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https://en.wikipedia.org/wiki/Symbolic%20language%20%28mathematics%29	In mathematics, a symbolic language is a language that uses characters or symbols to represent concepts, such as mathematical operations, expressions, and statements, and the entities or operands on which the operations are performed. See also Formal language Language of mathematics List of mathematical symbols Mathematical Alphanumeric Symbols Mathematical notation Notation (general) Symbolic language (other) References External links Mathematical Symbols Mathematical notation Writing systems
https://en.wikipedia.org/wiki/Miranda%20Oliveira	Miranda "Clarival" Oliveira is a former Brazilian soccer player who played in the NASL. Career statistics Club Notes References Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football forwards Madureira Esporte Clube players Club Olimpia footballers C.D. Marathón players Kansas City Spurs players Washington Darts players Montreal Olympique players North American Soccer League (1968–1984) players Expatriate men's footballers in Paraguay Brazilian expatriate sportspeople in Paraguay Expatriate men's footballers in El Salvador Brazilian expatriate sportspeople in El Salvador Expatriate men's footballers in Honduras Brazilian expatriate sportspeople in Honduras Expatriate men's soccer players in the United States Brazilian expatriate sportspeople in the United States Expatriate men's soccer players in Canada Brazilian expatriate sportspeople in Canada Year of birth missing (living people) Footballers from Rio de Janeiro (city)
https://en.wikipedia.org/wiki/Tibor%20Szalay	Tibor Szalay Csikos (born 26 January 1938) is a former Hungarian football player. Career statistics Club Notes References 1938 births Living people Hungarians in Slovakia People from Nové Zámky District Footballers from the Nitra Region Hungarian men's footballers Hungarian expatriate men's footballers Men's association football midfielders MTK Budapest FC players FK Austria Wien players Sevilla FC players FC Barcelona players New York Hungaria players Real Murcia CF players Beşiktaş J.K. footballers Philadelphia Spartans players Houston Stars players Kansas City Spurs players Philadelphia Ukrainians players Washington Darts players Cosmopolitan Soccer League players National Professional Soccer League (1967) players North American Soccer League (1968–1984) players American Soccer League (1933–1983) players Expatriate men's footballers in Austria Hungarian expatriate sportspeople in Austria Expatriate men's footballers in Spain Hungarian expatriate sportspeople in Spain Expatriate men's soccer players in the United States Hungarian expatriate sportspeople in the United States Expatriate men's footballers in Turkey Hungarian expatriate sportspeople in Turkey
https://en.wikipedia.org/wiki/Luciano%20Mac%C3%ADas	Luciano Antonio Macías Argencio (28 May 1935 – 5 August 2022) was an Ecuadorian soccer player who played as a defender in the NASL. He also played for the Ecuador national team. Career statistics Club International References 1935 births 2022 deaths Ecuadorian men's footballers Men's association football defenders Ecuador men's international footballers North American Soccer League (1968–1984) players Barcelona S.C. footballers Miami Toros players Ecuadorian football managers Barcelona S.C. managers Ecuadorian expatriate men's footballers Ecuadorian expatriate sportspeople in Venezuela Expatriate men's footballers in Venezuela Ecuadorian expatriate sportspeople in the United States Expatriate men's soccer players in the United States People from Santa Elena Province
https://en.wikipedia.org/wiki/Abbadia%20El%20Mustapha	Abbadia El Mustapha is a former Moroccan soccer player who played in the NASL. Career statistics Club Notes References Living people Moroccan men's footballers Moroccan expatriate men's footballers Men's association football forwards Montreal Olympique players North American Soccer League (1968–1984) players Expatriate men's soccer players in Canada Moroccan expatriate sportspeople in Canada Year of birth missing (living people)
https://en.wikipedia.org/wiki/Emanuel%20Carrette	Emanuel Carrette (born May 24, 1948), is a former Brazilian soccer player who played in the NASL. Career statistics Club Notes References Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football forwards CR Flamengo footballers Associação Desportiva Ferroviária Vale do Rio Doce players Ceará Sporting Club players New York Cosmos (1970–1985) players Denver Dynamos players Campeonato Brasileiro Série A players North American Soccer League (1968–1984) players Expatriate men's soccer players in the United States Brazilian expatriate sportspeople in the United States 1948 births
https://en.wikipedia.org/wiki/Richard%20Blackmore%20%28footballer%29	Richard Blackmore (born 18 October 1953), is a former English footballer who played in the NASL. He recorded a total of 407 appearances for Irish side Dundalk. Career statistics Club Notes References 1953 births Living people English men's footballers Men's association football goalkeepers Walsall F.C. players Bristol City F.C. players New York Cosmos (1970–1985) players Birmingham City F.C. players Dundalk F.C. players Denver Dynamos players Galway United F.C. players North American Soccer League (1968–1984) players English expatriate men's footballers Expatriate men's association footballers in the Republic of Ireland English expatriate sportspeople in Ireland Expatriate men's soccer players in the United States English expatriate sportspeople in the United States Footballers from Birmingham, West Midlands
https://en.wikipedia.org/wiki/Ceyhan%20Yazar	Ceyhan Yazar (born February 1, 1944), is a former Turkish soccer player who played in the NASL. Career statistics Club Notes References Living people Turkish men's footballers Turkish expatriate men's footballers Men's association football forwards Göztepe S.K. footballers Rochester Lancers (1967–1980) players New York Cosmos (1970–1985) players North American Soccer League (1968–1984) players Expatriate men's soccer players in the United States Turkish expatriate sportspeople in the United States 1944 births Sportspeople from Antalya
https://en.wikipedia.org/wiki/Finiteness%20properties%20of%20groups	In mathematics, finiteness properties of a group are a collection of properties that allow the use of various algebraic and topological tools, for example group cohomology, to study the group. It is mostly of interest for the study of infinite groups. Special cases of groups with finiteness properties are finitely generated and finitely presented groups. Topological finiteness properties Given an integer n ≥ 1, a group is said to be of type Fn if there exists an aspherical CW-complex whose fundamental group is isomorphic to (a classifying space for ) and whose n-skeleton is finite. A group is said to be of type F∞ if it is of type Fn for every n. It is of type F if there exists a finite aspherical CW-complex of which it is the fundamental group. For small values of n these conditions have more classical interpretations: a group is of type F1 if and only if it is finitely generated (the rose with petals indexed by a finite generating family is the 1-skeleton of a classifying space, the Cayley graph of the group for this generating family is the 1-skeleton of its universal cover); a group is of type F2 if and only if it is finitely presented (the presentation complex, i.e. the rose with petals indexed by a finite generating set and 2-cells corresponding to each relation, is the 2-skeleton of a classifying space, whose universal cover has the Cayley complex as its 2-skeleton). It is known that for every n ≥ 1 there are groups of type Fn which are not of type Fn+1. Finite groups are of type F∞ but not of type F. Thompson's group is an example of a torsion-free group which is of type F∞ but not of type F. A reformulation of the Fn property is that a group has it if and only if it acts properly discontinuously, freely and cocompactly on a CW-complex whose homotopy groups vanish. Another finiteness property can be formulated by replacing homotopy with homology: a group is said to be of type FHn if it acts as above on a CW-complex whose n first homology groups vanish. Algebraic finiteness properties Let be a group and its group ring. The group is said to be of type FPn if there exists a resolution of the trivial -module such that the n first terms are finitely generated projective -modules. The types FP∞ and FP are defined in the obvious way. The same statement with projective modules replaced by free modules defines the classes FLn for n ≥ 1, FL∞ and FL. It is also possible to define classes FPn(R) and FLn(R) for any commutative ring R, by replacing the group ring by in the definitions above. Either of the conditions Fn or FHn imply FPn and FLn (over any commutative ring). A group is of type FP1 if and only if it is finitely generated, but for any n ≥ 2 there exists groups which are of type FPn but not Fn. Group cohomology If a group is of type FPn then its cohomology groups are finitely generated for . If it is of type FP then it is of finite cohomological dimension. Thus finiteness properties play an important role i
https://en.wikipedia.org/wiki/Juliette%20Kennedy	Juliette Kennedy is an associate professor in the Department of Mathematics and Statistics at the University of Helsinki. Her main research interests are mathematical logic and the foundations of mathematics. In the course of her work she has published extensively on the works of Kurt Gödel. Education and career Kennedy is an associate professor in the Department of Mathematics and Statistics at the University of Helsinki. Research areas Kennedy's research at the University of Helsinki focuses on mathematical logic in the area of set-theoretic model theory and set theory. In the course of her mathematical work she also researches the history of mathematics and the foundations of mathematics. In this context she has sustained an extensive project to place the works of Kurt Gödel in its historical and foundational context. In 2017 she published her research on the interplay between the works of Alan Turing and that of Gödel, who in 1956 defined the P versus NP problem in a letter to John von Neumann. Books Kennedy and Roman Kossak are the editors of Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies, published as Book 36 in the series Lecture Notes in Logic in 2012 by Cambridge University Press. Kennedy is the editor of Interpreting Gödel: Critical Essays, published in 2014 by Cambridge University Press and reprinted in 2017. In the book Kennedy brought together leading contemporary philosophers and mathematicians to explore the impact of Gödel's work on the foundations and philosophy of mathematics. The logician Kurt Gödel has in 1931 formulated the incompleteness theorems, which among other things prove that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. References External links Publication list at DBLP Living people Women mathematicians Mathematical logicians Women logicians University of Helsinki Year of birth missing (living people)
https://en.wikipedia.org/wiki/Toma%20Niga	Toma Marinică Niga (born 15 August 1997) is a Romanian professional footballer who plays as a goalkeeper for Liga III club Foresta Suceava. Career statistics Club Statistics accurate as of match played 29 March 2019. Honours Club FCSB Cupa României: 2019–20 References External links 1997 births Living people Footballers from Suceava County Romanian men's footballers Men's association football goalkeepers Liga I players Liga II players Liga III players ACS Foresta Suceava players FC Steaua București players LPS HD Clinceni players FC Hermannstadt players FCSB II players
https://en.wikipedia.org/wiki/Kimar%2C%20Syria	Kimar (; ) is a village in northern Syria, administratively part of the Afrin District of the Aleppo Governorate, located northwest of Aleppo. According to the Syria Central Bureau of Statistics (CBS), it had a population of 660 in the 2004 census. Syrian Civil War On 4 May 2022, a Turkish soldier was killed after Kurdish forces shelled a Turkish military vehicle in the village. References Populated places in Afrin District Towns in Aleppo Governorate Kurdish settlements in Aleppo Governorate
https://en.wikipedia.org/wiki/Mike%20Wardrop	Michael Wardrop (born 23 December 1955) is an English former footballer who played as a midfielder for Manchester United and New York Cosmos. Career statistics Club Notes References Living people 1955 births English men's footballers English expatriate men's footballers Men's association football midfielders Manchester United F.C. players New York Cosmos (1970–1985) players Kettering Town F.C. players North American Soccer League (1968–1984) players Expatriate men's soccer players in the United States English expatriate sportspeople in the United States Footballers from Salford
https://en.wikipedia.org/wiki/Irhab%2C%20Syria	Irhab () is a village in northern Syria, administratively part of the Mount Simeon District of the Aleppo Governorate, located west of Aleppo. According to the Syria Central Bureau of Statistics (CBS), it had a population of 110 in the 2004 census. References Populated places in Mount Simeon District Towns in Aleppo Governorate
https://en.wikipedia.org/wiki/Jaime%20Delgado	Jaime Delgado (born January 11, 1943) is a former Ecuadorian soccer player who played in the NASL. Career statistics Club Notes References Living people Ecuadorian men's footballers Ecuadorian expatriate men's footballers Men's association football midfielders New York Cosmos (1970–1985) players Miami Toros players North American Soccer League (1968–1984) players Expatriate men's soccer players in the United States Ecuadorian expatriate sportspeople in the United States 1943 births
https://en.wikipedia.org/wiki/D%C3%A9%20%28footballer%2C%20born%201940%29	Ademar José Ribeiro (18 February 1940 — 12 April 1992), commonly known as Dé, was a Brazilian football player who played as a left back. He played in the NASL. Career statistics Club Notes Honours Palmeiras Torneio Roberto Gomes Pedrosa: 1969 References 1940 births 1992 deaths Footballers from São Paulo (state) Brazilian men's footballers Brazilian expatriate men's footballers Men's association football defenders Associação Atlética Portuguesa (Santos) players São Paulo FC players Sociedade Esportiva Palmeiras players Esporte Clube Noroeste players New York Cosmos (1970–1985) players North American Soccer League (1968–1984) players Expatriate men's soccer players in the United States Brazilian expatriate sportspeople in the United States
https://en.wikipedia.org/wiki/Roberto%20Mauro	Roberto Mauro de Oliveira (born April 12, 1941), is a former Brazilian soccer player who played in the NASL. Career statistics Club Notes References Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football forwards América Futebol Clube (MG) players Bangu Atlético Clube players Clube Atlético Mineiro players Washington Whips players Villa Nova Atlético Clube players North American Soccer League (1968–1984) players Expatriate men's soccer players in the United States Brazilian expatriate sportspeople in the United States 1941 births Footballers from Belo Horizonte
https://en.wikipedia.org/wiki/Z%C3%A9%20Maria%20%28footballer%2C%20born%201939%29	José Maria dos Santos Motta (born May 27, 1939), commonly known as Zé Maria, is a former Brazilian soccer player who played in the NASL. Career statistics Club Notes References Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football defenders Fluminense FC players Botafogo de Futebol e Regatas players Bonsucesso Futebol Clube players Clube Náutico Capibaribe players Olaria Atlético Clube players Sport Club Internacional players Baltimore Bays players Washington Whips players National Professional Soccer League (1967) players North American Soccer League (1968–1984) players Expatriate men's soccer players in the United States Brazilian expatriate sportspeople in the United States 1939 births Footballers from Piauí
https://en.wikipedia.org/wiki/Antonio%20de%20Oliveira	Antonio de Oliveira (born August 12, 1940), is a former Brazilian soccer player who played in the NASL. Career statistics Club Notes References Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football forwards Cruzeiro Esporte Clube players Washington Whips players North American Soccer League (1968–1984) players Expatriate men's soccer players in the United States Brazilian expatriate sportspeople in the United States 1940 births Footballers from Juiz de Fora
https://en.wikipedia.org/wiki/Ney%20Marques%20de%20Sousa	Ney Marques de Sousa is a Brazilian former professional footballer who played as a midfielder. He made 21 appearances in the NASL with the Washington Whips and Washington Diplomats. Career statistics References Brazilian men's footballers Brazilian expatriate men's footballers Men's association football midfielders Clube Atlético Mineiro players Washington Whips players Washington Diplomats (NASL) players North American Soccer League (1968–1984) players Expatriate men's soccer players in the United States Brazilian expatriate sportspeople in the United States Year of birth missing Year of death missing
https://en.wikipedia.org/wiki/Bianca%20Andreescu%20career%20statistics	This is a list of career statistics of Canadian tennis player Bianca Andreescu. To date, she has won three WTA singles titles, including one major title, one Premier Mandatory and one Premier 5. Performance timelines Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup, United Cup, Hopman Cup and Olympic Games are included in win–loss records. Singles Current through the 2023 Guadalajara Open. Doubles Significant finals Grand Slam tournament finals Singles: 1 (1 title) Mixed doubles: 1 (1 runner-up) WTA 1000 finals Singles: 3 (2 titles, 1 runner-up) WTA Tour finals Singles: 6 (3 titles, 3 runner-ups) Doubles: 1 (1 runner-up) WTA Challenger finals Singles: 1 (1 title) ITF Circuit finals Singles: 9 (5 titles, 4 runner-ups) Doubles: 4 (3 titles, 1 runner-up) Junior Grand Slam finals Doubles: 2 (2 titles) WTA Tour career earnings current as of 23 May 2022 Career Grand Slam statistics Seedings The tournaments won by Andreescu are in boldface, and advanced into finals are in italics. Best Grand Slam tournament results details Record against top 10 players Andreescu's record against players who have been ranked in the top 10. Active players are in boldface. Top 10 wins Andreescu has a 11–7 () record against players who were, at the time the match was played, ranked in the top 10. Longest winning streaks 17 match win streak (2019) Notes References External links Tennis career statistics
https://en.wikipedia.org/wiki/Whitehead%27s%20algorithm	Whitehead's algorithm is a mathematical algorithm in group theory for solving the automorphic equivalence problem in the finite rank free group Fn. The algorithm is based on a classic 1936 paper of J. H. C. Whitehead. It is still unknown (except for the case n = 2) if Whitehead's algorithm has polynomial time complexity. Statement of the problem Let be a free group of rank with a free basis . The automorphism problem, or the automorphic equivalence problem for asks, given two freely reduced words whether there exists an automorphism such that . Thus the automorphism problem asks, for whether . For one has if and only if , where are conjugacy classes in of accordingly. Therefore, the automorphism problem for is often formulated in terms of -equivalence of conjugacy classes of elements of . For an element , denotes the freely reduced length of with respect to , and denotes the cyclically reduced length of with respect to . For the automorphism problem, the length of an input is measured as or as , depending on whether one views as an element of or as defining the corresponding conjugacy class in . History The automorphism problem for was algorithmically solved by J. H. C. Whitehead in a classic 1936 paper, and his solution came to be known as Whitehead's algorithm. Whitehead used a topological approach in his paper. Namely, consider the 3-manifold , the connected sum of copies of . Then , and, moreover, up to a quotient by a finite normal subgroup isomorphic to , the mapping class group of is equal to ; see. Different free bases of can be represented by isotopy classes of "sphere systems" in , and the cyclically reduced form of an element , as well as the Whitehead graph of , can be "read-off" from how a loop in general position representing intersects the spheres in the system. Whitehead moves can be represented by certain kinds of topological "swapping" moves modifying the sphere system. Subsequently, Rapaport, and later, based on her work, Higgins and Lyndon, gave a purely combinatorial and algebraic re-interpretation of Whitehead's work and of Whitehead's algorithm. The exposition of Whitehead's algorithm in the book of Lyndon and Schupp is based on this combinatorial approach. Culler and Vogtmann, in their 1986 paper that introduced the Outer space, gave a hybrid approach to Whitehead's algorithm, presented in combinatorial terms but closely following Whitehead's original ideas. Whitehead's algorithm Our exposition regarding Whitehead's algorithm mostly follows Ch.I.4 in the book of Lyndon and Schupp, as well as. Overview The automorphism group has a particularly useful finite generating set of Whitehead automorphisms or Whitehead moves. Given the first part of Whitehead's algorithm consists of iteratively applying Whitehead moves to to take each of them to an ``automorphically minimal" form, where the cyclically reduced length strictly decreases at each step. Once we find automorphically these minim
https://en.wikipedia.org/wiki/Quasi-unmixed%20ring	In algebra, specifically in the theory of commutative rings, a quasi-unmixed ring (also called a formally equidimensional ring in EGA) is a Noetherian ring such that for each prime ideal p, the completion of the localization Ap is equidimensional, i.e. for each minimal prime ideal q in the completion , = the Krull dimension of Ap. Equivalent conditions A Noetherian integral domain is quasi-unmixed if and only if it satisfies Nagata's altitude formula. (See also: #formally catenary ring below.) Precisely, a quasi-unmixed ring is a ring in which the unmixed theorem, which characterizes a Cohen–Macaulay ring, holds for integral closure of an ideal; specifically, for a Noetherian ring , the following are equivalent: is quasi-unmixed. For each ideal I generated by a number of elements equal to its height, the integral closure is unmixed in height (each prime divisor has the same height as the others). For each ideal I generated by a number of elements equal to its height and for each integer n > 0, is unmixed. Formally catenary ring A Noetherian local ring is said to be formally catenary if for every prime ideal , is quasi-unmixed. As it turns out, this notion is redundant: Ratliff has shown that a Noetherian local ring is formally catenary if and only if it is universally catenary. References Appendix of Stephen McAdam, Asymptotic Prime Divisors. Lecture notes in Mathematics. Further reading Herrmann, M., S. Ikeda, and U. Orbanz: Equimultiplicity and Blowing Up. An Algebraic Study with an Appendix by B. Moonen. Springer Verlag, Berlin Heidelberg New-York, 1988. Algebra Commutative algebra
https://en.wikipedia.org/wiki/List%20of%20Major%20League%20Baseball%20career%20fielding%20errors%20as%20a%20right%20fielder%20leaders	In baseball statistics, an error is an act, in the judgment of the official scorer, of a fielder misplaying a ball in a manner that allows a batter or baserunner to advance one or more bases or allows an at bat to continue after the batter should have been put out. The right fielder (RF) is one of the three outfielders, the defensive positions in baseball farthest from the batter. Right field is the area of the outfield to the right of a person standing at home plate and facing toward the pitcher's mound. The outfielders must try to catch long fly balls before they hit the ground, or to quickly catch or retrieve and return to the infield any other balls entering the outfield. The right fielder must also be adept at navigating the area of right field where the foul line approaches the corner of the playing field and the walls of the seating areas. Being the outfielder farthest from third base, the right fielder often has to make longer throws than the other outfielders to throw out runners advancing around the bases, so they often have the strongest or most accurate throwing arm. The right fielder normally plays behind the second baseman and first baseman, who play in or near the infield; unlike catchers and most infielders (excepting first basemen), who are virtually exclusively right-handed, right fielders can be either right- or left-handed. In the scoring system used to record defensive plays, the right fielder is assigned the number 9, the highest number. The list of career leaders is dominated by players from the early 20th century; only six of the top 20 players were active after 1951, only one of whom played primarily in the American League. Only nine of the top 91 single-season totals were recorded after 1939, only four after 1979. To a large extent, the leaders reflect longevity rather than lower skill. Roberto Clemente, who tied a modern National League record with 131 errors as a right fielder, won twelve consecutive Gold Glove Awards for defensive excellence. Because game accounts and box scores often did not distinguish between the outfield positions, there has been some difficulty in determining precise defensive statistics prior to 1901; because of this, and because of the similarity in their roles, defensive statistics for the three positions are frequently combined. Although efforts to distinguish between the three positions regarding games played during this period and reconstruct the separate totals have been largely successful, separate error totals are unavailable; players whose totals are missing the figures for pre-1901 games are notated in the table below. Harry Hooper is the modern (post-1900) leader in career errors committed by a right fielder with 144. Dave Parker is second all-time, and holds the modern National League record with 134 career errors in right field. Only fourteen right fielders have committed more than 100 career errors at the position since 1900. Key List Stats updated through the 2022 season Ot
https://en.wikipedia.org/wiki/Luiz%20Rangel	Luiz Ronaldo Nunes Rangel (born 14 August 1956), commonly known as Luisinho Rangel, Luizinho or Luiz Rangel, is a former Brazilian soccer player who played in the NASL. Career statistics Club Notes References Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football midfielders Botafogo de Futebol e Regatas players Santa Cruz Futebol Clube players Los Angeles Aztecs players Americano FC players Volta Redonda FC players Fortaleza Esporte Clube players SC Vianense players North American Soccer League (1968–1984) players Expatriate men's soccer players in the United States Brazilian expatriate sportspeople in the United States Expatriate men's footballers in Portugal Brazilian expatriate sportspeople in Portugal 1956 births Footballers from Niterói
https://en.wikipedia.org/wiki/Jens%20H%C3%B8yrup	Jens Egede Høyrup, born 1943 in Copenhagen, is a Danish historian of mathematics, specializing in pre-modern and early modern mathematics, ancient Mesopotamian mathematics in particular. He is especially known for his interpretation of what has often been referred to as Old Babylonian "algebra" as consisting of concrete, geometric manipulations. Career Høyrup studied physics and mathematics at the University of Copenhagen, Niels Bohr Institute from 1962 to 1969 (also, in 1965/66, at the Institut Henri Poincaré in Paris), with a focus on theoretical physics. In 1969 he completed his studies (as Danish cand. Scient.) with a thesis on theoretical elementary particle physics and was assistant lecturer (Danish adjunkt) in physics at the Danish Academy for Engineering from 1971 to 1973. Starting in 1973 he was senior lecturer (Danish lektor) and in 1989 reader (Danish docent) for the history and philosophy of science at Roskilde University, most recently in the Section for Philosophy and Science Studies. In 1995 he habilitated (danish dr. Phil.). Since 2005 he is professor emeritus. In 2008/09 he held the Sarton Chair in History of Science at the Ghent University. He is currently Honorary Research Fellow at the Institute for the History of Natural Sciences of the Chinese Academy of Sciences and a visiting scholar at the Max Planck Institute for the History of Science in Berlin. In 2013, he was awarded the Kenneth O. May Medal and Prize of the International Commission on the History of Mathematics (ICHM) for "outstanding contributions to the history of mathematics". He lives partly in Rome. Scholarship Høyrup is an internationally acclaimed expert in the history of mathematics, especially Babylonian mathematics. His research is wide-ranging, and also includes studies of Greek, Latin, Chinese, medieval Islamic and European, and modern mathematics. He is interested in philosophical and sociological questions about mathematics and the history of science. For example, he argues that early Babylonian arithmetic emerged from the process of state formation. He has also written about mathematics and war. More recently, he has studied the early Italian abacus tradition, arguing that its origins lie prior to Fibonacci's Liber Abacci and "that it is much less directly influenced by the scholarly level of Arabic mathematics than generally thought." In the 1980s, Høyrup began a reanalysis of Old Babylonian "algebra", based on a close inspection of Babylonian arithmetical terminology. He pioneered the use of "conformal translation" in this context, thereby preserving the distinctions between different conceptions of what had been regarded as equivalent mathematical operations. He concluded, for example, the Babylonian mathematics includes two different additions and at least four different multiplications, and that these distinct operations corresponded to distinct cut-and-paste geometric operations with origins in the practical surveyor tradition. Usin
https://en.wikipedia.org/wiki/Systat%20%28BSD%29	systat is a BSD UNIX console application for displaying system statistics in fullscreen mode using ncurses/curses. It is available on, and by default ships in the base systems of, FreeBSD, NetBSD, OpenBSD and DragonFly BSD. It was first released as part of 4.3BSD in . Both internally and in the interface of the user the utility consists of several distinct modules and tabs, referred to as "displays" in FreeBSD, NetBSD and DragonFly, and "views" in OpenBSD, which are automatically refreshed every specified number of seconds. These modules cover all system components, including statistics resembling vmstat, iostat and netstat in all of the BSDs, as well as pf and sensors views in some of the BSDs. The systat utility is notably absent from OS X, where a GUI-based Activity Monitor performs similar functions. See also vmstat iostat top netstat References External links 1986 software BSD software Computer performance DragonFly BSD Environmental monitoring Free software programmed in C Free system software FreeBSD Motherboard NetBSD OpenBSD System administration System monitors Unix file system-related software Unix network-related software Utility software
https://en.wikipedia.org/wiki/Matongo%20%28Singida%20ward%29	Matongo is an administrative ward in the Mkalama District of the Singida Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 6,955 people in the ward, from 6,338 in 2012. Villages The ward has 18 villages. Matongo A Matongo B Kirumi Hindamili Mpondelo Isene Isene Kinyamapupu Igwilambao Idebe Kinyamkunde Manung'una Munung’una Mwamakiki Mabiha Mwamidu Mazangili Mazangili Tandusi Munguli Mkenka References Wards of Singida Region
https://en.wikipedia.org/wiki/Scott%20A.%20Mitchell	Scott Alan Mitchell is a researcher of applied mathematics in the Center for Computing Research at Sandia National Laboratories. Background Mitchell received a B.S in Applied Math, Engineering & Physics from the University of Wisconsin-Madison (1988), and an M.S. (1991) and Ph.D. (1993) in Applied Math from Cornell University. He worked the summer of 1991 at Xerox PARC (now PARC). Since 1992 he has been at Sandia National Laboratories in the Center for Computing Research, with several different roles. He researched theoretical computational geometry meshing from 1992—1993. He contributed to applied meshing in the CUBIT project: R&D 1993—2000, project leader 2000—2002, R&D 2015—. He managed Sandia's Optimization and Uncertainty Estimation department, and had programmatic roles on the Laboratory Directed Research and Development program and NNSA's ASC program from 2002-2007. He researched informatics and applying persistent homology from 2008-2011. Since 2011 he researches mesh generation and sampling. He served on the committee of the Meshing Roundtable and International Symposium on Computational Geometry SoCG conferences. He served as a guest editor for the journal CAD. As an adjunct professor, he taught a small graduate course on computational geometry at the University of New Mexico. He is a member of ACM and SIAM. Research He published algorithms in the areas of mesh generation, reconstruction and sampling, for the contexts of computational geometry, simulation, computer graphics and uncertainty quantification. His main contributions have been geometric algorithms with provable correctness and output quality guarantees. His PhD thesis was the first tetrahedral meshing algorithm with guarantees on both the number of elements and their shape. He is also well known for a series of papers on whisker weaving and other algorithms for hexahedral mesh generation using the dual spatial twist continuum. He used optimization for mesh generation, specifically interval assignment, deciding the right number of edges locally so the model can be meshed globally. Since 2011 he contributed sampling algorithms for computer graphics and uncertainty quantification, and algorithms for mesh generation (including duality) and surface reconstruction. References External links Applied mathematicians American computer scientists Mesh generation people Sandia National Laboratories people Cornell University alumni Living people University of Wisconsin–Madison College of Letters and Science alumni Year of birth missing (living people)
https://en.wikipedia.org/wiki/List%20of%20Major%20League%20Baseball%20career%20fielding%20errors%20as%20a%20pitcher%20leaders	In baseball statistics, an error is an act, in the judgment of the official scorer, of a fielder misplaying a ball in a manner that allows a batter or baserunner to advance one or more bases or allows an at bat to continue after the batter should have been put out. The pitcher is the player who pitches the baseball from the pitcher's mound toward the catcher to begin each play, with the goal of retiring a batter, who attempts to either make contact with the pitched ball or draw a walk. The pitcher is often considered the most important player on the defensive side of the game, playing the most difficult and specialized position, and as such is regarded as being at the right end of the defensive spectrum. Pitchers play far less than players at other positions, generally appearing in only two or three games per week; only one pitcher in major league history has appeared in 100 games in a single season. There are many different types of pitchers, generally divided between starting pitchers and relief pitchers, which include the middle reliever, lefty specialist, setup man, and closer. In the scoring system used to record defensive plays, the pitcher is assigned the number 1. The list of career leaders is dominated by players from the 19th century when fielding equipment was very rudimentary; baseball gloves only began to steadily gain acceptance in the 1880s, and were not uniformly worn until the mid-1890s, resulting in a much lower frequency of defensive miscues. The top 25 players in career errors began playing in the 19th century, most of them playing their entire careers before 1900; only four were active after 1901, none after 1911. Most of the top 92 played entirely in the 19th century, with only 19 making their major league debut after 1900; only six made their debut after 1940. The top 16 single-season totals were all recorded before 1890, the top 95 were recorded before 1904, and the top 297 were recorded before 1924. To a large extent, the leaders reflect longevity rather than lower skill. Jim Kaat and Greg Maddux, whose error totals of 56 and 53 rank fifth and seventh among pitchers since 1940, won sixteen and eighteen Gold Glove Awards respectively for defensive excellence. Bobby Mathews is the all-time leader in career errors committed by a pitcher with 220, more than twice as many as any pitcher who began playing after 1900; he is the only pitcher to commit more than 200 career errors. Tim Keefe is second with 166 career errors as a pitcher. A total of seventeen players have committed more than 100 career errors as pitchers. Justin Verlander, who had 34 errors through the 2022 season to place him tied for 234th all-time, is the leader among active players. Key List Other Hall of Famers References Baseball-Reference.com Major League Baseball statistics Major League Baseball lists
https://en.wikipedia.org/wiki/Jadav%20Chandra%20Chakravarti	Jadav Chandra Chakravarti (1855 – 26 November 1920) was a prominent Bengali mathematician of the Indian subcontinent. He was famous for his two books named Arithmetic and Algebra. Early life Chakravarti was born in 1855 at the village of Tatulia in Kamarkhanda, just few miles from Sirajganj city of the then British Raj (now Bangladesh) to Krishna Chandra Chakravarti and Durga Sundari. He moved to Kolkata for higher education and obtained his M.A. degree in mathematics from Presidency College at the University of Calcutta in 1882. While he was a student of Presidency, he taught physics and chemistry at St. Paul's Cathedral Mission College to pay for his University degree. Career Chakravarti started his career as a mathematics teacher at Kolkata City College. Then he joined at Aligarh Muslim College on 1 January 1888 at 200 rupees salary. In 1905, his salary was increased to 300 rupees. One of the famous students of his was Ziauddin Ahmad. He retired from Aligarh College on 28 February 1916. His first book Arithmetic was published in 1890 and his second book Algebra was published in 1912. His books were translated into a number of languages including Bengali, Urdu, Hindi, Assamese and Nepali. In 1901, he came back to his home town Sirajganj and founded a school for local children. After his retirement in 1916, he was also elected as the Chairman of Sirajganj Municipality. Before joining to Aligarh Univ. He was a high-level British officer, in the princely state of Cooch Behar. He was instrumental in fixing the match between Maharajah Nripendra Narayan of Cooch Behar and Sunity Devi D/O Sri Keshub Ch. Sen, the founder of the new dispensation. Jadav Babu served cooch behar for some years. Death Chakravarti died at the age of 69 on 26 November 1920 at his Kolkata residence. References 1855 births 1920 deaths Academic staff of Aligarh Muslim University Mathematics educators People from Sirajganj District University of Calcutta alumni Academic staff of the University of Calcutta Mathematicians from British India People from the Bengal Presidency
https://en.wikipedia.org/wiki/Tsang%20Tung%20Ming	Tsang Tung Ming (; born 21 July 1999) is a Hong Kong professional footballer. He plays as a Midfielder Career statistics Club Notes References Living people 1999 births Hong Kong men's footballers Men's association football midfielders Hong Kong Premier League players R&F (Hong Kong) players
https://en.wikipedia.org/wiki/Li%20Cheuk%20Hon	Li Cheuk Hon (; born 21 February 2000) is a Hong Kong professional footballer. Career statistics Club Notes References Living people 2000 births Hong Kong men's footballers Men's association football defenders Hong Kong Premier League players R&F (Hong Kong) players
https://en.wikipedia.org/wiki/Chris%20Mukiza	Chris Ndatira Mukiza is a Ugandan statistician, who is the executive director of the Uganda Bureau of Statistics, the government agency responsible for the collection, analysis, dissemination and storage of nationally important data. Education Mukiza holds a Doctor of Philosophy in Statistics, awarded in 2008, by the University of Southampton, in Southampton, United Kingdom. His PhD thesis was titled "Essays On Growth And Absolute Poverty: Evidence From Uganda". Career Mukiza joined UBOS in March 2000. From 2009 until 2019, he served as the Director of Macroeconomic statistics at UBOS. In that position, he was part of a seventeen-person senior management team at the government agency He beat out three other applicants for the position of executive director of UBOS, including Imelda Madgalene Atai, who has been the Acting Executive Director from July 2018 until March 2019. Dr. Chris Mukiza replaced Ben Paul Mungyereza, who resigned in early 2018. In his role as executive director, he also becomes a member of the UBOS board of directors. Mukiza previously (in 1992) worked as a statistician at the Ugandan Ministry of Finance, Planning and Economic Development. He then worked at the Uganda Revenue Authority from 1997 until 2000. He has plans to make the Uganda Bureau of Statistics, an excellent statistics production centre in the region and on the continent, according to remarks that he made upon his appointment as executive director. See also Richard Byarugaba References External links Website of Uganda Bureau of Statistics Living people Year of birth missing (living people) Ugandan statisticians People from Western Region, Uganda Alumni of the University of Southampton
https://en.wikipedia.org/wiki/AWM%20Service%20Award	The AWM Service Award is an annual award given by the Association for Women in Mathematics. The AWM depends largely on the work of volunteers. In order to recognize individuals for helping to promote and support women in mathematics through exceptional volunteer service to the association the AWM Executive Committee approved the AWM Service Award in 2012 and it was first awarded in 2013. The recipients of the award are recognized at the annual AWM Reception and Awards Presentation at the Joint Mathematics Meetings and in the Notices of the American Mathematical Society. List of Award Winners Recipient of the AWM Lifetime Service Award See also List of mathematics awards References External links Awards established in 2013 Service Award 2013 establishments in the United States Volunteering in the United States Volunteering awards
https://en.wikipedia.org/wiki/Hypercube%20%28communication%20pattern%29	-dimensional hypercube is a network topology for parallel computers with processing elements. The topology allows for an efficient implementation of some basic communication primitives such as Broadcast, All-Reduce, and Prefix sum. The processing elements are numbered through . Each processing element is adjacent to processing elements whose numbers differ in one and only one bit. The algorithms described in this page utilize this structure efficiently. Algorithm outline Most of the communication primitives presented in this article share a common template. Initially, each processing element possesses one message that must reach every other processing element during the course of the algorithm. The following pseudo code sketches the communication steps necessary. Hereby, Initialization, Operation, and Output are placeholders that depend on the given communication primitive (see next section). Input: message . Output: depends on Initialization, Operation and Output. Initialization for do Send to Receive from Operation endfor Output Each processing element iterates over its neighbors (the expression negates the -th bit in 's binary representation, therefore obtaining the numbers of its neighbors). In each iteration, each processing element exchanges a message with the neighbor and processes the received message afterwards. The processing operation depends on the communication primitive. Communication primitives Prefix sum In the beginning of a prefix sum operation, each processing element owns a message . The goal is to compute , where is an associative operation. The following pseudo code describes the algorithm. Input: message of processor . Output: prefix sum of processor . for do Send to Receive from if bit in is set then endfor The algorithm works as follows. Observe that hypercubes of dimension can be split into two hypercubes of dimension . Refer to the sub cube containing nodes with a leading 0 as the 0-sub cube and the sub cube consisting of nodes with a leading 1 as 1-sub cube. Once both sub cubes have calculated the prefix sum, the sum over all elements in the 0-sub cube has to be added to the every element in the 1-sub cube, since every processing element in the 0-sub cube has a lower rank than the processing elements in the 1-sub cube. The pseudo code stores the prefix sum in variable and the sum over all nodes in a sub cube in variable . This makes it possible for all nodes in 1-sub cube to receive the sum over the 0-sub cube in every step. This results in a factor of for and a factor of for : . All-gather / all-reduce All-gather operations start with each processing element having a message . The goal of the operation is for each processing element to know the messages of all other processing elements, i.e. where is concatenation. The operation can be implemented following the algorithm template. Input: message at processing uni
https://en.wikipedia.org/wiki/Wiris	Wiris Gustavo de Oliveira (born 4 July 2000), commonly known as Wiris, is a Brazilian footballer who plays as a midfielder for AE Paracatu. Career statistics Club Notes Honours Club Lokomotiv Plovdiv Bulgarian Cup: 2018–19 References 2000 births Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football midfielders Campo Grande Atlético Clube players PFC Lokomotiv Plovdiv players Fluminense FC players First Professional Football League (Bulgaria) players Brazilian expatriate sportspeople in Bulgaria Expatriate men's footballers in Bulgaria
https://en.wikipedia.org/wiki/BLIS%20%28software%29	In scientific computing, BLIS (BLAS-like Library Instantiation Software) is an open-source framework for implementing a superset of BLAS (Basic Linear Algebra Subprograms) functionality for specific processor types that was recently awarded the J. H. Wilkinson Prize for Numerical Software. It exposes that functionality through two traditional Application Programming Interfaces (APIs): the BLAS interface and the CBLAS interface. BLIS also includes two APIs native to the framework: a typed (BLAS-like) API and an object API. These native interfaces provide access to BLAS-like functionality that is not supported by, but closely related to, operations found in the BLAS (and CBLAS). The framework is developed and supported by the Science of High-Performance Computing (SHPC) group of the Oden Institute for Computational Engineering and Sciences at The University of Texas at Austin and the Matthews Research Group at Southern Methodist University. BLIS yields high performance on many current CPU microarchitectures in both single-threaded and multithreaded modes of execution. BLIS also offers competitive performance for some cases of matrix multiplication in which one or more matrix operands are unusually skinny and/or small. The framework achieves high performance by employing specialized kernels (typically written in GNU extended inline assembly syntax) along with cache and register blocking through matrix operands. BLIS also works on processors for which custom kernels have not yet been written; in those cases, the framework relies upon portable kernel implementations that perform at a lower rate of computation. BLIS is sometimes described as a refactoring of GotoBLAS2, which was created by Kazushige Goto at the Texas Advanced Computing Center. See also Automatically Tuned Linear Algebra Software (ATLAS) OpenBLAS Intel Math Kernel Library (MKL) References External links Numerical linear algebra Numerical software
https://en.wikipedia.org/wiki/Dmitry%20Kostomarov	Dmitry Pavlovich Kostomarov (; March 23, 1929 – August 9, 2014) was a Soviet and Russian mathematician, academician of the Russian Academy of Sciences, dean of the Faculty of Computational Mathematics and Cybernetics at Moscow State University (1990—1999), Professor, Dr.Sc. Biography Born into the family of an engineer, a representative of the noble family of the Kostomarovs. In 1947 he entered the Faculty of Engineering and Physics of the Moscow Mechanical Institute. In 1948 he transferred to the Faculty of Physics of Moscow State University, which he graduated with honors in 1952. From 1952 to 1955 he studied in the graduate school of the Faculty of Physics at the Department of Mathematics, where the scientific leaders were Yury Rabinovich and Alexander Samarskii. In 1956 he defended his thesis for the degree of Candidate of Physical and Mathematical Sciences, the thesis entitled «On the asymptotic behavior of solutions of systems of linear differential equations in the neighborhood of an irregular singular point». From 1955 he taught at the Moscow State University, assistant professor of mathematics at the Faculty of Physics (1955-1961), assistant professor (1961—1971). Since 1971 — at the faculty of the Faculty of the CMC of Moscow State University, associate professor of the department of computational mathematics (1971—1972). Doctor of Physical and Mathematical Sciences (1968), thesis: «Electromagnetic Waves in Plasma», since 1972 — Professor of the Faculty of the Faculty of the CMC, Head of the Department of Automation of Scientific Research of the Faculty of the CMC (since 1988). Dean of the Faculty of Computational Mathematics and Cybernetics (1990—1999). Scientific interests Fundamental results in the field of mathematical modeling in plasma physics, electrodynamics, nuclear physics. Main scientific publications He is the author of 10 monographs and more than 137 research papers. Awards and honours for achievements in the field of science (1976) (1980) USSR State Prize (1981) Order of the Red Banner of Labour (1990) for pedagogical activity (1996) Order of Honour (1999) Order of Friendship (2005) References Bibliography External links Dmitry Kostomarov on the website Russian Academy of Sciences Dmitry Kostomarov — scientific works on the website Math-Net.Ru Biography of Dmitry Kostomarov on the website of the MSU Faculty of Computational Mathematics and Cybernetics Dmitry Kostomarov — scientific works on the website ISTINA MSU 1929 births 2014 deaths 20th-century Russian mathematicians 20th-century Russian physicists 21st-century Russian mathematicians 21st-century Russian physicists Full Members of the Russian Academy of Sciences Moscow State University alumni Academic staff of Moscow State University Recipients of the Order of Honour (Russia) Recipients of the Order of the Red Banner of Labour Recipients of the USSR State Prize Russian computer scientists Russian mathematicians Russian physicists Soviet c
https://en.wikipedia.org/wiki/Alexander%20Brown%20%28mathematician%29	Alexander Brown FRSE FRSSAf (1878–1947) was a Scottish-born mathematician and educator in South Africa. He contributed to the study of the ratio of incommensurables in geometry and relations between the distances of a point from three vertices of a regular polygon. Career Brown was born in Dalkeith, near Edinburgh, Scotland on 5 May 1878. He attended Newton Public School and then George Watson's College, where he was the winner of the Wright Bursary in his final year. He matriculated at the University of Edinburgh in 1893 where he obtained a MA (Mathematics and Natural Science)(First Class) and a BSc (Mathematics and Natural Science)(Special Distinction) in 1897. While at Edinburgh University he held the first Heriot Bursary and Mackay Smith scholarship. On completion of his degrees he won the Vans Dunlop scholarship, the Baxter scholarship and the Drummond scholarship. He was mathematical master at the High School of Dundee from 1897 to 1899. In 1899 he won the Ferguson Scholarship in Mathematics and he went to Gonville and Caius College, Cambridge where he obtained a First Class in Mathematics in 1902. In 1903 he became Deputy Professor of Applied Mathematics and Physics for one year at the South African College, Cape Town in the absence of the holder of the chair, Carruthers Beattie, who was on a year-long magnetic survey of South Africa. In recognition of Brown's exceptional work during that year the College Council split the Chair and Beattie was offered the professorship of Physics while Brown was offered the professorship of Mathematics. He retained this position until his death on 27 January 1947. He was elected a Fellow of the Royal Society of Edinburgh in 1907. His proposers were George Chrystal, Arthur John Pressland, John Sturgeon Mackay and John Alison. In 1918 he was elected a Fellow of the Royal Society of South Africa. Personal life He married Mary Graham in 1911 and they had a daughter and a son. In his leisure time he was a great reader and a keen musician. Works He contributed to the study of the ratio of incommensurables in geometry and relations between the distances of a point from three vertices of a regular polygon. His paper on this subject was read before the Edinburgh Mathematical Society on 11 June 1909. Selected publications Brown, A. (1905) "Convergence of a Reversed Power Series" British Association Report Brown, A. (1907) "Examination of the Validity of an Approximate Solution of a Certain Velocity Equation" Transaction of the South African Philosophical Society, vol xvi, pt. 3 Brown, A. (1916) "The Equivalent Mass of a Spring Vibrating Longitudinally" Transactions of the Royal Society of South Africa vol. v, p. 565. Brown, A. (1916) "The Arrangement of Successive Convergents in the Order of Accuracy" Transactions of the Royal Society of South Africa vol. v, p. 653. Brown, A. (1916) "The Use of a Standard Parabola for Drawing Diagrams of Bending Moment and of Shear in a Beam Uniformly Loaded" Transactions
https://en.wikipedia.org/wiki/Leetsch%20C.%20Hsu	Xu Lizhi (; 23 September 1920 – 11 March 2019), better known as Leetsch Charles Hsu, was a Chinese mathematician and educator. He co-founded the Department of Mathematics of Jilin University and founded the Institute of Applied Mathematics and the Journal of Mathematical Research with Applications at the Dalian University of Technology. Together with American mathematician Henry W. Gould, he established the Gould–Hsu Matrix Inversion Formula in 1973. Early life and education Hsu was born on 23 September 1920 in Zhangjiagang, Jiangsu, Republic of China. His original name was Xu Quanyong (). Hsu studied at Jiangsu Provincial Luoshe Normal School before the outbreak of the Second Sino-Japanese War. In 1940, he passed the entrance examination for the temporary National Southwestern Associated University formed by Tsinghua and other universities in Kunming, and studied mathematics under Hua Luogeng and Pao-Lu Hsu. Upon graduation in 1945, he was hired by the university as a teaching assistant to Hua. Career After the end of the Sino-Japanese War, National Southwestern Associated University was disbanded in 1946 and Hsu joined Tsinghua University, which had been reestablished in Beijing. In 1949, Hsu was awarded a scholarship by the British Council for a two-year study in the United Kingdom. He spent the first year at the University of Aberdeen and the second at the University of Cambridge. In 1951, Hsu returned to China and became an associate professor of mathematics at Tsinghua University. He also taught at Beijing Normal University on a part-time basis. In 1952, Hsu, together with Wang Xianghao and Jiang Zejian (), moved to Changchun to help establish the Department of Mathematics at Northeast People's University (later renamed as Jilin University). He served as deputy chair of the department. He was promoted to full professor in 1956, and founded the study of computational mathematics at the university. In 1980, Hsu moved to the Dalian University of Technology, where he founded the Institute of Applied Mathematics. He also established the Journal of Mathematical Research and Exposition (later renamed as Journal of Mathematical Research with Applications 数学研究及应用) and served as its chief editor. He also served as Chair of the Mathematics Department of the Huazhong University of Science and Technology. From 1986 to 1987, he taught as a visiting professor at the Texas A&M University in the United States. He was named Honorary Dean of the School of Science of the Nanjing University of Aeronautics and Astronautics. In 2009, he was named by the Dalian University of Technology as one of the most important faculty members in the history of the university. Contributions Hsu made significant contributions to asymptotic analysis, approximation theory, and combinatorics. He began collaborating with American mathematician Henry W. Gould in 1965, years before US President Richard Nixon established official relations with the People's Republic of China
https://en.wikipedia.org/wiki/The%20Armory%20Volume%201	The Armory Volume 1 is a 1983 role-playing game supplement designed by Kevin Dockery and published by Firebird Limited. Contents The Armory Volume 1 is a supplement of game statistics from gunpowder weapons of the 14th-century to modern day weapons for Espionage! and Mercenaries, Spies and Private Eyes. Reception William A. Barton reviewed The Armory Volume 1 in Space Gamer No. 72. Barton commented that "The Armory Vol. 1 (second edition) is the best weapons reference book of its type I've seen yet. I recommend it to all gamers who care about the difference between various weapons and how they function in play." Reviews Adventurers Club #5 (Fall, 1984 Digest) References Role-playing game books Role-playing game supplements introduced in 1983
https://en.wikipedia.org/wiki/Song%20Sun	Song Sun (, born in 1987) is a Chinese mathematician whose research concerns geometry and topology. A Sloan Research Fellow, he is a professor at the Department of Mathematics of the University of California, Berkeley, where he has been since 2018. In 2019, he was awarded the Oswald Veblen Prize in Geometry. Biography Sun attended Huaining High School in Huaining County, Anhui, China, before being admitted to the Special Class for the Gifted Young at the University of Science and Technology of China in 2002. After graduating from the program with a B.S. in 2006, he moved to the United States to pursue graduate studies at the University of Wisconsin, obtaining his Ph.D in mathematics (differential geometry) in 2010. His doctoral advisor was Xiuxiong Chen, and his dissertation was titled "Kempf–Ness theorem and uniqueness of extremal metrics". Sun worked as a research associate at Imperial College London before becoming an assistant professor at Stony Brook University in 2013. He was awarded the Sloan Research Fellowship in 2014. In 2018, he was appointed an associate professor at the Department of Mathematics of the University of California, Berkeley. He was an invited speaker at the 2018 International Congress of Mathematicians, in Rio de Janeiro. For 2021 he received the Breakthrough Prize in Mathematics – New Horizons in Mathematics. Conjecture on Fano manifolds and Veblen Prize In 2019, Sun was awarded the prestigious Oswald Veblen Prize in Geometry, together with his former advisor Xiuxiong Chen and English mathematician Simon Donaldson, for proving a long-standing conjecture on Fano manifolds, which states that "a Fano manifold admits a Kähler–Einstein metric if and only if it is K-stable". It had been one of the most actively investigated topics in geometry since a rough version of it was conjectured in the 1980s by Fields Medalist Shing-Tung Yau, who had previously proved the Calabi conjecture. The conjecture was later given a precise formulation by Donaldson, based in part on earlier work of Chinese mathematician Gang Tian. The solution by Chen, Donaldson and Sun was published in the Journal of the American Mathematical Society in 2015 as a holistic three-article series, "Kähler–Einstein metrics on Fano manifolds, I, II and III". Major publications References Living people 21st-century Chinese mathematicians Academics of Imperial College London Differential geometers Mathematicians from Anhui People from Huaining County Sloan Research Fellows Stony Brook University faculty University of California, Berkeley faculty University of Science and Technology of China alumni University of Wisconsin–Madison College of Letters and Science alumni Year of birth missing (living people)
https://en.wikipedia.org/wiki/Arthur%20Smith%20%28Welsh%20footballer%29	Arthur Harold Smith was a Welsh footballer who played as a goalkeeper in the Football League for Wrexham. Personal life Smith's brother Cecil was also a footballer. Career statistics References Footballers from Wrexham Welsh men's footballers Wrexham A.F.C. players English Football League players Year of birth unknown Year of death unknown Men's association football goalkeepers Macclesfield Town F.C. players
https://en.wikipedia.org/wiki/Delta-matroid	In mathematics, a delta-matroid or Δ-matroid is a family of sets obeying an exchange axiom generalizing an axiom of matroids. A non-empty family of sets is a delta-matroid if, for every two sets and in the family, and for every element in their symmetric difference , there exists an such that is in the family. For the basis sets of a matroid, the corresponding exchange axiom requires in addition that and , ensuring that and have the same cardinality. For a delta-matroid, either of the two elements may belong to either of the two sets, and it is also allowed for the two elements to be equal. An alternative and equivalent definition is that a family of sets forms a delta-matroid when the convex hull of its indicator vectors (the analogue of a matroid polytope) has the property that every edge length is either one or the square root of two. Delta-matroids were defined by André Bouchet in 1987. Algorithms for matroid intersection and the matroid parity problem can be extended to some cases of delta-matroids. Delta-matroids have also been used to study constraint satisfaction problems. As a special case, an even delta-matroid is a delta-matroid in which either all sets have even number of elements, or all sets have an odd number of elements. If a constraint satisfaction problem has a Boolean variable on each edge of a planar graph, and if the variables of the edges incident to each vertex of the graph are constrained to belong to an even delta-matroid (possibly a different even delta-matroid for each vertex), then the problem can be solved in polynomial time. This result plays a key role in a characterization of the planar Boolean constraint satisfaction problems that can be solved in polynomial time. References Matroid theory
https://en.wikipedia.org/wiki/Faris%20Zubanovi%C4%87	Faris Zubanović (born 12 June 2000) is a Bosnian professional footballer who plays as a forward for Austrian club Kapfenberg and the Bosnia and Herzegovina U21 national team. Career statistics Club Personal life Faris is the son of Željezničar club legend Hadis Zubanović. References External links Faris Zubanović at Sofascore 2000 births Living people Footballers from Sarajevo Men's association football forwards Bosnia and Herzegovina men's footballers FK Željezničar Sarajevo players Fremad Amager players FK Velež Mostar players Premier League of Bosnia and Herzegovina players Danish 1st Division players Bosnia and Herzegovina expatriate men's footballers Expatriate men's footballers in Denmark Bosnia and Herzegovina expatriate sportspeople in Denmark
https://en.wikipedia.org/wiki/Sergei%20Evdokimov	Sergei Alekseevich Evdokimov (; December 12, 1950 — September 10, 2016) was a Russian mathematician who contributed to the theory of modular forms, computational complexity theory, algebraic combinatorics and p-adic analysis. Biography Sergei Evdokimov was born in Leningrad (now Saint Petersburg, Russia), and graduated from Leningrad State University, Dept. of Mathematics and Mechanics, in 1973 (Honours Diploma). During his studies, he attended a seminar on modular forms and started to work in this area under the supervision of professor Anatoli N. Andrianov. After graduation, he continued research in the theory of modular forms, and in 1977 earned his PhD degree (Candidate of Sciences) from Leningrad Department of Steklov Mathematical Institute of USSR Academy of Sciences with the thesis "Euler products for congruence subgroups of the Siegel group of genus". During 1981–1993 he was a senior researcher of Laboratory of Theory of Algorithms at Leningrad Institute for Informatics and Automation of USSR Academy of Sciences. That time his scientific interests were switched to the computational complexity of algorithms in algebra and number theory. He was an active participant of a seminar on computational complexity headed by Anatol Slissenko and Dima Grigoriev. From 1993 he also began active collaboration with Ilia Ponomarenko, in algebraic combinatorics, which lasted until the end of his life. Many of the results obtained in this collaboration were included in his DSc thesis "Schurity and separability of association schemes", that was defended in 2004. Starting in 2005, he was a leading researcher in St. Petersburg Department Mathematical Institute of Russian Academy of Sciences. Scientific activities During 1975-1982 Sergei had published a series of impressive papers on the arithmetic of Siegel modular forms. His PhD thesis contains very fine arithmetic constructions related to the ray classes of ideals of imaginary quadratic fields. Continuing his research on the theory of modular forms, he found an elegant analytical description of the Maass subspace of Siegel modular forms of genus 2, an explicit formula for the generating Hecke series of the symplectic group of genus 3, and the first explicit formulas for the action of degenerate Hecke operators on the space of theta-series In the mid-1980s, switching to the computational complexity of algorithms in algebra and number theory, he found a delicate and simple algorithm for factorization of polynomials over finite fields. The algorithm has a quasi-polynomial complexity under the assumption of generalized Riemann's hypothesis. Despite considerable efforts by mathematicians working in the theory of computational complexity, up to the present (2019), his estimate for the complexity of the factorization problem has not been improved. Starting in 1993, Sergei has been engaged into problems of algebraic combinatorics. Several profound results were obtained, including the refutation of the Sc
https://en.wikipedia.org/wiki/Robert%20Gladiador	Robert Lima Guimarães (born 2 January 1987), commonly known as Robert Gladiador, is a Brazilian footballer who last plays as a forward for Arema. Career statistics Club Notes Honours Club Al-Shabab Kuwaiti Division One: 2017–18 Arema Indonesia President's Cup: 2019 References 1987 births Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football forwards Cruzeiro Esporte Clube players Uberlândia Esporte Clube players Jiangsu F.C. players América Futebol Clube (MG) players Esporte Clube Democrata players Esporte Clube Bahia players Ipatinga Futebol Clube players Sociedade Esportiva e Recreativa Caxias do Sul players Sport Club Corinthians Alagoano players Clube Esportivo Lajeadense players Esporte Clube Passo Fundo players Sport Club São Paulo players Esporte Clube Pelotas players Clube Esportivo Bento Gonçalves players Rio Branco Atlético Clube players Sociedade Esportiva Recreativa e Cultural Brasil players Clube Atlético Itapemirim players Vitória Futebol Clube (ES) players Estrela do Norte Futebol Clube players Arema F.C. players Brazilian expatriate sportspeople in China Expatriate men's footballers in China Brazilian expatriate sportspeople in Saudi Arabia Expatriate men's footballers in Saudi Arabia Brazilian expatriate sportspeople in Kuwait Expatriate men's footballers in Kuwait Brazilian expatriate sportspeople in Indonesia Expatriate men's footballers in Indonesia Al-Shabab SC (Kuwait) players Kuwait Premier League players People from Curvelo Footballers from Minas Gerais
https://en.wikipedia.org/wiki/Xiuxiong%20Chen	Xiuxiong Chen () is a Chinese-American mathematician whose research concerns differential geometry and differential equations. A professor at Stony Brook University since 2010, he was elected a Fellow of the American Mathematical Society in 2015 and awarded the Oswald Veblen Prize in Geometry in 2019. In 2019, he was awarded the Simons Investigator award. Biography Chen was born in Qingtian County, Zhejiang, China. He entered the Department of Mathematics of the University of Science and Technology of China in 1982, and graduated in 1987. He subsequently studied under Peng Jiagui (彭家贵) at the Graduate School of the Chinese Academy of Sciences, where he earned his master's degree. In 1989 , he moved to the United States to study at the University of Pennsylvania. The last doctoral student of Eugenio Calabi, he obtained his Ph.D. in mathematics in 1994, with his dissertation on "Extremal Hermitian Matrices with Curvature Distortion in a Riemann Surface". Chen was an instructor at McMaster University in Canada from 1994 to 1996 . For the next two years he was a National Science Foundation postdoctoral fellow at Stanford University. He was an assistant professor at Princeton University from 1998 to 2002, before becoming an associate professor at the University of Wisconsin–Madison. He was promoted to full professor in 2005. Since October 2010 he has been a professor at Stony Brook University. In 2006, he founded the Pacific Rim Conference on Complex Geometry at the University of Science and Technology of China. As of 2019, Chen has advised 17 Ph.D. students, including Song Sun and Bing Wang (王兵). He was elected a Fellow of the American Mathematical Society in 2015 "for contributions to differential geometry, particularly the theory of extremal Kahler metrics". He was an invited speaker at the 2002 International Congress of Mathematicians, in Beijing. Conjecture on Fano manifolds and Veblen Prize In 2019, Chen was awarded the prestigious Oswald Veblen Prize in Geometry, together with English mathematician Simon Donaldson and Chen's former student Song Sun, for proving a long-standing conjecture on Fano manifolds, which states "that a Fano manifold admits a Kähler–Einstein metric if and only if it is K-stable". It had been one of the most actively investigated topics in geometry since a loose version of it was first proposed in the 1980s by eventual Fields Medalist Shing-Tung Yau after his proof of the Calabi conjecture. More precise versions were subsequently proposed by Chinese mathematician Gang Tian and Donaldson. The solution by Chen, Donaldson and Sun was published in the Journal of the American Mathematical Society in 2015 as a three-article series, "Kähler–Einstein metrics on Fano manifolds, I, II and III". Major publications Chen, Xiuxiong. The space of Kähler metrics. J. Differential Geom. 56 (2000), no. 2, 189–234. Chen, X. X.; Tian, G. Geometry of Kähler metrics and foliations by holomorphic discs. Publ. Math. Inst. Hautes É
https://en.wikipedia.org/wiki/Generalized%20Cohen%E2%80%93Macaulay%20ring	In algebra, a generalized Cohen–Macaulay ring is a commutative Noetherian local ring of Krull dimension d > 0 that satisfies any of the following equivalent conditions: For each integer , the length of the i-th local cohomology of A is finite: . where the sup is over all parameter ideals and is the multiplicity of . There is an -primary ideal such that for each system of parameters in , For each prime ideal of that is not , and is Cohen–Macaulay. The last condition implies that the localization is Cohen–Macaulay for each prime ideal . A standard example is the local ring at the vertex of an affine cone over a smooth projective variety. Historically, the notion grew up out of the study of a Buchsbaum ring, a Noetherian local ring A in which is constant for -primary ideals ; see the introduction of. References Ring theory
https://en.wikipedia.org/wiki/Sharon%20R.%20Browning	Sharon Ruth Browning is a statistical geneticist at the University of Washington, and a research professor with its Department of Biostatistics. Her research has various implications for the field of biogenetics. Education and career Browning has a B.Sc. from the University of Auckland (1995) and earned her Ph.D. in 1999 from the University of Washington. Following her Ph.D., she held positions at Texas A&M University, North Carolina State University, GlaxoSmithKline, and the University of Auckland before moving to the University of Washington in 2010. Research Browning is known for her research developing statistical methods for analysis of population genetic data. Her early work established the used of Markov chain modeling to examine association based genome mapping. Her work addresses how to handle missing data in whole-genome association studies. She has also defined the use of group association tests and examined relatedness of individuals based on shared gene content. Browning has also examined the genetic history of the Samoans. Browning and her research group also study the traces of genetic introgression from archaic humans into modern human DNA. In 2018, they discovered that humans in the distant past had mated with Denisovans in at least two separate events, the second of which may have occurred as humans migrated eastward into Asia and Oceania. Selected publications References External links Statistical geneticists Living people University of Washington faculty American geneticists 1973 births American women geneticists
https://en.wikipedia.org/wiki/Holly%20Krieger	Holly Krieger is a lecturer in mathematics at the University of Cambridge, where she is also the Corfield Fellow at Murray Edwards College. Her current research interests are in arithmetic and algebraic aspects of families of complex dynamical systems. She is well known for her appearances in the popular mathematics YouTube video series Numberphile. Career Originally from Champaign, Illinois, Krieger holds an undergraduate degree from the University of Illinois at Urbana–Champaign and master's and Ph.D. degrees from the University of Illinois at Chicago. She completed her Ph.D. in 2013; her dissertation, Primitive prime divisors in polynomial dynamics, was jointly supervised by Laura DeMarco and Ramin Takloo-Bighash. Subsequently, she held a National Science Foundation postdoctoral fellowship at Massachusetts Institute of Technology supervised by Bjorn Poonen, and in 2016, Krieger was hired as a lecturer at the University of Cambridge. Recognition In 2019, Krieger was the Australian Mathematical Sciences Institute Mahler Lecturer, which involved giving a series of seminars and public lectures across Australia. In 2020, she won a Whitehead Prize of the London Mathematical Society "for her deep contributions to arithmetic dynamics, to equidistribution, to bifurcation loci in families of rational maps, and her recent proof (with DeMarco and Ye) of uniform boundedness results for numbers of torsion points on families of bielliptic genus two curves in their Jacobians". Her work with DeMarco and Hexi Ye, "Uniform Manin–Mumford for a family of genus 2 curves", published in the Annals of Mathematics, also won the 2020 Alexanderson Award of the American Institute of Mathematics. References 21st-century American mathematicians American women mathematicians Living people University of Illinois Urbana-Champaign alumni University of Illinois Chicago alumni Academics of the University of Cambridge Year of birth missing (living people) 21st-century American women
https://en.wikipedia.org/wiki/Pavle%20Obradovi%C4%87	Pavle Obradović (; born 4 July 2001) is a Serbian professional footballer who plays for Al-Taawon on loan from Emirates. Career statistics References External links 2001 births Living people Men's association football forwards Serbian men's footballers Serbian expatriate men's footballers FK Borac Čačak players RC Strasbourg Alsace players Emirates Club players Al-Taawon (UAE) Club players Serbian First League players UAE Pro League players UAE First Division League players Serbian expatriate sportspeople in France Expatriate men's footballers in France Serbian expatriate sportspeople in the United Arab Emirates Expatriate men's footballers in the United Arab Emirates Sportspeople from Gornji Milanovac
https://en.wikipedia.org/wiki/Adri%C3%A0%20Mateo	Adrià Mateo López (born 16 March 1995), is a Spanish former footballer. On 29 October 2021 he scored from 71 metres in a First Division match against Raufoss. Career statistics Club References 1995 births Living people Spanish men's footballers Men's association football midfielders Levanger FK players Ranheim Fotball players Norwegian First Division players Eliteserien players Spanish expatriate men's footballers Expatriate men's footballers in Norway Spanish expatriate sportspeople in Norway
https://en.wikipedia.org/wiki/Daichi%20Tanabe	is a Japanese footballer. Career statistics Club Notes References Living people 2001 births Japanese men's footballers Japanese expatriate men's footballers Men's association football midfielders Japan Soccer College players Singapore Premier League players Albirex Niigata Singapore FC players Japanese expatriate sportspeople in Singapore Expatriate men's footballers in Singapore
https://en.wikipedia.org/wiki/Normally%20flat%20ring	In algebraic geometry, a normally flat ring along a proper ideal I is a local ring A such that is flat over for each integer . The notion was introduced by Hironaka in his proof of the resolution of singularities as a refinement of equimultiplicity and was later generalized by Alexander Grothendieck and others. References Herrmann, M., S. Ikeda, and U. Orbanz: Equimultiplicity and Blowing Up. An Algebraic Study with an Appendix by B. Moonen. Springer Verlag, Berlin Heidelberg New-York, 1988. Algebraic geometry
https://en.wikipedia.org/wiki/Sondre%20Liseth	Sondre Liseth (born 30 September 1997) is a Norwegian footballer who plays for Haugesund. Career statistics Club References 1997 births Living people Norwegian men's footballers Men's association football forwards Eliteserien players Norwegian First Division players Fana IL players Nest-Sotra Fotball players Mjøndalen IF Fotball players FK Haugesund players Footballers from Bergen
https://en.wikipedia.org/wiki/Jonathan%20Lindseth	Jonathan Lindseth (born 25 February 1996) is a Norwegian professional footballer who plays as a midfielder for First League club CSKA Sofia. Career statistics Club References 1996 births Living people Norwegian men's footballers Men's association football midfielders Eliteserien players Norwegian First Division players First Professional Football League (Bulgaria) players Odds BK players Mjøndalen IF Fotball players Sarpsborg 08 FF players PFC CSKA Sofia players Norwegian expatriate men's footballers Expatriate men's footballers in Bulgaria Footballers from Skien
https://en.wikipedia.org/wiki/Brayan%20Rojas	Brayan Rojas (born 30 November 1997) is a Costa Rican footballer who plays for Herediano. Career statistics Club References 1997 births Living people Costa Rican men's footballers Costa Rican expatriate men's footballers Men's association football forwards Liga FPD players Eliteserien players A.D. Carmelita footballers Tromsø IL players C.S. Herediano footballers Costa Rican expatriate sportspeople in Norway Expatriate men's footballers in Norway People from Naranjo (canton) Sportspeople from Alajuela Province
https://en.wikipedia.org/wiki/Carnot%27s%20theorem	Carnot's theorem or Carnot's principle may refer to: In geometry: Carnot's theorem (inradius, circumradius), describing a property of the incircle and the circumcircle of a triangle Carnot's theorem (conics), describing a relation between triangles and conic sections Carnot's theorem (perpendiculars), describing a property of certain perpendiculars on triangle sides In physics: Carnot's theorem (thermodynamics), setting a maximum efficiency obtainable from a heat engine See also Carnot cycle, in thermodynamics
https://en.wikipedia.org/wiki/Aleksa%20Uro%C5%A1evi%C4%87	Aleksa Urošević (; born 9 May 2000) is a Serbian footballer who plays for Bosnian club Radnik Bijeljina. Career statistics References External links 2000 births Living people Men's association football defenders Serbian men's footballers FK Borac Čačak players FK Spartak Subotica players FK Radnik Bijeljina players Serbian First League players Serbian SuperLiga players Premier League of Bosnia and Herzegovina players Serbian expatriate men's footballers Expatriate men's footballers in Bosnia and Herzegovina Serbian expatriate sportspeople in Bosnia and Herzegovina Footballers from Čačak
https://en.wikipedia.org/wiki/Barbara%20Fantechi	Barbara Fantechi is an Italian mathematician and Professor at the International School for Advanced Studies. Her research area is algebraic geometry. She is a member of the Accademia dei Lincei. Early life and education Fantechi received her Laurea from the University of Pisa in 1988, with thesis Secanti di varietà proiettive e applicazioni. Her doctoral advisor was Fabrizio Catanese. Research and career Her research considers algebraic geometry. She has developed the mathematical theories that underpin algebraic stacks. Stacks were first introduced to understand the moduli space of curves. Honours and awards In 2018, Fantechi received the Prof. Luigi Tartufari award from the Accademia dei Lincei. She was awarded the MSRI Chancellor's Professorship for 2017-2018, and spent a year at the University of California, Berkeley. In 2022, Fantechi was the first woman mathematician to become a member of the Accademia dei Lincei. Publications References External links 1966 births Living people 20th-century Italian mathematicians Italian women mathematicians 20th-century women mathematicians 21st-century women mathematicians 21st-century Italian mathematicians University of Pisa alumni Algebraic geometers 20th-century Italian women 21st-century Italian women
https://en.wikipedia.org/wiki/Virginia%20Warfield	Virginia "Ginger" Patricia McShane Warfield is an American mathematician and mathematical educator. She received the Louise Hay Award from the Association for Women in Mathematics in 2007. Education Warfield's father was mathematician Edward J. McShane. She received her Ph.D. in mathematics from Brown University in 1971. Her doctoral advisor was Wendell Fleming and the title of her dissertation was A Stochastic Maximum Principle. Career While making contributions to the field of stochastic analysis after her Ph.D., Warfield became more and more engrossed by the problems of mathematics education. She worked with Project SEED, a highly regarded mathematics program whose goal was to promote sense-making mathematical activities for fourth through sixth graders. She addressed issues of teacher preparation and enhancement. She collaborated with the French mathematician Guy Brousseau, a pioneer in the “didactics of mathematics,” the scientific study of issues in mathematics teaching and learning. She has been an active member of the Association for Women in Mathematics (AWM). She has chaired the Education Committee, has served as Education Column Editor for the AWM Newsletter, and was elected as a Member-at-large to the Executive Committee. She has been a member of the Mathematical Association of America’s committees on Professional Development and Mathematical Education of Teachers. Books Warfield is the author of the book Invitation to Didactique (self-published, 2007, and Springer Briefs in Education, 2014) and the co-author of Teaching Fractions through Situations: A Fundamental Experiment (with Guy Brousseau and Nadine Brousseau, Springer 2013). References 20th-century women mathematicians 21st-century women mathematicians American women mathematicians 20th-century American mathematicians 21st-century American mathematicians Year of birth missing (living people) Living people 20th-century American women 21st-century American women
https://en.wikipedia.org/wiki/Bettina%20Eick	Bettina Eick is a German mathematician specializing in computational group theory. She is Professor of Mathematics at the Technische Universität (TU) Braunschweig. Life and education Eick was born on May 16, 1968, in Bremervörde, Germany, to Hans and Eva Eick. She attended the Rheinische-Westfälische Technische Hochschule (RWTH) Aachen from 1987 to 1993. During that time she spent a year at the Queen Mary and Westfield College (currently known as Queen Mary University London) doing mathematical work under the direction of Charles Leedham-Green. In 1993 she completed her Diplom thesis under the supervision of Joachim Neubüser. In 1996, Eick earned her PhD also at RWTH Aachen under the supervision of Neubüser. Her dissertation was entitled Charakterisierung und Konstruktion von Frattinigruppen mit Anwendungen in der Konstruktion endlicher Gruppen (Characterization and Constructions of Frattini Groups with Applications to the Construction of Finite Groups). Career Eick began her career with postdoctoral positions at RWTH Aachen and the University of Würzburg. She received her habilitation at the University of Kassel in 2001 before joining TU Braunschweig. Eick is known for her work in algorithmic algebra and group theory. Her early work focused on the development of practical algorithms for polycyclic groups and the construction of finite groups. She is one of the main developers of the SmallGroups library. This database contains, among others, a complete list of all groups of order at most 2000, except for order 1024. The list includes more than 400 million finite groups and is available in the computer algebra systems GAP, Magma, SageMath, and Oscar. Since 2000, Eick has been a contributor to the "coclass project" that aims to classify groups of prime power order and other nilpotent algebraic objects using coclass as a primary invariant. In 2005, 2011, and 2017 she was a guest scientist at the University of Auckland working with Eamonn O'Brien and funded by the Feodor Lynen Research Fellowship from the Alexander von Humboldt Foundation. Eick is a coauthor of the computer algebra system GAP and has been a member of the GAP council since 2001 (chair since 2021). Selected publications External links at Technische Universität Braunschweig References 1968 births Living people German women mathematicians 21st-century German mathematicians Group theorists
https://en.wikipedia.org/wiki/Sims%20conjecture	In mathematics, the Sims conjecture is a result in group theory, originally proposed by Charles Sims. He conjectured that if is a primitive permutation group on a finite set and denotes the stabilizer of the point in , then there exists an integer-valued function such that for the length of any orbit of in the set . The conjecture was proven by Peter Cameron, Cheryl Praeger, Jan Saxl, and Gary Seitz using the classification of finite simple groups, in particular the fact that only finitely many isomorphism types of sporadic groups exist. The theorem reads precisely as follows. Thus, in a primitive permutation group with "large" stabilizers, these stabilizers cannot have any small orbit. A consequence of their proof is that there exist only finitely many connected distance-transitive graphs having degree greater than 2. References Algebraic graph theory Finite groups Permutation groups Theorems in graph theory Theorems in group theory
https://en.wikipedia.org/wiki/Matheus%20Peixoto	Matheus Vieira Campos Peixoto (born 16 November 1995) is a Brazilian footballer who plays for Atlético Goianiense, on loan from Metalist Kharkiv. Career statistics Honours Club Bahia Copa do Nordeste: 2017 Red Bull Bragantino Campeonato Brasileiro Série B: 2019 Campeonato Paulista Interior: 2020 Goiás Copa Verde: 2023 References External links 1995 births Living people Brazilian men's footballers Men's association football midfielders Campeonato Brasileiro Série A players Campeonato Brasileiro Série B players Campeonato Brasileiro Série C players Ukrainian First League players Brazilian expatriate men's footballers Expatriate men's footballers in Ukraine Brazilian expatriate sportspeople in Ukraine Audax Rio de Janeiro Esporte Clube players Esporte Clube Bahia players Fluminense de Feira Futebol Clube players Clube Atlético Bragantino players Sport Club do Recife players Red Bull Bragantino players Esporte Clube Juventude players FC Metalist Kharkiv players Ceará Sporting Club players Goiás Esporte Clube players
https://en.wikipedia.org/wiki/Jack%20Allen%20%28footballer%2C%20born%201889%29	Jack Allen (born 1889), sometimes known as Walter Allen, was an English footballer who played as a right back in the Football League for Chesterfield. Career statistics References English men's footballers Croydon Common F.C. players Southern Football League players English Football League players 1889 births Year of death unknown Men's association football fullbacks Footballers from Sheffield Colne F.C. players Doncaster Rovers F.C. players People from Darnall
https://en.wikipedia.org/wiki/Cartan%E2%80%93Ambrose%E2%80%93Hicks%20theorem	In mathematics, the Cartan–Ambrose–Hicks theorem is a theorem of Riemannian geometry, according to which the Riemannian metric is locally determined by the Riemann curvature tensor, or in other words, behavior of the curvature tensor under parallel translation determines the metric. The theorem is named after Élie Cartan, Warren Ambrose, and his PhD student Noel Hicks. Cartan proved the local version. Ambrose proved a global version that allows for isometries between general Riemannian manifolds with varying curvature, in 1956. This was further generalized by Hicks to general manifolds with affine connections in their tangent bundles, in 1959. A statement and proof of the theorem can be found in Introduction Let be connected, complete Riemannian manifolds. We consider the problem of isometrically mapping a small patch on to a small patch on . Let , and let be a linear isometry. This can be interpreted as isometrically mapping an infinitesimal patch (the tangent space) at to an infinitesimal patch at . Now we attempt to extend it to a finite (rather than infinitesimal) patch. For sufficiently small , the exponential maps are local diffeomorphisms. Here, is the ball centered on of radius One then defines a diffeomorphism by When is an isometry? Intuitively, it should be an isometry if it satisfies the two conditions: It is a linear isometry at the tangent space of every point on , that is, it is an isometry on the infinitesimal patches. It preserves the curvature tensor at the tangent space of every point on , that is, it preserves how the infinitesimal patches fit together. If is an isometry, it must preserve the geodesics. Thus, it is natural to consider the behavior of as we transport it along an arbitrary geodesic radius starting at . By property of the exponential mapping, maps it to a geodesic radius of starting at ,. Let be the parallel transport along (defined by the Levi-Civita connection), and be the parallel transport along , then we have the mapping between infinitesimal patches along the two geodesic radii: Cartan's theorem The original theorem proven by Cartan is the local version of the Cartan–Ambrose–Hicks theorem. is an isometry if and only if for all geodesic radii with , and all , we have where are Riemann curvature tensors of .In words, it states that is an isometry if and only if the only way to preserve its infinitesimal isometry also preserves the Riemannian curvature. Note that generally does not have to be a diffeomorphism, but only a locally isometric covering map. However, must be a global isometry if is simply connected. Cartan–Ambrose–Hicks theorem Theorem: For Riemann curvature tensors and all broken geodesics (a broken geodesic is a curve that is piecewise geodesic) with , for all . Then, if two broken geodesics beginning in have the same endpoint, then the corresponding broken geodesics (mapped by ) in also have the same end point. So there exists a ma
https://en.wikipedia.org/wiki/Russell%20T.%20Wilson	Russell Terrell Wilson was a mathematics professor and an American football, basketball and baseball coach. He was a 1906 graduate of Earlham College in Richmond, Indiana. He was a mathematics professor at the University of Southern California beginning in 1912. Wilson served as the head football coach at Whittier College in Whittier, California and Saint Mary's College of California between 1912 and 1919. Beginning in 1916, Wilson also served as a basketball and baseball coach at Stanford University. References Year of birth missing Year of death missing Earlham Quakers football players Saint Mary's Gaels football coaches Stanford Cardinal baseball coaches Stanford Cardinal men's basketball coaches Whittier Poets football coaches University of Southern California faculty
https://en.wikipedia.org/wiki/Arthur%20Hirsch	Arthur Hirsch (1866–1948) was a German mathematician. Life and work Hirsch completed his schooling in Königsberg in 1882 and then studied mathematics and physics in the universities of Berlin and Königsberg. Among his teachers at Königsberg were David Hilbert and Adolf Hurwitz. In 1892 he received a doctorate from Königsberg for a thesis about linear differential equations. The following year, he took his docent habilitation at Polytechnikum of Zurich, where he was, successively, assistant professor from 1893, titular professor from 1897 and ordinary professor from 1903 until his retirement in 1936. The work of Hirsch is primarily on differential equations and hypergeometric functions. He published seven papers about it in Mathematische Annalen. Hirsch was a member of the Swiss Mathematical Society from his foundation in 1910. References Bibliography External links , 19th-century German mathematicians 20th-century German mathematicians 1866 births 1948 deaths Scientists from Königsberg University of Königsberg alumni
https://en.wikipedia.org/wiki/Feodor%20Theilheimer	Feodor Theilheimer (1909–2000) was a German mathematician who studied mathematics and physics at the University of Erlangen. He lectured in mathematics at Trinity College and worked for the U.S. Department of Defense on the research and development of ship design and construction. Early life and career Theilheimer was born in Gunzenhausen, Germany on 18 June 1909, the youngest of six children, to Gustav Theilheimer and Rosa Theilheimer (née Waldmann). Gustav was a cattle dealer and hops buyer for breweries. Feodor went to Realschule in Gunzenhausen and Oberrealschule in Nuremberg. He attended the University of Erlangen where he studied mathematics and physics. From 1928 to 1931 he studied at the Telshe Yeshiva in Lithuania. In 1931 he attended the Hildesheimer Rabbinical Seminary in Berlin. In 1932 he started studying mathematics at the Friedrich-Wilhelms University of Berlin and received his PhD in 1936 with the thesis Ein Beitrag zur Theorie der charakteristischen Invarianten (A contribution to the theory of characteristic invariants). He was one of the last Jews to graduate from that university. Some of the mathematicians working in Berlin while Theilheimer was there were Ludwig Bieberbach, Alfred Brauer, Georg Feigl, Erhard Schmidt, Richard von Mises, and Issai Schur, his thesis advisor. He taught in Berlin for one year but as it became increasingly difficult to teach as a Jew in Germany under the Nazi regime, he emigrated to the USA in 1937. In the USA it was difficult to find work as a German immigrant and from 1937 to 1941 he tutored Jewish refugees in St Louis. In 1941 he joined Brown University and lectured a course entitled Program of Advanced Research and Instruction in Mechanics. In 1942 he was appointed lecturer in mathematics at Trinity College and was promoted to assistant professor in 1946. In 1948 he moved to Washington, DC where he worked for the U.S. Department of Defense as a mathematician on the research and development of ship design and construction. Theilheimer attended several meetings of the Mathematical Association of America over the period 1947 to 1955 and presented papers at these meetings. Works He completed his thesis on invariant theory in 1936 despite the challenges of being a non-Aryan. Most of his later career was in aerodynamics and ship modeling for example on the use of high speed computers to ease the drawing of ship lines. For this work he received the David W Taylor Award for Scientific Achievement. He worked on Fast Fourier transform algorithms and how to quickly factor matrices to a product of zeros. Private life In 1948 Theilheimer married Henriette "Henny" Rubel and they had one daughter, Rachel born in 1950 in Silver Spring, Maryland. They lived in Chevy Chase, Maryland. Theilheimer retired in 1977 but still taught mathematics courses at the University of Maryland until 1983. Theilheimer died on 24 December 2000 in Chevy Chase. His wife then moved to New York where she died in 2013. Sel
https://en.wikipedia.org/wiki/Tadashi%20Nagano	was a Taiwan-born Japanese mathematician who worked mainly on differential geometry and related subjects. Biography Nagano was born in Taipei in 1930, when Taiwan was administered by Japan. He returned to Japan for undergraduate study from 1951 to 1954 at the University of Tokyo, and defended his doctoral thesis under Kentaro Yano's supervision at University of Tokyo in 1959. He worked at the University of Tokyo from April in 1959 to May 1967 as a lecturer (1959-1962) and as an assistant professor (1962–1967). Nagano moved to United States to pursue an academic career with the University of Notre Dame in 1967. He became a full professor of University of Notre Dame in 1969. Tadashi Nagano was a visiting professor at University of California at Berkeley from 1962–1964, National Tsing Hua University in Taiwan twice, first in 1966 and then one more time in 1978. After a successful academic career with University of Notre Dame, Tadashi Nagano returned to Japan and became a professor with Sophia University in 1986. He retired from Sophia University at 70 years old in 2000. Tadashi Nagano co-authored 10 papers with Shoshichi Kobayashi in the interval 1966–1972, including A theorem on filtered Lie algebras and its applications, Bull. Amer. Math. Soc. 70 1964, pp. 401–403. Tadashi Nagano served an editor-in-chief of Tokyo Journal of Mathematics for several years since 1990. In 1994, Tadashi Nagano was presented with the Geometry Prize from Mathematical Society of Japan for his research achievements over a large field of the differential geometry including a geometric construction of compact symmetric spaces ((M+,M-)-method joint with Bang-Yen Chen). References 20th-century Japanese mathematicians People from Indiana Mathematicians from Tokyo Scientists from Taipei Japanese expatriates in the United States Academic staff of Sophia University Academic staff of the University of Tokyo Academic journal editors Differential geometers University of Tokyo alumni University of Notre Dame faculty 1930 births 2017 deaths
https://en.wikipedia.org/wiki/L%C3%A9o%20Rigo	Leonardo "Léo" Rigo da Silva (born 25 April 1995) is a Brazilian footballer who plays for Ferroviária as a centre-back. Career statistics References External links 1995 births Living people Brazilian men's footballers Men's association football midfielders Campeonato Brasileiro Série B players Campeonato Brasileiro Série C players Campeonato Brasileiro Série D players Guarani FC players Esporte Clube Água Santa players Clube Náutico Marcílio Dias players Clube Atlético Bragantino players Ituano FC players Londrina Esporte Clube players
https://en.wikipedia.org/wiki/Richard%20%28footballer%2C%20born%201999%29	Richard Alexandre Birkheun Rodrigues (born 11 October 1999), simply known as Richard, is a Brazilian footballer who plays as a winger for Chapecoense, on loan from CRB. Career statistics References External links 1999 births Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football forwards Sport Club Internacional players Vila Nova Futebol Clube players C.D. Tondela players B-SAD players Botafogo Futebol Clube (SP) players Associação Atlética Ponte Preta players Clube de Regatas Brasil players Associação Portuguesa de Desportos players Associação Chapecoense de Futebol players Campeonato Brasileiro Série B players Primeira Liga players Campeonato de Portugal (league) players Brazilian expatriate sportspeople in Portugal Expatriate men's footballers in Portugal
https://en.wikipedia.org/wiki/Z%C3%A9%20Ricardo%20%28footballer%2C%20born%201999%29	José Ricardo Araújo Fernandes (born 3 February 1999), commonly known as Zé Ricardo, is a Brazilian footballer who plays as a midfielder for Tombense. Career statistics Honours Club Goiás Copa Verde: 2023 References 1999 births Living people Footballers from Rio de Janeiro (city) Brazilian men's footballers Men's association football midfielders Campeonato Brasileiro Série B players Campeonato Brasileiro Série D players Fluminense FC players Boavista Sport Club players Londrina Esporte Clube players Tombense Futebol Clube players Goiás Esporte Clube players
https://en.wikipedia.org/wiki/Caio%20Vin%C3%ADcius	Caio Vinícius da Conceição (born 11 January 1999), known as Caio Vinícius or simply Caio, is a Brazilian footballer who plays as a defensive midfielder. Career statistics References External links 1999 births Living people Footballers from São Paulo (state) Brazilian men's footballers Men's association football midfielders Campeonato Brasileiro Série A players Campeonato Brasileiro Série B players Londrina Esporte Clube players Fluminense FC players Atlético Clube Goianiense players Oeste Futebol Clube players Goiás Esporte Clube players
https://en.wikipedia.org/wiki/Francisco%20Nev%C3%A1rez	Francisco Javier Nevárez Pulgarín (born 3 December 2000) is a Mexican professional footballer who plays as a defender for Liga MX club Juárez. Career statistics Club References External links 2000 births Living people Men's association football midfielders Liga MX players FC Juárez footballers Footballers from Chihuahua Sportspeople from Ciudad Juárez Mexican men's footballers
https://en.wikipedia.org/wiki/Traveling%20plane%20wave	In mathematics and physics, a traveling plane wave is a special case of plane wave, namely a field whose evolution in time can be described as simple translation of its values at a constant wave speed , along a fixed direction of propagation . Such a field can be written as where is a function of a single real parameter . The function describes the profile of the wave, namely the value of the field at time , for each displacement . For each displacement , the moving plane perpendicular to at distance from the origin is called a wavefront. This plane too travels along the direction of propagation with velocity ; and the value of the field is then the same, and constant in time, at every one of its points. The wave may be a scalar or vector field; its values are the values of . A sinusoidal plane wave is a special case, when is a sinusoidal function of . Properties A traveling plane wave can be studied by ignoring the dimensions of space perpendicular to the vector ; that is, by considering the wave on a one-dimensional medium, with a single position coordinate . For a scalar traveling plane wave in two or three dimensions, the gradient of the field is always collinear with the direction ; specifically, , where is the derivative of . Moreover, a traveling plane wave of any shape satisfies the partial differential equation Plane traveling waves are also special solutions of the wave equation in an homogeneous medium. See also Spherical wave Spherical sinusoidal wave Standing wave References Waves
https://en.wikipedia.org/wiki/Francis%20Swift	Francis Henry Swift (1827-1892) was Dean of Clonmacnoise from 1885 to 1892. Dowse was born in County Westmeath and educated at Trinity College, Dublin (BA in mathematics 1851, MA 1865) and ordained in 1856. After a curacy in Mullingar he held incumbencies at Clonfad and Castletown.He spent his whole career at Mullingar (curate from 1855 to 1865; incumbent thereafter) before his appointment to the deanery. References Alumni of Trinity College Dublin Deans of Clonmacnoise Christian clergy from County Westmeath 19th-century Irish Anglican priests 1827 births 1892 deaths
https://en.wikipedia.org/wiki/Geely%20Geometry	Geely Geometry (Chinese: 吉利几何; pinyin: Jílì jǐhé), or simply known as Geometry, is a car marque created by the Chinese car company Geely in April 2019. The Geely Geometry brand is mainly focused on the development of electric vehicles or NEVs. The Geometry brand has been reconsolidated into Geely Auto as an entry-level electric product series in March 2023. Products Current Geometry A/ A Pro/ G6- An electric compact sedan based on the Geely Emgrand GL Geometry C/ M6- An electric crossover based on the Geely Emgrand GS Geometry E- A subcompact electric crossover Geometry Panda/ M2 Former Geometry EX3- An subcompact crossover rebaged as Geely Yuanjing X3 References External links Official website (in Chinese) Geely brands Car manufacturers of China Chinese brands Electric vehicle manufacturers of China Chinese companies established in 2019 Vehicle manufacturing companies established in 2019
https://en.wikipedia.org/wiki/Geometry%20A	The Geometry A is a battery-powered compact sedan produced by Chinese auto manufacturer Geely under the Geely Geometry brand. Overview The Geometry A is the first model of the Geometry brand. It was developed based on the Geely Emgrand GL sedan. The A has a very low drag coefficient of . Powertrain The Geometry A comes in a choice of two battery capacities, a 51.9 kWh and a longer-range 61.9 kWh version with a range of 500 km (310 miles) on a single charge. The A powertrain provides a maximum power of and torque of , with acceleration to in 8.8 seconds. Geometry A Pro As of February 2021, teasers of the facelift of the Geometry A was revealed. The post facelift model is called the Geometry A Pro, and the updated model features an electric motor producing and of torque. The battery density of the Geometry A Pro is 183.23Wh/kg and the NEDC range is Geometry G6 The Geometry G6 is the facelifted variant of the Geometry A launched in September 2022. The G6 features restyled front and rear end designs as well as the Harmony OS operating system by Huawei. The power comes from a 150 kW electric motor with two variants offering a 480 km and 620 km electric range respectively. References External links Geometry Official Website Geometry vehicles Mid-size cars Front-wheel-drive vehicles Sedans Cars introduced in 2019 2010s cars Electric concept cars Cars of China Production electric cars
https://en.wikipedia.org/wiki/Tas%20Tsonis	Tas Tsonis is a computer scientist who continues to play a prominent role in using graphical algorithms, computer science, and computational geometry to automate the personalization of apparel and accessories. He has been granted twelve US patents based on mathematical and graphical algorithms. Tsonis co-founded Pulse Microsystems in 1982, with Brian Goldberg. Pulse is credited with "the first set of pattern archiving software, network management software and data acquisition software for embroidery industry." They patented methods to take artwork, stored using scalable vector graphics, and translate those into instruction for knitting and embroidery machines, enabling artwork to be incorporated into fabrics at the best resolution possible for the fabric under construction. In 2004 Tsonis and Goldberg co-founded Viigo, a firm that developed app software. Tsonis is a graduate of the University of Waterloo, and, in 2016, was honoured by the University with its annual J.W. Graham Medal. Each year the award recognizes one of the University's graduates who has played a significant role in the use of computers. References Canadian computer scientists 1953 births Living people University of Waterloo alumni
https://en.wikipedia.org/wiki/List%20of%20Colombia%20national%20football%20team%20managers	The Colombia national football team has been under the supervision of 41 different managers since its first match in 1938. Managers Last updated: Colombia vs. Chile, 12 September 2023. Statistics include official FIFA-recognised matches only. References Colombia
https://en.wikipedia.org/wiki/Finite%20type	Finite type refers to several related concepts in mathematics: Algebra of finite type, an associative algebra with finitely many generator Morphism of finite type, a morphism of schemes with underlying morphisms on affine opens given by algebras of finite type Scheme of finite type, a scheme over a field with a structure morphism of finite type Coxeter group of finite type, a Coxeter group whose Schläfli matrix has only positive eigenvalues Coxeter matrix of finite type, a Coxeter matrix whose associated Schläfli matrix has only positive eigenvalues Artin group of finite type, an Artin group arising as the finite Coxeter group of a Coxeter matrix of finite type Finite type invariant, a knot invariant that vanishes on knots with finitely many singularities Subshift of finite type, a shift space in symbolic dynamics
https://en.wikipedia.org/wiki/Genus%20g%20surface	In mathematics, a genus g surface (also known as a g-torus or g-holed torus) is a surface formed by the connected sum of g many tori: the interior of a disk is removed from each of g many tori and the boundaries of the g many disks are identified (glued together), forming a g-torus. The genus of such a surface is g. A genus g surface is a two-dimensional manifold. The classification theorem for surfaces states that every compact connected two-dimensional manifold is homeomorphic to either the sphere, the connected sum of tori, or the connected sum of real projective planes. Definition of genus The genus of a connected orientable surface is an integer representing the maximum number of cuttings along non-intersecting closed simple curves without rendering the resultant manifold disconnected. It is equal to the number of handles on it. Alternatively, it can be defined in terms of the Euler characteristic χ, via the relationship χ = 2 − 2g for closed surfaces, where g is the genus. The genus (sometimes called the demigenus or Euler genus) of a connected non-orientable closed surface is a positive integer representing the number of cross-caps attached to a sphere. Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − g, where g is the non-orientable genus. Genus 0 An orientable surface of genus zero is the sphere S2. Another surface of genus zero is the disc. Genus 1 A genus one orientable surface is the ordinary torus. A non-orientable surface of genus one is the projective plane. Elliptic curves over the complex numbers can be identified with genus 1 surfaces. The formulation of elliptic curves as the embedding of a torus in the complex projective plane follows naturally from a property of Weierstrass's elliptic functions that allows elliptic curves to be obtained from the quotient of the complex plane by a lattice. Genus 2 The term double torus is occasionally used to denote a genus 2 surface. A non-orientable surface of genus two is the Klein bottle. The Bolza surface is the most symmetric Riemann surface of genus 2, in the sense that it has the largest possible conformal automorphism group. Genus 3 The term triple torus is also occasionally used to denote a genus 3 surface. The Klein quartic is a compact Riemann surface of genus with the highest possible order automorphism group for compact Riemann surfaces of genus 3. It has namely order orientation-preserving automorphisms, and automorphisms if orientation may be reversed. See also Three-torus g-torus knot References Sources James R. Munkres, Topology, Second Edition, Prentice-Hall, 2000, . William S. Massey, Algebraic Topology: An Introduction, Harbrace, 1967. Topology Geometry Surfaces
https://en.wikipedia.org/wiki/Mihael%20Klepa%C4%8D	Mihael Klepač (born 19 September 1997) is a Croatian professional footballer who plays as a right winger for Swiss Super League club Yverdon-Sport. Career statistics Club References External links Mihael Klepač at Sofascore 1997 births Living people People from Našice Men's association football wingers Croatian men's footballers NK Osijek players NK Dugopolje players NK Varaždin (2012) players NK Rudeš players FK Željezničar Sarajevo players NK Aluminij players NŠ Mura players Yverdon-Sport FC players Croatian Football League players First Football League (Croatia) players Premier League of Bosnia and Herzegovina players Slovenian PrvaLiga players Swiss Super League players Croatian expatriate men's footballers Expatriate men's footballers in Bosnia and Herzegovina Croatian expatriate sportspeople in Bosnia and Herzegovina Expatriate men's footballers in Slovenia Croatian expatriate sportspeople in Slovenia Expatriate men's footballers in Switzerland Croatian expatriate sportspeople in Switzerland
https://en.wikipedia.org/wiki/Lev%20Tumarkin	Lev Abramovich Tumarkin (14 January 1904 – 1 August 1974) was a Russian mathematician. He was dean of the Faculty of Mechanics and Mathematics of Moscow State University. He was a student of Pavel Aleksandrov. He attended the First International Topological Conference in Moscow, 1935 as a host but made no presentation. References 1904 births 1974 deaths 20th-century Russian mathematicians
https://en.wikipedia.org/wiki/Emilio%20%C3%81lvarez%20%28Spanish%20footballer%29	Emilio Álvarez Blanco (born 19 October 1971), is a retired Spanish footballer who played as a goalkeeper. He used to serve as a goalkeeping coach for English side Manchester United. Career statistics Club Notes References 1971 births Living people Spanish men's footballers Men's association football goalkeepers Real Madrid CF players Rayo Vallecano players CF Palencia footballers Extremadura UD footballers Recreativo de Huelva players Elche CF players Algeciras CF footballers CD Mensajero players Segunda División B players Segunda División players Expatriate sports coaches
https://en.wikipedia.org/wiki/Gr%C3%BCnbaum%E2%80%93Rigby%20configuration	In geometry, the Grünbaum–Rigby configuration is a symmetric configuration consisting of 21 points and 21 lines, with four points on each line and four lines through each point. Originally studied by Felix Klein in the complex projective plane in connection with the Klein quartic, it was first realized in the Euclidean plane by Branko Grünbaum and John F. Rigby. History and notation The Grünbaum–Rigby configuration was known to Felix Klein, William Burnside, and H. S. M. Coxeter. Its original description by Klein in 1879 marked the first appearance in the mathematical literature of a 4-configuration, a system of points and lines with four points per line and four lines per point. In Klein's description, these points and lines belong to the complex projective plane, a space whose coordinates are complex numbers rather than the real-number coordinates of the Euclidean plane. The geometric realisation of this configuration as points and lines in the Euclidean plane, based on overlaying three regular heptagrams, was only established much later, by . Their paper on it became the first of a series of works on configurations by Grünbaum, and contained the first published graphical depiction of a 4-configuration. In the notation of configurations, configurations with 21 points, 21 lines, 4 points per line and 4 lines per point are denoted (214). However, the notation does not specify the configuration itself, only its type (the numbers of points, lines, and incidences). It also does not specify whether the configuration is purely combinatorial (an abstract incidence pattern of lines and points) or whether the points and lines of the configuration are realizable in the Euclidean plane or another standard geometry. The type (214) is highly ambiguous: there is an unknown but large number of (combinatorial) configurations of this type, 200 of which were listed by . Construction The Grünbaum–Rigby configuration can be constructed from the seven points of a regular heptagon and its 14 interior diagonals. To complete the 21 points and lines of the configuration, these must be augmented by 14 more points and seven more lines. The remaining 14 points of the configuration are the points where pairs of equal-length diagonals of the heptagon cross each other. These form two smaller heptagons, one for each of the two lengths of diagonal; the sides of these smaller heptagons are the diagonals of the outer heptagon. Each of the two smaller heptagons has 14 diagonals, seven of which are shared with the other smaller heptagon. The seven shared diagonals are the remaining seven lines of the configuration. The original construction of the Grünbaum–Rigby configuration by Klein viewed its points and lines as belonging to the complex projective plane, rather than the Euclidean plane. In this space, the points and lines form the perspective centers and axes of the perspective transformations of the Klein quartic. They have the same pattern of point-line intersections as
https://en.wikipedia.org/wiki/Sebasti%C3%A1n%20Mart%C3%ADnez%20%28footballer%2C%20born%202001%29	Sebastián Martínez Vidrio (born 6 January 2001) is a Mexican professional footballer who plays as a forward. He was included in The Guardian's "Next Generation 2018". Career statistics Club References External links Sebastián Martínez Vidrio at Liga MX 2001 births Living people Mexican men's footballers Mexico men's youth international footballers Men's association football forwards C.D. Guadalajara footballers Tercera División de México players Footballers from Veracruz People from Coatzacoalcos
https://en.wikipedia.org/wiki/Kong%20Ho-won	Kong Ho-won (; born 4 September 1997) is a South Korea footballer currently playing as a defender for Hougang United. Career statistics Club Notes References Living people 1997 births South Korean men's footballers Men's association football midfielders Singapore Premier League players Hougang United FC players Place of birth missing (living people) People from Paju Footballers from Gyeonggi Province
https://en.wikipedia.org/wiki/Takumu%20Nishihara	is a Japanese professional footballer who plays as a forward for Cambodian Premier League club Visakha. Career statistics Club Notes Honours Club Khonkaen United Thai League 3 (1): 2019 References 1992 births Living people Association football people from Hyōgo Prefecture Kansai University alumni Japanese men's footballers Japanese expatriate men's footballers Men's association football forwards FC Tiamo Hirakata players Ayeyawady United F.C. players F.C. Chanthabouly players Takumu Nishihara Expatriate men's footballers in Myanmar Japanese expatriate sportspeople in Myanmar Expatriate men's footballers in Laos Japanese expatriate sportspeople in Laos Expatriate men's footballers in Thailand Expatriate men's footballers in Cambodia Japanese expatriate sportspeople in Cambodia Japanese expatriate sportspeople in Thailand
https://en.wikipedia.org/wiki/Ryo%20Nakamura%20%28footballer%2C%20born%201989%29	is a Japanese footballer who currently plays for Shan United. Career statistics Club Notes References 1989 births Living people Japanese men's footballers Japanese expatriate men's footballers Men's association football midfielders Shan United F.C. players Expatriate men's footballers in Mongolia Expatriate men's footballers in Myanmar Japanese expatriate sportspeople in Myanmar
https://en.wikipedia.org/wiki/Ryo%20Nakamura%20%28footballer%2C%20born%201996%29	is a Japanese footballer who currently plays for Kamatamare Sanuki. Career statistics Club Notes References External links 1996 births Living people Japanese men's footballers Men's association football midfielders J3 League players Kamatamare Sanuki players Association football people from Kagoshima Prefecture
https://en.wikipedia.org/wiki/Lee%20Han-guk	Lee Han-guk is a South Korean footballer who last played for Shan United. Career statistics Club Notes References 1987 births Living people South Korean men's footballers South Korean expatriate men's footballers Men's association football midfielders Lee Han-guk Myanmar National League players Lee Han-guk Shan United F.C. players Expatriate men's footballers in Thailand South Korean expatriate sportspeople in Thailand Expatriate men's footballers in Myanmar South Korean expatriate sportspeople in Myanmar
https://en.wikipedia.org/wiki/Hedipo	Hédipo Gustavo da Conceiçao (born 7 February 1988), commonly known as Hédipo, is a Brazilian professional footballer who plays as a attacking midfielder. Career statistics Club Notes References 1988 births Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football forwards Sinop Futebol Clube players Clube Náutico Marcílio Dias players Juazeiro Social Clube players São Carlos Futebol Clube players Shan United F.C. players Persela Lamongan players FC Feronikeli 74 players Southern Myanmar F.C. players Kalteng Putra F.C. players Bhayangkara Presisi Indonesia F.C. players Becamex Binh Duong FC players SHB Da Nang FC players Persipura Jayapura players Myanmar National League players Liga 1 (Indonesia) players Football Superleague of Kosovo players V.League 1 players Brazilian expatriate sportspeople in Myanmar Expatriate men's footballers in Myanmar Brazilian expatriate sportspeople in Indonesia Expatriate men's footballers in Indonesia Brazilian expatriate sportspeople in Kosovo Expatriate men's footballers in Kosovo Brazilian expatriate sportspeople in Guatemala Expatriate men's footballers in Guatemala Brazilian expatriate sportspeople in East Timor Expatriate men's footballers in East Timor Brazilian expatriate sportspeople in Vietnam Expatriate men's footballers in Vietnam Brazilian expatriate sportspeople in Thailand Expatriate men's footballers in Thailand Footballers from Santa Catarina (state)
https://en.wikipedia.org/wiki/Jung%20Yoon-sik	Jung Yoon-sik is a South Korean footballer who last played for Nay Pyi Taw. Career statistics Club Notes References Living people South Korean men's footballers South Korean expatriate men's footballers Men's association football midfielders Myanmar National League players Expatriate men's footballers in Myanmar South Korean expatriate sportspeople in Myanmar Year of birth missing (living people)
https://en.wikipedia.org/wiki/Sashi%20Chalwe	Sashi Triehimus Chalwe (born 16 February 1983) is a former Zambian footballer. Career statistics Club Notes International International goals Scores and results list Zambia's goal tally first. References Living people 1983 births Zambian men's footballers Zambian expatriate men's footballers Men's association football defenders Hong Kong Premier League players Lusaka Dynamos F.C. players Mamelodi Sundowns F.C. players Bloemfontein Celtic F.C. players FC AK players Al Ahed FC players NAPSA Stars F.C. players Hong Kong Rangers FC players Expatriate men's soccer players in South Africa Zambian expatriate sportspeople in South Africa Expatriate men's footballers in Lebanon Expatriate men's footballers in Hong Kong Zambian expatriate sportspeople in Lebanon Lebanese Premier League players Zambia men's international footballers
https://en.wikipedia.org/wiki/Differentially%20private%20analysis%20of%20graphs	Differentially private analysis of graphs studies algorithms for computing accurate graph statistics while preserving differential privacy. Such algorithms are used for data represented in the form of a graph where nodes correspond to individuals and edges correspond to relationships between them. For examples, edges could correspond to friendships, sexual relationships, or communication patterns. A party that collected sensitive graph data can process it using a differentially private algorithm and publish the output of the algorithm. The goal of differentially private analysis of graphs is to design algorithms that compute accurate global information about graphs while preserving privacy of individuals whose data is stored in the graph. Variants Differential privacy imposes a restriction on the algorithm. Intuitively, it requires that the algorithm has roughly the same output distribution on neighboring inputs. If the input is a graph, there are two natural notions of neighboring inputs, edge neighbors and node neighbors, which yield two natural variants of differential privacy for graph data. Let ε be a positive real number and be a randomized algorithm that takes a graph as input and returns an output from a set . The algorithm is -differentially private if, for all neighboring graphs and and all subsets of , where the probability is taken over the randomness used by the algorithm. Edge differential privacy Two graphs are edge neighbors if they differ in one edge. An algorithm is -edge-differentially private if, in the definition above, the notion of edge neighbors is used. Intuitively, an edge differentially private algorithm has similar output distributions on any pair of graphs that differ in one edge, thus protecting changes to graph edges. Node differential privacy Two graphs are node neighbors if one can be obtained from the other by deleting a node and its adjacent edges. An algorithm is -node-differentially private if, in the definition above, the notion of node neighbors is used. Intuitively, a node differentially private algorithm has similar output distributions on any pair of graphs that differ in one one nodes and edges adjacent to it, thus protecting information pertaining to each individual. Node differential privacy give a stronger privacy protection than edge differential privacy. Research history The first edge differentially private algorithm was designed by Nissim, Raskhodnikova, and Smith. The distinction between edge and node differential privacy was first discussed by Hay, Miklau, and Jensen. However, it took several years before first node differentially private algorithms were published in Blocki et al., Kasiviswanathan et al., and Chen and Zhou. In all three papers, the algorithms are for releasing a single statistic, like a triangle count or counts of other subgraphs. Raskhodnikova and Smith gave the first node differentially private algorithm for releasing a vector, specifically, the degree count an
https://en.wikipedia.org/wiki/Samuel%20Go%C3%B1i	Samuel Goñi Villava (born 10 February 1994) is a Spanish footballer who played as a forward for Los Angeles Force in the National Independent Soccer Association. Career statistics Club Notes References External links Samuel Goñi at Bethel University Samuel Goñi at California State University Fullerton 1994 births Living people Spanish men's footballers Footballers from Navarre Cal State Fullerton Titans men's soccer players Men's association football forwards Segunda División B players USL League Two players Ascenso MX players Tercera División players CA Osasuna B players FC Golden State Force players Chattanooga FC players Celaya F.C. Premier players Spanish expatriate men's footballers Expatriate men's soccer players in the United States Spanish expatriate sportspeople in the United States Expatriate men's footballers in Mexico Spanish expatriate sportspeople in Mexico Bethel Wildcats men's soccer players Los Angeles Force players National Independent Soccer Association players

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