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https://en.wikipedia.org/wiki/Anthropology
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Anthropology is the scientific study of humanity, concerned with human behavior, human biology, cultures, societies, and linguistics, in both the present and past, including past human species. Social anthropology studies patterns of behavior, while cultural anthropology studies cultural meaning, including norms and values. A portmanteau term sociocultural anthropology is commonly used today. Linguistic anthropology studies how language influences social life. Biological or physical anthropology studies the biological development of humans.
Archaeological anthropology, often termed as "anthropology of the past," studies human activity through investigation of physical evidence. It is considered a branch of anthropology in North America and Asia, while in Europe, archaeology is viewed as a discipline in its own right or grouped under other related disciplines, such as history and palaeontology.
Etymology
The abstract noun anthropology is first attested in reference to history. Its present use first appeared in Renaissance Germany in the works of Magnus Hundt and Otto Casmann. Their Neo-Latin derived from the combining forms of the Greek words ánthrōpos (, "human") and lógos (, "study"). Its adjectival form appeared in the works of Aristotle. It began to be used in English, possibly via French , by the early 18th century.
Origin and development of the term
Through the 19th century
In 1647, the Bartholins, early scholars of the University of Copenhagen, defined as follows:
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https://en.wikipedia.org/wiki/Agricultural%20science
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Agricultural science (or agriscience for short) is a broad multidisciplinary field of biology that encompasses the parts of exact, natural, economic and social sciences that are used in the practice and understanding of agriculture. Professionals of the agricultural science are called agricultural scientists or agriculturists.
History
In the 18th century, Johann Friedrich Mayer conducted experiments on the use of gypsum (hydrated calcium sulphate) as a fertilizer.
In 1843, John Bennet Lawes and Joseph Henry Gilbert began a set of long-term field experiments at Rothamsted Research in England, some of which are still running as of 2018.
In the United States, a scientific revolution in agriculture began with the Hatch Act of 1887, which used the term "agricultural science". The Hatch Act was driven by farmers' interest in knowing the constituents of early artificial fertilizer. The Smith–Hughes Act of 1917 shifted agricultural education back to its vocational roots, but the scientific foundation had been built. For the next 44 years after 1906, federal expenditures on agricultural research in the United States outpaced private expenditures.
Prominent agricultural scientists
Wilbur Olin Atwater
Robert Bakewell
Norman Borlaug
Luther Burbank
George Washington Carver
Carl Henry Clerk
George C. Clerk
René Dumont
Sir Albert Howard
Kailas Nath Kaul
Thomas Lecky
Justus von Liebig
Jay Laurence Lush
Gregor Mendel
Louis Pasteur
M. S. Swaminathan
Jethro Tull
Artturi I
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https://en.wikipedia.org/wiki/Arithmetic%20mean
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In mathematics and statistics, the arithmetic mean ( ), arithmetic average, or just the mean or average (when the context is clear) is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an experiment, an observational study, or a survey. The term "arithmetic mean" is preferred in some mathematics and statistics contexts because it helps distinguish it from other types of means, such as geometric and harmonic.
In addition to mathematics and statistics, the arithmetic mean is frequently used in economics, anthropology, history, and almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population.
While the arithmetic mean is often used to report central tendencies, it is not a robust statistic: it is greatly influenced by outliers (values much larger or smaller than most others). For skewed distributions, such as the distribution of income for which a few people's incomes are substantially higher than most people's, the arithmetic mean may not coincide with one's notion of "middle". In that case, robust statistics, such as the median, may provide a better description of central tendency.
Definition
Given a data set , the arithmetic mean (also mean or average), denoted (read bar), is the mean of the values .
The arithmetic mean is a data set's most commonly used and readily understood measure of central tendency. In statistic
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https://en.wikipedia.org/wiki/Alkane
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In organic chemistry, an alkane, or paraffin (a historical trivial name that also has other meanings), is an acyclic saturated hydrocarbon. In other words, an alkane consists of hydrogen and carbon atoms arranged in a tree structure in which all the carbon–carbon bonds are single. Alkanes have the general chemical formula . The alkanes range in complexity from the simplest case of methane (), where n = 1 (sometimes called the parent molecule), to arbitrarily large and complex molecules, like pentacontane () or 6-ethyl-2-methyl-5-(1-methylethyl) octane, an isomer of tetradecane ().
The International Union of Pure and Applied Chemistry (IUPAC) defines alkanes as "acyclic branched or unbranched hydrocarbons having the general formula , and therefore consisting entirely of hydrogen atoms and saturated carbon atoms". However, some sources use the term to denote any saturated hydrocarbon, including those that are either monocyclic (i.e. the cycloalkanes) or polycyclic, despite their having a distinct general formula (i.e. cycloalkanes are ).
In an alkane, each carbon atom is sp3-hybridized with 4 sigma bonds (either C–C or C–H), and each hydrogen atom is joined to one of the carbon atoms (in a C–H bond). The longest series of linked carbon atoms in a molecule is known as its carbon skeleton or carbon backbone. The number of carbon atoms may be considered as the size of the alkane.
One group of the higher alkanes are waxes, solids at standard ambient temperature and pressure (SAT
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https://en.wikipedia.org/wiki/Argument%20%28disambiguation%29
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In logic and philosophy, an argument is an attempt to persuade someone of something, or give evidence or reasons for accepting a particular conclusion.
Argument may also refer to:
Mathematics and computer science
Argument (complex analysis), a function which returns the polar angle of a complex number
Command-line argument, an item of information provided to a program when it is started
Parameter (computer programming), a piece of data provided as input to a subroutine
Argument principle, a theorem in complex analysis
An argument of a function, also known as an independent variable
Language and rhetoric
Argument (literature), a brief summary, often in prose, of a poem or section of a poem or other work
Argument (linguistics), a phrase that appears in a syntactic relationship with the verb in a clause
Oral argument in the United States, a spoken presentation to a judge or appellate court by a lawyer (or parties when representing themselves) of the legal reasons why they should prevail
Closing argument, in law, the concluding statement of each party's counsel reiterating the important arguments in a court case
Other uses
Musical argument, a concept in the theory of musical form
Argument (ship), an Australian sloop wrecked in 1809
Das Argument, a German academic journal
Argument Clinic, a Monty Python sketch
A disagreement between two or more parties or the discussion of the disagreement
Argument (horse)
See also
The Argument (disambiguation)
argumentation
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https://en.wikipedia.org/wiki/Anatomy
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Anatomy () is the branch of biology concerned with the study of the structure of organisms and their parts. Anatomy is a branch of natural science that deals with the structural organization of living things. It is an old science, having its beginnings in prehistoric times. Anatomy is inherently tied to developmental biology, embryology, comparative anatomy, evolutionary biology, and phylogeny, as these are the processes by which anatomy is generated, both over immediate and long-term timescales. Anatomy and physiology, which study the structure and function of organisms and their parts respectively, make a natural pair of related disciplines, and are often studied together. Human anatomy is one of the essential basic sciences that are applied in medicine.
Anatomy is a complex and dynamic field that is constantly evolving as new discoveries are made. In recent years, there has been a significant increase in the use of advanced imaging techniques, such as MRI and CT scans, which allow for more detailed and accurate visualizations of the body's structures.
The discipline of anatomy is divided into macroscopic and microscopic parts. Macroscopic anatomy, or gross anatomy, is the examination of an animal's body parts using unaided eyesight. Gross anatomy also includes the branch of superficial anatomy. Microscopic anatomy involves the use of optical instruments in the study of the tissues of various structures, known as histology, and also in the study of cells.
The history of
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https://en.wikipedia.org/wiki/Albert%20Einstein
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Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist who is widely held to be one of the greatest and most influential scientists of all time. Best known for developing the theory of relativity, Einstein also made important contributions to quantum mechanics, and was thus a central figure in the revolutionary reshaping of the scientific understanding of nature that modern physics accomplished in the first decades of the twentieth century. His mass–energy equivalence formula , which arises from relativity theory, has been called "the world's most famous equation". He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect", a pivotal step in the development of quantum theory. His work is also known for its influence on the philosophy of science. In a 1999 poll of 130 leading physicists worldwide by the British journal Physics World, Einstein was ranked the greatest physicist of all time. His intellectual achievements and originality have made the word Einstein broadly synonymous with genius.
In 1905, a year sometimes described as his annus mirabilis (miracle year), Einstein published four groundbreaking papers. These outlined a theory of the photoelectric effect, explained Brownian motion, introduced his special theory of relativity—a theory which addressed the inability of classical mechanics to account satisfactorily for the behavior of
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https://en.wikipedia.org/wiki/Algorithms%20%28journal%29
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Algorithms is a monthly peer-reviewed open-access scientific journal of mathematics, covering design, analysis, and experiments on algorithms. The journal is published by MDPI and was established in 2008. The founding editor-in-chief was Kazuo Iwama (Kyoto University). From May 2014 to September 2019, the editor-in-chief was Henning Fernau (Universität Trier). The current editor-in-chief is Frank Werner (Otto-von-Guericke-Universität Magdeburg).
Abstracting and indexing
According to the Journal Citation Reports, the journal has a 2022 impact factor of 2.3.
The journal is abstracted and indexed in:
See also
Journals with similar scope include:
ACM Transactions on Algorithms
Algorithmica
Journal of Algorithms (Elsevier)
References
External links
Computer science journals
Open access journals
MDPI academic journals
English-language journals
Academic journals established in 2008
Mathematics journals
Monthly journals
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https://en.wikipedia.org/wiki/Algorithm
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In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually. Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus".
In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result.
As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.
History
Ancien
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https://en.wikipedia.org/wiki/Axiom%20of%20choice
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In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty. Informally put, the axiom of choice says that given any collection of sets, each containing at least one element, it is possible to construct a new set by arbitrarily choosing one element from each set, even if the collection is infinite. Formally, it states that for every indexed family of nonempty sets, there exists an indexed set such that for every . The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem.
In many cases, a set arising from choosing elements arbitrarily can be made without invoking the axiom of choice; this is, in particular, the case if the number of sets from which to choose the elements is finite, or if a canonical rule on how to choose the elements is available – some distinguishing property that happens to hold for exactly one element in each set. An illustrative example is sets picked from the natural numbers. From such sets, one may always select the smallest number, e.g. given the sets {{4, 5, 6}, {10, 12}, {1, 400, 617, 8000}}, the set containing each smallest element is {4, 10, 1}. In this case, "select the smallest number" is a choice function. Even if infinitely many sets were collected from the natural numbers, it will always be possible to choose the smallest element from each set to produce
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https://en.wikipedia.org/wiki/Advanced%20Chemistry
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Advanced Chemistry is a German hip hop group from Heidelberg, a scenic city in Baden-Württemberg, South Germany. Advanced Chemistry was founded in 1987 by Toni L, Linguist, Gee-One, DJ Mike MD (Mike Dippon) and MC Torch. Each member of the group holds German citizenship, and Toni L, Linguist, and Torch are of Italian, Ghanaian, and Haitian backgrounds, respectively.
Influenced by North American socially conscious rap and the Native tongues movement, Advanced Chemistry is regarded as one of the main pioneers in German hip hop. They were one of the first groups to rap in German (although their name is in English). Furthermore, their songs tackled controversial social and political issues, distinguishing them from early German hip hop group "Die Fantastischen Vier" (The Fantastic Four), which had a more light-hearted, playful, party image.
Career
Advanced Chemistry frequently rapped about their lives and experiences as children of immigrants, exposing the marginalization experienced by most ethnic minorities in Germany, and the feelings of frustration and resentment that being denied a German identity can cause. The song "Fremd im eigenen Land" (Foreign in your own nation) was released by Advanced Chemistry in November 1992. The single became a staple in the German hip hop scene. It made a strong statement about the status of immigrants throughout Germany, as the group was composed of multi-national and multi-racial members. The video shows several members brandishing their G
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https://en.wikipedia.org/wiki/Absolute%20value
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In mathematics, the absolute value or modulus of a real number , is the non-negative value without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and For example, the absolute value of 3 and the absolute value of −3 is The absolute value of a number may be thought of as its distance from zero.
Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.
Terminology and notation
In 1806, Jean-Robert Argand introduced the term module, meaning unit of measure in French, specifically for the complex absolute value, and it was borrowed into English in 1866 as the Latin equivalent modulus. The term absolute value has been used in this sense from at least 1806 in French and 1857 in English. The notation , with a vertical bar on each side, was introduced by Karl Weierstrass in 1841. Other names for absolute value include numerical value and magnitude. In programming languages and computational software packages, the absolute value of is generally represented by abs(x), or a similar expression.
The vertical bar notation also appears in a number of other mathematical contexts: for example, when applied to
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https://en.wikipedia.org/wiki/Alcohol%20%28chemistry%29
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In chemistry, an alcohol is a type of organic compound that carries at least one hydroxyl () functional group bound to a saturated carbon atom. Alcohols range from the simple, like methanol and ethanol, to complex, like sucrose and cholesterol. The presence of an OH group strongly modifies the properties of hydrocarbons, conferring hydrophilic (water-loving) properties. The OH group provides a site at which many reactions can occur.
History
The flammable nature of the exhalations of wine was already known to ancient natural philosophers such as Aristotle (384–322 BCE), Theophrastus (–287 BCE), and Pliny the Elder (23/24–79 CE). However, this did not immediately lead to the isolation of alcohol, even despite the development of more advanced distillation techniques in second- and third-century Roman Egypt. An important recognition, first found in one of the writings attributed to Jābir ibn Ḥayyān (ninth century CE), was that by adding salt to boiling wine, which increases the wine's relative volatility, the flammability of the resulting vapors may be enhanced. The distillation of wine is attested in Arabic works attributed to al-Kindī (–873 CE) and to al-Fārābī (–950), and in the 28th book of al-Zahrāwī's (Latin: Abulcasis, 936–1013) Kitāb al-Taṣrīf (later translated into Latin as Liber servatoris). In the twelfth century, recipes for the production of aqua ardens ("burning water", i.e., alcohol) by distilling wine with salt started to appear in a number of Latin works, and
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https://en.wikipedia.org/wiki/Algebraically%20closed%20field
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In mathematics, a field is algebraically closed if every non-constant polynomial in (the univariate polynomial ring with coefficients in ) has a root in .
Examples
As an example, the field of real numbers is not algebraically closed, because the polynomial equation has no solution in real numbers, even though all its coefficients (1 and 0) are real. The same argument proves that no subfield of the real field is algebraically closed; in particular, the field of rational numbers is not algebraically closed. By contrast, the fundamental theorem of algebra states that the field of complex numbers is algebraically closed. Another example of an algebraically closed field is the field of (complex) algebraic numbers.
No finite field F is algebraically closed, because if a1, a2, ..., an are the elements of F, then the polynomial (x − a1)(x − a2) ⋯ (x − an) + 1
has no zero in F. However, the union of all finite fields of a fixed characteristic p is an algebraically closed field, which is, in fact, the algebraic closure of the field with p elements.
Equivalent properties
Given a field F, the assertion "F is algebraically closed" is equivalent to other assertions:
The only irreducible polynomials are those of degree one
The field F is algebraically closed if and only if the only irreducible polynomials in the polynomial ring F[x] are those of degree one.
The assertion "the polynomials of degree one are irreducible" is trivially true for any field. If F is algebraically closed a
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https://en.wikipedia.org/wiki/Analysis
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Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.
The word comes from the Ancient Greek (analysis, "a breaking-up" or "an untying;" from ana- "up, throughout" and lysis "a loosening"). From it also comes the word's plural, analyses.
As a formal concept, the method has variously been ascribed to Alhazen, René Descartes (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name).
The converse of analysis is synthesis: putting the pieces back together again in a new or different whole.
Applications
Science
The field of chemistry uses analysis in three ways: to identify the components of a particular chemical compound (qualitative analysis), to identify the proportions of components in a mixture (quantitative analysis), and to break down chemical processes and examine chemical reactions between elements of matter. For an example of its use, analysis of the concentration of elements is important in managing a nuclear reactor, so nuclear scientists will analyze neutron activation to develop discrete measurements within vast samples. A matrix can have a considerable effect on the way a chemical ana
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https://en.wikipedia.org/wiki/Automorphism
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In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object.
Definition
In the context of abstract algebra, a mathematical object is an algebraic structure such as a group, ring, or vector space. An automorphism is simply a bijective homomorphism of an object with itself. (The definition of a homomorphism depends on the type of algebraic structure; see, for example, group homomorphism, ring homomorphism, and linear operator.)
The identity morphism (identity mapping) is called the trivial automorphism in some contexts. Respectively, other (non-identity) automorphisms are called nontrivial automorphisms.
The exact definition of an automorphism depends on the type of "mathematical object" in question and what, precisely, constitutes an "isomorphism" of that object. The most general setting in which these words have meaning is an abstract branch of mathematics called category theory. Category theory deals with abstract objects and morphisms between those objects.
In category theory, an automorphism is an endomorphism (i.e., a morphism from an object to itself) which is also an isomorphism (in the categorical sense of the word, meaning there exists a right and left inverse endomo
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https://en.wikipedia.org/wiki/Artificial%20intelligence
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Artificial intelligence (AI) is the intelligence of machines or software, as opposed to the intelligence of humans or animals. It is also the field of study in computer science that develops and studies intelligent machines. "AI" may also refer to the machines themselves.
AI technology is widely used throughout industry, government and science. Some high-profile applications are: advanced web search engines (e.g., Google Search), recommendation systems (used by YouTube, Amazon, and Netflix), understanding human speech (such as Siri and Alexa), self-driving cars (e.g., Waymo), generative or creative tools (ChatGPT and AI art), and competing at the highest level in strategic games (such as chess and Go).
Artificial intelligence was founded as an academic discipline in 1956. The field went through multiple cycles of optimism followed by disappointment and loss of funding, but after 2012, when deep learning surpassed all previous AI techniques, there was a vast increase in funding and interest.
The various sub-fields of AI research are centered around particular goals and the use of particular tools. The traditional goals of AI research include reasoning, knowledge representation, planning, learning, natural language processing, perception, and support for robotics. General intelligence (the ability to solve an arbitrary problem) is among the field's long-term goals.
To solve these problems, AI researchers have adapted and integrated a wide range of problem-solving techniques,
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https://en.wikipedia.org/wiki/APL
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APL is an abbreviation, acronym, or initialism that may refer to:
Science and technology
132524 APL, an asteroid
Abductor pollicis longus muscle, in the human hand
Acute promyelocytic leukemia, a subtype of acute myelogenous leukemia
Applied Physics Letters, a physics journal
Nampula Airport (IATA airport code: APL), in Mozambique
Computers
.apl, the file extension of the Monkey's Audio metadata file
AMD Performance Library, renamed Framewave, a computer compiler library
APL (programming language), an array-based programming language
APL (codepage), the character set for programming in APL
Address Prefix List, a DNS record type
Address programming language, an early high-level programming language developed in the Soviet Union
Advanced Physical Layer, an extension of Ethernet 10BASE-T1L for field devices
Alexa Presentation Language, a language for developing Amazon Alexa skills
Software licences
Adaptive Public License, an Open Source license from the University of Victoria, Canada
AROS Public License, a license of AROS Research Operating System
Arphic Public License, a free font license
Organizations
APL (shipping company), a Singapore-based container and shipping company
Aden Protectorate Levies, a militia force for local defense of the Aden Protectorate
Advanced Production and Loading, a Norwegian marine engineering company formed in 1993
Afghanistan Premier League, an Afghan Twenty20 cricket league
Afghan Premier League, a men's football league in Afghanis
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https://en.wikipedia.org/wiki/Antisymmetric%20relation
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In mathematics, a binary relation on a set is antisymmetric if there is no pair of distinct elements of each of which is related by to the other. More formally, is antisymmetric precisely if for all
or equivalently,
The definition of antisymmetry says nothing about whether actually holds or not for any . An antisymmetric relation on a set may be reflexive (that is, for all ), irreflexive (that is, for no ), or neither reflexive nor irreflexive. A relation is asymmetric if and only if it is both antisymmetric and irreflexive.
Examples
The divisibility relation on the natural numbers is an important example of an antisymmetric relation. In this context, antisymmetry means that the only way each of two numbers can be divisible by the other is if the two are, in fact, the same number; equivalently, if and are distinct and is a factor of then cannot be a factor of For example, 12 is divisible by 4, but 4 is not divisible by 12.
The usual order relation on the real numbers is antisymmetric: if for two real numbers and both inequalities and hold, then and must be equal. Similarly, the subset order on the subsets of any given set is antisymmetric: given two sets and if every element in also is in and every element in is also in then and must contain all the same elements and therefore be equal:
A real-life example of a relation that is typically antisymmetric is "paid the restaurant bill of" (understood as restricted to a given occasion). Typi
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https://en.wikipedia.org/wiki/Atomic
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Atomic may refer to:
Of or relating to the atom, the smallest particle of a chemical element that retains its chemical properties
Atomic physics, the study of the atom
Atomic Age, also known as the "Atomic Era"
Atomic scale, distances comparable to the dimensions of an atom
Atom (order theory), in mathematics
Atomic (cocktail), a champagne cocktail
Atomic (magazine), an Australian computing and technology magazine
Atomic Skis, an Austrian ski producer
Music
Atomic (band), a Norwegian jazz quintet
Atomic (Lit album), 2001
Atomic (Mogwai album), 2016
Atomic, an album by Rockets, 1982
Atomic (EP), by , 2013
"Atomic" (song), by Blondie, 1979
"Atomic", a song by Tiger Army from Tiger Army III: Ghost Tigers Rise
See also
Atom (disambiguation)
Atomicity (database systems)
Nuclear (disambiguation)
Atomism, philosophy about the basic building blocks of reality
Atomic City (disambiguation)
Atomic formula, a formula without subformulas
Atomic number, the number of protons found in the nucleus of an atom
Atomic chess, a chess variant
Atomic coffee machine, a 1950s stovetop coffee machine
Atomic operation, in computer science
Atomic TV, a channel launched in 1997 in Poland
Nuclear power
Nuclear weapon
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https://en.wikipedia.org/wiki/Acoustics
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Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries.
Hearing is one of the most crucial means of survival in the animal world and speech is one of the most distinctive characteristics of human development and culture. Accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound and hearing as a key element of mating rituals or for marking territories. Art, craft, science and technology have provoked one another to advance the whole, as in many other fields of knowledge. Robert Bruce Lindsay's "Wheel of Acoustics" is a well accepted overview of the various fields in acoustics.
History
Etymology
The word "acoustic" is derived from the Greek word ἀκουστικός (akoustikos), meaning "of or for hearing, ready to hear" and that from ἀκουστός (akoustos), "heard, audible", which in turn derives from the verb ἀκούω(akouo), "I hear".
The Latin synonym is "sonic", after which the term sonics used to be
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https://en.wikipedia.org/wiki/Atomic%20physics
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Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned with the way in which electrons are arranged around the nucleus and
the processes by which these arrangements change. This comprises ions, neutral atoms and, unless otherwise stated, it can be assumed that the term atom includes ions.
The term atomic physics can be associated with nuclear power and nuclear weapons, due to the synonymous use of atomic and nuclear in standard English. Physicists distinguish between atomic physics—which deals with the atom as a system consisting of a nucleus and electrons—and nuclear physics, which studies nuclear reactions and special properties of atomic nuclei.
As with many scientific fields, strict delineation can be highly contrived and atomic physics is often considered in the wider context of atomic, molecular, and optical physics. Physics research groups are usually so classified.
Isolated atoms
Atomic physics primarily considers atoms in isolation. Atomic models will consist of a single nucleus that may be surrounded by one or more bound electrons. It is not concerned with the formation of molecules (although much of the physics is identical), nor does it examine atoms in a solid state as condensed matter. It is concerned with processes such as ionization and excitation by photons or collisions w
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https://en.wikipedia.org/wiki/Atomic%20orbital
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In atomic theory and quantum mechanics, an atomic orbital () is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. The term atomic orbital may also refer to the physical region or space where the electron can be calculated to be present, as predicted by the particular mathematical form of the orbital.
Each orbital in an atom is characterized by a set of values of the three quantum numbers , , and , which respectively correspond to the electron's energy, its angular momentum, and an angular momentum vector component (magnetic quantum number). As an alternative to the magnetic quantum number, the orbitals are often labeled by the associated harmonic polynomials (e.g., xy, ). Each such orbital can be occupied by a maximum of two electrons, each with its own projection of spin . The simple names s orbital, p orbital, d orbital, and f orbital refer to orbitals with angular momentum quantum number and respectively. These names, together with the value of , are used to describe the electron configurations of atoms. They are derived from the description by early spectroscopists of certain series of alkali metal spectroscopic lines as sharp, principal, diffuse, and fundamental. Orbitals for > 3 continue alphabetically (g, h, i, k, ...), omitting j because some languages do not distinguish between the letters "
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https://en.wikipedia.org/wiki/Alan%20Turing
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Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. He is widely considered to be the father of theoretical computer science and artificial intelligence.
Born in Maida Vale, London, Turing was raised in southern England. He graduated at King's College, Cambridge, with a degree in mathematics. Whilst he was a fellow at Cambridge, he published a proof demonstrating that some purely mathematical yes–no questions can never be answered by computation. He defined a Turing machine and proved that the halting problem for Turing machines is undecidable. In 1938, he obtained his PhD from the Department of Mathematics at Princeton University. During the Second World War, Turing worked for the Government Code and Cypher School at Bletchley Park, Britain's codebreaking centre that produced Ultra intelligence. For a time he led Hut 8, the section that was responsible for German naval cryptanalysis. Here, he devised a number of techniques for speeding the breaking of German ciphers, including improvements to the pre-war Polish bomba method, an electromechanical machine that could find settings for the Enigma machine. Turing played a crucial
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https://en.wikipedia.org/wiki/Acoustic%20theory
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Acoustic theory is a scientific field that relates to the description of sound waves. It derives from fluid dynamics. See acoustics for the engineering approach.
For sound waves of any magnitude of a disturbance in velocity, pressure, and density we have
In the case that the fluctuations in velocity, density, and pressure are small, we can approximate these as
Where is the perturbed velocity of the fluid, is the pressure of the fluid at rest, is the perturbed pressure of the system as a function of space and time, is the density of the fluid at rest, and is the variance in the density of the fluid over space and time.
In the case that the velocity is irrotational (), we then have the acoustic wave equation that describes the system:
Where we have
Derivation for a medium at rest
Starting with the Continuity Equation and the Euler Equation:
If we take small perturbations of a constant pressure and density:
Then the equations of the system are
Noting that the equilibrium pressures and densities are constant, this simplifies to
A Moving Medium
Starting with
We can have these equations work for a moving medium by setting , where is the constant velocity that the whole fluid is moving at before being disturbed (equivalent to a moving observer) and is the fluid velocity.
In this case the equations look very similar:
Note that setting returns the equations at rest.
Linearized Waves
Starting with the above given equations of motion for a medium at
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https://en.wikipedia.org/wiki/Almost%20all
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In mathematics, the term "almost all" means "all but a negligible quantity". More precisely, if is a set, "almost all elements of " means "all elements of but those in a negligible subset of ". The meaning of "negligible" depends on the mathematical context; for instance, it can mean finite, countable, or null.
In contrast, "almost no" means "a negligible quantity"; that is, "almost no elements of " means "a negligible quantity of elements of ".
Meanings in different areas of mathematics
Prevalent meaning
Throughout mathematics, "almost all" is sometimes used to mean "all (elements of an infinite set) except for finitely many". This use occurs in philosophy as well. Similarly, "almost all" can mean "all (elements of an uncountable set) except for countably many".
Examples:
Almost all positive integers are greater than 1012.
Almost all prime numbers are odd (2 is the only exception).
Almost all polyhedra are irregular (as there are only nine exceptions: the five platonic solids and the four Kepler–Poinsot polyhedra).
If P is a nonzero polynomial, then P(x) ≠ 0 for almost all x (if not all x).
Meaning in measure theory
When speaking about the reals, sometimes "almost all" can mean "all reals except for a null set". Similarly, if S is some set of reals, "almost all numbers in S" can mean "all numbers in S except for those in a null set". The real line can be thought of as a one-dimensional Euclidean space. In the more general case of an n-dimensional space (where n
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https://en.wikipedia.org/wiki/Antimatter
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In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding particles in "ordinary" matter, and can be thought of as matter with reversed charge, parity, and time, known as CPT reversal. Antimatter occurs in natural processes like cosmic ray collisions and some types of radioactive decay, but only a tiny fraction of these have successfully been bound together in experiments to form antiatoms. Minuscule numbers of antiparticles can be generated at particle accelerators; however, total artificial production has been only a few nanograms. No macroscopic amount of antimatter has ever been assembled due to the extreme cost and difficulty of production and handling. Nonetheless, antimatter is an essential component of widely-available applications related to beta decay, such as positron emission tomography, radiation therapy, and industrial imaging.
In theory, a particle and its antiparticle (for example, a proton and an antiproton) have the same mass, but opposite electric charge, and other differences in quantum numbers.
A collision between any particle and its anti-particle partner leads to their mutual annihilation, giving rise to various proportions of intense photons (gamma rays), neutrinos, and sometimes less-massive particleantiparticle pairs. The majority of the total energy of annihilation emerges in the form of ionizing radiation. If surrounding matter is present, the energy content of this radiation will be abs
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https://en.wikipedia.org/wiki/Antiparticle
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In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antielectron). While the electron has a negative electric charge, the positron has a positive electric charge, and is produced naturally in certain types of radioactive decay. The opposite is also true: the antiparticle of the positron is the electron.
Some particles, such as the photon, are their own antiparticle. Otherwise, for each pair of antiparticle partners, one is designated as the normal particle (the one that occurs in matter usually interacted with in daily life). The other (usually given the prefix "anti-") is designated the antiparticle.
Particle–antiparticle pairs can annihilate each other, producing photons; since the charges of the particle and antiparticle are opposite, total charge is conserved. For example, the positrons produced in natural radioactive decay quickly annihilate themselves with electrons, producing pairs of gamma rays, a process exploited in positron emission tomography.
The laws of nature are very nearly symmetrical with respect to particles and antiparticles. For example, an antiproton and a positron can form an antihydrogen atom, which is believed to have the same properties as a hydrogen atom. This leads to the question of why the formation of matter after the Big Bang resulted in a universe consist
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https://en.wikipedia.org/wiki/Associative%20property
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In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.
Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is (after rewriting the expression with parentheses and in infix notation if necessary), rearranging the parentheses in such an expression will not change its value. Consider the following equations:
Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real numbers, it can be said that "addition and multiplication of real numbers are associative operations".
Associativity is not the same as commutativity, which addresses whether the order of two operands affects the result. For example, the order does not matter in the multiplication of real numbers, that is, , so we say that the multiplication of real numbers is a commutative operation. However, operations such as function composition and matrix multiplication are associative, but not (generally) commutative.
Associative operations are abundant in mathematics; in fact, many algebraic structures (such as sem
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https://en.wikipedia.org/wiki/Amine
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In chemistry, amines (, ) are compounds and functional groups that contain a basic nitrogen atom with a lone pair. Amines are formally derivatives of ammonia (), wherein one or more hydrogen atoms have been replaced by a substituent such as an alkyl or aryl group (these may respectively be called alkylamines and arylamines; amines in which both types of substituent are attached to one nitrogen atom may be called alkylarylamines). Important amines include amino acids, biogenic amines, trimethylamine, and aniline. Inorganic derivatives of ammonia are also called amines, such as monochloramine ().
The substituent is called an amino group.
Compounds with a nitrogen atom attached to a carbonyl group, thus having the structure , are called amides and have different chemical properties from amines.
Classification of amines
Amines can be classified according to the nature and number of substituents on nitrogen. Aliphatic amines contain only H and alkyl substituents. Aromatic amines have the nitrogen atom connected to an aromatic ring.
Amines, alkyl and aryl alike, are organized into three subcategories (see table) based on the number of carbon atoms adjacent to the nitrogen(how many hydrogen atoms of the ammonia molecule are replaced by hydrocarbon groups):
Primary (1°) amines—Primary amines arise when one of three hydrogen atoms in ammonia is replaced by an alkyl or aromatic group. Important primary alkyl amines include, methylamine, most amino acids, and the buffering agent
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https://en.wikipedia.org/wiki/Amide
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In organic chemistry, an amide, also known as an organic amide or a carboxamide, is a compound with the general formula , where R, R', and R″ represent any group, typically organyl groups or hydrogen atoms. The amide group is called a peptide bond when it is part of the main chain of a protein, and an isopeptide bond when it occurs in a side chain, such as in the amino acids asparagine and glutamine. It can be viewed as a derivative of a carboxylic acid () with the hydroxyl group () replaced by an amine group (); or, equivalently, an acyl (alkanoyl) group () joined to an amine group.
Common of amides are formamide (), acetamide (), benzamide (), and dimethylformamide (). Some uncommon examples of amides are N-chloroacetamide () and chloroformamide ().
Amides are qualified as primary, secondary, and tertiary according to whether the amine subgroup has the form , , or , where R and R' are groups other than hydrogen.
Nomenclature
The core of amides is called the amide group (specifically, carboxamide group).
In the usual nomenclature, one adds the term "amide" to the stem of the parent acid's name. For instance, the amide derived from acetic acid is named acetamide (CH3CONH2). IUPAC recommends ethanamide, but this and related formal names are rarely encountered. When the amide is derived from a primary or secondary amine, the substituents on nitrogen are indicated first in the name. Thus, the amide formed from dimethylamine and acetic acid is N,N-dimethylacetamide (CH3CONM
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https://en.wikipedia.org/wiki/Arthur%20Aikin
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Arthur Aikin (19 May 177315 April 1854) was an English chemist, mineralogist and scientific writer, and was a founding member of the Chemical Society (now the Royal Society of Chemistry). He first became its treasurer in 1841, and later became the society's second president.
Life
He was born at Warrington, Lancashire into a distinguished literary family of prominent Unitarians. The best known of these was his paternal aunt, Anna Laetitia Barbauld, a woman of letters who wrote poetry and essays as well as early children's literature. His father, Dr John Aikin, was a medical doctor, historian, and author. His grandfather, also called John (1713–1780), was a Unitarian scholar and theological tutor, closely associated with Warrington Academy. His sister Lucy (1781–1864) was a historical writer. Their brother Charles Rochemont Aikin was adopted by their famous aunt and brought up as their cousin.
Arthur Aikin studied chemistry under Joseph Priestley in the New College at Hackney, and gave attention to the practical applications of the science. In early life, he was a Unitarian minister for a short time. Aikin lectured on chemistry at Guy's Hospital for thirty-two years. He became the President of the British Mineralogical Society in 1801 for five years up until 1806 when the Society merged with the Askesian Society. From 1803 to 1808 he was editor of the Annual Review. In 1805 Aiken also became a proprietor of the London Institution, which was officially founded in 1806. He was
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https://en.wikipedia.org/wiki/Kolmogorov%20complexity
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In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It is named after Andrey Kolmogorov, who first published on the subject in 1963 and is a generalization of classical information theory.
The notion of Kolmogorov complexity can be used to state and prove impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem.
In particular, no program P computing a lower bound for each text's Kolmogorov complexity can return a value essentially larger than P's own length (see section ); hence no single program can compute the exact Kolmogorov complexity for infinitely many texts.
Definition
Consider the following two strings of 32 lowercase letters and digits:
abababababababababababababababab , and
4c1j5b2p0cv4w1x8rx2y39umgw5q85s7
The first string has a short English-language description, namely "write ab 16 times", which consists of 17 characters. The second one has no obvious simple description (using the same character set) other than writing down the string itself, i.e
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https://en.wikipedia.org/wiki/ATP
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ATP may refer to:
Science, technology and biology
Adenosine triphosphate, an organic chemical used for driving biological processes
ATPase, any enzyme that makes use of adenosine triphosphate
Advanced Technology Program, US government program
Anti-tachycardia pacing, process similar to a pacemaker
Alberta Taciuk process, for extracting oil from shale, etc.
Automated theorem proving, method of proving mathematical theorems by computer programs
Companies and organizations
Association of Tennis Professionals, men's professional tennis governing body
ATP Tour
American Technical Publishers, employee-owned publishing company
Armenia Tree Project, non-profit organization
Association for Transpersonal Psychology
ATP architects engineers, architecture- and engineering office for integrated design
ATP Oil and Gas, defunct US energy company
Entertainment, arts and media
Adenosine Tri-Phosphate (band), Japanese alternative rock/pop band
All Tomorrow's Parties (festival), UK organisation
ATP Recordings, record label
Alberta Theatre Projects, professional, not-for-profit, Canadian theatre company
Associated Talking Pictures, former name of Ealing Studios, a television and film production company
Transport
British Aerospace ATP, airliner
Airline transport pilot license
ATP Flight School, US
ATP (treaty), UN treaty that establishes standards for the international transport of perishable food
Aitape Airport, Papua New Guinea, IATA code
Anti-trespass panels, meant to deter
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https://en.wikipedia.org/wiki/ASA
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ASA as an abbreviation or initialism may refer to:
Biology and medicine
Accessible surface area of a biomolecule, accessible to a solvent
Acetylsalicylic acid, aspirin
Advanced surface ablation, refractive eye surgery
Anterior spinal artery, the blood vessel which supplies the anterior portion of the spinal cord
Antisperm antibodies, antibodies against sperm antigens
Argininosuccinic aciduria, a disorder of the urea cycle
ASA physical status classification system, rating of patients undergoing anesthesia
Education and research
African Studies Association of the United Kingdom
African Studies Association
Alandica Shipping Academy, Åland Islands, Finland
Albany Students' Association, at Massey University, Auckland, New Zealand
Alexander-Smith Academy, in Houston, Texas
Alpha Sigma Alpha, U.S. national sorority
American Society for Aesthetics, philosophical organization
American Student Assistance, national non-profit organization
American Studies Association
Arizona School for the Arts
Armenian Sisters Academy
Association of Social Anthropologists
Astronomical Society of Australia
Austrian Studies Association
Organizations
Acoustical Society of America, international scientific society
Advertising Standards Authority (disambiguation), advertising regulators in several countries
American Scientific Affiliation, an organization of Christians in science
American Society of Agronomy
American Society of Anesthesiologists
American Society of Appraisers
A
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https://en.wikipedia.org/wiki/Antoine%20Lavoisier
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Antoine-Laurent de Lavoisier ( ; ; 26 August 17438 May 1794), also Antoine Lavoisier after the French Revolution, was a French nobleman and chemist who was central to the 18th-century chemical revolution and who had a large influence on both the history of chemistry and the history of biology.
It is generally accepted that Lavoisier's great accomplishments in chemistry stem largely from his changing the science from a qualitative to a quantitative one. Lavoisier is most noted for his discovery of the role oxygen plays in combustion. He recognized and named oxygen (1778) and hydrogen (1783), and opposed phlogiston theory. Lavoisier helped construct the metric system, wrote the first extensive list of elements, and helped to reform chemical nomenclature. He predicted the existence of silicon (1787) and discovered that, although matter may change its form or shape, its mass always remains the same. His wife and laboratory assistant, Marie-Anne Paulze Lavoisier, became a renowned chemist in her own right.
Lavoisier was a powerful member of a number of aristocratic councils, and an administrator of the Ferme générale. The Ferme générale was one of the most hated components of the Ancien Régime because of the profits it took at the expense of the state, the secrecy of the terms of its contracts, and the violence of its armed agents. All of these political and economic activities enabled him to fund his scientific research. At the height of the French Revolution, he was charged wi
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https://en.wikipedia.org/wiki/Hermann%20Kolbe
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Adolph Wilhelm Hermann Kolbe (27 September 1818 – 25 November 1884) was a major contributor to the birth of modern organic chemistry. He was a professor at Marburg and Leipzig. Kolbe was the first to apply the term synthesis in a chemical context, and contributed to the philosophical demise of vitalism through synthesis of the organic substance acetic acid from carbon disulfide, and also contributed to the development of structural theory. This was done via modifications to the idea of "radicals" and accurate prediction of the existence of secondary and tertiary alcohols, and to the emerging array of organic reactions through his Kolbe electrolysis of carboxylate salts, the Kolbe-Schmitt reaction in the preparation of aspirin and the Kolbe nitrile synthesis. After studies with Wöhler and Bunsen, Kolbe was involved with the early internationalization of chemistry through work in London (with Frankland). He was elected to the Royal Swedish Academy of Sciences, and won the Royal Society of London's Davy Medal in the year of his death. Despite these accomplishments and his training important members of the next generation of chemists (including Zaitsev, Curtius, Beckmann, Graebe, Markovnikov, and others), Kolbe is best remembered for editing the Journal für Praktische Chemie for more than a decade, in which his vituperative essays on Kekulé's structure of benzene, van't Hoff's theory on the origin of chirality and Baeyer's reforms of nomenclature were personally critical and ling
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https://en.wikipedia.org/wiki/Augustin-Louis%20Cauchy
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Baron Augustin-Louis Cauchy ( , , ; 21 August 178923 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He was one of the first to state and rigorously prove theorems of calculus, rejecting the heuristic principle of the generality of algebra of earlier authors. He (nearly) single-handedly founded complex analysis and the study of permutation groups in abstract algebra.
A profound mathematician, Cauchy had a great influence over his contemporaries and successors; Hans Freudenthal stated: "More concepts and theorems have been named for Cauchy than for any other mathematician (in elasticity alone there are sixteen concepts and theorems named for Cauchy)." Cauchy was a prolific writer; he wrote approximately eight hundred research articles and five complete textbooks on a variety of topics in the fields of mathematics and mathematical physics.
Biography
Youth and education
Cauchy was the son of Louis François Cauchy (1760–1848) and Marie-Madeleine Desestre. Cauchy had two brothers: Alexandre Laurent Cauchy (1792–1857), who became a president of a division of the court of appeal in 1847 and a judge of the court of cassation in 1849, and Eugene François Cauchy (1802–1877), a publicist who also wrote several mathematical works.
Cauchy married Aloise de Bure in 1818. She was a close relative of the publisher who published most of Cauchy's w
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https://en.wikipedia.org/wiki/Alfred%20Jarry
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Alfred Jarry (; 8 September 1873 – 1 November 1907) was a French symbolist writer who is best known for his play Ubu Roi (1896), often cited as a forerunner of Dada and the Surrealist and Futurist movements of the 1920s and 1930s. He also coined the term and philosophical concept of 'pataphysics.
Jarry was born in Laval, Mayenne, France, and his mother was from Brittany. He wrote in a variety of hybrid genres and styles, prefiguring the postmodern, including novels, poems, short plays and opéras bouffes, absurdist essays and speculative journalism. His texts are considered examples of absurdist literature and postmodern philosophy.
Biography and works
His father Anselme Jarry (1837–1895) was a salesman who descended into alcoholism; his mother Caroline, née Quernest (1842–1893), was interested in music and literature, but her family had a streak of insanity, and her mother and brother were institutionalized. The couple had two surviving children, a daughter Caroline-Marie, called Charlotte (1865–1925), and Alfred. In 1879 Caroline left Anselme and took the children to Saint-Brieuc in Brittany.
In 1888 the family moved to Rennes, where Jarry entered the lycée at 15. There he led a group of boys who enjoyed poking fun at their well-meaning, but obese and incompetent physics teacher, a man named Hébert. Jarry and his classmate, Henri Morin, wrote a play they called Les Polonais and performed it with marionettes in the home of one of their friends. The main character, Père He
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https://en.wikipedia.org/wiki/Adaptive%20radiation
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In evolutionary biology, adaptive radiation is a process in which organisms diversify rapidly from an ancestral species into a multitude of new forms, particularly when a change in the environment makes new resources available, alters biotic interactions or opens new environmental niches. Starting with a single ancestor, this process results in the speciation and phenotypic adaptation of an array of species exhibiting different morphological and physiological traits. The prototypical example of adaptive radiation is finch speciation on the Galapagos ("Darwin's finches"), but examples are known from around the world.
Characteristics
Four features can be used to identify an adaptive radiation:
A common ancestry of component species: specifically a recent ancestry. Note that this is not the same as a monophyly in which all descendants of a common ancestor are included.
A phenotype-environment correlation: a significant association between environments and the morphological and physiological traits used to exploit those environments.
Trait utility: the performance or fitness advantages of trait values in their corresponding environments.
Rapid speciation: presence of one or more bursts in the emergence of new species around the time that ecological and phenotypic divergence is underway.
Conditions
Adaptive radiations are thought to be triggered by an ecological opportunity or a new adaptive zone. Sources of ecological opportunity can be the loss of antagonists (competitors o
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https://en.wikipedia.org/wiki/Agarose%20gel%20electrophoresis
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Agarose gel electrophoresis is a method of gel electrophoresis used in biochemistry, molecular biology, genetics, and clinical chemistry to separate a mixed population of macromolecules such as DNA or proteins in a matrix of agarose, one of the two main components of agar. The proteins may be separated by charge and/or size (isoelectric focusing agarose electrophoresis is essentially size independent), and the DNA and RNA fragments by length. Biomolecules are separated by applying an electric field to move the charged molecules through an agarose matrix, and the biomolecules are separated by size in the agarose gel matrix.
Agarose gel is easy to cast, has relatively fewer charged groups, and is particularly suitable for separating DNA of size range most often encountered in laboratories, which accounts for the popularity of its use. The separated DNA may be viewed with stain, most commonly under UV light, and the DNA fragments can be extracted from the gel with relative ease. Most agarose gels used are between 0.7–2% dissolved in a suitable electrophoresis buffer.
Properties of agarose gel
Agarose gel is a three-dimensional matrix formed of helical agarose molecules in supercoiled bundles that are aggregated into three-dimensional structures with channels and pores through which biomolecules can pass. The 3-D structure is held together with hydrogen bonds and can therefore be disrupted by heating back to a liquid state. The melting temperature is different from the gelling
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https://en.wikipedia.org/wiki/Allele
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An allele is a variation of the same sequence of nucleotides at the same place on a long DNA molecule, as described in leading textbooks on genetics and evolution. The word is a short form of "allelomorph".
"The chromosomal or genomic location of a gene or any other genetic element is called a locus (plural: loci) and alternative DNA sequences at a locus are called alleles."
The simplest alleles are single nucleotide polymorphisms (SNP), but they can also be insertions and deletions of up to several thousand base pairs.
Most alleles observed result in little or no change in the function of the gene product it codes for. However, sometimes different alleles can result in different observable phenotypic traits, such as different pigmentation. A notable example of this is Gregor Mendel's discovery that the white and purple flower colors in pea plants were the result of a single gene with two alleles.
Nearly all multicellular organisms have two sets of chromosomes at some point in their biological life cycle; that is, they are diploid. In this case, the chromosomes can be paired. Each chromosome in the pair contains the same genes in the same order, and place, along the length of the chromosome. For a given gene, if the two chromosomes contain the same allele, they, and the organism, are homozygous with respect to that gene. If the alleles are different, they, and the organism, are heterozygous with respect to that gene.
Popular definitions of 'allele' typically refer only t
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https://en.wikipedia.org/wiki/Annealing
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Annealing may refer to:
Annealing (biology), in genetics
Annealing (glass), heating a piece of glass to remove stress
Annealing (materials science), a heat treatment that alters the microstructure of a material
Quantum annealing, a method for solving combinatorial optimisation problems and ground states of glassy systems
Simulated annealing, a numerical optimization technique
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https://en.wikipedia.org/wiki/Absorption
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Absorption may refer to:
Chemistry and biology
Absorption (biology), digestion
Absorption (small intestine)
Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials
Absorption (skin), a route by which substances enter the body through the skin
Absorption (pharmacology), absorption of drugs into the body
Physics and chemical engineering
Absorption (acoustics), absorption of sound waves by a material
Absorption (electromagnetic radiation), absorption of light or other electromagnetic radiation by a material
Absorption air conditioning, a type of solar air conditioning
Absorption refrigerator, a refrigerator that runs on surplus heat rather than electricity
Dielectric absorption, the inability of a charged capacitor to completely discharge when briefly discharged
Mathematics and economics
Absorption (economics), the total demand of an economy for goods and services both from within and without
Absorption (logic), one of the rules of inference
Absorption costing, or total absorption costing, a method for appraising or valuing a firm's total inventory by including all the manufacturing costs incurred to produce those goods
Absorbing element, in mathematics, an element that does not change when it is combined in a binary operation with some other element
Absorption law, in mathematics, an identity linking a pair of binary operations
See also
Adsorption, the formation of a gas or liquid film on a solid surface
CO2 scrubber, device which abs
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https://en.wikipedia.org/wiki/Algebraic%20geometry
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Algebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.
The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular points, inflection points and points at infinity. More advanced questions involve the topology of the curve and the relationship between curves defined by different equations.
Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. As a study of systems of polynomial equations in several variables, the subject of algebraic geometry begins with finding specific solutions via equation solving, and then proceeds to understand the intrinsic properties of the totality of solutions of a system of equations. This
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https://en.wikipedia.org/wiki/Array%20%28data%20structure%29
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In computer science, an array is a data structure consisting of a collection of elements (values or variables), of same memory size, each identified by at least one array index or key. An array is stored such that the position of each element can be computed from its index tuple by a mathematical formula. The simplest type of data structure is a linear array, also called one-dimensional array.
For example, an array of ten 32-bit (4-byte) integer variables, with indices 0 through 9, may be stored as ten words at memory addresses 2000, 2004, 2008, ..., 2036, (in hexadecimal: 0x7D0, 0x7D4, 0x7D8, ..., 0x7F4) so that the element with index i has the address 2000 + (i × 4).
The memory address of the first element of an array is called first address, foundation address, or base address.
Because the mathematical concept of a matrix can be represented as a two-dimensional grid, two-dimensional arrays are also sometimes called "matrices". In some cases the term "vector" is used in computing to refer to an array, although tuples rather than vectors are the more mathematically correct equivalent. Tables are often implemented in the form of arrays, especially lookup tables; the word "table" is sometimes used as a synonym of array.
Arrays are among the oldest and most important data structures, and are used by almost every program. They are also used to implement many other data structures, such as lists and strings. They effectively exploit the addressing logic of computers. In most m
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https://en.wikipedia.org/wiki/A%20Fire%20Upon%20the%20Deep
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A Fire Upon the Deep is a 1992 science fiction novel by American writer Vernor Vinge. It is a space opera involving superhuman intelligences, aliens, variable physics, space battles, love, betrayal, genocide, and a communication medium resembling Usenet. A Fire Upon the Deep won the Hugo Award in 1993, sharing it with Doomsday Book by Connie Willis.
Besides the normal print book editions, the novel was also included on a CD-ROM sold by ClariNet Communications along with the other nominees for the 1993 Hugo awards. The CD-ROM edition included numerous annotations by Vinge on his thoughts and intentions about different parts of the book, and was later released as a standalone e-book.
Setting
The novel is set in various locations in the Milky Way. The galaxy is divided into four concentric volumes called the "Zones of Thought"; it is not clear to the novel's characters whether this is a natural phenomenon or an artificially produced one, but it seems to roughly correspond with galactic-scale stellar density and a Beyond region is mentioned in the Sculptor Galaxy as well. The Zones reflect fundamental differences in basic physical laws, and one of the main consequences is their effect on intelligence, both biological and artificial. Artificial intelligence and automation is most directly affected, in that advanced hardware and software from the Beyond or the Transcend will work less and less well as a ship "descends" towards the Unthinking Depths. But even biological intelligen
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https://en.wikipedia.org/wiki/Associative%20algebra
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In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center of A. This is thus an algebraic structure with an addition, a multiplication, and a scalar multiplication (the multiplication by the image by the ring homomorphism of an element of K). The addition and multiplication operations together give A the structure of a ring; the addition and scalar multiplication operations together give A the structure of a module or vector space over K. In this article we will also use the term [[algebra over a field|K-algebra]] to mean an associative algebra over K. A standard first example of a K-algebra is a ring of square matrices over a commutative ring K, with the usual matrix multiplication.
A commutative algebra is an associative algebra that has a commutative multiplication, or, equivalently, an associative algebra that is also a commutative ring.
In this article associative algebras are assumed to have a multiplicative identity, denoted 1; they are sometimes called unital associative algebras for clarification. In some areas of mathematics this assumption is not made, and we will call such structures non-unital associative algebras. We will also assume that all rings are unital, and all ring homomorphisms are unital.
Every ring is an associative algebra over its center and over the integers.
Definition
Let R be a commutative ring (so R could be a field). An associative R-algebra
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https://en.wikipedia.org/wiki/Axiom%20of%20regularity
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In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A. In first-order logic, the axiom reads:
The axiom of regularity together with the axiom of pairing implies that no set is an element of itself, and that there is no infinite sequence (an) such that ai+1 is an element of ai for all i. With the axiom of dependent choice (which is a weakened form of the axiom of choice), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true. Hence, in this context the axiom of regularity is equivalent to the sentence that there are no downward infinite membership chains.
The axiom is the contribution of ; it was adopted in a formulation closer to the one found in contemporary textbooks by . Virtually all results in the branches of mathematics based on set theory hold even in the absence of regularity; see chapter 3 of . However, regularity makes some properties of ordinals easier to prove; and it not only allows induction to be done on well-ordered sets but also on proper classes that are well-founded relational structures such as the lexicographical ordering on
Given the other axioms of Zermelo–Fraenkel set theory, the axiom of regularity is equivalent to the axiom of induction. The axiom of induction tends to be used in place of the axiom of regularity in intuitionistic theories (one
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https://en.wikipedia.org/wiki/AVL%20tree
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In computer science, an AVL tree (named after inventors Adelson-Velsky and Landis) is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Lookup, insertion, and deletion all take time in both the average and worst cases, where is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations.
The AVL tree is named after its two Soviet inventors, Georgy Adelson-Velsky and Evgenii Landis, who published it in their 1962 paper "An algorithm for the organization of information". It is the oldest self-balancing binary search tree data structure to be invented.
AVL trees are often compared with red–black trees because both support the same set of operations and take time for the basic operations. For lookup-intensive applications, AVL trees are faster than red–black trees because they are more strictly balanced. Similar to red–black trees, AVL trees are height-balanced. Both are, in general, neither weight-balanced nor -balanced for any ; that is, sibling nodes can have hugely differing numbers of descendants.
Definition
Balance factor
In a binary tree the balance factor of a node X is defined to be the height difference
of its two child sub-trees rooted by node X. A binary tree is defined to be an AVL tree if the invariant
h
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https://en.wikipedia.org/wiki/Aliphatic%20compound
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In organic chemistry, hydrocarbons (compounds composed solely of carbon and hydrogen) are divided into two classes: aromatic compounds and aliphatic compounds (; G. aleiphar, fat, oil). Aliphatic compounds can be saturated (in which all the C-C bonds are single requiring the structure to be completed, or 'saturated', by hydrogen) like hexane, or unsaturated, like hexene and hexyne. Open-chain compounds, whether straight or branched, and which contain no rings of any type, are always aliphatic. Cyclic compounds can be aliphatic if they are not aromatic.
Structure
Aliphatic compounds can be saturated, joined by single bonds (alkanes), or unsaturated, with double bonds (alkenes) or triple bonds (alkynes). If other elements (heteroatoms) are bound to the carbon chain, the most common being oxygen, nitrogen, sulfur, and chlorine, it is no longer a hydrocarbon, and therefore no longer an aliphatic compound. However, such compounds may still be referred to as aliphatic if the hydrocarbon portion of the molecule is aliphatic, e.g. aliphatic amines, to differentiate them from aromatic amines.
The least complex aliphatic compound is methane (CH4).
Properties
Most aliphatic compounds are flammable, allowing the use of hydrocarbons as fuel, such as methane in natural gas for stoves or heating; butane in torches and lighters; various aliphatic (as well as aromatic) hydrocarbons in liquid transportation fuels like petrol/gasoline, diesel, and jet fuel; and other uses such as ethyne
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https://en.wikipedia.org/wiki/Algebraic%20extension
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In mathematics, an algebraic extension is a field extension such that every element of the larger field is algebraic over the smaller field ; that is, every element of is a root of a non-zero polynomial with coefficients in . A field extension that is not algebraic, is said to be transcendental, and must contain transcendental elements, that is, elements that are not algebraic.
The algebraic extensions of the field of the rational numbers are called algebraic number fields and are the main objects of study of algebraic number theory. Another example of a common algebraic extension is the extension of the real numbers by the complex numbers.
Some properties
All transcendental extensions are of infinite degree. This in turn implies that all finite extensions are algebraic. The converse is not true however: there are infinite extensions which are algebraic. For instance, the field of all algebraic numbers is an infinite algebraic extension of the rational numbers.
Let be an extension field of , and . The smallest subfield of that contains and is commonly denoted If is algebraic over , then the elements of can be expressed as polynomials in with coefficients in K; that is, is also the smallest ring containing and . In this case, is a finite extension of (it is a finite dimensional -vector space), and all its elements are algebraic over . These properties do not hold if is not algebraic. For example, and they are both infinite dimensional vector spaces over
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https://en.wikipedia.org/wiki/Aage%20Bohr
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Aage Niels Bohr (; 19 June 1922 – 8 September 2009) was a Danish nuclear physicist who shared the Nobel Prize in Physics in 1975 with Ben Roy Mottelson and James Rainwater "for the discovery of the connection between collective motion and particle motion in atomic nuclei and the development of the theory of the structure of the atomic nucleus based on this connection". His father was Niels Bohr.
Starting from Rainwater's concept of an irregular-shaped liquid drop model of the nucleus, Bohr and Mottelson developed a detailed theory that was in close agreement with experiments.
Since his father, Niels Bohr, had won the prize in 1922, he and his father are one of the six pairs of fathers and sons who have both won the Nobel Prize and one of the four pairs who have both won the Nobel Prize in Physics.
Early life and education
Bohr was born in Copenhagen on 19 June 1922, the fourth of six sons of the physicist Niels Bohr and his wife Margrethe Bohr (née Nørlund). His oldest brother, Christian, died in a boating accident in 1934, and his youngest, Harald, was severely disabled and placed away from the home in Copenhagen at the age of four. He would later die from childhood meningitis. Of the others, Hans became a physician; Erik, a chemical engineer; and Ernest, a lawyer and Olympic athlete who played field hockey for Denmark at the 1948 Summer Olympics in London. The family lived at the Institute of Theoretical Physics at the University of Copenhagen, now known as the Niels Boh
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https://en.wikipedia.org/wiki/Analytic%20geometry
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In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.
Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.
History
Ancient Greece
The Greek mathematician Menaechmus solved problems and proved theorems by using a method that had a strong resemblance to the use of coordinates and it has sometimes been maintained that he had introduced analytic geometry.
Apollonius of Perga, in On Determinate Section, dealt with problems in a manner that may be called an analytic geometry of one dimension; with the question of finding points o
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https://en.wikipedia.org/wiki/Analysis%20of%20algorithms
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In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that relates the size of an algorithm's input to the number of steps it takes (its time complexity) or the number of storage locations it uses (its space complexity). An algorithm is said to be efficient when this function's values are small, or grow slowly compared to a growth in the size of the input. Different inputs of the same size may cause the algorithm to have different behavior, so best, worst and average case descriptions might all be of practical interest. When not otherwise specified, the function describing the performance of an algorithm is usually an upper bound, determined from the worst case inputs to the algorithm.
The term "analysis of algorithms" was coined by Donald Knuth. Algorithm analysis is an important part of a broader computational complexity theory, which provides theoretical estimates for the resources needed by any algorithm which solves a given computational problem. These estimates provide an insight into reasonable directions of search for efficient algorithms.
In theoretical analysis of algorithms it is common to estimate their complexity in the asymptotic sense, i.e., to estimate the complexity function for arbitrarily large input. Big O notation, Big-omega notation and Big-theta notation are used to this e
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https://en.wikipedia.org/wiki/Chemistry%20of%20ascorbic%20acid
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Ascorbic acid is an organic compound with formula , originally called hexuronic acid. It is a white solid, but impure samples can appear yellowish. It dissolves well in water to give mildly acidic solutions. It is a mild reducing agent.
Ascorbic acid exists as two enantiomers (mirror-image isomers), commonly denoted "" (for "levo") and "" (for "dextro"). The isomer is the one most often encountered: it occurs naturally in many foods, and is one form ("vitamer") of vitamin C, an essential nutrient for humans and many animals. Deficiency of vitamin C causes scurvy, formerly a major disease of sailors in long sea voyages. It is used as a food additive and a dietary supplement for its antioxidant properties. The "" form can be made via chemical synthesis but has no significant biological role.
History
The antiscorbutic properties of certain foods were demonstrated in the 18th century by James Lind. In 1907, Axel Holst and Theodor Frølich discovered that the antiscorbutic factor was a water-soluble chemical substance, distinct from the one that prevented beriberi. Between 1928 and 1932, Albert Szent-Györgyi isolated a candidate for this substance, which he called it "hexuronic acid", first from plants and later from animal adrenal glands. In 1932 Charles Glen King confirmed that it was indeed the antiscorbutic factor.
In 1933, sugar chemist Walter Norman Haworth, working with samples of "hexuronic acid" that Szent-Györgyi had isolated from paprika and sent him in the previo
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https://en.wikipedia.org/wiki/Actinide
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The actinide () or actinoid () series encompasses the 14 metallic chemical elements with atomic numbers from 89 to 102, actinium through nobelium. The actinide series derives its name from the first element in the series, actinium. The informal chemical symbol An is used in general discussions of actinide chemistry to refer to any actinide.
The 1985 IUPAC Red Book recommends that actinoid be used rather than actinide, since the suffix -ide normally indicates a negative ion. However, owing to widespread current use, actinide is still allowed. Since actinoid literally means actinium-like (cf. humanoid or android), it has been argued for semantic reasons that actinium cannot logically be an actinoid, but IUPAC acknowledges its inclusion based on common usage.
All the actinides are f-block elements. Lawrencium is sometimes considered one as well, despite being a d-block element and a transition metal. The series mostly corresponds to the filling of the 5f electron shell, although in the ground state many have anomalous configurations involving the filling of the 6d shell due to interelectronic repulsion. In comparison with the lanthanides, also mostly f-block elements, the actinides show much more variable valence. They all have very large atomic and ionic radii and exhibit an unusually large range of physical properties. While actinium and the late actinides (from americium onwards) behave similarly to the lanthanides, the elements thorium, protactinium, and uranium are much m
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https://en.wikipedia.org/wiki/Audio%20signal%20processing
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Audio signal processing is a subfield of signal processing that is concerned with the electronic manipulation of audio signals. Audio signals are electronic representations of sound waves—longitudinal waves which travel through air, consisting of compressions and rarefactions. The energy contained in audio signals or sound power level is typically measured in decibels. As audio signals may be represented in either digital or analog format, processing may occur in either domain. Analog processors operate directly on the electrical signal, while digital processors operate mathematically on its digital representation.
History
The motivation for audio signal processing began at the beginning of the 20th century with inventions like the telephone, phonograph, and radio that allowed for the transmission and storage of audio signals. Audio processing was necessary for early radio broadcasting, as there were many problems with studio-to-transmitter links. The theory of signal processing and its application to audio was largely developed at Bell Labs in the mid 20th century. Claude Shannon and Harry Nyquist's early work on communication theory, sampling theory and pulse-code modulation (PCM) laid the foundations for the field. In 1957, Max Mathews became the first person to synthesize audio from a computer, giving birth to computer music.
Major developments in digital audio coding and audio data compression include differential pulse-code modulation (DPCM) by C. Chapin Cutler at
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https://en.wikipedia.org/wiki/Abstract%20data%20type
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In computer science, an abstract data type (ADT) is a mathematical model for data types, defined by its behavior (semantics) from the point of view of a user of the data, specifically in terms of possible values, possible operations on data of this type, and the behavior of these operations. This mathematical model contrasts with data structures, which are concrete representations of data, and are the point of view of an implementer, not a user.
Formally, an ADT may be defined as a "class of objects whose logical behavior is defined by a set of values and a set of operations"; this is analogous to an algebraic structure in mathematics. What is meant by "behaviour" varies by author, with the two main types of formal specifications for behavior being axiomatic (algebraic) specification and an abstract model; these correspond to axiomatic semantics and operational semantics of an abstract machine, respectively. Some authors also include the computational complexity ("cost"), both in terms of time (for computing operations) and space (for representing values). In practice, many common data types are not ADTs, as the abstraction is not perfect, and users must be aware of issues like arithmetic overflow that are due to the representation. For example, integers are often stored as fixed-width values (32-bit or 64-bit binary numbers), and thus experience integer overflow if the maximum value is exceeded.
ADTs are a theoretical concept, in computer science, used in the design and an
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https://en.wikipedia.org/wiki/Analytical%20chemistry
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Analytical chemistry studies and uses instruments and methods to separate, identify, and quantify matter. In practice, separation, identification or quantification may constitute the entire analysis or be combined with another method. Separation isolates analytes. Qualitative analysis identifies analytes, while quantitative analysis determines the numerical amount or concentration.
Analytical chemistry consists of classical, wet chemical methods and modern, instrumental methods. Classical qualitative methods use separations such as precipitation, extraction, and distillation. Identification may be based on differences in color, odor, melting point, boiling point, solubility, radioactivity or reactivity. Classical quantitative analysis uses mass or volume changes to quantify amount. Instrumental methods may be used to separate samples using chromatography, electrophoresis or field flow fractionation. Then qualitative and quantitative analysis can be performed, often with the same instrument and may use light interaction, heat interaction, electric fields or magnetic fields. Often the same instrument can separate, identify and quantify an analyte.
Analytical chemistry is also focused on improvements in experimental design, chemometrics, and the creation of new measurement tools. Analytical chemistry has broad applications to medicine, science, and engineering.
History
Analytical chemistry has been important since the early days of chemistry, providing methods for determini
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https://en.wikipedia.org/wiki/Automated%20theorem%20proving
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Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science.
Logical foundations
While the roots of formalised logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalised mathematics. Frege's Begriffsschrift (1879) introduced both a complete propositional calculus and what is essentially modern predicate logic. His Foundations of Arithmetic, published in 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Russell and Whitehead in their influential Principia Mathematica, first published 1910–1913, and with a revised second edition in 1927. Russell and Whitehead thought they could derive all mathematical truth using axioms and inference rules of formal logic, in principle opening up the process to automatisation. In 1920, Thoralf Skolem simplified a previous result by Leopold Löwenheim, leading to the Löwenheim–Skolem theorem and, in 1930, to the notion of a Herbrand universe and a Herbrand interpretation that allowed (un)satisfiability of first-order formulas (and hence the validity of a theorem) to be reduced to (potentially infinitely many) propositional satisfiability problems.
In 1929, Mojżesz Presburger showed that the first-order theor
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https://en.wikipedia.org/wiki/Atomic%20absorption%20spectroscopy
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Atomic absorption spectroscopy (AAS) and atomic emission spectroscopy (AES) is a spectroanalytical procedure for the quantitative determination of chemical elements by free atoms in the gaseous state. Atomic absorption spectroscopy is based on absorption of light by free metallic ions.
In analytical chemistry the technique is used for determining the concentration of a particular element (the analyte) in a sample to be analyzed. AAS can be used to determine over 70 different elements in solution, or directly in solid samples via electrothermal vaporization, and is used in pharmacology, biophysics,
archaeology and toxicology research.
Atomic emission spectroscopy was first used as an analytical technique, and the underlying principles were established in the second half of the 19th century by Robert Wilhelm Bunsen and Gustav Robert Kirchhoff, both professors at the University of Heidelberg, Germany.
The modern form of AAS was largely developed during the 1950s by a team of Australian chemists. They were led by Sir Alan Walsh at the Commonwealth Scientific and Industrial Research Organisation (CSIRO), Division of Chemical Physics, in Melbourne, Australia.
Atomic absorption spectrometry has many uses in different areas of chemistry such as clinical analysis of metals in biological fluids and tissues such as whole blood, plasma, urine, saliva, brain tissue, liver, hair, muscle tissue. Atomic absorption spectrometry can be used in qualitative and quantitative analysis.
Princ
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https://en.wikipedia.org/wiki/Aberration
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An aberration is something that deviates from the normal way.
Aberration may also refer to:
Biology and medicine
Form (zoology) or aberration, a rare mutant butterfly or moth wing pattern
Cardiac aberrancy, aberration in the shape of the EKG signal
Chromosome aberration, abnormal number or structure of chromosomes
Entertainment
Aberration, a DLC for the video game Ark: Survival Evolved
Aberration (film), a 1997 horror film
Aberration (EP), by Neurosis, 1989
Aberrations, or abbies, human-like creatures in the American TV series Wayward Pines
Optics and physics
Astronomical aberration, phenomenon wherein objects appear to move about their true positions in the sky
Chromatic aberration, failure of a lens to focus all colors on the same point
Defocus aberration, in which an image is out of focus
Optical aberration, an imperfection in image formation by an optical system
Relativistic aberration, the distortion of light at high velocities
Spherical aberration, which occurs when light rays pass through a spherical lens near the edge
See also
Aberrant, a superhero role-playing game by White Wolf Game Studio
Aberrancy (geometry), the non-circularity of a curve
Abomination (Bible), a term used in Bible
Freak (disambiguation)
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https://en.wikipedia.org/wiki/Alkene
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In organic chemistry, an alkene is a hydrocarbon containing a carbon–carbon double bond. The double bond may be internal or in the terminal position. Terminal alkenes are also known as α-olefins.
The International Union of Pure and Applied Chemistry (IUPAC) recommends using the name "alkene" only for acyclic hydrocarbons with just one double bond; alkadiene, alkatriene, etc., or polyene for acyclic hydrocarbons with two or more double bonds; cycloalkene, cycloalkadiene, etc. for cyclic ones; and "olefin" for the general class – cyclic or acyclic, with one or more double bonds.
Acyclic alkenes, with only one double bond and no other functional groups (also known as mono-enes) form a homologous series of hydrocarbons with the general formula with n being 2 or more (which is two hydrogens less than the corresponding alkane). When n is four or more, isomers are possible, distinguished by the position and conformation of the double bond.
Alkenes are generally colorless non-polar compounds, somewhat similar to alkanes but more reactive. The first few members of the series are gases or liquids at room temperature. The simplest alkene, ethylene () (or "ethene" in the IUPAC nomenclature) is the organic compound produced on the largest scale industrially.
Aromatic compounds are often drawn as cyclic alkenes, however their structure and properties are sufficiently distinct that they are not classified as alkenes or olefins. Hydrocarbons with two overlapping double bonds () are cal
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https://en.wikipedia.org/wiki/Allenes
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In organic chemistry, allenes are organic compounds in which one carbon atom has double bonds with each of its two adjacent carbon atoms (, where R is H or some organyl group). Allenes are classified as cumulated dienes. The parent compound of this class is propadiene (), which is itself also called allene. An group of the structure is called allenyl, where R is H or some alkyl group. Compounds with an allene-type structure but with more than three carbon atoms are members of a larger class of compounds called cumulenes with bonding.
History
For many years, allenes were viewed as curiosities but thought to be synthetically useless and difficult to prepare and to work with. Reportedly, the first synthesis of an allene, glutinic acid, was performed in an attempt to prove the non-existence of this class of compounds. The situation began to change in the 1950s, and more than 300 papers on allenes have been published in 2012 alone. These compounds are not just interesting intermediates but synthetically valuable targets themselves; for example, over 150 natural products are known with an allene or cumulene fragment.
Structure and properties
Geometry
The central carbon atom of allenes forms two sigma bonds and two pi bonds. The central carbon atom is sp-hybridized, and the two terminal carbon atoms are sp2-hybridized. The bond angle formed by the three carbon atoms is 180°, indicating linear geometry for the central carbon atom. The two terminal carbon atoms are planar, and
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https://en.wikipedia.org/wiki/Alkyne
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Acetylene
Propyne
1-Butyne
In organic chemistry, an alkyne is an unsaturated hydrocarbon containing at least one carbon—carbon triple bond. The simplest acyclic alkynes with only one triple bond and no other functional groups form a homologous series with the general chemical formula . Alkynes are traditionally known as acetylenes, although the name acetylene also refers specifically to , known formally as ethyne using IUPAC nomenclature. Like other hydrocarbons, alkynes are generally hydrophobic.
Structure and bonding
In acetylene, the H–C≡C bond angles are 180°. By virtue of this bond angle, alkynes are rod-like. Correspondingly, cyclic alkynes are rare. Benzyne cannot be isolated. The C≡C bond distance of 118 picometers (for C2H2) is much shorter than the C=C distance in alkenes (132 pm, for C2H4) or the C–C bond in alkanes (153 pm).
The triple bond is very strong with a bond strength of 839 kJ/mol. The sigma bond contributes 369 kJ/mol, the first pi bond contributes 268 kJ/mol and the second pi-bond of 202 kJ/mol bond strength. Bonding usually discussed in the context of molecular orbital theory, which recognizes the triple bond as arising from overlap of s and p orbitals. In the language of valence bond theory, the carbon atoms in an alkyne bond are sp hybridized: they each have two unhybridized p orbitals and two sp hybrid orbitals. Overlap of an sp orbital from each atom forms one sp–sp sigma bond. Each p orbital on one atom overlaps one on the other atom, formin
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https://en.wikipedia.org/wiki/Annals%20of%20Mathematics
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The Annals of Mathematics is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study.
History
The journal was established as The Analyst in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the Annals of Mathematics. The new incarnation of the journal was edited by Ormond Stone (University of Virginia). It moved to Harvard in 1899 before reaching its current home in Princeton in 1911.
An important period for the journal was 1928–1958 with Solomon Lefschetz as editor. During this time, it became an increasingly well-known and respected journal. Its rise, in turn, stimulated American mathematics. Norman Steenrod characterized Lefschetz' impact as editor as follows: "The importance to American mathematicians of a first-class journal
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https://en.wikipedia.org/wiki/Andrei%20Sakharov
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Andrei Dmitrievich Sakharov (; 21 May 192114 December 1989) was a Soviet physicist and a Nobel Peace Prize laureate, which he was awarded in 1975 for emphasizing human rights around the world.
Although he spent his career in physics in the Soviet program of nuclear weapons, overseeing the development of thermonuclear weapons, Sakharov also did fundamental work in understanding particle physics, magnetism, and physical cosmology. Sakharov is mostly known for his political activism for individual freedom, human rights, civil liberties and reforms in Russia, for which he was deemed a dissident and faced persecution from the Soviet establishment.
In his memory, the Sakharov Prize was established and is awarded annually by the European Parliament for people and organizations dedicated to human rights and freedoms.
Biography
Family background and early life
Andrei Dmitrievich Sakharov was born in Moscow on 21 May 1921, to a Russian family. His father, Dmitri Ivanovich Sakharov, was a physics professor at the Second Moscow State University and an amateur pianist. His grandfather, Ivan, was a lawyer in the former Russian Empire who had displayed respect for social awareness and humanitarian principles (including advocating the abolition of capital punishment). Sakharov's mother, Yekaterina Alekseevna Sofiano, was a daughter of Aleksey Semenovich Sofiano, a general in the Tsarist Russian Army.
Sakharov's parents and paternal grandmother, Maria Petrovna, largely shaped his p
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https://en.wikipedia.org/wiki/Astrobiology
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Astrobiology is a scientific field within the life and environmental sciences that studies the origins, early evolution, distribution, and future of life in the universe by investigating its deterministic conditions and contingent events. As a discipline, astrobiology is founded on the premise that life may exist beyond Earth.
Research in astrobiology comprises three main areas: the study of habitable environments in the Solar System and beyond, the search for planetary biosignatures of past or present extraterrestrial life, and the study of the origin and early evolution of life on Earth.
The field of astrobiology has its origins in the 20th century with the advent of space exploration and the discovery of exoplanets. Early astrobiology research focused on the search for extraterrestrial life and the study of the potential for life to exist on other planets. In the 1960s and 1970s, NASA began its astrobiology pursuits within the Viking program, which was the first US mission to land on Mars and search for signs of life. This mission, along with other early space exploration missions, laid the foundation for the development of astrobiology as a discipline.
Regarding habitable environments, astrobiology investigates potential locations beyond Earth that could support life, such as Mars, Europa, and exoplanets, through research into the extremophiles populating austere environments on Earth, like volcanic and deep sea environments. Research within this topic is conducted ut
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https://en.wikipedia.org/wiki/Aerodynamics
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Aerodynamics ( aero (air) + (dynamics)) is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an important domain of study in aeronautics. The term aerodynamics is often used synonymously with gas dynamics, the difference being that "gas dynamics" applies to the study of the motion of all gases, and is not limited to air. The formal study of aerodynamics began in the modern sense in the eighteenth century, although observations of fundamental concepts such as aerodynamic drag were recorded much earlier. Most of the early efforts in aerodynamics were directed toward achieving heavier-than-air flight, which was first demonstrated by Otto Lilienthal in 1891. Since then, the use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simulations has formed a rational basis for the development of heavier-than-air flight and a number of other technologies. Recent work in aerodynamics has focused on issues related to compressible flow, turbulence, and boundary layers and has become increasingly computational in nature.
History
Modern aerodynamics only dates back to the seventeenth century, but aerodynamic forces have been harnessed by humans for thousands of years in sailboats and windmills, and images and stories of flight appear throughout recorded history, such as the A
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https://en.wikipedia.org/wiki/Ash
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Ash or ashes are the solid remnants of fires. Specifically, ash refers to all non-aqueous, non-gaseous residues that remain after something burns. In analytical chemistry, to analyse the mineral and metal content of chemical samples, ash is the non-gaseous, non-liquid residue after complete combustion.
Ashes as the end product of incomplete combustion are mostly mineral, but usually still contain an amount of combustible organic or other oxidizable residues. The best-known type of ash is wood ash, as a product of wood combustion in campfires, fireplaces, etc. The darker the wood ashes, the higher the content of remaining charcoal from incomplete combustion. The ashes are of different types. Some ashes contain natural compounds that make soil fertile. Others have chemical compounds that can be toxic but may break up in soil from chemical changes and microorganism activity.
Like soap, ash is also a disinfecting agent (alkaline). The World Health Organization recommends ash or sand as alternative for handwashing when soap is not available.
Natural occurrence
Ash occurs naturally from any fire that burns vegetation, and may disperse in the soil to fertilise it, or clump under it for long enough to carbonise into coal.
Specific types
Wood ash
Products of coal combustion
Bottom ash
Fly ash
Cigarette or cigar ash
Incinerator bottom ash, a form of ash produced in incinerators
Volcanic ash, ash that consists of fragmented glass, rock, and minerals that appears during an er
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https://en.wikipedia.org/wiki/Angular%20momentum
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In physics, angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, flying discs, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes form spirals and neutron stars have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it.
The three-dimensional angular momentum for a point particle is classically represented as a pseudovector , the cross product of the particle's position vector (relative to some origin) and its momentum vector; the latter is in Newtonian mechanics. Unlike linear momentum, angular momentum depends on where this origin is chosen, since the particle's position is measured from it.
Angular momentum is an extensive quantity; that is, the total angular momentum of any composite system is the sum of the angular momenta of its constituent parts. For a continuous rigid body or a fluid, the total angular momentum is the volume integral of angular momentum density (angular momentum per unit volume in the limit as volume shrinks to zero) over the entire body.
Similar to conservation of
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https://en.wikipedia.org/wiki/Amorphous%20solid
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In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid) is a solid that lacks the long-range order that is characteristic of a crystal. The terms "glass" and "glassy solid" are sometimes used synonymously with amorphous solid; however, these terms refer specifically to amorphous materials that undergo a glass transition. Examples of amorphous solids include glasses, metallic glasses, and certain types of plastics and polymers.
Etymology
The term comes from the Greek a ("without"), and morphé ("shape, form").
Structure
Amorphous materials have an internal structure consisting of interconnected structural blocks that can be similar to the basic structural units found in the corresponding crystalline phase of the same compound. Unlike in crystalline materials, however, no long-range order exists. Amorphous materials therefore cannot be defined by a finite unit cell. Statistical methods, such as the atomic density function and radial distribution function, are more useful in describing the structure of amorphous solids.
Although amorphous materials lack long range order, they exhibit localized order on small length scales. Localized order in amorphous materials can be categorized as short or medium range order. By convention, short range order extends only to the nearest neighbor shell, typically only 1-2 atomic spacings. Medium range order is then defined as the structural organization extending beyond the short range order, usually b
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https://en.wikipedia.org/wiki/Alkali
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In chemistry, an alkali (; from ) is a basic, ionic salt of an alkali metal or an alkaline earth metal. An alkali can also be defined as a base that dissolves in water. A solution of a soluble base has a pH greater than 7.0. The adjective alkaline, and less often, alkalescent, is commonly used in English as a synonym for basic, especially for bases soluble in water. This broad use of the term is likely to have come about because alkalis were the first bases known to obey the Arrhenius definition of a base, and they are still among the most common bases.
Etymology
The word "alkali" is derived from Arabic al qalīy (or alkali), meaning the calcined ashes (see calcination), referring to the original source of alkaline substances. A water-extract of burned plant ashes, called potash and composed mostly of potassium carbonate, was mildly basic. After heating this substance with calcium hydroxide (slaked lime), a far more strongly basic substance known as caustic potash (potassium hydroxide) was produced. Caustic potash was traditionally used in conjunction with animal fats to produce soft soaps, one of the caustic processes that rendered soaps from fats in the process of saponification, one known since antiquity. Plant potash lent the name to the element potassium, which was first derived from caustic potash, and also gave potassium its chemical symbol K (from the German name Kalium), which ultimately derived from alkali.
Common properties of alkalis and bases
Alkalis are all Arr
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https://en.wikipedia.org/wiki/Abelian%20group
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In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel.
The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified.
Definition
An abelian group is a set , together with an operation that combines any two elements and of to form another element of denoted . The symbol is a general placeholder for a concretely given operation. To qualify as an abelian group, the set and operation, , must satisfy four requirements known as the abelian group axioms (some authors include in the axioms some properties that belong to the definition of an operation: namely that the operation is defined for any ordered pair of elements of , that the result is well-defined, and that the result belongs to ):
Associativity For all , , and in , the equation holds.
Identity element There exists an element in ,
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https://en.wikipedia.org/wiki/Acid%E2%80%93base%20reaction
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In chemistry, an acid–base reaction is a chemical reaction that occurs between an acid and a base. It can be used to determine pH via titration. Several theoretical frameworks provide alternative conceptions of the reaction mechanisms and their application in solving related problems; these are called the acid–base theories, for example, Brønsted–Lowry acid–base theory.
Their importance becomes apparent in analyzing acid–base reactions for gaseous or liquid species, or when acid or base character may be somewhat less apparent. The first of these concepts was provided by the French chemist Antoine Lavoisier, around 1776.
It is important to think of the acid–base reaction models as theories that complement each other. For example, the current Lewis model has the broadest definition of what an acid and base are, with the Brønsted–Lowry theory being a subset of what acids and bases are, and the Arrhenius theory being the most restrictive.
Acid–base definitions
Historic development
The concept of an acid–base reaction was first proposed in 1754 by Guillaume-François Rouelle, who introduced the word "base" into chemistry to mean a substance which reacts with an acid to give it solid form (as a salt). Bases are mostly bitter in nature.
Lavoisier's oxygen theory of acids
The first scientific concept of acids and bases was provided by Lavoisier in around 1776. Since Lavoisier's knowledge of strong acids was mainly restricted to oxoacids, such as (nitric acid) and (sulfuric acid
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https://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric%20mean
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In mathematics, the arithmetic–geometric mean of two positive real numbers and is the mutual limit of a sequence of arithmetic means and a sequence of geometric means:
Begin the sequences with x and y:
Then define the two interdependent sequences and as
These two sequences converge to the same number, the arithmetic–geometric mean of and ; it is denoted by , or sometimes by or .
The arithmetic–geometric mean is used in fast algorithms for exponential and trigonometric functions, as well as some mathematical constants, in particular, computing .
The arithmetic–geometric mean can be extended to complex numbers and when the branches of the square root are allowed to be taken inconsistently, it is, in general, a multivalued function.
Example
To find the arithmetic–geometric mean of and , iterate as follows:
The first five iterations give the following values:
The number of digits in which and agree (underlined) approximately doubles with each iteration. The arithmetic–geometric mean of 24 and 6 is the common limit of these two sequences, which is approximately .
History
The first algorithm based on this sequence pair appeared in the works of Lagrange. Its properties were further analyzed by Gauss.
Properties
The geometric mean of two positive numbers is never bigger than the arithmetic mean (see inequality of arithmetic and geometric means). As a consequence, for , is an increasing sequence, is a decreasing sequence, and . These are strict inequalities if .
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https://en.wikipedia.org/wiki/Andrew%20S.%20Tanenbaum
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Andrew Stuart Tanenbaum (born March 16, 1944), sometimes referred to by the handle ast, is an American-Dutch computer scientist and professor emeritus of computer science at the Vrije Universiteit Amsterdam in the Netherlands.
He is the author of MINIX, a free Unix-like operating system for teaching purposes, and has written multiple computer science textbooks regarded as standard texts in the field. He regards his teaching job as his most important work. Since 2004 he has operated Electoral-vote.com, a website dedicated to analysis of polling data in federal elections in the United States.
Biography
Tanenbaum was born in New York City and grew up in suburban White Plains, New York, where he attended the White Plains High School. He is Jewish. His paternal grandfather was born in Khorostkiv in the Austro-Hungarian empire.
He received his Bachelor of Science degree in physics from MIT in 1965 and his PhD degree in astrophysics from the University of California, Berkeley in 1971. Tanenbaum also served as a lobbyist for the Sierra Club.
He moved to the Netherlands to live with his wife, who is Dutch, but he retains his United States citizenship. He taught courses on Computer Organization and Operating Systems and supervised the work of PhD candidates at the VU University Amsterdam. On July 9, 2014, he announced his retirement.
Teaching
Books
Tanenbaum's textbooks on computer science include:
Structured Computer Organization (1976)
Computer Networks, co-authored with Davi
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https://en.wikipedia.org/wiki/Arithmetic
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Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today.
History
The prehistory of arithmetic is limited to a small number of artifacts that may indicate the conception of addition and subtraction; the best-known is the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed.
The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations: addition, subtraction, multiplication, and division, as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but the characteristics of the particular numeral system strongly influence the complexity of the methods. The hieroglyphic system for Egyptian numerals, like the later Roman numerals, descended from tally marks used for counting. In both cases, this origin resulted in values that used a decimal base but did not include positional notation. Complex calculations with Roman numerals required the assistance of a counting board (or the Roman abacus) to obtain the results.
Early number systems that included positional notation were
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https://en.wikipedia.org/wiki/Algebraic%20closure
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In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics.
Using Zorn's lemma or the weaker ultrafilter lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K.
The algebraic closure of a field K can be thought of as the largest algebraic extension of K.
To see this, note that if L is any algebraic extension of K, then the algebraic closure of L is also an algebraic closure of K, and so L is contained within the algebraic closure of K.
The algebraic closure of K is also the smallest algebraically closed field containing K,
because if M is any algebraically closed field containing K, then the elements of M that are algebraic over K form an algebraic closure of K.
The algebraic closure of a field K has the same cardinality as K if K is infinite, and is countably infinite if K is finite.
Examples
The fundamental theorem of algebra states that the algebraic closure of the field of real numbers is the field of complex numbers.
The algebraic closure of the field of rational numbers is the field of algebraic numbers.
There are many countable algebraically closed fields within the complex numbers, and strictly containing
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https://en.wikipedia.org/wiki/Lockheed%20AC-130
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The Lockheed AC-130 gunship is a heavily armed, long-endurance, ground-attack variant of the C-130 Hercules transport, fixed-wing aircraft. It carries a wide array of ground-attack weapons that are integrated with sophisticated sensors, navigation, and fire-control systems. Unlike other modern military fixed-wing aircraft, the AC-130 relies on visual targeting. Because its large profile and low operating altitudes around 7,000 feet (2,100 m) make it an easy target, its close air support missions are usually flown at night.
The airframe is manufactured by Lockheed Martin, while Boeing is responsible for the conversion into a gunship and for aircraft support. Developed during the Vietnam War as "Project Gunship II", the AC-130 replaced the Douglas AC-47 Spooky, or "Gunship I". The sole operator is the United States Air Force, which uses the AC-130U Spooky and AC-130W Stinger II variants for close air support, air interdiction, and force protection, with the upgraded AC-130J Ghostrider entering service. Close air support roles include supporting ground troops, escorting convoys, and urban operations. Air-interdiction missions are conducted against planned targets and targets of opportunity. Force-protection missions include defending air bases and other facilities. AC-130Us are based at Hurlburt Field, Florida, while AC-130Ws are based at Cannon AFB, New Mexico; gunships can be deployed worldwide. The squadrons are part of the Air Force Special Operations Command (AFSOC), a com
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https://en.wikipedia.org/wiki/Ascending%20chain%20condition
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In mathematics, the ascending chain condition (ACC) and descending chain condition (DCC) are finiteness properties satisfied by some algebraic structures, most importantly ideals in certain commutative rings. These conditions played an important role in the development of the structure theory of commutative rings in the works of David Hilbert, Emmy Noether, and Emil Artin.
The conditions themselves can be stated in an abstract form, so that they make sense for any partially ordered set. This point of view is useful in abstract algebraic dimension theory due to Gabriel and Rentschler.
Definition
A partially ordered set (poset) P is said to satisfy the ascending chain condition (ACC) if no infinite strictly ascending sequence
of elements of P exists.
Equivalently, every weakly ascending sequence
of elements of P eventually stabilizes, meaning that there exists a positive integer n such that
Similarly, P is said to satisfy the descending chain condition (DCC) if there is no infinite descending chain of elements of P. Equivalently, every weakly descending sequence
of elements of P eventually stabilizes.
Comments
Assuming the axiom of dependent choice, the descending chain condition on (possibly infinite) poset P is equivalent to P being well-founded: every nonempty subset of P has a minimal element (also called the minimal condition or minimum condition). A totally ordered set that is well-founded is a well-ordered set.
Similarly, the ascending chain condition is
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https://en.wikipedia.org/wiki/Bjarne%20Stroustrup
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Bjarne Stroustrup (; ; born 30 December 1950) is a computer scientist, most notable for the invention and development of the C++ programming language. Stroustrup served as a visiting professor of computer science at Columbia University in the City of New York beginning in 2014, where he has been a full professor since 2022.
Early life and education
Stroustrup was born in Aarhus, Denmark. His family was working class, and he attended local schools.
He attended Aarhus University from 1969 to 1975 and graduated with a Candidatus Scientiarum in mathematics with computer science. His interests focused on microprogramming and machine architecture. He learned the fundamentals of object-oriented programming from its inventor, Kristen Nygaard, who frequently visited Aarhus.
In 1979, he received his PhD in computer science from the University of Cambridge, where his research on distributed computing was supervised by David Wheeler.
Career and research
In 1979, Stroustrup began his career as a member of technical staff in the Computer Science Research Center of Bell Labs in Murray Hill, New Jersey, USA. There, he began his work on C++ and programming techniques. Stroustrup was the head of AT&T Bell Labs' Large-scale Programming Research department, from its creation until late 2002. In 1993, he was made a Bell Labs fellow and in 1996, an AT&T Fellow.
From 2002 to 2014, Stroustrup was the College of Engineering Chair Professor in Computer Science at Texas A&M University. From 2011,
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https://en.wikipedia.org/wiki/Biotic
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Biotics describe living or once living components of a community; for example organisms, such as animals and plants.
Biotic may refer to:
Life, the condition of living organisms
Biology, the study of life
Biotic material, which is derived from living organisms
Biotic components in ecology
Biotic potential, an organism's reproductive capacity
Biotic community, all the interacting organisms living together in a specific habitat
Biotic energy, a vital force theorized by biochemist Benjamin Moore
Biotic Baking Brigade, an unofficial group of pie-throwing activists
See also
Abiotic
Antibiotics are agents that either kill bacteria or inhibit their growth
Prebiotics are non-digestible food ingredients that stimulate the growth or activity of bacteria in the digestive system
Probiotics consist of a live culture of bacteria that inhibit or interfere with colonization by microbial pathogens
Synbiotics refer to nutritional supplements combining probiotics and prebiotics
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https://en.wikipedia.org/wiki/Body
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Body may refer to:
In science
Physical body, an object in physics that represents a large amount, has mass or takes up space
Body (biology), the physical material of an organism
Body plan, the physical features shared by a group of animals
Human body, the entire structure of a human organism
Dead body, cadaver, or corpse, a dead human body
(living) matter, see: Mind–body problem, the relationship between mind and matter in philosophy
Aggregates within living matter, such as inclusion bodies
In arts and entertainment
In film and television
Body (2015 Polish film), a 2015 Polish film
Body (2015 American film), a 2015 American film
"Body" (Wonder Showzen episode), a 2006 episode of American sketch comedy television series Wonder Showzen
"Body", an episode of the Adult Swim television series, Off the Air
In literature and publishing
body text, the text forming the main content of any printed matter
body (typography), the size of a piece of metal type
B.O.D.Y. (manga), by Ao Mimori
B O D Y, an international online literary magazine
In music
Electronic body music, a genre
"Body" (Dreezy song), 2016
"Body" (The Jacksons song), a song by The Jacksons from Victory, 1984
"Body", a 2022 song by Ella Henderson from her second album Everything I Didn't Say
"Body" (Ja Rule song), a 2007 hip-hop song
"Body" (Loud Luxury song), a 2017 house song
"Body" (Marques Houston song), a 2009 R&B song
"Body" (Megan Thee Stallion song), a song by Megan Thee Stallion from Goo
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https://en.wikipedia.org/wiki/Binary
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Binary may refer to:
Science and technology
Mathematics
Binary number, a representation of numbers using only two digits (0 and 1)
Binary function, a function that takes two arguments
Binary operation, a mathematical operation that takes two arguments
Binary relation, a relation involving two elements
Binary-coded decimal, a method for encoding for decimal digits in binary sequences
Finger binary, a system for counting in binary numbers on the fingers of human hands
Computing
Binary code, the digital representation of text and data
Bit, or binary digit, the basic unit of information in computers
Binary file, composed of something other than human-readable text
Executable, a type of binary file that contains machine code for the computer to execute
Binary tree, a computer tree data structure in which each node has at most two children
Astronomy
Binary star, a star system with two stars in it
Binary planet, two planetary bodies of comparable mass orbiting each other
Binary asteroid, two asteroids orbiting each other
Biology
Binary fission, the splitting of a single-celled organism into two daughter cells
Chemistry
Binary phase, a chemical compound containing two different chemical elements
Arts and entertainment
Binary (comics), a superheroine in the Marvel Universe
Binary (Doctor Who audio)
Music
Binary form, a way of structuring a piece of music
Binary (Ani DiFranco album), 2017
Binary (Kay Tse album), 2008
"Binary" (song), a 2007 single b
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https://en.wikipedia.org/wiki/Biostatistics
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Biostatistics (also known as biometry) is a branch of statistics that applies statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experiments and the interpretation of the results.
History
Biostatistics and genetics
Biostatistical modeling forms an important part of numerous modern biological theories. Genetics studies, since its beginning, used statistical concepts to understand observed experimental results. Some genetics scientists even contributed with statistical advances with the development of methods and tools. Gregor Mendel started the genetics studies investigating genetics segregation patterns in families of peas and used statistics to explain the collected data. In the early 1900s, after the rediscovery of Mendel's Mendelian inheritance work, there were gaps in understanding between genetics and evolutionary Darwinism. Francis Galton tried to expand Mendel's discoveries with human data and proposed a different model with fractions of the heredity coming from each ancestral composing an infinite series. He called this the theory of "Law of Ancestral Heredity". His ideas were strongly disagreed by William Bateson, who followed Mendel's conclusions, that genetic inheritance were exclusively from the parents, half from each of them. This led to a vigorous debate between the biometricians, who supported Galton's ideas, as Raphael Weldon, Arthur Dukinfield Darbi
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https://en.wikipedia.org/wiki/Binary%20relation
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In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. A binary relation over sets and is a new set of ordered pairs consisting of elements from and from . It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element is related to an element , if and only if the pair belongs to the set of ordered pairs that defines the binary relation. A binary relation is the most studied special case of an -ary relation over sets , which is a subset of the Cartesian product
An example of a binary relation is the "divides" relation over the set of prime numbers and the set of integers , in which each prime is related to each integer that is a multiple of , but not to an integer that is not a multiple of . In this relation, for instance, the prime number 2 is related to numbers such as −4, 0, 6, 10, but not to 1 or 9, just as the prime number 3 is related to 0, 6, and 9, but not to 4 or 13.
Binary relations are used in many branches of mathematics to model a wide variety of concepts. These include, among others:
the "is greater than", "is equal to", and "divides" relations in arithmetic;
the "is congruent to" relation in geometry;
the "is adjacent to" relation in graph theory;
the "is orthogonal to" relation in linear algebra.
A function may be defined as a special kind of binary relation. Binary relations are also heavil
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https://en.wikipedia.org/wiki/Binary%20function
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In mathematics, a binary function (also called bivariate function, or function of two variables) is a function that takes two inputs.
Precisely stated, a function is binary if there exists sets such that
where is the Cartesian product of and
Alternative definitions
Set-theoretically, a binary function can be represented as a subset of the Cartesian product , where belongs to the subset if and only if .
Conversely, a subset defines a binary function if and only if for any and , there exists a unique such that belongs to .
is then defined to be this .
Alternatively, a binary function may be interpreted as simply a function from to .
Even when thought of this way, however, one generally writes instead of .
(That is, the same pair of parentheses is used to indicate both function application and the formation of an ordered pair.)
Examples
Division of whole numbers can be thought of as a function. If is the set of integers, is the set of natural numbers (except for zero), and is the set of rational numbers, then division is a binary function .
Another example is that of inner products, or more generally functions of the form , where , are real-valued vectors of appropriate size and is a matrix. If is a positive definite matrix, this yields an inner product.
Functions of two real variables
Functions whose domain is a subset of are often also called functions of two variables even if their domain does not form a rectangle and thus the cartesian product of t
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https://en.wikipedia.org/wiki/Binary%20operation
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In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two.
More specifically, an internal binary operation on a set is a binary operation whose two domains and the codomain are the same set. Examples include the familiar arithmetic operations of addition, subtraction, and multiplication. Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups.
An operation of arity two that involves several sets is sometimes also called a binary operation. For example, scalar multiplication of vector spaces takes a scalar and a vector to produce a vector, and scalar product takes two vectors to produce a scalar. Such binary operations may also be called binary functions.
Binary operations are the keystone of most structures that are studied in algebra, in particular in semigroups, monoids, groups, rings, fields, and vector spaces.
Terminology
More precisely, a binary operation on a set is a mapping of the elements of the Cartesian product to :
Because the result of performing the operation on a pair of elements of is again an element of , the operation is called a closed (or internal) binary operation on (or sometimes expressed as having the property of closure).
If is not a function but a partial function, then is called a partial binary operation. For
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https://en.wikipedia.org/wiki/Biochemistry
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Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology, and metabolism. Over the last decades of the 20th century, biochemistry has become successful at explaining living processes through these three disciplines. Almost all areas of the life sciences are being uncovered and developed through biochemical methodology and research. Biochemistry focuses on understanding the chemical basis which allows biological molecules to give rise to the processes that occur within living cells and between cells, in turn relating greatly to the understanding of tissues and organs, as well as organism structure and function. Biochemistry is closely related to molecular biology, which is the study of the molecular mechanisms of biological phenomena.
Much of biochemistry deals with the structures, bonding, functions, and interactions of biological macromolecules, such as proteins, nucleic acids, carbohydrates, and lipids. They provide the structure of cells and perform many of the functions associated with life. The chemistry of the cell also depends upon the reactions of small molecules and ions. These can be inorganic (for example, water and metal ions) or organic (for example, the amino acids, which are used to synthesize proteins). The mechanisms used by cells to harness energy from their environment v
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https://en.wikipedia.org/wiki/Bandwidth%20%28signal%20processing%29
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Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to passband bandwidth or baseband bandwidth. Passband bandwidth is the difference between the upper and lower cutoff frequencies of, for example, a band-pass filter, a communication channel, or a signal spectrum. Baseband bandwidth applies to a low-pass filter or baseband signal; the bandwidth is equal to its upper cutoff frequency.
Bandwidth in hertz is a central concept in many fields, including electronics, information theory, digital communications, radio communications, signal processing, and spectroscopy and is one of the determinants of the capacity of a given communication channel.
A key characteristic of bandwidth is that any band of a given width can carry the same amount of information, regardless of where that band is located in the frequency spectrum. For example, a 3 kHz band can carry a telephone conversation whether that band is at baseband (as in a POTS telephone line) or modulated to some higher frequency. However, wide bandwidths are easier to obtain and process at higher frequencies because the is smaller.
Overview
Bandwidth is a key concept in many telecommunications applications. In radio communications, for example, bandwidth is the frequency range occupied by a modulated carrier signal. An FM radio receiver's tuner spans a limited range of frequencies. A gov
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https://en.wikipedia.org/wiki/Bicarbonate
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In inorganic chemistry, bicarbonate (IUPAC-recommended nomenclature: hydrogencarbonate) is an intermediate form in the deprotonation of carbonic acid. It is a polyatomic anion with the chemical formula .
Bicarbonate serves a crucial biochemical role in the physiological pH buffering system.
The term "bicarbonate" was coined in 1814 by the English chemist William Hyde Wollaston. The name lives on as a trivial name.
Chemical properties
The bicarbonate ion (hydrogencarbonate ion) is an anion with the empirical formula and a molecular mass of 61.01 daltons; it consists of one central carbon atom surrounded by three oxygen atoms in a trigonal planar arrangement, with a hydrogen atom attached to one of the oxygens. It is isoelectronic with nitric acid . The bicarbonate ion carries a negative one formal charge and is an amphiprotic species which has both acidic and basic properties. It is both the conjugate base of carbonic acid ; and the conjugate acid of , the carbonate ion, as shown by these equilibrium reactions:
+ 2 H2O + H2O + OH− H2CO3 + 2 OH−
H2CO3 + 2 H2O + H3O+ + H2O + 2 H3O+.
A bicarbonate salt forms when a positively charged ion attaches to the negatively charged oxygen atoms of the ion, forming an ionic compound. Many bicarbonates are soluble in water at standard temperature and pressure; in particular, sodium bicarbonate contributes to total dissolved solids, a common parameter for assessing water quality.
Physiological role
Bicarbonate () is a vital c
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https://en.wikipedia.org/wiki/Banach%20space
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In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space.
Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly.
Maurice René Fréchet was the first to use the term "Banach space" and Banach in turn then coined the term "Fréchet space".
Banach spaces originally grew out of the study of function spaces by Hilbert, Fréchet, and Riesz earlier in the century. Banach spaces play a central role in functional analysis. In other areas of analysis, the spaces under study are often Banach spaces.
Definition
A Banach space is a complete normed space
A normed space is a pair
consisting of a vector space over a scalar field (where is commonly or ) together with a distinguished
norm Like all norms, this norm induces a translation invariant
distance function, called the canonical or (norm) induced metric, defined for all vectors by
This makes into a metric space
A sequence is called or or if for every real there exists some index such that
whenever and are greater than
The normed space is called a and the canonical metric
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https://en.wikipedia.org/wiki/Borsuk%E2%80%93Ulam%20theorem
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In mathematics, the Borsuk–Ulam theorem states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point. Here, two points on a sphere are called antipodal if they are in exactly opposite directions from the sphere's center.
Formally: if is continuous then there exists an such that: .
The case can be illustrated by saying that there always exist a pair of opposite points on the Earth's equator with the same temperature. The same is true for any circle. This assumes the temperature varies continuously in space, which is, however, not always the case.
The case is often illustrated by saying that at any moment, there is always a pair of antipodal points on the Earth's surface with equal temperatures and equal barometric pressures, assuming that both parameters vary continuously in space. Since temperature, pressure or other such physical variables do not necessarily vary continuously, the predictions of the theorem are unlikely to be true in some necessary sense (as following from a mathematical necessity).
The Borsuk–Ulam theorem has several equivalent statements in terms of odd functions. Recall that is the n-sphere and is the n-ball:
If is a continuous odd function, then there exists an such that: .
If is a continuous function which is odd on (the boundary of ), then there exists an such that: .
History
According to , the first historical mention of the statement of the Borsuk–Ulam theor
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https://en.wikipedia.org/wiki/BPP%20%28complexity%29
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In computational complexity theory, a branch of computer science, bounded-error probabilistic polynomial time (BPP) is the class of decision problems solvable by a probabilistic Turing machine in polynomial time with an error probability bounded by 1/3 for all instances.
BPP is one of the largest practical classes of problems, meaning most problems of interest in BPP have efficient probabilistic algorithms that can be run quickly on real modern machines. BPP also contains P, the class of problems solvable in polynomial time with a deterministic machine, since a deterministic machine is a special case of a probabilistic machine.
Informally, a problem is in BPP if there is an algorithm for it that has the following properties:
It is allowed to flip coins and make random decisions
It is guaranteed to run in polynomial time
On any given run of the algorithm, it has a probability of at most 1/3 of giving the wrong answer, whether the answer is YES or NO.
Definition
A language L is in BPP if and only if there exists a probabilistic Turing machine M, such that
M runs for polynomial time on all inputs
For all x in L, M outputs 1 with probability greater than or equal to 2/3
For all x not in L, M outputs 1 with probability less than or equal to 1/3
Unlike the complexity class ZPP, the machine M is required to run for polynomial time on all inputs, regardless of the outcome of the random coin flips.
Alternatively, BPP can be defined using only deterministic Turing machines. A
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https://en.wikipedia.org/wiki/Boltzmann%20distribution
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In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system. The distribution is expressed in the form:
where is the probability of the system being in state , is the exponential function, is the energy of that state, and a constant of the distribution is the product of the Boltzmann constant and thermodynamic temperature . The symbol denotes proportionality (see for the proportionality constant).
The term system here has a wide meaning; it can range from a collection of 'sufficient number' of atoms or a single atom to a macroscopic system such as a natural gas storage tank. Therefore the Boltzmann distribution can be used to solve a wide variety of problems. The distribution shows that states with lower energy will always have a higher probability of being occupied.
The ratio of probabilities of two states is known as the Boltzmann factor and characteristically only depends on the states' energy difference:
The Boltzmann distribution is named after Ludwig Boltzmann who first formulated it in 1868 during his studies of the statistical mechanics of gases in thermal equilibrium. Boltzmann's statistical work is borne out in his paper “On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability
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https://en.wikipedia.org/wiki/Bertrand%20Russell
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Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, artificial intelligence, cognitive science, computer science, and various areas of analytic philosophy, especially philosophy of mathematics, philosophy of language, epistemology, and metaphysics.
He was one of the early 20th century's most prominent logicians and a founder of analytic philosophy, along with his predecessor Gottlob Frege, his friend and colleague G. E. Moore, and his student and protégé Ludwig Wittgenstein. Russell with Moore led the British "revolt against idealism". Together with his former teacher A. N. Whitehead, Russell wrote Principia Mathematica, a milestone in the development of classical logic and a major attempt to reduce the whole of mathematics to logic (see Logicism). Russell's article "On Denoting" has been considered a "paradigm of philosophy".
Russell was a pacifist who championed anti-imperialism and chaired the India League. He went to prison for his pacifism during World War I, but also saw the war against Adolf Hitler's Nazi Germany as a necessary "lesser of two evils". In the wake of World War II, he welcomed American global hegemony in favour of either Soviet hegemony or no (or ineffective) world leadership, even if it were to come at the cost of using their nuclear weapons. He would later criticis
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https://en.wikipedia.org/wiki/Bill%20Schelter
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William Frederick Schelter (1947 – July 30, 2001) was a professor of mathematics at The University of Texas at Austin and a Lisp developer and programmer. Schelter is credited with the development of the GNU Common Lisp (GCL) implementation of Common Lisp and the GPL'd version of the computer algebra system Macsyma called Maxima. Schelter authored Austin Kyoto Common Lisp (AKCL) under contract with IBM. AKCL formed the foundation for Axiom, another computer algebra system. AKCL eventually became GNU Common Lisp. He is also credited with the first port of the GNU C compiler to the Intel 386 architecture, used in the original implementation of the Linux kernel.
Schelter obtained his Ph.D. at McGill University in 1972. His mathematical specialties were noncommutative ring theory and computational algebra and its applications, including automated theorem proving in geometry.
In the summer of 2001, age 54, he died suddenly of a heart attack while traveling in Russia.
References
S. Chou and W. Schelter. Proving Geometry Theorems with Rewrite Rules Journal of Automated Reasoning, 1986.
External links
Maxima homepage. Maxima is now available under GPL.
1947 births
2001 deaths
Lisp (programming language) people
20th-century American mathematicians
Computer programmers
University of Texas at Austin faculty
McGill University Faculty of Science alumni
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https://en.wikipedia.org/wiki/Botany
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Botany, also called plant science (or plant sciences), plant biology or phytology, is the science of plant life and a branch of biology. A botanist, plant scientist or phytologist is a scientist who specialises in this field. The term "botany" comes from the Ancient Greek word () meaning "pasture", "herbs" "grass", or "fodder"; is in turn derived from (), "to feed" or "to graze". Traditionally, botany has also included the study of fungi and algae by mycologists and phycologists respectively, with the study of these three groups of organisms remaining within the sphere of interest of the International Botanical Congress. Nowadays, botanists (in the strict sense) study approximately 410,000 species of land plants of which some 391,000 species are vascular plants (including approximately 369,000 species of flowering plants), and approximately 20,000 are bryophytes.
Botany originated in prehistory as herbalism with the efforts of early humans to identify – and later cultivate – plants that were edible, poisonous, and possibly medicinal, making it one of the first endeavours of human investigation. Medieval physic gardens, often attached to monasteries, contained plants possibly having medicinal benefit. They were forerunners of the first botanical gardens attached to universities, founded from the 1540s onwards. One of the earliest was the Padua botanical garden. These gardens facilitated the academic study of plants. Efforts to catalogue and describe their collections were
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