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Bott Generator
Bott is an English and German surname. Notable people with the surname include: *Catherine Bott, English soprano * Charlie Bott, English rugby player * François Bott (born 1935) * John Bott *Leon Bott, Australian rugby league footballer * Leonidas Bott (1889–1969), Australian cricketer *Lloyd Bott (1917–2004), senior Australian public servant *Mark Bott, English cricketer * Markus Bott (born 1962), German boxer *Martin Bott, English geophysicist * Nina Bott (born 1978), German actress * Randy L. Bott *Raoul Bott, mathematician *Richard Bott *Violet Elizabeth Bott the character in a Richmal Crompton novel. * Wilf Bott See also *Atiyah–Bott fixed-point theorem *Borel–Weil–Bott theorem *Bott periodicity theorem *Bott residue formula In mathematics, the Bott residue formula, introduced by , describes a sum over the fixed points of a holomorphic vector field of a compact complex manifold. Statement If ''v'' is a holomorphic vector field on a compact complex manifold ''M' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Language
English is a West Germanic language of the Indo-European language family, with its earliest forms spoken by the inhabitants of early medieval England. It is named after the Angles, one of the ancient Germanic peoples that migrated to the island of Great Britain. Existing on a dialect continuum with Scots, and then closest related to the Low Saxon and Frisian languages, English is genealogically West Germanic. However, its vocabulary is also distinctively influenced by dialects of France (about 29% of Modern English words) and Latin (also about 29%), plus some grammar and a small amount of core vocabulary influenced by Old Norse (a North Germanic language). Speakers of English are called Anglophones. The earliest forms of English, collectively known as Old English, evolved from a group of West Germanic (Ingvaeonic) dialects brought to Great Britain by Anglo-Saxon settlers in the 5th century and further mutated by Norse-speaking Viking settlers starting in the 8th and 9th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randy L
Randy is a given name, popular in the United States and Canada. It is primarily a masculine name. It was originally derived from the names Randall, Randolf, Randolph, as well as Bertrand and Andrew, and may be a short form (hypocorism) of them. ''Randi'' is approximately the feminine equivalent of Randy. People with the given name A *Randy Abbey (born 1974), Ghanaian media personality *Randy Adler (??–2016), American bishop *Randy Albelda (born 1955), American economist * Randy Allen (other), multiple people *Randy Ambrosie (born 1963), Canadian sports executive *Randy Anderson (1959–2002), American wrestling referee *Randy Angst, American politician *Randy Armstrong (other), multiple people *Randy Arozarena (born 1995), Cuban baseball player *Randy Asadoor (born 1962), American baseball player *Randy Atcher (1918–2002), American television personality *Randy Avent, American electrical engineer *Randy Avon (born 1940), American politician *Randy Awre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bot (other)
Bot may refer to: Sciences Computing and technology * Chatbot, a computer program that converses in natural language * Internet bot, a software application that runs automated tasks (scripts) over the Internet **a Spambot, an internet bot designed to assist in the sending of spam * Internet Relay Chat bot, a set of scripts or an independent program that connects to Internet Relay Chat as a client * Robot, or "bot", a mechanical device that can perform physical tasks * Social bot, a type of chatbot that is employed in social media networks to automatically generate messages **Twitter bot, a program used to produce automated posts on the Twitter microblogging service * Trading bot, a program in an Automated trading system that is linked to an exchange or broker that automates trading using algorithms, there are trading bot providers such as HaasOnline, Cryptohopper, and MetaTrader 4 * Video game bot, a computer-controlled player or opponent * Wikipedia bot, an internet bot which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bott Residue Formula
In mathematics, the Bott residue formula, introduced by , describes a sum over the fixed points of a holomorphic vector field of a compact complex manifold. Statement If ''v'' is a holomorphic vector field on a compact complex manifold ''M'', then : \sum_\frac = \int_M P(i\Theta/2\pi) where *The sum is over the fixed points ''p'' of the vector field ''v'' *The linear transformation ''A''''p'' is the action induced by ''v'' on the holomorphic tangent space at ''p'' *''P'' is an invariant polynomial function of matrices of degree dim(''M'') *Θ is a curvature matrix of the holomorphic tangent bundle See also *Atiyah–Bott fixed-point theorem * Holomorphic Lefschetz fixed-point formula References * *{{Citation , last1=Griffiths , first1=Phillip , author1-link=Phillip Griffiths , last2=Harris , first2=Joseph , author2-link=Joe Harris (mathematician) , title=Principles of algebraic geometry , publisher=John Wiley & Sons John Wiley & Sons, Inc., commonly known as Wile ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bott Periodicity Theorem
In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by , which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres. Bott periodicity can be formulated in numerous ways, with the periodicity in question always appearing as a period-2 phenomenon, with respect to dimension, for the theory associated to the unitary group. See for example topological K-theory. There are corresponding period-8 phenomena for the matching theories, (real) KO-theory and ( quaternionic) KSp-theory, associated to the real orthogonal group and the quaternionic symplectic group, respectively. The J-homomorphism is a homomorphism from the homotopy groups of orthogonal groups to stable homotopy groups of spheres, which causes the period 8 Bott periodicity to be visible in the stable homotopy groups of spheres. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borel–Weil–Bott Theorem
In mathematics, the Borel–Weil–Bott theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can be obtained from holomorphic sections of certain complex vector bundles, and, more generally, from higher sheaf cohomology groups associated to such bundles. It is built on the earlier Borel–Weil theorem of Armand Borel and André Weil, dealing just with the space of sections (the zeroth cohomology group), the extension to higher cohomology groups being provided by Raoul Bott. One can equivalently, through Serre's GAGA, view this as a result in complex algebraic geometry in the Zariski topology. Formulation Let be a semisimple Lie group or algebraic group over \mathbb C, and fix a maximal torus along with a Borel subgroup which contains . Let be an integral weight of ; defines in a natural way a one-dimensional representation of , by pulling back the representation on , where is the unipotent radical of . Since we can th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atiyah–Bott Fixed-point Theorem
In mathematics, the Atiyah–Bott fixed-point theorem, proven by Michael Atiyah and Raoul Bott in the 1960s, is a general form of the Lefschetz fixed-point theorem for smooth manifolds ''M'', which uses an elliptic complex on ''M''. This is a system of elliptic differential operators on vector bundles, generalizing the de Rham complex constructed from smooth differential forms which appears in the original Lefschetz fixed-point theorem. Formulation The idea is to find the correct replacement for the Lefschetz number, which in the classical result is an integer counting the correct contribution of a fixed point of a smooth mapping f\colon M \to M. Intuitively, the fixed points are the points of intersection of the graph of ''f'' with the diagonal (graph of the identity mapping) in M\times M, and the Lefschetz number thereby becomes an intersection number. The Atiyah–Bott theorem is an equation in which the LHS must be the outcome of a global topological (homological) calcul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilf Bott
Wilfred Bott (25 April 1907 – July 1992) was an English professional footballer who played as a left winger in the Football League. Career Born in Featherstone, Yorkshire, to parents Frederick and Harriet, Bott played for Edlington Colliery Welfare before moving to Football League side Doncaster Rovers in 1927. In his time at Doncaster he scored 33 goals in 120 league and cup games, his last season being the most successful with 17 goals in 28 games including two hat−tricks within three games. His performances brought the attentions of other teams and led to his transfer for a reported "substantial fee" to First Division Huddersfield Town towards the end of the 1930−31 season. Following a very successful period at Huddersfield, Bott went on to have spells at Newcastle United, Queens Park Rangers, Colchester United and Lancaster Town. Honours Club ; Huddersfield Town * Football League First Division The Football League First Division was a division of the Footba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richmal Crompton
Richmal Crompton Lamburn (15 November 1890 – 11 January 1969) was a popular English writer, best known for her ''Just William'' series of books, humorous short stories, and to a lesser extent adult fiction books. Life Richmal Crompton Lamburn was born in Bury, Lancashire, the second child of the Rev. Edward John Sewell Lamburn, a Classics master at Bury Grammar School and his wife Clara (née Crompton). Her brother, John Battersby Crompton Lamburn, also became a writer, remembered under the name John Lambourne for his fantasy novel ''The Kingdom That Was'' (1931) and under the name "John Crompton" for his books on natural history. Richmal Crompton attended St Elphin's Boarding School for the daughters of the clergy, originally based in Warrington, Lancashire. She later moved with the school to a new location in Darley Dale, near Matlock, Derbyshire in 1904. In order to further her chosen career as a schoolteacher, she won a scholarship to Royal Holloway College, part of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Just William
''Just William'' is the first book of children's short stories about the young school boy William Brown, written by Richmal Crompton, and published in 1922. The book was the first in the series of William Brown books which was the basis for numerous television series, films and radio adaptations. ''Just William'' is also sometimes used as a title for the series of books as a whole, and is also the name of various television, film and radio adaptations of the books. The William stories first appeared in ''Home'' magazine and ''Happy Mag''. Short stories The book contains the following short stories: * William Goes to the Pictures – William's aunt gives him a shilling, so he buys sweets and goes to the cinema. On his way home he is obsessed with acting out what he has seen. * William the Intruder – William steals the attentions of his brother's new crush. * William Below Stairs – William runs away from home after reading a book about a boy who ran away and made a fortune ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Bott
Richard Bott (born 1968) is a minister of the United Church of Canada who served as the 43rd Moderator of that church from 2018 to 2022. Early life and education Bott was born in Marathon, Ontario and grew up there. Following graduation from high school, he attended University of Ottawa, where he earned his Bachelor of Social Sciences degree in 1990. He then earned his Master of Divinity (M.Div.) degree from Queen's University in 1994. Ministry Following graduation, Bott was ordained as a minister of the United Church. Over the next 24 years he served at five churches in Ontario and British Columbia. During that time, he earned a Diploma in Stewardship Studies from Queen's Theological College (1996), a Certificate in Dispute Resolution from Laurentian University (1998) and a Doctor of Ministry from Ashland Theological Seminary (2003). In 2000, Bott also became a liturgical writer, publishing articles, prayers and liturgy in a variety of Christian publications. Moderat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raoul Bott
Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem. Early life Bott was born in Budapest, Hungary, the son of Margit Kovács and Rudolph Bott. His father was of Austrian descent, and his mother was of Hungarian Jewish descent; Bott was raised a Catholic by his mother and stepfather. Bott grew up in Czechoslovakia and spent his working life in the United States. His family emigrated to Canada in 1938, and subsequently he served in the Canadian Army in Europe during World War II. Career Bott later went to college at McGill University in Montreal, where he studied electrical engineering. He then earned a PhD in mathematics from Carnegie Mellon University in Pittsburgh in 1949. His thesis, titled ''Electrical Network Theory'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
