OpenLLM-France/wikimedia huggingface dataset:
# Markerless Tracking/Related Work

This page sumarizes related work for the research project Markerless Tracking.

## Recognition

Blanz et. al. showed how to use computer generated images of faces to recognize real ones. This work is based on a morphable face model which was presented before.
Not jet reviewd:

## Tracking

Motion Capturing could greatly improve with analysis-by-synthesis as stated by Moeslund and Granum.
Not jet reviewd:

## Theory

Not jet reviewd:

## Commercial

Organic Motion's solution to Motion Capturing was presented at SIGGRAPH 2007 (demo video) and is the first commercial available product to track all bodyparts including bones, geometry and textures. Their website claims that "Tschesnok created a thinking system which looks at people in a manner very similar to the way the brain process human vision.". Obviously it is not quite clear how this works. Hopefully their pending patent will be available soon.

## Interdisciplinary

As briefly described in neuro-scientists found evidence that the nervous system use probabilistic population codecs.
# Motivation and emotion/Wikiversity/Tables

Tables can be an effective way to organise and summarise information. Tables should be captioned (using APA style) to explain their relevance to the text. Plus each table should be referred to at least once in the main text (e.g., see Table 1 and Table 2).
Here are some example 3 x 3 tables which could be adapted:
Table 1.
Example of a Table with an APA Style Caption
| Children | Gather | Round |
| Mary | had | a |
| little | lamb | it's |
| fleece | was | white |
Table 2.
Another Example of a Table with an APA Style Caption
| Nursery | Rhyme | Time |
| Incy | Wincy | spider |
| climbed | up | the |
| water | spout | down |
Table 3.
Example of a Sortable Table with an APA Style Caption
| Fruit | Price/kg | Popularity |
| Tomatoes | $6.00 | 1st |
| Bananas | $5.00 | 2nd |
| Watermelon | $2.99 | 3rd |
| Oranges | $3.85 | 4th |
| Apples | $4.95 | 5th |
| Grapes | $9.50 | 6th |
| Mangoes | $12.00 | 7th |
| Avocados | $12.00 | 8th |
# Motivational interviewing

This psychology resource is a "stub". Learn how you can help Wikiversity to develop it.
This Medicine resource is a "stub". Learn how you can help Wikiversity to develop it.
Motivational interviewing was developed by William Miller and Stephen Rollnick as a counseling approach to helping clients discover their own desire to change unhealthy behaviors. The work of MI begain in chemical dependancy but it has been found to be useful in other forms psychotherapy.
# Movie Reviews

Everyone is welcome to contribute to this project by writing a review of a movie.

## How to write a movie review

Enter title that is not already on the list below and start your draft. First-time editors are welcome. Reviews of movies not available for free on the internet are welcome. Multiple reviews of the same movie are welcome (just give the review a slightly different name.)
If you wish to change your title, or have any other questions, visit us at Wikiversity:Colloquium.

## List of Movie reviews

We currently have only two reviews:
* Paris, Texas
* The Magic Flute

## Free Movies on the Internet

This section is experimental because it is not yet known if movies posted on sites like YouTube remain for a sufficient amount of time for this list to be maintained. The following list of X Bergman films was posted on March 3, 2024. Let's see how long this list lasts.
* Important: The current understanding at Wikiversity is that any link to the showing of a movie must be absolutely free. All links to pages that charge the viewer to see the film are websites are prohibited.

### The Bergman Collection

The only film that has a review is The Magic Flute, and it is under construction. Do not hesitate to write your own review any film that already has an review. Wikiversity welcomes parallel efforts: Just give the subpage a slightly different name. See Wikipedia:Ingmar Bergman)
* Summer Interlude (1951)-YouTube (see on Wikipedia:Summer Interlude)
* Summer with Monika (1953)-YouTube (see on Wikipedia:Summer with Monika)
* Dreams-YouTube (see on Wikipedia:Dreams (1955 film))
* Smiles of a Summer Night (1955)-YouTube (see on Wikipedia:Smiles of a Summer Night)
* The Seventh Seal (1957)-YouTube (see on Wikipedia:The Seventh Seal)
* Wild Strawberries (1957)-YouTube (see on Wikipedia:Wild Strawberries (film))
* The Virgin Spring (1960)-YouTube (see on Wikipedia:The Virgin Spring)
* The Magic Flute-YouTube (see on Wikipedia:The Magic Flute (1975 film))Y Done: See The Magic Flute review.
* Hour of the Wolf (1968)-YouTube (see on Wikipedia:Hour of the Wolf)
* Shame-YouTube (see on Wikipedia:Shame (1968 film))
* The Passion of Anna (1969)-YouTube (see on Wikipedia:The Passion of Anna)

### Other movies currently available at no cost on the internet

Please list any movie you find on the internet that can viewed for free. We will know when the movie was added and will watch to see how long the link remains active.
* insert URL here
* insert URL here
# Motivation and emotion/Wikiversity/Social contributions

A brief overview of social contributions, with links to more detailed information.

## What are social contributions?

* Any publicly viewable contribution to the internet that enhances the motivation and emotion project beyond the chapter you are working on.
* e.g., direct edit to a book chapter (current or past) or provide feedback on its talk page or contribute to a UCLearn discussion or social media thread in some way that directly or indirectly improves the quality of book chapter project beyond the chapter you are individually working on.

## Why social contributions?

* Encourage and support peer feedback
* Enhance communication skills
* Reward student engagement

## Types of social contribution

Social contributions can include:
* Direct editing to improve past or current chapters (e.g., adding new info/content, fixing errors, improving layout/formatting, adding relevant links) - examples
* Provide feedback on chapter talk pages (e.g., especially about chapter plans and/or drafts)
* Discussion
** UCLearn discussion forum posts e.g., respond to requests for feedback
** X - posts that discuss and promote the project using #emot24

## Summarising social contributions

* Summarising social contributions with links to evidence

## Topic development

* Make at least three different types of social contribution and summarise them with direct links to evidence on your Wikiversity user page
* See the topic development guidelines for more details

## Book chapter

* Contributions with direct links to evidence are assessed according to their quality, quantity, and timeliness
* See the book chapter guidelines for more details
# Mathematics for Applied Sciences (Osnabrück 2011-2012)/Part I/Exercise sheet 28

    Warm-up-exercises

### Exercise

Let $x\in \mathbb {R}$ and consider the function
    $f\colon \mathbb {R} _{+}\longrightarrow \mathbb {R} ,t\longmapsto f(t)=t^{x}e^{-t}.$
Determine the extrema of this function.

### Exercise

    $\operatorname {Fac} \,{\left({\frac {2k-1}{2}}\right)}={\frac {\prod _{i=1}^{k}(2i-1)}{2^{k}}}\cdot {\sqrt {\pi }}\,$
holds.

### Exercise

a) Prove that for $x\geq 1$ the estimate
    $\int _{1}^{\infty }t^{x}e^{-t}dt\leq 1\,$
holds.
b) Prove that the function $H(x)$ defined by
    $H(x)=\int _{1}^{\infty }t^{x}e^{-t}dt\,$
for $x\geq 1$ is increasing.
c) Prove that $10!\geq e^{11}+1$.
d) Prove that for the factorial function for $x\geq 10$ the estimate
    $\operatorname {Fac} \,x\geq e^{x}\,$
holds.

### Exercise

Solve the initial value problem
    $y'=\sin t{\text{ with }}y(\pi )=7$

### Exercise

Solve the initial value problem
    $y'=3t^{2}-4t+7{\text{ with }}y(2)=5$

### Exercise

Find all the solutions for the ordinary differential equation
    $y'=y\,.$

### Exercise

Convince yourself that in a location-independent differential equation (i.e. $f(t,y)$ does not depend on $y$) the difference between two solutions $y_{1}$ and $y_{2}$ does not depend on time, that is $y_{1}(t)-y_{2}(t)$ is constant. Show with an example that this may not happen in a time-independent differential equation.
    Hand-in-exercises

### Exercise

Prove that for the factorial function the relationship
    $\operatorname {Fac} \,x=\int _{0}^{1}(-\ln t)^{x}dt\,$
holds.

### Exercise

Solve the initial value problem
    $y'=3t^{3}-2t+5{\text{ with }}y(3)=4$

### Exercise

Find a solution for the ordinary differential equation
    $y'=t+y\,.$

### Exercise

Solve the initial value problem
    $y'={\frac {t^{3}}{t^{2}+1}}{\text{ with }}y(1)=2$
# Mathematics for Applied Sciences (Osnabrück 2011-2012)/Part I/Exercise sheet 29

    Warm-up-exercises

### Exercise

Find the solutions to the ordinary differential equation
    $y'=-{\frac {y}{t}}\,.$

### Exercise

Find the solutions to the ordinary differential equation
    $y'={\frac {y}{t^{2}}}\,.$

### Exercise

Find the solutions to the ordinary differential equation
    $y'=e^{t}y\,.$

### Exercise

Find the solutions of the inhomogeneous linear differential equation
    $y'=y+7\,.$

### Exercise

Find the solutions to the inhomogeneous linear differential equation
    $y'=y+{\frac {\sinh t}{\cosh ^{2}t}}\,.$

### Exercise

Let
    $f\colon I\longrightarrow \mathbb {R} _{+}$
be a differentiable function on the interval $I\subseteq \mathbb {R}$. Find a homogeneous linear ordinary differential equation for which $f$ is a solution.

### Exercise

Let
    $y'=g(t)y\,$
be a homogeneous linear ordinary differential equation with a function $g$ differentiable infinitely many times and let $y$ be a differentiable solution.
a) Prove that $y$ is also infinitely differentiable.
b) Let $y(t_{0})=0$ for a time-point $t_{0}$. Prove, using the formula
    $(f\cdot g)^{(n)}=\sum _{k=0}^{n}{\binom {n}{k}}f^{(k)}\cdot g^{(n-k)}\,,$
that $y^{(n)}(t_{0})=0$ for all $n\in \mathbb {N}$.

### Exercise

a) Find all solutions for the ordinary differential equation ($t\in \mathbb {R}$)
    $y'={\frac {y}{t}}\,.$
b) Find all solutions for the ordinary differential equation ($t\in \mathbb {R}$)
    $y'={\frac {y}{t}}+t^{7}\,.$
c) Solve the initial value problem
    $y'={\frac {y}{t}}+t^{7}{\text{ and }}y(1)=5.$
The following statement is called the superposition principle for inhomogeneous linear differential equations. It says in particular that the difference of two solutions of an inhomogeneous linear differential equation is a solution of the corresponding homogeneous linear differential equation.

### Exercise

Let $I\subseteq \mathbb {R}$ be a real interval and let
    $g,h_{1},h_{2}\colon I\longrightarrow \mathbb {R}$
be functions. Let $y_{1}$ be a solution to the differential equation $y'=g(t)y+h_{1}(t)$ and let $y_{2}$ be a solution to the differential equation $y'=g(t)y+h_{2}(t)$. Prove that $y_{1}+y_{2}$ is a solution to the differential equation
    $y'=g(t)y+h_{1}(t)+h_{2}(t)\,.$
    Hand-in-exercises

### Exercise

Confirm by computation that the function
    $y(t)=c{\frac {\sqrt {t-1}}{\sqrt {t+1}}}\,$
found in the example satisfies the differential equation
    $y'=y/(t^{2}-1)\,.$

### Exercise

Find the solutions to the ordinary differential equation
    $y'={\frac {y}{t^{2}-3}}\,.$

### Exercise

Solve the initial value problem
    $y'={\frac {t}{t^{2}+2}}y{\text{ with }}y(3)=7$

### Exercise

Find the solutions to the inhomogeneous linear differential equation
    $y'=y+e^{2t}-4e^{-3t}+1\,.$

### Exercise

Find the solutions to the inhomogeneous linear differential equation
    $y'={\frac {y}{t}}+{\frac {t^{3}-2t+5}{t^{2}-3}}\,.$
# Mathematics for Applied Sciences (Osnabrück 2011-2012)/Part I/Exercise sheet 30

    Warm-up-exercises

### Exercise

Sketch the underlying vector fields of the differential equations
    $y'={\frac {1}{y}},\,y'=ty^{3}{\text{ and }}y'=-ty^{3}$
as well as the solution curves given in [[|the examples]].

### Exercise

Confirm by derivation that the curves we have found in the examples are the solution curves of the differential equations
    $y'={\frac {1}{y}},\,y'=ty^{3}{\text{ and }}y'=-ty^{3}.$

### Exercise

Interpret a location-independent differential equation as a differential equations with separable variables using the theorem for differential equations with separable variables.

### Exercise

Determine all the solutions to the differential equation
    $y'=y\,,$
using the theorem for differential equations with separable variables.

### Exercise

Determine all the solutions to the differential equation
    $y'=e^{y}\,,$
using the theorem for differential equations with separable variables.

### Exercise

Determine all the solutions to the differential equation
    $y'={\frac {1}{\sin y}}\,,$
using the theorem for differential equations with separable variables.

### Exercise

Solve the differential equation
    $y'=ty\,$
using the theorem for differential equations with separable variables.

### Exercise

Consider the solutions
    $y(t)={\frac {g}{1+\exp(-st)}}\,$
to the logistic differential equation we have found in an example.
a) Sketch up the graph of this function (for suitable $s$ and $g$).
b) Determine the limits for $t\rightarrow \infty$ and $t\rightarrow -\infty$.
c) Study the monotony behavior of these functions.
d) For which $t$ does the derivative of $y(t)$ have a maximum (For the function itself, this represents an inflection point).

### Exercise

Find a solution for the ordinary differential equation
    $y'={\frac {t}{t^{2}-1}}y^{2}\,$
with $t>1$ and $y<0$.

### Exercise

Determine the solutions for the differential equation ($y>0$)
    $y'=t^{2}y^{3}\,$
using separation of variables. Where are the solutions defined?
    Hand-in-exercises

### Exercise

Prove that a differential equation of the shape
    $y'=g(t)\cdot y^{2}\,$
with a continuous function
    $g\colon \mathbb {R} \longrightarrow \mathbb {R} ,t\longmapsto g(t),$
on an interval $I'$ has the solution
    $y(t)=-{\frac {1}{G(t)}}\,,$
where $G$ is an antiderivative of $g$ such that $G(I')\subseteq \mathbb {R} _{+}$.

### Exercise

Determine all the solutions to the differential equation
    $y'=ty^{2},\,y>0,$
using the theorem for differential equations with separable variables.

### Exercise

Determine all the solutions to the differential equation
    $y'=t^{3}y^{3},\,y>0,$
using the theorem for differential equations with separable variables.

### Exercise

Determine the solutions to the differential equation
    $y'=ty+t\,$
by using the approach for
a) inhomogeneous linear equations,
b) separable variables.
# Mathematics for Applied Sciences (Osnabrück 2011-2012)/Part I/Exercise sheets

Exercise sheet 1
Exercise sheet 2
Exercise sheet 3
Exercise sheet 4
Exercise sheet 5
Exercise sheet 6
Exercise sheet 7
Exercise sheet 8
Exercise sheet 9
Exercise sheet 10
Exercise sheet 11
Exercise sheet 12
Exercise sheet 13
Exercise sheet 14
Exercise sheet 15
Exercise sheet 16
Exercise sheet 17
Exercise sheet 18
Exercise sheet 19
Exercise sheet 20
Exercise sheet 21
Exercise sheet 22
Exercise sheet 23
Exercise sheet 24
Exercise sheet 25
Exercise sheet 26
Exercise sheet 27
Exercise sheet 28
Exercise sheet 29
Exercise sheet 30
Exercise sheet x
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Characteristic polynomial/Insert and direct determinant/Exercise/Exercisereferencenumber

Exercise 28.4
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Complex numbers/Conjugation/Real part imaginary part/Fact/Proof/Exercise/Exercisereferencenumber

Exercise 5.35
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Complex numbers/Field/Fact/Proof/Exercise/Exercisereferencenumber

Exercise 5.32
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Complex numbers/Real and imaginary part/Properties/Fact/Proof/Exercise/Exercisereferencenumber

Exercise 5.34
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Binomial coefficient/Sum in Pascal triangle/Fact/Proof/Exercise/Exercisereferencenumber

Exercise 4.13
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Complex Conjugation/Rules/Fact/Proof/Exercise/Exercisereferencenumber

Exercise 3.41
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/4-number-problem/Ordered by size/Matrix/Exercise/Exercisereferencenumber

Exercise 24.31
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Compact interval/Real function/Riemann integrable on partition/Fact/Proof/Exercise/Exercisereferencenumber

Exercise 18.14
# Prioritizing Content
### Prioritizing Content

After identifying a list of potential tasks and subtasks that may need to be trained, you will need to identify and select those tasks that should be trained. As an instructional designer, you need to be careful not to select and train tasks just because they were identified during the Task Analysis. Many designers identify training content by using their best estimation of what needs to be trained ("best guess"), but that is not the best way to select the content. Instead, you should adopt and use a systematic process that will help you identify the correct tasks based on reasoning and analysis.
There are many reasons why you may not want to select a task for training. The following list identifies some common reasons for not selecting a task for training:
* The student should already possess the knowledge, skill or ability/attitude (KSA)
* The task will be trained later after scaffolding is provided
* The task is accomplished infrequently
* There isn’t enough time
* The return on the investment is not adequate to justify the cost
QUESTION #1: Why would you not want to train a task that is accomplished infrequently?
Think about how you would answer this question before clicking on the answer below.
ANSWER #1

### Instruments for Prioritizing Content

There are a variety of instruments (tools) that can be used to help you select and prioritize content for physical tasks that need to be trained.
The three instuments in the table below are the tools we recommend. When selecting the appropriate tool(s) to use, review them in the order listed.
| INSRUMENT NAME | INSTRUMENT DESCRIPTION | USE |
| CSS Decision Tree | Evaluates for prior experience | Used first. Fast but less accurate |
| DCF Decision Tree | Evaluates Difficulty, Criticality and Frequency | Used 2nd. Less specific than the ACL form |
| ACL Data Analysis Form | Evaluates specific criteria for each task/subtask | Provides a high degree of accuracy; harder to complete |

## Navigation

| < Back | Home | Next > |
# Principles of electricity
### Electrical Circuit Theory

* Lecture 1: Electrons and Electric Fields
* Lecture 2: Voltage
* Lecture 3: Electrical current
* Lecture 4: Ohm's Law: Resistance
* Lecture 5: Henry's Law: Inductance
* Lecture 6: Faraday's Law: Capacitance
# Prioritizing Content/ANSWER

* ANSWER #1
* QUESTION #1: Why would you not want to train a task that is accomplished infrequently?
* Skills need to be transferred to the workplace and used and reinforced. Infrequent tasks are better when supported through the use of a job aid, electronic performance support system (EPSS), or other means. Teaching a skill that is not going to be used within a reasonable length of time can contribute to unnecessary overload. Instead, focus on skills that are used often and/or are critical.

## Navigation

| < Back | Home | Next > |
# PlanetPhysics/Space Time Continuum of the Special Theory of Relativity Considered As a Euclidean Continuum

\subsection{The Space-Time Continuum of the Special Theory of Relativity Considered as a Euclidean Continuum} From Relativity: The Special and General Theory by Albert Einstein
We are now in a position to formulate more exactly the idea of Minkowski, which was only vaguely indicated in section 17. In accordance with the special theory of relativity, certain co-ordinate systems are given preference for the description of the four-dimensional, space-time continuum. We called these ``Galileian co-ordinate systems." For these systems, the four co-ordinates </math>x, y, z, t$,whichdetermineaneventor---inotherwords,apointofthefour-dimensionalcontinuum---aredefinedphysicallyinasimplemanner,assetforthindetailinthefirstpartofthisbook.ForthetransitionfromoneGalileiansystemtoanother,whichismovinguniformlywithreferencetothefirst,theequationsoftheLorentztransformationarevalid.Theselastformthebasisforthederivationofdeductionsfromthespecialtheoryofrelativity,andinthemselvestheyarenothingmorethantheexpressionoftheuniversalvalidityofthelawoftransmissionoflightforallGalileiansystemsofreference.MinkowskifoundthattheLorentztransformationssatisfythefollowingsimpleconditions.Letusconsidertwoneighboringevents,therelativepositionofwhichinthefour-dimensionalcontinuumisgivenwithrespecttoaGalileianreference-body<math>K$ by the space co-ordinate differences $dx,dy,dz$ and the time-difference $dt$. With reference to a second Galileian system we shall suppose that the corresponding differences for these two events are $dx',dy',dz',dt'$. Then these magnitudes always fulfill the condition \footnotemark.
$dx^{2}+dy^{2}+dz^{2}-c^{2}dt^{2}=dx'2+dy'2+dz'2-c^{2}dt'^{2}$
The validity of the Lorentz transformation follows from this condition. We can express this as follows: The magnitude
$ds^{2}=dx^{2}+dy^{2}+dz^{2}-c^{2}dt^{2}$
\noindent which belongs to two adjacent points of the four-dimensional space-time continuum, has the same value for all selected (Galileian) reference-bodies. If we replace $x,y,z$, ${\sqrt {-I}}\cdot ct$ , by </math>x_1, x_2, x_3, x_4$,wealsoobtaintheresultthat<math>ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}+dx_{4}^{2}$
\noindent is independent of the choice of the body of reference. We call the magnitude ds the "distance" apart of the two events or four-dimensional points.
Thus, if we choose as time-variable the imaginary variable ${\sqrt {-I}}\cdot ct$ instead of the real quantity $t$, we can regard the space-time continuum---accordance with the special theory of relativity---as a "Euclidean" four-dimensional continuum, a result which follows from the considerations of the preceding section.