced. This must equal the amount of money being used over that period of time; otherwise, some production would not have occurred.
# PSP/Homebrew releases

This page is a timelined list of homebrew releases and updates, used for the "Latest homebrew releases" section on the Homepage.

## Adding an item

* Log in to Wikibooks. Editing is disabled if you don't have an account.
* Add your application to the top of the list, using the following format. Please include the application's creator, version number, and a link to a page on this wikibook about the application.
** Format: '''YYYY/MM/DD:''' [[<Application>]] released by [[User:<Author>|<Author>]].
** Example: '''11 October 24:''' [[RockPaperScissors64]] 1.2 released by [[User:DevDude|DevDude]]
* There should not be more than one entry at a time for any specific app. If there is an update, remove the older one from the list rather than another app.

## Releases

* 2015/01/21 - In response to the release of firmware 6.61, Quikrazor updates ME/LME CFW to 6.61, and works with The Zett to update PRO CFW.
* 2014/12/14 PSP ME/LME Rev 2.3/10.3 released by Rahim-US. This adds full 64MB support on PSP games (2000/3000 only) .DAX format support, and PRO-Online support for ME.
* 2013/02/13: 6.60 PRO-C2 released by the PRO Team.
# PSP/Install 6.60 PRO

* Download 6.60 PRO-C.
* Extract the file.
* Copy the contents of the extracted folder into the root of the Memory Stick (ex. PSP -> ms0:\PSP, seplugins -> ms0:\seplugins)
* From the XMB (main psp menu), run PROUPDATE from Game - Memory stick.
* Press X to install CFW.
# PSP/Install 6.20 PRO

* Download 6.20 PRO-C.
* Extract the file.
* Copy the contents of the extracted folder into the root of the Memory Stick (ex. PSP -> ms0:\PSP, seplugins -> ms0:\seplugins)
* From the XMB (main psp menu), run PROUPDATE from Game - Memory stick.
* Press X to install CFW. You have now installed Temporary 6.20 PRO CFW.
* To install permanent CFW, run 620 PRO-C Permanent Patch.
* Press X to start installation. It will ask you to test the system before installing; Press X.
* If there were no problems, run 620 PRO-C Permanent Patch again. Press X to start, but press O to skip test mode.
* On the root of your Memory Stick, a vshorig.prx file has been created. Do not ever delete it; you will need this file to uninstall 6.20. Back it up somewhere safe on your computer, in case your memory stick fails.
* You have now installed Permanent 6.20 PRO CFW.
# PSP/Homebrew List

This is a list of the best PSP homebrew to have ever been created.

## Homebrew Games

* Doom :P (A classic)
* Wagic
* Lamecraft
* Cave Story
* PSP Revolution
* Squarez (Move your square to collect points, avoid the enemy squares, fun game :P)
* Pang (Button popping game, also fun :D)
* PSP Revolution (DDR-Clone)
* 48-hour pong (3D Pong game)
* rRootage
* Super Mini Mario (Interesting mario clone, able to create your own levels)
* Webfest
* Best Homebrew Games
* OpenTTD - Never updated since 1.50.

### Visual Novels

* ONScripter (needs source code refactoring)
** Translations by dsoul (CLANNAD only works on Slim)

### Unfiled Emus

* SNES9XTYL Source Code

## UMD Toolkits

* UMD Killer
* UMD Disc Changer - For games with multiple discs.

## Miscellaneous

* PXDrum

## Sources

* Popopola's List of Recommended Homebrew
* PSP-Hacks
# PSP/Install 6.20 OFW

* Download OFW 6.20 (use this version for PSP Go), and extract the file.
* Copy EBOOT.PBP to PSP/GAME/UPDATE/
* From the XMB (main psp menu) run the update from Game –> Memory Stick.
* You have successfully installed OFW 6.20.
# PSP/Install LME CFW

* Download LME 1.8, and extract it.
* Copy the entire contents of the extracted folder to the root of the memory stick.
* Go to Game -> Memory Stick and run the LME Installer for 660.
* Press X to install. Your PSP will then restart.
* Go to Game -> Memory Stick and run the LME Launcher for 660. Your PSP will restart, again.
* 6.60 LME is now installed on your PSP.
* Once your PSP completely runs out of power, custom firmware will be uninstalled.
* Now just run LME Launcher for 660 to restore it.
# DESCRIPTION:

Returns the UTF encoding from the BOM (byte order marker): + for BE; - for LE.
UTF? is a function value.

# ARGUMENTS

* data -- (Type: binary)
# DESCRIPTION:

Defines words local to a block.
USE is a native value.

# ARGUMENTS

* words -- Local word(s) to the block (Type: block word)
* body -- Block to evaluate (Type: block)
# DESCRIPTION:

Returns TRUE if the word has been set.
VALUE? is a native value.

# ARGUMENTS

* value -- (Type: any)
# DESCRIPTION:

Returns a copy of the values of an object.
VALUES-OF is a function value.

# ARGUMENTS

* value -- (Type: any)
# DESCRIPTION:

(undocumented)
VBUG is a function value.

# ARGUMENTS

* msg -- (Type: block any-string)
# DESCRIPTION:

Displays a window face.
VIEW is a function value.

# ARGUMENTS

* view-face -- (Type: object)

# REFINEMENTS

* /new -- Creates a new window and returns immediately
* /offset
** xy -- Offset of window on screen (Type: pair)
* /options
** opts -- Window options [no-title no-border resize] (Type: block word)
* /title
** text -- Window bar title (Type: string)
# Rebol Programming/view-root

VIEW-ROOT is a file of value: %/c/documents%20and%20settings/max/dati%20applicazioni/rebol/

# NOTE

It's a path set by Rebol, depending on OS type (Linux, Windows, Mac, ...) and user folder.
# Rebol Programming/user-prefs

USER-PREFS is an object of value:
# Rebol Programming/view-prefs

VIEW-PREFS is a none of value: none
# Linear Algebra/Basis Vectors
## Definitions

A basis of a vector space V is a set of vectors which have the following properties:
* They are linearly independent.
* Their linear combinations build up every vector of V.
A vector space is of dimension d if there exists d linearly independent vectors and that any d+1 vectors are linearly dependent.

## Remarkable theorems
### Theorem

In a vector space of dimension d, any d linearly independent vectors form a basis for that vector space.

#### Proof

Let there be d vectors. Let x be another vector. Then those d vectors and x are linearly dependent, so x is linearly dependent on those d vectors. Hence, those d vectors form a basis.

### Theorem

If a vector space has d vectors for a basis, then it is of dimension d.

#### Proof
### Theorem (completion)

If you have m linearly independent vectors in a vector space of dimension n (with m<=n), then you can choose n-m vectors which form a basis of the vector space along with the starting m vectors.

#### Proof

Those m vectors do not form a basis since it is not equal to n, so there exists a vector in the vector space linearly independent of them. Continuing choosing vectors independent of the previous ones in this fashion until one has n vectors.
# Linear Algebra/Augmented Matrices

The Augmented matrix is a Matrix that is constructed by combining both the Coefficient matrix and a vector which might represent the solution for the system of equations. Or can be constructed by combining two matrices. But an important rule must be taken in consideration the two matrices must have the same number of rows. For example if we have a matrix of size (m x n) matrix we should have another matrix of size (m x k) where n is a positive natural number.
$A_{(mxn)}={\begin{bmatrix}a11&a12&.&.&.&a1n\\a21&a22&.&.&.&a2n\\.&.&.&.&.&.\\.&.&.&.&.&.\\.&.&.&.&.&.\\am1&am2&.&.&.&amn\end{bmatrix}}$
$B_{(mxk)}={\begin{bmatrix}b11&b12&.&.&.&b1n\\b21&b22&.&.&.&b2n\\.&.&.&.&.&.\\.&.&.&.&.&.\\.&.&.&.&.&.\\bm1&bm2&.&.&.&bmn\end{bmatrix}}$
The Augmented matrix (A|B) in this case will be:
$(A|B)={\begin{bmatrix}a11&a12&.&.&.&a1n\\a21&a22&.&.&.&a2n\\.&.&.&.&.&.\\.&.&.&.&.&.\\.&.&.&.&.&.\\am1&am2&.&.&.&amn\end{bmatrix}}\quad {\Bigg |}\quad {\begin{bmatrix}b11&b12&.&.&.&b1n\\b21&b22&.&.&.&b2n\\.&.&.&.&.&.\\.&.&.&.&.&.\\.&.&.&.&.&.\\bm1&bm2&.&.&.&bmn\end{bmatrix}}$
Also if we have a system of equations we can express it as an augmented matrix which makes it easier to work with. And, this becomes very useful when we have systems that have relatively large dimensions, for Example:
$2x+3y+4z=9\,$ $3x+5y+8z=21\,$ $4x+9y+z=17\,$
Can Be Expressed as the following augmented matrix:
${\begin{bmatrix}2&3&4\\3&5&8\\4&9&1\end{bmatrix}}{\Bigg |}{\begin{bmatrix}9\\21\\17\end{bmatrix}}$
Finally, the augmented matrix is very useful when it comes to solving systems, finding the inverse of a matrix, etc...
# Linear Algebra/Automation

This is a PASCAL routine to do $k\rho _{i}+\rho _{j}$ to an augmented matrix.
Of course this is only one part of a whole program, but it makes the point that Gaussian reduction is ideal for computer coding.
There are pitfalls, however. For example, some arise from the computer's use of finite-precision approximations of real numbers.
These systems provide a simple example.
(The second two lines are hard to tell apart.) Both have $(1,1)$ as their unique solution.
In the first system, some small change in the numbers will produce only a small change in the solution:
    ${\begin{array}{*{2}{rc}r}x&+&2y&=&3\\3x&-&2y&=&1.008\end{array}}$
gives a solution of $(1.002,0.999)$. Geometrically, changing one of the lines by a small amount does not change the intersection point by very much.
That's not true for the second system. A small change in the coefficients
    ${\begin{array}{*{2}{rc}r}x&+&2y&=&3\\1.000\,000\,01x&+&2y&=&3.000\,000\,03\end{array}}$
leads to a completely different answer: $(3,0)$.
The solution of the second example varies wildly, depending on a $9$-th digit. That's bad news for a machine using $8$ digits to represent reals. In short, systems that are nearly singular may be hard to compute with.
Another thing that can go wrong is error propagation. In a system with a large number of equations (say, 100 or more), small rounding errors early in the procedure can snowball to overwhelm the solution at the end.
These issues, and many others like them, are outside the scope of this book, but remember that just because Gauss' method always works in theory and just because a program correctly implements that method and just because the answer appears on green-bar paper, doesn't mean that answer is right. In practice, always use a package where experts have worked hard to counter what can go wrong.
# Linear Algebra/Basis and Dimension

The prior section ends with the statement that a spanning set is minimal when it is linearly independent and a linearly independent set is maximal when it spans the space. So the notions of minimal spanning set and maximal independent set coincide. In this section we will name this idea and study its properties.
# Linear Algebra/Appendix

Mathematics is made of arguments (reasoned discourse that is, not crockery-throwing). This section is a reference to the most used techniques. A reader having trouble with, say, proof by contradiction, can turn here for an outline of that method.
But this section gives only a sketch. For more, these are classics: Methods of Logic by Quine, Induction and Analogy in Mathematics by Pólya, and Naive Set Theory by Halmos. Reader can also read the wikibook Mathematical Proof.
# Roulette
## Contents

* History of Roulette
* Game Mechanics
** Table Layouts (American, European, etc)
** Wheel Layouts
** Non-Mechanical Random Number Generators, and how they relate
* Statistical Systems
** Progressive
** Regressive
** Other Systems
* Mechanical Systems
* Math & Probability – the man behind the curtain
* Famous Stories, Myths, and Urban Legends
* Changing the Odds - cheating, biased wheels, etc
* Appendices
** Online Casinos
** Outside Links
# Rotorcraft Fundamentals

Rotorcraft Fundamentals is designed as a technical manual for applicants who are preparing for their private, commercial, or flight instructor pilot certificates with a helicopter or gyroplane class rating. Certificated flight instructors may find this handbook a valuable training aid, since detailed coverage of aerodynamics, flight controls, systems, performance, flight maneuvers, emergencies, and aeronautical decision making is included.

## Table of Chapters

* Introduction to the Helicopter
* General Aerodynamics
* Aerodynamics of Flight
* Helicopter Flight Controls
* Helicopter Systems
* Helicopter Flight Manual
* Weight and Balance
* Performance
* Basic Flight Maneuvers
* Advanced Flight Maneuvers
* Helicopter Emergencies
* Attitude Instrument Flying
* Night Operations
* Aeronautical Decision Making
* Introduction to the Gyroplane
* Aerodynamics of the Gyroplane
* Gyroplane Flight Controls
* Gyroplane Systems
* Gyroplane Flight Manual
* Flight Operations
* Gyroplane Emergencies
    Glossary
    Index

## Sources

The majority of the text, diagrams, and pictures in this book have been taken from:
| [FAA: Rotorcraft] | U.S. Department of Transportation, Federal Aviation Administration Rotorcraft Flying Handbook. Public Domain. |

## References

The authors highly recommend the following reference materials:

## Contributors

HaugenHaus A large portion of my contribution was to adapt the print version of [FAA: Rotorcraft] to use as a wikibook.