source
stringlengths 31
207
| text
stringlengths 12
1.5k
|
|---|---|
https://en.wikipedia.org/wiki/Quantitative%20analysis
|
Quantitative analysis may refer to:
Quantitative research, application of mathematics and statistics in economics and marketing
Quantitative analysis (chemistry), the determination of the absolute or relative abundance of one or more substances present in a sample
Quantitative analysis (finance), the use of mathematical and statistical methods in finance and investment management
Quantitative analysis of behavior, quantitative models in the experimental analysis of behavior
Mathematical psychology, an approach to psychological research using mathematical modeling of perceptual, cognitive and motor processes
Statistics, the collection, organization, analysis, interpretation and presentation of data
See also
QA (disambiguation)
|
https://en.wikipedia.org/wiki/Discretization%20error
|
In numerical analysis, computational physics, and simulation, discretization error is the error resulting from the fact that a function of a continuous variable is represented in the computer by a finite number of evaluations, for example, on a lattice. Discretization error can usually be reduced by using a more finely spaced lattice, with an increased computational cost.
Examples
Discretization error is the principal source of error in methods of finite differences and the pseudo-spectral method of computational physics.
When we define the derivative of as or , where is a finitely small number, the difference between the first formula and this approximation is known as discretization error.
Related phenomena
In signal processing, the analog of discretization is sampling, and results in no loss if the conditions of the sampling theorem are satisfied, otherwise the resulting error is called aliasing.
Discretization error, which arises from finite resolution in the domain, should not be confused with quantization error, which is finite resolution in the range (values), nor in round-off error arising from floating-point arithmetic. Discretization error would occur even if it were possible to represent the values exactly and use exact arithmetic – it is the error from representing a function by its values at a discrete set of points, not an error in these values.
References
See also
Discretization
Linear multistep method
Quantization error
Numerical analysis
|
https://en.wikipedia.org/wiki/Preferred
|
Preferred may refer to:
Chase Sapphire Preferred, a credit card
Preferred frame, in physics, a special hypothetical frame of reference
Preferred number, standard guidelines for choosing exact product dimensions within a given set of constraints
Preferred stock, a class of stock
See also
Preference
|
https://en.wikipedia.org/wiki/William%20E.%20Thornton
|
William Edgar Thornton (April 14, 1929 – January 11, 2021) was an American NASA astronaut. He received a Bachelor of Science degree in physics from University of North Carolina and a doctorate in medicine, also from UNC. He flew on Challenger twice, the STS-8 and STS-51-B missions.
Early life and education
William Edgar Thornton was born on April 14, 1929. He attended primary and secondary schools in Faison, North Carolina. He received a bachelor of science degree in physics from the University of North Carolina (UNC) in 1952. In 1963, he received a doctorate in medicine from UNC.
Experience
Following graduation from the University of North Carolina and having completed Air Force ROTC training, Thornton served as officer-in-charge of the Instrumentation Lab at the Flight Test Air Proving Ground. He later became a consultant to Air Proving Ground Command.
As chief engineer of the electronics division of the Del Mar Engineering Labs at Los Angeles from 1956 to 1959, he also organized and directed its Avionics Division. He returned to the University of North Carolina Medical School in 1959, graduated in 1963, and completed internship training in 1964 at the Wilford Hall USAF Hospital at Lackland Air Force Base, San Antonio, Texas.
Thornton returned to active duty with the United States Air Force and was then assigned to the USAF Aerospace Medical Division, Brooks Air Force Base, San Antonio, where he completed the Primary Flight Surgeon's training in 1964. It was during his
|
https://en.wikipedia.org/wiki/Excited%20state
|
In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). Excitation refers to an increase in energy level above a chosen starting point, usually the ground state, but sometimes an already excited state. The temperature of a group of particles is indicative of the level of excitation (with the notable exception of systems that exhibit negative temperature).
The lifetime of a system in an excited state is usually short: spontaneous or induced emission of a quantum of energy (such as a photon or a phonon) usually occurs shortly after the system is promoted to the excited state, returning the system to a state with lower energy (a less excited state or the ground state). This return to a lower energy level is often loosely described as decay and is the inverse of excitation.
Long-lived excited states are often called metastable. Long-lived nuclear isomers and singlet oxygen are two examples of this.
Atomic excitation
Atoms can be excited by heat, electricity, or light. The hydrogen atom provides a simple example of this concept.
The ground state of the hydrogen atom has the atom's single electron in the lowest possible orbital (that is, the spherically symmetric "1s" wave function, which, so far, has been demonstrated to have the lowest possible quantum numbers). By giving the atom additional energy (for example,
|
https://en.wikipedia.org/wiki/Map%20%28mathematics%29
|
In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper.
The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. In category theory, a map may refer to a morphism. The term transformation can be used interchangeably, but transformation often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory.
Maps as functions
In many branches of mathematics, the term map is used to mean a function, sometimes with a specific property of particular importance to that branch. For instance, a "map" is a "continuous function" in topology, a "linear transformation" in linear algebra, etc.
Some authors, such as Serge Lang, use "function" only to refer to maps in which the codomain is a set of numbers (i.e. a subset of R or C), and reserve the term mapping for more general functions.
Maps of certain kinds are the subjects of many important theories. These include homomorphisms in abstract algebra, isometries in geometry, operators in analysis and representations in group theory.
In the theory of dynamical systems, a map denotes an evolution function used to create discrete dynamical systems.
A partial map is
|
https://en.wikipedia.org/wiki/Amos%20Dolbear
|
Amos Emerson Dolbear (November 10, 1837 – February 23, 1910) was an American physicist and inventor. Dolbear researched electrical spark conversion into sound waves and electrical impulses. He was a professor at University of Kentucky in Lexington from 1868 until 1874. In 1874 he became the chair of the physics department at Tufts University in Medford, Massachusetts. He is known for his 1882 invention of a system for transmitting telegraph signals without wires. In 1899 his patent for it was purchased in an unsuccessful attempt to interfere with Guglielmo Marconi's wireless telegraphy patents in the United States.
Biography
Amos Dolbear was born in Norwich, Connecticut, on November 10, 1837. He was a graduate of Ohio Wesleyan University, in Delaware, Ohio. While a student there, he had made a "talking telegraph" and invented a receiver containing two features of the modern telephone: a permanent magnet and a metallic diaphragm that he made from a tintype. He invented the first telephone receiver with a permanent magnet in 1865, 11 years before Alexander Graham Bell patented his model. Later, Dolbear couldn't prove his claim, so Bell kept the patent. Dolbear lost his case before the U. S. Supreme Court, (Dolbear et al. v. American Bell Telephone Company). The June 18, 1881, edition of Scientific American reported:
In 1876, Dolbear patented a magneto electric telephone. He patented a static telephone in 1879.
In 1883, Dolbear was able to communicate over a distance of a
|
https://en.wikipedia.org/wiki/Acanthus
|
Acanthus (: acanthus, rarely acanthuses in English, or acanthi in Latin), its feminine form acantha (plural: acanthae), the Latinised form of the ancient Greek word acanthos or akanthos, or the prefix acantho-, may refer to:
Biology
Acanthus (plant), a genus containing plants used for ornament and in traditional medicine
Acanthus (ornament), ornamental forms in architecture using the leaf shape
Acanthus, an entomological term for a thorn-like projection on an insect, typically a single-celled cuticular growth without tormogen (socket) or sensory cells
Mythology
Acantha, a figure in Greek mythology associated with the Acanthus plant
Acanthus, son of Autonous who received his name after the plant, which was common in his infertile homeland
People
Acanthus of Sparta, an ancient athlete
Acanthus, the pen-name of the cartoonist Frank Hoar
Places
Acanthus, Ontario, a modern Canadian town
Acanthus (Caria), a town of ancient Caria, near Bybassus
Acanthus (Egypt), an ancient Egyptian city
Akanthos (Greece), an ancient Greek city in Greek Macedonia
Acantha, County Offaly, a townland in the civil parish of Durrow, barony of Ballycowan, Ireland
Other uses
Acanthus path, a fictional tradition of enchanters, magicians and witches in the game Mage: The Awakening
See also
List of commonly used taxonomic affixes
|
https://en.wikipedia.org/wiki/Absolute
|
Absolute may refer to:
Companies
Absolute Entertainment, a video game publisher
Absolute Radio, (formerly Virgin Radio), an independent national radio station in the USA
Absolute Software Corporation, specializes in security and data risk management
Absolut Vodka, a brand of Swedish vodka
Mathematics and science
Absolute (geometry), the quadric at nothing
Absolute (perfumery), a fragrance substance produced by solvent extraction
Absolute Infinite or Tav (number), an impossible (God-like) number larger than all numbers
Absolute magnitude, the brightness of a star
Absolute value, a notion in mathematics, commonly a number's numerical value without regard to its sign
Absolute pressure, the pressure in a fluid, measured relative to a vacuum
Absolute temperature, a temperature on the thermodynamic temperature scale
Absolute zero, the lower limit of the thermodynamic temperature scale, -273.15 °C
Absoluteness (logic), a concept in mathematical logic
Music
Absolute (production team), a British music writing and production team
Absolute (record compilation), a brand of compilation albums from EVA Records
Absolute (Aion album), 1994
Absolute (Time-Life album), an R&B compilation, 2003
The Absolute (album), by Ace Augustine, 2011
Absolute, an album by Kublai Khan, 2019
Absolute, an album by the Scientists, 1991
"Absolute", a song by The Fray from The Fray, 2009
Absolute (song), a 1985 song by Scritti Politti
Politics and law
Absolute defence, a factual circums
|
https://en.wikipedia.org/wiki/Zero-dimensional%20space
|
In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space. A graphical illustration of a nildimensional space is a point.
Definition
Specifically:
A topological space is zero-dimensional with respect to the Lebesgue covering dimension if every open cover of the space has a refinement which is a cover by disjoint open sets.
A topological space is zero-dimensional with respect to the finite-to-finite covering dimension if every finite open cover of the space has a refinement that is a finite open cover such that any point in the space is contained in exactly one open set of this refinement.
A topological space is zero-dimensional with respect to the small inductive dimension if it has a base consisting of clopen sets.
The three notions above agree for separable, metrisable spaces.
Properties of spaces with small inductive dimension zero
A zero-dimensional Hausdorff space is necessarily totally disconnected, but the converse fails. However, a locally compact Hausdorff space is zero-dimensional if and only if it is totally disconnected. (See for the non-trivial direction.)
Zero-dimensional Polish spaces are a particularly convenient setting for descriptive set theory. Examples of such spaces include the Cantor space and Baire space.
Hausdorff zero-dimensional spaces are precisely the subspaces of top
|
https://en.wikipedia.org/wiki/Interaction%20protocol
|
Within the fields of computer science and robotics, interaction protocols are possible communication scenarios between individual agents in multi-agent systems. Some protocols are described quite qualitatively (for example, many parts of the traffic code), but others have a formal model, whose implementations can be tested for conformance (for example, some cryptographic protocols).
FIPA defines markup for interaction protocol diagrams and several standard interaction protocols, including Dutch auction, English auction and reply-response.
See also
Multi-agent planning
References
Data interchange standards
Markup languages
|
https://en.wikipedia.org/wiki/Claude%20Berrou
|
Claude Berrou (; born 23 September 1951 in Penmarch) is a French professor in electrical engineering at École Nationale Supérieure des Télécommunications de Bretagne, now IMT Atlantique. He is the sole inventor of a groundbreaking quasi-optimal error-correcting coding scheme called turbo codes as evidenced by the sole inventorship credit given on the fundamental patent for turbo codes. The original patent filing for turbo codes issued in the US as US Patent 5,446,747.
A 1993 paper entitled "Near Shannon Limit Error-correcting Coding and Decoding: Turbo-codes" published in the Proceedings of IEEE International Communications Conference was the first public disclosure of turbo codes. This 1993 paper listed three authors because it was formed from three separate submissions that were combined due to space constraints. The three authors listed on the 1993 paper are: Berrou, Glavieux, and Thitimajshima. Because the 1993 paper was the first public introduction of turbo codes (patents remain unpublished until issued), coinventorship credit for the discovery to turbo code is often erroneously given to Glavieux and/or Thitimajshima. While Berrou and Glavieux did go on to do supplemental work together, the original development of turbo codes was performed by Berrou alone.
Berrou also codeveloped turbo equalization (see turbo equalizer.) Turbo equalization is also known as iterative reception or iterative detection.
Turbo codes have been used in all the major cellular communic
|
https://en.wikipedia.org/wiki/Alain%20Glavieux
|
Alain Glavieux (; 4 July 1949, Paris – 25 September 2004) was a French professor in electrical engineering at École Nationale Supérieure des Télécommunications de Bretagne. He was the coinventor with Claude Berrou and Punya Thitimajshima of a groundbreaking coding scheme called turbo codes.
Glavieux received the Golden Jubilee Award for Technological Innovation from the IEEE Information Theory Society together with Berrou and Thitimajshima in 1998, the IEEE Richard W. Hamming Medal together with Berrou in 2003, and the French Academy of Sciences Grand Prix France Telecom award in 2003.
He died on 25 September 2004 at the age of 55 from illness.
References
2004 deaths
French electrical engineers
Télécom Paris alumni
French information theorists
1949 births
French telecommunications engineers
Electrical engineering academics
|
https://en.wikipedia.org/wiki/Time-resolved%20spectroscopy
|
In physics and physical chemistry, time-resolved spectroscopy is the study of dynamic processes in materials or chemical compounds by means of spectroscopic techniques. Most often, processes are studied after the illumination of a material occurs, but in principle, the technique can be applied to any process that leads to a change in properties of a material. With the help of pulsed lasers, it is possible to study processes that occur on time scales as short as 10−16 seconds. All time-resolved spectra are suitable to be analyzed using the two-dimensional correlation method for a correlation map between the peaks.
Transient-absorption spectroscopy
Transient-absorption spectroscopy (TAS), also known as flash photolysis, is an extension of absorption spectroscopy. Ultrafast transient absorption spectroscopy, an example of non-linear spectroscopy, measures changes in the absorbance/transmittance in the sample. Here, the absorbance at a particular wavelength or range of wavelengths of a sample is measured as a function of time after excitation by a flash of light. In a typical experiment, both the light for excitation ('pump') and the light for measuring the absorbance ('probe') are generated by a pulsed laser. If the process under study is slow, then the time resolution can be obtained with a continuous (i.e., not pulsed) probe beam and repeated conventional spectrophotometric techniques.
Time-resolved absorption spectroscopy relies on our ability to resolve two physical acti
|
https://en.wikipedia.org/wiki/Cyril%20Clarke
|
Sir Cyril Astley Clarke, KBE, FRCP, FRCOG, (Hon) FRC Path, FRS (22 August 1907 – 21 November 2000) was a British physician, geneticist and lepidopterist. He was honoured for his pioneering work on prevention of Rh disease of the newborn, and also for his work on the genetics of the Lepidoptera (butterflies and moths).
Biography
Cyril Clarke was born on 22 August 1907 in Leicester, England and received his school education at Wyggeston Grammar School for Boys, Leicester and at the independent Oundle School near Peterborough. His interest in butterflies and moths began at school. His studied natural science at Gonville and Caius College, Cambridge, graduating in 1929, and then medicine at Guy's Hospital, London, graduating in 1932. During the Second World War he worked as a medical specialist in the Royal Naval Volunteer Reserve. After the war Clarke worked as a registrar at the Queen Elizabeth Hospital in Birmingham and then as Consultant Physician at the United Liverpool Hospitals. In 1963 he was appointed Director of the Nuffield Unit of Medical Genetics based at the University of Liverpool and two years later was made Professor of Medicine. He held these posts until his retirement in 1972. In retirement he served as President of the Royal College of Physicians (1972–1977)
Clarke helped to develop the technique of giving Rh-negative women inter-muscular injections of anti-RhD antibodies during pregnancy to prevent Rh disease in their newborn babies. This was one of the maj
|
https://en.wikipedia.org/wiki/Philip%20Sheppard%20%28biologist%29
|
Professor Philip MacDonald Sheppard, F.R.S. (27 July 1921 – 17 October 1976) was a British geneticist and lepidopterist. He made advances in ecological and population genetics in lepidopterans, pulmonate land snails and humans. In medical genetics, he worked with Sir Cyril Clarke on Rh disease.
He was born on 27 July 1921 in Marlborough, Wiltshire, England and attended Marlborough College from 1935 to 1939.
1940 to 1945 - Royal Air Force Volunteer Reserve (prisoner-of-war from 1942 to 1945). Participated, as an earth-bearer, in one of the famous tunnel escapes; it is unclear whether this was the "Wooden Horse" escape, or the "Great" Escape
1946 to 1948 - Studied Zoology at Worcester College, University of Oxford.
1956 to 1959 - Lecturer at Liverpool University
1959 to 1962 - Reader at Liverpool University
1963 to 1976 - Professor of genetics at Liverpool University
18 March 1965 - FRS
1974 - Darwin Medal of the Royal Society
1975 - Linnean Medal (Gold Medal) for Zoology from the Linnean Society of London
Cyril Clarke answered an advert in an insect magazine for swallowtail butterfly pupa that had been placed by Sheppard. They met and began working together in their common interest of lepidopterology. They also worked on Rh disease.
In 1961 Sheppard started a colony of scarlet tiger moths by the Wirral Way, West Kirby, Merseyside, which were rediscovered in 1988 by Cyril Clarke, who continued to observe them in his retirement to study changes in the moth population.
Shep
|
https://en.wikipedia.org/wiki/Utility%20fog
|
Utility fog (also referred to as foglets) is a hypothetical collection of tiny nanobots that can replicate a physical structure. As such, it is a form of self-reconfiguring modular robotics.
Conception
The term was coined by John Storrs Hall in 1989. Hall thought of it as a nanotechnological replacement for car seatbelts. The robots would be microscopic, with extending arms reaching in several different directions, and could perform three-dimensional lattice reconfiguration. Grabbers at the ends of the arms would allow the robots (or foglets) to mechanically link to one another and share both information and energy, enabling them to act as a continuous substance with mechanical and optical properties that could be varied over a wide range. Each foglet would have substantial computing power, and would be able to communicate with its neighbors.
In the original application as a replacement for seatbelts, the swarm of robots would be widely spread out, and the arms loose, allowing air flow between them. In the event of a collision the arms would lock into their current position, as if the air around the passengers had abruptly frozen solid. The result would be to spread any impact over the entire surface of the passenger's body.
While the foglets would be micro-scale, construction of the foglets would require full molecular nanotechnology. Hall suggests that each bot may be in the shape of a dodecahedron with twelve arms extending outwards. Each arm would have four degrees of
|
https://en.wikipedia.org/wiki/Ed%20Sciaky
|
Edward Leon Sciaky (April 2, 1948–January 29, 2004) was an American rock radio disc jockey who spent his broadcasting career in the Philadelphia area.
Early life
He was born in New York City and raised in Philadelphia, where he graduated from Central High School, and then from Temple University where he majored in mathematics.
Career
Sciaky became known for promoting new talent, helping establish the careers of scores of artists, most notably Bruce Springsteen, Billy Joel, David Bowie, Janis Ian, and Yes. Sciaky can also be heard introducing AC/DC on the Live from the Atlantic Studios CD off their 1997 boxset, Bonfire.
He was one of the first FM disc jockeys who thrived when given the chance to choose their own music, venturing beyond playing pop hits. Frequently, he would play lesser known songs that had personal meaning for himself or listeners. He was a good friend to many musicians who enjoyed his intelligent interviews and his knowledge of rock-n-roll. One of his best recording artist friends was Billy Joel, who at 23, had just released his Cold Spring Harbor album and was trying to promote it. Sciaky subsequently featured it on one his Sigma Sound broadcasts.
Sciaky provided the master tape of Yes's live version of The Beatles' "I'm Down" for the band's 1992 Yesyears box set.
Sciaky's broadcasting career, all in the Philadelphia area, covered WRTI, WHAT, WXUR (in Media; unrelated to the modern WXUR), WDAS, WMMR, WIOQ, WYSP, WMMR (again), and finally WMGK.
In 2003
|
https://en.wikipedia.org/wiki/Semi-locally%20simply%20connected
|
In mathematics, specifically algebraic topology, semi-locally simply connected is a certain local connectedness condition that arises in the theory of covering spaces. Roughly speaking, a topological space X is semi-locally simply connected if there is a lower bound on the sizes of the “holes” in X. This condition is necessary for most of the theory of covering spaces, including the existence of a universal cover and the Galois correspondence between covering spaces and subgroups of the fundamental group.
Most “nice” spaces such as manifolds and CW complexes are semi-locally simply connected, and topological spaces that do not satisfy this condition are considered somewhat pathological. The standard example of a non-semi-locally simply connected space is the Hawaiian earring.
Definition
A space X is called semi-locally simply connected if every point in X has a neighborhood U with the property that every loop in U can be contracted to a single point within X (i.e. every loop in U is nullhomotopic in X). The neighborhood U need not be simply connected: though every loop in U must be contractible within X, the contraction is not required to take place inside of U. For this reason, a space can be semi-locally simply connected without being locally simply connected.
Equivalent to this definition, a space X is semi-locally simply connected if every point in X has a neighborhood U for which the homomorphism from the fundamental group of U to the fundamental group of X, induced b
|
https://en.wikipedia.org/wiki/Cadmium%20pigments
|
Cadmium pigments are a class of pigments that contain cadmium. Most of the cadmium produced worldwide has been for use in rechargeable nickel–cadmium batteries, which have been replaced by other rechargeable nickel-chemistry cell varieties such as NiMH cells, but about half of the remaining consumption of cadmium, which is approximately annually, is used to produce colored cadmium pigments. The principal pigments are a family of yellow, orange and red cadmium sulfides and sulfoselenides, as well as compounds with other metals.
Cadmium is toxic to humans and other animals in very small amounts, especially when it is inhaled, which often happens when working with powdered pigment or breathing the dust from chalk pastels. As a result, it is not appropriate for children to use any art supplies that contain cadmium pigments. However, because the pigments have some desirable qualities, such as resistance to fading, some adult artists continue to use them.
Artists' paints
Brilliantly colored, with good permanence and tinting power, cadmium yellow, cadmium orange and cadmium red are familiar artists’ colors, and are frequently employed as architectural paints, as they can add life and vibrancy to renderings. Their greatest use is in the coloring of plastics and specialty paints, which must resist processing or service temperatures up to . The colorfastness or permanence of cadmium requires protection from the element's tendency to slowly form carbonate salts with exposure to a
|
https://en.wikipedia.org/wiki/The%20Codebreakers
|
The Codebreakers – The Story of Secret Writing () is a book by David Kahn, published in 1967, comprehensively chronicling the history of cryptography from ancient Egypt to the time of its writing. The United States government attempted to have the book altered before publication, and it succeeded in part.
Overview
Bradford Hardie III, an American cryptographer during World War II, contributed insider information, German translations from original documents, and intimate real-time operational explanations to The Codebreakers.
The Codebreakers is widely regarded as the best account of the history of cryptography up to its publication. William Crowell, the former deputy director of the National Security Agency, was quoted in Newsday magazine: "Before he (Kahn) came along, the best you could do was buy an explanatory book that usually was too technical and terribly dull."
The Puzzle Palace (1982), written by James Bamford, gives a history of the writing and publication of The Codebreakers. Kahn, then a journalist, was contracted to write a book on cryptology in 1961. He began writing it part-time, and then he quit his job to work on it full-time. The book was to include information on the NSA and, according to Bamford, the agency attempted to stop its publication. The NSA considered various options, including writing a negative review of Kahn's work to be published in the press to discredit him.
A committee of the United States Intelligence Board concluded that the book was "
|
https://en.wikipedia.org/wiki/Hyperpolarization%20%28biology%29
|
Hyperpolarization is a change in a cell's membrane potential that makes it more negative. It is the opposite of a depolarization. It inhibits action potentials by increasing the stimulus required to move the membrane potential to the action potential threshold.
Hyperpolarization is often caused by efflux of K+ (a cation) through K+ channels, or influx of Cl– (an anion) through Cl– channels. On the other hand, influx of cations, e.g. Na+ through Na+ channels or Ca2+ through Ca2+ channels, inhibits hyperpolarization. If a cell has Na+ or Ca2+ currents at rest, then inhibition of those currents will also result in a hyperpolarization. This voltage-gated ion channel response is how the hyperpolarization state is achieved. In neurons, the cell enters a state of hyperpolarization immediately following the generation of an action potential. While hyperpolarized, the neuron is in a refractory period that lasts roughly 2 milliseconds, during which the neuron is unable to generate subsequent action potentials. Sodium-potassium ATPases redistribute K+ and Na+ ions until the membrane potential is back to its resting potential of around –70 millivolts, at which point the neuron is once again ready to transmit another action potential.
Voltage-gated ion channels and hyperpolarization
Voltage gated ion channels respond to changes in the membrane potential. Voltage gated potassium, chloride and sodium channels are key components in the generation of the action potential as well as hyper-
|
https://en.wikipedia.org/wiki/Regular%20polytope
|
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or -faces (for all , where is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are regular polytopes of dimension .
Regular polytopes are the generalized analog in any number of dimensions of regular polygons (for example, the square or the regular pentagon) and regular polyhedra (for example, the cube). The strong symmetry of the regular polytopes gives them an aesthetic quality that interests both non-mathematicians and mathematicians.
Classically, a regular polytope in dimensions may be defined as having regular facets (-faces) and regular vertex figures. These two conditions are sufficient to ensure that all faces are alike and all vertices are alike. Note, however, that this definition does not work for abstract polytopes.
A regular polytope can be represented by a Schläfli symbol of the form with regular facets as and regular vertex figures as
Classification and description
Regular polytopes are classified primarily according to their dimensionality.
They can be further classified according to symmetry. For example, the cube and the regular octahedron share the same symmetry, as do the regular dodecahedron and icosahedron. Indeed, symmetry groups are sometimes named after regular polytopes, for example the tetrahedral and icosahedr
|
https://en.wikipedia.org/wiki/Complex%20structure
|
A complex structure may refer to:
In mathematics
Almost complex manifold
Complex manifold
Linear complex structure
Generalized complex structure
Complex structure deformation
Complex vector bundle#Complex structure
In law
Complex structure theory in English law
See also
Real structure
|
https://en.wikipedia.org/wiki/Georg%20Wittig
|
Georg Wittig (; 16 June 1897 – 26 August 1987) was a German chemist who reported a method for synthesis of alkenes from aldehydes and ketones using compounds called phosphonium ylides in the Wittig reaction. He shared the Nobel Prize in Chemistry with Herbert C. Brown in 1979.
Biography
Wittig was born in Berlin, Germany and shortly after his birth moved with his family to Kassel, where his father was professor at the applied arts high school. He attended school in Kassel and started studying chemistry at the University of Tübingen 1916. He was drafted and became a lieutenant in the cavalry of Hesse-Kassel (or Hesse-Cassel). After being an Allied prisoner of war from 1918 until 1919, Wittig found it hard to restart his chemistry studies owing to overcrowding at the universities. By a direct plea to Karl von Auwers, who was professor for organic chemistry at the University of Marburg at the time, he was able to resume university study and after 3 years was awarded the Ph.D. in organic chemistry.
Karl von Auwers was able to convince him to start an academic career, leading to his habilitation in 1926. He became a close friend of Karl Ziegler, who was also doing his habilitation with Auwers during that time. The successor of Karl von Auwers, Hans Meerwein, accepted Wittig as lecturer, partly because he was impressed by the new 400-page book on stereochemistry that Wittig had written. In 1931 Wittig married Waltraud Ernst, a colleague from the Auwers working group. The invitati
|
https://en.wikipedia.org/wiki/Racemization
|
In chemistry, racemization is a conversion, by heat or by chemical reaction, of an optically active compound into a racemic (optically inactive) form. This creates a 1:1 molar ratio of enantiomers and is referred to as a racemic mixture (i.e. contain equal amount of (+) and (−) forms). Plus and minus forms are called Dextrorotation and levorotation. The D and L enantiomers are present in equal quantities, the resulting sample is described as a racemic mixture or a racemate. Racemization can proceed through a number of different mechanisms, and it has particular significance in pharmacology as different enantiomers may have different pharmaceutical effects.
Stereochemistry
Chiral molecules have two forms (at each point of asymmetry), which differ in their optical characteristics: The levorotatory form (the (−)-form) will rotate counter-clockwise on the plane of polarization of a beam of light, whereas the dextrorotatory form (the (+)-form) will rotate clockwise on the plane of polarization of a beam of light. The two forms, which are non-superposable when rotated in 3-dimensional space, are said to be enantiomers. The notation is not to be confused with D and L naming of molecules which refers to the similarity in structure to D-glyceraldehyde and L-glyceraldehyde. Also, (R)- and (S)- refer to the chemical structure of the molecule based on Cahn–Ingold–Prelog priority rules of naming rather than rotation of light. R/S notation is the primary notation used for +/- now becaus
|
https://en.wikipedia.org/wiki/Locally%20convex%20topological%20vector%20space
|
In functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can be defined as topological vector spaces whose topology is generated by translations of balanced, absorbent, convex sets. Alternatively they can be defined as a vector space with a family of seminorms, and a topology can be defined in terms of that family. Although in general such spaces are not necessarily normable, the existence of a convex local base for the zero vector is strong enough for the Hahn–Banach theorem to hold, yielding a sufficiently rich theory of continuous linear functionals.
Fréchet spaces are locally convex spaces that are completely metrizable (with a choice of complete metric). They are generalizations of Banach spaces, which are complete vector spaces with respect to a metric generated by a norm.
History
Metrizable topologies on vector spaces have been studied since their introduction in Maurice Fréchet's 1902 PhD thesis Sur quelques points du calcul fonctionnel (wherein the notion of a metric was first introduced).
After the notion of a general topological space was defined by Felix Hausdorff in 1914, although locally convex topologies were implicitly used by some mathematicians, up to 1934 only John von Neumann would seem to have explicitly defined the weak topology on Hilbert spaces and strong operator topology on operators on Hilb
|
https://en.wikipedia.org/wiki/Glycoside
|
In chemistry, a glycoside is a molecule in which a sugar is bound to another functional group via a glycosidic bond. Glycosides play numerous important roles in living organisms. Many plants store chemicals in the form of inactive glycosides. These can be activated by enzyme hydrolysis, which causes the sugar part to be broken off, making the chemical available for use. Many such plant glycosides are used as medications. Several species of Heliconius butterfly are capable of incorporating these plant compounds as a form of chemical defense against predators. In animals and humans, poisons are often bound to sugar molecules as part of their elimination from the body.
In formal terms, a glycoside is any molecule in which a sugar group is bonded through its anomeric carbon to another group via a glycosidic bond. Glycosides can be linked by an O- (an O-glycoside), N- (a glycosylamine), S-(a thioglycoside), or C- (a C-glycoside) glycosidic bond. According to the IUPAC, the name "C-glycoside" is a misnomer; the preferred term is "C-glycosyl compound". The given definition is the one used by IUPAC, which recommends the Haworth projection to correctly assign stereochemical configurations.
Many authors require in addition that the sugar be bonded to a non-sugar for the molecule to qualify as a glycoside, thus excluding polysaccharides. The sugar group is then known as the glycone and the non-sugar group as the aglycone or genin part of the glycoside. The glycone can consist of a s
|
https://en.wikipedia.org/wiki/Quadratic%20integral
|
In mathematics, a quadratic integral is an integral of the form
It can be evaluated by completing the square in the denominator.
Positive-discriminant case
Assume that the discriminant q = b2 − 4ac is positive. In that case, define u and A by
and
The quadratic integral can now be written as
The partial fraction decomposition
allows us to evaluate the integral:
The final result for the original integral, under the assumption that q > 0, is
Negative-discriminant case
In case the discriminant q = b2 − 4ac is negative, the second term in the denominator in
is positive. Then the integral becomes
References
Weisstein, Eric W. "Quadratic Integral." From MathWorld--A Wolfram Web Resource, wherein the following is referenced:
Integral calculus
|
https://en.wikipedia.org/wiki/Space-cadet%20keyboard
|
The space-cadet keyboard is a keyboard designed by John L. Kulp in 1978 and used on Lisp machines at Massachusetts Institute of Technology (MIT), which inspired several still-current jargon terms in the field of computer science and influenced the design of Emacs. It was inspired by the Knight keyboard, which was developed for the Knight TV system, used with MIT's Incompatible Timesharing System.
Description
The space-cadet keyboard was equipped with seven modifier keys: four keys for bucky bits (, , , and ), and three shift keys, called , , and (which was labeled on the front of the key; the top was labeled ). had been introduced on the earlier Knight keyboard, while and were introduced by this keyboard. Each group was in a row, thus allowing easy chording, or pressing of several modifier keys; for example, could be pressed with the fingers of one hand, while the other hand pressed another key.
Many keys had three symbols on them, accessible by means of the shift keys: a letter and a symbol on the top, and a Greek letter on the front. For example, the key had a "G" and an up-arrow ("↑") on the top, and the Greek letter gamma ("") on the front. By pressing this key with one hand while playing an appropriate "chord" with the other hand on the shift keys, the user could get the following results:
Each of these might, in addition, be typed with any combination of the , , , and keys. By combining the modifier keys, it is possible to make . This allowed the user to type
|
https://en.wikipedia.org/wiki/Pisot%E2%80%93Vijayaraghavan%20number
|
In mathematics, a Pisot–Vijayaraghavan number, also called simply a Pisot number or a PV number, is a real algebraic integer greater than 1, all of whose Galois conjugates are less than 1 in absolute value. These numbers were discovered by Axel Thue in 1912 and rediscovered by G. H. Hardy in 1919 within the context of diophantine approximation. They became widely known after the publication of Charles Pisot's dissertation in 1938. They also occur in the uniqueness problem for Fourier series. Tirukkannapuram Vijayaraghavan and Raphael Salem continued their study in the 1940s. Salem numbers are a closely related set of numbers.
A characteristic property of PV numbers is that their powers approach integers at an exponential rate. Pisot proved a remarkable converse: if α > 1 is a real number such that the sequence
measuring the distance from its consecutive powers to the nearest integer is square-summable, or ℓ 2, then α is a Pisot number (and, in particular, algebraic). Building on this characterization of PV numbers, Salem showed that the set S of all PV numbers is closed. Its minimal element is a cubic irrationality known as the plastic number. Much is known about the accumulation points of S. The smallest of them is the golden ratio.
Definition and properties
An algebraic integer of degree n is a root α of an irreducible monic polynomial P(x) of degree n with integer coefficients, its minimal polynomial. The other roots of P(x) are called the conjugates of α. If α > 1
|
https://en.wikipedia.org/wiki/Friedrich%20Amelung
|
Friedrich Ludwig Balthasar Amelung ( – ) was a Baltic German cultural historian, businessman and chess endgame composer.
Amelung was born at Võisiku () manor in Governorate of Livonia of the Russian Empire (present-day Jõgeva County in Estonia). 1862–1864 he studied philosophy and chemistry at the University of Dorpat. 1864–1879 and 1885–1902 he was the director of the Rõika-Meleski mirror factory which he inherited from his father. Amelung published writings about the culture and history of Estonian localities like Viljandi, Tallinn and Põltsamaa.
Amelung was known as a chess player and a famous chess quiz's author. 1879–1885 he lived in Reval (now Tallinn) and studied the chess history of the Baltics. Between 1888 and 1908 he edited the chess magazine Baltische Schachblätter. In 1898 he established the Baltic Chess Society. Amelung published about 230 endgame studies, making him the first chess historian in the Baltic States.
He played a few games with Adolf Anderssen, Gustav Neumann, Carl Mayet, Emil Schallopp, Andreas Ascharin, Emanuel Schiffers.
He died in 1909 in Riga and is buried at the Kolga-Jaani cemetery in Estonia.
References
External links
ARVES Composers biographical data.
Lewis Stiller: Multilinear Algebra and Chess Endgames, in: Games of No Chance, 29 (1996), p. 151-192 (Amelung's contribution to endgame analysis)
1842 births
1909 deaths
People from Põltsamaa Parish
People from the Governorate of Livonia
Baltic-German people
Chess composers
Chess p
|
https://en.wikipedia.org/wiki/Nucleophilic%20addition
|
In organic chemistry, a nucleophilic addition reaction is an addition reaction where a chemical compound with an electrophilic double or triple bond reacts with a nucleophile, such that the double or triple bond is broken. Nucleophilic additions differ from electrophilic additions in that the former reactions involve the group to which atoms are added accepting electron pairs, whereas the latter reactions involve the group donating electron pairs.
Addition to carbon–heteroatom double bonds
Nucleophilic addition reactions of nucleophiles with electrophilic double or triple bond (π bonds) create a new carbon center with two additional single, or σ, bonds. Addition of a nucleophile to carbon–heteroatom double or triple bonds such as >C=O or -C≡N show great variety. These types of bonds are polar (have a large difference in electronegativity between the two atoms); consequently, their carbon atoms carries a partial positive charge. This makes the molecule an electrophile, and the carbon atom the electrophilic center; this atom is the primary target for the nucleophile. Chemists have developed a geometric system to describe the approach of the nucleophile to the electrophilic center, using two angles, the Bürgi–Dunitz and the Flippin–Lodge angles after scientists that first studied and described them.
This type of reaction is also called a 1,2-nucleophilic addition. The stereochemistry of this type of nucleophilic attack is not an issue, when both alkyl substituents are dissimi
|
https://en.wikipedia.org/wiki/Organolithium%20reagent
|
In organometallic chemistry, organolithium reagents are chemical compounds that contain carbon–lithium (C–Li) bonds. These reagents are important in organic synthesis, and are frequently used to transfer the organic group or the lithium atom to the substrates in synthetic steps, through nucleophilic addition or simple deprotonation. Organolithium reagents are used in industry as an initiator for anionic polymerization, which leads to the production of various elastomers. They have also been applied in asymmetric synthesis in the pharmaceutical industry. Due to the large difference in electronegativity between the carbon atom and the lithium atom, the C−Li bond is highly ionic. Owing to the polar nature of the C−Li bond, organolithium reagents are good nucleophiles and strong bases. For laboratory organic synthesis, many organolithium reagents are commercially available in solution form. These reagents are highly reactive, and are sometimes pyrophoric.
History and development
Studies of organolithium reagents began in the 1930s and were pioneered by Karl Ziegler, Georg Wittig, and Henry Gilman. In comparison with Grignard (magnesium) reagents, organolithium reagents can often perform the same reactions with increased rates and higher yields, such as in the case of metalation.
Since then, organolithium reagents have overtaken Grignard reagents in common usage.
Structure
Although simple alkyllithium species are often represented as monomer RLi, they exist as aggregates (oligo
|
https://en.wikipedia.org/wiki/Regioselectivity
|
In organic chemistry, regioselectivity is the preference of chemical bonding or breaking in one direction over all other possible directions. It can often apply to which of many possible positions a reagent will affect, such as which proton a strong base will abstract from an organic molecule, or where on a substituted benzene ring a further substituent will be added.
A specific example is a halohydrin formation reaction with 2-propenylbenzene:
Because of the preference for the formation of one product over another, the reaction is selective. This reaction is regioselective because it selectively generates one constitutional isomer rather than the other.
Various examples of regioselectivity have been formulated as rules for certain classes of compounds under certain conditions, many of which are named. Among the first introduced to chemistry students are Markovnikov's rule for the addition of protic acids to alkenes, and the Fürst-Plattner rule for the addition of nucleophiles to derivatives of cyclohexene, especially epoxide derivatives.
Regioselectivity in ring-closure reactions is subject to Baldwin's rules. If there are two or more orientations that can be generated during a reaction, one of them is dominant (e.g., Markovnikov/anti-Markovnikov addition across a double bond)
Regioselectivity can also be applied to specific reactions such as addition to pi ligands.
Selectivity also occurs in carbene insertions, for example in the Baeyer-Villiger reaction. In this rea
|
https://en.wikipedia.org/wiki/William%20S.%20Clark
|
William Smith Clark (July 31, 1826 – March 9, 1886) was an American professor of chemistry, botany, and zoology; a colonel during the American Civil War; and a leader in agricultural education. Raised and schooled in Easthampton, Massachusetts, Clark spent most of his adult life in Amherst, Massachusetts. He graduated from Amherst College in 1848 and obtained a doctorate in chemistry from Georgia Augusta University in Göttingen in 1852. He then served as professor of chemistry at Amherst College from 1852 to 1867. During the Civil War, he was granted leave from Amherst to serve with the 21st Regiment Massachusetts Volunteer Infantry, eventually achieving the rank of colonel and the command of that unit.
In 1867, Clark became the third president of the Massachusetts Agricultural College (MAC), now the University of Massachusetts Amherst. He was the first to appoint a faculty and admit a class of students. Although initially successful, MAC was criticized by politicians and newspaper editors who felt it was a waste of funding in a state that was growing increasingly industrial. Farmers of western Massachusetts were slow to support the college. Despite these obstacles, Clark's success in organizing an innovative academic institution earned him international attention.
Japanese officials, striving to achieve rapid modernization of that country in the wake of the Meiji Restoration, were especially intrigued by Clark's work. In 1876, the Japanese government hired Clark as a fo
|
https://en.wikipedia.org/wiki/List%20of%20mathematics%20history%20topics
|
This is a list of mathematics history topics, by Wikipedia page. See also list of mathematicians, timeline of mathematics, history of mathematics, list of publications in mathematics.
1729 (anecdote)
Adequality
Archimedes Palimpsest
Archimedes' use of infinitesimals
Arithmetization of analysis
Brachistochrone curve
Chinese mathematics
Cours d'Analyse
Edinburgh Mathematical Society
Erlangen programme
Fermat's Last Theorem
Greek mathematics
Thomas Little Heath
Hilbert's problems
History of topos theory
Hyperbolic quaternion
Indian mathematics
Islamic mathematics
Italian school of algebraic geometry
Kraków School of Mathematics
Law of Continuity
Lwów School of Mathematics
Nicolas Bourbaki
Non-Euclidean geometry
Scottish Café
Seven bridges of Königsberg
Spectral theory
Synthetic geometry
Tautochrone curve
Unifying theories in mathematics
Waring's problem
Warsaw School of Mathematics
Academic positions
Lowndean Professor of Astronomy and Geometry
Lucasian professor
Rouse Ball Professor of Mathematics
Sadleirian Chair
See also
History
|
https://en.wikipedia.org/wiki/Koszul%20complex
|
The Koszul complex is a concept in mathematics introduced by Jean-Louis Koszul.
Definition
Let A be a commutative ring and s: Ar → A an A-linear map. Its Koszul complex Ks is
where the maps send
where means the term is omitted and means the wedge product. One may replace Ar with any A-module.
Motivating example
Let M be a manifold, variety, scheme, ..., and A be the ring of functions on it, denoted .
The map s : Ar → A corresponds to picking r functions . When r = 1, the Koszul complex is
whose cokernel is the ring of functions on the zero locus f = 0. In general, the Koszul complex is
The cokernel of the last map is again functions on the zero locus f1 = ... = fr = 0. It is the tensor product of the r many Koszul complexes for fi = 0, so its dimensions are given by binomial coefficients.
In pictures: given functions si, how do we define the locus where they all vanish?
In algebraic geometry, the ring of functions of the zero locus is A/(s1, ..., sr). In derived algebraic geometry, the dg ring of functions is the Koszul complex. If the loci si = 0 intersect transversely, these are equivalent.
Thus: Koszul complexes are derived intersections of zero loci.
Properties
Algebra structure
First, the Koszul complex Ks of (A,s) is a chain complex: the composition of any two maps is zero. Second, the map
makes it into a dg algebra.
As a tensor product
The Koszul complex is a tensor product: if s = (s1, ..., sr), then
where ⊗ denotes the derived tensor produ
|
https://en.wikipedia.org/wiki/History%20of%20cryptography
|
Cryptography, the use of codes and ciphers to protect secrets, began thousands of years ago. Until recent decades, it has been the story of what might be called classical cryptography — that is, of methods of encryption that use pen and paper, or perhaps simple mechanical aids. In the early 20th century, the invention of complex mechanical and electromechanical machines, such as the Enigma rotor machine, provided more sophisticated and efficient means of encryption; and the subsequent introduction of electronics and computing has allowed elaborate schemes of still greater complexity, most of which are entirely unsuited to pen and paper.
The development of cryptography has been paralleled by the development of cryptanalysis — the "breaking" of codes and ciphers. The discovery and application, early on, of frequency analysis to the reading of encrypted communications has, on occasion, altered the course of history. Thus the Zimmermann Telegram triggered the United States' entry into World War I; and Allies reading of Nazi Germany's ciphers shortened World War II, in some evaluations by as much as two years.
Until the 1960s, secure cryptography was largely the preserve of governments. Two events have since brought it squarely into the public domain: the creation of a public encryption standard (DES), and the invention of public-key cryptography.
Antiquity
The earliest known use of cryptography is found in non-standard hieroglyphs carved into the wall of a tomb from the Ol
|
https://en.wikipedia.org/wiki/Kurt%20Reidemeister
|
Kurt Werner Friedrich Reidemeister (13 October 1893 – 8 July 1971) was a mathematician born in Braunschweig (Brunswick), Germany.
Life
He was a brother of Marie Neurath.
Beginning in 1912, he studied in Freiburg, Munich, Marburg, and Göttingen. In 1920, he got the (master's degree) in mathematics, philosophy, physics, chemistry, and geology.
He received his doctorate in 1921 with a thesis in algebraic number theory at the University of Hamburg under the supervision of Erich Hecke.
He became interested in differential geometry; he edited Wilhelm Blaschke's second volume on the topic, and both made an acclaimed contribution to the Jena DMV conference in September 1921.
In October 1922 or 1923 he was appointed assistant professor at the University of Vienna. While there he became familiar with the work of Wilhelm Wirtinger on knot theory, and became closely connected to Hans Hahn and the Vienna Circle. Its 1929 manifesto lists one of Reidemeister's publications in a bibliography of closely related authors.
In 1925 he became a full professor at the University of Königsberg; he stayed until 1933, when he was regarded politically unsound by the Nazis and dismissed from his position. Whilst there he organised the Second Conference on the Epistemology of the Exact Sciences in conjunction with journal Erkenntnis.
Blaschke managed to get a promise about Reidemeister's reappointment, and in autumn 1934 he got the chair of Kurt Hensel at the University of Marburg. He stayed there,
|
https://en.wikipedia.org/wiki/Helpers%20at%20the%20nest
|
Helpers at the nest is a term used in behavioural ecology and evolutionary biology to describe a social structure in which juveniles and sexually mature adolescents of either one or both sexes remain in association with their parents and help them raise subsequent broods or litters, instead of dispersing and beginning to reproduce themselves. This phenomenon was first studied in birds where it occurs most frequently, but it is also known in animals from many different groups including mammals and insects. It is a simple form of co-operative breeding. The effects of helpers usually amount to a net benefit, however, benefits are not uniformly distributed by all helpers nor across all species that exhibit this behaviour. There are multiple proposed explanations for the behaviour, but its variability and broad taxonomic occurrences result in simultaneously plausible theories.
The term "helper" was coined by Alexander Skutch in 1935 and defined more carefully in 1961 in the avian context as "a bird which assists in the nesting of an individual other than its mate, or feeds or otherwise attends a bird of whatever age which is neither its mate nor its dependent offspring." The term has been criticised as being anthropomorphic, but it remains in use. Other terms used especially in mammals, depending on the specific contexts, are non-maternal (care by other than the mother), alloparental (care by other than the parents), cooperative (care by non-breeding helpers) and communal (care
|
https://en.wikipedia.org/wiki/The%20Dancing%20Wu%20Li%20Masters
|
The Dancing Wu Li Masters is a 1979 book by Gary Zukav, a popular science work exploring modern physics, and quantum phenomena in particular. It was awarded a 1980 U.S. National Book Award in category of Science. Although it explores empirical topics in modern physics research, The Dancing Wu Li Masters gained attention for leveraging metaphors taken from eastern spiritual movements, in particular the Huayen school of Buddhism with the monk Fazang's treatise on the Golden Lion, to explain quantum phenomena and has been regarded by some reviewers as a New Age work, although the book is mostly concerned with the work of pioneers in western physics down through the ages.
The toneless pinyin phrase Wu Li in the title is most accurately rendered in Chinese characters, one Chinese translation of the word "physics" in the light of the book's subject matter. This becomes somewhat of a pun as there are many other Chinese characters that could be rendered as "wu li" in atonal pinyin, and chapters of the book are each titled with alternative translations of Wu Li, such as "Nonsense", "My Way" and "I Clutch My Ideas". Zukav participated as a journalist in a 1976 physics conference of eastern and western scientists at Esalen Institute, California; and he used the occasion as material for his book. At the conference, it was said that the Chinese term for physics is 'Wu Li', or "patterns of organic energy." Zukav, among others, conceptualized 'physics' as the dance of the Wu Li Master
|
https://en.wikipedia.org/wiki/Bruno%20Rossi
|
Bruno Benedetto Rossi (; ; 13 April 1905 – 21 November 1993) was an Italian experimental physicist. He made major contributions to particle physics and the study of cosmic rays. A 1927 graduate of the University of Bologna, he became interested in cosmic rays. To study them, he invented an improved electronic coincidence circuit, and travelled to Eritrea to conduct experiments that showed that cosmic ray intensity from the West was significantly larger than that from the East.
Forced to emigrate in October 1938 due to the Italian racial laws, Rossi moved to Denmark, where he worked with Niels Bohr. He then moved to Britain, where he worked with Patrick Blackett at the University of Manchester. Finally he went to the United States, where he worked with Enrico Fermi at the University of Chicago, and later at Cornell University. Rossi stayed in the United States, and became an American Citizen.
During World War II, Rossi worked on radar at the MIT Radiation Laboratory, and he played a pivotal role in the Manhattan Project, heading the group at the Los Alamos Laboratory that carried out the RaLa Experiments. After the war, he was recruited by Jerrold Zacharias at MIT, where Rossi continued his pre-war research into cosmic rays.
In the 1960s, he pioneered X-ray astronomy and space plasma physics. His instrumentation on Explorer 10 detected the magnetopause, and he initiated the rocket experiments that discovered Scorpius X-1, the first extra-solar source of X-rays.
Italy
Ro
|
https://en.wikipedia.org/wiki/Rein%20Taagepera
|
Rein Taagepera (born 28 February 1933) is an Estonian political scientist and former politician.
Education
Born in Tartu, Estonia, Taagepera fled from Soviet-occupied Estonia in 1944. Taagepera graduated from high school in Marrakech, Morocco, and then studied physics in Canada and the United States. He received a B.A. Sc (Nuclear Engineering) in 1959 and a M.A. (Physics) in 1961 from the University of Toronto, and a Ph.D. from the University of Delaware in 1965. Working in industry until 1970, he received another M.A. in international relations in 1969 and moved to academia as a political scientist at the University of California, Irvine, where he stayed for his entire American career. Taagepera is professor emeritus at the University of Tartu.
Political career
Taagepera served as president of the Association for the Advancement of Baltic Studies from 1986 until 1988. In 1991, he returned to Estonia as the founding dean of a new School of Social Sciences at the University of Tartu, which merged into a full-fledged faculty in 1994, and where he also became professor of political science (1994–1998).
In 1991, he was a member of the Estonian Constitutional Assembly, and in 1992, he ran as a presidential candidate against Arnold Rüütel (3rd President of the Republic of Estonia, 2001–2006), and Lennart Meri (2nd President of the Republic of Estonia, 1992–2001), who won the election. Taagepera came in third with 23% of the popular vote. Later Taagepera admitted that one of th
|
https://en.wikipedia.org/wiki/UFT
|
UFT may stand for:
Upper fibers of trapezius
Unified field theory, a theory in physics
United Faculty of Theology in Melbourne, Victoria
United Federation of Teachers, a New York union
Universidade Federal do Tocantins, a Brazilian university
Finis Terrae University (Universidad Finis Terrae), a Chilean university
Tegafur/uracil, a chemotherapy drug used in the treatment of cancer
Ultimate Family Tree, a discontinued genealogy program from Ancestry.com
Micro Focus Unified Functional Testing, a testing and quality assurance software solution
|
https://en.wikipedia.org/wiki/Reflection%20%28physics%29
|
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection (for example at a mirror) the angle at which the wave is incident on the surface equals the angle at which it is reflected.
In acoustics, reflection causes echoes and is used in sonar. In geology, it is important in the study of seismic waves. Reflection is observed with surface waves in bodies of water. Reflection is observed with many types of electromagnetic wave, besides visible light. Reflection of VHF and higher frequencies is important for radio transmission and for radar. Even hard X-rays and gamma rays can be reflected at shallow angles with special "grazing" mirrors.
Reflection of light
Reflection of light is either specular (mirror-like) or diffuse (retaining the energy, but losing the image) depending on the nature of the interface. In specular reflection the phase of the reflected waves depends on the choice of the origin of coordinates, but the relative phase between s and p (TE and TM) polarizations is fixed by the properties of the media and of the interface between them.
A mirror provides the most common model for specular light reflection, and typically consists of a glass sheet with a metallic coating where the significant reflection occurs. Reflection is enhance
|
https://en.wikipedia.org/wiki/Attraction
|
Attraction may refer to:
Interpersonal attraction, the attraction between people which leads to friendships, platonic and romantic relationships
Sexual attraction
Object or event that is attractive
Tourist attraction, a place of interest where tourists visit
Amusement park attraction
Attraction in physics
Electromagnetic attraction
Magnetism
Gravity
Strong nuclear force
Weak nuclear force
Other uses
Attraction basin (a.k.a. attractor), in dynamical systems
Attraction (grammar), the process by which a relative pronoun takes on the case of its antecedent
Attraction (horse) (foaled 2001)
Attraction (2017 film), a Russian science fiction action film focusing upon an extraterrestrial spaceship crash-landing
Attraction (2018 film), a Bulgarian romantic comedy film
See also
Attractive nuisance doctrine
Attract (disambiguation)
Law of attraction (disambiguation)
|
https://en.wikipedia.org/wiki/Priority%20inversion
|
In computer science, priority inversion is a scenario in scheduling in which a high-priority task is indirectly superseded by a lower-priority task effectively inverting the assigned priorities of the tasks. This violates the priority model that high-priority tasks can only be prevented from running by higher-priority tasks. Inversion occurs when there is a resource contention with a low-priority task that is then preempted by a medium-priority task.
Formulation
Consider two tasks H and L, of high and low priority respectively, either of which can acquire exclusive use of a shared resource R. If H attempts to acquire R after L has acquired it, then H becomes blocked until L relinquishes the resource. Sharing an exclusive-use resource (R in this case) in a well-designed system typically involves L relinquishing R promptly so that H (a higher-priority task) does not stay blocked for excessive periods of time. Despite good design, however, it is possible that a third task M of medium priority becomes runnable during L's use of R. At this point, M being higher in priority than L, preempts L (since M does not depend on R), causing L to not be able to relinquish R promptly, in turn causing H—the highest-priority process—to be unable to run (that is, H suffers unexpected blockage indirectly caused by lower-priority tasks like M).
Consequences
In some cases, priority inversion can occur without causing immediate harm—the delayed execution of the high-priority task goes unnoticed,
|
https://en.wikipedia.org/wiki/Erwin%20Stresemann
|
Erwin Friedrich Theodor Stresemann (22 November 1889, in Dresden – 20 November 1972, in East Berlin) was a German naturalist and ornithologist. Stresemann was an ornithologist of extensive breadth who compiled one of the first and most comprehensive accounts of avian biology of its time as part of the Handbuch der Zoologie (Handbook of Zoology). In the process of his studies on birds, he also produced one of the most extensive historical accounts on the development of the science of ornithology. He influenced numerous ornithologists around him and oversaw the development of ornithology in Germany as editor of the Journal für Ornithologie. He also took an interest in poetry, philosophy and linguistics. He published a monograph on the Paulohi language based on studies made during his ornithological expedition to the Indonesian island.
Early life
Stresemann was born in Dresden to Richard, an apothecary and Marie. His grandfather Theodor owned the Zum Roten Adler pharmacy in Berlin-Kölln while his father and a brother Gustav owned the Mohrenapotheke in Dresden from 1876. The family was affluent, providing a stimulating environment and he took an interest in beetles and maintained a vivarium. When he joined the Vitzthum Gymnasium, the teacher of mathematics and biology, Dr. Otto Koepert, gave Erwin the job of organizing the school's collection of American and African birds. At a comparatively young age he was able to travel to Heligoland, Bornholm and Moscow. After high school
|
https://en.wikipedia.org/wiki/Schur%27s%20lemma
|
In mathematics, Schur's lemma is an elementary but extremely useful statement in representation theory of groups and algebras. In the group case it says that if M and N are two finite-dimensional irreducible representations
of a group G and φ is a linear map from M to N that commutes with the action of the group, then either φ is invertible, or φ = 0. An important special case occurs when M = N, i.e. φ is a self-map; in particular, any element of the center of a group must act as a scalar operator (a scalar multiple of the identity) on M. The lemma is named after Issai Schur who used it to prove the Schur orthogonality relations and develop the basics of the representation theory of finite groups. Schur's lemma admits generalisations to Lie groups and Lie algebras, the most common of which are due to Jacques Dixmier and Daniel Quillen.
Representation theory of groups
Representation theory is the study of homomorphisms from a group, G, into the general linear group GL(V) of a vector space V; i.e., into the group of automorphisms of V. (Let us here restrict ourselves to the case when the underlying field of V is , the field of complex numbers.) Such a homomorphism is called a representation of G on V. A representation on V is a special case of a group action on V, but rather than permit any arbitrary bijections (permutations) of the underlying set of V, we restrict ourselves to invertible linear transformations.
Let ρ be a representation of G on V. It may be the case that V
|
https://en.wikipedia.org/wiki/Von%20Karman%20Institute%20for%20Fluid%20Dynamics
|
The von Karman Institute for Fluid Dynamics (VKI) is a non-profit educational and scientific organization which specializes in three specific fields: aeronautics and aerospace, environment and applied fluid dynamics, turbomachinery and propulsion. Founded in 1956, it is located in Sint-Genesius-Rode, Belgium.
About
The von Karman Institute for Fluid Dynamics is a non-profit international, educational and scientific organization which is working in three specific fields: aeronautics and aerospace, environment and applied fluid dynamics, turbomachinery and propulsion.
The VKI provides education in these specific areas for students from all over the world. A hundred students come to the Institute each year to study fluid dynamics, for a PhD programme, a research master in Fluid Dynamics, a final year project and also to gather further knowledge while doing a work placement in a specific area.
Each year, Lecture Series and events are being organized inside and outside of the organization. These events emphasize on topics of great importance such as aerodynamics, fluid mechanics, heat transfer with application to aeronautics, space, turbomachinery, the environment and also industrial fluid dynamics. The Institute has built an international renown in these domains. Students who study these fields, researchers, industrials and engineers want to follow these Lecture Series. The information presented is accurate and reliable.
History
In the course of 1955, Professor Theodore vo
|
https://en.wikipedia.org/wiki/Land%20survey
|
Land survey may refer to:
Topographic surveying and mapping, the survey of landscape features for general mapping purposes
Civil engineering surveying, a survey of local topographic features for engineering purposes
Cadastral surveying, the surveying of specific land parcels to define ownership
See also
Surveying, which outlines techniques and principles of land survey
Cartography, the process by which land survey information is used to create maps
Geodesy
Public Land Survey System, the method of determining township boundaries in the USA
Construction engineering, a primary use of Land Survey products
|
https://en.wikipedia.org/wiki/Iwahori%E2%80%93Hecke%20algebra
|
In mathematics, the Iwahori–Hecke algebra, or Hecke algebra, named for Erich Hecke and Nagayoshi Iwahori, is a deformation of the group algebra of a Coxeter group.
Hecke algebras are quotients of the group rings of Artin braid groups. This connection found a spectacular application in Vaughan Jones' construction of new invariants of knots. Representations of Hecke algebras led to discovery of quantum groups by Michio Jimbo. Michael Freedman proposed Hecke algebras as a foundation for topological quantum computation.
Hecke algebras of Coxeter groups
Start with the following data:
(W, S) is a Coxeter system with the Coxeter matrix M = (mst),
R is a commutative ring with identity.
{qs | s ∈ S} is a family of units of R such that qs = qt whenever s and t are conjugate in W
A is the ring of Laurent polynomials over Z with indeterminates qs (and the above restriction that qs = qt whenever s and t are conjugated), that is A = Z [q]
Multiparameter Hecke Algebras
The multiparameter Hecke algebra HR(W,S,q) is a unital, associative R-algebra with generators Ts for all s ∈ S and relations:
Braid Relations: Ts Tt Ts ... = Tt Ts Tt ..., where each side has mst < ∞ factors and s,t belong to S.
Quadratic Relation: For all s in S we have: (Ts - qs)(Ts + 1) = 0.
Warning: in later books and papers, Lusztig used a modified form of the quadratic relation that reads After extending the scalars to include the half integer powers q the resulting Hecke algebra is isomorphic to the previ
|
https://en.wikipedia.org/wiki/Hecke%20operator
|
In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by , is a certain kind of "averaging" operator that plays a significant role in the structure of vector spaces of modular forms and more general automorphic representations.
History
used Hecke operators on modular forms in a paper on the special cusp form of Ramanujan, ahead of the general theory given by . Mordell proved that the Ramanujan tau function, expressing the coefficients of the Ramanujan form,
is a multiplicative function:
The idea goes back to earlier work of Adolf Hurwitz, who treated algebraic correspondences between modular curves which realise some individual Hecke operators.
Mathematical description
Hecke operators can be realized in a number of contexts. The simplest meaning is combinatorial, namely as taking for a given integer some function defined on the lattices of fixed rank to
with the sum taken over all the that are subgroups of of index . For example, with and two dimensions, there are three such . Modular forms are particular kinds of functions of a lattice, subject to conditions making them analytic functions and homogeneous with respect to homotheties, as well as moderate growth at infinity; these conditions are preserved by the summation, and so Hecke operators preserve the space of modular forms of a given weight.
Another way to express Hecke operators is by means of double cosets in the modular group. In the contemporary adelic approac
|
https://en.wikipedia.org/wiki/Hydraulic%20engineering
|
Hydraulic engineering as a sub-discipline of civil engineering is concerned with the flow and conveyance of fluids, principally water and sewage. One feature of these systems is the extensive use of gravity as the motive force to cause the movement of the fluids. This area of civil engineering is intimately related to the design of bridges, dams, channels, canals, and levees, and to both sanitary and environmental engineering.
Hydraulic engineering is the application of the principles of fluid mechanics to problems dealing with the collection, storage, control, transport, regulation, measurement, and use of water. Before beginning a hydraulic engineering project, one must figure out how much water is involved. The hydraulic engineer is concerned with the transport of sediment by the river, the interaction of the water with its alluvial boundary, and the occurrence of scour and deposition. "The hydraulic engineer actually develops conceptual designs for the various features which interact with water such as spillways and outlet works for dams, culverts for highways, canals and related structures for irrigation projects, and cooling-water facilities for thermal power plants."
Fundamental principles
A few examples of the fundamental principles of hydraulic engineering include fluid mechanics, fluid flow, behavior of real fluids, hydrology, pipelines, open channel hydraulics, mechanics of sediment transport, physical modeling, hydraulic machines, and drainage hydraulics.
F
|
https://en.wikipedia.org/wiki/Tosyl%20group
|
In organic chemistry, a toluenesulfonyl group (tosyl group, abbreviated Ts or Tos) is a univalent functional group with the chemical formula . It consists of a tolyl group, , joined to a sulfonyl group, , with the open valence on sulfur. This group is usually derived from the compound tosyl chloride, (abbreviated TsCl), which forms esters and amides of toluenesulfonic acid, (abbreviated TsOH). The para orientation illustrated (p-toluenesulfonyl) is most common, and by convention tosyl without a prefix refers to the p-toluenesulfonyl group.
The toluenesulfonate (or tosylate) group refers to the (–OTs) group, with an additional oxygen attached to sulfur and open valence on an oxygen. In a chemical name, the term tosylate may either refer to the salts containing the anion of p-toluenesulfonic acid, (e.g., sodium p-toluenesulfonate), or it may refer to esters of p-toluenesulfonic acid, TsOR (R = organyl group).
Applications
For SN2 reactions, alkyl alcohols can also be converted to alkyl tosylates, often through addition of tosyl chloride. In this reaction, the lone pair of the alcohol oxygen attacks the sulfur of the tosyl chloride, displacing the chloride and forming the tosylate with retention of reactant stereochemistry. This is useful because alcohols are poor leaving groups in SN2 reactions, in contrast to the tosylate group. It is the transformation of alkyl alcohols to alkyl tosylates that allows an SN2 reaction to occur in the presence of a good nucleophile.
A to
|
https://en.wikipedia.org/wiki/Radon%20measure
|
In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the -algebra of Borel sets of a Hausdorff topological space that is finite on all compact sets, outer regular on all Borel sets, and inner regular on open sets. These conditions guarantee that the measure is "compatible" with the topology of the space, and most measures used in mathematical analysis and in number theory are indeed Radon measures.
Motivation
A common problem is to find a good notion of a measure on a topological space that is compatible with the topology in some sense. One way to do this is to define a measure on the Borel sets of the topological space. In general there are several problems with this: for example, such a measure may not have a well defined support. Another approach to measure theory is to restrict to locally compact Hausdorff spaces, and only consider the measures that correspond to positive linear functionals on the space of continuous functions with compact support (some authors use this as the definition of a Radon measure). This produces a good theory with no pathological problems, but does not apply to spaces that are not locally compact. If there is no restriction to non-negative measures and complex measures are allowed, then Radon measures can be defined as the continuous dual space on the space of continuous functions with compact support. If such a Radon measure is real then it can be decomposed into the difference of two p
|
https://en.wikipedia.org/wiki/List%20of%20numeral%20system%20topics
|
This is a list of Wikipedia articles on topics of numeral system and "numeric representations"
See also: computer numbering formats and number names.
Arranged by base
Radix, radix point, mixed radix, base (mathematics)
Unary numeral system (base 1)
Binary numeral system (base 2)
Negative base numeral system (base −2)
Ternary numeral system numeral system (base 3)
Balanced ternary numeral system (base 3)
Negative base numeral system (base −3)
Quaternary numeral system (base 4)
Quater-imaginary base (base 2)
Quinary numeral system (base 5)
Senary numeral system (base 6)
Septenary numeral system (base 7)
Octal numeral system (base 8)
Nonary (novenary) numeral system (base 9)
Decimal (denary) numeral system (base 10)
Negative base numeral system (base −10)
Duodecimal (dozenal) numeral system (base 12)
Hexadecimal numeral system (base 16)
Vigesimal numeral system (base 20)
Sexagesimal numeral system (base 60)
Arranged by culture
Other
Numeral system topics
|
https://en.wikipedia.org/wiki/Oxonium%20ion
|
In chemistry, an oxonium ion is any cation containing an oxygen atom that has three bonds and 1+ formal charge. The simplest oxonium ion is the hydronium ion ().
Alkyloxonium
Hydronium is one of a series of oxonium ions with the formula RnH3−nO+.
Oxygen is usually pyramidal with an sp3 hybridization. Those with n = 1 are called primary oxonium ions, an example being protonated alcohol (e.g. methanol). In acidic media, the oxonium functional group produced by protonating an alcohol can be a leaving group in the E2 elimination reaction. The product is an alkene. Extreme acidity, heat, and dehydrating conditions are usually required. Other hydrocarbon oxonium ions are formed by protonation or alkylation of alcohols or ethers (R−C−−R1R2).
Secondary oxonium ions have the formula R2OH+, an example being protonated ethers.
Tertiary oxonium ions have the formula R3O+, an example being trimethyloxonium. Tertiary alkyloxonium salts are useful alkylating agents. For example, triethyloxonium tetrafluoroborate ()(), a white crystalline solid, can be used, for example, to produce ethyl esters when the conditions of traditional Fischer esterification are unsuitable. It is also used for preparation of enol ethers and related functional groups.
Oxatriquinane and oxatriquinacene are unusually stable oxonium ions, first described in 2008. Oxatriquinane does not react with boiling water or with alcohols, thiols, halide ions, or amines, although it does react with stronger nucleophiles such a
|
https://en.wikipedia.org/wiki/Sulfonate
|
In organosulfur chemistry, a sulfonate is a salt or ester of a sulfonic acid. It contains the functional group , where R is an organic group. Sulfonates are the conjugate bases of sulfonic acids. Sulfonates are generally stable in water, non-oxidizing, and colorless. Many useful compounds and even some biochemicals feature sulfonates.
Sulfonate salts
Anions with the general formula are called sulfonates. They are the conjugate bases of sulfonic acids with formula . As sulfonic acids tend to be strong acids, the corresponding sulfonates are weak bases. Due to the stability of sulfonate anions, the cations of sulfonate salts such as scandium triflate have application as Lewis acids.
A classic preparation of sulfonates is the Strecker sulfite alkylation, in which an alkali sulfite salt displaces a halide, typically in the presence of an iodine catalyst:
RX + M2SO3 -> RSO3M + MX
An alternative is the condensation of a sulfonyl halide with an alcohol in pyridine:
ROH{} + R'SO2Cl\ \overset{Pyr}{->}\ ROSO2R' + HCl
Sulfonic esters
Esters with the general formula R1SO2OR2 are called sulfonic esters. Individual members of the category are named analogously to how ordinary carboxyl esters are named. For example, if the R2 group is a methyl group and the R1 group is a trifluoromethyl group, the resulting compound is methyl trifluoromethanesulfonate.
Sulfonic esters are used as reagents in organic synthesis, chiefly because the RSO3− group is a good leaving group, especially
|
https://en.wikipedia.org/wiki/Scott%20Hudson%20%28electrical%20engineer%29
|
Raymond Scott Hudson (born 1959) is a professor of electrical engineering and computer science at Washington State University. Hudson was educated at Caltech, where he received his bachelor's degree in engineering and applied science in 1985, his master's degree in electrical engineering in 1986, and his PhD in electrical engineering in 1990. His research interests include radar imaging, optical signal processing, and radar astronomy.
From August 19 to 22 of 1989, Hudson and Steven Ostro observed 4769 Castalia from the Arecibo Observatory, producing the first direct image of an asteroid.
The main-belt asteroid 5723 Hudson, discovered by Edward Bowell at Lowell Observatory in 1986, was named in his honour. The official naming citation was published on 9 September 1995 ().
References
External links
Profile of Scott Hudson
Scott Hudson's web page at WSU
1959 births
Living people
American astronomers
American electrical engineers
California Institute of Technology alumni
Washington State University faculty
|
https://en.wikipedia.org/wiki/FST
|
FST may refer to:
Arts and entertainment
Finlands Svenska Television, now Yle Fem, the Swedish-language department of the Finnish Broadcasting Company
Florida Studio Theatre, in Sarasota, Florida, United States
Free Southern Theater, in Mississippi, United States
Biology
Fixation index (FST), in population genetics
Follistatin, a mammalian glycoprotein (and gene)
Education
Franciscan School of Theology, in California, United States
French School of Thessaloniki, in Greece
The interdisciplinary field of food science and technology
Government and politics
Fermanagh and South Tyrone (Assembly constituency), in Northern Ireland
Fermanagh and South Tyrone (UK Parliament constituency), in Northern Ireland
Financial Secretary to the Treasury, of the United Kingdom
Foreign Sports Talent Scheme, of Singapore
Military
Fire Support Team of the Royal Artillery
Fleet Survey Team of the United States Navy
Forward surgical teams of the United States Army
Technology
Feature Selection Toolbox, machine learning software
File Streaming Technology, a digital audio format
Finite-state transducer
Full-Scale Tunnel, a demolished NASA wind tunnel
Transport
Fenchurch Street railway station, in London
First Stop Travel, a Scottish bus operator
Fort Stockton–Pecos County Airport, in Texas, United States
Sint-Truiden railway station, in Belgium
Other uses
Family Survival Trust, in the United Kingdom
Foundation for Science and Technology, in the United Kingdom
Fie
|
https://en.wikipedia.org/wiki/Gnome%20sort
|
Gnome sort (nicknamed stupid sort) is a variation of the insertion sort sorting algorithm that does not use nested loops. Gnome sort was originally proposed by Iranian computer scientist Hamid Sarbazi-Azad (professor of Computer Science and Engineering at Sharif University of Technology) in 2000. The sort was first called stupid sort (not to be confused with bogosort), and then later described by Dick Grune and named gnome sort.
Gnome sort performs at least as many comparisons as insertion sort and has the same asymptotic run time characteristics. Gnome sort works by building a sorted list one element at a time, getting each item to the proper place in a series of swaps. The average running time is O(n2) but tends towards O(n) if the list is initially almost sorted.
Dick Grune described the sorting method with the following story:
Pseudocode
Here is pseudocode for the gnome sort using a zero-based array:
procedure gnomeSort(a[]):
pos := 0
while pos < length(a):
if (pos == 0 or a[pos] >= a[pos-1]):
pos := pos + 1
else:
swap a[pos] and a[pos-1]
pos := pos - 1
Example
Given an unsorted array, a = [5, 3, 2, 4], the gnome sort takes the following steps during the while loop. The current position is highlighted in bold and indicated as a value of the variable pos.
Notes
References
External links
Gnome sort
Sorting algorithms
Comparison sorts
Stable sorts
|
https://en.wikipedia.org/wiki/Protonation
|
In chemistry, protonation (or hydronation) is the adding of a proton (or hydron, or hydrogen cation), usually denoted by H+, to an atom, molecule, or ion, forming a conjugate acid. (The complementary process, when a proton is removed from a Brønsted–Lowry acid, is deprotonation.) Some examples include
The protonation of water by sulfuric acid:
H2SO4 + H2O H3O+ +
The protonation of isobutene in the formation of a carbocation:
(CH3)2C=CH2 + HBF4 (CH3)3C+ +
The protonation of ammonia in the formation of ammonium chloride from ammonia and hydrogen chloride:
NH3(g) + HCl(g) → NH4Cl(s)
Protonation is a fundamental chemical reaction and is a step in many stoichiometric and catalytic processes. Some ions and molecules can undergo more than one protonation and are labeled polybasic, which is true of many biological macromolecules. Protonation and deprotonation (removal of a proton) occur in most acid–base reactions; they are the core of most acid–base reaction theories. A Brønsted–Lowry acid is defined as a chemical substance that protonates another substance. Upon protonating a substrate, the mass and the charge of the species each increase by one unit, making it an essential step in certain analytical procedures such as electrospray mass spectrometry. Protonating or deprotonating a molecule or ion can change many other chemical properties, not just the charge and mass, for example solubility, hydrophilicity, reduction potential, and optical properties can change.
Rates
Protona
|
https://en.wikipedia.org/wiki/European%20Society%20for%20Evolutionary%20Biology
|
The European Society for Evolutionary Biology (ESEB) was founded in 1987 in Basel (Switzerland) with around 450 evolutionary biologists attending the inaugural congress. It is an academic society that brings together more than 1500 evolutionary biologists from across Europe and beyond. The founding of the society was closely linked with the launch of the society's journal, the Journal of Evolutionary Biology with the first issue appearing in 1988. ESEB aims at supporting the study of evolution. Beside publishing the journal and co-publishing Evolution Letters, the society organises a biannual congress and supports other events to promote advances in evolutionary biology. ESEB also supports activities to promote a scientific view of evolution in research and education.
Its objectives are to "Support the study of organic evolution and the integration of those scientific fields that are concerned with evolution: molecular and microbial evolution, behaviour, genetics, ecology, life histories, development, paleontology, systematics and morphology."
ESEB supports young researchers through sponsoring the annual EMPSEB (European Meeting of PhD Students in Evolutionary Biology) research conference for Ph.D. students.
Presidents
Source: ESEB
1987–1989 : Arthur Cain (first president)
1989–1991 : Bengt Bengtsson
1991–1993 : John Maynard Smith
1993–1995 : John L. Harper
1995–1997 : Wim Scharloo
1997–1999 : Stephen Stearns
1999–2001 : Godfrey Hewitt
2001–2003 : Deborah Charlesw
|
https://en.wikipedia.org/wiki/Imine
|
In organic chemistry, an imine ( or ) is a functional group or organic compound containing a carbon–nitrogen double bond (). The nitrogen atom can be attached to a hydrogen or an organic group (R). The carbon atom has two additional single bonds. Imines are common in synthetic and naturally occurring compounds and they participate in many reactions.
Structure
For ketimines and aldimines, respectively, the five core atoms (C2C=NX and C(H)C=NX, X = H or C) are coplanar. Planarity results from the sp2-hybridization of the mutually double-bonded carbon and the nitrogen atoms. The C=N distance is 1.29-1.31 Å for nonconjugated imines and 1.35 Å for conjugated imines. By contrast, C-N distances in amines and nitriles are 1.47 and 1.16 Å, respectively. Rotation about the C=N bond is slow. Using NMR spectroscopy, both E- and Z-isomers of aldimines have been detected. Owing to steric effects, the E isomer is favored.
Nomenclature and classification
The term "imine" was coined in 1883 by the German chemist Albert Ladenburg.
Usually imines refer to compounds with the general formula R2C=NR, as discussed below. In the older literature, imine refers to the aza-analogue of an epoxide. Thus, ethylenimine is the three-membered ring species aziridine C2H4NH. The relationship of imines to amines having double and single bonds can be correlated with imides and amides, as in succinimide vs acetamide.
Imines are related to ketones and aldehydes by replacement of the oxygen with an NR
|
https://en.wikipedia.org/wiki/Schiff%20base
|
In organic chemistry, a Schiff base (named after Hugo Schiff) is a compound with the general structure ( = alkyl or aryl, but not hydrogen). They can be considered a sub-class of imines, being either secondary ketimines or secondary aldimines depending on their structure. Anil refers to a common subset of Schiff bases: imines derived from anilines. The term can be synonymous with azomethine which refers specifically to secondary aldimines (i.e. where R' ≠ H).
Synthesis
Schiff bases can be synthesized from an aliphatic or aromatic amine and a carbonyl compound by nucleophilic addition forming a hemiaminal, followed by a dehydration to generate an imine. In a typical reaction, 4,4'-oxydianiline reacts with o-vanillin:
Biochemistry
Schiff bases have been investigated in relation to a wide range of contexts, including antimicrobial, antiviral and anticancer activity. They have also been considered for the inhibition of amyloid-β aggregation.
Schiff bases are common enzymatic intermediates where an amine, such as the terminal group of a lysine residue, reversibly reacts with an aldehyde or ketone of a cofactor or substrate. The common enzyme cofactor pyridoxal phosphate (PLP) forms a Schiff base with a lysine residue and is transaldiminated to the substrate(s). Similarly, the cofactor retinal forms a Schiff base in rhodopsins, including human rhodopsin (via Lysine 296), which is key in the photoreception mechanism.
Coordination chemistry
The term Schiff base is normally
|
https://en.wikipedia.org/wiki/Fischer%20projection
|
In chemistry, the Fischer projection, devised by Emil Fischer in 1891, is a two-dimensional representation of a three-dimensional organic molecule by projection. Fischer projections were originally proposed for the depiction of carbohydrates and used by chemists, particularly in organic chemistry and biochemistry. The use of Fischer projections in non-carbohydrates is discouraged, as such drawings are ambiguous and easily confused with other types of drawing. The main purpose of Fischer projections is to show the chirality of a molecule and to distinguish between a pair of enantiomers. Some notable uses include drawing sugars and depicting isomers.
Conventions
All bonds are depicted as horizontal or vertical lines. The carbon chain is depicted vertically, with carbon atoms sometimes not shown and represented by the center of crossing lines (see figure below). The orientation of the carbon chain is so that the first carbon (C1) is at the top. In an aldose, C1 is the carbon of the aldehyde group; in a ketose, C1 is the carbon closest to the ketone group, which is typically found at C2.
The proper way to view a Fischer projection is to vertically orient the molecule in relation to the carbon chain, have all horizontal bonds point toward the viewer, and orient all vertical bonds to point away from the viewer. Molecules with a simple tetrahedral geometry can be easily rotated in space so that this condition is met (see figures). Fischer projections are commonly constructed beg
|
https://en.wikipedia.org/wiki/Amino%20sugar
|
In organic chemistry, an amino sugar is a sugar molecule in which a hydroxyl group has been replaced with an amine group. More than 60 amino sugars are known, with one of the most abundant being N-Acetyl--glucosamine (a 2-amino-2-deoxysugar), which is the main component of chitin.
Derivatives of amine containing sugars, such as N-acetylglucosamine and sialic acid, whose nitrogens are part of more complex functional groups rather than formally being amines, are also considered amino sugars. Aminoglycosides are a class of antimicrobial compounds that inhibit bacterial protein synthesis. These compounds are conjugates of amino sugars and aminocyclitols.
Synthesis
From glycals
Glycals are cyclic enol ether derivatives of monosaccharides, having a double bond between carbon atoms 1 and 2 of the ring. N-functionalized of glycals at the C2 position, combined with glycosidic bond formation at C1 is a common strategy for the synthesis of amino sugars. This can be achieved using azides with subsequent reduction yielding the amino sugar. One advantage of introducing azide moiety at C-2 lies in its non-participatory ability, which could serve as the basis of stereoselective synthesis of 1.2-cis-glycosidic linkage.
Azides give high regioselectivity, however stereoselectivity both at C-1 and C-2 is generally poor. Usually anomeric mixtures will be obtained and the stereochemistry formed at C-2 is heavily dependent upon the starting substrates. For galactal, addition of azide to the do
|
https://en.wikipedia.org/wiki/Mutarotation
|
In stereochemistry, mutarotation is the change in optical rotation of a chiral material due to a change in equilibrium between the two constituent anomers (i.e. the interconversion of their respective stereocenters). Cyclic sugars show mutarotation as α and β anomeric forms interconvert.
The optical rotation of the solution depends on the optical rotation of each anomer and their ratio in the solution.
Mutarotation was discovered by French chemist Augustin-Pierre Dubrunfaut in 1844, when he noticed that the specific rotation of aqueous sugar solution changes with time.
Measurement
The α and β anomers are diastereomers of each other and usually have different specific rotations. A solution or liquid sample of a pure α anomer will rotate plane polarised light by a different amount and/or in the opposite direction than the pure β anomer of that compound. The optical rotation of the solution depends on the optical rotation of each anomer and their ratio in the solution.
For example, if a solution of β-D-glucopyranose is dissolved in water, its specific optical rotation will be +18.7°. Over time, some of the β-D-glucopyranose will undergo mutarotation to become α-D-glucopyranose, which has an optical rotation of +112.2°. The rotation of the solution will increase from +18.7° to an equilibrium value of +52.7° as some of the β form is converted to the α form. The equilibrium mixture is about 64% of β-D-glucopyranose and about 36% of α-D-glucopyranose, though there are also trace
|
https://en.wikipedia.org/wiki/Stereocenter
|
In stereochemistry, a stereocenter of a molecule is an atom (center), axis or plane that is the focus of stereoisomerism; that is, when having at least three different groups bound to the stereocenter, interchanging any two different groups creates a new stereoisomer. Stereocenters are also referred to as stereogenic centers.
A stereocenter is geometrically defined as a point (location) in a molecule; a stereocenter is usually but not always a specific atom, often carbon. Stereocenters can exist on chiral or achiral molecules; stereocenters can contain single bonds or double bonds. The number of hypothetical stereoisomers can be predicted by using 2n, with n being the number of tetrahedral stereocenters; however, exceptions such as meso compounds can reduce the prediction to below the expected 2n.
Chirality centers are a type of stereocenter with four different substituent groups; chirality centers are a specific subset of stereocenters because they can only have sp3 hybridization, meaning that they can only have single bonds.
Location
Stereocenters can exist on chiral or achiral molecules. They are defined as a location (point) within a molecule, rather than a particular atom, in which the interchanging of two groups creates a stereoisomer. A stereocenter can have either four different attachment groups, or three different attachment groups where one group is connected by a double bond. Since stereocenters can exist on achiral molecules, stereocenters can have either s
|
https://en.wikipedia.org/wiki/Haworth%20projection
|
In chemistry, a Haworth projection is a common way of writing a structural formula to represent the cyclic structure of monosaccharides with a simple three-dimensional perspective. Haworth projection approximate the shapes of the actual molecules better for furanoses -which are in reality nearly planar- than for pyranoses which exist in solution in the chair conformation. Organic chemistry and especially biochemistry are the areas of chemistry that use the Haworth projection the most.
The Haworth projection was named after the British chemist Sir Norman Haworth.
A Haworth projection has the following characteristics:
Carbon is the implicit type of atom. In the example on the right, the atoms numbered from 1 to 6 are all carbon atoms. Carbon 1 is known as the anomeric carbon.
Hydrogen atoms on carbon are implicit. In the example, atoms 1 to 6 have extra hydrogen atoms not depicted.
A thicker line indicates atoms that are closer to the observer. In the example on the right, atoms 2 and 3 (and their corresponding OH groups) are the closest to the observer. Atoms 1 and 4 are farther from the observer. Atom 5 and the other atoms are the farthest.
The groups below the plane of the ring in Haworth projections correspond to those on the right-hand side of a Fischer projection. This rule does not apply to the groups on the two ring carbons bonded to the endocyclic oxygen atom. combined with hydrogen.
See also
Skeletal formula
Natta projection
Newman projection
References
|
https://en.wikipedia.org/wiki/Diastereomer
|
In stereochemistry, diastereomers (sometimes called diastereoisomers) are a type of stereoisomer. Diastereomers are defined as non-mirror image, non-identical stereoisomers. Hence, they occur when two or more stereoisomers of a compound have different configurations at one or more (but not all) of the equivalent (related) stereocenters and are not mirror images of each other.
When two diastereoisomers differ from each other at only one stereocenter, they are epimers. Each stereocenter gives rise to two different configurations and thus typically increases the number of stereoisomers by a factor of two.
Diastereomers differ from enantiomers in that the latter are pairs of stereoisomers that differ in all stereocenters and are therefore mirror images of one another.
Enantiomers of a compound with more than one stereocenter are also diastereomers of the other stereoisomers of that compound that are not their mirror image (that is, excluding the opposing enantiomer).
Diastereomers have different physical properties (unlike most aspects of enantiomers) and often different chemical reactivity.
Diastereomers differ not only in physical properties but also in chemical reactivity — how a compound reacts with others. Glucose and galactose, for instance, are diastereomers. Even though they share the same molar weight, glucose is more stable than galactose. This difference in stability causes galactose to be absorbed slightly faster than glucose in human body.
Diastereoselectivity is
|
https://en.wikipedia.org/wiki/Homotopy%20lifting%20property
|
In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property (also known as an instance of the right lifting property or the covering homotopy axiom) is a technical condition on a continuous function from a topological space E to another one, B. It is designed to support the picture of E "above" B by allowing a homotopy taking place in B to be moved "upstairs" to E.
For example, a covering map has a property of unique local lifting of paths to a given sheet; the uniqueness is because the fibers of a covering map are discrete spaces. The homotopy lifting property will hold in many situations, such as the projection in a vector bundle, fiber bundle or fibration, where there need be no unique way of lifting.
Formal definition
Assume all maps are continuous functions between topological spaces. Given a map , and a space , one says that has the homotopy lifting property, or that has the homotopy lifting property with respect to , if:
for any homotopy , and
for any map lifting (i.e., so that ),
there exists a homotopy lifting (i.e., so that ) which also satisfies .
The following diagram depicts this situation:
The outer square (without the dotted arrow) commutes if and only if the hypotheses of the lifting property are true. A lifting corresponds to a dotted arrow making the diagram commute. This diagram is dual to that of the homotopy extension property; this duality is loosely referred to as Eckmann–Hilton duality.
If th
|
https://en.wikipedia.org/wiki/Rigid-framed%20power%20kite
|
A Rigid-framed power kite consists of a single skin and a rigid frame. They are often used in the popular sport of kite surfing. Typically it has four lines and a pair of handles; or a particular style of bar, again with 4 lines. (See also kite control systems) The best known commercial kite of this type is the Peter Lynn C-Quad.
This type of foil kite is related to the leading edge inflatable kite and the bow kite, which have a similar shape but typically do not include a rigid frame.
Kites
|
https://en.wikipedia.org/wiki/Ciphertext-only%20attack
|
In cryptography, a ciphertext-only attack (COA) or known ciphertext attack is an attack model for cryptanalysis where the attacker is assumed to have access only to a set of ciphertexts. While the attacker has no channel providing access to the plaintext prior to encryption, in all practical ciphertext-only attacks, the attacker still has some knowledge of the plaintext. For instance, the attacker might know the language in which the plaintext is written or the expected statistical distribution of characters in the plaintext. Standard protocol data and messages are commonly part of the plaintext in many deployed systems, and can usually be guessed or known efficiently as part of a ciphertext-only attack on these systems.
Attack
The attack is completely successful if the corresponding plaintexts can be deduced, or even better, the key. The ability to obtain any information at all about the underlying plaintext beyond what was pre-known to the attacker is still considered a success. For example, if an adversary is sending ciphertext continuously to maintain traffic-flow security, it would be very useful to be able to distinguish real messages from nulls. Even making an informed guess of the existence of real messages would facilitate traffic analysis.
In the history of cryptography, early ciphers, implemented using pen-and-paper, were routinely broken using ciphertexts alone. Cryptographers developed statistical techniques for attacking ciphertext, such as frequency analys
|
https://en.wikipedia.org/wiki/Leading%20edge%20inflatable%20kite
|
A leading edge inflatable kite (LEI) is a single skin kite with inflatable bladders providing structure. It is useful as a power or traction kite. These kites are flown using 2, 4 or 5 control lines and a bar. (See also: kite control systems) A LEI is a great kite for water use because the inflated bladders cause it to float on the water surface. A LEI can sit on the water for an indefinite time and still be relaunched because, unlike a foil kite, there are no chambers that can fill with water. Generally used for kitesurfing and kiteboarding, leading edge inflatable kites come in many different sizes, most commonly from 5 to 18 square metres.
Based on their design Leading Edge Inflatable kites can be broken down into four categories: C-kites, hybrid kites, delta kites, and bow kites.
C-kites
C-kites are the oldest style of LEI used for traction kiting. They typically come with four lines, and some have the option of an additional 5th line for safety and easy relaunching. The main difference between C-kites and other LEI styles is that they do not have any lines that support the leading edge of the kite (called bridles). The lines on a C-kite attach to the four corners of the kite. Hybrid kites, together with bow kites and later delta kites are all subtypes of a SLE-kite (Supported Leading Edge), defined by having a bridle which supports the leading edge. C-kites are the preferred kite of wake-style kiteboarders.
SLE sub-types
Bow kites
All of the Bow kite's advantages
|
https://en.wikipedia.org/wiki/Deterministic%20system
|
In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state.
In physics
Physical laws that are described by differential equations represent deterministic systems, even though the state of the system at a given point in time may be difficult to describe explicitly.
In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic. However, the relationship between a system's wave function and the observable properties of the system appears to be non-deterministic.
In mathematics
The systems studied in chaos theory are deterministic. If the initial state were known exactly, then the future state of such a system could theoretically be predicted. However, in practice, knowledge about the future state is limited by the precision with which the initial state can be measured, and chaotic systems are characterized by a strong dependence on the initial conditions. This sensitivity to initial conditions can be measured with Lyapunov exponents.
Markov chains and other random walks are not deterministic systems, because their development depends on random choices.
In computer science
A deterministic model of computation, for example a deterministic Turing machine, is a model of computation s
|
https://en.wikipedia.org/wiki/Kite%20control%20systems
|
Kite types, kite mooring, and kite applications result in a wide variety of kite control systems. Contemporary manufacturers, kite athletes, kite pilots, scientists, and engineers are expanding the possibilities.
Single-line kite control systems
High-altitude attempt single-line control systems
On-board angle-of-attack mechanisms were used in the 2000 altitude record-making flight; the operators' designed adjuster limited kite line tension to not more than 100 pounds by altering the angle of attack of the kite's wing body. The kite's line had a control: a line payout meter that did not function in the record-setting flight. However, some special tether line lower end used bungee and pulley arrangements to lower the impact of gusts on the long tether. Control of a kite includes how other aircraft see the kite system; the team placed a radio beacon (using two-meter frequency detectable for 50 miles) on the kite; for sight visibility, strobe lights were hung from the kite's nose. Control via use of reels and pulleys become critical when tension is high; the team had to repair and replace parts during the flight session.
Auxiliary control
Auxiliary devices have been invented and used for controlling single-line kites. Devices on board the kite's wing can react to the kite-line's tension or to the kite's angle of attack with the ambient stream in which the kite is flying. Special reel devices allow kite-line length and tension control. Moving the kite's line lower end left or
|
https://en.wikipedia.org/wiki/State%20University%20of%20New%20York%20College%20of%20Environmental%20Science%20and%20Forestry
|
The State University of New York College of Environmental Science and Forestry (ESF) is a public research university in Syracuse, New York focused on the environment and natural resources. It is part of the State University of New York (SUNY) system. ESF is immediately adjacent to Syracuse University, within which it was founded, and with which it maintains a special relationship. It is classified among "R2: Doctoral Universities – High research activity".
ESF operates education and research facilities also in the Adirondack Park (including the Ranger School in Wanakena), the Thousand Islands, elsewhere in central New York, and Costa Rica. The college's curricula focus on the understanding, management, and sustainability of the environment and natural resources.
History
Founding
The New York State College of Forestry at Syracuse University was established on July 28, 1911, through a bill signed by New York Governor John Alden Dix. The previous year, Governor Hughes had vetoed a bill authorizing such a college. Both bills followed the state's defunding in 1903 of the New York State College of Forestry at Cornell. Originally a unit of Syracuse University, in 1913, the college was made a separate, legal entity.
Syracuse native and constitutional lawyer Louis Marshall, with a summer residence at Knollwood Club on Saranac Lake and a prime mover for the establishment of the Adirondack and Catskill Forest Preserve (New York), became a Syracuse University Trustee in 1910. He co
|
https://en.wikipedia.org/wiki/Secondary
|
Secondary may refer to:
Science and nature
Secondary emission, of particles
Secondary electrons, electrons generated as ionization products
The secondary winding, or the electrical or electronic circuit connected to the secondary winding in a transformer
Secondary (chemistry), a term used in organic chemistry to classify various types of compounds
Secondary color, color made from mixing primary colors
Secondary mirror, second mirror element/focusing surface in a reflecting telescope
Secondary craters, often called "secondaries"
Secondary consumer, in ecology
An antiquated name for the Mesozoic in geosciences
Secondary feathers, flight feathers attached to the ulna on the wings of birds
Society and culture
Secondary (football), a position in American football and Canadian football
Secondary dominant in music
Secondary education, education which typically takes place after six years of primary education
Secondary school, the type of school at the secondary level of education
Secondary market, an aftermarket where financial assets are traded
See also
Second (disambiguation)
Binary (disambiguation)
Primary (disambiguation)
Tertiary (disambiguation)
|
https://en.wikipedia.org/wiki/Constructible%20polygon
|
In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not. There are infinitely many constructible polygons, but only 31 with an odd number of sides are known.
Conditions for constructibility
Some regular polygons are easy to construct with compass and straightedge; others are not. The ancient Greek mathematicians knew how to construct a regular polygon with 3, 4, or 5 sides, and they knew how to construct a regular polygon with double the number of sides of a given regular polygon. This led to the question being posed: is it possible to construct all regular polygons with compass and straightedge? If not, which n-gons (that is, polygons with n edges) are constructible and which are not?
Carl Friedrich Gauss proved the constructibility of the regular 17-gon in 1796. Five years later, he developed the theory of Gaussian periods in his Disquisitiones Arithmeticae. This theory allowed him to formulate a sufficient condition for the constructibility of regular polygons. Gauss stated without proof that this condition was also necessary, but never published his proof. A full proof of necessity was given by Pierre Wantzel in 1837. The result is known as the Gauss–Wantzel theorem:
A regular n-gon can be constructed with compass and straightedge if and only if n is a power of 2 or the product of a power of 2 and a
|
https://en.wikipedia.org/wiki/Charles-Eug%C3%A8ne%20Delaunay
|
Charles-Eugène Delaunay (; 9 April 1816 – 5 August 1872) was a French astronomer and mathematician. His lunar motion studies were important in advancing both the theory of planetary motion and mathematics.
Life
Born in Lusigny-sur-Barse, France, to Jacques‐Hubert Delaunay and Catherine Choiselat, Delaunay studied under Jean-Baptiste Biot at the Sorbonne. He worked on the mechanics of the Moon as a special case of the three-body problem. He published two volumes on the topic, each of 900 pages in length, in 1860 and 1867. The work hints at chaos in the system, and clearly demonstrates the problem of so-called "small denominators" in perturbation theory. His infinite series expression for finding the position of the Moon converged too slowly to be of practical use but was a catalyst in the development of functional analysis and computer algebra.
Delaunay became director of the Paris Observatory in 1870 but drowned in a boating accident near Cherbourg, France, two years later. He was followed by Jean Claude Bouquet at the Academy. Peter Guthrie Tait in his book An Elementary Treatise on Quaternions edition 1867 on page 244 named Didonia in honour of Delaunay.
Honours
Member of the Académie des Sciences, (1855)
Gold Medal of the Royal Astronomical Society, (1870)
His name is one of the 72 names inscribed on the Eiffel Tower.
References
Bibliography
By Delaunay
About Delaunay
[Anon.] (2001) "Delaunay, Charles-Eugène", ''Encyclopædia Britannica, Deluxe edition CD-ROM
Some
|
https://en.wikipedia.org/wiki/256%20%28number%29
|
256 (two hundred [and] fifty-six) is the natural number following 255 and preceding 257.
In mathematics
256 is a composite number, with the factorization 256 = 28, which makes it a power of two.
256 is 4 raised to the 4th power, so in tetration notation, 256 is 24.
256 is the value of the expression , where .
256 is a perfect square (162).
256 is the only 3-digit number that is zenzizenzizenzic. It is 2 to the 8th power or .
256 is the lowest number that is a product of eight prime factors.
256 is the number of parts in all compositions of 7.
In computing
One octet (in most cases one byte) is equal to eight bits and has 28 or 256 possible values, counting from 0 to 255. The number 256 often appears in computer applications (especially on 8-bit systems) such as:
The typical number of different values in each color channel of a digital color image (256 values for red, 256 values for green, and 256 values for blue used for 24-bit color) (see color space or Web colors).
The number of colors available in a GIF or a 256-color (8-bit) bitmap.
The number of characters in extended ASCII and Latin-1.
The number of columns available in a Microsoft Excel worksheet until Excel 2007.
The split-screen level in Pac-Man, which results from the use of a single byte to store the internal level counter.
A 256-bit integer can represent up to 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936 values.
The number of bits in the S
|
https://en.wikipedia.org/wiki/George%20Turner%20%28British%20politician%29
|
George Turner (born 9 August 1940) is a Labour Party politician in the United Kingdom.
Early life
Turner attended Laxton Grammar School (now part of Oundle School) on North Street in Oundle. At Imperial College London he gained a BSc in Physics, then obtained a PhD in Physics from Gonville and Caius College, Cambridge. He then became Head of the Electrical Engineering Department at the University of East Anglia.
Parliamentary career
Turner contested North West Norfolk on behalf of Labour in 1992, but failed to be elected. He was returned as the Member of Parliament (MP) for the constituency in 1997, but lost his seat back to Henry Bellingham of the Conservative Party – whom he had first defeated – in 2001.
In defeating Bellingham in 1997 Turner benefitted from a somewhat curious echo of a famous historical episode, as noted by the Conservative peer and historian Lord Lexden during a debate in the House of Lords in 2012. Referring to Spencer Perceval, the only Prime Minister to have been assassinated, Lexden remarked in that debate: "My Lords, would my noble friend think of reminding Mr Henry Bellingham that he has already experienced the Perceval family's taste for revenge, having been deprived of his Commons seat at the 1997 election by a direct descendant of the assassinated Prime Minister?" Perceval's descendant was a third candidate in the constituency, Roger Percival of the Referendum Party, who in Lexden's view had deprived Bellingham (in turn a kinsman of Spencer Pe
|
https://en.wikipedia.org/wiki/Hypercharge
|
In particle physics, the hypercharge (a portmanteau of hyperonic and charge) Y of a particle is a quantum number conserved under the strong interaction. The concept of hypercharge provides a single charge operator that accounts for properties of isospin, electric charge, and flavour. The hypercharge is useful to classify hadrons; the similarly named weak hypercharge has an analogous role in the electroweak interaction.
Definition
Hypercharge is one of two quantum numbers of the SU(3) model of hadrons, alongside isospin . The isospin alone was sufficient for two quark flavours — namely and — whereas presently 6 flavours of quarks are known.
SU(3) weight diagrams (see below) are 2 dimensional, with the coordinates referring to two quantum numbers: (also known as ), which is the component of isospin, and , which is the hypercharge (defined by strangeness , charm , bottomness , topness , and baryon number ). Mathematically, hypercharge is
Strong interactions conserve hypercharge (and weak hypercharge), but weak interactions do not.
Relation with electric charge and isospin
The Gell-Mann–Nishijima formula relates isospin and electric charge
where I3 is the third component of isospin and Q is the particle's charge.
Isospin creates multiplets of particles whose average charge is related to the hypercharge by:
since the hypercharge is the same for all members of a multiplet, and the average of the I3 values is 0.
These definitions in their original form hold only for th
|
https://en.wikipedia.org/wiki/Bisect
|
Bisect, or similar, may refer to:
Mathematics
Bisection, in geometry, dividing something into two equal parts
Bisection method, a root-finding algorithm
Equidistant set
Other uses
Bisect (philately), the use of postage stamp halves
Bisector (music), a half octave in diatonic set theory
Bisection (software engineering), for finding code changes
bisection of earthworms to study regeneration
|
https://en.wikipedia.org/wiki/Ernest%20Esclangon
|
Ernest Benjamin Esclangon (17 March 1876 – 28 January 1954) was a French astronomer and mathematician.
Born in Mison, Alpes-de-Haute-Provence, in 1895 he started to study mathematics at the École Normale Supérieure, graduating in 1898. Looking for some means of financial support while he completed his doctorate on quasi-periodic functions, he took a post at the Bordeaux Observatory, teaching some mathematics at the university.
During World War I, he worked on ballistics and developed a novel method for precisely locating enemy artillery. When a gun is fired, it initiates a spherical shock wave but the projectile also generates a conical wave. By using the sound of distant guns to compare the two waves, Escaglon was able to make accurate predictions of gun locations.
After the armistice in 1919, Esclangon became director of the Strasbourg Observatory and professor of astronomy at the university the following year. In 1929, he was appointed director of the Paris Observatory and of the International Time Bureau, and elected to the Bureau des Longitudes in 1932. He is perhaps best remembered for initiating in 1933 the first speaking clock service, reportedly to relieve the observatory staff from the numerous telephone calls requesting the exact time. He was elected to the Académie des Sciences in 1939.
Esclangon was the President of the Société astronomique de France (SAF), the French astronomical society, from 1933–1935. In 1935, he received the Prix Jules Janssen, the socie
|
https://en.wikipedia.org/wiki/Computer%20science%20and%20engineering
|
Computer science and engineering (CSE) is an academic program at many universities which comprises computer science classes (e.g. data structures and algorithms) and computer engineering classes (e.g computer architecture). There is no clear division in computing between science and engineering, just like in the field of materials science and engineering. CSE is also a term often used in Europe to translate the name of engineering informatics academic programs. It is offered in both undergraduate as well postgraduate with specializations.
Academic courses
Academic programs vary between colleges, but typically include a combination of topics in computer science, computer engineering, and electrical engineering. Undergraduate courses usually include programming, algorithms and data structures, computer architecture, operating systems, computer networks, parallel computing, embedded systems, algorithms design, circuit analysis and electronics, digital logic and processor design, computer graphics, scientific computing, software engineering, database systems, digital signal processing, virtualization, computer simulations and games programming. CSE programs also include core subjects of theoretical computer science such as theory of computation, numerical methods, machine learning, programming theory and paradigms. Modern academic programs also cover emerging computing fields like image processing, data science, robotics, bio-inspired computing, computational biology, autonomic
|
https://en.wikipedia.org/wiki/University%20of%20Beira%20Interior
|
The University of Beira Interior (UBI; Portuguese: ) is a public university located in the city of Covilhã, Portugal. It was created in 1979, and has about 6,879 students distributed across a multiplicity of graduation courses, awarding all academic degrees in fields ranging from medicine, biochemistry, biomedical sciences and industrial design to aeronautical engineering, fashion design, mathematics, economics and philosophy. The university is named after the historical Beira region, meaning , the most interior area of Beira, mainly composed by the district of Guarda and the district of Castelo Branco, in today's Centro region.
History
In August 1973, following a major change in the national higher education system, the government established a polytechnical institution in Covilhã, the Polytechnic Institute of Covilhã (IPC - Instituto Politécnico da Covilhã), which was the first higher education institution in the city. Over the years, the IPC facilities, as well as the enrolment and staff, never ceased to grow. This growth and the region's needs, led the IPC to a remarkable level of achievements that granted it, in 1979, to be promoted, by the Portuguese Ministry of Education, to a higher institutional level, university institute. Seven years later, in 1986, the University Institute of Beira Interior was granted full university status and renamed University of Beira Interior ().
The first rector was Professor Cândido Manuel Passos Morgado, from August 21, 1980 until Janu
|
https://en.wikipedia.org/wiki/Dan%20Grimaldi
|
Dan Grimaldi (born March 7, 1946) is an American actor and mathematics professor who is known for his roles as twins Philly and Patsy Parisi on the HBO television series The Sopranos, various characters on Law & Order (1991-2001), Don't Go in the House (1979), The Junkman (1983), Men of Respect (1990), and The Yards (2000).
Education
Grimaldi has a bachelor's degree in mathematics from Fordham University, a master's degree in operations research from New York University, and a PhD in data processing from the City University of New York, and teaches in the Department of Mathematics and Computer Science at Kingsborough Community College in Brooklyn, New York.
Career
In addition to his role on The Sopranos, he has also had some minor film credits, most notably as mother-fixated pyromaniac Donny Kohler in the 1980 slasher film Don't Go in the House, and some guest TV appearances, including several episodes on Law & Order as well as appearing in 2011 as Tommy Barrone Sr. in "Moonlighting", the 9th episode of the 2nd season of the CBS show Blue Bloods. He appeared as an executive in the 2000 film The Yards and Grimaldi also voices "Frank" for the video game Mafia.
Filmography
Film
Television
Video games
References
External links
HBO.com
1946 births
Living people
American male television actors
American male voice actors
CUNY Graduate Center alumni
Fordham University alumni
American people of Italian descent
Mathematics educators
Male actors from New York City
New York Uni
|
https://en.wikipedia.org/wiki/Jo%C5%BEef%20Stefan%20Institute
|
The Jožef Stefan Institute (IJS, JSI) () is the largest research institute in Slovenia. The main research areas are physics, chemistry, molecular biology, biotechnology, information technologies, reactor physics, energy and environment. At the beginning of 2013 the institute had 962 employees, of whom 404 were PhD scientists.
The mission of the Jožef Stefan Institute is the accumulation and dissemination of knowledge at the frontiers of natural science and technology for the benefit of society at large through the pursuit of education, learning, research, and development of high technology at the highest international levels of excellence.
History
The institute was founded by the State Security Administration (Yugoslavia) in 1949 for atomic weapons research. Initially, the Vinča Nuclear Institute in Belgrade was established in 1948, followed by the Ruđer Bošković Institute in Zagreb in 1950 and the Jožef Stefan Institute as an Institute for Physics in the Slovenian Academy of Sciences and Arts. It is named after the distinguished 19th century physicist Josef Stefan (), best known for his work on the Stefan–Boltzmann law of black-body radiation.
IJS is involved in a wide variety of fields of scientific and economic interest. After close to 60 years of scientific achievement, the institute has become part of the image of Slovenia.
Over the last 60 years it has created a number of important institutions, such as the University of Nova Gorica, the Jožef Stefan International P
|
https://en.wikipedia.org/wiki/Submanifold
|
In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions.
Formal definition
In the following we assume all manifolds are differentiable manifolds of class Cr for a fixed , and all morphisms are differentiable of class Cr.
Immersed submanifolds
An immersed submanifold of a manifold M is the image S of an immersion map ; in general this image will not be a submanifold as a subset, and an immersion map need not even be injective (one-to-one) – it can have self-intersections.
More narrowly, one can require that the map be an injection (one-to-one), in which we call it an injective immersion, and define an immersed submanifold to be the image subset S together with a topology and differential structure such that S is a manifold and the inclusion f is a diffeomorphism: this is just the topology on N, which in general will not agree with the subset topology: in general the subset S is not a submanifold of M, in the subset topology.
Given any injective immersion the image of N in M can be uniquely given the structure of an immersed submanifold so that is a diffeomorphism. It follows that immersed submanifolds are precisely the images of injective immersions.
The submanifold topology on an immersed submanifold need not be
|
https://en.wikipedia.org/wiki/Codimension
|
In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.
For affine and projective algebraic varieties, the codimension equals the height of the defining ideal. For this reason, the height of an ideal is often called its codimension.
The dual concept is relative dimension.
Definition
Codimension is a relative concept: it is only defined for one object inside another. There is no “codimension of a vector space (in isolation)”, only the codimension of a vector subspace.
If W is a linear subspace of a finite-dimensional vector space V, then the codimension of W in V is the difference between the dimensions:
It is the complement of the dimension of W, in that, with the dimension of W, it adds up to the dimension of the ambient space V:
Similarly, if N is a submanifold or subvariety in M, then the codimension of N in M is
Just as the dimension of a submanifold is the dimension of the tangent bundle (the number of dimensions that you can move on the submanifold), the codimension is the dimension of the normal bundle (the number of dimensions you can move off the submanifold).
More generally, if W is a linear subspace of a (possibly infinite dimensional) vector space V then the codimension of W in V is the dimension (possibly infinite) of the quotient space V/W, which is more abstractly known as the cokernel of the inclusion. For finite-dimensional vector space
|
https://en.wikipedia.org/wiki/Singular%20perturbation
|
In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero. More precisely, the solution cannot be uniformly approximated by an asymptotic expansion
as . Here is the small parameter of the problem and are a sequence of functions of of increasing order, such as . This is in contrast to regular perturbation problems, for which a uniform approximation of this form can be obtained. Singularly perturbed problems are generally characterized by dynamics operating on multiple scales. Several classes of singular perturbations are outlined below.
The term "singular perturbation" was
coined in the 1940s by Kurt Otto Friedrichs and Wolfgang R. Wasow.
Methods of analysis
A perturbed problem whose solution can be approximated on the whole problem domain, whether space or time, by a single asymptotic expansion has a regular perturbation. Most often in applications, an acceptable approximation to a regularly perturbed problem is found by simply replacing the small parameter by zero everywhere in the problem statement. This corresponds to taking only the first term of the expansion, yielding an approximation that converges, perhaps slowly, to the true solution as decreases. The solution to a singularly perturbed problem cannot be approximated in this way: As seen in the examples below, a singular perturbation generally occurs when a problem's small parameter multiplies its highest operat
|
https://en.wikipedia.org/wiki/Expander
|
Expander may refer to:
Dynamic range compression operated in reverse
Part of the process of signal compression
Part of the process of companding
A component used to connect SCSI computer data storage, devices together
Turboexpander, a turbine for high-pressure gas
Expander graph, a sparse graph used in the combinatorics branch of mathematics
StuffIt Expander, a computer file decompressor software utility
Micro Expander, also known as the Expander, an 8-bit S-100 microcomputer released in 1981
"Expander" (song), a 1994 song by The Future Sound of London
Orthodontic expander, a device to widen the upper jaw
Disclosure widget, a widget that hides non-essential settings or information, also known as an expander
See also
Xpander (disambiguation)
|
https://en.wikipedia.org/wiki/Locking
|
Locking may refer to:
Locking (computer science)
Locking, Somerset, a village and civil parish in the United Kingdom
RAF Locking, a former Royal Air Force base
Locking Castle, a former castle
Brian Locking (born 1938), rock guitarist
Norm Locking (1911–1995), National Hockey League player
Locking (dance), a style of funk dance invented in the early 1970s
Prevention of a screw thread from turning when undesired
See also
Lockin (disambiguation)
Lock (disambiguation)
|
https://en.wikipedia.org/wiki/Density%20of%20states
|
In solid-state physics and condensed matter physics, the density of states (DOS) of a system describes the number of modes per unit frequency range. The density of states is defined as where is the number of states in the system of volume whose energies lie in the range from to . It is mathematically represented as a distribution by a probability density function, and it is generally an average over the space and time domains of the various states occupied by the system. The density of states is directly related to the dispersion relations of the properties of the system. High DOS at a specific energy level means that many states are available for occupation.
Generally, the density of states of matter is continuous. In isolated systems however, such as atoms or molecules in the gas phase, the density distribution is discrete, like a spectral density. Local variations, most often due to distortions of the original system, are often referred to as local densities of states (LDOSs).
Introduction
In quantum mechanical systems, waves, or wave-like particles, can occupy modes or states with wavelengths and propagation directions dictated by the system. For example, in some systems, the interatomic spacing and the atomic charge of a material might allow only electrons of certain wavelengths to exist. In other systems, the crystalline structure of a material might allow waves to propagate in one direction, while suppressing wave propagation in another direction. Often, only sp
|
https://en.wikipedia.org/wiki/W.%20Richard%20Stevens
|
William Richard (Rich) Stevens (February 5, 1951September 1, 1999) was a Northern Rhodesia–born American author of computer science books, in particular books on Unix and TCP/IP.
Biography
Richard Stevens was born in 1951 in Luanshya, Northern Rhodesia (now Zambia), where his father worked for the copper industry. The family later moved to Salt Lake City, Utah, Hurley, New Mexico, Washington, D.C., and Phalaborwa, South Africa. Stevens attended Fishburne Military School in Waynesboro, Virginia. He received a bachelor's degree in aerospace engineering from the University of Michigan in 1973 and both a master's degree (in 1978) and PhD (in 1982) in systems engineering from the University of Arizona. He moved to Tucson in 1975 where he was employed at Kitt Peak National Observatory as a computer programmer until 1982. From 1982 until 1990 he was Vice President of Computing Services at Health Systems International in New Haven, Connecticut. Stevens moved back to Tucson in 1990 where he pursued his career as an author and consultant. He was also an avid pilot and a part-time flight instructor during the 1970s.
Stevens died in 1999, at the age of 48. In 2000, he was posthumously awarded the USENIX Lifetime Achievement Award.
Books
1990 – UNIX Network Programming –
1992 – Advanced Programming in the UNIX Environment –
1994 – TCP/IP Illustrated, Volume 1: The Protocols –
1995 – TCP/IP Illustrated, Volume 2: The Implementation (with Gary R. Wright) –
1996 – TCP/IP Illust
|
https://en.wikipedia.org/wiki/Cubic%20surface
|
In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine space, and so cubic surfaces are generally considered in projective 3-space . The theory also becomes more uniform by focusing on surfaces over the complex numbers rather than the real numbers; note that a complex surface has real dimension 4. A simple example is the Fermat cubic surface
in . Many properties of cubic surfaces hold more generally for del Pezzo surfaces.
Rationality of cubic surfaces
A central feature of smooth cubic surfaces X over an algebraically closed field is that they are all rational, as shown by Alfred Clebsch in 1866. That is, there is a one-to-one correspondence defined by rational functions between the projective plane minus a lower-dimensional subset and X minus a lower-dimensional subset. More generally, every irreducible cubic surface (possibly singular) over an algebraically closed field is rational unless it is the projective cone over a cubic curve. In this respect, cubic surfaces are much simpler than smooth surfaces of degree at least 4 in , which are never rational. In characteristic zero, smooth surfaces of degree at least 4 in are not even uniruled.
More strongly, Clebsch showed that every smooth cubic surface in over an algebraically closed field is isomorphic to the blow-up of at
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.