OpenLLM-France/wikimedia huggingface dataset:
# Physics with Calculus/Mechanics/Velocity and Acceleration

Conservation of mass : The total mass in a closed system remains constant. Mass can not be created or destroyed[*]. It can, however, change forms.
Density is defined as mass divided by volume
$\rho ={\frac {m}{V}}$
[*] Usually. There are exceptions in some extreme situations.
# Physics with Calculus/Modern/The Bohr Model

If we have an electron orbiting the nucleus, the electron is accelerating towards the nucleus. It is well known that an accelerating charge produces radiation, which contains energy. Therefore, as the electron orbits, it loses energy and consequently will eventually fall into the nucleus. The classical model of electrons orbiting a nucleus must therefore be wrong because not only do we not observe the radiation, but the electrons do NOT fall into the nucleus.
Bohr proposed that the angular momentum of the electrons could only take on discrete values, say, $n\hbar$. The energy of the electrons is also quantized as a result, so unless an electron gets enough energy to jump energy levels, it cannot emit a photon; that is, it will not radiate.
We will work through a very simple case of the Bohr model.
Assume we have a single electron of mass m orbiting a single proton in a circular orbit, and the angular momentum is $n\hbar$ where n is any integer greater than zero. Also assume that the mass of an electron is negligible compared to that of a proton.
$L=mvr=n\hbar$
$F={\frac {ke^{2}}{r^{2}}}={\frac {mv^{2}}{r}}$
$v^{2}={\frac {ke^{2}}{mr}}$
$v={\frac {ke^{2}}{mvr}}={\frac {ke^{2}}{n\hbar }}$
$r={\frac {n\hbar }{mv}}=n^{2}{\frac {\hbar ^{2}}{mke^{2}}}$
$E={\frac {1}{2}}mv^{2}-{\frac {ke^{2}}{r}}=-{\frac {1}{2}}{\frac {ke^{2}}{r}}=-{\frac {1}{2}}{\frac {m(ke^{2})^{2}}{n^{2}\hbar ^{2}}}$.
The Bohr model, surprisingly, makes very good predictions about the energy of the photons emitted from an electron jumping levels. We could continue our model and calculate such things as the magnetic moment of hydrogen and figure out what we expect the magnetic properties to be.

### Flaws of the Bohr Model

Only works for hydrogenic(one-electron) atoms.
The assumption of discrete angular momentum values is unexplained.
# Physics with Calculus/Mechanics/Relative Motion

In an approximation termed Galilean relativity, when two objects are moving at ${\vec {u}}$ and ${\vec {v}}$ relative to a common inertial reference frame, the relative velocity between the two objects, in the frame of reference where one of them is still, is
${\vec {v}}_{\mathrm {ref} }={\vec {v}}-{\vec {u}}$
# Physics with Calculus/Modern/Atoms
### Atoms

The atom was, until comparatively recently, thought to be the fundamental building block of matter, and for the purposes of this textbook, we will treat it as though it were.
The atom consists of three types of particles: the electron, the proton, and the neutron.
The protons and the neutrons are contained within a very small amount of volume in the center of the atom called the nucleus. Protons have a net positive charge of 1 e, where e is the fundamental unit of charge, equal to about $1.6\times 10^{-19}$ coulombs. Neutrons have no net electric charge and are very slightly more massive than a proton.
Electrons are in orbit around the nucleus of the atom, and have a net negative charge of -1e. Their mass is much less than that of the proton and neutron, and so the electrons are generally left out when determining the mass of an atom.
The electrons are, in microscopic terms, astonishingly distant from the nucleus. If we take a hydrogen atom (1 electron and 1 proton) to be about an angstrom in diameter (1 angstrom is $10^{-10}$ meters), then the approximate diameter of the nucleus is $10^{-15}$m. In more familiar terms, if the nucleus was an inch in diameter, the first electron would be about 830 feet away.
Masses
Proton: $1.6726\times 10^{-27}$kg
Neutron: $1.6749\times 10^{-27}$kg
Electron:$9.1094\times 10^{-31}$kg
Charges
Proton: +1e
Electron:-1e
Neutron: 0
where e=$1.6022\times 10^{-19}$C
# Question Writer Manual/Quiz Options/Metadata
## Metadata (SCORM)

If you publish your quiz as SCORM you can add Metadata to your quiz. Metadata will be used to identify your content in the Learning Management System (LMS) or Virtual Learning Environment (VLE). You can add the following 4 metatdata elements to the question:
* Title
* Description
* Identifier
* Keywords
# Question Writer Manual/Quiz Options/Quiz Details/Feedback Method
## Feedback Method

You can select from the 3 choices in the drop down box:
* After Each Question
* End of Quiz
* No Question Feedback
If you select After Each Question, the quiz taker will see if they answered correctly as soon as they click on the next question button.
If you select End of Quiz, the quiz taker will be shown their performance on each question as a review at the end of the quiz.
If you select No Question Feedback, the quiz taker will not receive feedback on individual questions.
* If you have the Professional version of Question Writer there is also a tick box where you can opt to Show Question Feedback For Incorrect Answers only – if the quiz taker gets an answer correct they will not be given feedback for that question.
# Question Writer Manual/Quiz Options/Quiz Details/Introduction Screen
## Introduction Screen
### Ask for Name/User ID

If you tick the Ask for Name box the quiz will start by asking for a name or ID number. This is useful if you want to monitor individual scores. If you're using the e-mail results service or viewing results online, the user's name/ID can be used to reference the user's results.

### Display Instructions

If you tick the Display Instructions box a short message will be shown to the quiz taker at the start of the quiz. You can amend the text of this message if you wish.
# Question Writer Manual/Quiz Options/Quiz Details/Pass Score Percentage
## Pass Score Percentage

Enter the passing % score as a number – you can set this figure as high or low as you like. The default is set at 80%. Only enter the number here - you won't be able to enter the percentage(%) sign.
# Question Writer Manual/Quiz Options/Other Labels
## Other Labels

This section allows you to customize other text labels giving you the maximum opportunity to personalize your quiz.
# Question Writer Manual/Quiz Options/Question Options
## Question Options

* General Question Properties
* Question Scoring Options
* Fill in the Blank Question Options
# Question Writer Manual/Quiz Options/Question Options/General Question Properties
## General Question Properties

This properties window contains a series of tick boxes relating to the appearance of the question on the screen, most of which are self explanatory.

### Show Question Number

The question number can be displayed at the top of each question page using this option

### Randomize Question Options

This randomizes the order in which answer options are displayed in Multiple Choice, Multiple Response and Partial Credit question types. In Sequencing and Matching question types, options are always randomized.

### Display Point Values For Questions

The number of points awarded for each questions is shown to bottom right hand side of the question if this option is selected.

### Display Title With Each Question

This option displays the title of the quiz at the top of each question page.

### Use Image Zooming

When an image or piece of Flash is displayed with a question, it can optionally be shown in the top left hand corner and zoomed to full size when the mouse moves over it. If this option is not selected, the image appears at its default size at the top of the question.

### Never Show Back Button with Questions

* When this box is ticked the back button will not appear in each question, this means that quiz takers will not be given the option to go back over earlier answers.

### Force Attempt at Every Question

* When this box is ticked the quiz takers will have to enter an answer before they can proceed to the next question. This ensures that they attempt each question in the quiz.
# Question Writer Manual/Quiz Options/Quiz Details
## Quiz Details

* Title
* Pass Score Percentage
* Feedback Method
* Time Limit the Quiz
* Randomization
* Number of Pre-Randomized Quizzes to Generate

### Introduction to Quiz Details

When you click on the quiz properties the following screen will open where you can input the basic settings for your quiz.
# Question Writer Manual/Quiz Options/Question Options/Fill in the Blank Question Options
## Fill in the Blank Question Options
### Fill In The Blank Answers Must Use Correct Capitalization

This determines whether the scoring for Fill In The Blank style questions is case sensitive. If Correct Capitalization is required and the required answer was 'Blue' but the quiz taker entered 'blue' - they would not score any points.
* Award Points for Answers with Spelling Errors
* A very big drawback to Fill In the Blank questions is having to identify the exact characters that a quiz taker must type in to get a question right. This feature allows you to award full or partial marks to quiz takers who come close enough.
* You can also specify how close they have to be. The default setting is 30%, meaning 3 errors in a 10 letter word or 1 in a 4 letter word.
* An error is either
* Wrong letter (Necessery)
* Missing letter (Necesary)
* Extra letter (Neccessary)
* Two letters switched around (Recieve)
* Where case-correct answers are required, switching the case of a letter is also marked as a single error. (washington)
* You can still define multiple correct answers, and the one with fewest errors compared to the student's answers will be used
* Award only Partial Credit for Spelling Errors
* This tick box enables partial credit to be awarded for partially correct answers.
# Question Writer Manual/Quiz Options/Question Options/Question Scoring Options
## Question Scoring Options
### Award Partial Credit for Sequencing and Matching Questions

* This tick box allows you to give quiz takers credit for an answer that is not 100% correct in the sequencing and matching question types.
* For matching questions a score based on the number of correct matches is awarded.
* For sequencing questions, a more complex scoring method is used by calculating the number of correct relative pairs sequenced. (There's a blog article here that goes into more detail, ).

### Allow Overall Negative Marks From Partial Credit Questions

* You can choose whether or not you allow negative scores for Partial Credit Questions. These negative scores will the be set against positive scores achieved in other questions. If you don't allow negative scores, the minimum score that can be awarded for any question is 0.

### Allow Overall Negative Mark for Whole Quiz

* If you tick this box and you have used negative scoring you will be able to award an overall negative score for the quiz.
# Pinyin/Bible/Judges

Chapter 1
# Pinyin/Bible/Numbers

Chapter 1
# Pinyin/Bible/Leviticus

Chapter 1
# Pinyin/Bible/Leviticus/Chapter 1

See also
* 1:1 And the voice of the Lord came to Moses out of the Tent of meeting, saying,
* Shern de shengyin chuarn daoh Huihyihshih duih Moses shuo,
* 1:2 Give these orders to the children of Israel: When anyone of you makes an offering to the Lord, you are to take it from the cattle, from the herd or from the flock.
* gaohsuh Israel rern, rur yaoh gohngfehng Shern, corng niur her yarng qurn zhong xuaan gohngwuh.
* 1:3 If the offering is a burned offering of the herd, let him give a male without a mark: he is to give it at the door of the Tent of meeting so that he may be pleasing to the Lord.
* 1:4 And he is to put his hand on the head of the burned offering and it will be taken for him, to take away his sin.
* 1:5 And the ox is to be put to death before the Lord: then Aaron's sons, the priests, are to take the blood and put some of it on and round the altar which is at the door of the Tent of meeting.
* 1:6 And the burned offering is to be skinned and cut up into its parts.
* 1:7 And Aaron's sons, the priests, are to put fire on the altar and put the wood in order on the fire:
* 1:8 And Aaron's sons, the priests, are to put the parts, the head and the fat, in order on the wood which is on the fire on the altar:
* 1:9 But its inside parts and its legs are to be washed with water, and it will all be burned on the altar by the priest for a burned offering, an offering made by fire, for a sweet smell to the Lord.
* 1:10 And if his offering is of the flock, a burned offering of sheep or goats, let him give a male without a mark.
* 1:11 And he is to put it to death on the north side of the altar before the Lord: and Aaron's sons, the priests, are to put some of the blood on and round the altar.
* 1:12 And the offering is to be cut into its parts, with its head and its fat; and the priest is to put them in order on the wood which is on the fire on the altar:
* 1:13 But the inside parts and the legs are to be washed with water; and the priest will make an offering of all of it, burning it on the altar: it is a burned offering, an offering made by fire, for a sweet smell to the Lord.
* 1:14 And if his offering to the Lord is a burned offering of birds, then he is to make his offering of doves or of young pigeons.
* 1:15 And the priest is to take it to the altar, and after its head has been twisted off, it is to be burned on the altar, and its blood drained out on the side of the altar:
* 1:16 And he is to take away its stomach, with its feathers, and put it down by the east side of the altar, where the burned waste is put:
* 1:17 And let it be broken open at the wings, but not cut in two; and let it be burned on the altar by the priest on the wood which is on the fire; it is a burned offering; an offering made by fire for a sweet smell to the Lord.
# Pinyin/Bible/Ruth

Chapter 1
# Modelling Theory and Practice/Motivation and Summary
## Approach

* structural: the nice thing about mathematics is that "1 + 1 = 2" can stand for one cow plus another one makes two cows as well as ???. In the same way this book cares about structures first, such as orders, trees, etc, that then can become 'alive' in various domains.
* relational: in a mathematical language there are two kinds of ??? symbols: functions like "+" and relations like "=" or ">". Here we focus on the relations.
* discrete/ finite: ???
* bottom-up (simple to complex): the book starts with very simple structures, like unary relations (all they can express is: does sth have a certain property - yes/ no). It is like with the periodic table: the simpler atoms occur more often in nature, just because of their simplicity. However this does not mean that they are the most interesting ones to study, this is why one of the important assumptions (inspired by practical experience) is that a lot of the relevant structures in 'real life' are simpler than we think (or than things like UML may suggest)
* case based: in order to connect such solely structural thing to the 'real world', the book provides emperical cases of applications, s.t. a modeller can use them as a kind of experience base in its everyday modelling. This corresponds to the way humans approach problems and is known as Case-based reasoning. Notice that thus we do not model the modelling process itself. Instead the book leaves it to the modeller to extract the models from the empirical cases, in a way it is best suited to its domain and experience.
# Modelling Theory and Practice/Overview and Trivial Cases
## The Notion of a Property of something

Property: separate sheep from goats -> look for property.
We write R(x) for an element x having property R.
Properties can be used to define sets. (intensional definition)
Set can also be defined by specifying every of its objects. (extensional definition)

## Overview of Relations

'Relation' among objects, e.g. person drives car, formally written: Drives(person, car), Drives(Walter, Mini)
Notations: table, matrix, graph, ...
Binary relation: R(x, y), e.g. ...
N-ary relation: R(x$_1$, x$_2$, x$_3$, ..., x$_n$), e.g. ...
Property = unary relation R(x).
Structure of this chapter:
* Trivial Cases: R(x)
* Modelling with Concepts: R(x), S(y), T(z)
* Modelling with Modules: R(x, y, z)
Where concepts and modules are the basic approaches to handle complexity in the two directions.
Moreover, the directions of course can be combined. This is analysed in the next chapter.
Not covered: Soft relations, ...
# Modelling Theory and Practice/Modelling with Concepts

| | composite | even | odd | prime | square |
| 1 | | | √ | | √ |
| 2 | | √ | | √ | |
| 3 | | | √ | √ | |
| 4 | √ | √ | | | √ |
| 5 | | | √ | √ | |
| 6 | √ | √ | | | |
| 7 | | | √ | √ | |
| 8 | √ | √ | | | |
| 9 | √ | | √ | | √ |
| 10 | √ | √ | | | |
Start: single property R(x). Now: extend by further properties R(x), S(x), T(x).
Can be shown in a table like:
Problem: how to keep the overview? Solution: by introducing concepts.
What is a concept:
* Intuition
* Characteristics
* Definition
* Hasse diagram
Basic structures
* linear order
* taxonomy (tree)
* diamond
Formal concept analysis
Fundamental theorem of concept analysis: the set of concepts are a lattice.
More complex structures.
# Models and Theories in Human-Computer Interaction/A Route of Understanding and Analyzing a Phenomenon - Activity Theory
### A Route of Understanding

Activity theory enables the studying the context in which a human interacts with computers, it provides a framework to reason an entire work system beyond an individual user. Activity Theory provides focus on the following items (from Carroll) -
* analysis and design focused on a particular work process with concerns for the social reality around that process.
* analysis and design focused on actual usage
* focus on the development of expertise
* active user participation in the development process
One of the strengths of Activity Theory is that it provides a mechanism to bridge the gap between the a individual user and the social reality around them. Meaning it takes into account the environment, personal interaction, what going on in the local area. Giving you a very comprehensive picture vs early HCI theories.
# Modelling Theory and Practice/Models and Abstraction
## Models

Herbert Stachowiak, 1973

### Fundamental Properties of the general Concept of Models

* Mapping: Models are always models of something, i.e. mappings from, representations of natural or artificial originals, that can be models themselves.
* Reduction: Models in general capture not all attributes of the original represented by them, but rather only those seeming relevant to their model creators and/ or model users.
* Pragmatism: Models are not uniquely assigned to their originals per se. They fulfill their replacement function a) for particular - cognitive and/ or acting, model using subjects, b) within particular time intervals and c) restricted to particular mental or actual operations.

### Remarks

* Of particular importantance is the aspect of pragmatism: "Beyond mapping and reduction the general notion of model needs to be relativised in three ways. Models are not only models of something. They are also models for someone, a human or an artificial model user. At this, they fulfill they function over time, within a time interval. Finally, they are models for a certain purpose. Alternatively this could be expressed as: a pragmatic complete determination of the notion of model has not only to consider the question 'what of' something is a model, but also 'whom for', when, and 'what for' it is a model, wrt. its specific function."
* Moreover Stachowiak provides a more formal explication of the concept of model. For our purposes the above colloquial description is sufficient.
* For example ...
* This book relates to the above properties in the following way:
** Mapping: This book in the first place covers the right hand side of the mapping, i.e. the structures one might map to. The structures presented start from very basic ones, becoming more and more complex in a (hopefully) systematic way. Thus it provides the modeler with a basic repertoire for mapping its originals to. Of course the underlying assumption is, that the simple strcutures are more relevant than the more complex ones ...
** Reduction: The book is purely structural, i.e. it is not about any concrete area of knowledge, it's like mathematics: one cow plus another one make two cows, as well as one electron plus another one make two electrons. In terms of maths it's 1+1. Thus, the structures in this book contain no semantics from any kind of application domain.
** Pragmatism is difficult to approach, since it is a quite 'soft' aspect, relative to the eyes of every beholder. The approach of this book to pragmatism is case based, i.e. providing empirical cases on a restricted subject area and in a systematic way, s.t. they can be fit by a modeller for its purposes. See Case-based reasoning.

## Literature

* Stachowiak, Herbert (1973). Allgemeine Modelltheorie [General Model Theory] (in german (DE)). Springer. ISBN ISBN 3-211-81106-0. {{cite book}}: Check |isbn= value: invalid character (help)CS1 maint: unrecognized language (link)
* Translation by modelpractice
# Linear Algebra with Differential Equations/Homogeneous Linear Differential Equations/Repeated Eigenvalue Method

When the eigenvalue is repeated we have a similar problem as in normal differential equations when a root is repeated, we get the same solution repeated, which isn't linearly independent, and which suggest there is a different solution. Because the case is very similar to normal differential equations, let us try $\mathbf {X} =\mathbf {u} te^{\mathbf {\lambda } t}$ for $\mathbf {X} '=\mathbf {A} \mathbf {X}$ and we see that this does not work; however, $\mathbf {X} =(\mathbf {B} t+\mathbf {C} )e^{\mathbf {\lambda } t}$ DOES work (For the observant reader, this gives a hint to the changes in the Method of Undetermined Coefficients as compared to differential equations without linear algebra).
In fact if we use this we see that $\mathbf {B} =\mathbf {u}$ where $\mathbf {u}$ is a typical eigenvector; and we see that $\mathbf {C} =\mathbf {n}$ where $\mathbf {n}$ is a normal eigenvector defined by $(\mathbf {A} -\lambda \mathbf {I} )\mathbf {C} =\mathbf {B}$
Thus our fundamental set of solutions is: $\{\mathbf {u} te^{\lambda t}+\mathbf {n} e^{\lambda t};\mathbf {u} e^{\lambda t}\}$
Using the same process of derivation, higher-order problems can be solved similarly.
# Linear Algebra with Differential Equations/Heterogeneous Linear Differential Equations/Variation of Parameters

As with the variation of parameters in the normal differential equations (a lot of similarities here!) we take a fundamental solution and by using a product with a to-be-found vector, see if we can come upon another independent solution by these means. In other words, since the general solution can be expressed as $\mathbf {c\psi }$ where $\mathbf {c}$ is the constant matrix and $\mathbf {\psi }$ is the augmented set of independent solutions to the homogeneous equation, we try out a form like so:
$\mathbf {X} =\mathbf {u\psi }$
And determine $\mathbf {u}$ to find a unique solution. The math is fairly straightforward and left as an exercise for the reader, and leaves us with:
$\mathbf {X} =\mathbf {\psi } (t)\mathbf {\psi } ^{-1}(t_{0})\mathbf {X} ^{0}+\mathbf {\psi } (t)\int _{t_{0}}^{t}\mathbf {\psi } ^{-1}(s)\mathbf {g} (s)ds$
... which is a fairly strong, striaghtforward, yet exceedingly complicated formula.