OpenLLM-France/wikimedia huggingface dataset:
# PlanetPhysics/Alternative Definition of Small Category

A (small) category ${\mathcal {C}}$ consists of a set of objects $C_{0}$ and a set of arrows $C_{1}$ together with the following structure:
* a source map $s:C_{1}\to C_{0}$ assigning an object $s(f)$ to each arrow $f\in C_{1}$ ,
* a target map: $t:C_{1}\to C_{0}$ assigning an object t(f) to each arrow $f\in C_{1}$ ,
* an identity map $1:C_{0}\to C_{1}$ assigning to each object $A$ an arrow $1_{A}$ with $s(1_{A})=t(1_{A})=A,$
* a composition map $\circ :C_{1}\times C_{1}\to C_{1}$ assigning to each pair of arrows $f,g$ , such that $s(g)=t(f)$, a third arrow $g\circ f$ with $s(g\circ f)=s(f)$ and $t(g\circ f)=t(g)$.
* The composition thus defined "$\circ$" is associative, that is, $h\circ (g\circ f)=(h\circ g)\circ f$ whenever these compositions make sense.
* the identity map satisfies $f\circ 1_{A}=f$ for any $f$ such that $s(f)=A$ and $1_{A}\circ g=g$, and any $g$ such that $t(g)=A$.
# Fluid Mechanics for Mechanical Engineers/External Flows
## External Viscous Flows

THIS SECTION HAS TO BE WRITTEN
# Fluid Mechanics for Mechanical Engineers/Energy Considerations in Internal Flows

>back to Chapters of Fluid Mechanics for Mechanical Engineers

### Losses and Energy consideration

* Velocity profiles for laminar (upper) and turbulent (lower) states at the same mass flow rate
# Polynomial function/R/Continuous/Fact/Proof2

Due to example and fact, the powers
    $\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto x^{n},$
are continuous for every $n\in \mathbb {N}$. Hence, also the functions
    $\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto ax^{n},$
are continuous for every $a\in \mathbb {R}$ and therefore, again due to fact, the functions
    $\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{1}x+a_{0},$
are continuous.
# Polynomial function/R/Continuous/Fact

Polynomial functions
    $P\colon \mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto P(x),$
# Polynomial ring/Endomorphism/Matrix/Insertion/Remark

Let $K$ be a field, $V$ a finite-dimensional $K$-vector space and
    $f\colon V\longrightarrow V$
a linear mapping. Let $v_{1},\ldots ,v_{n}$ be a basis of $V$, and let $M$ denote the corresponding matrix. Due to fact, we have a correspondence between compositions of linear mappings and matrix multiplication. In particular, $f^{n}$ corresponds with $M^{n}$. In the same way, the scalar multiplication and the addition on the space of endomorphisms $\operatorname {End} _{\left(V\right)}$ and on the space of matrices correspond to each other. Therefore, instead of the assignment $P\mapsto P(f)$, we can also work with the assignment $P\mapsto P(M)$.
# Polynomial ring/Endomorphism/Inserting/Ring homomorphism (without concept)/Fact

Let $K$ be a field, $V$ a $K$-vector space, and
    $f\colon V\longrightarrow V$
a linear mapping. Then the mapping
    $K[X]\longrightarrow \operatorname {End} _{\left(V\right)},P\longmapsto P(f),$
has the following properties.
* For a constant polynomial $P=a_{0}$, we have In particular, the zero polynomial is sent to the zero mapping and the constant $1$-polynomial is sent to the identity.
    $P(f)=a_{0}(f)=a_{0}f^{0}=a_{0}\operatorname {Id} _{V}\,.$
* We have for all polynomials $P,Q\in K[X]$.
    $(P+Q)(f)=P(f)+Q(f)=Q(f)+P(f)\,$
* We have for all polynomials $P,Q\in K[X]$.
    $(P\cdot Q)(f)=P(f)\circ Q(f)=Q(f)\circ P(f)\,$
* We have for all $n\in \mathbb {N}$.
    $(X^{n})(f)=f^{n}\,$
# Polynomial ring/Endomorphism/Inserting/Ring homomorphism (without concept)/Fact/Proof

(1) and (4) are inherent in the definition of the substitution homomorphism. From this, also (2) and (3) follows.
# Polynomial function/R/Degree d/(d+1)-te Derivative/Exercise

Prove that a polynomial $P\in \mathbb {R} [X]$ has degree $\leq d$ (or it is $P=0$), if and only if the $(d+1)$-th derivative of $P$ is the zero poynomial.
# Polynomial function/R/Odd/Exercise

Let
    $P=\sum _{k=0}^{d}a_{k}x^{k}\in \mathbb {R} [X]\,$
be a polynomial. Show that $P$ is an odd function if and only if $a_{k}=0$ for all even indices.
# Polynomial ring/Basis/Example

In the polynomial ring $K[X]$ over a field $K$, the powers $X^{n}$, $n\in \mathbb {N}$, form a basis. By definition, every polynomial
    $a_{n}X^{n}+a_{n-1}X^{n-1}+\cdots +a_{2}X^{2}+a_{1}X+a_{0}$
is a linear combination of the powers $X^{0}=1,X^{1}=X,\ldots ,X^{n}$. Moreover, these powers are linearly independent. For if
    $a_{n}X^{n}+a_{n-1}X^{n-1}+\cdots +a_{2}X^{2}+a_{1}X+a_{0}=0\,,$
then all coefficients equal $0$ (this is part of the concept of a polynomial).
# Polynomial ring/Differential operators/Not commutative/Exercise

Show that the ring of differential operators on $K[X_{1},\ldots ,X_{n}]$ is not commutative.
# Project management/Introduction
## 00 PROJECT MANAGEMENT - An Introduction to what follows

The following Project Management (in short PM) pages headline numbered from 00 (= this page) to 100:
* Is based on the visual concept of MIND MAPS, a method to visualize information in a brain-user-friendly way
* Is a work in progress, i.e. sometimes even a referenced page may not exist yet
* Sometimes shows the same subject from different angles, e.g. the first lessons
* Originates from personal experience of using PM for some decades
* Combines ideas of different schools of thought in the area of PM, partially covered in the bibliography (still to come)
* Transcends occasionally the usual structure of PM to include, among others, ideas covered under the term “soft sciences”
* Are used in teaching projects at University level and also for post graduate / Master courses
* Are to be dealt with the way of Supermarket Shopping: Take what is suitable and leave the rest away!
Franz Kies 14:36, 12 March 2008 (UTC)
# Instructional design/Psychomotor behaviors/Self Talk in Psychomotor Skills/Review answers

Lesson work sheet
1. What are the similarities between each of these cases?
| | Question 3A: Complete this section after reading the case studies and prior to reading the rest of the lesson. For each performer, write in the space below what would you do if you were the performer’s instructor/coach? | Question 3B: Complete this section after reading the entire lesson. For each performer, write in the space below what would you do if you were the performer’s instructor/coach? |
| Anna | - - - - - - - | - - - - - - - |
| Tom | - - - - - - - | - - - - - - - |
| Tracy | - - - - - - - | - - - - - - - |
| Your own experience | - - - - - - - | - - - - - - - - |
< Back
# Instructional design/Psychomotor behaviors/Self Talk in Psychomotor Skills/Review your answers

Lesson work sheet answers
1. What are the similarities between each of these cases?
* Each of the performers likely have the skills and knowledge to perform well in these tasks
* Each of the performer is operating under potentially high stress circumstances
* Each of the performer's performance gaps are unlikely to be caused by a lack of motivation or lack of skills or knowledge
| | Question 3B: Complete this section after reading the entire lesson. For each performer, write in the space below what would you do if you were the performer’s instructor/coach? Include your diagnostic steps and at least one of the 5 methods discussed. Below are some suggested strategies. Your answers may differ from these examples. |
| Sara | - Ask Sara what she thinks about when she is playing. - Prior to going on stage, have her breath deeply for 5 minutes. - Have her set of goal of getting to the end of each page of music and focusing on that as she is playing. |
| Bob | - Ask Bob how he feels about presenting. - Instruct Bob the night before the presentation to picture himself articulate and at ease in front of a large audience as he is giving the presentation. - Have him bring a laser pointer to his presentation. During the presentation, if he notices he is getting nervous, have him practice focusing on how the laser pointer feels in his hand. |
| Tracy | - Ask Tracy how she feels physically right before the start of the race. - Right before the race and during the first 100 meters, have her repeat in her head the word "pace". |
< Back
# Instructional design/R2D2

Segment 1: Introduction to R2D2
“Why learn R2D2? Why is it useful? What does it do?”
R2D2 (which stands for Read, Reflect, Display, and Do) is a model designed to help online instructors and/or online course designers to integrate learning activities that accommodate all learning styles. Although web-based learning has become increasingly popular, many of the activities used in web-based learning are predominantly text-based and do not take learning styles into consideration. The R2D2 model provides 4 phases that it recommends for inclusion in all online courses. By including these 4 phases in your instruction, you automatically make your learning activities attractive to all learning styles and create an interactive course that utilizes many tools that the internet and online learning can provide.
The R2D2 model is intended to provide guidance to online course designers, online trainers, and/or online teachers that will help them integrate non-text based instruction that is appealing to different learning preferences. The authors of the model think it is important to facilitate the movement from text-based learning toward learning activities that integrate collaboration and promote hands-on and active learning.
During this Wikiversity learning module you will be able to:
* become familiar with the R2D2 model,
* identify the 4 main phases of the R2D2 model,
* describe each phase as well as give example activities from each phase of the model,
* match activities to the correct phase,
* use a performance checklist that will help you to utilize the model,
* share with others how you might use this model in your situation, and
* gain additional resources that might also help you in planning your project.
The R2D2 Navigation list below will be found at the bottom of each page to provide users the capability to navigate throughout this learning module.
Please click on the "Segment 2" link to proceed to the next segment in this Wikiversity lesson on the R2D2 model.
R2D2 Navigation
* Segment 1: Introduction to R2D2 (You are here)
* Segment 2: R2D2-The Four Phases Overview
* Segment 3: Phase 1 (Reading)-Verbal/Auditory
* Segment 4: Phase 2 (Reflecting)-Reflective/Observational
* Segment 5: Phase 3 (Displaying)-Visual
* Segment 6: Phase 4 (Doing)-Hands-On
* Segment 7: Activities per phase
* Segment 8: Your thoughts...
* Segment 9: Conclusion/Resources
* Instructional Design Main Menu
# Instructional design/Psychomotor behaviors/Self Talk in Psychomotor Skills/Lesson worksheet

Lesson work sheet
1. What are the similarities between each of these cases?
2. Write a paragraph about an experience of your own. Include the task, how difficult it is for you to complete, how you felt and why you think you felt the way you do.
| | 3A: Complete this section after reading the case studies and prior to reading the rest of the lesson. For each performer, write in the space below what you do as the performer’s instructor/coach? | 3B: Complete this section after reading the entire lesson. For each performer, write in the space below what would you do as the performer's instructor/coach? Include your diagnostic steps and at least one of the 5 methods discussed. |
| Sara | - - - - - - - | - - - - - - - |
| Bob | - - - - - - - | - - - - - - - |
| Tracy | - - - - - - - | - - - - - - - |
| Your own experience | - - - - - - - | - - - - - - - |
4. Compare your responses between questions 3A. and 3B. What has changed? What will you do differently? Post your responses to the lesson's discussion tab.
5. Which of the 6 strategies for addressing self talk issues seem most effective to you and why? Post your responses to the lesson's discussion tab.
6. Adam Gopnik, published author and writer for the New Yorker, discussed in a live lecture how he dealt with writer's block by actually creating a methaphor for writing as a physical task. He tells himself he's riding a bike and makes up visual milestones he has to pass in order to complete the writing task. How else could psychomotor self talk strategies be applied to other cognitive skill areas? Post your ideas in this lesson's discussion page.
< Back
# Instructional design/Psychomotor behaviors/Strategies in Psychomotor Evaluations
## Introduction

| Instructional Design | Psychomotor Behaviors |
# Instructional design/R2D2/Activities per phase

Below are three quizzes that provide you with sample online instructional strategies that you could employ in your online course/training. Each quiz contains 10 sample online instructional strategies. Your task is to determine whether each strategy would be best used for the Reading, Reflecting, Displaying, or Doing phase of the R2D2 model. Keep track of which phase(s) you have difficulty on and navigate back to those segments for additional review as needed. The answers are provided for you to check your answers on each one. Once you have completed a quiz with 7 out of 10 correct, then please proceed to the next segment. If you are unable to do so, then please navigate back through this tutorial to review before attempting the quizzes again.
Please click below to see the answers for each quiz.
* Answer key to Quiz 1
* Answer key to Quiz 2
* Answer key to Quiz 3
Please click on the "Segment 8" link to proceed to the next segment in this Wikiversity lesson on the R2D2 model.
R2D2 Navigation
* Segment 1: Introduction to R2D2
* Segment 2: R2D2-The Four Phases Overview
* Segment 3: Phase 1 (Reading)-Verbal/Auditory
* Segment 4: Phase 2 (Reflecting)-Reflective/Observational
* Segment 5: Phase 3 (Displaying)-Visual
* Segment 6: Phase 4 (Doing)-Hands-On
* Segment 7: Activities per phase (You are here)
* Segment 8: Your thoughts...
* Segment 9: Conclusion/Resources
* Instructional Design Main Menu
# Instructional design/R2D2/(Displaying)-Visual

Phase 3 is focused on visual learners and providing all learners an opportunity to represent what they have learned. Many of us, when faced with learning a difficult task, have been helped with the use of visual aids, charts, figures, and tables. Visuals can be used to help learners master a concept, but they also can be used so that learners can show the learning taking place as they complete a course/training. (A wonderful example of this is in Segment 2 of this training where there was a link provided to a visual representation of this model.) Utilizing active knowledge construction strategies like having learners make concept maps leads to memories that can be easily recalled rather than learning that was passively received.
Visual learning activities can easily be integrated with other activities. When combined with other instructional strategies like podcasts or written text, dual encoding takes place and learning occurs more deeply and is more easily recalled by learners. This may make visual activities difficult to recognize as being phase 3, so specifically watch for ways that learners are either acquiring knowledge or displaying knowledge through a visual.
The authors recognize that this phase of the R2D2 model is more than likely the least developed. There are many reasons why this is so, but bandwidth and/or hardware/software for producing these activities may be lacking. As the Internet continues to grow in popularity and as individuals develop easier and less expensive ways for producing this type of content, they believe that this may be the phase of the model with the greatest potential for growth.
Below are some examples of visual learning:
* Pictures (Photographs)
* Animations (Learners only watch, but are unable to manipulate these moving images. Here is a sample on DNA replication: http://www.mcb.harvard.edu/losick/images/trombonefinald.swf)
* Videos (Learners create their own videos of the content.)
* Graphics (Created pictures, not photographs.)
* Flowcharts (Learners create linked boxes that show relationships and/or steps in a process. Sample flowcharts: http://www.rff.com/flowchart_samples.htm)
* Diagrams (Pictures with labels. Here is the human heart: http://www.rkm.com.au/anatomy/heart.html)
* Charts (Graphical representation of data. This article has a number of well-constructed charts: http://christianschooljournal.com/?p=526)
* Virtual Tours (Museums are now hosting these. How about visiting the Smithsonian Museum of Natural History? http://www.mnh.si.edu/panoramas/flashVersion/index.html)
* Maps
Please click on the "Segment 6" link to proceed to the next segment in this Wikiversity lesson on the R2D2 model.
R2D2 Navigation
* Segment 1: Introduction to R2D2
* Segment 2: R2D2-The Four Phases Overview
* Segment 3: Phase 1 (Reading)-Verbal/Auditory
* Segment 4: Phase 2 (Reflecting)-Reflective/Observational
* Segment 5: Phase 3 (Displaying)-Visual (You are here)
* Segment 6: Phase 4 (Doing)-Hands-On
* Segment 7: Activities per phase
* Segment 8: Your thoughts...
* Segment 9: Conclusion/Resources
* Instructional Design Main Menu
# Instructional design/R2D2/(Doing)-Hands-On

Phase 4 of the R2D2 model is primarily focused on those learners who like to "do" something with the knowledge that they have acquired, reflected on, and represented in some way. This phase is concerned with the application of knowledge toward a complex task. Phase 4 allows learners to experiment with their knowledge and attempt to evaluate or solve a complex task without much outside guidance. It is a great way for you, as the instructor or trainer, to analyze where strengths and deficiencies lie in learner understanding and then supply scaffolding as necessary to help the learner in their complex task.
The authors caution that these activities can be integrated into other phases as well, allowing you to know where your learners are having difficulty. However, be careful that you do not overwhelm your learners by giving them a task for which they do not yet have enough background knowledge. Doing so may result in frustrated learners who have difficulty knowing where to begin. The authors recommend that you provide practice activities within each step of the R2D2 model, but keep complex tasks as an activity that you take on once knowledge acquisition, reflection, and representation of knowledge has been completed successfully.
Learners who will prefer this phase (kinesthetic) are those who enjoy trying out what they have learned. These learners prefer to manipulate what they have learned and learn from feeling, interacting, and repetitive practice. Here are some examples of ways in which these learners can interact with their learning in an online environment:
* Simulations (Interactive animations for learners. For physics teachers, PhET is the best: http://phet.colorado.edu/en/simulations/category/physics)
* Games (Review for assessments using popular games. Here, a Jeopardy Game Review for multiplication facts: http://www.math-play.com/Multiplicaton-Jeopardy/Multiplication-Jeopardy.html)
* Cases and Scenarios (Learners analyze and learn from real cases. Here is a link to 18 virtual autopsies: http://www.merlot.org/merlot/viewMaterial.htm?id=78489)
* Wikipedia (Online encyclopedia where learners share knowledge and anyone can edit. http://en.wikiversity.org/)
* Real-World Data Collection (Learners perform research on the internet to collect, analyze, and report information.)
* Learning by Doing Galleries (Create a course website or gallery to show previous completed student work.)
Please click on the "Segment 7" link to proceed to the next segment in this Wikiversity lesson on the R2D2 model.
R2D2 Navigation
* Segment 1: Introduction to R2D2
* Segment 2: R2D2-The Four Phases Overview
* Segment 3: Phase 1 (Reading)-Verbal/Auditory
* Segment 4: Phase 2 (Reflecting)-Reflective/Observational
* Segment 5: Phase 3 (Displaying)-Visual
* Segment 6: Phase 4 (Doing)-Hands-On (You are here)
* Segment 7: Activities per phase
* Segment 8: Your thoughts...
* Segment 9: Conclusion/Resources
* Instructional Design Main Menu
# Ramazzini Center/MScPubHealth SDU Thesis Projects/Composting and recycling for household and industrial waste management in Chitwan, Nepal (CAR-Nepal)

Title of project Composting and recycling for household and industrial waste management in Chitwan, Nepal (CAR-Nepal) - and/or ?

#### MScPubHealth Students

Suyasha Koirala, Aayushi Thapa

#### Supervisors

Olaf Jensen, Erik Jørs

#### Tasks to be done

* Create an account in Wikiversity
* Select and complete relevant methodology courses: Theoretical Program - open here

#### 9. Presentation ppt exam
## METHODOLOGY

* Start and complete a research project
* Electronic Research tools_1
* Electronic Research tools 2
* Reading of scientific articles
* Theoretical epidemiology and biostatstics
* Checklists manuscript

##### References

* How to write medical articles
# Random

Learning and research project about randomness and wikis - feel free to join in.
A launching point for exploring Wikiversity - visit random links and see what you find....

## Examples and navigation

* Random 'pre-selected' Wikiversity page
* Random page in the main namespace (same as "Random Page" on sister projects)
* Random topic
* Special:RandomRootpage/Topic
* Random school
* Random portal
* Random draft
* Random page about Wikiversity
* {{Random mascot}}
* {{Coin toss}}
* {{Dice}}
* {{Die roll}}
* Extension:Random (sandbox server) e.g., use it to roll a die.
# Recurrent Neural Networks

A recurrent neural network (RNN) is a class of artificial neural networks where connections between nodes form a directed graph along a temporal sequence. This allows it to exhibit temporal dynamic behavior. Derived from feedforward neural networks, RNNs can use their internal state (memory) to process variable length sequences of inputs. This makes them applicable to tasks such as unsegmented, connected handwriting recognition or speech recognition.
This resource hosts a persistent conversation about academic papers that describe Attention Based Models. This is done by creating a page for each paper in the discussion and writing the relevant questions and comments in the page.

## Discussions

* Vaswani et al. 2017 Attention is All you Need

## See Also

* Wikipedia: Recurrent neural network
# Recursion/Induction/Remark

Closely related with induction is the principle of recursive definition. Here, one would like to define for every natural number $n$ a mathematical expression. This can be done by assigning to $0$ explicitly an expression and to describe how the expression for $n+1$ might be computed from the expression for $n$. This rule is called the recursive step. The inductive structure of the natural numbers ensures that for every natural number a unique expression is determined. For example, one can define an expression $F(n)$ by the initial step
    $F(0):=7\,$
and the recursive step
    $F(n+1):=F(n)\cdot n-n^{2}+3\,.$
# Rectangular area/River/1000 qm/Minimal fence/Exercise

Next to a rectilinear river we want to fence a rectangular area of $1000m^{2}$, one side of the area is the river itself. For the other three sides, we need a fence. Which is the minimal length of the fence we need?