OpenLLM-France/wikimedia huggingface dataset:
# Numerical Analysis/stability of RK methods/exercises
## Exercises
### Ex:1

find the stability function for RK2 which is given by: $y_{n+1}=y_{n}+hf(t+{\frac {h}{2}},y_{n}+{\frac {hf(t_{n},y_{n})}{2}})$
Solution:
applying this method to the test equation $y'=\lambda y$
    we get ${\begin{aligned}y_{n+1}&=y_{n}+h\lambda y_{n}+{\frac {(h\lambda )^{2}}{2}}y_{n}\\\Rightarrow \end{aligned}}$
the stability polynomial $\phi (z)=1+h\lambda +{\frac {(h\lambda )^{2}}{2}}$

### Ex:2

find the absolute stability region for RK2.
Solution:
by setting $z=h\lambda$
    $\Rightarrow$ the abs.stability region is given by $\{z\in \mathbb {C} ||1+h\lambda +{\frac {(h\lambda )^{2}}{2}}|<1\}$

### Ex:3

find the characteristic polynomial for RK2.
Solution:
it is $r^{i+1}=(1+z+{\frac {z^{2}}{2}})r^{i}$ divide both sides of the equation by $r^{i};r\neq 0$ you get $r^{i+1}=(1+z+{\frac {z^{2}}{2}})r^{i}$
    $\Rightarrow \phi (r,z)=r-1+z+{\frac {z^{2}}{2}}$

### Ex:4

is RK2 stable, if it is what type of stability.
Solution:
you get $r^{i+1}=(1+z+{\frac {z^{2}}{2}})r^{i}$ by setting z=0,
    $\Rightarrow r=1$
    so the method is strongly stable since r=1, is the only root, and has a value of 1.

### Ex:5

Determine the stability of Back ward Euler method.
Solution:
$y_{n+1}=y_{n}+hf(t_{n+1},y_{n+1})$
    by applying this method to the test equation
    then $y_{n+1}=y_{n}+h\lambda y_{n+1}$
    and so $y_{n+1}={\frac {1}{1+h\lambda }}y_{n}$
    call $z=h\lambda$ and so:
    $G(z)\longrightarrow 0$ as $Re(z)\longrightarrow \infty$
    and so this is L-Stable method when applied to stiff equation.
# Numerical Linear Algebra/Con exercises

Problem
# Sofia coppola
## Aesthetic strategies
### Muted colors
### Needle drops

Sentence on Phoenix and Sofia. Sentence on Phoenix and Sofia. Yellow
# Socratic Methods/prompts

If you would like to practice Socratic Methods, choose a question from this list to begin with, or chose any other unsettled question that you are interested in exploring.

## The Nature of Virtue

* What is virtue?
* What is civility?
* What is fidelity?
* What is wisdom?
* What is temperance?
* What is courage?
* What is justice?
* What is fairness?
* What is generosity?
* Is generosity a virtue?
* Why is generosity a virtue?
* What is compassion?
* What is mercy?
* Is mercy a virtue?
* Why is mercy a virtue?
* What is gratitude?
* What is humility?
* Who is humble?
* Is humility a weakness?
* What is simplicity?
* What is tolerance?
* Is tolerance strength?
* What is purity?
* What is gentleness?
* Is gentleness a virtue?
* What is good faith?
* What is truth?
* Is telling a lie ever better than telling the truth?
* What is humor?
* What is love?
* What is good?

## The Nature of Aesthetics

* What is beauty?
* What is quality?
* What is poetry?
* What is passion?

## The Nature of Truth

* What is truth?
* What is reality?
* What is faith?
* What is hope?
* Is faith the same as hope?
* What is epistemology?
* What is science?
* What are facts?
* What can we know?
* What can’t we know?
* Is faith a reliable epistemology?
* Is the scientific method a reliable epistemology?

## Existential Concerns

* What gives life meaning?
* What matters?
* How can I live wisely?
* Who am I?
* What should I do?
* What is the most important thing I can do?
* What is the ugliest truth about life?
* What is the most beautiful truth about life?
* What makes a life worth living?
* What is the meaning of life?

## Ethics and Morality

* What is morality?
* What is ethics?
* What is the basis for morality?
* How can I determine if I am acting ethically?
* Does evil exist?
* What is good?
* Is legal justice the same as moral justice?
* Would you rather be the king of hell or a citizen in paradise?
Also consider this list of moral issues.

## Exploring Worldviews

The Wikiversity course Exploring Worldviews asks many questions that are useful as prompts. Most of the questions are in the lengthy assignment section of the course.
# Software/Protel

Placeholder for creation of educational resources for Protel (Altium) software.
It's been proposed to move resources from http://protel-users.org here. Please discuss on the attached Talk page. ("Discuss" tab above).
# Spanish/Verbs/E

* escribir
* escojer
# Spanish/Verbs/C

* cambiar
* caminar
* comer
# Spanish/Verbs/D

* dar
* deber
* decir
* describir
* desayunarse
* destruir
* dibujar
* dormir
# Relative projective curve/Behavior of Hilbert-Kunz slopes/Fact

Let
    $C\longrightarrow \operatorname {Spec} {\left(\mathbb {Z} _{g}\right)}$
be a smooth projective relative curve and let ${\mathcal {T}}$ be a vector bundle over $C$. For the generic fiber $C_{0}$ let
    $\mu _{HK}({\mathcal {T}}_{0})=\sum _{\ell }r_{\ell }\mu _{\ell }^{2}\,,$
where the $\mu _{\ell }$ are the slopes (and $r_{\ell }$ the ranks) in the Harder-Narasimhan filtration of ${\mathcal {T}}_{0}$, and for every prime number let
    ${\bar {\mu }}_{HK}({\mathcal {T}}_{p})={\frac {\sum _{k}r_{k}\mu _{k}^{2}}{p^{e}}}\,,$
where the $\mu _{k}$ are the slopes in the strong Harder-Narasimhan filtration of $F^{e*}({\mathcal {T}}_{p})$ on the fiber $C_{p}$.
    $\lim _{p\rightarrow \infty }{\bar {\mu }}_{HK}({\mathcal {T}}_{p})=\mu _{HK}({\mathcal {T}}_{0})\,$
# Relational biology

Welcome to the Department of Relational and Integrative Biology!
Relational Biology is a branch of Mathematical biophysics and Biomathematics focused on identifying and studying the abstract relations in an organism that make possible its physiological functions. It is therefore, also of the fundamental network connectivities and biotopology charactersitic of hierarchically organized, highly complex biological systems. It is therefore closely related to the fields of Systems biology and Complex Systems Biology, also known as Integrative Biology

## Welcome

* Welcome to Wikiversity, Relational biology!
* You can contact us with questions at the colloquium or get in touch with me personally if you would like some help.
* Remember to sign your comments when participating in discussions. Using the signature icon makes it simple.
* We invite you to be bold and assume good faith. Please abide by our civility, privacy, and terms of use policies.
* To find your way around, check out:
* Introduction to Wikiversity
* Take a guided tour and learn
* Browse or visit an educational level portal: pre-school | primary | secondary | tertiary | non-formal
* Explore links in left-hand navigation menu
* Read an introduction for teachers
* Learn how to write an educational resource
* Find out about research activities
* Give feedback about your observations
* Discuss issues or ask questions at the colloquium
* To get started, experiment in the sandbox or on your userpage.
* See you around Wikiversity! --~~~~

## New Relational Biology projects

* Category Theory in Biology
* Relational biology/Category of Relational Metabolic Graphs
* Relational biology/Organismic Sets and Supercategories

### Lessons

* Lesson 1: Category of Metabolic-Replication Systems
* Lesson 2: Sets and Functions (Nov 5, 2007)
* Lesson 2.5: Equivalence of categories
* Lesson 3: Products and Coproducts of Sets (Nov 5, 2007)
* Lesson 4: Monoids (Nov 5, 2007)
* Lesson 5: Categories (Nov 5, 2007)
* Lesson 6: Products and Coproducts (Nov 5, 2007)
* Lesson 7: Products are Limits (Nov 5, 2007)
* Lesson 8: Equalizers (Nov 5, 2007)
* Lesson 9: Pullbacks (Nov 5, 2007)
* Lesson 10: Limits (Nov 5, 2007)
* Lesson 11: Exponentials (Nov 5, 2007)
* Ideas for a new lesson:
** generalized elements?
** Hom(C,-) functors?
** Yoneda embedding?
# Relative term

☞ This page belongs to resource collections on Logic and Inquiry.
A relative term is a logical term that requires reference to any number of other objects, called the correlates of the term, in order to denote a definite object, called the relate$^1$ of the relative term in question. A relative term is typically expressed in ordinary language by means of a phrase with explicit or implicit blanks, for example, “lover of __”, or “giver of __ to __”.
1. Pronounced with the accent on the first syllable.

## Syllabus
### Focal nodes

* Inquiry Live
* Logic Live

### Peer nodes

* Relative Term @ InterSciWiki
* Relative Term @ Subject Wikis
* Relative Term @ Wikiversity
* Relative Term @ Wikiversity Beta
# Relationships (Psychology A-Level)
## Relationship Formation

You will learn the 4 Explanations of Formation of Relationships (Proximity, Reciprocal Liking, Similarity and Physical Attractiveness). You will also learn about the Socio-Biological Explanation and the Reinforcement and Needs Satisfaction Theory

### Explanation of Formation
#### Proximity

Proximity (or the Meer Exposure Effect) tells us that when you see someone more often, you find yourself more attracted to them. This mainly revolves around the distance that you live from the person, so the further you live from someone, the less likely you are to meet and form a relationship.

#### Reciprocal Liking

Reciprocal Liking shows that the other person must like you, and you must like them in order to form the relationship. This can act as a Self Fulfilling Prophecy because if you believe the other person likes you, you will feel more confident in yourself and they will be more likely to like you.

#### Similarity

Similarity shows that we are more likely to form relationships with people that we have things in common with. This will increase the likelihood of the two people meeting, and also getting along together. Elaine Hatfield (1961) proposed the Matching Hypothesis, which shows that people will usually form relationships with those of a similar attractiveness level, and that these are the people that we will have long standing relationships with.

#### Physical Attractiveness

Physical Attractiveness shows that we have to find the person attractive before we can form a relationship with them. This is the most immediate factor that you will notice about the other person.

### Research and Evaluation
#### Proximity

Festinger (1950) found that those who live closest to each other have more friendly relationships than those who live further away from each other. This shows that proximity is included in the formation of relationships, and therefore is supporting evidence for the Proximity Explanation.
Although, a criticism of this is that the experiment was done in 1950. This was before the internet and mobile phones were invented, and cars were not as popular as they are now. This shows that we have other means of communication with people so we do not have to be in close proximity to someone to be able to contact them. This does not support proximity as it shows that it is outdated and subject to an age bias. Bossard carried out a study on 5000 married couples and found that before they got married, they lived near each other. This supports the view that Proximity affects relationship formation.

#### Similarity

Newcombe (1961) carried out an experiment where he paired participants with someone similar to them and let them meet and interact with each other. The results show that the people in the study continued to be friends after the study. This supports the view that Similarity affects the formation of relationships.
Go back to Psychology (A-Level)
# Software applications/Overview/Pega/Functionality/Co-Browsing

See https://pdn.pega.com/pegatube/pega-techtalk-episode-1-creating-collaborative-experiences-with-co-browse for more info.
# Software applications/Overview/Pencil

* Category:
* Website: http://pencil.evolus.vn/
# Software applications/Overview/Pocket

* Website: https://getpocket.com
* Wikipedia: Pocket
Pocket, previously known as Read It Later, is an application and service for managing a reading list of articles from the Internet.
# Software applications/Overview/Pega/Possible improvements

One of the ambitions of Pegasystems is to make Pega more simpel. On this page you can find some suggestions to improve Pega.
# Software applications/Overview/Prezi

* Category: Presentation
* Website: https://prezi.com

## Index

* Functionality
# Software applications/Overview/Part-up/Wiki

In November 2015 we created a wiki on Miraheze.org.
# Software applications/Overview/Pega

* Pega is a platform for creating business applications.
* Pega is created by Pegasystems

## Index

* Functionality
* Possible improvements
# Software applications/Overview/Racontr

* Category: Storytelling
* Website: https://racontr.com/
# Software applications/Overview/SharePoint

* Categorie: Collaboration
* Wikipedia: SharePoint
SharePoint combines various functions which are traditionally separate applications: intranet, extranet, content management, document management, personal cloud, enterprise social networking, enterprise search, business intelligence, workflow management, web content management, and an enterprise application store.

## To-do

* http://wiki.uky.edu/sharepoint/Wiki%20Pages/How%20To%20Use%20SharePoint%20Wiki%20Sites.aspx

## Index

* Functionality
* Improvements
* Roadmap
# Open Science literacy in EAP/Ideas for EAP tasks

Go back to The collaborative potential of multimodal online course materials
This page represents a collection of ideas and inspirations for EAP (English for Academic Purposes) professionals who are interested in using fully-online, multimodal course materials into their teaching. Each sub-section of this page is dedicated to a different type of EAP task which students can complete, using fully-online resources.

## Writing
### Summarizing & Paraphrasing
#### Example task: Paraphrasing

Read the first six paragraphs from today's reading and identify the author's main arguments. Using your own words, summarize these ideas on your own Wikiversity page. When paraphrasing, make sure not to copy and paste chunks from the original source, as this would count as patch-writing (unintentional plagiarism). Remember also to cite your source(s) with the "cite" and "insert reference list" functions. Keep in mind that you are creating an Open Access Wikiversity page, which should be coherent and ready-friendly, i.e.: spell-checked, thoroughly researched, and well-structured.

### Citing & Referencing
#### Example task: Consistency

Visit the Wikiversity page we discussed last session. You will notice that its citation style is not consistent. Using the "edit" function, make the necessary changes for the page to follow one, clear style of citation. You can choose to follow Harvard, Chicago, MLA, APA, or another citation style you deem appropriate.

### Outlining & Structuring
#### Example task: Comparing different types of structures

Re-visit the last two Wikiversity pages we most recently discussed. Compare their structures. In how far do they make use of headings and formatting to ensure a reader-friendly experience? In what way are they similar? How do they differ? In groups, exchange ideas and opinions and prepare to share your thoughts in plenary after the break.

## Collaboration & Peer-review
### Groupwork
#### Example task: Digital literacy

Visit the Wikiversity page we discussed lst session. Take a close look at the images embedded into the page, the hyperlinks inserted, and the citations used. Critically evaluate the state of the page. Could it be improved in any way? Do you have ideas to make certain aspects of it more accessible to a wide variety of audiences? Keep in mind what we discussed about captions, active hyperlinks, and reference lists and, in groups, discuss strategies to improve the page in terms of style, format, accessibility, and functionality. Do not edit the original page. Instead, copy the "source" information to create a new page. You can make any edits and changes you see fit to your own, new version of the original page.
# Open Science/Week 6: Diverse Paths to Open Science
### Learning Outcomes

* Compare multiple schools of thought that feature in the development of open science.
* Explain how earlier schools of thought about open science are reflected in the UNESCO Recommendation.
* Analyze key relationships between the priorities of open access and replicability in open science.

### Readings

Open Science: One Term, Five Schools of Thought, Fecher B., Friesike S. In: Bartling S., Friesike S. (eds) Opening Science, 2014, CC BY-NC. 30 pages.
Plan S Principles, Coalition S, 2018, Copyright © 2021 European Science Foundation.
"From the 'Replicability Crisis' to Open Science Practices" in Rajiv S. Jhangiani; I-Chant A. Chiang; Carrie Cuttler; and Dana C. Leighton, Research Methods in Psychology - 4th Edition , 2019, licensed under a CC BY-NC-SA 4.0 International License, except where otherwise noted, 7 pages.

### Discussion Question

Consider the five schools of thought that contribute to open science. Describe how one of these schools of thought is relevant to a scientific context with which you are familiar. You can describe an institutional, geographic, or disciplinary context. End your post with a question posed to other participants in the discussion.

### Self-check Questions

* 1 2 Fecher, Benedikt; Friesike, Sascha (2014). Bartling, Sönke. ed. Open Science: One Term, Five Schools of Thought (in en). Cham: Springer International Publishing. pp. 17–47. doi:10.1007/978-3-319-00026-8_2. ISBN 978-3-319-00026-8. https://doi.org/10.1007/978-3-319-00026-8_2.
* ↑ "Plan S Principles | Plan S". www.coalition-s.org. Retrieved 2021-12-17.
* ↑ "From the 'Replicability Crisis' to Open Science Practices" in Jhangiani, Rajiv (2019). Research methods in psychology. I-Chant A. Chiang, Carrie Cuttler, Dana C. Leighton, Kwantlen Polytechnic University, BC Open Textbook Project, BCcampus (4th edition ed.). Surrey, B.C.. ISBN 978-1-9991981-0-7. OCLC 1156393793. https://www.worldcat.org/oclc/1156393793.
# Open Science literacy in EAP/Demo page

Go back to A space for collaboration

## Creating your page

This is a page to demonstrate
# Open Science literacy in EAP/In what way have you benefitted from Open Science or accessible knowledge?

Go back to: Open Science literacy in EAP
Think about the resources in your life which may qualify as "Open Science" or "accessible knowledge". This is a collaborative task, meaning that anyone can add to the table below:
| | Physical | Digital |
| Course | Public lectures at the University of Vienna, public lecture at the Royal Edinburgh Society on World Refugee Day | audited courses on Coding on coursera, audited classes about Psychology on edx |
| Library | Central University in Edinburgh | |
| Event | | online conference about Ecocritism in Humanities "Humanities on the Brink" |
| Site | "take as you wish" stands of free books in the city centre | wikipedia, wikiversity, wikimedia commons, pixabay, gephi, gephi videos, |
| Database | | doaj, ERIC, zenodo, free book samples on Kindle, google books |
| Museum | National museum of Scotland, Writer's Museum in Edinburgh | |
| Teachers | free after-school tutoring | Youtube tutorials, free classes to audit on coursera/ edx |

### Discussion

In this space, feel free to share your thoughts on Open Science in physical and/ or digital forms. You can do so anonymously or not.
* "Open Science is combatting the commercialization of academic research" - anonymous researcher & teacher in Higher Education
* "By sharing Open Science resources with our learners, we can help them develop a greater sense of agency and academic identity throughout and beyond their studies" - Katie Reschenhofer, EAP instructor
# Open Science/Week 9: Capacity Building for Open Science
### Learning Outcomes

* Describe approaches to helping people develop knowledge and skills relevant to open science.
* Explain how early career researchers benefit from learning about open science.

### Readings

“Stepping up Open Science Training for European Research" by Schmidt, Birgit, Orth, Astrid, Franck, Gwen, Kuchma, Iryna, Knoth, Petr, and Carvalho, José in Publications 4, no. 2:16,2016, Creative Commons Attribution 4.0 International. 10 pages.
“Open Science Challenges, Benefits and Tips in Early Career and Beyond,” by Allen, C & Mehler, DMA in PLoS Biol 17(5): e3000246, 2019, Creative Commons Attribution 4.0 International. 14 pages.
Note: There is a published correction to the Allen & Mehler reading. The correction relates to inaccurate and incomplete citations. This may provide an opportunity to help students learn about the importance of accurate citations and the level of scrutiny they receive in the publication process. You may want to connect the example to the authors’ position on how to handle mistakes in published research.

### Discussion Question

Based on what you’ve learned about the FOSTER (Facilitate Open Science Training for European Research) program from the article "Stepping up Open Science Training for European Research" by Schmidt and colleagues, describe how you would create an open science training in your national context. A thorough answer will reference at least 3 objectives and activities and will be informed by the article’s conclusions. You may also want to draw on the article by Allen & Mehler, “Open Science Challenges, Benefits and Tips in Early Career and Beyond," for information about benefits of open science training for early career researchers. Conclude your post with a question for others in the class.

### Self-check Questions

* ↑ Schmidt, Birgit; Orth, Astrid; Franck, Gwen; Kuchma, Iryna; Knoth, Petr; Carvalho, José (2016-06). "Stepping up Open Science Training for European Research". Publications 4 (2): 16. doi:10.3390/publications4020016. https://www.mdpi.com/2304-6775/4/2/16.
* ↑ Allen, Christopher; Mehler, David M. A. (2019-05-01). "Open science challenges, benefits and tips in early career and beyond". PLOS Biology 17 (5): e3000246. doi:10.1371/journal.pbio.3000246. ISSN 1545-7885. PMID 31042704. PMC PMC6513108. https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.3000246.
# Open Science literacy in EAP/Example page

Go back to The collaborative potential of multimodal online course materials
This example page can be used as a template by students/ learners/ contributors who want to link their own page to the Wikiversity course "The collaborative potential of multimodal online course materials".

## Subheadings

Using the heading-function, students can structure their pages to be more audience-friendly.

## Text types

Students can write abstracts, reports, reflections, and other short texts right here, on this page.
The teacher can then edit the page and make comments which are only visible in the editing view of the page. Click "Edit" in the tab above to view a comment here.

## Images from WikiCommons

Images from open image sharing sites, such as WikiMedia Commons, can be inserted to make pages more lively and engaging.

## Reference list

Using the "Insert" function, students can add a reference list to their pages. This reminds students to take academic citation seriously, even when working in a fully-online, multimodal, and interactive space.
* ↑ Wikimedia Commons. Commons Logo. https://commons.wikimedia.org/wiki/File:Commons-logo-en.svg. Last accessed 12 October 2023.