OpenLLM-France/wikimedia huggingface dataset:
# Boolf prop/3-ary/twist xors (1, 2)

Number of blocks: 32 Integer partition: 32⋅8
| # | twist xors (1, 2) | block |
| 8 | (0, 0) | [0, 23, 104, 127, 128, 151, 232, 255] |
| 8 | (7, 0) | [1, 22, 105, 126, 129, 150, 233, 254] |
| 8 | (1, 6) | [2, 21, 106, 125, 130, 149, 234, 253] |
| 8 | (6, 6) | [3, 20, 107, 124, 131, 148, 235, 252] |
| 8 | (2, 5) | [4, 19, 108, 123, 132, 147, 236, 251] |
| 8 | (5, 5) | [5, 18, 109, 122, 133, 146, 237, 250] |
| 8 | (3, 3) | [6, 17, 110, 121, 134, 145, 238, 249] |
| 8 | (4, 3) | [7, 16, 111, 120, 135, 144, 239, 248] |
| 8 | (0, 3) | [8, 31, 96, 119, 136, 159, 224, 247] |
| 8 | (7, 3) | [9, 30, 97, 118, 137, 158, 225, 246] |
| 8 | (1, 5) | [10, 29, 98, 117, 138, 157, 226, 245] |
| 8 | (6, 5) | [11, 28, 99, 116, 139, 156, 227, 244] |
| 8 | (2, 6) | [12, 27, 100, 115, 140, 155, 228, 243] |
| 8 | (5, 6) | [13, 26, 101, 114, 141, 154, 229, 242] |
| 8 | (3, 0) | [14, 25, 102, 113, 142, 153, 230, 241] |
| 8 | (4, 0) | [15, 24, 103, 112, 143, 152, 231, 240] |
| 8 | (0, 5) | [32, 55, 72, 95, 160, 183, 200, 223] |
| 8 | (7, 5) | [33, 54, 73, 94, 161, 182, 201, 222] |
| 8 | (1, 3) | [34, 53, 74, 93, 162, 181, 202, 221] |
| 8 | (6, 3) | [35, 52, 75, 92, 163, 180, 203, 220] |
| 8 | (2, 0) | [36, 51, 76, 91, 164, 179, 204, 219] |
| 8 | (5, 0) | [37, 50, 77, 90, 165, 178, 205, 218] |
| 8 | (3, 6) | [38, 49, 78, 89, 166, 177, 206, 217] |
| 8 | (4, 6) | [39, 48, 79, 88, 167, 176, 207, 216] |
| 8 | (0, 6) | [40, 63, 64, 87, 168, 191, 192, 215] |
| 8 | (7, 6) | [41, 62, 65, 86, 169, 190, 193, 214] |
| 8 | (1, 0) | [42, 61, 66, 85, 170, 189, 194, 213] |
| 8 | (6, 0) | [43, 60, 67, 84, 171, 188, 195, 212] |
| 8 | (2, 3) | [44, 59, 68, 83, 172, 187, 196, 211] |
| 8 | (5, 3) | [45, 58, 69, 82, 173, 186, 197, 210] |
| 8 | (3, 5) | [46, 57, 70, 81, 174, 185, 198, 209] |
| 8 | (4, 5) | [47, 56, 71, 80, 175, 184, 199, 208] |
# Boolf prop/3-ary/twist xors (2, 3)

Number of blocks: 8 Integer partition: 8⋅32
| # | twist xors (2, 3) | block |
| 32 | (0, 0) | [0, 15, 23, 24, 36, 43, 51, 60, 66, 77, 85, 90, 102, 105, 113, 126, 129, 142, 150, 153, 165, 170, 178, 189, 195, 204, 212, 219, 231, 232, 240, 255] |
| 32 | (0, 7) | [1, 14, 22, 25, 37, 42, 50, 61, 67, 76, 84, 91, 103, 104, 112, 127, 128, 143, 151, 152, 164, 171, 179, 188, 194, 205, 213, 218, 230, 233, 241, 254] |
| 32 | (6, 7) | [2, 13, 21, 26, 38, 41, 49, 62, 64, 79, 87, 88, 100, 107, 115, 124, 131, 140, 148, 155, 167, 168, 176, 191, 193, 206, 214, 217, 229, 234, 242, 253] |
| 32 | (6, 0) | [3, 12, 20, 27, 39, 40, 48, 63, 65, 78, 86, 89, 101, 106, 114, 125, 130, 141, 149, 154, 166, 169, 177, 190, 192, 207, 215, 216, 228, 235, 243, 252] |
| 32 | (5, 7) | [4, 11, 19, 28, 32, 47, 55, 56, 70, 73, 81, 94, 98, 109, 117, 122, 133, 138, 146, 157, 161, 174, 182, 185, 199, 200, 208, 223, 227, 236, 244, 251] |
| 32 | (5, 0) | [5, 10, 18, 29, 33, 46, 54, 57, 71, 72, 80, 95, 99, 108, 116, 123, 132, 139, 147, 156, 160, 175, 183, 184, 198, 201, 209, 222, 226, 237, 245, 250] |
| 32 | (3, 0) | [6, 9, 17, 30, 34, 45, 53, 58, 68, 75, 83, 92, 96, 111, 119, 120, 135, 136, 144, 159, 163, 172, 180, 187, 197, 202, 210, 221, 225, 238, 246, 249] |
| 32 | (3, 7) | [7, 8, 16, 31, 35, 44, 52, 59, 69, 74, 82, 93, 97, 110, 118, 121, 134, 137, 145, 158, 162, 173, 181, 186, 196, 203, 211, 220, 224, 239, 247, 248] |
# Decimal expansion/Periodic/Newspaper/Exercise

Have you ever seen in a newspaper an expression of the form $2.{\overline {17}}$ (a vinculum to indicate a repeating decimal) or $2.17171717...$? Why not? What kind of decimal expansions occur in a newspaper (in a manual, as a result of a measurement, in a technical description)?
# Riemann mapping theorem
## Introduction

The (small) Riemann Mapping Theorem is a result in Complex Analysis named after Bernhard Riemann.

### History

Bernhard Riemann outlined a proof in 1851 in his dissertation. In 1922, the theorem was finally proven by Lipót Fejér and Frigyes Riesz. A widely used proof today, which employs the Montel's theorem, was given by Alexander Ostrowski in 1929. The Riemann Mapping Theorem has a generalization known as the large Riemann Mapping Theorem.

## Riemann Mapping Theorem

Every Connected space Domain (mathematical analysis) $G\subsetneq \mathbb {C}$ can be mapped biholomorphically onto the Unit circle $\mathbb {D}$.

### Remark - Open Unit Disk

The open unit disk $\mathbb {D}$ is defined as
    $\mathbb {D} :=\{z\in \mathbb {C} :|z|<1\}.$

### Notation - Proper Subset

The notation $G\subsetneq \mathbb {C}$ means “proper Subset,” indicating that the domain $G$ is not equal to $\mathbb {C}$.

### Characterization of Open Sets

An open set in $\mathbb {C}$ can be characterized by the property that every point in it is surrounded by a disk entirely contained within the set. In other words, it consists only of interior points.

### Remark - Biholomorphic

A mapping is biholomorphic if it is holomorphic and its Inverse function also exists and is holomorphic. Such mappings are, in particular, Homeomorphism, i.e., continuous in both directions.

### Simply Connected Domains

From this and using the Riemann Mapping Theorem, it can be concluded that all simply connected domains that are proper subsets of $\mathbb {C}$ are topologically equivalent. In fact, $\mathbb {C}$ itself is also topologically equivalent to these domains.

### Existence of Biholomorphic Mappings

For any point $z$ in the simply connected domain $G$, the following holds:
    There exists exactly one biholomorphic function $h$ from $G$ auf $\mathbb {D}$
mit $h(z)=0$ und $h'(z)>0$.

## Large Riemann Mapping Theorem

The Large Riemann Mapping Theorem, also known as the Uniformization Theorem (proven by Paul Koebe and Henri Poincaré), generalizes the above theorem. It states:
    Every simply connected Riemann surface is biholomorphically equivalent to exactly one of the following surfaces:
* The unit disk $\mathbb {D}$, or the hyperbolic half-plane $\mathbb {H}$ (which is equivalent to it),
* The complex plane $\mathbb {C}$, or
* The Riemann sphere $\mathbb {P} ^{1}(\mathbb {C} ).$.

### Remark - Liouville's Theorem

It is relatively straightforward to see that the three mentioned Riemann surfaces are pairwise not biholomorphically equivalent. A biholomorphic mapping from $\mathbb {C}$ to $\mathbb {D}$ is not possible due to Liouville's Theorem (as a holomorphic function on $\mathbb {C}$ that is bounded must be constant), and the Riemann sphere is compact and therefore not homeomorphic, and hence not biholomorphically equivalent, to $\mathbb {D}$ or $\mathbb {C}$.

### Dependencies of Proofs

It should be noted that the first Riemann Mapping Theorem (or at least its proof ideas) is used in the proof of the Large Riemann Mapping Theorem. Thus, this does not provide an independent derivation of the Riemann Mapping Theorem.
# Permutation/Cycle/Definition

Let $M$ be a finite set and let $\pi$ be a permutation on $M$. Then $\pi$ is called a cycle of order $r$ (or of length $r$), if there exists a subset $Z\subseteq M$, containing $r$ elements and such that $\pi$ is on $M\setminus Z$ the identity and such that $\pi$ commutes the elements of $Z$ in a cyclic way. If $Z=\{z,\pi (z),\,\pi ^{2}(z),\ldots ,\pi ^{r-1}(z)\}$, then we write
    $\pi =\langle z,\pi (z),\,\pi ^{2}(z),\ldots ,\pi ^{r-1}(z)\rangle \,.$
# Complex Analysis/Schwarz's Lemma

The Schwarz Lemma is a statement about the growth behavior of holomorphic functions on the unit disk.

## Statement

Let $\mathbb {D} :=\{z\in \mathbb {C} :|z|<1\}$ be the unit disk, and let $f\colon \mathbb {D} \to \mathbb {D}$ be holomorphic with $f(0)=0$. Then the following hold:
* $|f(z)|\leq |z|$ for all $z\in \mathbb {D}$
* $|f'(0)|\leq 1$
* If $|f'(0)|=1$ or $|f(z_{0})|=|z_{0}|$ for some $z_{0}\in \mathbb {D} \setminus {0}$, then $f$ is a rotation, i.e., there exists a $\lambda$ with $|\lambda |=1$ such that $f(z)={\lambda }z$ for all $z\in \mathbb {D}$.

## Proof

Define $g\colon \mathbb {D} \to \mathbb {C}$ by
$g(z)=\left\{{\begin{array}{rr}\displaystyle {\frac {f(z)}{z}},&z\neq 0\\f'(0),&z=0\end{array}}\right.$
Then $g$ is continuous and therefore, by the Riemann Removability Theorem, also holomorphic. Let $r<1$. By the Maximum Principle, for $|z|\leq r$, we have:
$|g(z)|\leq \max _{|z|=r}|g(z)|={\frac {\max _{|z|=r}|f(z)|}{r}}\leq {\frac {1}{r}}.$
As $r\to 1$, it follows that $|g(z)|\leq 1$, hence $|f(z)|\leq |z|$ for all $z\in \mathbb {D}$, proving the first two statements. If equality holds in either case, then $|g|$ has a local maximum in the interior of $\mathbb {D}$. By the Maximum Modulus Principle, $g$ must be constant. This constant $\lambda$ has modulus $1$, and the claim follows. See Fischer, p. 286.

### See Also

* $\mathrm {Aut} (\mathbb {D} )$ using this lemma.

### Translation and Version Control

This page was translated based on the following Wikiversity source page and uses the concept of Translation and Version Control for a transparent language fork in a Wikiversity:
* Source: Lemma von Schwarz - URL:
https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Lemma_von_Schwarz
* Date: 01/08/2024
# Basic Scratch Coding/Hello World

Hello World is typically one's first program in any programming language, such as Python. In Scratch, however, this is conveyed by the use of sprites (characters), which can be programmed to say and think certain things. In this subpage, we will use this technique in Scratch, with the use of “say blocks”, which are used to make a character say something (in this case Hello World) in a speech bubble.

## Starting Up Scratch

To start up scratch, first open your offline editor (if you have already installed it) or the online editor at https://scratch.mit.edu, and press the “Create” tab on the top of the website, which will automatically create a fresh, new project for you to work on. If you are using the offline editor, open up your app, which will create a project for you straight away. This might take longer on some systems, though.

## Setting Up Your Sprites

For this project, you will only need the basic Scratch cat, which will be there whenever you start up a new project on Scratch. Alternatively, you may also pick a sprite, which can be found by hovering over to the button which has a cat and a plus symbol as a symbol, and then pressing any of the options shown above, depending on what you want to do.
There are four options when it comes to adding sprites into Scratch:
* Surprise – a random sprite which the algorithm chooses from all sprites from its library
* Choose a Sprite – an option which allows you to choose a sprite (character) from Scratch’s library
* Paint – an option which allows you to create a sprite using the in-built editor of Scratch, with either the vector or the bitmap editor
* Upload a Sprite – an option which allows you to upload your own sprites from your computer using an image
You can use any of these options for your sprite, or stick to the basic Scratch cat.

## Creating the Project

You will only require 2 blocks for this simple project, which are the “When green flag clicked” and the “say (text)” blocks, which are in the “Looks” and “Events” tabs respectively. (If you are on Scratch 1.4, the green flag block will be in the “Control” tab.). You only need to combine these two blocks to create this simple program. To do this, click on your current sprite and put the say block underneath it. Next, change the text from “Hello!” to “Hello World!” which will change the text. What does this show? I

## Troubleshooting

Compare your project to the one seen in the image. Are there any problems? Try and troubleshoot them and see where you went wrong. (If you are using the "think blocks", this will not apply.)

## Conclusion

What have you learned from here? Can you apply this project in other programming languages? How would you refine it so you can make it more original? Will you add any more actions? Take some time to think about these questions slowly. Also, take some time to experiment with the code and make it however you want.
# Blockly

Blockly is a client-side JavaScript library for creating visual block programming languages and editors. It is a project of Google and is open-source under the Apache 2.0 License. It typically runs in a web browser, and visually resembles Scratch. Blockly uses visual blocks that link together to make writing code easier, and can generate JavaScript, Python, PHP, Lua or Dart code. It can also be customized to generate code in any textual computer language.
List of Free online Blockly IDE:
* Blockly
* Gameblox
* Micro:bit
* Scratch
* Snap
* Tynker

## Multimedia

* YouTube: Coding with Blocks in Google Blockly
* YouTube: Blockly Tutorial

## Activities
### Tutorials

* Complete one or more of the following tutorials:
** TechAdvisor: How to Code with Google Blockly
** Learneroo: Beginning Blockly

### Games

* Play Code.org: Classic Maze.

### Programming

* Use AppSpot: Blockly Demo Code to generate source code in JavaScript, Python, PHP, Lua, and Dart.
* See Programming Fundamentals and Programming Challenges for potential programming activities.

## See Also

* Programming Fundamentals
* Category:Block programming
# Complex Analysis/Harmonic function
## Definition

Let $U\subseteq \mathbb {C}$ be an open set. A function $u\colon U\to \mathbb {R}$ is called harmonic if it is twice differentiable and satisfies
$\Delta u:={\frac {\partial ^{2}u}{\partial x^{2}}}+{\frac {\partial ^{2}u}{\partial y^{2}}}=0$
have. The real part of a holomorphic function is harmonic, as follows from the Cauchy-Riemann-Differential equation. Interestingly, the converse also holds: every harmonic function is the real part of a holomorphic function.

### Connection to Holomorphic Functions

Let $U\subseteq \mathbb {C}$ be simply connected. For $u\in C^{2}(U,\mathbb {R} )$, the following are equivalent:
* $\Delta u=0$
* There exists $v\in C^{2}(U,\mathbb {R} )$ such that $u+iv$ is holomorphic.

### Proof

(2). $\implies$ (1).By the Cauchy-Riemann-Differential equation, we have:
${\begin{array}{rl}{\frac {\partial ^{2}u}{\partial x^{2}}}+{\frac {\partial ^{2}u}{\partial y^{2}}}&={\frac {\partial }{\partial x}}\left({\frac {\partial u}{\partial x}}\right)+{\frac {\partial }{\partial y}}\left({\frac {\partial u}{\partial y}}\right)\\&={\frac {\partial }{\partial x}}\left({\frac {\partial v}{\partial y}}\right)+{\frac {\partial }{\partial y}}\left(-{\frac {\partial v}{\partial x}}\right)\\&={\frac {\partial ^{2}v}{\partial x\partial y}}-{\frac {\partial ^{2}v}{\partial y\partial x}}\\&=0.\end{array}}$
since partial derivatives commute.
1. $\implies$ 2.Define the function $\textstyle g:={\frac {\partial u}{\partial x}}-i{\frac {\partial u}{\partial y}}$. By the Cauchy-Riemann-Differential equation, $g$ is holomorphic.since$U$ is simply connected, there exists a primitive $f\colon U\to \mathbb {C}$ from $g$, assume (by Adding a constant) ,that $u(z_{0})=f(z_{0})$ for a $z_{0}\in U$ applies. write $f=u_{1}+iv_{1}$. it is
${\frac {\partial u_{1}}{\partial x}}-i{\frac {\partial u_{1}}{\partial y}}=f'=g={\frac {\partial u}{\partial x}}-i{\frac {\partial u}{\partial y}}$
so is $u_{1}-u$ constant. because $u_{1}(z_{0})=f(z_{0})=u(z_{0})$ ist $u_{1}=u$ und $v:=v_{1}$ does what is desired.

### Translation and Version Control

This page was translated based on the following Wikiversity source page and uses the concept of Translation and Version Control for a transparent language fork in a Wikiversity:
* Source: Harmonische Funktion - URL:
https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Harmonische_Funktion
* Date: 01/08/2024
# Motivation and emotion/Book

* Motivation and emotion (Book)Understanding and improving our motivational and emotional lives using psychological science
* Use this page to navigate over 1,500 chapters

## Volumes

| 2025 | 2024 | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2011 | 2010 |

## Topics

Browse by topic:

## Overview

This project provides 1,500+ student-developed open educational resources about how the psychological science about motivation and emotion can be used to improve human lives. The work is developed and shared via Wikiversity, an open wiki platform supported by the Wikimedia Foundation. The students engaged in this learning and assessment exercise for the 3rd year undergraduate psychology unit, motivation and emotion, at the University of Canberra, Australia.
Continue reading ...
# Three-dimensional chess
## Pieces

There are eight likely equivalents to rook, knight, bishop and queen, which have octahedral symmetry. There are two more likely pieces with pyritohedral and tetrahedral symmetry. (Each with two different orientations.) The 3D chess variant examined here has 15 named pieces.
Pieces can be bound in two different ways: Bishop and jester are bound to black or white fields. This shall be called parity. Envoy and ward can reach only a quarter of all fields, which shall be called red, green, blue and yellow. The term color shall be used for them. So each field has a parity and a color. (It is not enough to extend the checkered pattern of the plane into space.)

### Shapes

The major pieces are represented by polyhedra, whose faces are orthogonal to the direction of capture. (The design for the pawns is similar.) In the small images below, the face colors denote direction types, e.g. dark red for axis, blue for plane diagonal, and dark green for space diagonal.
basic :
* (0, 0, 1) cube rook
* (0, 1, 1) rhombic dodecahedron bishop
* (1, 1, 1) octahedron envoy
combinations :
* small rhombicuboctahedron queen
* great rhombicuboctahedron king
* cuboctahedron marshal
jumpers :
* (0, 1, 2) tetrakis hexahedron knight
* (1, 1, 2) deltoidal icositetrahedron* jester
* (1, 2, 2) triakis octahedron* archer
reductions :
* pyritohedra squire (half knight)
* tetrahedra ward (half envoy)
pawns :
The traditional pawn captures along plane diagonals. Another one could capture along space diagonals. One could also combine the two.
To fill the second plane with cheap cover, one may add a weak pawn, that captures only forward. :
* front dog
* plane diagonal pike
* space diagonal lance
* both diagonals colonel
* The shapes of jester and archer are not Catalan, but integral.

### Moves

These images indicate the directions of capture as points in a grid. (In the parity layout the piece is on a white field. In the color layout it is on a yellow field.)
basic :
combinations :
jumpers :
reductions :
pawns :

## Space

An 8×8×8 cube (with 512 fields) would probably be too big. A 6×6×6 cube (with 216 fields) or 6×6×8 cuboid (with 288 fields) seem reasonable.

### Possible starting positions

Every piece in the first plane, except queen and king, should exist twice. That would be 20 pieces. The arrangement below is one example how that could look. It is not yet tested. If the black positions are mirrored, no green pieces of the same type can threaten each other (but octahedra and tetrahedra can).
white polyhedra :
white pawns :
black pawns :
black polyhedra :
# Theological Academy: Practice of Reciting

Place the sutra text in front of you so that you can read it comfortably.
Sit in the correct stance. Arch your lower back, straighten your back and neck.
Read the text.

### Variations

* Read out loud. You need to read this loud enough.
* Place the text so that it is located slightly above eye level.
* If you need a break from the sitting posture, you can continue reading while standing.
# Buddhism
## Courses/Learning Projects and Learning Materials

The courses here can be learned as a complete Diploma, Undergraduate Degree or Post Graduate Degree programs. Alternatively, it can be taken as standalone elective classes, which we had separated into Undergraduate Elective Courses and Post Graduate Elective Courses.
* Introduction
* Early History
* Geographical Expansion
* Pali Language
* Introduction to Sanskrit Language
* Pre-Buddhist Indian Thought and Culture
* Emergence and Basic Buddhist Teachings
* Origins
* Philosophy of Early History Buddhist Schools
* Philosophy of Mahayana Buddhist Schools
* South Asian Culture
* North American Culture

### Schools

The various schools of Buddhism makes an interesting studies, especially how these had developed and marginalized the many schools that had one time flourished. The key schools examined here are:
* Schools/Theravāda
* Schools/Sthaviravāda
* Schools/Vajrayāna
* Schools/Mahāsaṃghika
* Schools/Mahāyāna
# Theology

Theology is the systematic study of the nature of the divine and, more broadly, of religious belief. It is taught as an academic discipline, typically in universities and seminaries. It occupies itself with the unique content of analyzing the supernatural, but also deals with religious epistemology, asks and seeks to answer the question of revelation. Revelation pertains to the acceptance of God, gods, or deities, as not only transcendent or above the natural world, but also willing and able to interact with the natural world and, in particular, to reveal themselves to humankind. While theology has turned into a secular field, religious adherents still consider theology to be a discipline that helps them live and understand concepts such as life and love and that helps them lead lives of obedience to the deities they follow or worship.
In its strict sense, theology is not a science insofar as theology does not study religion, but teaches this religion. Unlike Religious studies.

## See Also

* School:Theology
* School:Religious Studies
* Wikipedia: Theology
# CIVICS

For learning resources pertaining to government operations, see Civics.
CIVICS means "Caucasus Virtual Institute of Conservation Science and Education". It is a collaborative activity of scientists and professionals from several European and Asian countries.
CIVICS starts with content generated by the project "Socio-economic Tools for Integrated Conservation Planning in the Multi-Ethnic South Caucasus" funded from 2011-2014 by the German Ministry of Education and Development (BMBF).
CIVICS will contain some purely educational material. Foremost, it is meant to be a platform for research at the moment.

## Resources

Special:Prefixindex/CIVICS/

## Weblinks

* Environmentral and Resource Economics at Georg-August-Universität Göttingen
* International Center for Environmental Research