OpenLLM-France/wikimedia huggingface dataset:
# Differential equations/Laplace transforms
### Definition

For some problems, the Laplace transform can convert the problem into a more solvable form. The Laplace transform equation is defined as $L(f(t))=\int _{0}^{\infty }e^{-st}f(t)dt=F(s)$, for the values of $s$ such that the integral exists. There are many properties of the Laplace transform that make it desirable to work with, such as linearity, or in other words, $L(\alpha f(t)+\beta g(t))=\alpha L(f(t))+\beta L(g(t))$ .

### Solution

To illustrate how to solve a differential equation using the Laplace transform, let's take the following equation: $y''+2y'+y=0,y(0)=1,y'(0)=1$ . The Laplace transform usually is suited for equations with initial conditions.
* Take the Laplace transform of both sides ($L(y''+2y'+y)=L(0)=0$ ).
* Use the associative property to split the left side into terms ($L(y'')+2L(y')+L(y)=0$ ).
* Use the theorem $L(y')=sL(y)-y(0)$ , and by extension, $L(y'')=s^{2}L(y)-sy(0)-y'(0)$ to modify the terms into scalars and multiples of $L(y)$ ($s^{2}L(y)-sy(0)-y'(0)+2\left[sL(y)-y(0)\right]+L(y)=0$ ).
* Solve for the Laplacian ($L(y)={\frac {s+3}{s^{2}+2s+1}}={\frac {s+3}{(s+1)^{2}}}$ ).
* Take the inverse Laplace transform of both sides to get the solution, solving by method of partial fractions as needed: ($L(y)={\frac {s+1+2}{(s+1)^{2}}}={\frac {1}{s+1}}+{\frac {2}{(s+1)^{2}}},y(t)=e^{-t}+2te^{-t}$ ).
* For reference, here are some basic Laplace transforms:
** $L(1)={\frac {1}{s}}$
** $L(t^{n})={\frac {n!}{s^{n+1}}},n=1,2,3,\cdots$
** $L(e^{at})={\frac {1}{s-a}}$
** $L(\sin at)={\frac {a}{s^{2}+a^{2}}}$
** $L(\sinh at)={\frac {a}{s^{2}-a^{2}}}$
** $L(\cos at)={\frac {s}{s^{2}+a^{2}}}$
** $L(\cosh at)={\frac {s}{s^{2}-a^{2}}}$
* For reference, here are some theorems for the Laplace transforms:
** $L(e^{at}f(t))=F(s-a)$
** $L(t\cdot f(t))=-F'(s)$
** $L(f^{(n)}(t))=s^{n}F(s)-s^{n-1}f(0)-s^{n-2}f(0)\cdots$
** $L(f(t-a)\cdot U(t-a)=e^{-as}F(s),a>0$
# Differential equations/Homogeneous differential equations
## Homogeneous
### Definition

The word “homogeneous” can mean different things depending on what kind of differential equation you’re working with. A homogeneous equation in this sense is defined as one where the following relationship is true:
$\textstyle f(tx,ty)=t\cdot f(x,y)$

### Solution

The solution to a homogeneous equation is to:
* Use the substitution $\textstyle y=ux$ where $u$ is a substitution variable.
* Implicitly differentiate the above equation to get ${\frac {dy}{dx}}=x{\frac {du}{dx}}+u$.
* Replace $\textstyle {\frac {dy}{dx}}$ and $\textstyle y$ with these expressions.
* Solve for $u$.
* Substitute with the expression $u={\frac {y}{x}}$ Then solve for $\textstyle y$.
The advantage of this method is that the function is in terms of 2 variables, but we simplify the equation by relating $\textstyle y$ and $\textstyle x$ to each other.
# Differential equations/Integrating factors
### Definition

If the expression $M(x,y)dx+N(x,y)dy=0$ is not exact or homogeneous, an integrating factor $I(x)$ can be found so that the equation:
$I(x)M(x,y)dx+I(x)N(x,y)dy=0$
is exact.

### Solution

There are 2 approaches to a solution.
* If the function is of the form ${\frac {dy}{dx}}+p(x)y=r(x)$ , then the integrating factor is $I(x)=e^{\int p(x)dx}$. OR If the function is of the standard form $M(x,y)dx+N(x,y)dy=0$ , then the integrating factor is $I(x)=e^{\int {\frac {M_{y}-N_{x}}{N}}dx}$ or $I(x)=e^{\int {\frac {N_{x}-M_{y}}{M}}dy}$.
* Substitute the integration factor into the equation $I(x)M(x,y)dx+I(x)N(x,y)dy=0$ and solve.
# Differential equations/Linear homogeneous differential equations
## Second Order Differential Equations

A second order differential equation has a given function and terms including the first and second derivatives of that function. There are many techniques that are employed to find solutions to these problems. Different types of problems need different techniques to solve them.

## Homogeneous
### Definition

For second order differential equations, a homogeneous equation is one where the right hand side is zero (e.g. $y''+by'+cy=0$ ).

### Solution

* A general solution to this equation is $y=e^{mx}$ . Substitute this into the equation.
* After dividing by the exponential part, the equation should resolve to the form $m^{2}+bm+c=0$ .
* Solve the quadratic equation using the quadratic formula to get the roots of $m$.
* If there are 2 roots, the solution is $y=Ae^{m_{1}x}+Be^{m_{2}x}$ . If there is 1 root, the solution is $y=Ae^{mx}+Bxe^{mx}$ .
# Differential equations/Assignment 1

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics and other disciplines.
# Differential equations/Exact differential equations
### Definition

A differential equation of is said to be exact if it can be written in the form $M(x,y)dx+N(x,y)dy=0$ where $M$ and $N$ have continuous partial derivatives such that ${\frac {\partial M}{\partial y}}={\frac {\partial N}{\partial x}}$.

### Solution

Solving the differential equation consists of the following steps:
* Create a function $f(x,y):=\int M(x,y)dx$. While integrating, add a constant function $g(y)$ that is a function of $y$. This is a term that becomes zero if function $f(x,y)$ is differentiated with respect to $x$.
* Differentiate the function $f(x,y)$ with respect to ${\frac {\partial f}{\partial y}}$. Set ${\frac {\partial f}{\partial y}}=N(x,y)$. Solve for the function $g(y)$.
# Differential equations/Introduction to First Order Linear Differential Equations

A differential equation $y'=f(t,y(t))$ is a first order differential equation. When placed in the form $y'+p(t)y=g(t)$ where $p(t)$ and $g(t)$ are functions defined on an interval $a<t<b$ is called a first order linear differential equation.
For example:
* $y'+3y=t$ where $p(t)=3$ and $g(t)=t$
* For $e^{t}y'+3y=sin(t)$ we divide through by $e^{t}$ to place the equation in the proper form and $y'+{\frac {3}{e^{t}}}y={\frac {sin(t)}{e^{t}}}$ $p(t)=3e^{-t}$ and $g(t)=sin(t)e^{-t}$
Method
# Differential equations/Ordinary Differential Equations

Work in progress
For engineers and scientists, your introduction to a differential equation probably occurred in your Calculus I class, where you were introduced to the derivative of a function (i.e. ${\frac {d}{dx}}f(x)$. At the same time you were taking introductory physics where concepts such as Newton's second law of motion (for linear motion) was presented as $F=ma$, and when combined with ${\frac {d^{2}}{dt^{2}}}x={\frac {d}{dt}}v=a$ led to the differential equation , $F=m{\frac {d^{2}}{dt^{2}}}x$ .
Similarly many fundamental laws of science are expressed as differential equations:
* Law of Conservation of Mass: Rate of Mass In - Rate of Mass Out = Rate of Change of Mass content
* Law of Conservation of Energy: Rate of Energy In - Rate of Energy Out = Rate of Change of Energy content
Each of these represents the change in a quantity (dependent variable) with respect to an independent variable (such as time).
An nth order differential equation is of the form $y^{(n)}=f(t,y,y',...,y^{(n-1)}$). For example, when Newton's second law of motion, $F=ma$, is applied to a moving object the resulting differential equation is $my''(t)=f(t,y(t),y'(t))$
# Boolean domain

☞ This page belongs to resource collections on Logic and Inquiry.
A boolean domain $\mathbb {B}$ is a generic 2-element set, say, $\mathbb {B} =\{0,1\}$ , whose elements are interpreted as logical values, typically, $0={\text{false}}$ and $1={\text{true}}$
A boolean variable $x$ is a variable that takes its value from a boolean domain, as $x\in \mathbb {B}$ .

## Syllabus
### Focal nodes

* Inquiry Live
* Logic Live

### Peer nodes

* Boolean Domain @ InterSciWiki
* Boolean Domain @ Subject Wikis
* Boolean Domain @ Wikiversity
* Boolean Domain @ Wikiversity Beta
# Book Reviews/Writing a review/analysis topics to cover
## Analysis Topics to Cover

Analysis is conclusory. In analyzing the book you present your opinions as conclusions and then support these conclusions with evidence drawn from the book. Consider these topics:
* Identify or formulate the book’s thesis statement. Judge how important that thesis is and how well (how convincingly) the book proves the thesis. Did the book influence your thinking?
* Choose the one adjective that best describes this book. Consider these suggestions, or choose some other descriptor: accessible, archaic, authoritative, autobiographical, bland, boring, captivating, comprehensive, confusing, creative, dated, disjointed, disorganized, dull, encyclopedic, engaging, enlightening, entertaining, erudite, exciting, exhilarating, factual, fanciful, fascinating, fast-paced, fragmented, frivolous, fun, funny, hackneyed, heart-wrenching, helpful, hilarious, incoherent, indecipherable, informative, innovative, inspiring, interesting, intriguing, important, irreverent, lackluster, liberating, long-winded, mediocre, misinformed, monotonous, obsolete, obvious, opaque, pedantic, penetrating, poorly-researched, pornographic, pretentious, profound, rambling, relevant, revolutionary, rousing, scandalous, scintillating, sexy, shocking, sloppy, slow-going, sophomoric, steamy, strident, surprising, suspenseful, tedious, thought-provoking, trashy, trivial, uninspired, unoriginal, up-to-date, well-organized, well-researched, well-written, whiney, witty,
* Assess the argument, evidence, and exposition—clarity of expression and writing style—of the book.
* Describe, discuss, and assess the author’s use of logos—argument by logic, pathos—argument by emotions, and ethos—argument based on character and values.
* What surprised you, what disappointed you, what informed you, what entertained you, what make you think, what provoked you?
* Identify the standards (norms, reference model) you are using to judge the book. For example, “Good writing is clear thinking made visible” is one such norm. After stating the norm, explicitly assess the book’s adherence to that standard.
# Boolean-valued function

☞ This page belongs to resource collections on Logic and Inquiry.
A boolean-valued function is a function of the type $f:X\to \mathbb {B} ,$ where $X\!$ is an arbitrary set and where $\mathbb {B}$ is a boolean domain.
In the formal sciences — mathematics, mathematical logic, statistics — and their applied disciplines, a boolean-valued function may also be referred to as a characteristic function, indicator function, predicate, or proposition. In all of these uses it is understood that the various terms refer to a mathematical object and not the corresponding sign or syntactic expression.
In formal semantic theories of truth, a truth predicate is a predicate on the sentences of a formal language, interpreted for logic, that formalizes the intuitive concept that is normally expressed by saying that a sentence is true. A truth predicate may have additional domains beyond the formal language domain, if that is what is required to determine a final truth value.

## Examples

A binary sequence is a boolean-valued function $f:\mathbb {N} ^{+}\to \mathbb {B}$, where $\mathbb {N} ^{+}=\{1,2,3,\ldots \},$. In other words, $f\!$ is an infinite sequence of 0's and 1's.
A binary sequence of length $k\!$ is a boolean-valued function $f:[k]\to \mathbb {B}$, where $[k]=\{1,2,\ldots k\}.$
# Boot loader
## Overview

After powering up and running any diagnostics required or requested, the computer's startup code will find a small program called the boot loader. After loading the boot loader to a known place in memory, the startup code will transfer control to it.
The boot loader will then perform a number of simple functions in preparation for loading the actual operating system. Most boot loaders will initialize the CPU to a known state, identify some hardware (not all devices are identified), then locate, load, and execute the kernel.
The boot loader is sometimes designed to be an integral part of the operating system (e.g. Microsoft Windows NT$^{TM}$ and later). In other designs, the boot loader is a separate program, often written by different authors (e.g. GNU GRUB).
Boot loaders can sometimes be chained, with the first boot loader loading and passing control to a second boot loader. This is how GNU GRUB and LILO load the Microsoft Windows$^{TM}$ boot loader "ntldr" on the x86 PC.

## Examples

* GNU GRUB (GRand Unified Bootloader)
* FreeBSD Boot Loader
* LILO (The LInux LOader)

## Boot Loader Tutorials/References

* The Booting Process [From Power On to OS load]
* Hello World Boot Loader
* Another Hello World Boot Loader
* The booting process
# Boolean function

☞ This page belongs to resource collections on Logic and Inquiry.
A finitary boolean function is a function of the form $f:\mathbb {B} ^{k}\to \mathbb {B} ,$ where $\mathbb {B} =\{0,1\}$ is a boolean domain and where $k\!$ is a nonnegative integer. In the case where $k=0,\!$ the function is simply a constant element of $\mathbb {B} .$
There are $2^{2^{k}}$ such functions. These play a basic role in questions of complexity theory as well as the design of circuits and chips for digital computers.

## Syllabus
### Focal nodes

* Inquiry Live
* Logic Live

### Peer nodes

* Boolean Function @ InterSciWiki
* Boolean Function @ Subject Wikis
* Boolean Function @ Wikiversity
* Boolean Function @ Wikiversity Beta
# Dominant group/Bibliography

An advanced search on Google Scholar using "dominant group" as of September 3, 2013, has yielded about 82,800 results. Any of these plus those that may include synonyms may be used for the course.
Prehistory
Ancient history
Early modern history
Modern history
# Dominant group/Artifact laboratory

Def. "[a]n object, such as a tool, weapon or ornament, ... structure or finding in an experiment or investigation ... made or shaped by some agent or intelligence, ... [as] a result of external action, the test arrangement, or an experimental error ... rather than an inherent element" is called an artifact, or artefact.
Are dominant group and some or all of its relative synonyms artifacts? Dominant group may be only an artifact.

## Archaeology

It "is the study of human activity in the past, primarily through the recovery and analysis of the material culture and environmental data that they have left behind, which includes artifacts, architecture, biofacts and cultural landscapes (the archaeological record)."

## Mythology

"Cultural artifact is a term used in the social sciences, particularly anthropology, ethnology, and sociology ... for anything created by humans which gives information about the culture of its creator and users. Usage of this term encompasses the type of archaeological artifact which is recovered at archaeological sites; however, current objects of modern or near-modern society are also cultural artifacts. For example, in an anthropological context, a 17th-century lathe, a piece of faience, or a television each provide a wealth of information about the time in which they were manufactured and used. Cultural artifacts can provide knowledge about technological processes, economy and social makeup, and a host of other subjects."
# Dominant group/Budget

Costs: intellectual effort, computer use time and resources, possible publication costs, a trip to a conference in a neat location.
Course Development by a Single Faculty Member :
| Project Director: | (online) Wikiversity User: Marshallsumter | Project Grant Period: | Course host website: |
| | (offline) as indicated in application package | 5/1/2014-4/30/2016 | Wikiversity |
Budget :
| | Computational Details/Notes | Year 1 | Year 2 | Project Total |
| 1. Salaries & Wages | | | | |
| Project Director Stipend | | $12,500 | $12,500 | $25,000 |
| 2. Fringe Benefits | | | | |
| Project Director (Social Security contribution) | 13.333% of funded portion | $1,667 | $1,667 | $3,334 |
| 3. Travel | | | | |
| Archives access (e.g. Library of Congress) | 1 person, 2-days; $250 per diem x 2 days Airfare: $500 | $1,000 | $1,000 | $2,000 |
| Conference | 1 person, 2-day conference; $250 per diem x 2 days Airfare: $500 | $1,000 | | $1,000 |
| 4. Services | | | | |
| Photocopying | Library or Interlibrary loan (ILL) | $100 | $100 | $200 |
| Local university library card | | $100 | $100 | $200 |
| Journal article access (not available by ILL, archive access, or local library) | | $2,000 | $2,000 | $4,000 |
| 5. Publication | | | | |
| Page costs | | | $2,000 | $2,000 |
| 6. Supplies & Materials | | | | |
| 7. Other costs | | | | |
| 8. Total Direct Costs | Per Year | $16,700 | $17,700 | $34,400 |
| 9. Total Indirect Costs | Per Year | $2,004 | $2,124 | $4,128 |
| Indirect Cost Calculation: Rate of 12% of direct cost per year | | | | |
| 10. Total Project Costs (Direct and Indirect costs for entire project) | | 18,704 | 19,824 | $38,528 |
| 11. Project Funding | | | | $38,528 |
| a. Requested from NEH | Outright: | | | $38,528 |
| | Matching Funds: | | | $0 |
| | Total Requested from NEH: | | | $38,528 |
| b. Cost Sharing | Applicant's Contributions: | | | $0 |
| | Third Party Contributions: | | | $0 |
| | Project Income: | | | $0 |
| | Other Federal Agencies: | | | $0 |
| | Total Cost Share: | | | $0 |
| 12. Total Project Funding | | | | $38,528 |
# English-Chinese/The band played loud music

The band played loud music.
乐队 演奏了 响亮的 音乐。
# English-Chinese/The blast had blown a hole in the wall

The blast had blown a hole in the wall.
爆炸在墙上炸开了一个洞。
# English-Chinese/The basic principles of good diets are so simple: eat less, move more, eat more fruits and vegetables
## English

The basic principles of good diets are so simple: eat less, move more, eat more fruits and vegetables.

## Hanzi

良好饮食的基本原则是如此简单：少吃，多运动，多吃蔬果。

## Pinyin

Liánghǎo yǐnshí de jīběn yuánzé shì rúcǐ jiǎndān: Shǎo chī, duō yùndòng, duō chī shūguǒ.
# English-Chinese/The beetroot is the taproot portion of the beet plant

The beetroot is the taproot portion of the beet plant.
甜菜根是甜菜植物的主根部分。
# English-Chinese/The body needs protein to make blood cells

The body needs protein to make blood cells.
身体需要蛋白质来制造血细胞。
# English-Chinese/The book is 5 euro

The book is 5 euro.
这本书 5 euro。
# English-Chinese/The average life expectancy of patients with schizophrenia is 10-25 years shorter than the normal

The average life expectancy of patients with schizophrenia is 10-25 years shorter than the normal.
精神分裂症患者的平均寿命比正常人短10-25年。
# English-Chinese/The baby boy started to crawl towards me

The baby boy started to crawl towards me.
男婴开始向我爬来。
# English-Chinese/The best combination of protein sources depends on the region of the world, access, cost, amino acid types and nutrition balance, as well as acquired tastes

The best combination of protein sources depends on the region of the world, access, cost, amino acid types and nutrition balance, as well as acquired tastes.
蛋白质来源的最佳组合取决于世界的地区，获取，成本，氨基酸类型和营养平衡，以及获得的口味。
# English-Chinese/The bird balanced easily on the wire for a few moments before flying off

The bird balanced easily on the wire for a few moments before flying off.
这只 鸟 飞走 之前 在 电线上 轻松地 站了 一会儿。
# European History/Class Structure

Team Nova Gaming Voic Andrei Popa Cristi Marc Rareș Nastase Alexandru Popa Tudor

## Current Proposal

It has been proposed that the following categories be adopted to divide projects into:
   * Primary/Elementary
   * Secondary/High School
   * Beginning University/College (AA Level)
   * Advanced University (BA Level)
   * Superior University | Thesis-level | Honors Project (MA Level)
   * Graduate (PHD Level)

## Proposed Home Page Layout for Policy

Welcome to the Wikiversity! This policy concerns the class structuring for easy navigation. The classes within the European and American History Departments have a special designated title and class level. The title of the class allows you to quickly understand the course material while the level will help you gauge your possible ability to complete the class. All classes have no minimum requirements; however, some professors will suggest that some classes be take in a certain order to maximize your learning experience. Listed below are the Class Level and their appropriate level in the normal scholastic institutions.
   * Primary/Elementary
   * Secondary/High School
   * Beginning University/College (AA Level)
   * Advanced University (BA Level)
   * Superior University | Thesis-level | Honors Project (MA Level)
   * Graduate (PHD Level)
# Evaluating Evidence/Interpretation goes beyond observation

Compare these two pet diaries, each found on the Internet, as each observer interprets similar events through their own preconceptions…

## Excerpts from a Dog's Diary…

8:00 am - Dog food! My favorite thing! 9:30 am - A car ride! My favorite thing! 9:40 am - A walk in the park! My favorite thing! 10:30 am - Got rubbed and petted! My favorite thing! 12:00 pm - Lunch! My favorite thing! 1:00 pm - Played in the yard! My favorite thing! 3:00 pm - Wagged my tail! My favorite thing! 5:00 pm - Milk bones! My favorite thing! 6:00 pm - Oooh, Bath. Bummer. 7:00 pm - Got to play ball! My favorite thing! 8:00 pm - Wow! Watched TV with the people! My favorite thing! 11:00 pm - Sleeping on the bed! My favorite thing!

## Excerpts from a Cat's Daily Diary…

Day 983 of my captivity.
My captors continue to taunt me with bizarre little dangling objects.
They dine lavishly on fresh meat, while the other inmates and I are fed hash or some sort of dry nuggets. Although I make my contempt for the rations perfectly clear, I nevertheless must eat something in order to keep up my strength.
The only thing that keeps me going is my dream of escape. In an attempt to disgust them, I once again vomit on the carpet.
Today I decapitated a mouse and dropped its headless body at their feet. I had hoped this would strike fear into their hearts, since it clearly demonstrates what I am capable of. However, they merely made condescending comments about what a ‘good little hunter’ I am. Bastards.
There was some sort of assembly of their accomplices tonight. I was placed in solitary confinement for the duration of the event. However, I could hear the noises and smell the food. I overheard that my confinement was due to the power of ‘allergies.’ I must learn what this means and how to use it to my advantage.
Today I was almost successful in an attempt to assassinate one of my tormentors by weaving around his feet as he was walking. I must try this again tomorrow—but at the top of the stairs.
I am convinced that the other prisoners here are flunkies and snitches. The dog receives special privileges. He is regularly released—and seems to be more than willing to return. He is obviously retarded.
The bird has got to be an informant. I observe him communicating with the guards regularly. I am certain that he reports my every move. My captors have arranged protective custody for him in an elevated cell, so he is safe. For now…