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19,447 | # Group (mathematics)
## Elementary consequences of the group axioms {#elementary_consequences_of_the_group_axioms}
### Equivalent definition with relaxed axioms {#equivalent_definition_with_relaxed_axioms}
The group axioms for identity and inverses may be \"weakened\" to assert only the existence of a left identity ... | 451 | Group (mathematics) | 6 |
19,447 | # Group (mathematics)
## Basic concepts {#basic_concepts}
When studying sets, one uses concepts such as subset, function, and quotient by an equivalence relation. When studying groups, one uses instead subgroups, homomorphisms, and quotient groups. These are the analogues that take the group structure into account.
... | 1,286 | Group (mathematics) | 7 |
19,447 | # Group (mathematics)
## Basic concepts {#basic_concepts}
### Presentations
Every group is isomorphic to a quotient of a free group, in many ways.
For example, the dihedral group $\mathrm{D}_4$ is generated by the right rotation $r_1$ and the reflection $f_{\mathrm{v}}$ in a vertical line (every element of $\mathrm{... | 208 | Group (mathematics) | 8 |
19,447 | # Group (mathematics)
## Examples and applications {#examples_and_applications}
thumb\|right\|A periodic wallpaper pattern gives rise to a wallpaper group. Examples and applications of groups abound. A starting point is the group $\Z$ of integers with addition as group operation, introduced above. If instead of addit... | 400 | Group (mathematics) | 9 |
19,447 | # Group (mathematics)
## Examples and applications {#examples_and_applications}
### Numbers
Many number systems, such as the integers and the rationals, enjoy a naturally given group structure. In some cases, such as with the rationals, both addition and multiplication operations give rise to group structures. Such n... | 368 | Group (mathematics) | 10 |
19,447 | # Group (mathematics)
## Examples and applications {#examples_and_applications}
### Modular arithmetic {#modular_arithmetic}
Modular arithmetic for a *modulus* $n$ defines any two elements $a$ and $b$ that differ by a multiple of $n$ to be equivalent, denoted by `{{tmath|1= a \equiv b\pmod{n} }}`{=mediawiki}. Every i... | 479 | Group (mathematics) | 11 |
19,447 | # Group (mathematics)
## Examples and applications {#examples_and_applications}
### Cyclic groups {#cyclic_groups}
A *cyclic group* is a group all of whose elements are powers of a particular element `{{tmath|1= a }}`{=mediawiki}. In multiplicative notation, the elements of the group are $\dots, a^{-3}, a^{-2}, a^{-1... | 377 | Group (mathematics) | 12 |
19,447 | # Group (mathematics)
## Examples and applications {#examples_and_applications}
### Symmetry groups {#symmetry_groups}
upright=.75\|thumb\|The (2,3,7) triangle group, a hyperbolic reflection group, acts on this tiling of the hyperbolic plane
*Symmetry groups* are groups consisting of symmetries of given mathematical... | 915 | Group (mathematics) | 13 |
19,447 | # Group (mathematics)
## Finite groups {#finite_groups}
A group is called *finite* if it has a finite number of elements. The number of elements is called the order of the group. An important class is the *symmetric groups* `{{tmath|1= \mathrm{S}_N }}`{=mediawiki}, the groups of permutations of $N$ objects. For examp... | 661 | Group (mathematics) | 14 |
19,447 | # Group (mathematics)
## Groups with additional structure {#groups_with_additional_structure}
An equivalent definition of group consists of replacing the \"there exist\" part of the group axioms by operations whose result is the element that must exist. So, a group is a set $G$ equipped with a binary operation $G \ti... | 635 | Group (mathematics) | 15 |
19,447 | # Group (mathematics)
## Generalizations
More general structures may be defined by relaxing some of the axioms defining a group. The table gives a list of several structures generalizing groups.
For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is call... | 298 | Group (mathematics) | 16 |
19,456 | # Max Horkheimer
**Max Horkheimer** (`{{IPAc-en|ˈ|h|ɔːr|k|h|aɪ|m|ər}}`{=mediawiki} `{{respell|HORK|hy|mər}}`{=mediawiki}; `{{IPA|de|ˈhɔɐ̯kˌhaɪmɐ|lang}}`{=mediawiki}; 14 February 1895 -- 7 July 1973) was a German philosopher and sociologist best known for his role in developing critical theory as director of the Instit... | 550 | Max Horkheimer | 0 |
19,456 | # Max Horkheimer
## Biography
### Institute of Social Research (Institut für Sozialforschung) {#institute_of_social_research_institut_für_sozialforschung}
In 1926, Horkheimer was an \"unsalaried lecturer in Frankfurt.\" Shortly after, in 1930, he was promoted to professor of philosophy at the University of Frankfurt ... | 746 | Max Horkheimer | 1 |
19,456 | # Max Horkheimer
## Thought
Horkheimer\'s work is marked by a concern to show the relation between affect (especially suffering) and concepts (understood as action-guiding expressions of reason). In that, he responded critically to what he saw as the one-sidedness of both neo-Kantianism (with its focus on concepts) a... | 372 | Max Horkheimer | 2 |
19,456 | # Max Horkheimer
## Thought
### Writing
#### *Between Philosophy and Social Science* {#between_philosophy_and_social_science}
*Between Philosophy and Social Science* appeared between 1930 and 1938, during the time the Frankfurt school moved from Frankfurt to Geneva to Columbia University. It included: \"Materialism ... | 1,164 | Max Horkheimer | 3 |
19,456 | # Max Horkheimer
## Criticisms
Perry Anderson sees Horkheimer\'s attempt to make the Institute purely academic as \"symptomatic of a more universal process, the emergence of a \'Western Marxism\' divorced from the working-class movement and dominated by academic philosophers and the \'product of defeat{{\'\"}} becaus... | 698 | Max Horkheimer | 4 |
19,500 | # Mervyn Peake
**Mervyn Laurence Peake** (9 July 1911 -- 17 November 1968) was a British writer, artist, poet, and illustrator. He is best known for what are usually referred to as the *Gormenghast* books. The four works were part of what Peake conceived as a lengthy cycle, the completion of which was prevented by his... | 278 | Mervyn Peake | 0 |
19,500 | # Mervyn Peake
## Early life {#early_life}
Mervyn Peake was born of British parents in Kuling located on top of Mount Lu in Jiujiang in 1911, only three months before the revolution and the founding of the Republic of China. His father, Ernest Cromwell Peake, was a medical missionary doctor with the London Missionary... | 352 | Mervyn Peake | 1 |
19,500 | # Mervyn Peake
## Career
His early career in the 1930s was as a painter in London, although he lived on the Channel Island of Sark for a time. He first moved to Sark in 1932 where his former teacher Eric Drake was setting up an artists\' colony. In 1934, Peake exhibited with the Sark artists both in the Sark Gallery ... | 484 | Mervyn Peake | 2 |
19,500 | # Mervyn Peake
## Career
### Illustration and writing {#illustration_and_writing}
The five years between 1943 and 1948 were some of the most productive of his career. He finished *Titus Groan* and *Gormenghast* and completed some of his most acclaimed illustrations for books by other authors, including Lewis Carroll\... | 365 | Mervyn Peake | 3 |
19,500 | # Mervyn Peake
## Later life {#later_life}
In 1956, Mervyn and Maeve visited Spain, financed by a friend who hoped that Peake\'s health, which was already declining, would be improved by the holiday. That year his novella *Boy in Darkness* was published beside stories by William Golding and John Wyndham in a volume c... | 330 | Mervyn Peake | 4 |
19,500 | # Mervyn Peake
## Death
Throughout the 1960s, Peake\'s health declined into physical and mental incapacitation, and he died on 17 November 1968 at a care home run by his brother-in-law, at Burcot, near Oxford. He was buried in the churchyard of St Mary\'s in the village of Burpham, West Sussex.
A 2003 study publishe... | 371 | Mervyn Peake | 5 |
19,500 | # Mervyn Peake
## Dramatic adaptations of Peake\'s work {#dramatic_adaptations_of_peakes_work}
In 1983, the Australian Broadcasting Corporation broadcast eight hour-long episodes for radio dramatising the complete Gormenghast Trilogy. This was the first to include the third book *Titus Alone*.
In 1984, BBC Radio 4 b... | 628 | Mervyn Peake | 6 |
19,509 | # Finitary relation
In mathematics, a **finitary relation** over a sequence of sets `{{nowrap|''X''<sub>1</sub>, ..., ''X''<sub>''n''</sub>}}`{=mediawiki} is a subset of the Cartesian product `{{nowrap|''X''<sub>1</sub> × ... × ''X''<sub>''n''</sub>}}`{=mediawiki}; that is, it is a set of *n*-tuples `{{nowrap|(''x''<s... | 985 | Finitary relation | 0 |
19,509 | # Finitary relation
## Specific values of *n* {#specific_values_of_n}
### Unary
Unary (1-ary) relations can be viewed as a collection of members (such as the collection of Nobel laureates) having some property (such as that of having been awarded the Nobel Prize).
Every nullary function is a unary relation.
### Bin... | 156 | Finitary relation | 1 |
19,509 | # Finitary relation
## Example
Consider the ternary relation *R* \"*x* thinks that *y* likes *z*\" over the set of people `{{nowrap|1=''P'' = {{mset| Alice, Bob, Charles, Denise }}}}`{=mediawiki}, defined by:
: .
*R* can be represented equivalently by the following table:
*x* *y* *z*
--------- --... | 304 | Finitary relation | 2 |
19,513 | # Intuitionism
In the philosophy of mathematics, **intuitionism**, or **neointuitionism** (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objecti... | 672 | Intuitionism | 0 |
19,513 | # Intuitionism
## Infinity
Among the different formulations of intuitionism, there are several different positions on the meaning and reality of infinity.
The term potential infinity refers to a mathematical procedure in which there is an unending series of steps. After each step has been completed, there is always ... | 277 | Intuitionism | 1 |
19,513 | # Intuitionism
## History
Intuitionism\'s history can be traced to two controversies in nineteenth century mathematics.
The first of these was the invention of transfinite arithmetic by Georg Cantor and its subsequent rejection by a number of prominent mathematicians including most famously his teacher Leopold Krone... | 345 | Intuitionism | 2 |
19,514 | # May 6
| 3 | May 6 | 0 |
19,531 | # Monkey Island
***Monkey Island*** is a series of adventure games. The first four games were produced and published by LucasArts, earlier known as Lucasfilm Games. The fifth was developed by Telltale Games with LucasArts, while the sixth was developed by Terrible Toybox with Lucasfilm Games and Devolver Digital.
The... | 319 | Monkey Island | 0 |
19,531 | # Monkey Island
## Media
### Games
#### *The Secret of Monkey Island* {#the_secret_of_monkey_island}
The series debuted in 1990 with *The Secret of Monkey Island* on the Amiga, MS-DOS, Atari ST and Macintosh platforms; the game was later ported to FM Towns and Mega-CD (1993). A remake version with updated graphics ... | 1,006 | Monkey Island | 1 |
19,531 | # Monkey Island
## Media
### Games
#### Other appearances {#other_appearances}
Stan\'s Used Coffins is referred to in one of the levels of the LucasArts game *Outlaws*. In *Indiana Jones and the Infernal Machine*, Guybrush can be accessed as a playable character via a cheat code; in addition, a *Monkey Island*-themed... | 458 | Monkey Island | 2 |
19,531 | # Monkey Island
## Media
### Cancelled film {#cancelled_film}
Shortly after Pixar, a spinout from Lucasfilm, found success with the first *Toy Story* film in 1995, there had been a push across Hollywood for more digitally animated films. Lucasfilm\'s Industrial Light & Magic (ILM), in the midst of transitioning from ... | 524 | Monkey Island | 3 |
19,531 | # Monkey Island
## The \"Secret\" of Monkey Island {#the_secret_of_monkey_island_1}
None of the first five games explicitly reveal the \"Secret of Monkey Island\". The team behind *Escape from Monkey Island* attempted to resolve the issue by showing that the Giant Monkey Head was actually the control room of a Giant ... | 299 | Monkey Island | 4 |
19,532 | # Cardiff Arms Park
**Cardiff Arms Park** (*Parc yr Arfau Caerdydd*), also known as **The Arms Park**, is primarily a rugby union stadium, and also has a bowling green. It is situated in Cardiff, Wales, next to the Millennium Stadium. The Arms Park was host to the British Empire and Commonwealth Games in 1958, and hos... | 325 | Cardiff Arms Park | 0 |
19,532 | # Cardiff Arms Park
## History
### Early history of the site {#early_history_of_the_site}
The Cardiff Arms Park site was originally called the Great Park, a swampy meadow behind the Cardiff Arms Hotel. The hotel was built by Sir Thomas Morgan, during the reign of Charles I. Cardiff Arms Park was named after this hot... | 879 | Cardiff Arms Park | 1 |
19,532 | # Cardiff Arms Park
## History
### Millennium Stadium {#millennium_stadium}
*Main article: Millennium Stadium*
Thirteen years after the National Stadium had opened in 1984, it was considered too small and did not have the facilities required of the time and it was demolished and a new stadium, the Millennium Stadium... | 154 | Cardiff Arms Park | 2 |
19,532 | # Cardiff Arms Park
## Current site {#current_site}
### Rugby ground {#rugby_ground}
Only the rugby ground and the Cardiff Athletic Bowls Club now use the name Cardiff Arms Park. The rugby ground has two main stands, the North Stand and the South Stand. Both the Stands have terracing below seating. The other stands ... | 867 | Cardiff Arms Park | 3 |
19,532 | # Cardiff Arms Park
## Usage
### Association football {#association_football}
The Riverside Football Club, founded in 1899, played some matches at the Arms Park until 1910, when they moved to Ninian Park, and later became Cardiff City Football Club.
On 31 May 1989, Wales played its first international game against ... | 783 | Cardiff Arms Park | 4 |
19,532 | # Cardiff Arms Park
## Usage
### Rugby union {#rugby_union}
In 1876, the Cardiff RFC was formed and soon after they also used the park. On 12 April 1884, the first international match was played at the ground between Wales and Ireland, when 5,000 people watched Wales beat Ireland by two tries and a drop goal to nil.
... | 890 | Cardiff Arms Park | 5 |
19,532 | # Cardiff Arms Park
## Usage
### Music concerts {#music_concerts}
Major music concerts were also held at the National Stadium from 1987 until 1996, they included Tina Turner, U2, Michael Jackson, The Rolling Stones, Dire Straits, Bon Jovi and R.E.M. The last music concert was held on 14 July 1996. Jehovah\'s Witnesse... | 60 | Cardiff Arms Park | 6 |
19,532 | # Cardiff Arms Park
## Singing tradition {#singing_tradition}
The National Stadium was known primarily as the venue for massed voices singing such hymns as \"Cwm Rhondda\", \"Calon Lân\", \"Men of Harlech\" and \"Hen Wlad Fy Nhadau\" (\"Land of my Fathers\" -- the national anthem of Wales). The legendary atmosphere i... | 135 | Cardiff Arms Park | 7 |
19,544 | # Microevolution
**Microevolution** is the change in allele frequencies that occurs over time within a population. This change is due to four different processes: mutation, selection (natural and artificial), gene flow and genetic drift. This change happens over a relatively short (in evolutionary terms) amount of tim... | 1,128 | Microevolution | 0 |
19,544 | # Microevolution
## Four processes {#four_processes}
### Genetic drift {#genetic_drift}
Genetic drift is the change in the relative frequency in which a gene variant (allele) occurs in a population due to random sampling. That is, the alleles in the offspring in the population are a random sample of those in the pare... | 1,034 | Microevolution | 1 |
19,544 | # Microevolution
## Origin and extended use of the term {#origin_and_extended_use_of_the_term}
### Origin
The term *microevolution* was first used by botanist Robert Greenleaf Leavitt in the journal *Botanical Gazette* in 1909, addressing what he called the \"mystery\" of how formlessness gives rise to form.
: *.... | 532 | Microevolution | 2 |
19,550 | # Multiple inheritance
**Multiple inheritance** is a feature of some object-oriented computer programming languages in which an object or class can inherit features from more than one parent object or parent class. It is distinct from single inheritance, where an object or class may only inherit from one particular ob... | 374 | Multiple inheritance | 0 |
19,550 | # Multiple inheritance
## The diamond problem {#the_diamond_problem}
The \"**diamond problem**\" (sometimes referred to as the \"Deadly Diamond of Death\") is an ambiguity that arises when two classes B and C inherit from A, and class D inherits from both B and C. If there is a method in A that B and C have overridde... | 1,607 | Multiple inheritance | 1 |
19,550 | # Multiple inheritance
## The diamond problem {#the_diamond_problem}
### Mitigation
Moreover, Ada, C#, Java, Object Pascal, Objective-C, Swift and PHP allow multiple-inheritance of interfaces (called protocols in Objective-C and Swift). Interfaces are like abstract base classes that specify method signatures without ... | 171 | Multiple inheritance | 2 |
19,555 | # Molecule
A **molecule** is a group of two or more atoms that are held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and *molec... | 287 | Molecule | 0 |
19,555 | # Molecule
## History
The definition of the molecule has evolved as knowledge of the structure of molecules has increased. Earlier definitions were less precise, defining molecules as the smallest particles of pure chemical substances that still retain their composition and chemical properties. This definition often ... | 858 | Molecule | 1 |
19,555 | # Molecule
## Prevalence
Molecules as components of matter are common. They also make up most of the oceans and atmosphere. Most organic substances are molecules. The substances of life are molecules, e.g. proteins, the amino acids of which they are composed, the nucleic acids (DNA and RNA), sugars, carbohydrates, fa... | 631 | Molecule | 2 |
19,555 | # Molecule
## Molecular formulas {#molecular_formulas}
### Chemical formula types {#chemical_formula_types}
The chemical formula for a molecule uses one line of chemical element symbols, numbers, and sometimes also other symbols, such as parentheses, dashes, brackets, and *plus* (+) and *minus* (−) signs. These are ... | 373 | Molecule | 3 |
19,555 | # Molecule
## Molecular geometry {#molecular_geometry}
Molecules have fixed equilibrium geometries---bond lengths and angles--- about which they continuously oscillate through vibrational and rotational motions. A pure substance is composed of molecules with the same average geometrical structure. The chemical formul... | 368 | Molecule | 4 |
19,555 | # Molecule
## Theoretical aspects {#theoretical_aspects}
The study of molecules by molecular physics and theoretical chemistry is largely based on quantum mechanics and is essential for the understanding of the chemical bond. The simplest of molecules is the hydrogen molecule-ion, H~2~^+^, and the simplest of all the... | 284 | Molecule | 5 |
19,559 | # Mechanics
`{{Classical mechanics |branches}}`{=mediawiki} `{{Quantum mechanics |background}}`{=mediawiki}
**Mechanics** (`{{etymology|grc|''{{wikt-lang|grc|μηχανική}}'' ({{grc-transl|μηχανική}})|of [[machine]]s}}`{=mediawiki}) is the area of physics concerned with the relationships between force, matter, and motion... | 986 | Mechanics | 0 |
19,559 | # Mechanics
## Sub-disciplines {#sub_disciplines}
The following are the three main designations consisting of various subjects that are studied in mechanics.
Note that there is also the \"theory of fields\" which constitutes a separate discipline in physics, formally treated as distinct from mechanics, whether it be... | 1,042 | Mechanics | 1 |
19,566 | # Main-group element
In chemistry and atomic physics, the **main group** is the group of elements (sometimes called the **representative elements**) whose lightest members are represented by helium, lithium, beryllium, boron, carbon, nitrogen, oxygen, and fluorine as arranged in the periodic table of the elements. The... | 299 | Main-group element | 0 |
19,570 | # Midrash
***Midrash*** (`{{IPAc-en|ˈ|m|ɪ|d|r|ɑː|ʃ}}`{=mediawiki}; *מִדְרָשׁ\]\]*; `{{abbr|pl.|plural}}`{=mediawiki} *מִדְרָשִׁים* `{{transliteration|he|midrashim}}`{=mediawiki} or `{{Script/Hebrew|מִדְרָשׁוֹת}}`{=mediawiki} *midrashot*) is an expansive Jewish Biblical exegesis using a rabbinic mode of interpretation ... | 614 | Midrash | 0 |
19,570 | # Midrash
## As method {#as_method}
Midrash is now viewed more as method than genre, although the rabbinic midrashim do constitute a distinct literary genre. According to the *Encyclopaedia Britannica*, \"Midrash was initially a philological method of interpreting the literal meaning of biblical texts. In time it dev... | 346 | Midrash | 1 |
19,570 | # Midrash
## Jewish midrashic literature {#jewish_midrashic_literature}
Numerous Jewish midrashim previously preserved in manuscript form have been published in print, including those denominated as smaller or minor midrashim. Bernard H. Mehlman and Seth M. Limmer deprecate this usage, claiming that the term \"minor\... | 510 | Midrash | 2 |
19,570 | # Midrash
## Classical compilations {#classical_compilations}
### Tannaitic
- **Alphabet of Rabbi Akiva**. This book is a midrash on the names of the letters of the hebrew alphabet.
- **Mekhilta**. The Mekhilta essentially functions as a commentary on the Book of Exodus. There are two versions of this midrash co... | 561 | Midrash | 3 |
19,570 | # Midrash
## Classical compilations {#classical_compilations}
### Post-Talmudic {#post_talmudic}
- *Midrash Qohelet*, on Ecclesiastes (probably before middle of 9th century).
- *Midrash Esther*, on Esther (940 CE).
- The *Pesikta*, a compilation of homilies on special Pentateuchal and Prophetic lessons (early 8... | 372 | Midrash | 4 |
19,570 | # Midrash
## Classical compilations {#classical_compilations}
### Midrash Rabbah {#midrash_rabbah}
- **Midrash Rabba** --- widely studied are the *Rabboth* (great commentaries), a collection of ten midrashim on different books of the Bible (namely, the five books of the Torah and the Five Megillot). Although referr... | 397 | Midrash | 5 |
19,570 | # Midrash
## Contemporary views {#contemporary_views}
According to Carol Bakhos, recent studies that use literary-critical tools to concentrate on the cultural and literary aspects of midrash have led to a rediscovery of the importance of these texts for finding insights into the rabbinic culture that created them. M... | 283 | Midrash | 6 |
19,583 | # Monomer
A **monomer** (`{{IPAc-en|ˈ|m|ɒ|n|ə|m|ər}}`{=mediawiki} `{{respell|MON|ə|mər}}`{=mediawiki}; *mono-*, \"one\" + *-mer*, \"part\") is a molecule that can react together with other monomer molecules to form a larger polymer chain or two- or three-dimensional network in a process called polymerization.`{{Quote ... | 565 | Monomer | 0 |
19,593 | # Missouria
The **Missouria** or **Missouri** (in their own language, **Niúachi**, also spelled **Niutachi**) are a Native American tribe that originated in the Great Lakes region of what is now the United States before European contact. The tribe belongs to the Chiwere division of the Siouan language family, together... | 784 | Missouria | 0 |
19,609 | # Memory leak
In computer science, a **memory leak** is a type of resource leak that occurs when a computer program incorrectly manages memory allocations in a way that memory which is no longer needed is not released. A memory leak may also happen when an object is stored in memory but cannot be accessed by the runni... | 385 | Memory leak | 0 |
19,609 | # Memory leak
## Effects
### Out-of-memory condition {#out_of_memory_condition}
If a program uses all available memory before being terminated (whether there is virtual memory or only main memory, such as on an embedded system) any attempt to allocate more memory will fail. This usually causes the program attempting ... | 378 | Memory leak | 1 |
19,609 | # Memory leak
## Programming issues {#programming_issues}
Memory leaks are a common error in programming, especially when using languages that have no built in automatic garbage collection, such as C and C++. Typically, a memory leak occurs because dynamically allocated memory has become unreachable. The prevalence o... | 402 | Memory leak | 2 |
19,609 | # Memory leak
## RAII
Resource acquisition is initialization (RAII) is an approach to the problem commonly taken in C++, D, and Ada. It involves associating scoped objects with the acquired resources, and automatically releasing the resources once the objects are out of scope. Unlike garbage collection, RAII has the ... | 514 | Memory leak | 3 |
19,609 | # Memory leak
## Examples
### Pseudocode
The following example, written in pseudocode, is intended to show how a memory leak can come about, and its effects, without needing any programming knowledge. The program in this case is part of some very simple software designed to control an elevator. This part of the prog... | 548 | Memory leak | 4 |
19,614 | # Molecular orbital
In chemistry, a **molecular orbital** is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms *ato... | 289 | Molecular orbital | 0 |
19,614 | # Molecular orbital
## Overview
A molecular orbital (MO) can be used to represent the regions in a molecule where an electron occupying that orbital is likely to be found. Molecular orbitals are approximate solutions to the Schrödinger equation for the electrons in the electric field of the molecule\'s atomic nuclei.... | 581 | Molecular orbital | 1 |
19,614 | # Molecular orbital
## Qualitative discussion {#qualitative_discussion}
For an imprecise, but qualitatively useful, discussion of the molecular structure, the molecular orbitals can be obtained from the \"Linear combination of atomic orbitals molecular orbital method\" ansatz. Here, the molecular orbitals are express... | 478 | Molecular orbital | 2 |
19,614 | # Molecular orbital
## Qualitative discussion {#qualitative_discussion}
### Sigma and pi labels for MOs {#sigma_and_pi_labels_for_mos}
The type of interaction between atomic orbitals can be further categorized by the molecular-orbital symmetry labels σ (sigma), π (pi), δ (delta), φ (phi), γ (gamma) etc. These are the... | 616 | Molecular orbital | 3 |
19,614 | # Molecular orbital
## Qualitative discussion {#qualitative_discussion}
### MO diagrams {#mo_diagrams}
The qualitative approach of MO analysis uses a molecular orbital diagram to visualize bonding interactions in a molecule. In this type of diagram, the molecular orbitals are represented by horizontal lines; the high... | 436 | Molecular orbital | 4 |
19,614 | # Molecular orbital
## Qualitative discussion {#qualitative_discussion}
### Bonding in molecular orbitals {#bonding_in_molecular_orbitals}
#### Orbital degeneracy {#orbital_degeneracy}
Molecular orbitals are said to be degenerate if they have the same energy. For example, in the homonuclear diatomic molecules of the... | 407 | Molecular orbital | 5 |
19,614 | # Molecular orbital
## Examples
### Homonuclear diatomics {#homonuclear_diatomics}
Homonuclear diatomic MOs contain equal contributions from each atomic orbital in the basis set. This is shown in the homonuclear diatomic MO diagrams for H~2~, He~2~, and Li~2~, all of which containing symmetric orbitals.
#### H~2~
... | 588 | Molecular orbital | 6 |
19,614 | # Molecular orbital
## Examples
### Heteronuclear diatomics {#heteronuclear_diatomics}
While MOs for homonuclear diatomic molecules contain equal contributions from each interacting atomic orbital, MOs for heteronuclear diatomics contain different atomic orbital contributions. Orbital interactions to produce bonding ... | 390 | Molecular orbital | 7 |
19,615 | # Systems Concepts
**Systems Concepts, Inc.** (now the **SC Group**), was a company co-founded by Stewart Nelson and Mike Levitt focused on making hardware products related to the DEC PDP-10 series of computers. One of its major products was the SA-10, an interface which allowed PDP-10s to be connected to disk and tap... | 530 | Systems Concepts | 0 |
19,624 | # May 27
| 3 | May 27 | 0 |
19,629 | # May 10
| 3 | May 10 | 0 |
19,631 | # May 17
| 3 | May 17 | 0 |
19,638 | # MEMS
**MEMS** (**micro-electromechanical systems**) is the technology of microscopic devices incorporating both electronic and moving parts. MEMS are made up of components between 1 and 100 micrometres in size (i.e., 0.001 to 0.1 mm), and MEMS devices generally range in size from 20 micrometres to a millimetre (i.e.... | 498 | MEMS | 0 |
19,638 | # MEMS
## Materials
The fabrication of MEMS evolved from the process technology in semiconductor device fabrication, i.e. the basic techniques are deposition of material layers, patterning by photolithography and etching to produce the required shapes.
Silicon: Silicon is the material used to create most integrated ... | 503 | MEMS | 1 |
19,638 | # MEMS
## Basic processes {#basic_processes}
### Deposition processes {#deposition_processes}
One of the basic building blocks in MEMS processing is the ability to deposit thin films of material with a thickness anywhere from one micrometre to about 100 micrometres. The NEMS process is the same, although the measure... | 860 | MEMS | 2 |
19,638 | # MEMS
## Basic processes {#basic_processes}
### Etching processes {#etching_processes}
There are two basic categories of etching processes: wet etching and dry etching. In the former, the material is dissolved when immersed in a chemical solution. In the latter, the material is sputtered or dissolved using reactive ... | 500 | MEMS | 3 |
19,638 | # MEMS
## Basic processes {#basic_processes}
### Etching processes {#etching_processes}
#### Dry etching {#dry_etching}
Xenon difluoride (`{{chem|XeF|2}}`{=mediawiki}) is a dry vapor phase isotropic etch for silicon originally applied for MEMS in 1995 at University of California, Los Angeles. Primarily used for relea... | 876 | MEMS | 4 |
19,638 | # MEMS
## Manufacturing technologies {#manufacturing_technologies}
Bulk micromachining is the oldest paradigm of silicon-based MEMS. The whole thickness of a silicon wafer is used for building the micro-mechanical structures. Silicon is machined using various etching processes. Bulk micromachining has been essential ... | 542 | MEMS | 5 |
19,638 | # MEMS
## Applications
Some common commercial applications of MEMS include:
- Inkjet printers, which use piezoelectrics or thermal bubble ejection to deposit ink on paper.
- Accelerometers in modern cars for a large number of purposes including airbag deployment and electronic stability control.
- Inertial mea... | 607 | MEMS | 6 |
19,652 | # Monoid
Monad}} `{{Algebraic structures |group}}`{=mediawiki}
In abstract algebra, a **monoid** is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with addition form a monoid, the identity element being `{{math|0}}`{=mediawiki}.
Monoids are semigrou... | 388 | Monoid | 0 |
19,652 | # Monoid
## Monoid structures {#monoid_structures}
### Submonoids
A **submonoid** of a monoid `{{math|(''M'', •)}}`{=mediawiki} is a subset `{{math|''N''}}`{=mediawiki} of `{{math|''M''}}`{=mediawiki} that is closed under the monoid operation and contains the identity element `{{math|''e''}}`{=mediawiki} of `{{math|... | 329 | Monoid | 1 |
19,652 | # Monoid
## Examples
- Out of the 16 possible binary Boolean operators, four have a two-sided identity that is also commutative and associative. These four each make the set `{{math|{{mset|False, True}}}}`{=mediawiki} a commutative monoid. Under the standard definitions, AND and XNOR have the identity `{{math|True}... | 1,065 | Monoid | 2 |
19,652 | # Monoid
## Properties
The monoid axioms imply that the identity element `{{math|''e''}}`{=mediawiki} is unique: If `{{math|''e''}}`{=mediawiki} and `{{math|''f''}}`{=mediawiki} are identity elements of a monoid, then `{{math|1=''e'' = ''ef'' = ''f''}}`{=mediawiki}.
### Products and powers {#products_and_powers}
Fo... | 668 | Monoid | 3 |
19,652 | # Monoid
## Acts and operator monoids {#acts_and_operator_monoids}
Let `{{math|''M''}}`{=mediawiki} be a monoid, with the binary operation denoted by `{{math|•}}`{=mediawiki} and the identity element denoted by `{{math|''e''}}`{=mediawiki}. Then a (left) **`{{math|''M''}}`{=mediawiki}-act** (or left act over `{{math|... | 864 | Monoid | 4 |
19,652 | # Monoid
## Monoids in computer science {#monoids_in_computer_science}
In computer science, many abstract data types can be endowed with a monoid structure. In a common pattern, a sequence of elements of a monoid is \"folded\" or \"accumulated\" to produce a final value. For instance, many iterative algorithms need t... | 564 | Monoid | 5 |
19,655 | # May 23
| 3 | May 23 | 0 |
19,667 | # Michael Ventris
**Michael George Francis Ventris**, `{{post-nominals|country=GBR|size=100%|OBE}}`{=mediawiki} (`{{IPAc-en|ˈ|v|ɛ|n|t|r|ɪ|s}}`{=mediawiki}; 12 July 1922 -- 6 September 1956) was an English architect, classicist and philologist who deciphered Linear B, the ancient Mycenaean Greek script. A student of la... | 369 | Michael Ventris | 0 |
19,667 | # Michael Ventris
## Young adult {#young_adult}
Ventris\'s father died in 1938, and his mother, Dora, became administrator of the estate. With the German invasion of Poland in 1939, Dora lost her private income, and in 1940 her father died. Ventris lost his mother to clinical depression and an overdose of barbiturate... | 490 | Michael Ventris | 1 |
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