OpenLLM-France/wikimedia huggingface dataset:
# Natural numbers/Factorial/Definition

For a natural number $n$, one puts
    $n!:=n(n-1)(n-2)\cdots 3\cdot 2\cdot 1\,,$
and calls this $n$ factorial.
# Natural numbers/Induction/Product of powers/Exercise

Prove, by induction, that the following inequality holds
    $1\cdot 2^{2}\cdot 3^{3}\cdots n^{n}\leq n^{\frac {n(n+1)}{2}}\,.$
# Natural numbers/Proofs/Induction principle/Fact

Suppose that for every natural number $n$ a statement $A(n)$ is given. Suppose further that the following conditions are fulfilled.
* $A(0)$ is true.
* For all $n$ we have: if $A(n)$ holds, then also $A(n+1)$ holds.
$A(n)$
$n$
# Natural logarithm/Taylor series via derivative in 1/Example

We would like to determine the Taylor series of the natural logarithm in the point $1$. The derivative of the natural logarithm equals $1/x$, due to fact. This function has the power series expansion
    ${\frac {1}{x}}=\sum _{k=0}^{\infty }(-1)^{k}(x-1)^{k}\,,$
due to fact (which converges for $\vert {x-1}\vert <1$). Therefore, because of fact, the power series expansion of the natural logarithm is
    $\sum _{k=1}^{\infty }{\frac {(-1)^{k-1}}{k}}(x-1)^{k}.$
Setting $z=x-1$, we may write this series as
    $z-{\frac {z^{2}}{2}}+{\frac {z^{3}}{3}}-{\frac {z^{4}}{4}}+{\frac {z^{5}}{5}}-\ldots .$
# Natural number/Even number/Definition

A natural number $n$ is called even, if it can be written in the form $n=2k$ with some natural number $k$.
# Natural numbers/Prime number/Definition

A natural number $n\geq 2$ is called a prime number if it is only divisible by $1$ and by $n$.
# Maritime Health Research and Education-NET/The International Type 2 Diabetes Mellitus and Hypertension Research Group/Contribute to the Revision of the EU Ships Medical Chest
## Contribute to the Revision of the EU Ships Medical Chest

During sailing it shall be possible to measure blood pressure in individuals having treatment for high blood pressure. At least two automatic apparatus should be available on all ships in case one of the devices breaks Ships Medical Chest
Self-monitoring of blood glucose for non-insulin-treated adults with Type 2 diabetes is necessary. Instructions and relevant equipment in the medical chest on board are needed and have been added to the actual revision of the International Medical Guide for Ships and the Medical Inventory lists. A few crew embers on board shall know how to measure blood glucose and to treat severe hypoglycemia using glucagon, which must be present on all ship chests.FG
# Maritime Health Research and Education-NET/THE MARITIME OH PORTAL

The Maritime Occupational Health Portal
There is a gab of current and updated scientific information about the most important work exposures at sea for prevention, training and education in maritime occupational health and safety. This Portal is intended to have 1. The relevant and easy understandable maritime OH knowledge and 2. Guidelines for how to analyse the workplaces and implement good OH conditions. The intention is to share the available new knowledge based on health registers, literature reviews and the results on new knowledge on the 4 main strategic subjects produced MAHRE-Net activities. Part 2, the education and training is already available by the institutions like the Danish "Seahealth and Wellfare"and the Danish Fishermen’s Occupational Health Services and similar organisations in other countriesThe European Agency for Safety and Health at Work also provides training and information ressources for the fishermen, but scarse for seafarers and stevedores. The intention is to link the knowledge part with the guidelines parts in a permanent updated "first stop" evidence and training ressource for each of the specific maritime type of jobs and ships to comply with the main national prevention strategies. This model is inspired from the Norwegian "Arbejdsmiljøportal" "Arbejdsmiljøportalen" underscores the need to work efficiently and correctly and by the use of: 1. continously updated factual knowledge as basis and 2. the guidelines, instructions and training we know will work. Similarly we must have a "Maritime Occupational Health Portal" to present the updated specific exposure and health indicators for the specific ship types profiles from the facts produced by the MAHRE-Net and other ongoing surveillance that are important to have as the basis and effect measure. MAHRE-Net will produce some of the relevant knowledge part of maritime occupational health while the other institutions will produce the guidelines and solutions which we know work effectively. In conclusion: The Portal unites: 1. the latest updated knowledge about the risk indicators for specific areas of the maritime workplaces 2. The latest and known effective solutions for the environment in the specific workplaces by links to the specific institutions that produce the instructions. This collaboration will be done within the new strategy for occupational health: the "Tre-parts aftaler om Arbejdsmiljø" 22 Dec 2020 with probably similar agreements in other countries. The agreement opens up for the effective collaboration of the knowledge producing institutes and the training and education units. There is a need to continuously evaluate the content and the usability by the users and then correct the content in a way that is easy and understandable for the users. There will also be a continuously evaluation and update of the content so that it is the most recent and new knowledge presented. And not to forget the effect measure of the implemented improvement at the workplace.
# Maritime Health Research and Education-NET/The International Type 2 Diabetes Mellitus and Hypertension Research Group/Maritime Health Review e-journal

Researchers and academic staff in universities are key players in promoting SDGs. Contribution of scientists in different disciplines enlightens policy-makers and politicians on certain goals that need to be addressed in the future as well as on the extent of success or failure in achieving a certain goal. The SDGs are based on the presence of serious global problems that need to be addressed and solved through research and innovation. Researchers are in a position to provide genuine solutions and inventions to various national and international problems facing the pathway to achieving the 2030 agenda [10]. Local and international authorities need to adopt research results and recommendations made by academic staff and put them into a practical agenda to strengthen partnership with all stakeholders and to accelerate the practical steps toward achieving SDGs. Sweileh WM. Bibliometric analysis of scientific publications on “sustainable development goals” with emphasis on “good health and well-being” goal (2015–2019). Globalization and Health. 2020 Jul 28;16(1):68.
The meaning is that one and I don’t know when a publication come out what can you be useful. I want to do a new search for new articles within the Maritime health area
Will the goal to strengthen the STD 17 goals mainly are most often good health and well-being for all. What we can do is to ask who will and can implement this wishes it has been expressed in the in the manuscript. What should be done by the shareholders going through one by one, legal, ship gup owners, seafarers, unions, schools, government. What is the need for further research.
I will goal is to bring this knowledge to all shareholders and to ask especially students all companies to discuss what can be done.
We made a contract with persons will say they can come with a short abstract and a reference. And try to give an answer to these things. It must not be more than 100 to 200 words in all.
What is the need for further research.
I will goal is to bringWhat is the need for further research.
I will goal is toWhat is the need for further research.
What is the need for further research.What is the need for further research
Will
# Math Adventures/Triangular numbers

This activity introduces the triangular numbers and explores various applications.
In the image on the right notice the spheres are arranged to form an equilateral triangle.
Here is a tabulation of the number of objects in each row, and the total number of objects.
Triangular Numbers :
| Row Number | Number of objects in this row | Total Number of Objects |
| 1 | 1 | 1 |
| 2 | 2 | 3 |
| 3 | 3 | 6 |
| 4 | 4 | 10 |
The last column corresponds to the triangular numbers.
Extend this sequence. (Hint, the number of objects in each row equals the row number.)
(Answer: The sequence of triangular numbers begins: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136…)

## Analysis

The nth triangular number is given by the following formulas.
$T_{n}=\sum _{k=1}^{n}k=1+2+3+\dotsb +n={\frac {n(n+1)}{2}}$
What is the 10th triangular number? (Answer 10(10+1)/2 = 55. Note the sequence shown above begins with $T_{0}$)

### Fully Connected Networks

In a fully connected network every node has a direct link to very other node. The figure on the right illustrates a fully connected network with 6 nodes. Note that it includes 15 connections. In general, a fully connected network with $n$ nodes has $T_{n-1}$ connections. This is analogous to counting the number of handshakes if each person in a room with n people shakes hands once with each person.
There are approximately 5080 public airports in the United States. How many routes would be required to allow for a direct flight between any two of these airports? (Answer, $T_{5079}$ = 12,900,660 routes).
What network topologies do the airlines use to reduce the number of individual routes while allowing efficient travel between any two airports. (Answer, airlines often use a hub-and spoke network architecture.)

### Pascal’s Triangle

${\begin{array}{c}1\\1\quad 1\\1\quad 2\quad 1\\1\quad 3\quad 3\quad 1\\1\quad 4\quad 6\quad 4\quad 1\\1\quad 5\quad 10\quad 10\quad 5\quad 1\\1\quad 6\quad 15\quad 20\quad 15\quad 6\quad 1\\1\quad 7\quad 21\quad 35\quad 35\quad 21\quad 7\quad 1\\\end{array}}$
In Pascal’s triangle, shown at the right, each number is the sum of the two numbers directly above it. Notice the diagonals containing the sequence 1, 3, 6, 10, 15, 21, …. These diagonals are formed from the triangular numbers.
# Math Adventures/Volume of a rotating rectangle

A 5x10 cm rectangle is rotated about its diagonal.
What is the volume of the 3 dimensional solid it sweeps out?
# Math Adventures/Triangle Test Cases

Consider a computer program that
* accepts 3 numbers as input,
* treats each of these numbers as representing the length of the side of a triangle, and
* responds with "Is a triangle" or "Is not a triangle" as output.
Generate a comprehensive set of test cases.
Compare your list of test cases to this list of test cases.
Is your list of test cases complete? Are you missing any valid test cases?
Is your list of text cases efficient? Are there any redundant or unnecessary test cases?

## Further Reading

Students who are interested in learning more about software testing may wish to read these books:
* Myers, Glenford J. (1979). The art of software testing. Business data processing, a Wiley series. New York: Wiley. ISBN 978-0-471-04328-7.
* Kaner, Cem; Falk, Jack; Nguyen, Hung Quoc; Nguyen, Hung Quock (1999). Testing computer software (2. ed ed.). New York Weinheim: Wiley. ISBN 978-0-471-35846-6.
# Math Adventures/Triangle Test Cases/Test Cases

To ensure that the program correctly identifies whether the given lengths can form a triangle, we need to test various scenarios, including valid triangles, invalid triangles, and edge cases. The comprehensive set of test cases should cover different types of triangles (equilateral, isosceles, and scalene), as well as scenarios where the input lengths do not form a triangle. Here is a comprehensive set of test cases:
Test Cases
* Valid Triangles (All types):
** Equilateral Triangle:
*** Input: (3, 3, 3)
*** Output: "Is a triangle"
** Isosceles Triangle:
*** Input: (5, 5, 8)
*** Output: "Is a triangle"
*** Input: (7, 7, 7)
*** Output: "Is a triangle"
** Scalene Triangle:
*** Input: (3, 4, 5)
*** Output: "Is a triangle"
*** Input: (6, 8, 10)
*** Output: "Is a triangle"
* Invalid Triangles (Sum of two sides not greater than the third):
** Input: (1, 2, 3)
*** Output: "Is not a triangle"
** Input: (5, 1, 1)
*** Output: "Is not a triangle"
** Input: (10, 2, 7)
*** Output: "Is not a triangle"
* Edge Cases:
** Zero Length:
*** Input: (0, 5, 5)
*** Output: "Is not a triangle"
** Negative Length:
*** Input: (-3, 4, 5)
*** Output: "Is not a triangle"
*** Input: (-1, -1, -1)
*** Output: "Is not a triangle"
** Very Large Numbers:
*** Input: (1000000, 1000001, 1000002)
*** Output: "Is a triangle"
** Floating Point Precision:
*** Input: (0.1, 0.1, 0.1)
*** Output: "Is a triangle"
*** Input: (0.1, 0.2, 0.3)
*** Output: "Is not a triangle"
* Boundary Cases:
** Minimum Boundary for forming a triangle:
*** Input: (1, 1, 1.9999999999999998)
*** Output: "Is a triangle" (just barely a triangle due to floating point precision)
*** Input: (1, 1, 2)
*** Output: "Is not a triangle"
** Sides forming a degenerate triangle (where sum of two sides equals the third):
*** Input: (1, 2, 3)
*** Output: "Is not a triangle"
*** Input: (2, 2, 4)
*** Output: "Is not a triangle"
* Mixed Valid and Invalid Inputs:
** Input: (1, 1, 2.0000000001)
*** Output: "Is a triangle" (floating point precision just makes it a triangle)
** Input: (100, 1, 1)
*** Output: "Is not a triangle"
Summary
* Valid Triangles: Include a variety of equilateral, isosceles, and scalene triangles.
* Invalid Triangles: Include cases where the sum of any two sides is not greater than the third side.
* Edge Cases: Cover zero, negative, very large numbers, and floating-point precision issues.
* Boundary Cases: Test the minimum boundary conditions and degenerate triangles.
* Mixed Cases: Ensure mixed scenarios of almost valid/invalid triangles are covered.
These test cases ensure comprehensive coverage of different scenarios to verify the program's correctness in identifying valid and invalid triangles.
# Math Adventures/Peanut Butter Power

Answer these questions to get a better understanding of the power of peanut butter.
* How many food calories are in one pound of peanut butter?
* How many thermochemical calories are in one pound of peanut butter?
* How many kWh of energy is stored in one pound of peanut butter?
* How many kWh of energy is stored in the battery of a Tesla Model 3 (long-range battery) automobile?
* How many pounds of peanut butter is this equivalent to?
* How much does the battery in a Tesla Model 3 weigh?
* How can we use peanut butter to power more devices?
# Math Adventures/Roll the dice

This simple activity introduces the student to random events, addition, graphing, combinations, probability distributions, and the law of large numbers.

## Activity

Collect two six-sided dice and a pencil. Click to expand the “Roll the Dice” worksheet shown at the right and print out a copy. (Alternatively use graph paper or draw a similar worksheet.) Sit at a table or flat worksurface, and carry out the following steps:
* Roll both dice.
* Add the resulting dot counts together to obtain a number ranging from 2 and 12.
* Mark an X in the grid box above that number on the worksheet.
* Repeat this a few dozen times. As numbers repeat, stack the X marks to create a bar chart.
What pattern emerges?
How can that pattern be explained?

## Analysis

Although the result of each individual die is uniformly distributed, the sum of the two dice is not. This is because there is only one outcome that results in a sum of 2 or 12, yet there are 6 outcomes that result in a 7. The table below enumerates the possible outcomes.
The student is likely to notice that the resulting pattern does not conform to the predicted probabilities. The nature of a random event is that it is not predictable and variation in the outcome is expected. As the number of trials increases, the resulting pattern is likely to conform more closely to the predicted probabilities.
Sum of Two Dice :
| + | 1 | 2 | 3 | 4 | 5 | 6 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
# Math Adventures/Tetrahedron in a Cube

A tetrahedron can be inscribed within a cube such that four of the eight vertices of the cube are coincident with the four vertices of the tetrahedron, as shown in the diagram on the right.
* Calculate the ratio of the area of the cube to the area of the tetrahedron.
* Calculate the ratio of the volume of the cube to the volume of the tetrahedron.
# Mobile learning/Design

* Learning Design
* Usability Design
* Design Patterns
# Mobile learning/Design/Patterns
## Design Patterns for Mobile Apps and Mobile Learning

* Android Patterns: a set of interaction patterns that can help you design Android apps. An interaction pattern is a short hand summary of a design solution that has proven to work more than once. Please be inspired: use them as a guide, not as a law.
# Mobile learning/Features

Features and Characteristics of Mobile Technology, and their Educational Implications

## Pervasive, Personal

Always with you, everyone has one.

## Access to Knowledge

When & where you need it

## Context Aware

Information adaptive to location, activity, time.

## Social Ambiance

Your friends are in your pocket

## Content delivery

Podcasts, etc. Evans, C. (2008), 'The effectiveness of m-learning in the form of podcast revision lectures in higher education', Computers & Education 50 (2) , 491 - 498. http://uwpodcast.pbworks.com/f/Podcast_Effectiveness.pdf
   In this paper we describe a study of the effectiveness of mobile learning m-learning in the form of podcasting, for teaching undergraduate students in Higher Education. Podcasting involves downloading a series of audio or video broadcasts files onto a digital media player, via a computer, over a period of weeks. These can then be watched or listened to when, where and as often as students choose. The use of digital media players, popularised by Apple's iPodTM, is widespread amongst undergraduate students.
# Model of nutrition in plants and animals

Green plants prepare their own food from carbon dioxide, water by using sunlight energy in the presence of chlorophyll. This process is known as photosynthesis. Therefore, green plants are known as autotrophs.
On the other hand, animals depend on other organisms for food. They cannot make their own food and are known as heterotrophs. All living organisms need energy to perform various life processes.
There are more than 40 different kinds of nutrients in food and they can generally be classified into the following 7 major groups: Carbohydrates. Proteins. Fats. Vitamins. Minerals. Dietary fibre. Water.
The mode of nutrition where organisms depend on other organisms for their food requirements is called heterotrophic nutrition. Animals are called consumers as they depend on autotrophs for their nutrition requirements. So nutrition in animals is heterotrophic in nature.
# Mobile learning/Theory
## Theory of Mobile Learning
### Readings

Sharples, M.; Taylor, J. & Vavoula, G. (2007), A theory of learning for the mobile age, in R. Andrews & C. Haythornthwaite, ed., 'The Sage Handbook of Elearning Research' , Springer, pp. 221-247
   Our aim is to propose a theory of learning for a mobile society. It encompasses both learning supported by mobile devices such as cellular mobile phones, portable computers and personal audio players, and also learning in an era characterised by mobility of people and knowledge Rheingold, 2002 where the technology may be embedded in fixed objects such as ‘walk up and use’ information terminals. For brevity we shall refer to these together as mobile learning
# Mobile learning/references

http://www.bibsonomy.org/tag/mlearning
# Mobile learning/Introduction

What is Mobile Learning, and why all the fuss about it?
Amber Case: We are all cyborgs now - http://www.ted.com/talks/amber_case_we_are_all_cyborgs_now.html

## Readings

Traxler, J. (2009), 'Learning in a mobile age', International Journal of Mobile and Blended Learning 1 (1) , 1-12. http://www.learninglab.org.uk/documents/resources/Learning%20in%20a%20Mobile%20age.pdf
   The launch of the International Journal of Mobile and Blended Learning is one of several indicators that mobile learning globally is reaching a critical and sustainable momentum and identity. The past six or seven years have seen a host of pilots and initiatives across sectors and across countries and these have established firstly that mobile learning takes learning to individuals, communities and countries where access to learning was challenging or problematic and secondly that mobile learning enhances, enriches and extends how learning is understood. Environmental factors have meant that this development has been haphazard. The mobile learning community is now faced with broader challenges of scale, durability, equity, embedding and blending in addition to the earlier and more specific challenges of pedagogy and technology, but these developments take place in the context of societies where mobile devices, systems and technologies have a far wider impact than just mobile learning as it is currently conceived. This paper looks at the definition and evolution of mobile learning as the starting point for a discussion of this wider impact.
# Mobile learning/Issues

Issues in Mobile Learning: Challenges and Opportunities

## Readings

Kukulska-Hulme, A. (2010), 'Learning cultures on the move: where are we heading?', Journal of Educational Technology and Society 13 (4) , 4--14. http://oro.open.ac.uk/25679/
   The paper analyzes the globally recognized cultural move towards a more learner-centred education and discusses the implications for the adoption of mobile technologies and design for learning. Current expectations vis-à-vis learner attributes, skills and competences are explored. The pervasiveness of mobile technologies is precipitating these developments, whilst also generating a distinct mobile culture where learners take mobility and context-awareness as starting points and become more visible as innovators, creators and producers. Language learning, one of the most popular application areas of mobile learning, provides fertile ground for the growth of this phenomenon. The paper reviews several innovative language learning applications and concludes by indicating the directions in which we are heading.
# Molecular evolution/Intermediate filament proteins

Welcome to the Wikiversity learning project for exploration of the molecular evolution of intermediate filament proteins.
The intermediate filament proteins are a major family of cytoskeletal proteins. Most eukaryotic organisms have genes that code for intermediate filament proteins. As more genomes are sequenced, an increasing complete understanding of the evolution of protein families becomes possible. Are intermediate filament proteins related to any proteins of prokayotic organisms? At what points during the evolution of eukaryotes did the various subtypes of intermediate filament proteins arise? What new biological functions and specializations were facilitated by the evolution of the members of this multigene family?

## Start here

Explore the Conserved Domain Database online resources from the National Library of Medicine.
A Conserved Domain relatedness tree exploring tool is available for Windows.

### Your turn

Add what you learn to this page.

## Keratins

Keratin 18 is one of the major keratin proteins of human epithelial cells. There are two major families of keratins, type I and type II. Keratin 18 is type I and often forms intermediate filaments by combining with a type II partner, keratin 8. Keratin filaments containing keratins 8 and 18 are found in the earliest epithelial cells of mammalian embryos. The functional role of early embryo keratin 8 has been investigated in transgenic mice lacking keratin 8. Mice lacking keratin 8 have disrupted placental barrier function.

## Lamins

Lamins are intermediate filament family proteins found in the nuclei of metazoans. It has been suggested that during mitosis lamin B forms a matrix for assembly of microtubules.