OpenLLM-France/wikimedia huggingface dataset:
# African Arthropods

This is an informal learning project for Alandmanson and anyone that wishes to join in. See Discuss: African Arthropods project.

## African Chelicerates

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## African Crustaceans

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## African Hexapods

    African Insects
   * Diptera
   ** Acalyptrate flies
   * Hymenoptera
   ** African Chalcidoidea
   *** African Encyrtidae
   *** Key to the genera of Afrotropical Encyrtidae
   *** African chalcid wasps with branched antennae
   *** Wasps associated with plant galls
   ** African Diaprioidea
   ** African Aculeata
   *** African potter wasps
   *** South African species of Philanthus
   * Lepidoptera

## African Myriapods

       No sub-pages yet
The extant Arthropoda of Africa can be subdivided into four Subphyla (and about 15 Classes). This classification is that followed by iNaturalist (July 2022).
African Chelicerates - Including mites, harvestmen, solifuges, spiders, tailless whip scorpions, and sea spiders.
African Crustaceans - Including branchiopods, barnacles, crabs, lobsters, crayfish, shrimp, fish lice, tongue worms, and ostracods.
African Hexapods - Including springtails and insects.
African Myriapods - Including centipedes, millipedes, pauropodans, and symphylans.

## Subphylum Chelicerata

* Class Arachnida — Arachnids
* Mites
* Harvestmen
* Solifuges
* Spiders
* Tailless whip scorpions
* Class Pycnogonida — Sea Siders or Pycnogonids
* Sea Spiders

## Subphylum Crustacea

* Class Branchiopoda — Branchiopods
* Fairy shrimps
* Class Hexanauplia — Barnacles and Copepods
* Barnacles
* Copepods
* Class Malacostraca — Malacostracans, including crabs, lobsters, crayfish, shrimp, krill, prawns, woodlice, amphipods, and mantis shrimp
* Crabs
* Isopods
* Mantis shrimps
* Class Ichthyostraca — Includes Branchiura, fish lice and Pentastomida, tongue worms
* Fish lice
* Subclass [[w:Mystacocarida|Mystacocarida] — Mystacocaridans
* Mystacocarids
* Class Ostracoda — Ostracods
* Ostracods

## Subphylum Hexapoda

* Class Entognatha — Entognathans, including springtails
* Coneheads
* Two-pronged bristletails
* Slender springtails
* Plump springtails
* Globular springtails
* Class Insecta — Insects
* Butterflies and moths
* Beetles
* Ants, bees, wasps, and sawflies
* True bugs, hoppers, aphids, and allies
* Flies

## Subphylum Myriapoda

* Class Chilopoda — Centipedes
* Tropical centipedes
* Tropical centipedes
* House centipedes
* Class Diplopoda — Millipedes
* Chilognatha
* Class Pauropoda — Pauropodans
* Tetramerocerata
* Class Symphyla — Symphylans
* Scutigerellidae

## Arthropods in South Africa

Ferncliffe Nature Reserve Arthropods on Ficus burkei Hymenoptera of South Africa

## See Also

* Animal Phyla/Arthropoda
* Wikipedia: Arthropoda
* Wikipedia: Africa
* Wikipedia: Afrotropical biogeographic realm
* Evolution of Arthropods - palaeontologyonline.com
# Thinking Tools/New car decision matrix

This decision matrix can be used to choose among several new car alternatives being considered for purchase.
| | Mazda 6 | Nissan Altima | Nissan Maxima |
| Safety High = 5 | 5 Cell contribution is 5x5=25 | 5 | 5 |
| Reliability High = 5 | 5 | 3 | 5 |
| Low Cost Medium = 4 | 4 | 4 | 2 |
| Space Medium = 4 | 4 | 4 | 5 |
| Service Medium =4 | 5 | 4 | 4 |
| Performance Low = 2 | 5 | 4 | 5 |
| Aesthetics Low = 2 | 5 | 3 | 5 |
| Total: | 122 | 97 | 114 |
Begin by creating an affinity diagram on the topic “What is important to consider when choosing a new car”. Using the resulting affinity diagram as a starting point, create a tree diagram with the topic “What decision criteria will be used to choose a new car”.
Each row label represents a decision criterion identified from the tree diagram. The importance of each criterion is determined, quantified and recorded. Here high importance is assigned a weight of 5. Each column represents an alternative being evaluated, in this case three different car models. The rating of each alternative for each criterion is decided, quantified, and recorded in the corresponding cell. For example, the Mazda 6 is high in safety, so it is rated 5. The contribution of that rating is calculated as the score (5) multiplied by the criterion weight (5) for a total of 25 for that cell. The total score of each alternative is computed by summing the contribution of each cell in the column representing that alternative. Here the Mazda 6 gets the highest score of 122.
# Group theory/Subgroup/Equivalence relation/Definition

Subgroup/Situation We set $x\sim _{H}y$ (and say that $x$ and $y$ are equivalent) if $x^{-1}y\in H$.
# Cosets/Additive case/Z and vector space/Example

In an (additively written) commutative group like $\mathbb {Z}$ or a vector space $V$, and of a given subgroup $H$, the equivalence relation $x\sim _{H}y$ means $y-x\in H$, that is, there exists a $h\in H$ such that
    $y=x+h\,.$
The equivalence classes are of the form $x+H={\left\{x+h\mid h\in H\right\}}$. In case $H=\mathbb {Z} d\subseteq \mathbb {Z}$ with a fixed $d$, the equivalence classes have the form
    $H=\mathbb {Z} d,\,1+H=\{\ldots ,1-d,1,1+d,1+2d,\ldots \},\,2+H=\{\ldots ,2-d,2,2+d,2+2d,\ldots \},\ldots .$
These classes encompass those integer numbers that have, upon division by $d$, the remainder $0$, or $1$, or $2$, etc. They form a partition of $\mathbb {Z}$.
If $H=U\subseteq V$ is a linear subspace, then the equivalence classes have the form $v+U={\left\{v+u\mid u\in U\right\}}$ for a vector $v\in V$. This is ther affine space with starting point $v$ and the translating space $U$ (in the sense of definition). The equivalence classes form a family of affine subspaces parallel to each other.
# Group theory/Cosets/Properties/Fact

Let $G$ be a group, and let $H\subseteq G$ be a subgroup. Let $x,y\in G$ be elements.
* $x\in yH$.
* $y\in xH$.
* $y^{-1}x\in H$.
* $x^{-1}y\in H$.
* $xH\cap yH\neq \emptyset$.
* $x\sim _{H}y$.
* $xH=yH$.
# Group theory/Cosets/Properties/Fact/Proof

The equivalence between $(1)$ and $(3)$ (and between $(2)$ and $(4)$) follows by multiplication with $y^{-1}$ and with $y$. The equivalence between $(3)$ and $(4)$ follows by going to the inverse elements. From $(1)$ we get $(5)$ because of $1\in H$. If $(5)$ holds, then this means that $xh_{1}=yh_{2}$ holds with certain $h_{1},h_{2}\in H$. Therefore, $x=yh_{2}h_{1}^{-1}$, and $(1)$ is satisfied. (4) and (6) are equivalent due to the definition. Since the left cosets are the equivalence classes, the equivalence between (5) and (7) follows.
# Group theory/Left and right coset/Definition

Let $G$ be a group, and let $H\subseteq G$ be a subgroup. For every $x\in G$, the subset
    $xH={\left\{xh\mid h\in H\right\}}\,$
is called the left coset of $x$ in $G$ with respect to $H$. Every subset of this form is called a left coset. Accordingly, a set of the form
    $Hx={\left\{hx\mid h\in H\right\}}\,$
is called the right coset (of $x$).
# Group theory (algebra)/Lagrange's theorem/Fact

Finite group/Situation and let $H\subseteq G$ denote a
subgroup of $G$.
${\#\left(H\right)}$
${\#\left(G\right)}$
# Group theory (algebra)/Lagrange's theorem/Fact/Proof

We consider the left cosets $gH:={\left\{gh\mid h\in H\right\}}$ for all $g\in G$. The mapping
    $H\longrightarrow gH,h\longmapsto gh,$
is a bijection between $H$ and $gH$, so that all cosets have the same number of elements (namely ${\#\left(H\right)}$). The cosets form (as they are the equivalence classes) a partition of $G$. Hence, ${\#\left(G\right)}$ is a multiple of ${\#\left(H\right)}$.
# Group theory/Lagrange/Order of an element/Fact

Let $G$ be a finite group, and let $g\in G$ denote an element.
order of $g$ divides the
# Group theory/Lagrange/Order of an element/Fact/Proof

Let $H$ be the subgroup generated by $g$. Due to fact, we have
    $[[:Template:Op:Groupelementorder]]=[[:Template:Op:Grouporder/ord]]\,.$
Therefore, due to fact, this number divides the group order of $G$.
# Group theory/Index/Definition

For a subgroup $H\subseteq G$, the cardinality of the (left- or right--)cosets is called the index of $H$ in $G$, denoted as
    $\operatorname {ind} _{G}H.$
# Group theory/Group order/Definition

For a finite group $G$, its cardinality is called the group order, written as
    $\operatorname {ord} \,(G)={\#\left(G\right)}\,.$
# Normal subgroup/Kernel/Introduction/Section
## Definition

Subgroup/Normal subgroup/Definition
For a normal subgroup, it is not necessary to distinguish between left cosets and right cosets; we just talk about cosets. Instead of $xH$ or $Hx$, we write usually $[x]$. The equality $xH=Hx$ does not mean that $xh=hx$ for all $h\in H$; it only means that for every $h\in H$, there exists a ${\tilde {h}}\in H$ fulfilling $xh={\tilde {h}}x$.

## Lemma
### Proof

$\Box$

## Lemma
### Proof

$\Box$
# Bible/King James/Documentary Hypothesis

The documentary hypothesis hypothesizes four primary sources (traditionally known as J, E, P, and D) for the Torah. These translations are based on the King James version of the Bible. This learning resource employs the latest iteration of the Documentary Hypothesis, known as the New Documentary Hypothesis. The New Documentary Hypothesis considers the four main sources to have been independent at the moment of redaction into the Torah, with a number of insertions into the redacted document by later scribes.
The resource provides two ways to view the sources. The first method highlights the various sources as one reads through the Torah. The second method extracts each source's content from the Torah, and compiles it into a single, flowing document.

## The text with sources highlighted

* Genesis
* Exodus
* Leviticus
* Numbers
* Deuteronomy
* Joshua

## The Sources

* Jahwist source ("J")
** The Song of Lamech
** The Blessing of Jacob
** The Song of the Sea
* Elohist source ("E")
** The Covenant Code
* Priestly source ("P")
** The narrative elements of P
** The legal elements in "P"
*** The Levitical laws
*** The Holiness code ("H")
**** The list of sexual prohibitions
*** The list of clean and unclean animals
** Ritual elements in "P"
*** The guides to ritual
*** The description of the tabernacle, incense, and vestments
*** The list of duties of the Levite families
** Tallies in "P"
*** The list of altar dedication offerings
*** The list of spoils from the midianites
** Genealogies in "P"
*** The Genealogy of the children of Abraham
*** The genealogy of nations
** Specifications of the components of Israel in "P"
*** The Israelite census
*** The description of the limits of Canaan
* Deuteronomist source ("D")
** First Deuteronomists Version ("Dtr1")
*** The Narrative elements in "Dtr1"
*** The Deuteronomic Laws
*** Words for rituals in "Dtr1"
**** The Prayer of the Tithe
**** The Prayer of Firstfruits
**** The List of Mount Ebal curses
**** The Pairs of Curses and Blessings
*** The List of clean and unclean food
** Additions for the Second Deuteronomist Version ("Dtr2")
*** The Song of Moses
*** The Blessing of Moses
*** Threats and Promises
* Redaction Sources ("R")
** Book of generations
** The stations list
** Additional Rituals
** Explanatory Additions
** Resolution of conflicts between sources
* Sources by Chapter and Verse
# Open Educational Resources

Open educational resources (OER) are freely accessible, openly licensed text, media, and other digital assets that are useful for teaching, learning, and assessing as well as for research purposes. Communities use and alter OER according to their requirements and constraints. A scientific analysis of these alteration, forking or extension of OER provide insights in the drivers and needs of communities.

## Contents

The following resources can be found in these Subpages:
* Introduction - Introduction to OER
* Lesson - Lesson on OER
* Sources - Sources of OER (table of resources w/ counts of data available from each)
* Student Authoring - Resources supporting student-authored content
* Adoptions - Schools and courses using OER
* Classifying educational resources
* Open Courses - Open course lists
* Open Textbooks - Open textbook lists
* Training - For teachers
* Geographic Information Systems and tailored educational resources for a specific region
* Tailored WikiBooks
* Green Open Access
* Wikiversity:Edit-a-thon to create OER

## Learning Activities

* (w:en:UNESCO) Explore the recommendation of UNESCO on Open Educational Resources and derive an application to your institutional setting:
** as a teacher for designing classroom activities,
** as a learner/student to perform the learning tasks in the classroom (e.g. supporting material as OER for performing a learning task)
* (Digital Public Good) Explore and compare the concept of
** digital public good,
** common goods and
** OER
    and identify similarities and differences between these concepts. How can digital public goods can trigger as building blocks for an Open Innovation Ecosystem. What are the benefits, challenges and constraints?

## See Also

* Intellectual Honesty
* Open academia
* Open Badges as digital certificates and record of achievements for OER courses and learning activities
* Open Community Approach and OER as one main constituent
* PanDocElectron for using Wikiversity Resource as Slide Presentations with the option to annotate slides in a browser with a stylus
* Reproducible Science
* Open educational resources (Wikipedia)
* Open Innovation Ecosystem

## External Learning Resources for OER

* Lumen Learning: Adopting Open Educational Resources in the Classroom
* Hawaii.edu: OER Training
# Abenaki

The Abenaki people, also known as the Abnaki, Wabanaki or the Alnôbak, are one of the indigenous tribes of northeastern North America, some of the original occupants of New England, southern Quebec and the southern Canadian Maritimes. The name Abenaki is derived from the word Wabanaki, the eastern Algonquian word for "Dawn Land", which is their name for their homeland. The Abenakis were one of the original five members of the Wabanaki Confederacy.

## Readings

* Wikipedia: Abenaki
* Wikipedia: Wabanaki

## Handouts

* Primary school handout
# Menomonie, Wisconsin History/yangj28

The Tainter gate is a type floodgate used for dams. The design was invented by Jeremiah Burnham Tainter. The idea came to Tainter when he set out to create an efficient water control device to be used for the logging industry . His brother, Andrew Tainter was part owner of the Knapp Stout and Company, Company. Floodgates were used to control water levels in order to move lumber downstream on the Red Cedar River to Dunnville, the Chippewa River and on to the Mississippi River. The Tainter gate design has been very successful and is still used today throughout the world. There are currently 321 Tainter gates being used in the upper basin of the Mississippi River.

## Tainter Gate
#### History

Jeremiah B. Tainter simply redesigned a basic but clumsy floodgate that was originally developed in the east. His floodgate was designed to use an arm like gate that can be lifted to control the water level using chains. Today we use gearboxes or electric motors to power the gate. Tainter’s idea of the floodgate had become such popular design for dams that it is used very often today as water control dams for the Upper Mississippi River, the Columbia River Basin, including the Bonneville and Grand Coulee dams. The floodgate is also being used around the world such as Switzerland, Italy and many other countries.

### Uses of the Tainter gate

Tainter's had designed the floodgate to open while releasing a rush of water that would carry lumber down to Dunnville and the larger part of the Chippewa River. Today the Tainter gate now applies to what dams are made for: flood suppression, irrigation, human consumption, industrial use, aquaculture, and navigability.

## Jeremiah Burnham Tainter
### Background

Jeremiah B. Tainter was never seen as one of the popular siblings. He often hid in his older, and more successful brother, Andrew Tainter. However, he had many ideas when designing water control devices. At the age of 26, Tainter came to Menomonie and worked in the Knapp, Stout mills. While working as a millwright, he wanted a way to release enough water to help workers move lumber from his company’s territory to Dunnville and the Chippewa River. By doing some surveying around the town, he eventually came to the conclusion of creating a gate to open up and let a rush of water strong enough to carry the logs down stream, “...he cleverly designed it so that the rush of water helped both to open and to close the gates with a minimum of manpower”.
Jeremiah B. Tainter was known for many things because of his popularity, however, the Tainter gate will always honor his name today by still being a popular design for a floodgate.

## External Links

Tainter Gate
Jeremiah Burnham Tainter
Tainter Gate History
# Invertible matrix/Field/Similar/Introduction/Section
## Definition

Let $K$ be a field, and let $M$ denote an $n\times n$-matrix over $K$. Then $M$ is called invertible, if there exists a matrix $A\in \operatorname {Mat} _{n}(K)$ such that
    $A\circ M=E_{n}=M\circ A\,$

## Definition

Let $K$ denote a field. For an invertible matrix $M\in \operatorname {Mat} _{n}(K)$, the matrix $A\in \operatorname {Mat} _{n}(K)$ fulfilling
    $A\circ M=E_{n}=M\circ A\,,$
is called the inverse matrix of $M$. It is denoted by
    $M^{-1}.$
The product of invertible matrices is again invertible. Due to fact, the matrix describing a base change is invertible, and the matrix of the reversed base change is its inverse matrix.

## Definition

For a field $K$ and $n\in \mathbb {N} _{+}$, the set of all invertible $n\times n$-matrices with entries in $K$ is called the general linear group
$K$
$\operatorname {GL} _{n}\!{\left(K\right)}$

## Definition

Two square matrices $M,N\in \operatorname {Mat} _{n}(K)$ are called similar, if there exists an invertible matrix $B$ with
$M=BNB^{-1}$
For a linear mapping $\varphi \colon V\rightarrow V$, the describing matrices with respect to two bases are similar to each other, due to fact.
# Linear mapping/Matrix to basis/Injective and columns linearly independent/Fact/Proof

The mapping $\varphi$ has the property
    $\varphi (v_{j})=\sum _{i=1}^{m}s_{ij}w_{i}\,,$
where $s_{ij}$ is the $i$-th entry of the $j$-th column vector $s_{j}$. Therefore,
    $\varphi {\left(\sum _{j=1}^{n}a_{j}v_{j}\right)}=\sum _{j=1}^{n}a_{j}{\left(\sum _{i=1}^{m}s_{ij}w_{i}\right)}=\sum _{i=1}^{m}{\left(\sum _{j=1}^{n}a_{j}s_{ij}\right)}w_{i}\,.$
This is $0$ if and only if $\sum _{j=1}^{n}a_{j}s_{ij}=0$ for all $i$, and this is equivalent with
    $\sum _{j=1}^{n}a_{j}s_{j}=0\,.$
For this vector equation, there exists a nontrivial tuple ${\left(a_{1},\ldots ,a_{n}\right)}$, if and only if the columns are linearly dependent, and this holds if and only if the kernel of $\varphi$ is not trivial. Due to fact, this is equivalent with $\varphi$ not being injective.
# Upper triangular matrix/Invertible/Inverse matrix/Exercise

Let $M$ denote an invertible upper triangular matrix. Show that the inverse matrix $M^{-1}$ is also an upper triangular matrix.
# Upper triangular matrix/Invertible/Diagonal elements/Exercise

Let $M$ denote an invertible upper triangular matrix. Show that the diagonal elements of $M$ are not $0$.
# Linear algebra (Osnabrück 2024-2025)/Upper triangular matrix/Invertible/Diagonal elements/Exercise/Exercisereferencenumber

Exercise 12.6
# Linear algebra (Osnabrück 2024-2025)/Linear mapping/Matrix for basis/Surjective and column generating system/Exercise/Exercisereferencenumber

Exercise 12.7
# Linear algebra (Osnabrück 2024-2025)/Matrix/Elementary row operations/Elementary matrix from left/Fact/Proof/Exercise/Exercisereferencenumber

Exercise 12.8
# Linear algebra (Osnabrück 2024-2025)/Elementary row operations/Column rank constant/Exercise/Exercisereferencenumber

Exercise 12.20
# Linear algebra (Osnabrück 2024-2025)/Linear mapping/Matrix and basis/Rank/Fact/Proof/Exercise/Exercisereferencenumber

Exercise 12.30
# Invertible matrix/Staircase form/Identity matrix/Fact/Proof

This rests on the manipulations of the elimination procedure, and on the fact that elementary row manipulations are achieved, due to fact, by multiplications with elementary matrices from the left. In doing this, it can not happen that a zero-column or a zero-row arises, because the elementary matrices are invertible, and, in each step, invertibility is preserved. If we have an invertible upper triangular matrix, then the diagonal entries are not $0$ by exercise, and, by multiplication with a scalar, we can normalize them to $1$. With this, we can further achieve, in every column, that all entries above the diagonal entry are $0$.
# Invertible matrix/Find inverse matrix/Table/Method

Let $M$ denote a square matrix. How can we decide whether the matrix is invertible, and how can we find the inverse matrix $M^{-1}$?
For this we write down a table, on the left-hand side we write down the matrix $M$, and on the right-hand side we write down the identity matrix (of the right size). Now we apply on both sides step by step the same elementary row manipulations. The goal is to produce in the left-hand column, starting with the matrix, in the end the identity matrix. This is possible if and only if the matrix is invertible. We claim that we produce, by this method, in the right column the matrix $M^{-1}$ in the end. This rests on the following invariance principle. Every elementary row manipulation can be realized, according to fact, as a matrix multiplication with some elementary matrix $E$ from the left. If in the table we have somewhere the pair
    $(M_{1},M_{2}),$
after the next step (in the next line) we have
    $(EM_{1},EM_{2}).$
If we multiply the inverse of the second matrix (which we do not know yet; however, we do know its existence, in case the matrix is invertible) with the first matrix, then we get
    $(EM_{1})^{-1}EM_{2}=M_{1}^{-1}E^{-1}EM_{2}=M_{1}^{-1}M_{2}\,.$
This means that this expression is not changed in each single step. In the beginning, this expression equals $M^{-1}E_{n}$, hence in the end, the pair $(E_{n},N)$ must fulfil
    $N=E_{n}^{-1}N=M^{-1}E_{n}=M^{-1}\,.$
# Math Adventures/German Tank Problem

The German tank problem is a set of statistics problems named for an important historical application.
During the course of the Second World War, the Western Allies made sustained efforts to determine the extent of German production and approached this in two major ways: conventional intelligence gathering and statistical estimation. In many cases, statistical analysis substantially improved on conventional intelligence. In some cases, conventional intelligence was used in conjunction with statistical methods, as was the case in estimation of Panther tank production just prior to D-Day.
How can a sample of serial numbers, obtained from equipment (tanks in the historical case) observed in the field, be used to estimate the number of units being manufactured?
Describe your proposed solution before reading about various expert solutions.
# Base change/7-4/81 and 46/73/Point with coordinates -25/General/Exercise

We consider the families of vectors
    ${\mathfrak {v}}={\begin{pmatrix}7\\-4\end{pmatrix}},\,{\begin{pmatrix}8\\1\end{pmatrix}}\,\,{\text{ and }}\,\,{\mathfrak {u}}={\begin{pmatrix}4\\6\end{pmatrix}},\,{\begin{pmatrix}7\\3\end{pmatrix}}$
in $\mathbb {R} ^{2}$.
a) Show that ${\mathfrak {v}}$ and ${\mathfrak {u}}$ are both a basis of $\mathbb {R} ^{2}$.
b) Let $P\in \mathbb {R} ^{2}$ denote the point that has the coordinates $(-2,5)$ with respect to the basis ${\mathfrak {v}}$. What are the coordinates of this point with respect to the basis ${\mathfrak {u}}$?
c) Determine the transformation matrix that describes the change of bases from ${\mathfrak {v}}$ to ${\mathfrak {u}}$.