Split (1)

train · 40.2k rows

source stringlengths 31 168	text stringlengths 51 3k
https://en.wikipedia.org/wiki/Franklin%20P.%20Peterson	Franklin Paul Peterson (1930–2000) was an American mathematician specializing in algebraic topology. He was a professor of mathematics at the Massachusetts Institute of Technology. Life and career Peterson was born in Aurora, Illinois, on August 27, 1930, the older of two brothers. His father died when he was young, and he was raised by his mother and uncle. He attended Northwestern University, graduating in 1952, and earned his Ph.D. in 1955 from Princeton University under the supervision of Norman Steenrod. After postdoctoral studies at Princeton, he joined the MIT faculty in 1958. Peterson edited the Transactions of the American Mathematical Society from 1966 to 1970. He also served for many years as treasurer of the AMS; in that role he played a key role in resolving tensions between the dual directors of the society as it was then structured, and worked to build up a large reserve fund for the society. Peterson married Marilyn Rutz in 1959. He died of a stroke on September 1, 2000, near Washington, DC. Contributions Peterson's early research used cohomology to study homotopy equivalence. Later, he did important work on the properties of loop spaces. The Peterson–Stein formula is named after him, after he wrote about it with Norman Stein in 1960. He also introduced the Brown–Peterson cohomology with Edgar H. Brown in 1966. He advised over 20 doctoral students (different sources give different numbers, in part because Robert E. Mosher, whom Peterson considered his first student, had a different official advisor) and has over 100 academic descendants. Selected publications . . . . Part II (with Frederick R. Cohen), pp. 41–51. References 1930 births 2000 deaths 20th-century American mathematicians Northwestern University alumni Princeton University alumni Massachusetts Institute of Technology School of Science faculty Topologists Mathematicians from Illinois People from Aurora, Illinois
https://en.wikipedia.org/wiki/Lucas%20Coelho	Lucas Heinzen Coelho (born 20 July 1994) is a Brazilian professional footballer who plays as a forward for Boa Esporte. Career statistics References External links Lucas Coelho profile. Portal Oficial do Grêmio. Lucas Coelho profile. Goal. Lucas Coelho at ZeroZero 1994 births Living people People from Lages Brazilian men's footballers Men's association football forwards Campeonato Brasileiro Série A players Campeonato Brasileiro Série B players Grêmio Foot-Ball Porto Alegrense players Goiás Esporte Clube players Avaí FC players ABC Futebol Clube players Criciúma Esporte Clube players Cianorte Futebol Clube players Esporte Clube Cruzeiro players Footballers from Santa Catarina (state)
https://en.wikipedia.org/wiki/2006%E2%80%9307%20PFC%20Levski%20Sofia%20season	The 2006–07 season was Levski Sofia's 85th season in the First League. This article shows player statistics and all matches (official and friendly) that the club has played during the 2006–07 season. First-team squad Squad at end of season Left club during season Competitions Bulgarian Supercup A Group Table Results summary Results by round Fixtures and results Bulgarian Cup Champions League Second qualifying round Third qualifying round Group stage References External links 2006–07 Levski Sofia season PFC Levski Sofia seasons Levski Sofia Bulgarian football championship-winning seasons
https://en.wikipedia.org/wiki/Steric%205-cubes	In five-dimensional geometry, a steric 5-cube or (steric 5-demicube or sterihalf 5-cube) is a convex uniform 5-polytope. There are unique 4 steric forms of the 5-cube. Steric 5-cubes have half the vertices of stericated 5-cubes. Steric 5-cube Alternate names Steric penteract, runcinated demipenteract Small prismated hemipenteract (siphin) (Jonathan Bowers) Cartesian coordinates The Cartesian coordinates for the 80 vertices of a steric 5-cube centered at the origin are the permutations of (±1,±1,±1,±1,±3) with an odd number of plus signs. Images Related polytopes Stericantic 5-cube Alternate names Prismatotruncated hemipenteract (pithin) (Jonathan Bowers) Cartesian coordinates The Cartesian coordinates for the 480 vertices of a stericantic 5-cube centered at the origin are coordinate permutations: (±1,±1,±3,±3,±5) with an odd number of plus signs. Images Steriruncic 5-cube Alternate names Prismatorhombated hemipenteract (pirhin) (Jonathan Bowers) Cartesian coordinates The Cartesian coordinates for the 320 vertices of a steriruncic 5-cube centered at the origin are coordinate permutations: (±1,±1,±1,±3,±5) with an odd number of plus signs. Images Steriruncicantic 5-cube Alternate names Great prismated hemipenteract (giphin) (Jonathan Bowers) Cartesian coordinates The Cartesian coordinates for the 960 vertices of a steriruncicantic 5-cube centered at the origin are coordinate permutations: (±1,±1,±3,±5,±7) with an odd number of plus signs. Images Related polytopes This polytope is based on the 5-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family. There are 23 uniform polytera (uniform 5-polytope) that can be constructed from the D symmetry of the 5-demicube, of which are unique to this family, and 15 are shared within the 5-cube family. References Further reading External links Polytopes of Various Dimensions Multi-dimensional Glossary 5-polytopes
https://en.wikipedia.org/wiki/Walter%20%28footballer%2C%20born%201987%29	Walter Leandro Capeloza Artune (born 18 November 1987), simply known as Walter, is a Brazilian professional footballer who plays as a goalkeeper for Cuiabá. Career statistics Honours Corinthians Campeonato Brasileiro Série A: 2015, 2017 Recopa Sudamericana: 2013 Campeonato Paulista: 2017, 2018, 2019 Cuiabá Campeonato Mato-Grossense: 2021, 2022 References External links Player profile 1987 births Living people Footballers from São Paulo (state) Brazilian men's footballers Men's association football goalkeepers Campeonato Brasileiro Série A players Campeonato Brasileiro Série C players Campeonato Brasileiro Série D players Esporte Clube XV de Novembro (Jaú) players Iraty Sport Club players Rio Branco Sport Club players Londrina Esporte Clube players J. Malucelli Futebol players Sociedade Esportiva e Recreativa Caxias do Sul players Esporte Clube Novo Hamburgo players União Agrícola Barbarense Futebol Clube players Esporte Clube Noroeste players Sport Club Corinthians Paulista players Esporte Clube XV de Novembro (Piracicaba) players Cuiabá Esporte Clube players Sportspeople from Jaú
https://en.wikipedia.org/wiki/Thabo%20Qalinge	Thabo Qalinge (born 28 August 1991) is a South African soccer player who plays for AmaZulu F.C. in the Premier Soccer League. Career statistics References 1991 births Living people Soccer players from Soweto South African men's soccer players National First Division players South African Premier Division players SuperSport United F.C. players Mpumalanga Black Aces F.C. players Orlando Pirates F.C. players AmaZulu F.C. players Men's association football midfielders
https://en.wikipedia.org/wiki/Cantellated%2024-cell%20honeycomb	In four-dimensional Euclidean geometry, the cantellated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a cantellation of the regular 24-cell honeycomb, containing rectified tesseract, cantellated 24-cell, and tetrahedral prism cells. Alternate names Cantellated icositetrachoric tetracomb/honeycomb Small rhombated demitesseractic tetracom (sricot) Small prismatodisicositetrachoric tetracomb Related honeycombs See also Regular and uniform honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb References Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, p. 296, Table II: Regular honeycombs Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 112 o3o3x4o3x - sricot - O112 5-polytopes Honeycombs (geometry)
https://en.wikipedia.org/wiki/Cantitruncated%2024-cell%20honeycomb	In four-dimensional Euclidean geometry, the cantitruncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a cantitruncation of the regular 24-cell honeycomb, containing truncated tesseract, cantitruncated 24-cell, and tetrahedral prism cells. Alternate names Cantelltaed icositetrachoric tetracomb/honeycomb Great rhombated icositetrachoric tetracomb (gricot) Great prismatodisicositetrachoric tetracomb Related honeycombs See also Regular and uniform honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb References Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, p. 296, Table II: Regular honeycombs Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 114 o3o3x4x3x - gricot - O114 5-polytopes Honeycombs (geometry) Truncated tilings
https://en.wikipedia.org/wiki/Runcinated%2024-cell%20honeycomb	In four-dimensional Euclidean geometry, the runcinated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a runcination of the regular 24-cell honeycomb, containing runcinated 24-cell, 24-cell, octahedral prism, and 3-3 duoprism cells. Alternate names Runcinated icositetrachoric tetracomb/honeycomb Small prismated icositetrachoric tetracomb (spict) Small prismatotetracontaoctachoric tetracomb Related honeycombs See also Regular and uniform honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb References Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, p. 296, Table II: Regular honeycombs Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 115 o3x3o4o3x - spict - O115 5-polytopes Honeycombs (geometry)
https://en.wikipedia.org/wiki/Runcinated%2016-cell%20honeycomb	In four-dimensional Euclidean geometry, the runcinated 16-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a runcination of the regular 16-cell honeycomb, containing Rectified 24-cell, runcinated tesseract, cuboctahedral prism, and 3-3 duoprism cells. Alternate names Runcinated hexadecachoric tetracomb/honeycomb Small prismated demitesseractic tetracomb (spaht) Small disicositetrachoric tetracomb Related honeycombs See also Regular and uniform honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb References Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, p. 296, Table II: Regular honeycombs Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 122 x3o3o4x3o - spaht - O122 5-polytopes Honeycombs (geometry)
https://en.wikipedia.org/wiki/Stericated%2024-cell%20honeycomb	In four-dimensional Euclidean geometry, the stericated 24-cell honeycomb (or stericated 16-cell honeycomb) is a uniform space-filling honeycomb. It can be seen as a sterication of the regular 24-cell honeycomb, containing 24-cell, 16-cell, octahedral prism, tetrahedral prism, and 3-3 duoprism cells. Alternate names Stericated icositetrachoric/hexadecaachoric tetracomb/honeycomb Small cellated demitesseractic tetracomb (scicot) Related honeycombs See also Regular and uniform honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb References Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, p. 296, Table II: Regular honeycombs Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 121 (Wrongly named runcinated icositetrachoric honeycomb) x3o3o4o3x - scicot - O121 5-polytopes Honeycombs (geometry)
https://en.wikipedia.org/wiki/Bitruncated%2024-cell%20honeycomb	In four-dimensional Euclidean geometry, the bitruncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a bitruncation of the regular 24-cell honeycomb, constructed by truncated tesseract and bitruncated 24-cell cells. Alternate names Bitruncated icositetrachoric tetracomb/honeycomb Small tetracontaoctachoric tetracomb (baticot) Related honeycombs See also Regular and uniform honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb References Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, p. 296, Table II: Regular honeycombs Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 113 o3o3x4x3o - baticot - O113 o3o3x4o3x - sricot - O112 5-polytopes Honeycombs (geometry) Bitruncated tilings
https://en.wikipedia.org/wiki/Luca%20Amato	Luca Amato (born 24 August 1996, in Cologne) is a German motorcycle racer. Career statistics CEV Buckler Moto3 Championship Races by year (key) (Races in bold indicate pole position, races in italics indicate fastest lap) Grand Prix motorcycle racing By season By class Races by year External links 1996 births Living people German motorcycle racers Moto3 World Championship riders Sportspeople from Cologne
https://en.wikipedia.org/wiki/Neil%20Anderson%20%28Idaho%20politician%29	Neil Alan Anderson (born February 21, 1947) is a Republican Idaho State Representative since 2012 representing District 31 in the A seat. Education Anderson earned his associate degree in mathematics from Ricks College and his bachelor's degree in business from Idaho State University. Elections References External links Neil A. Anderson at the Idaho Legislature Campaign site Biography at Ballotpedia Financial information (state office) at the National Institute for Money in State Politics 1947 births Living people Brigham Young University–Idaho alumni Idaho State University alumni Republican Party members of the Idaho House of Representatives People from Blackfoot, Idaho People from Rexburg, Idaho 21st-century American politicians
https://en.wikipedia.org/wiki/David%20Cubillo	David García Cubillo (born 6 January 1978 in Madrid) is a Spanish retired footballer who played as a midfielder, and is a current manager. Managerial statistics References External links 1978 births Living people Footballers from Madrid Spanish men's footballers Men's association football midfielders La Liga players Segunda División players Segunda División B players Tercera División players Atlético Madrid B players Atlético Madrid footballers Xerez CD footballers Recreativo de Huelva players Getafe CF footballers Rayo Vallecano players CF Fuenlabrada footballers UB Conquense footballers Spanish football managers Segunda División B managers Marbella FC managers Hércules CF managers
https://en.wikipedia.org/wiki/Linear%20equation%20over%20a%20ring	In algebra, linear equations and systems of linear equations over a field are widely studied. "Over a field" means that the coefficients of the equations and the solutions that one is looking for belong to a given field, commonly the real or the complex numbers. This article is devoted to the same problems where "field" is replaced by "commutative ring", or, typically "Noetherian integral domain". In the case of a single equation, the problem splits in two parts. First, the ideal membership problem, which consists, given a non-homogeneous equation with and in a given ring , to decide if it has a solution with in , and, if any, to provide one. This amounts to decide if belongs to the ideal generated by the . The simplest instance of this problem is, for and , to decide if is a unit in . The syzygy problem consists, given elements in , to provide a system of generators of the module of the syzygies of that is a system of generators of the submodule of those elements in that are solutions of the homogeneous equation The simplest case, when amounts to find a system of generators of the annihilator of . Given a solution of the ideal membership problem, one obtains all the solutions by adding to it the elements of the module of syzygies. In other words, all the solutions are provided by the solution of these two partial problems. In the case of several equations, the same decomposition into subproblems occurs. The first problem becomes the submodule membership problem. The second one is also called the syzygy problem. A ring such that there are algorithms for the arithmetic operations (addition, subtraction, multiplication) and for the above problems may be called a computable ring, or effective ring. One may also say that linear algebra on the ring is effective. The article considers the main rings for which linear algebra is effective. Generalities To be able to solve the syzygy problem, it is necessary that the module of syzygies is finitely generated, because it is impossible to output an infinite list. Therefore, the problems considered here make sense only for a Noetherian ring, or at least a coherent ring. In fact, this article is restricted to Noetherian integral domains because of the following result. Given a Noetherian integral domain, if there are algorithms to solve the ideal membership problem and the syzygies problem for a single equation, then one may deduce from them algorithms for the similar problems concerning systems of equations. This theorem is useful to prove the existence of algorithms. However, in practice, the algorithms for the systems are designed directly. A field is an effective ring as soon one has algorithms for addition, subtraction, multiplication, and computation of multiplicative inverses. In fact, solving the submodule membership problem is what is commonly called solving the system, and solving the syzygy problem is the computation of the null space of the matrix of a system of linear equa
https://en.wikipedia.org/wiki/Bell%20triangle	In mathematics, the Bell triangle is a triangle of numbers analogous to Pascal's triangle, whose values count partitions of a set in which a given element is the largest singleton. It is named for its close connection to the Bell numbers, which may be found on both sides of the triangle, and which are in turn named after Eric Temple Bell. The Bell triangle has been discovered independently by multiple authors, beginning with and including also and , and for that reason has also been called Aitken's array or the Peirce triangle. Values Different sources give the same triangle in different orientations, some flipped from each other. In a format similar to that of Pascal's triangle, and in the order listed in the Online Encyclopedia of Integer Sequences, its first few rows are: 1 1 2 2 3 5 5 7 10 15 15 20 27 37 52 52 67 87 114 151 203 203 255 322 409 523 674 877 Construction The Bell triangle may be constructed by placing the number 1 in its first position. After that placement, the leftmost value in each row of the triangle is filled by copying the rightmost value in the previous row. The remaining positions in each row are filled by a rule very similar to that for Pascal's triangle: they are the sum of the two values to the left and upper left of the position. Thus, after the initial placement of the number 1 in the top row, it is the last position in its row and is copied to the leftmost position in the next row. The third value in the triangle, 2, is the sum of the two previous values above-left and left of it. As the last value in its row, the 2 is copied into the third row, and the process continues in the same way. Combinatorial interpretation The Bell numbers themselves, on the left and right sides of the triangle, count the number of ways of partitioning a finite set into subsets, or equivalently the number of equivalence relations on the set. provide the following combinatorial interpretation of each value in the triangle. Following Sun and Wu, let An,k denote the value that is k positions from the left in the nth row of the triangle, with the top of the triangle numbered as A1,1. Then An,k counts the number of partitions of the set {1, 2, ..., n + 1} in which the element k + 1 is the only element of its set and each higher-numbered element is in a set of more than one element. That is, k + 1 must be the largest singleton of the partition. For instance, the number 3 in the middle of the third row of the triangle would be labeled, in their notation, as A3,2, and counts the number of partitions of {1, 2, 3, 4} in which 3 is the largest singleton element. There are three such partitions: {1}, {2, 4}, {3} {1, 4}, {2}, {3} {1, 2, 4}, {3}. The remaining partitions of these four elements either do not have 3 in a set by itself, or they have a larger singleton set {4}, and in either case are not counte
https://en.wikipedia.org/wiki/Maria%20Magdalena%20Mathsdotter	Maria Magdalena Mathsdotter (21 March 1835 – 31 March 1873) was a Swedish Sami who in 1864 took the initiative to the foundation of schools for Sami children in Lapland. Life Mathsdotter was born 21 March 1835 in Fjällfjäll, Vilhelmina in Lapland. She came from a poor background with her father looking after reindeer during their migration back and forth from summer to winter. She attended school in very poor conditions in 1843 and 1844. In the winter of 1864, Maria Magdalena Mathsdotter traveled from her home in Åsele to Stockholm on skies and by foot to ask for an audience with the monarch. She arrived in February. She was given a meeting with both the monarch, Charles XV of Sweden, as well as with the Queen, Louise of the Netherlands, and the Queen dowager, Josephine of Leuchtenberg. Her purpose was to organize a new school boarding system for the Sami children. Previously, Sami children had been forced to learn Christianity and other legally mandatory subjects in schools long from home and their parents, since there were no schools for them in Lapland. This also had the consequence that their schooling was very shallow, as it often became but a short schooling under those circumstances. Her initiative was approved and a society, the so-called Femöresföreningen ("five penny association"), was founded to finance a school in Vilhelmina in 1865, which was to be the first of many. Her initiative was viewed upon as a virtuous wish for the Samis to be better educated within religion, and she was therefore officially celebrated as a role model. She was described as modest and humble, as she did not wish for her name to be made public. Mathsdotter made contact with a pastor from the French Reformed Church in Stockholm, Henri Roehrich, who assisted her. Her trip resulted in the establishment of two schools and orphanages. In 1866 she travelled again to Stockholm and although she did not again meet the King she wanted to meet Pastor Roehrich again. This time she was concerned that settlers were overriding the rights of the Sami in Wilhelmina. She was put in contact with Erik Viktor Almquist who was the local governor in Vasterbottens in northern Sweden.. He took up Mathsdotter's case and in 1871 the law was changed to establish better rights for the Sami people. The effort of Maria Mathsdotter created great attention also internationally, and she was portrayed in the press in Germany, Great Britain, France, The Netherlands and Switzerland, where new collections of funds for the schools were made. In France, the paper "La Laponie et Maria Mathsdotter" was printed. The Netherlands were particularly interested in contributing with funds, and Maria Mathsdotter was included in a contemporary dictionary of notable Swedish women. References Anteckningar om svenska qvinnor Sameskolor inom Åsele lappmark: Biografier Roehrich, H. (1866). Lappland och Maria Magdalena Mathsdotter. Stockholm. Libris 655207 Further reading Swedish Sámi people 1835 bi
https://en.wikipedia.org/wiki/Steritruncated%2016-cell%20honeycomb	In four-dimensional Euclidean geometry, the steritruncated 16-cell honeycomb is a uniform space-filling honeycomb, with runcinated 24-cell, truncated 16-cell, octahedral prism, 3-6 duoprism, and truncated tetrahedral prism cells. Alternate names Celliprismated icositetrachoric tetracomb (capicot) Great prismatotetracontaoctachoric tetracomb Related honeycombs See also Regular and uniform honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb References Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, p. 296, Table II: Regular honeycombs Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 121 (Wrongly named runcinated icositetrachoric honeycomb) x3x3o4o3x - capicot - O127 5-polytopes Honeycombs (geometry) Truncated tilings
https://en.wikipedia.org/wiki/Edinburgh%20Mathematical%20Notes	Edinburgh Mathematical Notes was a mathematics journal published from 1909 until 1961 by the Edinburgh Mathematical Society. The journal was originally named Mathematical Notes, with the subtitle A Review of Elementary Mathematics and Science. Its creation was the suggestion of George Alexander Gibson, a professor at University of Glasgow, who wished to remove the more elementary or pedagogical articles from the Proceedings of the Edinburgh Mathematical Society. Is founding editor was Peter Pinkerton, who at the time headed the mathematics department of George Watson's College and later became rector of the High School of Glasgow. 21 issues of the journal were published from 1909 to 1916. During World War I, the journal went on hiatus, resumed publishing for two issues in 1924 and 1925, and then it went on hiatus again until 1929. In 1939, it changed its name from Mathematical Notes to Edinburgh Mathematical Notes. In 1958 its issues began being published as issues of the Proceedings of the Edinburgh Mathematical Society, and after 1961 they became incorporated into a department of the Proceedings rather than being published separately. After 1967 it stopped appearing altogether. The archives of the journal are available online to subscribers through the Cambridge University Press. References Mathematics journals Publications established in 1909 Publications disestablished in 1961 1909 establishments in Scotland 1961 disestablishments in Scotland
https://en.wikipedia.org/wiki/Polling%20system	In queueing theory, a discipline within the mathematical theory of probability, a polling system or polling model is a system where a single server visits a set of queues in some order. The model has applications in computer networks and telecommunications, manufacturing and road traffic management. The term polling system was coined at least as early as 1968 and the earliest study of such a system in 1957 where a single repairman servicing machines in the British cotton industry was modelled. Typically it is assumed that the server visits the different queues in a cyclic manner. Exact results exist for waiting times, marginal queue lengths and joint queue lengths at polling epochs in certain models. Mean value analysis techniques can be applied to compute average quantities. In a fluid limit, where a very large number of small jobs arrive the individual nodes can be viewed to behave similarly to fluid queues (with a two state process). Model definition A group of n queues are served by a single server, typically in a cyclic order 1, 2, …, n, 1, …. New jobs arrive at queue i according to a Poisson process of rate λi and are served on a first-come, first-served basis with each job having a service time denoted by an independent and identically distributed random variables Si. The server chooses when to progress to the next node according to one of the following criteria: exhaustive service, where a node continues to receive service until the buffer is empty. gated service, where the node serves all traffic that was present at the instant that the server arrived and started serving, but subsequent arrivals during this service time must wait until the next server visit. limited service, where a maximum fixed number of jobs can be served in each visit by the server. If a queueing node is empty the server immediately moves to serve the next queueing node. The time taken to switch from serving node i − 1 and node i is denoted by the random variable di. Utilization Define ρi = λi E(Si) and write ρ = ρ1 + ρ2 + … + ρn. Then ρ is the long-run fraction of time the server spends attending to customers. Waiting time Expected waiting time For gated service, the expected waiting time at node i is and for exhaustive service where Ci is a random variable denoting the time between entries to node i and The variance of Ci is more complicated and a straightforward calculation requires solving n2 linear equations and n2 unknowns, however it is possible to compute from n equations. Heavy traffic The workload process can be approximated by a reflected Brownian motion in a heavily loaded and suitably scaled system if switching servers is immediate and a Bessel process when switching servers takes time. Applications Polling systems have been used to model Token Ring networks. External links Bibliography on polling models (papers published 1984–1993) by Hideaki Takagi References Queueing theory
https://en.wikipedia.org/wiki/Markov%20reward%20model	In probability theory, a Markov reward model or Markov reward process is a stochastic process which extends either a Markov chain or continuous-time Markov chain by adding a reward rate to each state. An additional variable records the reward accumulated up to the current time. Features of interest in the model include expected reward at a given time and expected time to accumulate a given reward. The model appears in Ronald A. Howard's book. The models are often studied in the context of Markov decision processes where a decision strategy can impact the rewards received. The Markov Reward Model Checker tool can be used to numerically compute transient and stationary properties of Markov reward models. Markov chain See Markov Chain See Markov chain Monte Carlo Continuous-time Markov chain The accumulated reward at a time t can be computed numerically over the time domain or by evaluating the linear hyperbolic system of equations which describe the accumulated reward using transform methods or finite difference methods. References Markov processes
https://en.wikipedia.org/wiki/Fluid%20limit	In queueing theory, a discipline within the mathematical theory of probability, a fluid limit, fluid approximation or fluid analysis of a stochastic model is a deterministic real-valued process which approximates the evolution of a given stochastic process, usually subject to some scaling or limiting criteria. Fluid limits were first introduced by Thomas G. Kurtz publishing a law of large numbers and central limit theorem for Markov chains. It is known that a queueing network can be stable, but have an unstable fluid limit. References Queueing theory
https://en.wikipedia.org/wiki/Cleiton%20%28footballer%2C%20born%201979%29	Cleiton Oliveira Pinto (born 21 December 1979), commonly known as Cleiton, is a retired Brazilian footballer who played as a midfielder. Azerbaijan Career statistics References External links Men's association football midfielders 1979 births Living people Shamakhi FK players Expatriate men's footballers in Azerbaijan Expatriate men's footballers in Portugal Brazilian expatriate men's footballers Brazilian expatriate sportspeople in Azerbaijan Brazilian men's footballers People from Barreiras Footballers from Bahia
https://en.wikipedia.org/wiki/2007%E2%80%9308%20PFC%20Levski%20Sofia%20season	The 2007–08 season is Levski Sofia's 86th season in the First League. This article shows player statistics and all matches (official and friendly) that the club has played during the 2007–08 season. Transfers Summer transfers In: Out: Winter transfers In: Out: Squad Competitions Bulgarian Supercup A Group Table Results summary Results by round Fixtures and results Bulgarian Cup UEFA Champions League Second qualifying round External links 2007–08 Levski Sofia season PFC Levski Sofia seasons Levski Sofia
https://en.wikipedia.org/wiki/Vyacheslav%20Kalashnikov%20Polishchuk	Vyacheslav Vitalievich Kalashnikov (born November 6, 1955) is a Russian mathematics professor and researcher currently working at the Tec de Monterrey, Monterrey Campus in Mexico. His work has been recognized by awards from the Ukrainian Academy of Sciences and the Central Economic Mathematical Institute of the Russian Academy of Sciences and is also a Level III member of Mexico’s Sistema Nacional de Investigadores. Biography He was born in Vladivostok, Russia and is married to mathematician Nataliya Kalashnykova. They have one daughter. Kalashnikov obtained his bachelors and masters in mathematics from the Novosibirsk State University in Novosibirsk, Siberia. He went on to obtain his doctorate here and at the Central Economic Mathematical Institute of the Russian Academy of Sciences in Moscow in mathematical cybernetics . He began his career as an associate professor at the Altai State University in Barnaul, Russia and in 1985 he became a researcher with the Mathematics Institute of the Russian Science Academy in Novosibirsk before moving onto the Sumy State University in Sumy, Ukraine in 1989. In 1995 he began working at the Central Economic Mathematical Instituteof the Russian Academy of Sciencesas head researcher. In 1998 he became the assistant director of the economics department of the University of Humanistic Sciences in Moscow. In 2002, he was invited to teach at the Universidad Autónoma de Nuevo León by CONACYT for a two-year contract. At the time, he spoke no Spanish but was able to teach classes in English. At the end of the contract, he decided to stay in Mexico because his wife found a teaching position and his daughter had begun medical school in Mexico. He has been a researcher and professor at Tec de Monterrey, Monterrey Campus since 2004, mostly doing research but also teaching problem solving methods for bi level programming. He now speaks Spanish fluently. Kalashnikov’s main research specialty is optimization, especially in complementarity and unequal variables. In 2002 he published the book “Complementarity, Equilibrium, Efficiency and Economics” in London. In addition he has authored or co-authored eight book chapters and published twenty five journal articles. He has presented his work in conferences in Mexico and abroad. In 1993 Kalashnikov received a medal from the Ukrainian Academy of Sciences and in 1997 an award from the Central Economic Mathematical Institute for his research work. Since 2015, he has had Level III membership in the Sistema Nacional de Investigadores (National Roster of Researchers) of Mexico. He also appears in the seventh edition of Five Hundred Leaders of Influence. He is a member of the Russian Association of Mathematical Programming, the American Mathematical Society and the Mexican Mathematical Society. References See also List of Monterrey Institute of Technology and Higher Education faculty Academic staff of the Monterrey Institute of Technology and Higher Education Living people 195
https://en.wikipedia.org/wiki/Bene%C5%A1%20method	In queueing theory, a discipline within the mathematical theory of probability, Beneš approach or Beneš method is a result for an exact or good approximation to the probability distribution of queue length. It was introduced by Václav E. Beneš in 1963. The method introduces a quantity referred to as the "virtual waiting time" to define the remaining workload in the queue at any time. This process is a step function which jumps upward with new arrivals to the system and otherwise is linear with negative gradient. By giving a relation for the distribution of unfinished work in terms of the excess work, the difference between arrivals and potential service capacity, it turns a time-dependent virtual waiting time problem into "an integral that, in principle, can be solved." References Queueing theory
https://en.wikipedia.org/wiki/Isotypical%20representation	In group theory, an isotypical, primary or factor representation of a group G is a unitary representation such that any two subrepresentations have equivalent sub-subrepresentations. This is related to the notion of a primary or factor representation of a C*-algebra, or to the factor for a von Neumann algebra: the representation of G is isotypical iff is a factor. This term more generally used in the context of semisimple modules. Property One of the interesting property of this notion lies in the fact that two isotypical representations are either quasi-equivalent or disjoint (in analogy with the fact that irreducible representations are either unitarily equivalent or disjoint). This can be understood through the correspondence between factor representations and minimal central projection (in a von Neumann algebra),. Two minimal central projections are then either equal or orthogonal. Example Let G be a compact group. A corollary of the Peter–Weyl theorem has that any unitary representation on a separable Hilbert space is a possibly infinite direct sum of finite dimensional irreducible representations. An isotypical representation is any direct sum of equivalent irreducible representations that appear (typically multiple times) in . References Bibliography Further reading Mackey "Lie Groups", Claudio Procesi, def. p. 156. "Group and symmetries", Yvette Kosmann-Schwarzbach Unitary representation theory Module theory
https://en.wikipedia.org/wiki/Mart%C3%ADn%20Rodr%C3%ADguez%20%28Chilean%20footballer%29	Martín Vladimir Rodríguez Torrejón (born 5 August 1994), nicknamed Tin Rodríguez, is a Chilean professional footballer who plays as a midfielder for Major League Soccer side D.C. United. Statistics International goals (Chile score listed first, score column indicates score after each Rodríguez goal) Club Huachipato Primera División (1): 2012–C Colo-Colo Primera División (1): 2015–A Copa Chile (1): 2016 References External links 1994 births Living people People from Chañaral Province Sportspeople from Atacama Region Chilean men's footballers Chile men's international footballers Chile men's under-20 international footballers Chilean expatriate men's footballers Huachipato FC footballers Colo-Colo footballers Cruz Azul footballers Club Universidad Nacional footballers Atlético Morelia players Mazatlán F.C. footballers Altay S.K. footballers D.C. United players Chilean Primera División players Liga MX players Süper Lig players Major League Soccer players Expatriate men's footballers in Mexico Chilean expatriate sportspeople in Mexico Expatriate men's footballers in Turkey Chilean expatriate sportspeople in Turkey Expatriate men's soccer players in the United States Chilean expatriate sportspeople in the United States Men's association football midfielders Men's association football forwards 2017 FIFA Confederations Cup players
https://en.wikipedia.org/wiki/David%20R.%20Morrison%20%28mathematician%29	David Robert Morrison (born July 29, 1955, in Oakland, California) is an American mathematician and theoretical physicist. He works on string theory and algebraic geometry, especially its relations to theoretical physics. Morrison studied at Princeton University with bachelor's degree in 1976 and at Harvard University with master's degree in 1977 and PhD under Phillip Griffiths in 1980 with thesis Semistable Degenerations of Enriques' and Hyperelliptic Surfaces. From 1980 he was an instructor and from 1982 an assistant professor at Princeton University and in the academic year 1984–1985 a visiting scientist at the University of Kyoto (as Fellow der Japan Society for the Promotion of Science). In 1986 he became an associate professor and in 1992 a professor of mathematics at Duke University and then in 1997 "James B. Duke Professor of Mathematics and Physics". While at Duke, Morrison advised multiple PhD students, including Antonella Grassi and Carina Curto. Since 2006 he has been a professor at the University of California, Santa Barbara. Although Morrison began his career as a mathematician in classical algebraic geometry, in his later career he has also been a string theorist. He works on the interfaces and mutual fertilization of algebraic geometry and string theory, especially mirror symmetry. In 1992–1993, 1996–1997 and 2000 he was at the Institute for Advanced Study. In 1995 he was a visiting professor at Cornell University, in 2005 at the Kavli Institute for Theoretical Physics, and in 2006 a research professor at MSRI. In 2015 he became a member of the American Academy of Arts and Sciences, in 2013 a Fellow of the American Mathematical Society, in 2005 a Senior Scholar at the Clay Mathematics Institute and in 2005–2006 a Guggenheim Fellow. He is a co-editor of selected works of his thesis supervisor Phillip Griffiths. Morrison was an invited speaker at the International Congress of Mathematicians in Zürich in 1994 (Mirror Symmetry and Moduli Spaces of Superconformal Field Theories). Works Quantum field theory, supersymmetry, and enumerative geometry. Freed, Daniel S. and Morrison, David R. and Singer, Isadore editors. IAS/Park City Mathematics Series, Vol. 11. American Mathematical Society Providence, RI viii+285. Papers from the Graduate Summer School of the IAS/Park City Mathematics Institute held in Princeton, NJ, 2001. (2006) Quantum fields and strings: a course for mathematicians. Vol. 1, 2. Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997. Edited by Pierre Deligne, Pavel Etingof, Daniel S. Freed, Lisa C. Jeffrey, David Kazhdan, John W. Morgan, David R. Morrison and Edward Witten. American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, 1999. Vol. 1: xxii+723 pp.; Vol. 2: pp. i--xxiv and 727–1501. , 81-06 (81T30 81Txx) Mirror symmetry and rational curves on quintic threefolds: A guide for mathematicians, J. Amer
https://en.wikipedia.org/wiki/Cauchy%E2%80%93Euler%20operator	In mathematics a Cauchy–Euler operator is a differential operator of the form for a polynomial p. It is named after Augustin-Louis Cauchy and Leonhard Euler. The simplest example is that in which p(x) = x, which has eigenvalues n = 0, 1, 2, 3, ... and corresponding eigenfunctions xn. See also Cauchy–Euler equation Sturm–Liouville theory References Differential operators
https://en.wikipedia.org/wiki/Uzi%20Vishne	Uzi Vishne is Professor of Mathematics at Bar Ilan University, Israel. His main interests are division algebras, Gelfand–Kirillov dimension, Coxeter groups, Artin groups, combinatorial group theory, monomial algebras, and arithmetic of algebraic groups. He's been the dean of Exact Sciences since October 2021. Selected publications External links http://u.cs.biu.ac.il/~vishne/ mathematics genealogy project Uzi Vishne user page at Hebrew Wikipedia Israeli mathematicians Academic staff of Bar-Ilan University Living people Group theorists Year of birth missing (living people)
https://en.wikipedia.org/wiki/Jason%20Rosenhouse	Jason Rosenhouse is an American author and professor of mathematics at James Madison University, where he was originally appointed an assistant professor in 2003. He became a full professor in 2014. His research focuses on algebraic graph theory, as well as analytic number theory. He ran the blog Evolution Blog at National Geographic's ScienceBlogs, where he frequently criticized creationism. In late 2016 he announced that he was abandoning the blogging format. He has contributed to the pro-evolution blog The Panda's Thumb, and has also contributed to the Huffington Post about topics such as the Higgs boson, in addition to creationism. Personal life Jason grew up in New Jersey. While in middle school and high school, he was a prolific chess player, attending both tournaments and chess camp. Education Rosenhouse has a bachelor's degree from Brown University in mathematics (1995), and an M.A. (1997) and PhD in mathematics (2000), both from Dartmouth College. His PhD thesis was entitled "Isoperimetric numbers of certain Cayley graphs associated to PSL (2, [zeta subscript n])". Career In 2000, Rosenhouse accepted a position at Kansas State University's mathematics department, at a time when the state school board was embroiled in a dispute over teaching creationism in schools. The school board's elimination of evolution from science textbooks introduced him to the creationist community, and he says that his time spent with them has convinced him that "the task of reconciling science with faith is far more difficult than is sometimes pretended." Selected publications Peer-reviewed papers Books The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser, Oxford University Press Among the Creationists: Dispatches from the Anti-Evolutionist Front Line, Oxford University Press Taking Sudoku Seriously: The Math Behind the World's Most Popular Pencil Puzzle, Oxford University Press Games for Your Mind: The History and Future of Logic Puzzles , Princeton University Press References James Madison University faculty Dartmouth College alumni Living people 21st-century American mathematicians American atheists Critics of creationism Year of birth missing (living people) Brown University alumni
https://en.wikipedia.org/wiki/Jo%20Boaler	Jo Boaler (born 18 February 1964) is a British education author and Nomellini-Olivier Professor of Mathematics Education at the Stanford Graduate School of Education. Boaler is involved in promoting reform mathematics and equitable mathematics classrooms. She is the co-founder and faculty director of youcubed a Stanford centre that offers free mathematics education resources to teachers, students and parents. She is the author of nine books, including Limitless Mind (2019), Mathematical Mindsets (2016), What's Math Got To Do With It? (2009) and The Elephant in the Classroom (2010), all written for teachers and parents with the goal of improving mathematics education in both the US and UK. Education and training Boaler received a Bachelors in Psychology from Liverpool University in 1985. Boaler then began her career as a secondary mathematics teacher in urban London secondary schools, including Haverstock School, Camden. After her early career in secondary mathematics education, Boaler received a master's degree in Mathematics Education from King's College London with distinction in 1991. She completed her PhD in mathematics education at the same university and won the award for best PhD in education from the British Educational Research Association in 1997. Academic career Early career During the early part of Boaler's career, she conducted longitudinal studies of students learning mathematics through different approaches. Her first three-year study in England was published as "Experiencing School Mathematics: Teaching Styles, Sex, and Setting." In 1998, Boaler became an Assistant Professor of Mathematics Education at Stanford University in the Graduate School of Education. She became an associate professor in 2000 and left as a full professor in 2006. From 2000 to 2004, Boaler served as the president of the International Organization of Women and Mathematics Education. In 2000, she was awarded a presidential Early Career Award from the National Science Foundation. The NSF funded study would come to be known as the Railside study. This was a longitudinal study across three schools in northern California. The goal of the study was to compare the impact of traditional math curriculum and the reform curriculum developed by Boaler. A key distinction between the two approaches was that the traditional approach allowed students to take algebra in 8th grade, whereas algebra was delayed until 9th grade in the reform curriculum. Preliminary findings for the study were released in 2005. The findings were promising and were used to support further reform efforts. Believing the preliminary results "too good to be true", Stanford mathematician R. James Milgram, CSULA professor Wayne Bishop, and statistician Paul Clopton investigated Boaler's claims and published a 20-page report writing that Boaler's claims were exaggerated. In 2005, Milgram formally charged Boaler with scientific misconduct with Stanford. Stanford's preliminary investigation concl
https://en.wikipedia.org/wiki/Margaret%20Rock	Margaret Alice Rock (7 July 1903 – 26 August 1983) was one of the 8000 women mathematicians who worked in Bletchley Park during World War II. With her maths skills and education, Rock was able to decode the Enigma Machine against the German Army. Her work during the war was classified by the Official Secrets Act 1939, so much of her work was not revealed during her lifetime. Early life Rock was born and raised in Hammersmith, London to parents of Frank Ernest Rock and Alice Margaret Simmonds. Rock attended Edmonton elementary and North Middlesex School. Rock's father served in the Royal Navy as a surgeon between 1894 and 1896 while her mother took care of her and her brother. Frank Rock would send letters to his children frequently, to stay in communication in 1914, just before World War I. In 1917, Margaret, her mother and brother settled in Portsmouth, London, after moving frequently for three years. Rock attended Portsmouth High School, an all female private boarding school. Her father died when HMS Laurentic sank off the coast of Ireland having struck two mines laid by a German U-boat. Rock was encouraged by the letters her late father wrote to her, telling her to keep up with her studies and to be successful in the future. Her brother, John Frank Rock, became a Lieutenant in the Royal Engineers. Education Rock passed the London General School Exam in June 1919. During high school, she received honours in the classes of French, mathematics, and music. Rock went to Bedford College, University of London, to earn a Bachelors of Arts Degree in 1921. After college, Rock was employed as a statistician by the National Association of Manufacturers (The Federation of British Industry). Rock predicted the economic market and how different businesses and companies would respond to the market. In her free time, Margaret and her brother would travel to different countries such as Italy, France, Switzerland, and Sri Lanka. World War II In the beginning of World War II, Rock and her mother evacuated London to Cranleigh, Surrey. Margaret quit her old job, wanting a career in a time when the woman's role was primarily to be the wife and stay-at-home mother. She was then recruited for a new job at Bletchley Park on 15 April 1940. She worked for Admiral Sir Hugh Sinclair, who was the Head of Government Code and Cypher School and Secret Intelligence Service. She trained and worked alongside mathematicians and professors to break and decode enemy messages with the Enigma machine. Margaret went to work for Alfred Dilwyn Knox, where Margaret worked closely with Mavis Lever on the same projects. While working for Dilwyn Knox she became the most senior cryptographer. Knox employed women, because he believed they had great skill with cryptography work. Margaret Rock on August 1940, was considered by Dilwyn Knox to be the 4th or 5th best in the whole Enigma staff. She specialized in German and Russian code breaking. Code breaking was used to verify which indiv
https://en.wikipedia.org/wiki/Florence%20Yeldham	Florence Annie Yeldham (30 October 1877 – 10 January 1945) was a British school teacher and historian of arithmetic. She supported the idea of following the history of mathematics as a motive to teach arithmetic. Early life and education Florence Yeldham was born at School House, Brightling, Battle, East Sussex, on 30 October 1877, the daughter of school teacher Thomas Yeldham, who later became a school inspector, and his wife, Elizabeth Ann Chesterfield. She was the second daughter and second of at least seven children. She was not originally from London but moved there from Sussex and studied in James Allen's Girls' School, Dulwich. James Allen's Girls' School awarded her an exhibition to go to Bedford College, University of London, from where she matriculated in 1895. Yeldham graduated with a BSc (division two) in 1900, having chosen papers in pure mathematics, experimental physics, and zoology. Whilst she is listed as having gained honours, which one would have expected, no details have been found. Career Although she did not enjoy a remarkable teaching career, Yeldham wrote books herself. She produced her first printed work in 1913. Her works include The Story of Reckoning in the Middle Ages, The Teaching of Arithmetic Through 400 Years, 1535–1935, A Study of Mathematical Methods in England to the Thirteenth Century and Percentage Tables. Her books were well regarded and included reference material which was not easily available. Yeldham fell victim to chronic arthritis, which made her final years uncomfortable. She died while staying at Metropolitan Convalescent Home, Walton-on-Thames, Surrey, where she spent the last six months of her life. References 1877 births 1945 deaths 19th-century British mathematicians 20th-century British mathematicians British non-fiction writers People from Brightling British women mathematicians People educated at James Allen's Girls' School Alumni of Bedford College, London 20th-century English women writers 20th-century English writers 19th-century English women writers 19th-century British writers 20th-century British women scientists Schoolteachers from Sussex 20th-century women mathematicians
https://en.wikipedia.org/wiki/Sphere%20packing%20in%20a%20cube	In geometry, sphere packing in a cube is a three-dimensional sphere packing problem with the objective of packing spheres inside a cube. It is the three-dimensional equivalent of the circle packing in a square problem in two dimensions. The problem consists of determining the optimal packing of a given number of spheres inside the cube. See also Packing problem Sphere packing in a cylinder References Packing problems Spheres Cubes
https://en.wikipedia.org/wiki/Andr%C3%A1s%20Farkas	András Farkas (born 3 December 1992) is a Hungarian professional footballer. Club statistics Updated to games played as of 18 November 2014. References External links HLSZ 1992 births Living people Footballers from Kecskemét Hungarian men's footballers Men's association football defenders Kecskeméti TE players Bajai LSE footballers Ceglédi VSE footballers Kazincbarcikai SC footballers Tiszakécske FC footballers Nemzeti Bajnokság I players Nemzeti Bajnokság II players
https://en.wikipedia.org/wiki/Alec%20Acton	Alec Edward Acton (1938–1994) was an English professional footballer who played in the Football League as a defender for Stockport County. Career statistics Source: References 1938 births 1994 deaths Footballers from Leicester English men's footballers Men's association football defenders Stoke City F.C. players Stockport County F.C. players English Football League players People from Harborough District Footballers from Leicestershire
https://en.wikipedia.org/wiki/Gerrit%20Bol	Gerrit Bol (May 29, 1906 in Amsterdam – February 21, 1989 in Freiburg) was a Dutch mathematician who specialized in geometry. He is known for introducing Bol loops in 1937, and Bol’s conjecture on sextactic points. Life Bol earned his PhD in 1928 at Leiden University under Willem van der Woude. In the 1930s, he worked at the University of Hamburg on the geometry of webs under Wilhelm Blaschke and later projective differential geometry. In 1931 he earned a habilitation. In 1933 Bol signed the Loyalty Oath of German Professors to Adolf Hitler and the National Socialist State. In 1942–1945 during World War II, Bol fought on the Dutch side, and was taken prisoner. On the authority of Blaschke, he was released. After the war, Bol became professor at the Albert-Ludwigs-University of Freiburg, until retirement there in 1971. Works References M. Barner, F. Flohr, Commemorating Gerrit Bol, Freiburg University leaves 104, 1989, pp. 10f. Hala Pflugfelder Orlik: Historical notes on loop theory, Commentationes Mathematicae Universitatis Carolinae 41, 2000, pp. 359–370 (online: cmuc0002.htm) External links 1906 births 1989 deaths 20th-century Dutch mathematicians Differential geometers Dutch expatriates in Germany Group theorists Leiden University alumni Scientists from Amsterdam Academic staff of the University of Freiburg
https://en.wikipedia.org/wiki/Plotly	Plotly is a technical computing company headquartered in Montreal, Quebec, that develops online data analytics and visualization tools. Plotly provides online graphing, analytics, and statistics tools for individuals and collaboration, as well as scientific graphing libraries for Python, R, MATLAB, Perl, Julia, Arduino, JavaScript and REST. History Plotly was founded by Alex Johnson, Jack Parmer, Chris Parmer, and Matthew Sundquist. The founders' backgrounds are in science, energy, and data analysis and visualization. Early employees include Christophe Viau, a Canadian software engineer and Ben Postlethwaite, a Canadian geophysicist. Plotly was named one of the Top 20 Hottest Innovative Companies in Canada by the Canadian Innovation Exchange. Plotly was featured in "startup row" at PyCon 2013, and sponsored the SciPy 2018 conference. Plotly raised $5.5 million during its Series A funding, led by MHS Capital, Siemens Venture Capital, Rho Ventures, Real Ventures, and Silicon Valley Bank. The Boston Globe and Washington Post newsrooms have produced data journalism using Plotly. In 2020, Plotly was named a Best Place to Work by the Canadian SME National Business Awards, and nominated as Business of the Year. Products Plotly offers open-source and enterprise products. Dash is an open-source Python, R, and Julia framework for building web-based analytic applications. Many specialized open-source Dash libraries exist that are tailored for building domain-specific Dash components and applications. Some examples are Dash DAQ, for building data acquisition GUIs to use with scientific instruments, and Dash Bio, which enables users to build custom chart types, sequence analysis tools, and 3D rendering tools for bioinformatics applications. Dash Enterprise is Plotly’s paid product for building, testing, deploying, managing and scaling Dash applications organization-wide. Chart Studio Cloud is a free, online tool for creating interactive graphs. It has a point-and-click graphical user interface for importing and analyzing data into a grid and using stats tools. Graphs can be embedded or downloaded. Chart Studio Enterprise is a paid product that allows teams to create, style, and share interactive graphs on a single platform. It offers expanded authentication and file export options, and does not limit sharing and viewing. Data visualization libraries Plotly.js is an open-source JavaScript library for creating graphs and powers Plotly.py for Python, as well as Plotly.R for R, MATLAB, Node.js, Julia, and Arduino and a REST API. Plotly can also be used to style interactive graphs with Jupyter notebook. Figure Converters which convert matplotlib, ggplot2, and IGOR Pro graphs into interactive, online graphs. Data visualization libraries Plotly provides a collection of supported chart types across several programming languages: Dash Dash is a Python framework built on top of React, a JavaScript library. But Dash also works for R, and most recently supports
https://en.wikipedia.org/wiki/Hee%20Oh	Hee Oh (, born 1969) is a South Korean mathematician who works in dynamical systems. She has made contributions to dynamics and its connections to number theory. She is a student of homogeneous dynamics and has worked extensively on counting and equidistribution for Apollonian circle packings, Sierpinski carpets and Schottky dances. She is currently the Abraham Robinson Professor of Mathematics at Yale University. Career She graduated with a bachelor's degree from Seoul National University in 1992 and obtained her Ph.D from Yale University in 1997 under the guidance of Gregory Margulis. She held several faculty positions, including ones at Princeton University, California Institute of Technology and Brown University, before joining the Department of Mathematics at Yale University as the first female tenured professor in Mathematics there.<ref>"Korean becomes Yale's 1st female math professor", The Chosun Ilbo, retrieved 2013-10-30</ref> She will serve as Vice President of the American Mathematical Society, February 1, 2021 – January 31, 2024. Honours Hee Oh was an invited speaker at the International Congress of Mathematicians in Hyderabad in 2010, and gave a joint invited address at the 2012 AMS-MAA Joint Mathematics Meeting. In 2012 she became an inaugural fellow of the American Mathematical Society. Since 2010, she has served on the scientific advisory board of the American Institute of Mathematics. She is the 2015 recipient of the Ruth Lyttle Satter Prize in Mathematics. She was named MSRI Simons Professor for 2014-2015. Selected publications with Laurent Clozel, Emmanuel Ullmo: Hecke operators and equidistribution of Hecke points, Inventiones mathematicae, vol. 144, 2001, pp. 327–351 Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants, Duke Mathematical Journal, vol. 113, 2002, pp. 133–192 with Alex Eskin, Shahar Mozes: On uniform exponential growth for linear groups, Inventiones mathematicae, vol. 160, 2005, pp. 1–30 Proceedings of International Congress of Mathematicians (2010): Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond'' with Alex Kontorovich: Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds, Journal of the American Mathematical Society, vol. 24, 2011, pp. 603–648 with Nimish Shah: The asymptotic distribution of circles in the orbits of Kleinian groups, Inventiones mathematicae, vol. 187, 2012, pp. 1–35 with Nimish Shah: Equidistribution and counting for orbits of geometrically finite hyperbolic groups, Journal of the American Mathematical Society, vol. 26, 2013, pp. 511–562 with Amir Mohammadi: Ergodicity of unipotent flows and Kleinian groups, Journal of the American Mathematical Society, vol. 28, 2015, pp. 531–577 with Dale Winter: Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of SL_2(Z), Journal of the American Mathematical
https://en.wikipedia.org/wiki/2005%E2%80%9306%20PFC%20Levski%20Sofia%20season	The 2005–06 season was Levski Sofia's 84th season in the First League. This article shows player statistics and all matches (official and friendly) that the club has played during the 2005–06 season. First-team squad Squad at end of season Left club during season Results Bulgarian Supercup A Group Table Results summary Results by round Fixtures and results Bulgarian Cup UEFA Cup Second qualifying round First round Group stage Round of 32 Round of 16 Quarter-finals References External links 2005–06 Levski Sofia season PFC Levski Sofia seasons Levski Sofia Bulgarian football championship-winning seasons
https://en.wikipedia.org/wiki/Luo%20Hongxian	Luo Hongxian (; 1504 – 1564) was a Ming dynasty Chinese cartographer. He also studied astronomy, geography, irrigation methods, military affairs and mathematics. After passing the Imperial Examinations with the rank of jinshi in 1529, Luo worked as a senior compiler at the Hanlin Academy. He was a student of the philosophies of the Neo-Confucian Wang Yangming. Hearing of raids by wokou pirates on China's south-eastern shores, he began collating cartographical information for the Ming government, spending three years in research. During this period, he discovered the Yutu (Terrestrial Map), an atlas of China created by Zhu Siben during the Yuan dynasty some 300 years earlier around 1320, which he adapted and expanded using Chinese measuring methods to create his Guang Yu Tu 廣與圖 (Enlarged territorial atlas), a work that covered the entire country. It was first published in 1561, and remained the principal reference work in Chinese cartography until the 17th century. The map included mountains, rivers, boundaries, roads, and other landmarks. Luo's maps and geographical knowledge were put to use in the defense of the coast, and he was offered several government posts as a result but declined these offers. Martino Martini, an Italian Jesuit in China, drew his own Novus Atlas Sinensis (based on the Guang Yu Tu), which was published in Amsterdam by Joan Blaeu in 1655. Martini's map remained the standard European view of China until 1737, when Jean Baptiste d'Anville published his Atlas de la Chine. His work would go on to influence other maps such as the Da Ming Guangyu Kao (An Examination of the Enlarged Terrestrial [Map] of the Great Ming Dynasty from 1610) and Chen Zushou's Huang Ming Zhifang Ditu (An Administrative Map of the Ming Dynasty from 1636), which were banned during the Qing dynasty period. References Chinese cartographers Ming dynasty people 1504 births 1564 deaths
https://en.wikipedia.org/wiki/Palatini%20identity	In general relativity and tensor calculus, the Palatini identity is where denotes the variation of Christoffel symbols and indicates covariant differentiation. The "same" identity holds for the Lie derivative . In fact, one has where denotes any vector field on the spacetime manifold . Proof The Riemann curvature tensor is defined in terms of the Levi-Civita connection as . Its variation is . While the connection is not a tensor, the difference between two connections is, so we can take its covariant derivative . Solving this equation for and substituting the result in , all the -like terms cancel, leaving only . Finally, the variation of the Ricci curvature tensor follows by contracting two indices, proving the identity . See also Einstein–Hilbert action Palatini variation Ricci calculus Tensor calculus Christoffel symbols Riemann curvature tensor Notes References [English translation by R. Hojman and C. Mukku in P. G. Bergmann and V. De Sabbata (eds.) Cosmology and Gravitation, Plenum Press, New York (1980)] Equations of physics Tensors General relativity
https://en.wikipedia.org/wiki/Median%20follow-up	In statistics, median follow-up is the median time between a specified event and the time when data on outcomes are gathered. The concept is used in cancer survival analyses. Many cancer studies aim to assess the time between two events of interest, such as from treatment to remission, treatment to relapse, or diagnosis to death. This duration is generically called survival time, even if the end point is not death. Time-to-event studies must have sufficiently long follow-up durations to capture enough events to reveal meaningful patterns in the data. A short follow-up duration is appropriate for studying very severe cancers with poor prognoses, whereas a long follow-up duration is better suited to studying less-severe disease, or participants with good prognoses. Median follow-up time is included in about half the survival analyses published in cancer journals, but of those, only 31% specify the method used to compute it. References Biostatistics
https://en.wikipedia.org/wiki/Violence%20against%20doctors%20in%20China	Violence against doctors and other medical practitioners in China has been reported as an increasing problem. National Ministry of Health statistics indicate that the number of violent incidents against hospitals and medical staff increased from about 10,000 in 2005 to more than 17,000 in 2010. A survey by the Chinese Hospital Association reported an average of 27.3 assaults per hospital per year in 2012, up from 20.6 assaults per hospital per year in 2006. In 2012, an editorial in The Lancet described the situation as a "crisis" for the practice of medicine in China. Causes Since the 2000s in China, violence against doctors has been on the rise, and is a significant threat to the safety of Chinese medical personnel. Doctor-patient relationships in China have also been damaged in recent years. The relationship between doctors and patients should be characterised by mutual trust and mutual respect. Doctors take it as their responsibility to treat diseases and save others. Patients also trust and are grateful to doctors. However in today's China, the relationship between medical staff and patients is particularly acute. Both doctors and patients are under pressure that should not be their own. The causes of violence against doctors in China are closely related to patients, doctors and hospitals, the government's health care system, and incorrect media reports. As most patients lack medical knowledge, they have to rely on doctors' expertise during the entire treatment process. Patients and their families have mythified the doctor, holding the belief that the doctor would save the patient's life. Facts have proven that no doctor can save every patient, so if trust between patients and medical staff is broken, it may lead to patients' great disappointment towards medical personnel. This great sense of psychological loss, as well as the life and economic pressure suffered by patients during the treatment, will eventually lead to their violent behavior towards medical personnel. The lack of understanding of medical science and the high expectation of treatment are also critical reasons that could spark violent behaviours. For example, on May 11, 2002, Yuan Xiaoping, a doctor at the First Affiliated Hospital of South China University in Hengyang City, Hunan Province, was attacked and insulted by a violent mob of a hundred people, as parents of the child could not accept the death, causing them to vent their dissatisfaction on the doctor. China has not yet imposed direct punishments on hospitals and doctors. As a result, patients have no places to complain and can only become targets of exploitation. Using violence to vent the heart's dissatisfaction and pressure seems to have become the only feasible way and method. It was not until 2019 that the Chinese government promulgated the "Measures for the Management of Complaints by Medical Institutions," which clarified the methods for patient complaints and regulated hospitals and management departments
https://en.wikipedia.org/wiki/Matrix%20analysis	In mathematics, particularly in linear algebra and applications, matrix analysis is the study of matrices and their algebraic properties. Some particular topics out of many include; operations defined on matrices (such as matrix addition, matrix multiplication and operations derived from these), functions of matrices (such as matrix exponentiation and matrix logarithm, and even sines and cosines etc. of matrices), and the eigenvalues of matrices (eigendecomposition of a matrix, eigenvalue perturbation theory). Matrix spaces The set of all m × n matrices over a field F denoted in this article Mmn(F) form a vector space. Examples of F include the set of rational numbers , the real numbers , and set of complex numbers . The spaces Mmn(F) and Mpq(F) are different spaces if m and p are unequal, and if n and q are unequal; for instance M32(F) ≠ M23(F). Two m × n matrices A and B in Mmn(F) can be added together to form another matrix in the space Mmn(F): and multiplied by a α in F, to obtain another matrix in Mmn(F): Combining these two properties, a linear combination of matrices A and B are in Mmn(F) is another matrix in Mmn(F): where α and β are numbers in F. Any matrix can be expressed as a linear combination of basis matrices, which play the role of the basis vectors for the matrix space. For example, for the set of 2 × 2 matrices over the field of real numbers, , one legitimate basis set of matrices is: because any 2 × 2 matrix can be expressed as: where a, b, c,d are all real numbers. This idea applies to other fields and matrices of higher dimensions. Determinants The determinant of a square matrix is an important property. The determinant indicates if a matrix is invertible (i.e. the inverse of a matrix exists when the determinant is nonzero). Determinants are used for finding eigenvalues of matrices (see below), and for solving a system of linear equations (see Cramer's rule). Eigenvalues and eigenvectors of matrices Definitions An n × n matrix A has eigenvectors x and eigenvalues λ defined by the relation: In words, the matrix multiplication of A followed by an eigenvector x (here an n-dimensional column matrix), is the same as multiplying the eigenvector by the eigenvalue. For an n × n matrix, there are n eigenvalues. The eigenvalues are the roots of the characteristic polynomial: where I is the n × n identity matrix. Roots of polynomials, in this context the eigenvalues, can all be different, or some may be equal (in which case eigenvalue has multiplicity, the number of times an eigenvalue occurs). After solving for the eigenvalues, the eigenvectors corresponding to the eigenvalues can be found by the defining equation. Perturbations of eigenvalues Matrix similarity Two n × n matrices A and B are similar if they are related by a similarity transformation: The matrix P is called a similarity matrix, and is necessarily invertible. Unitary similarity Canonical forms Row echelon form Jordan normal form Weyr canonical fo
https://en.wikipedia.org/wiki/Shepherd%20Group	Shepherd group may refer to: Shepherd Building Group Shephard groups, in mathematics
https://en.wikipedia.org/wiki/Brauner%20space	In functional analysis and related areas of mathematics a Brauner space is a complete compactly generated locally convex space having a sequence of compact sets such that every other compact set is contained in some . Brauner spaces are named after Kalman George Brauner, who began their study. All Brauner spaces are stereotype and are in the stereotype duality relations with Fréchet spaces: for any Fréchet space its stereotype dual space is a Brauner space, and vice versa, for any Brauner space its stereotype dual space is a Fréchet space. Special cases of Brauner spaces are Smith spaces. Examples Let be a -compact locally compact topological space, and the Fréchet space of all continuous functions on (with values in or ), endowed with the usual topology of uniform convergence on compact sets in . The dual space of Radon measures with compact support on with the topology of uniform convergence on compact sets in is a Brauner space. Let be a smooth manifold, and the Fréchet space of all smooth functions on (with values in or ), endowed with the usual topology of uniform convergence with each derivative on compact sets in . The dual space of distributions with compact support in with the topology of uniform convergence on bounded sets in is a Brauner space. Let be a Stein manifold and the Fréchet space of all holomorphic functions on with the usual topology of uniform convergence on compact sets in . The dual space of analytic functionals on with the topology of uniform convergence on bounded sets in is a Brauner space. In the special case when possesses a structure of a topological group the spaces , , become natural examples of stereotype group algebras. Let be a complex affine algebraic variety. The space of polynomials (or regular functions) on , being endowed with the strongest locally convex topology, becomes a Brauner space. Its stereotype dual space (of currents on ) is a Fréchet space. In the special case when is an affine algebraic group, becomes an example of a stereotype group algebra. Let be a compactly generated Stein group. The space of all holomorphic functions of exponential type on is a Brauner space with respect to a natural topology. See also Stereotype space Smith space Notes References Functional analysis Topological vector spaces
https://en.wikipedia.org/wiki/Mil%C3%A1n%20F%C3%B6ldes	Milán Földes (born 9 April 1993 in Székesfehérvár) is a Hungarian professional footballer who plays for FC Dabas. Club statistics Updated to games played as of 4 March 2014. References MLSZ 1993 births Living people Footballers from Székesfehérvár Hungarian men's footballers Men's association football defenders Kaposvári Rákóczi FC players Nemzeti Bajnokság I players
https://en.wikipedia.org/wiki/Luka%20Domini%C4%87	Luka Dominić (born 1 December 1993 in Čakovec) is a Croatian professional footballer who plays for Jadran-Galeb. Club statistics Updated to games played as of 18 May 2014. References MLSZ 1993 births Living people Sportspeople from Čakovec Men's association football midfielders Croatian men's footballers Kaposvári Rákóczi FC players Nemzeti Bajnokság I players Nemzeti Bajnokság II players Croatian expatriate men's footballers Expatriate men's footballers in Hungary Croatian expatriate sportspeople in Hungary
https://en.wikipedia.org/wiki/Zsolt%20Tar	Zsolt Tar (born 13 February 1993) is a Hungarian professional footballer who plays for FC Ajka. Club statistics Updated to games played as of 9 August 2020. References Tar Zsolt at HLSZ.hu 1993 births Living people People from Kunhegyes Hungarian men's footballers Men's association football defenders Fehérvár FC players Puskás Akadémia FC players Nemzeti Bajnokság I players Nemzeti Bajnokság II players Győri ETO FC players Aqvital FC Csákvár players FC Ajka players Footballers from Jász-Nagykun-Szolnok County
https://en.wikipedia.org/wiki/2011%20Bangladeshi%20census	In 2011, the Bangladesh Bureau of Statistics, conducted a national census in Bangladesh, which provided a provisional estimate of the total population of the country as 142,319,000. The previous decennial census was the 2001 census. Data were recorded from all of the districts and upazilas and main cities in Bangladesh including statistical data on population size, households, sex and age distribution, marital status, economically active population, literacy and educational attainment, religion, number of children etc. Bangladesh and India also conducted their first joint census of areas along their border in 2011. According to the census, Hindus constituted 8.5 per cent of the population as of 2011, down from 9.6 per cent in the 2001 census. Bangladesh have a population of 144,043,697 as per 2011 census report. Majority of 130,201,097 reported that they were Muslims, 12,301,331 reported as Hindus, 864,262 as Buddhists, 532,961 as Christians and 201,661 as others. See also Demographics of Bangladesh 1991 Census of Bangladesh 2001 Census of Bangladesh 2022 Census of Bangladesh References Censuses in Bangladesh Census Bangladesh
https://en.wikipedia.org/wiki/Upper%20bound%20theorem	In mathematics, the upper bound theorem states that cyclic polytopes have the largest possible number of faces among all convex polytopes with a given dimension and number of vertices. It is one of the central results of polyhedral combinatorics. Originally known as the upper bound conjecture, this statement was formulated by Theodore Motzkin, proved in 1970 by Peter McMullen, and strengthened from polytopes to subdivisions of a sphere in 1975 by Richard P. Stanley. Cyclic polytopes The cyclic polytope may be defined as the convex hull of vertices on the moment curve, the set of -dimensional points with coordinates . The precise choice of which points on this curve are selected is irrelevant for the combinatorial structure of this polytope. The number of -dimensional faces of is given by the formula and completely determine via the Dehn–Sommerville equations. The same formula for the number of faces holds more generally for any neighborly polytope. Statement The upper bound theorem states that if is a simplicial sphere of dimension with vertices, then The difference between for the dimension of the simplicial sphere, and for the dimension of the cyclic polytope, comes from the fact that the surface of a -dimensional polytope (such as the cyclic polytope) is a -dimensional subdivision of a sphere. Therefore, the upper bound theorem implies that the number of faces of an arbitrary polytope can never be more than the number of faces of a cyclic or neighborly polytope with the same dimension and number of vertices. Asymptotically, this implies that there are at most faces of all dimensions. The same bounds hold as well for convex polytopes that are not simplicial, as perturbing the vertices of such a polytope (and taking the convex hull of the perturbed vertices) can only increase the number of faces. History The upper bound conjecture for simplicial polytopes was proposed by Motzkin in 1957 and proved by McMullen in 1970. A key ingredient in his proof was the following reformulation in terms of h-vectors: Victor Klee suggested that the same statement should hold for all simplicial spheres and this was indeed established in 1975 by Stanley using the notion of a Stanley–Reisner ring and homological methods. For a nice historical account of this theorem see Stanley's article "How the upper bound conjecture was proved". References Polyhedral combinatorics
https://en.wikipedia.org/wiki/Peter%20McMullen	Peter McMullen (born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at University College London. Education and career McMullen earned bachelor's and master's degrees from Trinity College, Cambridge, and studied at the University of Birmingham, where he received his doctorate in 1968. and taught at Western Washington University from 1968 to 1969. In 1978 he earned his Doctor of Science at University College London where he still works as a professor emeritus. In 2006 he was accepted as a corresponding member of the Austrian Academy of Sciences. Contributions McMullen is known for his work in polyhedral combinatorics and discrete geometry, and in particular for proving what was then called the upper bound conjecture and now is the upper bound theorem. This result states that cyclic polytopes have the maximum possible number of faces among all polytopes with a given dimension and number of vertices. McMullen also formulated the g-conjecture, later the g-theorem of Louis Billera, Carl W. Lee, and Richard P. Stanley, characterizing the f-vectors of simplicial spheres. The McMullen problem is an unsolved question in discrete geometry named after McMullen, concerning the number of points in general position for which a projective transformation into convex position can be guaranteed to exist. It was credited to a private communication from McMullen in a 1972 paper by David G. Larman. He is also known for his 1960s drawing, by hand, of a 2-dimensional representation of the Gosset polytope 421, the vertices of which form the vectors of the E8 root system. Awards and honours McMullen was invited to speak at the 1974 International Congress of Mathematicians in Vancouver; his contribution there had the title Metrical and combinatorial properties of convex polytopes. He was elected as a foreign member of the Austrian Academy of Sciences in 2006. In 2012 he became an inaugural fellow of the American Mathematical Society. Selected publications Research papers . . . Survey articles . Updated as "Valuations and dissections" (by McMullen alone) in Handbook of convex geometry (1993), . Books . . References 1942 births Living people 20th-century British mathematicians 21st-century British mathematicians Alumni of Trinity College, Cambridge Western Washington University faculty Academics of University College London Fellows of the American Mathematical Society Members of the Austrian Academy of Sciences British geometers
https://en.wikipedia.org/wiki/Marie-Louise%20Michelsohn	Marie-Louise Michelsohn (born October 8, 1941) is a professor of mathematics at State University of New York at Stony Brook. Education Michelsohn attended the Bronx High School of Science. She attended the University of Chicago for her undergraduate and graduate studies, including her PhD. She spent a year as a visiting professor at University of California at San Diego. She spent a year l'Institut des Hautes Études Scientifiques outside of Paris, France. She then joined the faculty of State University of New York at Stony Brook. Mathematical work Michelsohn's PhD was in the field of topology. As of 2020, she has published twenty articles, on topics including complex geometry, spin manifolds and the Dirac operator, and the theory of algebraic cycles. Half of her work has been in collaboration with Blaine Lawson. With Lawson, she wrote a textbook on spin geometry which has become the standard reference for the field. In her most widely-known work, published in 1982, Michelsohn introduced the notion of a balanced metric on a complex manifold. These are hermitian metrics for which the penultimate power of the associated Kähler form is closed, i.e. in which is the Kähler form and is the complex dimension. It is trivial to see that every Kähler metric is a balanced metric. As for Kähler metrics, the above definition of a balanced metric automatically places cohomological restrictions on the underlying manifold; by Stokes' theorem, every codimension-one complex subvariety is homologically nontrivial. For instance, the Calabi-Eckmann complex manifolds do not support any balanced metrics. Michelsohn also recast the definition of a balanced metric in terms of the torsion tensor and in terms of the Dirac operator. In parallel to a work of Reese Harvey and Blaine Lawson's on Kähler metrics, Michelsohn obtained a full characterization, in terms of the cohomological theory of currents, of which complex manifolds admit balanced metrics. Balanced metrics are, in part, of interest due to their role in the Strominger system arising from string theory. Masters athletics Michelsohn is also an accomplished middle and long-distance runner. She holds five masters athletics world records including through three age divisions of the 2000 metres steeplechase which she has held since 2002. In addition to the world records, she holds 6 more outdoor American records and 10 indoor American records, running the table of all official indoor distances 800 metres and above in both the W65 and W70 divisions. Notable publications Notes References Notable Women in Mathematics, a Biographical Dictionary, edited by Charlene Morrow and Teri Perl, Greenwood Press, 1998. p 142–147. 1941 births American women mathematicians Living people 21st-century American mathematicians 20th-century American mathematicians 20th-century women mathematicians 21st-century women mathematicians 20th-century American women 21st-century American women
https://en.wikipedia.org/wiki/Homotopy%20hypothesis	In category theory, a branch of mathematics, Grothendieck's homotopy hypothesis states that the ∞-groupoids are spaces. If we model our ∞-groupoids as Kan complexes, then the homotopy types of the geometric realizations of these sets give models for every homotopy type. It is conjectured that there are many different "equivalent" models for ∞-groupoids all which can be realized as homotopy types. See also Pursuing Stacks N-group (category theory) References John Baez, The Homotopy Hypothesis External links What is the mistake in the proof of the Homotopy hypothesis by Kapranov and Voevodsky? Jacob Lurie's Home Page Homotopy theory Higher category theory Hypotheses Conjectures
https://en.wikipedia.org/wiki/%E2%88%9E-groupoid	In category theory, a branch of mathematics, an ∞-groupoid is an abstract homotopical model for topological spaces. One model uses Kan complexes which are fibrant objects in the category of simplicial sets (with the standard model structure). It is an ∞-category generalization of a groupoid, a category in which every morphism is an isomorphism. The homotopy hypothesis states that ∞-groupoids are equivalent to spaces up to homotopy. Globular Groupoids Alexander Grothendieck suggested in Pursuing Stacks that there should be an extraordinarily simple model of ∞-groupoids using globular sets, originally called hemispherical complexes. These sets are constructed as presheaves on the globular category . This is defined as the category whose objects are finite ordinals and morphisms are given bysuch that the globular relations holdThese encode the fact that -morphisms should not be able to see -morphisms. When writing these down as a globular set , the source and target maps are then written asWe can also consider globular objects in a category as functorsThere was hope originally that such a strict model would be sufficient for homotopy theory, but there is evidence suggesting otherwise. It turns out for its associated homotopy -type can never be modeled as a strict globular groupoid for . This is because strict ∞-groupoids only model spaces with a trivial Whitehead product. Examples Fundamental ∞-groupoid Given a topological space there should be an associated fundamental ∞-groupoid where the objects are points , 1-morphisms are represented as paths, 2-morphisms are homotopies of paths, 3-morphisms are homotopies of homotopies, and so on. From this infinity groupoid we can find an -groupoid called the fundamental -groupoid whose homotopy type is that of . Note that taking the fundamental ∞-groupoid of a space such that is equivalent to the fundamental n-groupoid . Such a space can be found using the Whitehead tower. Abelian globular groupoids One useful case of globular groupoids comes from a chain complex which is bounded above, hence let's consider a chain complex . There is an associated globular groupoid. Intuitively, the objects are the elements in , morphisms come from through the chain complex map , and higher -morphisms can be found from the higher chain complex maps . We can form a globular set withand the source morphism is the projection mapand the target morphism is the addition of the chain complex map together with the projection map. This forms a globular groupoid giving a wide class of examples of strict globular groupoids. Moreover, because strict groupoids embed inside weak groupoids, they can act as weak groupoids as well. Applications Higher local systems One of the basic theorems about local systems is that they can be equivalently described as a functor from the fundamental groupoid to the category of Abelian groups, the category of -modules, or some other abelian category. That is, a local system is e
https://en.wikipedia.org/wiki/Simplicial%20localization	In category theory, a branch of mathematics, the simplicial localization of a category C with respect to a class W of morphisms of C is a simplicial category LC whose is the localization of C with respect to W; that is, for any objects x, y in C. The notion is due to Dwyer and Kan. References W. G. Dwyer and Dan Kan, Simplicial localizations of categories http://math.mit.edu/~mdono/_Juvitop.pdf External links Category theory
https://en.wikipedia.org/wiki/Stable%20model%20category	In category theory, a branch of mathematics, a stable model category is a pointed model category in which the suspension functor is an equivalence of the homotopy category with itself. The prototypical examples are the category of spectra in the stable homotopy theory and the category of chain complex of R-modules. On the other hand, the category of pointed topological spaces and the category of pointed simplicial sets are not stable model categories. Any stable model category is equivalent to a category of presheaves of spectra. References Mark Hovey: Model Categories, 1999, . Category theory
https://en.wikipedia.org/wiki/Moment%20measure	In probability and statistics, a moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. Moment measures generalize the idea of (raw) moments of random variables, hence arise often in the study of point processes and related fields. An example of a moment measure is the first moment measure of a point process, often called mean measure or intensity measure, which gives the expected or average number of points of the point process being located in some region of space. In other words, if the number of points of a point process located in some region of space is a random variable, then the first moment measure corresponds to the first moment of this random variable. Moment measures feature prominently in the study of point processes as well as the related fields of stochastic geometry and spatial statistics whose applications are found in numerous scientific and engineering disciplines such as biology, geology, physics, and telecommunications. Point process notation Point processes are mathematical objects that are defined on some underlying mathematical space. Since these processes are often used to represent collections of points randomly scattered in physical space, time or both, the underlying space is usually d-dimensional Euclidean space denoted here by , but they can be defined on more abstract mathematical spaces. Point processes have a number of interpretations, which is reflected by the various types of point process notation. For example, if a point belongs to or is a member of a point process, denoted by , then this can be written as: and represents the point process being interpreted as a random set. Alternatively, the number of points of located in some Borel set is often written as: which reflects a random measure interpretation for point processes. These two notations are often used in parallel or interchangeably. Definitions n-th power of a point process For some integer , the -th power of a point process is defined as: where is a collection of not necessarily disjoint Borel sets (in ), which form a -fold Cartesian product of sets denoted by . The symbol denotes standard multiplication. The notation reflects the interpretation of the point process as a random measure. The -th power of a point process can be equivalently defined as: where summation is performed over all -tuples of (possibly repeating) points, and denotes an indicator function such that is a Dirac measure. This definition can be contrasted with the definition of the n-factorial power of a point process for which each n-tuples consists of n distinct points. n-th moment measure The -th moment measure is defined as: where the E denotes the expectation (operator) of th
https://en.wikipedia.org/wiki/Factorial%20moment%20measure	In probability and statistics, a factorial moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. Moment measures generalize the idea of factorial moments, which are useful for studying non-negative integer-valued random variables. The first factorial moment measure of a point process coincides with its first moment measure or intensity measure, which gives the expected or average number of points of the point process located in some region of space. In general, if the number of points in some region is considered as a random variable, then the moment factorial measure of this region is the factorial moment of this random variable. Factorial moment measures completely characterize a wide class of point processes, which means they can be used to uniquely identify a point process. If a factorial moment measure is absolutely continuous, then with respect to the Lebesgue measure it is said to have a density (which is a generalized form of a derivative), and this density is known by a number of names such as factorial moment density and product density, as well as coincidence density, joint intensity , correlation function or multivariate frequency spectrum The first and second factorial moment densities of a point process are used in the definition of the pair correlation function, which gives a way to statistically quantify the strength of interaction or correlation between points of a point process. Factorial moment measures serve as useful tools in the study of point processes as well as the related fields of stochastic geometry and spatial statistics, which are applied in various scientific and engineering disciplines such as biology, geology, physics, and telecommunications. Point process notation Point processes are mathematical objects that are defined on some underlying mathematical space. Since these processes are often used to represent collections of points randomly scattered in space, time or both, the underlying space is usually d-dimensional Euclidean space denoted here by Rd, but they can be defined on more abstract mathematical spaces. Point processes have a number of interpretations, which is reflected by the various types of point process notation. For example, if a point belongs to or is a member of a point process, denoted by N, then this can be written as: and represents the point process being interpreted as a random set. Alternatively, the number of points of N located in some Borel set B is often written as: which reflects a random measure interpretation for point processes. These two notations are often used in parallel or interchangeably. Definitions n th factorial power of a point process For some positive integer , the -th factorial pow
https://en.wikipedia.org/wiki/Spacetime%20triangle%20diagram%20technique	In physics and mathematics, the spacetime triangle diagram (STTD) technique, also known as the Smirnov method of incomplete separation of variables, is the direct space-time domain method for electromagnetic and scalar wave motion. Basic stages (Electromagnetics) The system of Maxwell's equations is reduced to a second-order PDE for the field components, or potentials, or their derivatives. The spatial variables are separated using convenient expansions into series and/or integral transforms—except one that remains bounded with the time variable, resulting in a PDE of hyperbolic type. The resulting hyperbolic PDE and the simultaneously transformed initial conditions compose a problem, which is solved using the Riemann–Volterra integral formula. This yields the generic solution expressed via a double integral over a triangle domain in the bounded-coordinate—time space. Then this domain is replaced by a more complicated but smaller one, in which the integrant is essentially nonzero, found using a strictly formalized procedure involving specific spacetime triangle diagrams (see, e.g., Refs.). In the majority of cases the obtained solutions, being multiplied by known functions of the previously separated variables, result in the expressions of a clear physical meaning (nonsteady-state modes). In many cases, however, more explicit solutions can be found summing up the expansions or doing the inverse integral transform. STTD versus Green's function technique The STTD technique belongs to the second among the two principal ansätze for theoretical treatment of waves — the frequency domain and the direct spacetime domain. The most well-established method for the inhomogeneous (source-related) descriptive equations of wave motion is one based on the Green's function technique. For the circumstances described in Section 6.4 and Chapter 14 of Jackson's Classical Electrodynamics, it can be reduced to calculation of the wave field via retarded potentials (in particular, the Liénard–Wiechert potentials). Despite certain similarity between Green's and Riemann–Volterra methods (in some literature the Riemann function is called the Riemann–Green function ), their application to the problems of wave motion results in distinct situations: The definitions of both Green's function and corresponding Green's solution are not unique as they leave room for addition of arbitrary solution of the homogeneous equation; in some circumstances the particular choice of Green's function and the final solution are defined by boundary condition(s) or plausibility and physical admissibility of the constructed wavefunctions. The Riemann function is a solution of the homogeneous equation that additionally must take a certain value at the characteristics and thus is defined in a unique way. In contrast to Green's method that provides a particular solution of the inhomogeneous equation, the Riemann–Volterra method is related to the corresponding problem, comprising the PDE
https://en.wikipedia.org/wiki/Central%20differencing%20scheme	In applied mathematics, the central differencing scheme is a finite difference method that optimizes the approximation for the differential operator in the central node of the considered patch and provides numerical solutions to differential equations. It is one of the schemes used to solve the integrated convection–diffusion equation and to calculate the transported property Φ at the e and w faces, where e and w are short for east and west (compass directions being customarily used to indicate directions on computational grids). The method's advantages are that it is easy to understand and implement, at least for simple material relations; and that its convergence rate is faster than some other finite differencing methods, such as forward and backward differencing. The right side of the convection-diffusion equation, which basically highlights the diffusion terms, can be represented using central difference approximation. To simplify the solution and analysis, linear interpolation can be used logically to compute the cell face values for the left side of this equation, which is nothing but the convective terms. Therefore, cell face values of property for a uniform grid can be written as: Steady-state convection diffusion equation The convection–diffusion equation is a collective representation of diffusion and convection equations, and describes or explains every physical phenomenon involving convection and diffusion in the transference of particles, energy and other physical quantities inside a physical system: where is diffusion coefficient and is the property. Formulation of steady-state convection diffusion equation Formal integration of steady-state convection–diffusion equation over a control volume gives This equation represents flux balance in a control volume. The left side gives the net convective flux, and the right side contains the net diffusive flux and the generation or destruction of the property within the control volume. In the absence of source term equation, one becomes Continuity equation: Assuming a control volume and integrating equation 2 over control volume gives: Integration of equation 3 yields: It is convenient to define two variables to represent the convective mass flux per unit area and diffusion conductance at cell faces, for example: Assuming , we can write integrated convection–diffusion equation as: And integrated continuity equation as: In a central differencing scheme, we try linear interpolation to compute cell face values for convection terms. For a uniform grid, we can write cell face values of property as On substituting this into integrated convection-diffusion equation, we obtain: And on rearranging: Different aspects of central differencing scheme Conservativeness Conservation is ensured in central differencing scheme since overall flux balance is obtained by summing the net flux through each control volume taking into account the boundary fluxes for the control volumes around n
https://en.wikipedia.org/wiki/Masamichi%20Takesaki	Masamichi Takesaki (竹崎正道; born July 18, 1933, in Sendai) is a Japanese mathematician working in the theory of operator algebras. Takesaki studied at Tohoku University, earning a bachelor's degree in 1956, a master's degree in 1958 and a doctorate in 1965. Beginning in 1958 he was a research assistant at the Tokyo Institute of Technology and from 1965 to 1968 he was an associate professor at Tohoku University. From 1968 to 1969 he was a visiting associate professor at the University of Pennsylvania. In 1970, he became a professor at the University of California, Los Angeles. He was also a visiting professor at Aix-Marseille University (1973–74) and Bielefeld University (1975–76). He is known for the Tomita–Takesaki theory, which is about modular automorphisms of von Neumann algebras. This theory was initially developed by Minoru Tomita until 1967, but his work was published only partially (in Japanese) and was quite difficult to understand, drawing little notice, before being presented by Takesaki in 1970 in a book. In 1970, he was an invited speaker at the International Congress of Mathematicians in Nice; his talk was about one parameter automorphism groups and states of operator algebras. In 1990 he was awarded the Fujiwara Science Prize. He is a fellow of the American Mathematical Society. Works Tomita's theory of modular Hilbert algebras and its applications, lecture notes mathematics, band 128, Springer Verlag 1970 Theory of operator algebras, 3 volumes, encyclopedia of mathematical sciences, Springer-Verlag, 2001–2003 (the first volume was published 1979 in 1. Edition) See also Nuclear C*-algebra References External links Homepage Conference on 70th birthday Master class in Modular Theory of von Neumann algebras Șerban Strătilă and Masamichi Takesaki 1933 births Living people 20th-century Japanese mathematicians 21st-century Japanese mathematicians Tohoku University alumni Academic staff of Tohoku University University of California, Los Angeles faculty Fellows of the American Mathematical Society
https://en.wikipedia.org/wiki/Cours%20d%27Analyse	Cours d'Analyse de l’École Royale Polytechnique; I.re Partie. Analyse algébrique ("Analysis Course" in English) is a seminal textbook in infinitesimal calculus published by Augustin-Louis Cauchy in 1821. The article follows the translation by Bradley and Sandifer in describing its contents. Introduction On page 1 of the Introduction, Cauchy writes: "In speaking of the continuity of functions, I could not dispense with a treatment of the principal properties of infinitely small quantities, properties which serve as the foundation of the infinitesimal calculus." The translators comment in a footnote: "It is interesting that Cauchy does not also mention limits here." Cauchy continues: "As for the methods, I have sought to give them all the rigor which one demands from geometry, so that one need never rely on arguments drawn from the generality of algebra." Preliminaries On page 6, Cauchy first discusses variable quantities and then introduces the limit notion in the following terms: "When the values successively attributed to a particular variable indefinitely approach a fixed value in such a way as to end up by differing from it by as little as we wish, this fixed value is called the limit of all the other values." On page 7, Cauchy defines an infinitesimal as follows: "When the successive numerical values of such a variable decrease indefinitely, in such a way as to fall below any given number, this variable becomes what we call infinitesimal, or an infinitely small quantity." Cauchy adds: "A variable of this kind has zero as its limit." On page 10, Bradley and Sandifer confuse the versed cosine with the coversed sine. Cauchy originally defined the sinus versus (versine) as siv(θ) = 1− cos(θ) and the cosinus versus (what is now also known as coversine) as cosiv(θ) = 1− sin(θ). In the translation, however, the cosinus versus (and cosiv) are incorrectly associated with the versed cosine (what is now also known as vercosine) rather than the coversed sine. The notation lim is introduced on page 12. The translators observe in a footnote: "The notation “Lim.” for limit was first used by Simon Antoine Jean L'Huilier (1750–1840) in [L’Huilier 1787, p. 31]. Cauchy wrote this as “lim.” in [Cauchy 1821, p. 13]. The period had disappeared by [Cauchy 1897, p. 26]." Chapter 2 This chapter has the long title "On infinitely small and infinitely large quantities, and on the continuity of functions. Singular values of functions in various particular cases." On page 21, Cauchy writes: "We say that a variable quantity becomes infinitely small when its numerical value decreases indefinitely in such a way as to converge towards the limit zero." On the same page, we find the only explicit example of such a variable to be found in Cauchy, namely On page 22, Cauchy starts the discussion of orders of magnitude of infinitesimals as follows: "Let be an infinitely small quantity, that is a variable whose numerical value decreases indefinitely. When the various in
https://en.wikipedia.org/wiki/Richard%20Gasquet%20career%20statistics	This page is a list of the main career statistics of French tennis player, Richard Gasquet. To date, he has won 16 ATP singles titles. He was also the runner-up at the 2005 Hamburg Masters and Canada Masters in 2006 and 2012, a semifinalist at the 2007 and 2015 Wimbledon Championships and 2013 US Open and a bronze medallist in men's doubles with Julien Benneteau at the 2012 London Olympics. On 9 July 2007, Gasquet achieved a career high singles ranking of world No. 7. Significant finals Grand Slam tournaments Mixed doubles: 1 (1 title) Olympic Games Doubles: 1 (1 bronze medal) Masters 1000 tournaments Singles: 3 (3 runner-ups) Doubles: 1 (1 runner-up) ATP Tour career finals Singles: 33 (16 titles, 17 runner-ups) Doubles: 4 (2 titles, 2 runner-ups) National representation Team competition finals: 5 (2 titles, 3 runner-ups) Exhibition Finals Singles performance timeline Current through the 2023 US Open. 1Held as Hamburg Masters until 2008, Madrid Masters (clay) 2009–present. 2Held as Madrid Masters (hardcourt) until 2008, and Shanghai Masters 2009–present. Gasquet withdrew from the 2007 US Open due to illness, having won his opening round. Record against top 10 players Gasquet's record against players who have been ranked in the top 10, with those who are active in boldface. Only ATP Tour main draw matches are considered: Top 10 wins He has a win-loss record against players who were, at the time the match was played, ranked in the top 10. ATP career earnings Statistics correct . References External links Tennis career statistics
https://en.wikipedia.org/wiki/Near%20polygon	In mathematics, a near polygon is an incidence geometry introduced by Ernest E. Shult and Arthur Yanushka in 1980. Shult and Yanushka showed the connection between the so-called tetrahedrally closed line-systems in Euclidean spaces and a class of point-line geometries which they called near polygons. These structures generalise the notion of generalized polygon as every generalized 2n-gon is a near 2n-gon of a particular kind. Near polygons were extensively studied and connection between them and dual polar spaces was shown in 1980s and early 1990s. Some sporadic simple groups, for example the Hall-Janko group and the Mathieu groups, act as automorphism groups of near polygons. Definition A near 2d-gon is an incidence structure (), where is the set of points, is the set of lines and is the incidence relation, such that: The maximum distance between two points (the so-called diameter) is d. For every point and every line there exists a unique point on which is nearest to . Note that the distance are measured in the collinearity graph of points, i.e., the graph formed by taking points as vertices and joining a pair of vertices if they are incident with a common line. We can also give an alternate graph theoretic definition, a near 2d-gon is a connected graph of finite diameter d with the property that for every vertex x and every maximal clique M there exists a unique vertex x in M nearest to x. The maximal cliques of such a graph correspond to the lines in the incidence structure definition. A near 0-gon (d = 0) is a single point while a near 2-gon (d = 1) is just a single line, i.e., a complete graph. A near quadrangle (d = 2) is same as a (possibly degenerate) generalized quadrangle. In fact, it can be shown that every generalized 2d-gon is a near 2d-gon that satisfies the following two additional conditions: Every point is incident with at least two lines. For every two points x, y at distance i < d, there exists a unique neighbour of y at distance i − 1 from x. A near polygon is called dense if every line is incident with at least three points and if every two points at distance two have at least two common neighbours. It is said to have order (s, t) if every line is incident with precisely s + 1 points and every point is incident with precisely t + 1 lines. Dense near polygons have a rich theory and several classes of them (like the slim dense near polygons) have been completely classified. Examples All connected bipartite graphs are near polygons. In fact, any near polygon that has precisely two points per line must be a connected bipartite graph. All finite generalized polygons except the projective planes. All dual polar spaces. The Hall–Janko near octagon, also known as the Cohen-Tits near octagon associated with the Hall–Janko group. It can be constructed by choosing the conjugacy class of 315 central involutions of the Hall-Janko group as points and lines as three element subsets {x, y, xy} whenever x and
https://en.wikipedia.org/wiki/Isaac%20Oliseh	Isaac Oliseh (born 3 August 1993) is a Nigerian footballer who plays as a midfielder for Jomala IK in Finland. References External links Isaac Oliseh – Danish Superliga player statistics at danskfodbold.com 1993 births Living people Nigerian men's footballers FC Midtjylland players Thisted FC players Danish Superliga players Nigerian expatriate men's footballers Expatriate men's footballers in Denmark Expatriate men's footballers in Finland Men's association football midfielders
https://en.wikipedia.org/wiki/Truncated%20triangular%20trapezohedron	In geometry, the truncated triangular trapezohedron is the first in an infinite series of truncated trapezohedra. It has 6 pentagon and 2 triangle faces. Geometry This polyhedron can be constructed by truncating two opposite vertices of a cube, of a trigonal trapezohedron (a convex polyhedron with six congruent rhombus sides, formed by stretching or shrinking a cube along one of its long diagonals), or of a rhombohedron or parallelepiped (less symmetric polyhedra that still have the same combinatorial structure as a cube). In the case of a cube, or of a trigonal trapezohedron where the two truncated vertices are the ones on the stretching axes, the resulting shape has three-fold rotational symmetry. Dürer's solid This polyhedron is sometimes called Dürer's solid, from its appearance in Albrecht Dürer's 1514 engraving Melencolia I. The graph formed by its edges and vertices is called the Dürer graph. The shape of the solid depicted by Dürer is a subject of some academic debate. According to , the hypothesis that the shape is a misdrawn truncated cube was promoted by ; however most sources agree that it is the truncation of a rhombohedron. Despite this agreement, the exact geometry of this rhombohedron is the subject of several contradictory theories: claims that the rhombi of the rhombohedron from which this shape is formed have 5:6 as the ratio between their short and long diagonals, from which the acute angles of the rhombi would be approximately 80°. and instead conclude that the ratio is √3:2 and that the angle is approximately 82°. measures features of the drawing and finds that the angle is approximately 79°. She and a later author, Wolf von Engelhardt (see ) argue that this choice of angle comes from its physical occurrence in calcite crystals. argues based on the writings of Dürer that all vertices of Dürer's solid lie on a common sphere, and further claims that the rhombus angles are 72°. lists several other scholars who also favor the 72° theory, beginning with Paul Grodzinski in 1955. He argues that this theory is motivated less by analysis of the actual drawing, and more by aesthetic principles relating to regular pentagons and the golden ratio. analyzes a 1510 sketch by Dürer of the same solid, from which he confirms Schreiber's hypothesis that the shape has a circumsphere but with rhombus angles of approximately 79.5°. argues that the shape is intended to depict a solution to the famous geometric problem of doubling the cube, which Dürer also wrote about in 1525. He therefore concludes that (before the corners are cut off) the shape is a cube stretched along its long diagonal. More specifically, he argues that Dürer drew an actual cube, with the long diagonal parallel to the perspective plane, and then enlarged his drawing by some factor in the direction of the long diagonal; the result would be the same as if he had drawn the elongated solid. The enlargement factor that is relevant for doubling the cube is 21/3 ≈ 1.253,
https://en.wikipedia.org/wiki/Explicit%20algebraic%20stress%20model	The algebraic stress model arises in computational fluid dynamics. Two main approaches can be undertaken. In the first, the transport of the turbulent stresses is assumed proportional to the turbulent kinetic energy; while in the second, convective and diffusive effects are assumed to be negligible. Algebraic stress models can only be used where convective and diffusive fluxes are negligible, i.e. source dominated flows. In order to simplify the existing EASM and to achieve an efficient numerical implementation the underlying tensor basis plays an important role. The five-term tensor basis that is introduced here tries to combine an optimum of accuracy of the complete basis with the advantages of a pure 2d concept. Therefore a suitable five-term basis is identified. Based on that the new model is designed and validated in combination with different eddy-viscosity type background models. Integrity basis In the frame work of single-point closures (Reynolds-stress transport models = RSTM) still provide the best representation of flow physics. Due to numeric requirements an explicit formulation based on a low number of tensors is desirable and was already introduced originally most explicit algebraic stress models are formulated using a 10-term basis: The reduction of the tensor basis however requires an enormous mathematical effort, to transform the algebraic stress formulation for a given linear algebraic RSTM into a given tensor basis by keeping all important properties of the underlying model. This transformation can be applied to an arbitrary tensor basis. In the present investigations an optimum set of basis tensors and the corresponding coefficients is to be found. Projection method The projection method was introduced to enable an approximate solution of the algebraic transport equation of the Reynolds-stresses. In contrast to the approach of the tensor basis is not inserted in the algebraic equation, instead the algebraic equation is projected. Therefore, the chosen basis tensors does not need to form a complete integrity basis. However, the projection will fail if the basis tensor are linear dependent. In the case of a complete basis the projection leads to the same solution as the direct insertion, otherwise an approximate solution in the sense is obtained. An example In order to prove, that the projection method will lead to the same solution as the direct insertion, the EASM for two-dimensional flows is derived. In two-dimensional flows only the tensors are independent. The projection leads then to the same coefficients. This two-dimensional EASM is used as starting point for an optimized EASM which includes three-dimensional effects. For example the shear stress variation in a rotating pipe cannot be predicted with quadratic tensors. Hence, the EASM was extended with a cubic tensor. In order to do not affect the performance in 2D flows, a tensor was chosen that vanish in 2d flows. This offers the concentration of the coefficient de
https://en.wikipedia.org/wiki/Colombia%20national%20football%20team%20results%20%281926%E2%80%931979%29	This page details the match results and statistics of the Colombia national football team from 1926 to 1979. Key Key to matches Att.=Match attendance (H)=Home ground (A)=Away ground (N)=Neutral ground Key to record by opponent Pld=Games played W=Games won D=Games drawn L=Games lost GF=Goals for GA=Goals against Results Colombia's score is shown first in each case. Notes Record by opponent References Colombia national football team results
https://en.wikipedia.org/wiki/Spherical%20category	In category theory, a branch of mathematics, a spherical category is a pivotal category (a monoidal category with traces) in which left and right traces coincide. Spherical fusion categories give rise to a family of three-dimensional topological state sum models (a particular formulation of a topological quantum field theory), the Turaev-Viro model, or rather Turaev-Viro-Barrett-Westbury model. References Category theory
https://en.wikipedia.org/wiki/Reviel%20Netz	Reviel Netz (born January 2, 1968) is an Israeli scholar of the history of pre-modern mathematics, who is currently a professor of classics and of philosophy at Stanford University. Life and work Netz was born January 2, 1968, in Tel Aviv, Israel to Israeli author and Yoel Netz, an entrepreneur and translator of Russian classics. From 1983 to 1992, Netz studied at the Tel Aviv University, obtaining a B.A. in Ancient History and an M.A. in History and the Philosophy of Science; from 1993 to 1995 studied classics at Christ College, Cambridge University, where he obtained his doctorate in 1995. From 1996 to 1999 Netz worked as a post-doctoral research fellow at Gonville and Caius College, Cambridge, and concurrently in 1998 and 1999 worked as a post-doctoral fellow at MIT. In the fall of 1999 he took a position as an assistant professor in the Stanford University Department of Classics, where he has continued to teach and publish today. Netz is married to Maya Arad, an Israeli writer who is widely considered "the foremost Hebrew writer outside Israel". The couple has two daughters. Netz's major research interest include the wider issues of the history of cognitive practices; for example the history of the book, visual culture, literacy and numeracy. He is the author of a number of works in field, including volumes I and II of The Archimedes Palimpsest. He also co-authored The Archimedes Codex with William Noel on the same subject matter, but oriented towards a public audience. It received the Neumann Prize as well as several works published by the Cambridge University Press, including The Shaping of Deduction in Greek Mathematics: a Study in Cognitive History (1999, Runciman Award), The Transformation of Early Mediterranean Mathematics: From Problems to Equations (2004), and Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic (2009). In 2014 he was awarded the Commandino Medal at the Urbino University for his contributions to the history of science. Netz has also appeared as a subject matter expert on PBS's Nova concerning ancient mathematics. In addition to his work on the history of mathematics, Netz has published some Hebrew poetry, including "Adayin Baḥutz" in 1999. Selected publications The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History, Cambridge: Cambridge University Press, 1999, . The Works of Archimedes: Translation and Commentary, Vol. I: The Two Books "On The Sphere and the Cylinder", Cambridge: Cambridge University Press, 2004 and 2009 . Barbed Wire: an Ecology of Modernity, Middletown, CT: Wesleyan University Press, 2007, . With William Noel, The Archimedes Codex: Revealing the Secrets of the World's Greatest Palimpsest, London: Weidenfeld & Nicolson, 2007, . The Transformation of Mathematics in the Early Mediterranean World: from Problems to Equations, Cambridge: Cambridge University Press, 2007 . Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic, Cambridge: Cambridge University P
https://en.wikipedia.org/wiki/Fiber%20functor	In category theory, a branch of mathematics, a fiber functor is a faithful k-linear tensor functor from a tensor category to the category of finite-dimensional k-vector spaces. Definition A fiber functor (or fibre functor) is a loose concept which has multiple definitions depending on the formalism considered. One of the main initial motivations for fiber functors comes from Topos theory. Recall a topos is the category of sheaves over a site. If a site is just a single object, as with a point, then the topos of the point is equivalent to the category of sets, . If we have the topos of sheaves on a topological space , denoted , then to give a point in is equivalent to defining adjoint functorsThe functor sends a sheaf on to its fiber over the point ; that is, its stalk. From covering spaces Consider the category of covering spaces over a topological space , denoted . Then, from a point there is a fiber functorsending a covering space to the fiber . This functor has automorphisms coming from since the fundamental group acts on covering spaces on a topological space . In particular, it acts on the set . In fact, the only automorphisms of come from . With étale topologies There is an algebraic analogue of covering spaces coming from the étale topology on a connected scheme . The underlying site consists of finite étale covers, which are finite flat surjective morphisms such that the fiber over every geometric point is the spectrum of a finite étale -algebra. For a fixed geometric point , consider the geometric fiber and let be the underlying set of -points. Then,is a fiber functor where is the topos from the finite étale topology on . In fact, it is a theorem of Grothendieck the automorphisms of form a profinite group, denoted , and induce a continuous group action on these finite fiber sets, giving an equivalence between covers and the finite sets with such actions. From Tannakian categories Another class of fiber functors come from cohomological realizations of motives in algebraic geometry. For example, the De Rham cohomology functor sends a motive to its underlying de-Rham cohomology groups . See also Topos Étale topology Motive (algebraic geometry) Anabelian geometry References External links SGA 4 and SGA 4 IV Motivic Galois group - https://web.archive.org/web/20200408142431/https://www.him.uni-bonn.de/fileadmin/him/Lecture_Notes/motivic_Galois_group.pdf Category theory Monoidal categories
https://en.wikipedia.org/wiki/Erik%20Jan%C5%BEa	Erik Janža (born 21 June 1993) is a Slovenian professional footballer who plays as a left-back for Górnik Zabrze and the Slovenia national team. Career statistics International Scores and results list Slovenia's goal tally first, score column indicates score after each Janža goal. Honours Maribor Slovenian Championship: 2014–15 Slovenian Cup: 2015–16 References External links Erik Janža profile at NZS 1993 births Living people Sportspeople from Murska Sobota Slovenian men's footballers Men's association football fullbacks Slovenia men's youth international footballers Slovenia men's under-21 international footballers Slovenia men's international footballers Slovenian expatriate men's footballers ND Mura 05 players NK Domžale players NK Maribor players FC Viktoria Plzeň players Pafos FC players NK Osijek players Górnik Zabrze players Slovenian Second League players Slovenian PrvaLiga players Czech First League players Cypriot First Division players Croatian Football League players Ekstraklasa players Slovenian expatriate sportspeople in the Czech Republic Expatriate men's footballers in the Czech Republic Slovenian expatriate sportspeople in Cyprus Expatriate men's footballers in Cyprus Slovenian expatriate sportspeople in Croatia Expatriate men's footballers in Croatia Slovenian expatriate sportspeople in Poland Expatriate men's footballers in Poland
https://en.wikipedia.org/wiki/Alexander%20Skugarev	Alexander Petrovich Skugarev (; born 13 March 1975) is a retired Russian professional ice hockey center. Career statistics External links 1975 births Amur Khabarovsk players Avtomobilist Yekaterinburg players Barys Nur-Sultan players HC CSKA Moscow players HC Dynamo Moscow players Krylya Sovetov Moscow players Lokomotiv Yaroslavl players Living people Russian ice hockey centres People from Angarsk Sportspeople from Irkutsk Oblast
https://en.wikipedia.org/wiki/Bloch%27s%20formula	In algebraic K-theory, a branch of mathematics, Bloch's formula, introduced by Spencer Bloch for , states that the Chow group of a smooth variety X over a field is isomorphic to the cohomology of X with coefficients in the K-theory of the structure sheaf ; that is, where the right-hand side is the sheaf cohomology; is the sheaf associated to the presheaf , U Zariski open subsets of X. The general case is due to Quillen. For q = 1, one recovers . (see also Picard group.) The formula for the mixed characteristic is still open. References Daniel Quillen: Higher algebraic K-theory: I. In: H. Bass (ed.): Higher K-Theories. Lecture Notes in Mathematics, vol. 341. Springer-Verlag, Berlin 1973. Algebraic K-theory Algebraic geometry Theorems in algebraic topology
https://en.wikipedia.org/wiki/Privacy-preserving%20computational%20geometry	Privacy-preserving computational geometry is the research area on the intersection of the domains of secure multi-party computation (SMC) and computational geometry. Classical problems of computational geometry reconsidered from the point of view of SMC include shape intersection, private point inclusion problem, range searching, convex hull, and more. A pioneering work in this area was a 2001 paper by Atallah and Du, in which the secure point in polygon inclusion and polygonal intersection problems were considered. Other problems are computation of the distance between two private points and secure two-party point-circle inclusion problem. Problem statements The problems use the conventional "Alice and Bob" terminology. In all problems the required solution is a protocol of information exchange during which no additional information is revealed beyond what may be inferred from the answer to the required question. Point-in-polygon: Alice has a point a, and Bob has a polygon B. They need to determine whether a is inside B. Polygon pair intersection: Alice has a polygon A, and Bob has a polygon B. They need to determine whether A intersects B. References Theory of cryptography Computational geometry Computational fields of study
https://en.wikipedia.org/wiki/Dan%20Laksov	Dan Laksov (10 July 1940 – 25 October 2013) was a Norwegian-Swedish mathematician and human rights activist. He was primarily active within the field of algebraic geometry. Biography Laksov was born in Oslo in 1940, the same year that Norway was occupied by Nazi Germany. He was a son of Amalie Laksov (née Scheer) and Håkon Laksov (ne Laks), both born 1911; the family were Jews. The ancestors on both sides had immigrated from Russia via the Baltics to Norway in the late 19th century. Håkon Laksov was a lawyer and active in the Jewish community. In the book I slik en natt. Historien om deportasjonen av jøder fra Norge by Kristian Ottosen, the escape of Amalie and Dan from Norway in November 1942 is chronicled. Håkon and Amalie's four brothers were all captured in October 1942 as a part of the arresting of all Norwegian Jews, shipped on SS Donau to Auschwitz in November 1942 and perished there sometime in early 1943. Amalie had been tipped off ahead of the next wave of arrests and managed to hide together with her young son at various addresses in Oslo before being able to flee to Sweden, where they reunited with Amalie's mother and two aunts and spent the rest of the war in Norrköping. The family's apartment was usurped by the family of a leading Young Nazi leader, Bjørn Østring, but retrieved after the war. In 1945 Dan returned to Oslo where he lived with his grandparents, while Amalie commuted to Bergen. After finishing secondary school, he studied one year at a commercial high school before entering University of Bergen in 1960 where he studied mathematics. He graduated in 1964 and after one year of non-armed conscription service, he travelled to Paris on a scholarship to study at Institut Henri Poincaré. In Paris he encountered Steven Kleiman and in 1967 Laksov became one of Kleiman's Ph.D. students at Columbia University, and when Kleiman moved to Massachusetts Institute of Technology (MIT) in 1968 Laksov followed him. Laksov took his Ph.D. from MIT in 1972 and wrote a thesis with the title The Structure of Schubert Schemes and Schubert Cycles. He remained one year at MIT as a postdoc. During the next couple of years he mostly alternated between Oslo and Stockholm. 1978–1981 he was head of algebraic geometry at the Mittag-Leffler Institute in Stockholm. 1981–1984 he was a senior lecturer at the University of Stockholm and 1984–1986 he was professor of mathematics at Uppsala University. From 1986 to his retirement he was professor of mathematics at the Royal Institute of Technology in Stockholm . He also served as a director of the Mittag-Leffler Institute during the period 1986–1994 and was editor of the institute's journal Acta Mathematica. His main contributions were in algebra, algebraic geometry and Schubert calculus. He was a foreign member of the Royal Swedish Academy of Sciences and a fellow of the Norwegian Academy of Science and Letters. In 2008 he received an honorary degree at the University of Bergen. In 1983, his mother Amali
https://en.wikipedia.org/wiki/The%20Game%20of%20Life%20%28disambiguation%29	The Game of Life, also known as Life, is an 1860 board game by Milton Bradley. Game of Life also often refers to: Conway's Game of Life, in mathematics, a cellular automaton Game of Life or The Game of Life may also refer to: Games Jinsei Game, the 1967 Japanese version of the board game The Game of Life Card Game, a 2002 card game based on the board game The Game of Life/Yahtzee/Payday, a 2005 video game based on the board game The Game of Life: Twists & Turns, a 2007 board game variant of the original game Other Game of Life (film) (2007, 2011), a film originally titled Oranges The Game of Life (TV programme), a 1986 ABC programme "The Game of Life", a song by Scorpions from their album Humanity: Hour I The Game of Life (1922 film), a 1922 film by G. B. Samuelson The Game of Life (album), a 2007 music album by Arsonists Get All the Girls The Game of Life (book), a 1925 book by Florence Scovel Shinn Da Game of Life (film), a 1998 direct-to-video short film starring Snoop Dogg Da Game of Life, a 2001 rap music album by Totally Insane See also Evolution: The Game of Intelligent Life Life simulation game
https://en.wikipedia.org/wiki/String%20phenomenology	String phenomenology is a branch of theoretical physics that uses tools from mathematics and computer science to study the implications of string theory for particle physics and cosmology. In cosmology, string phenomenology studies, among others, implications of string theory for inflation, dark matter and dark energy. In particle physics, efforts include finding realistic or semi-realistic models of particle physics within the string theory landscape. The term "realistic" is usually taken to mean that the low energy limit of string theory yields a model which bears a resemblance to the Minimal Supersymmetric Standard Model (MSSM) or the Standard Model (SM). The latter is obtained after supersymmetry breaking or by starting from a string theory without (target space) supersymmetry. A complementary approach to studying the landscape of string theory solutions is to look at the swampland, which consists of low-energy theories that are not compatible with string theory or sometimes even any quantum theory of gravity. See also String cosmology String theory landscape Swampland References String theory Physics beyond the Standard Model Physical cosmology
https://en.wikipedia.org/wiki/Peter%20Landweber	Peter Steven Landweber (born August 17, 1940, in Washington D. C.) is an American mathematician working in algebraic topology. Landweber studied at the University of Iowa (B.SC. 1960) and Harvard University (master's degree 1961), where he graduated in 1965 after studying under Raoul Bott (Künneth formulas for bordism theories). He was then Assistant Professor at the University of Virginia (from 1965) and at Yale University from 1968 to 1970. From 1967 to 1968 he was at the Institute for Advanced Study in Princeton, New Jersey. In 1970, he became Associate Professor at Rutgers University, where he taught from 1974 until his retirement in 2007. From 1974 to 1975 he was a NATO fellow at the University of Cambridge. Since 2007, he is a Professor Emeritus at Rutgers University. Landweber studied complex bordism in algebraic topology (introducing Landweber–Novikov algebra in the 1960s). In the beginning of the 1970s, he proved his exact functor theorem, which allows the construction of a homology theory from a formal group law. In 1986 he introduced elliptic cohomology with Douglas C. Ravenel and Robert E. Stong, which is a generalized cohomology theory with applications to modular forms and elliptic curves. From 1989 to 1992 he was Chairman of the Russian translation Committee of the American Mathematical Society. He is also a fellow of the society. Peter Landweber is the elder son of the engineer Louis Landweber and the father of the molecular biologist Laura Faye Landweber (born 1967) and of the mathematician Gregory David Landweber (born 1971). Selected publications (Ed.): elliptic curves and modular forms in algebraic topology (= lecture notes in mathematics. ) issue 1326). Springer 1988 (proceedings of a Conference at the Institute for Advanced Study in 1986). Landweber: other elliptic and modular forms. PP. 55–86; Elliptic genera-of introductory overview. pg. 1–10. References External links Haynes Miller : A marriage of manifolds and algebra: The mathematical work of Peter Landweber Web page on his 60th birthday 1940 births Living people 20th-century American mathematicians 21st-century American mathematicians University of Iowa alumni Harvard University alumni University of Virginia faculty Yale University faculty Rutgers University faculty Fellows of the American Mathematical Society Mathematicians from Washington, D.C. Topologists
https://en.wikipedia.org/wiki/Pierre%20Schapira%20%28mathematician%29	Pierre Schapira (born April 28, 1943) is a French mathematician. He specializes in algebraic analysis, especially Mikio Sato's microlocal analysis, together with the mathematical concepts of sheaves and derived categories. Schapira received his doctorate for work on hyperfunctions. Although these were already in use in France by André Martineau, they were further developed by Schapira and Jacques-Louis Lions. This work earned Shapira an invitation to Kyoto University, where he met Masaki Kashiwara. Together, they developed the microlocal theory of sheaves, and have co-authored many papers spanning several decades. He served as a professor at the Paris 13 University in the 1980s and has been a professor at the Pierre and Marie Curie University since the 1990s. In 1990, he was an invited speaker at the International Congress of Mathematicians in Kyoto, speaking on sheaf theory for partial differential equations. Schapira was inducted as a fellow of the American Mathematical Society with the Society's inaugural class of Fellows in 2013. See also Mikio Sato Masaki Kashiwara Jean Leray Alexander Grothendieck References External links Pierre Schapira's page at Institut de Mathématiques de Jussieu-Paris Rive Gauche Videos of Pierre Schapira in the AV-Portal of the German National Library of Science and Technology 1943 births Living people 20th-century French mathematicians 21st-century French mathematicians Academic staff of the University of Paris Fellows of the American Mathematical Society
https://en.wikipedia.org/wiki/Daryono	Daryono (5 March 1994 – 9 November 2020) was an Indonesian professional footballer who played as a goalkeeper. On 9 November 2020, Daryono died because of the disease dengue fever. Career statistics Club Honours Club honors Persija Jakarta Liga 1: 2018 Indonesia President's Cup: 2018 References 1994 births 2020 deaths Men's association football goalkeepers Badak Lampung F.C. players Liga 1 (Indonesia) players Liga 2 (Indonesia) players Persija Jakarta players Footballers from Semarang Indonesian men's footballers Infectious disease deaths in Indonesia Deaths from dengue fever
https://en.wikipedia.org/wiki/Stefan%20%C4%90or%C4%91evi%C4%87%20%28footballer%2C%20born%201991%29	Stefan Đorđević (; also transliterated Stefan Djordjević; born 13 March 1991) is a Serbian professional footballer who plays as a defender for Vojvodina in the Serbian SuperLiga. Career statistics Honours Vojvodina Serbian Cup: 2019–20 References External links Stefan Đorđević at Utakmica.rs 1991 births Living people Footballers from Novi Sad Men's association football defenders Serbian men's footballers FK Proleter Novi Sad players FK Spartak Subotica players FK Banat Zrenjanin players FK Voždovac players Red Star Belgrade footballers FK Borac Čačak players Catania FC players FK Radnički Niš players FK Vojvodina players Serbian SuperLiga players Serbian First League players Serie C players Serbian expatriate men's footballers Expatriate men's footballers in Italy
https://en.wikipedia.org/wiki/Mfulupinga%20Nlando%20Victor	Mfulupinga Nlando Victor (15 December 1944 – 2 July 2004) was a member of the Angola National Assembly and a teacher of mathematics. He was distinguished as founder of the political party PDP-ANA and President of the same. On 2 July 2004, 60-year-old Victor died as a result of an assault by fatal gunshot wound. Biography Mfulupinga Nlandu Victor was born on 15 December 1944 in the municipality of Maquela do Zombo, Uige province, Angola. He was in exile in what was then Congo Leopoldville, due to colonial repression. During his time here, he focused on devoting himself to his studies and the mobilization of Angolan students outside the country. Later, he was elected president of the Angolan college students in the Democratic Republic of the Congo. He organized and directed the first congress of Angolan students in exile, which hosted about 500 participants from various continents, held in Kinshasa (DRC). He returned to Angola after independence in 1975 and became a member of the Interim Board of the Association. Mfulupinga Victor created a focus group that culminated on 17 March 1991 with the constitution of the PDP - ANA, where he served as the president of the party. He was a professor at Agostinho Neto University, where he taught mathematics and held the positions of head of the Mathematics Department at the Faculty of Economics and Head of the Department of Mathematics and Engineering in the College of Geographical Sciences. After founding the PDP - ANA, of which he served as president, he was elected as a deputy to the National Assembly in the legislatures from 1992 to 1996. From 1996 to 2004, he was a member of the 6th Commission and the Council of the Republic. Mfulupinga Nlandu Victor was killed on 2 July 2004 in Luanda, hours after attending a meeting of the Council of the Republic. He was hit by gunfire from a machine gun, it was speculated to be that of an AK, while driving his car outside the headquarters of his party around the Cassenda, Maianga district neighborhood. The politician received treatment at the Clinic Endiama on Luanda Island, where he eventually succumbed to his injuries. The perpetrators fled with the vehicle's deputy and still have not been caught, decades later. The politician left behind a widow and five children. References Angolan politicians 2004 deaths 1944 births Academic staff of the Agostinho Neto University
https://en.wikipedia.org/wiki/Urs%20Schreiber	Urs Schreiber (born 1974) is a mathematician specializing in the connection between mathematics and theoretical physics (especially string theory) and currently working as a researcher at New York University Abu Dhabi. He was previously a researcher at the Czech Academy of Sciences, Institute of Mathematics, Department for Algebra, Geometry and Mathematical Physics. Education Schreiber obtained his doctorate from the University of Duisburg-Essen in 2005 with a thesis supervised by Robert Graham and titled From Loop Space Mechanics to Nonabelian Strings. Work Schreiber's research fields include the mathematical foundation of quantum field theory. Schreiber is a co-creator of the nLab, a wiki for research mathematicians and physicists working in higher category theory. Selected writings With Hisham Sati, Mathematical Foundations of Quantum Field and Perturbative String Theory, Proceedings of Symposia in Pure Mathematics, volume 83 AMS (2011) Notes References Interview of John Baez and Urs Schreiber External links Home page in nLab Category theorists 21st-century German mathematicians Living people 1974 births Science bloggers
https://en.wikipedia.org/wiki/Frobenius%20category	In category theory, a branch of mathematics, a Frobenius category is an exact category with enough projectives and enough injectives, where the classes of projectives and injectives coincide. It is an analog of a Frobenius algebra. Properties The stable category of a Frobenius category is canonically a triangulated category. See also Dagger compact category Tannakian category References Section 13.4 of Monoidal categories
https://en.wikipedia.org/wiki/Kenneth%20Brown%20%28mathematician%29	Kenneth Stephen Brown (born 1945) is a professor of mathematics at Cornell University, working in category theory and cohomology theory. Among other things, he is known for Ken Brown's lemma in the theory of model categories. He is also the author of the book Cohomology of Groups (Graduate Texts in Mathematics 87, Springer, 1982). Brown earned his Ph.D. in 1971 from the Massachusetts Institute of Technology, under the supervision of Daniel Quillen, with thesis Abstract Homotopy Theory and Generalized Sheaf Cohomology. He was an invited speaker at the International Congress of Mathematicians in 1978 in Helsinki. In 2012 he became a fellow of the American Mathematical Society. References 1945 births Place of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians Massachusetts Institute of Technology School of Science alumni Cornell University faculty Fellows of the American Mathematical Society Category theorists Topologists
https://en.wikipedia.org/wiki/2013%20CECAFA%20Cup%20statistics	The following article contains statistics for the 2013 CECAFA Cup, which took place in Kenya from 27 November to 12 December 2013. Goals scored from penalty shoot-outs are not counted. Goalscorers 5 goals Salah Ibrahim 3 goals Jockins Atudo Allan Wanga Ronald Kampamba Festus Mbewe 2 goals Mrisho Ngasa Mbwana Samatta Emmanuel Okwi Dan Sserunkuma Bornwell Mwape 1 goal Fiston Abdul Razak Christophe Nduwarugira Fasika Asfaw Saladin Bargicho Biruk Kalbore Yonathan Kebede Yussuf Saleh Jacob Keli Clifton Miheso David Owino Michel Ndahinduka Richard Justin Lado Fabiano Lako Moaaz Abdelraheem Muhannad El Tahir Haruna Chanongo Said Morad Khalid Aucho Hamis Kiiza Martin Kayongo-Mutumba Awadh Juma Issa Abdi Kassim Adeyum Saleh 1 own goal Saladin Bargicho (playing against Sudan) Scoring Wins and losses Disciplinary record By team By individual Overall statistics Bold numbers indicate maximum values in each column. See also 2013 CECAFA Cup schedule References statistics
https://en.wikipedia.org/wiki/Jerrold%20B.%20Tunnell	Jerrold Bates Tunnell (September 16, 1950 – April 1, 2022) was a mathematician known for his work in number theory. He was an associate professor of mathematics at Rutgers University. Early life and education Tunnell was born on September 16, 1950, in Dallas, Texas. He graduated from Harvey Mudd College in 1972. He received his PhD in Mathematics from Harvard University in 1977. His thesis, On the Local Langlands Conjecture for GL(2), was advised by John Tate. Career After graduation, Tunnell taught at Princeton University and was a member of the Institute for Advanced Study from 1982 to 1983. He joined the mathematics faculty at Rutgers University in 1983, eventually becoming an associate professor of mathematics. He advised 7 PhD students. Research In 1981, Tunnell generalized Langlands' work on the Artin conjecture, establishing a special case known as the Langlands–Tunnell theorem that later became a key component in the proof of Fermat's Last Theorem. He proved Tunnell's theorem in 1983, which gives a partial unconditional solution to the congruent number problem and a complete solution conditional on the Birch and Swinnerton-Dyer conjecture. Awards and honors In 2013, Tunnell was elected in the inaugural class of Fellows of the American Mathematical Society. Personal life Starting in 2004, Tunnell made cross-country cycling trips from Highland Park, New Jersey, to Syracuse, New York, in every U.S. election cycle. Tunnell died on April 1, 2022, in rural Texas. He was hit by a truck while riding his bicycle from St. Augustine, Florida, to his 50th class reunion at Harvey Mudd College in Claremont, California. References External links 1950 births 2022 deaths 20th-century American mathematicians 21st-century American mathematicians Rutgers University faculty Fellows of the American Mathematical Society Harvard University alumni Harvey Mudd College alumni Educators from Texas Writers from Dallas Road incident deaths in Texas
https://en.wikipedia.org/wiki/Jonathan%20Rosenberg%20%28mathematician%29	Jonathan Micah Rosenberg (born December 30, 1951 in Chicago, Illinois) is an American mathematician, working in algebraic topology, operator algebras, K-theory and representation theory, with applications to string theory (especially dualities) in physics. Rosenberg received his Ph.D. in 1976, under the supervision of Marc Rieffel, from the University of California, Berkeley (Group C-algebras and square integrable representations). From 1977 to 1981 he was an assistant professor at the University of Pennsylvania. Since 1981, he has been at the University of Maryland at College Park where he is the Ruth M. Davis Professor of Mathematics. He is also a fellow of the American Mathematical Society (AMS). He studies operator algebras and their relations with topology, geometry, with the unitary representation theory of Lie groups, K-theory and index theory. Along with H. Blaine Lawson and Mikhail Leonidovich Gromov, he is known for the Gromov–Lawson–Rosenberg conjecture. Since 2015 he has been a managing editor of the Annals of K-Theory. During 2007-2015 he was an editor of the Journal of K-Theory. Before that, he was an associate editor of the Journal of the AMS (2000-2003), and of the Proceedings of the AMS (1988-1992). He was a Sloan Fellow from 1981 to 1984. Writings Algebraic K-Theory and its Applications, Graduate Texts in Mathematics, Springer Verlag 1996 With Kevin Coombes, Ronald Lipsman: Multivariable calculus and Mathematica: with applications to geometry and physics, Springer Verlag 1998 With Joachim Cuntz, Ralf Meyer: Topological and bivariant K-theory, Birkhauser 2007 Editor Robert Doran, Greg Friedman: Superstrings, geometry, topology and C algebras, Proc. Symposia in Pure Mathematics, American Mathematical Society in 2010 (CBMS-NSF regional conference in Fort Worth 2009) With Claude Schochet: The Künneth theorem and the universal coefficient theorem for equivariant K-theory and KK-theory, Memoirs American Mathematical Society 1988 With Claude Schochet: The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor. Duke Math J. 55 (1987), no 2, 431–474. Editor Steven C. Ferry, Andrew Ranicki: Novikov Conjectures, Rigidity and Index Theorem, London Mathematical Society Lecture Notes Series 226, Cambridge University Press, 1995, 2 volumes (Oberwolfach Meeting 1993) C-algebras, positive scalar curvature, and the Novikov Conjecture, Part 1, Publ Math IHES, Volume 58, 1983, pp. 197–212, Part 2, in H. Araki, Eros, EC (ed.) Geometric Methods in Operator Algebras, Pitman Research Notes in Math 123 (1986), Longman / Wiley, pp. 341, part 3, Topology 25 (1986), 319 C -algebras, positive scalar curvature, and the Novikov conjecture. Inst Hautes Etudes Sci. No Publ Math. 58 (1983), 197-212 (1984). Editor with Sylvain Cappell, Andrew Ranicki: Surveys on Surgery Theory. Papers dedicated to CTC Wall, Princeton University Press, 2 vols, 2001 The KO-assembly map and positive scalar curvature, in S. Jackowski, B.
https://en.wikipedia.org/wiki/Ron%20Donagi	Ron Yehuda Donagi (born March 9, 1956) is an American mathematician, working in algebraic geometry and string theory. Career Donagi received a Ph.D. in 1977 under the supervision of Phillip Griffiths from Harvard University (On the geometry of Grassmannians). Currently, he is a professor at the University of Pennsylvania. From 1981 to 1982, from 1996 to 1997 and in 2013 he was at the Institute for Advanced Study, where he worked with Edward Witten. In the 1980s Donagi applied algebraic geometry to string theory and related theories such as supersymmetric Yang-Mills theories in order to develop models for heterotic string theory from suitable compactifications. Among his achievements in classical algebraic geometry are his work on the Schottky problem and generalizing the Torelli theorem. He is a fellow of the American Mathematical Society. Writings With Tony Pantev: Torus fibrations, Gerbes and duality, Memoirs AMS 2008 Editor with Mauro Francaviglia: Integrable systems and quantum groups (CIME Lectures, Montcatini Terme, June 1993), Springer Verlag 1996 Publisher: Curves, Jacobians, and Abelian varieties, Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on the Schottky problem, AMS 1992 With Katrin Wendland (Eds.): From Hodge theory to integrability and TQFT: tt *-geometry (Workshop University of Augsburg 2007), AMS 2008 With Witten: Supersymmetric Yang-Mills Systems and Integrable Systems, Nucl. Phys. B, 460, 1996, 299-344, Arxiv With Josh Guffin, Sheldon Katz, Eric Sharpe, A mathematical theory of quantum sheaf cohomology, Preprint 2011 With Guffin, Katz, Sharpe: Physical aspects of quantum sheaf cohomology for deformation of tangent bundles of toric varieties, Preprint 2011 With Vincent Bouchard, on SU (5) Heterotic standard model, Phys. Lett. B, 633, 2006, 783-791 References External links Homepage 1956 births Living people 20th-century American mathematicians 21st-century American mathematicians Harvard University alumni University of Pennsylvania faculty Mathematicians at the University of Pennsylvania Fellows of the American Mathematical Society
https://en.wikipedia.org/wiki/Peponia%2C%20Kozani	Peponia () is a village and a community of the Voio municipality. In the late Ottoman period, it was inhabited by Vallahades; in the 1900 statistics of Vasil Kanchov, where the town appears under its Bulgarian name "Laya", it was inhabited by some 300 "Greek Muslims". Before the 2011 local government reform it was part of the municipality of Neapoli, of which it was a municipal district. The 2011 census recorded 70 inhabitants in the village. References Populated places in Kozani (regional unit) Voio (municipality)
https://en.wikipedia.org/wiki/Time%20domain%20electromagnetics	In physics and mathematics, time domain electromagnetics refers to one of two general groups of techniques (in mathematics, often called ansätze) that describe electromagnetic wave motion. In contrast with frequency domain electromagnetics, which are based on the Fourier or Laplace transform, time domain keeps time as an explicit independent variable in descriptive equations or wave motion. References S. M. Rao, E. K. Miller, Time Domain Electromagnetics, Academic Press: San Diego etc., 1999. External links The Virtual Institute for Nonlinear Optics (VINO), a research collaboration devoted to the investigation of X-waves and conical waves in general Nolinear X-waves page at the nlo.phys.uniroma1.it website. Wave mechanics
https://en.wikipedia.org/wiki/Soccer%20records%20and%20statistics%20in%20South%20Africa	The top tier of football in South Africa was renamed the Premier Soccer League, for the start of the 1996-97 season. The following page details the football records and statistics of the Premier Division since that date. Titles Most titles: 13 Mamelodi Sundowns Most consecutive title wins: 6 Mamelodi Sundowns: (2017-18, 2018-19, 2019-20, 2020-21, 2021-22, 2022-23) Biggest title winning margin (34 games): 8 points Manning Rangers: (1996-97)Biggest title winning margin (30 games): 16 points Mamelodi Sundowns: (2021-2022)Smallest title winning margin: 0 points and +5 goal difference — (1998-99) Mamelodi Sundowns (+44) over Kaizer Chiefs (+39) WinsMost wins in a season (34 games): 23 Manning Rangers (1996-97) Mamelodi Sundowns (1998-99), (1999-2000) Kaizer Chiefs (1998-99)Most wins in a season (30 games): 22 Mamelodi Sundowns (2015-16)Most wins in total: 384 Mamelodi Sundowns DrawsMost draws in a season (34 games): 16 draws Supersport United (1996-97) Jomo Cosmos (1996-97)Most draws in a season (30 games): 20 draws Moroka Swallows (2020-2021)Most draws in total: 239 Kaizer ChiefsMost home draws in a season (34 games):Most home draws in a season (30 games):Most away draws in a season (34 games):Most away draws in a season (30 games):Fewest draws in a season: 3 draws Santos (1997-98)Fewest home draws in a season:Fewest away draws in a season:Most consecutive draws in a season:LossesMost losses in a season (34 games): 28 Mother City (1999–2000)Fewest losses in a season (30 games): 1 Mamelodi Sundowns (2020–2021)Most losses in total: 184 Amazulu AttendanceHighest attendance: 92,515 Kaizer Chiefs v. Orlando Pirates (2010-2011) GoalsMost goals in a season: 73 Kaizer Chiefs (1998–1999)Fewest goals in a season: 22 Mother City (1999–2000)Most goals conceded in a season: 85 Mother City (1999–2000)Fewest goals conceded in a season: 11 Kaizer Chiefs (2003–2004)Best goal difference in a season: +44 Mamelodi Sundowns (1998–1999)Worst goal difference in a season: -63 Mother City (1999–2000)Most goals by relegated team: Most goals in total: 753 Kaizer ChiefsMost goals conceded: 771 Moroka SwallowsLargest goal deficit overcome to win: Largest goal deficit overcome to draw:PointsMost points in a season: 71 Mamelodi Sundowns (2015-2016) Fewest points in a season: 10 Mother City (1999–2000)Fewest away points in a season: 0 Mother City (1999–2000)Fewest points surviving relegation:Promotion and change in positionSurviving promoted clubs: Relegated promoted clubs: Promoted but never relegated:Biggest rise in position:Biggest fall in position:Lowest finish by defending champions:MiscellaneousMost Premier Soccer League Medals: 10 Denis Onyango – Premier Soccer League: 2007–08, 2008–09, 2009–10, 2015–16, 2017–18, 2018–19, 2019–20, 2020–21, 2021–22, 2022–23 Appearances and goalsMost Premier Soccer League appearances: 316 Edries Burton (1996/1997–2006/2007)Most Premier Soccer League appearances for one club: 316 Edries Burton (Engen Santos)Oldest player: 46 years
https://en.wikipedia.org/wiki/Simple%20space	In algebraic topology, a branch of mathematics, a simple space is a connected topological space that has a homotopy type of a CW complex and whose fundamental group is abelian and acts trivially on the homotopy and homology of the universal covering space. Though not all authors include the assumption on the homotopy type. Examples Topological groups For example, any topological group is a simple space (provided it satisfies the condition on the homotopy type). Eilenberg-Maclane spaces Most Eilenberg-Maclane spaces are simple since the only nontrivial homotopy group is in degree . This means the only non-simple spaces are for nonabelian. Universal covers Every connected topological space has an associated universal space from the universal cover since and the universal cover of a universal cover is the universal cover itself. References Dennis Sullivan, Geometric Topology Algebraic topology
https://en.wikipedia.org/wiki/Assouad%20dimension	In mathematics — specifically, in fractal geometry — the Assouad dimension is a definition of fractal dimension for subsets of a metric space. It was introduced by Patrice Assouad in his 1977 PhD thesis and later published in 1979, although the same notion had been studied in 1928 by Georges Bouligand. As well as being used to study fractals, the Assouad dimension has also been used to study quasiconformal mappings and embeddability problems. Definition Let be a metric space, and let be a non-empty subset of . For , let denote the least number of metric open balls of radius less than or equal to with which it is possible to cover the set . The Assouad dimension of is defined to be the infimal for which there exist positive constants and so that, whenever the following bound holds: The intuition underlying this definition is that, for a set with "ordinary" integer dimension , the number of small balls of radius needed to cover the intersection of a larger ball of radius with will scale like . Relationships to other notions of dimension The Assouad dimension of a metric space is always greater than or equal to its Assouad–Nagata dimension. The Assouad dimension of a metric space is always greater than or equal to its upper box dimension, which in turn is greater than or equal to the Hausdorff dimension. The Lebesgue covering dimension of a metrizable space is the minimal Assouad dimension of any metric on . In particular, for every metrizable space there is a metric for which the Assouad dimension is equal to the Lebesgue covering dimension. References Further reading Dimension theory Fractals Metric geometry

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.