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https://en.wikipedia.org/wiki/Diamond%20theorem
In mathematics, diamond theorem may refer to: Aztec diamond theorem on tilings Diamond isomorphism theorem on modular lattices Haran's diamond theorem on Hilbertian fields Cullinane diamond theorem on the Galois geometry of graphic patterns See also Diamond (disambiguation)
https://en.wikipedia.org/wiki/Zariski%27s%20lemma
In algebra, Zariski's lemma, proved by , states that, if a field is finitely generated as an associative algebra over another field , then is a finite field extension of (that is, it is also finitely generated as a vector space). An important application of the lemma is a proof of the weak form of Hilbert's Nullstellensatz: if I is a proper ideal of (k algebraically closed field), then I has a zero; i.e., there is a point x in such that for all f in I. (Proof: replacing I by a maximal ideal , we can assume is maximal. Let and be the natural surjection. By the lemma is a finite extension. Since k is algebraically closed that extension must be k. Then for any , ; that is to say, is a zero of .) The lemma may also be understood from the following perspective. In general, a ring R is a Jacobson ring if and only if every finitely generated R-algebra that is a field is finite over R. Thus, the lemma follows from the fact that a field is a Jacobson ring. Proofs Two direct proofs, one of which is due to Zariski, are given in Atiyah–MacDonald. For Zariski's original proof, see the original paper. Another direct proof in the language of Jacobson rings is given below. The lemma is also a consequence of the Noether normalization lemma. Indeed, by the normalization lemma, K is a finite module over the polynomial ring where are elements of K that are algebraically independent over k. But since K has Krull dimension zero and since an integral ring extension (e.g., a finite ring extension) preserves Krull dimensions, the polynomial ring must have dimension zero; i.e., . The following characterization of a Jacobson ring contains Zariski's lemma as a special case. Recall that a ring is a Jacobson ring if every prime ideal is an intersection of maximal ideals. (When A is a field, A is a Jacobson ring and the theorem below is precisely Zariski's lemma.) Proof: 2. 1.: Let be a prime ideal of A and set . We need to show the Jacobson radical of B is zero. For that end, let f be a nonzero element of B. Let be a maximal ideal of the localization . Then is a field that is a finitely generated A-algebra and so is finite over A by assumption; thus it is finite over and so is finite over the subring where . By integrality, is a maximal ideal not containing f. 1. 2.: Since a factor ring of a Jacobson ring is Jacobson, we can assume B contains A as a subring. Then the assertion is a consequence of the next algebraic fact: (*) Let be integral domains such that B is finitely generated as A-algebra. Then there exists a nonzero a in A such that every ring homomorphism , K an algebraically closed field, with extends to . Indeed, choose a maximal ideal of A not containing a. Writing K for some algebraic closure of , the canonical map extends to . Since B is a field, is injective and so B is algebraic (thus finite algebraic) over . We now prove (*). If B contains an element that is transcendental over A, then it contains a polynomial ring over A to
https://en.wikipedia.org/wiki/Empirical%20likelihood
In probability theory and statistics, empirical likelihood (EL) is a nonparametric method for estimating the parameters of statistical models. It requires fewer assumptions about the error distribution while retaining some of the merits in likelihood-based inference. The estimation method requires that the data are independent and identically distributed (iid). It performs well even when the distribution is asymmetric or censored. EL methods can also handle constraints and prior information on parameters. Art Owen pioneered work in this area with his 1988 paper. Definition Given a set of i.i.d. realizations of random variables , then the empirical distribution function is , with the indicator function and the (normalized) weights . Then, the empirical likelihood is: where is a small number (potentially the difference to the next smaller sample). Important is the that the empirical likelihood estimation can be augmented with side information by using further constraints (similar to the generalized estimating equations approach) for the empirical distribution function. E.g. a constraint like the following can be incorporated using a Lagrange multiplier which implies . With similar constraints, we could also model correlation. Discrete random variables The empirical-likelihood method can also be also employed for discrete distributions. Given such that Then the empirical likelihood is again . Using the Lagrangian multiplier method to maximize the logarithm of the empirical likelihood subject to the trivial normalization constraint, we find as a maximum. Therefore, is the empirical distribution function. Estimation Procedure EL estimates are calculated by maximizing the empirical likelihood function (see above) subject to constraints based on the estimating function and the trivial assumption that the probability weights of the likelihood function sum to 1. This procedure is represented as: subject to the constraints The value of the theta parameter can be found by solving the Lagrangian function There is a clear analogy between this maximization problem and the one solved for maximum entropy. The parameters are nuisance parameters. Empirical Likelihood Ratio (ELR) An empirical likelihood ratio function is defined and used to obtain confidence intervals parameter of interest θ similar to parametric likelihood ratio confidence intervals. Let L(F) be the empirical likelihood of function , then the ELR would be: . Consider sets of the form . Under such conditions a test of rejects when t does not belong to , that is, when no distribution F with has likelihood . The central result is for the mean of X. Clearly, some restrictions on are needed, or else whenever . To see this, let: If is small enough and , then . But then, as ranges through , so does the mean of , tracing out . The problem can be solved by restricting to distributions F that are supported in a bounded set. It turns out to be possible to restrict a
https://en.wikipedia.org/wiki/Norman%20H.%20Anning
Norman Herbert Anning ( – ) was a mathematician, assistant professor, professor emeritus, and instructor in mathematics, recognized and acclaimed in mathematics for publishing a proof of the characterization of the infinite sets of points in the plane with mutually integer distances, known as the Erdős–Anning theorem. Life Anning was originally from Holland Township (currently Chatsworth), Grey County, Ontario, Canada. In 1902, he won a scholarship to Queen's University, and received the Arts bachelor's degree in 1905, and the Arts master's degree in 1906 from the same institution. Academic career Anning served in the faculty of the University of Michigan since 1920, until he retired on 1953. From 1909 to 1910, he held a teaching position in the department of Mathematics and Science at Chilliwack High School, British Columbia. He was a member of the Mathematical Association of America to which he contributed for many years. Besides being a member of the Mathematical Association of America, Anning was appointed as chairperson at the University of Michigan from 1951 to 1952, and treasurer secretary from 1925 to 1926 at the same institution. With Paul Erdős, he published a paper in 1945 containing what is now known as the Erdős–Anning theorem. The theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line. Anning retired on August 28, 1953. He died in Sunnydale, California on May 1, 1963. Publications References 20th-century American mathematicians Canadian mathematicians University of Michigan faculty 1883 births 1963 deaths People from Grey County Queen's University at Kingston alumni Canadian educators
https://en.wikipedia.org/wiki/2012%E2%80%9313%20Al-Shoalah%20season
For the 2012–13 season, Al-Shoalah competed in the first tier of Saudi Arabian football, Saudi Professional League. League table Squad statistics |} Source: Top scorers Source: Disciplinary record Source: Transfers Summer Transfers In Out Winter Transfers In Out Results Pro League Crown Prince Cup References Al-Shoalah Al-Shoulla FC
https://en.wikipedia.org/wiki/Vietnam%20University%20Admission%20Rankings
The University Admission Rankings is a national ranking of Vietnamese high schools based on the average grades of the annual university entrance exam. The statistics is published by the Ministry of Education and Training. 2012 Ranking (*) denotes a national public magnet high school. 2011 Ranking (*) denotes a national public magnet high school. References High schools in Vietnam High schools for the gifted in Vietnam Schools in Vietnam
https://en.wikipedia.org/wiki/Mylar%20balloon%20%28geometry%29
In geometry, a mylar balloon is a surface of revolution. While a sphere is the surface that encloses a maximal volume for a given surface area, the mylar balloon instead maximizes volume for a given generatrix arc length. It resembles a slightly flattened sphere. The shape is approximately realized by inflating a physical balloon made of two circular sheets of flexible, inelastic material; for example, a popular type of toy balloon made of aluminized plastic. Perhaps counterintuitively, the surface area of the inflated balloon is less than the surface area of the circular sheets. This is due to physical crimping of the surface, which increases near the rim. "Mylar balloon" is the name for the figure given by W. Paulson, who first investigated the shape. The term was subsequently adopted by other writers. "Mylar" is a trademark of DuPont. Definition The positive portion of the generatrix of the balloon is the function z(x) where for a given generatrix length a: (i.e.: the generatrix length is given) is a maximum (i.e.: the volume is maximum) Here, the radius r is determined from the constraints. Parametric characterization The parametric equations for the generatrix of a balloon of radius r are given by: (where E and F are elliptic integrals of the second and first kind) Measurement The "thickness" of the balloon (that is, the distance across at the axis of rotation) can be determined by calculating from the parametric equations above. The thickness τ is given by while the generatrix length a is given by where r is the radius; A ≈ 1.3110287771 and B ≈ 0.5990701173 are the first and second lemniscate constants. Volume The volume of the balloon is given by: where a is the arc length of the generatrix). or alternatively: where τ is the thickness at the axis of rotation. Surface area The surface area S of the balloon is given by where r is the radius of the balloon. Derivation Substituting into the parametric equation for z(u) given in yields the following equation for z in terms of x: The above equation has the following derivative: Thus, the surface area is given by the following: Solving the above integral yields . Surface geometry The ratio of the principal curvatures at every point on the mylar balloon is exactly 2, making it an interesting case of a Weingarten surface. Moreover, this single property fully characterizes the balloon. The balloon is evidently flatter at the axis of rotation; this point is actually has zero curvature in any direction. See also Paper bag problem References Surfaces
https://en.wikipedia.org/wiki/Epigroup
In abstract algebra, an epigroup is a semigroup in which every element has a power that belongs to a subgroup. Formally, for all x in a semigroup S, there exists a positive integer n and a subgroup G of S such that xn belongs to G. Epigroups are known by wide variety of other names, including quasi-periodic semigroup, group-bound semigroup, completely π-regular semigroup, strongly π-regular semigroup (sπr), or just π-regular semigroup (although the latter is ambiguous). More generally, in an arbitrary semigroup an element is called group-bound if it has a power that belongs to a subgroup. Epigroups have applications to ring theory. Many of their properties are studied in this context. Epigroups were first studied by Douglas Munn in 1961, who called them pseudoinvertible. Properties Epigroups are a generalization of periodic semigroups, thus all finite semigroups are also epigroups. The class of epigroups also contains all completely regular semigroups and all completely 0-simple semigroups. All epigroups are also eventually regular semigroups. (also known as π-regular semigroups) A cancellative epigroup is a group. Green's relations D and J coincide for any epigroup. If S is an epigroup, any regular subsemigroup of S is also an epigroup. In an epigroup the Nambooripad order (as extended by P.R. Jones) and the natural partial order (of Mitsch) coincide. Examples The semigroup of all square matrices of a given size over a division ring is an epigroup. The multiplicative semigroup of every semisimple Artinian ring is an epigroup. Any algebraic semigroup is an epigroup. Structure By analogy with periodic semigroups, an epigroup S is partitioned in classes given by its idempotents, which act as identities for each subgroup. For each idempotent e of S, the set: is called a unipotency class (whereas for periodic semigroups the usual name is torsion class.) Subsemigroups of an epigroup need not be epigroups, but if they are, then they are called subepigroups. If an epigroup S has a partition in unipotent subepigroups (i.e. each containing a single idempotent), then this partition is unique, and its components are precisely the unipotency classes defined above; such an epigroup is called unipotently partionable. However, not every epigroup has this property. A simple counterexample is the Brandt semigroup with five elements B2 because the unipotency class of its zero element is not a subsemigroup. B2 is actually the quintessential epigroup that is not unipotently partionable. An epigroup is unipotently partionable if and only if it contains no subsemigroup that is an ideal extension of a unipotent epigroup by B2. See also Special classes of semigroups References Semigroup theory Algebraic structures
https://en.wikipedia.org/wiki/G%C3%A1bor%20Pozs%C3%A1r
Gábor Pozsár (born 29 March 1981) is a Hungarian former football forward. Club statistics Updated to games played as of 1 June 2014. External links HLSZ MLSZ Futball-adattar 1981 births 21st-century Hungarian people Footballers from Békéscsaba Living people Hungarian men's footballers Men's association football forwards Békéscsaba 1912 Előre footballers Orosháza FC players Szolnoki MÁV FC footballers Szeged-Csanád Grosics Akadémia footballers Nemzeti Bajnokság I players Nemzeti Bajnokság II players
https://en.wikipedia.org/wiki/Lehrbuch%20der%20Topologie
In mathematics, Lehrbuch der Topologie (German for "textbook of topology") is a book by Herbert Seifert and William Threlfall, first published in 1934 and published in an English translation in 1980. It was one of the earliest textbooks on algebraic topology, and was the standard reference on this topic for many years. Albert W. Tucker wrote a review. Notes References Reprinted by Chelsea Publishing Company 1947 and AMS 2004. History of mathematics Mathematics textbooks Algebraic topology 1934 non-fiction books German books
https://en.wikipedia.org/wiki/William%20Threlfall
William Richard Maximilian Hugo Threlfall (25 June 1888, in Dresden – 4 April 1949, in Oberwolfach) was a British-born German mathematician who worked on algebraic topology. He was a coauthor of the standard textbook Lehrbuch der Topologie. In 1933 he signed the Vow of allegiance of the Professors of the German Universities and High-Schools to Adolf Hitler and the National Socialistic State. Publications Seifert, Threlfall: Lehrbuch der Topologie, Teubner 1934 Seifert, Threlfall: Variationsrechnung im Großen, Teubner 1938 See also Möbius–Kantor graph Schwarz triangle tessellation References Gabriele Dörflinger: William R. M. H. Threlfall 1888 births 1949 deaths 20th-century German mathematicians Topologists
https://en.wikipedia.org/wiki/Tree%20diagram%20%28probability%20theory%29
In probability theory, a tree diagram may be used to represent a probability space. A tree diagram may represent a series of independent events (such as a set of coin flips) or conditional probabilities (such as drawing cards from a deck, without replacing the cards). Each node on the diagram represents an event and is associated with the probability of that event. The root node represents the certain event and therefore has probability 1. Each set of sibling nodes represents an exclusive and exhaustive partition of the parent event. The probability associated with a node is the chance of that event occurring after the parent event occurs. The probability that the series of events leading to a particular node will occur is equal to the product of that node and its parents' probabilities. See also Decision tree Markov chain Notes References Charles Henry Brase, Corrinne Pellillo Brase: Understanding Basic Statistics. Cengage Learning, 2012, , pp. 205–208 (online copy at Google) External links tree diagrams - examples and applications Tree Diagrams Experiment (probability theory)
https://en.wikipedia.org/wiki/Agrawal%27s%20conjecture
In number theory, Agrawal's conjecture, due to Manindra Agrawal in 2002, forms the basis for the cyclotomic AKS test. Agrawal's conjecture states formally: Let and be two coprime positive integers. If then either is prime or Ramifications If Agrawal's conjecture were true, it would decrease the runtime complexity of the AKS primality test from to . Truth or falsehood The conjecture was formulated by Rajat Bhattacharjee and Prashant Pandey in their 2001 thesis. It has been computationally verified for and , and for . However, a heuristic argument by Carl Pomerance and Hendrik W. Lenstra suggests there are infinitely many counterexamples. In particular, the heuristic shows that such counterexamples have asymptotic density greater than for any . Assuming Agrawal's conjecture is false by the above argument, Roman B. Popovych conjectures a modified version may still be true: Let and be two coprime positive integers. If and then either is prime or . Distributed computing Both Agrawal's conjecture and Popovych's conjecture were tested by distributed computing project Primaboinca which ran from 2010 to 2020, based on BOINC. The project found no counterexample, searching in . Notes External links Primaboinca project Conjectures about prime numbers
https://en.wikipedia.org/wiki/Maxim%20Krivonozhkin
Maxim Krivonozhkin (born 18 February 1984) is a Russian professional ice hockey forward currently playing for HC Sibir Novosibirsk of the Kontinental Hockey League. Career statistics External links 1984 births Living people Amur Khabarovsk players Beibarys Atyrau players Buran Voronezh players HC CSK VVS Samara players HC Lada Togliatti players HC Sibir Novosibirsk players HC Yugra players Kristall Saratov players Russian ice hockey forwards Toros Neftekamsk players Traktor Chelyabinsk players Yertis Pavlodar players Sportspeople from Saratov
https://en.wikipedia.org/wiki/Nathan%20Altshiller%20Court
Nathan Altshiller Court (January 22, 1881 – July 20, 1968) was a Polish–American mathematician. He was a geometer and the author of the popular book College Geometry, who spent most of his career at the University of Oklahoma. Biography Nathan A. Court was born Natan Altszyller on 22 January 1881, in Warsaw, Russian Poland, the eldest of nine children. He attended primary and secondary school in Warsaw, but due to anti-Jewish discrimination could not attend university there. In 1907 he moved to Belgium where he attended the University of Liège and the University of Ghent, receiving his D.Sc. in 1911. Immediately afterward he moved to New York City, anglicizing his name to Nathan Altshiller. Though he could not read or write in English when he arrived, within weeks he began lecturing in advanced mathematics at Columbia University, and at the beginning of the next semester he was hired as a mathematics instructor teaching evening classes while doing his graduate work in Mathematics and Astronomy during the day. In 1912 he married Sophie Ravitch, whom he had known in Warsaw. He left New York in 1913, teaching for two years at the University of Washington in Seattle where his son Arnold was born in 1914, and for two years at the University of Colorado. In 1916 he moved to the University of Oklahoma, where he remained for the rest of his career. In 1919, he became a U.S. citizen and changed his last name to Court, keeping Altshiller as a middle name. The first edition of his best known book, College Geometry, a university-level textbook in synthetic geometry, was published in 1925. In 1935 he published the solid geometry textbook Modern Pure Solid Geometry and became a full professor at the University of Oklahoma. He continued teaching there until his retirement in 1951. College Geometry was continually in print without revision for over 25 years, but a revised edition was published in 1952. A collection of his essays, Mathematics in Fun and in Earnest, was published in 1958. Court died of heart attack in Norman, Oklahoma on 20 July 1968. In his recognition, the Nathan A. Court Award was established by the OU Department of Mathematics, given to an outstanding freshman or sophomore math major. Works College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle, 2nd ed., Barnes & Noble, 1952 [1st ed. 1925] Modern Pure Solid Geometry, Macmillan, 1935 Mathematics in Fun and in Earnest, Dial Press, 1958 Court wrote over 100 scholarly papers. He was a frequent contributor to The American Mathematical Monthlys problem section. References 1881 births 1968 deaths Geometers 20th-century American mathematicians Emigrants from Congress Poland to the United States Jewish American academics University of Oklahoma faculty
https://en.wikipedia.org/wiki/New%20Zealand%20men%27s%20national%20football%20team%20records%20and%20statistics
This page details New Zealand men's national football team records and statistics; the most capped players, the players with the most goals and New Zealand's match record by opponent. Individual records Manager records Team records Biggest victory 13–0 vs. , 16 August 1981 Heaviest defeat 0–10 vs. , 11 July 1936 Biggest away victory 10–0 vs. , 4 June 2004 Biggest away defeat 0–7 vs. , 25 June 1995 Biggest victory at the World Cup finals None Heaviest defeat at the World Cup finals 0–4 vs. , 23 June 1982 Biggest victory at the OFC Nations Cup finals 10–0 vs. , 4 June 2004 First defeat to a non-Oceania team 1–2 vs. , 2 July 1927 Most consecutive victories 7, 31 August 1958 vs. – 4 June 1962 vs. 7, 1 October 1978 vs. – 8 October 1979 vs. Most consecutive matches without defeat 11, 25 April 1981 vs. – 7 September 1981 vs. Most consecutive matches without victory 16, 23 July 1927 – 19 September 1951 Most consecutive defeats 16, 23 July 1927 – 19 September 1951 Most consecutive draws 4, 15 June 2010 – 9 October 2010 Most consecutive matches without scoring 5, 28 June 1997 – 7 February 1998 Most consecutive matches without conceding a goal 10, Achieved on two occasions, most recently 3 May 1981 – 7 September 1981 Best / Worst Results Best Worst FIFA Rankings Best Ranking   Worst Ranking   Best Mover   Worst Mover Competition records FIFA World Cup OFC Nations Cup FIFA Confederations Cup Head-to-head record The list shown below shows the national football team of New Zealand's all-time international record against opposing nations. The stats are composed of FIFA World Cup, FIFA Confederations Cup and, OFC Nations Cup, as well as numerous international friendly tournaments and matches. The following tables show New Zealand's all-time international record, correct as of 17 October 2023 vs. Australia. AFC CAF CONCACAF CONMEBOL OFC UEFA Full Confederation record B team results Match results and statistics of the New Zealand national football B team from its first match in 1927 until the match against Wellington Phoenix FC in 2015: Key Key to matches Att. = Match attendance (H) = Home ground (A) = Away ground (N) = Neutral ground Key to record by opponent Pld = Games played W = Games won D = Games drawn L = Games lost GF = Goals for GA = Goals against A-International results Results by year References New Zealand men's national football team National association football team records and statistics
https://en.wikipedia.org/wiki/Saeed%20Al-Harbi
Saeed Al-Harbi is a Saudi Arabian football player who plays as a goalkeeper. Career statistics Club References External links slstat.com Profile 1982 births Living people Saudi Arabian men's footballers Al Shabab FC (Riyadh) players Al-Hazem F.C. players Al-Shoulla FC players Bisha FC players Al-Zulfi FC players Saudi First Division League players Saudi Pro League players Saudi Second Division players Men's association football goalkeepers
https://en.wikipedia.org/wiki/Tom%C3%A1%C5%A1%20Mik%C3%BA%C5%A1
Tomáš Mikúš (born 1 July 1993) is a Slovak professional ice hockey left winger currently playing for HC Nové Zámky of the Slovak Extraliga. Career statistics Regular season and playoffs International External links 1993 births Living people HC Slovan Bratislava players HK 36 Skalica players Slovak ice hockey right wingers Hokki players HC Olomouc players HK Nitra players HC Karlovy Vary players PSG Berani Zlín players HC Nové Zámky players Ice hockey people from Skalica Slovak expatriate ice hockey players in Finland Slovak expatriate ice hockey players in the Czech Republic
https://en.wikipedia.org/wiki/Gerald%20D%27Mello
Gerard Francis D'Mello (born 25 February 1986) is an Indian footballer who plays as a goalkeeper for Sporting Clube de Goa in the I-League. Career statistics Club Statistics accurate as of 11 May 2013 References Indian men's footballers 1986 births Living people I-League players Sporting Clube de Goa players Men's association football goalkeepers Footballers from Goa
https://en.wikipedia.org/wiki/Football%20records%20and%20statistics%20in%20the%20Czech%20Republic
This page details football records in the Czech Republic. Team records Most championships won Overall 11, Sparta Prague (1993–94, 1994–95, 1996–97, 1997–98, 1998–99, 1999–00, 2000–01, 2002–03, 2004–05, 2006–07, 2009–10) Consecutives 5, Sparta Prague (1996–97, 1997–98, 1998–99, 1999–00, 2000–01) Most seasons in Czech First League 27, Slavia Prague 27, Slovan Liberec 27, Sparta Prague Most games won 499, Sparta Prague Most games drawn 227, Banik Ostrava Most games lost 292, Zbrojovka Brno Individual records League Appearances Including appearances in the Czechoslovak era 465, Jaroslav Šilhavý Czech First League (since 1993) Source: 436, Stanislav Vlček 432, Martin Vaniak 432, Rudolf Otepka 426, Pavel Horváth 418, David Lafata League Goalscorers 198, David Lafata Czech First League (since 1993) Source: 198, David Lafata 134, Horst Siegl 125, Libor Došek 94, Milan Škoda 94, Stanislav Vlček 92, Luděk Zelenka Attendance records Top 10 Highest Attendances The top ten highest league attendances have all been at Stadion Za Lužánkami in Brno. Total Titles Won References External links Official Gambrinus liga website Records Czech Republic
https://en.wikipedia.org/wiki/Frank%20Plastria
Frank A. A. Plastria (born 30 October 1948 in Sint-Agatha-Berchem, Belgium) is a Belgian operations researcher, a professor in the department of mathematics, operational research, statistics and information systems for management at Vrije Universiteit Brussel, known for his work on facility location. His work has been published in journals such as the European Journal of Operational Research, Discrete Applied Mathematics and Mathematical Programming. Plastria earned his Ph.D. in 1983 from the Vrije Universiteit Brussel. From its founding in 2002 until 2009 he was editor-in-chief of 4OR: A Quarterly Journal of Operations Research, and he is the editor-in-chief of Studies in Locational Analysis. In 2002–2003 he was president of SOGESCI-B.V.W.B. (ORBEL), the Belgian Operations Research society. References External links Home page 1948 births Living people Academic staff of Vrije Universiteit Brussel Belgian operations researchers
https://en.wikipedia.org/wiki/Thomas%20Lauth
Thomas Lauth (19 August 1758, Strasbourg – 16 September 1826) was a French anatomist. He was the father of anatomist Ernest Alexandre Lauth (1803–1837). Background He studied philosophy, mathematics, science and medicine at the University of Strasbourg, receiving his doctorate in 1781. After graduation, he continued his medical studies in Paris with Pierre-Joseph Desault (1738-1795), and in London with John Hunter (1728-1793). Following his return to Strasbourg he worked as an obstetrical adjunct. In 1785 he was appointed a full professor of anatomy and surgery in Strasbourg. In 1794, with the creation of the Ecole de Santé, his post became the chair of anatomy and physiology, and in 1808 it was renamed as the chair of normal and pathological anatomy. Anatomical eponyms "Lauth's canal": Also known as the "sinus venosus sclerae". "Lauth's ligament": Also known as the transverse ligament of the atlas. Written works Dissertatio inauguralis botanica de Acere, 1781 - monograph on the genus Acer. Scriptorum Latinorum de aneurysmatibus collectio, 1785 Nosologia chirurgica, 1788 - Surgical nosology. Elemens de myologie et de syndesmologie, 1798 - Elements of myology and syndesmology. Histoire de l'anatomie, 1815 - History of anatomy. De l'esprit de l'instruction publique, 1816. References French anatomists 1758 births 1826 deaths Physicians from Strasbourg Academic staff of the University of Strasbourg University of Strasbourg alumni
https://en.wikipedia.org/wiki/Lord%27s%20paradox
In statistics, Lord's paradox raises the issue of when it is appropriate to control for baseline status. In three papers, Frederic M. Lord gave examples when statisticians could reach different conclusions depending on whether they adjust for pre-existing differences. Holland & Rubin (1983) use these examples to illustrate how there may be multiple valid descriptive comparisons in the data, but causal conclusions require an underlying (untestable) causal model. Pearl used these examples to illustrate how graphical causal models resolve the issue of when control for baseline status is appropriate. Lord's formulation The most famous formulation of Lord's paradox comes from his 1967 paper: “A large university is interested in investigating the effects on the students of the diet provided in the university dining halls and any sex differences in these effects. Various types of data are gathered. In particular, the weight of each student at the time of his arrival in September and his weight the following June are recorded.” (Lord 1967, p. 304) In both September and June, the overall distribution of male weights is the same, although individuals' weights have changed, and likewise for the distribution of female weights. Lord imagines two statisticians who use different common statistical methods but reach opposite conclusions. One statistician does not adjust for initial weight, instead using t-test and comparing gain scores (individuals' average final weight − average initial weight) as the outcome. The first statistician claims no significant difference between genders: "[A]s far as these data are concerned, there is no evidence of any interesting effect of diet (or of anything else) on student weights. In particular, there is no evidence of any differential effect on the two sexes, since neither group shows any systematic change." (pg. 305) Visually, the first statistician sees that neither group mean ('A' and 'B') has changed, and concludes that the new diet had no causal impact. The second statistician adjusts for initial weight, using analysis of covariance (ANCOVA), and compares (adjusted) final weights as the outcome. He finds a significant difference between the two dining halls. Visually, the second statistician fits a regression model (green dotted lines), finds that the intercept differs for boys vs girls, and concludes that the new diet had a larger impact for males. Lord concluded: "there simply is no logical or statistical procedure that can be counted on to make proper allowance for uncontrolled preexisting differences between groups." Responses There have been many attempts and interpretations of the paradox, along with its relationship to other statistical paradoxes. While initially framed as a paradox, later authors have used the example to clarify the importance of untestable assumptions in causal inference. Importance of modeling assumptions Bock (1975) Bock responded to the paradox by positing that both stat
https://en.wikipedia.org/wiki/James%20Eells
James Eells (October 25, 1926 – February 14, 2007) was an American mathematician, who specialized in mathematical analysis. Biography Eells studied mathematics at Bowdoin College in Maine and earned his undergraduate degree in 1947. After graduation he spent one year teaching mathematics at Robert College in Istanbul and starting in 1948 was for two years an instructor at Amherst College in Amherst, Massachusetts. Next he undertook graduate study at Harvard University, where in 1954 he received his Ph.D under Hassler Whitney with thesis Geometric Aspects of Integration Theory. In the academic year 1955–1956 he was at the Institute for Advanced Study (and subsequently in 1962–1963, 1972–1973, 1977, and 1982). He taught at Columbia University for several years. In 1964 he became a full professor at Cornell University. In 1963 and in 1966–1967 he was at the University of Cambridge, and after a visit to the new mathematics department developed by Erik Christopher Zeeman at the University of Warwick Eells became a professor of mathematical analysis there in 1969. Eells organized many of the University of Warwick Symposia in mathematics. In 1986 he became the first director of the mathematics section of the Abdus Salam International Centre for Theoretical Physics in Trieste; for six years he served as director in addition to his appointment at the University of Warwick. In 1992 he retired and lived in Cambridge. Eells did research on global analysis, especially, harmonic maps on Riemannian manifolds, which are important in the theory of minimal surfaces and theoretical physics. His doctoral students included John C. Wood. In 1970 he was an invited speaker at the International Mathematical Congress in Nice (On Fredholm manifolds with K. D. Elworthy). He was co-editor of the collected works of Hassler Whitney. Eells's doctoral students include luc LEMAIRE Peter Štefan (1941–1978), Giorgio Valli (1960–1999) and . Eells was married since 1950 and had a son and three daughters. Publications with J. H. Sampson: Singularities of smooth maps, London, Nelson 1967 with Luc Lemaire: ; re-published with a follow-up report in the books Harmonic Maps, 1992, and Two Reports on Harmonic Maps, 1994, by publisher World Scientific with Luc Lemaire: Selected topics in harmonic maps, AMS 1983 with Andrea Ratto: Harmonic maps and minimal immersions with symmetries – methods of ordinary differential equations applied to elliptic variational problems, Princeton University Press 1993 with B. Fuglede: Harmonic maps between Riemannian polyhedra, Cambridge University Press 2001 See also Eells–Kuiper manifold References External links Toledo, Domingo. James Eells 1926–2007. Notices Amer. Math. Soc. 55 (2008), no. 6, 704–706. Chiang, Yuan-Jen; Ratto, Andrea. Paying tribute to James Eells and Joseph H, Sampson: in commemoration of the fiftieth anniversary of their pioneering work on harmonic maps. Notices Amer. Math. Soc. 62 (2015), no. 4, 388–393. 20th-centu
https://en.wikipedia.org/wiki/Thorsten%20Schulz
Thorsten Schulz (born 5 December 1984) is a German footballer who plays as a right-back. Career statistics References External links 1984 births Living people Men's association football fullbacks German men's footballers FC Energie Cottbus II players SpVgg Unterhaching II players SpVgg Unterhaching players VfR Aalen players Dynamo Dresden players FC Erzgebirge Aue players 3. Liga players People from Groß-Gerau Footballers from Darmstadt (region)
https://en.wikipedia.org/wiki/Mathematical%20physiology
Mathematical physiology is an interdisciplinary science. Primarily, it investigates ways in which mathematics may be used to give insight into physiological questions. In turn, it also describes how physiological questions can lead to new mathematical problems. The field may be broadly grouped into two physiological application areas: cell physiology – including mathematical treatments of biochemical reactions, ionic flow and regulation of function – and systems physiology – including electrocardiology, circulation and digestion. References Mathematical and theoretical biology Physiology Systems biology
https://en.wikipedia.org/wiki/1974%E2%80%9375%20Cambridge%20United%20F.C.%20season
The 1974–75 season was Cambridge United's fifth season in the Football League. Final league table Results Football League Fourth Division FA Cup League Cup Squad statistics References Cambridge 1974–75 at statto.com Player information sourced from The English National Football Archive Cambridge United F.C. seasons Cambridge United
https://en.wikipedia.org/wiki/British%20Mathematical%20Olympiad%20Subtrust
The British Mathematical Olympiad Subtrust (BMOS) is a section of the United Kingdom Mathematics Trust which currently runs the British Mathematical Olympiad as well as the UK Mathematical Olympiad for Girls, several training camps throughout the year such as a winter camp in Hungary, an Easter camp at Trinity College, Cambridge, and other training and selection of the International Mathematical Olympiad team. Since 1999, it also organizes the UK National Mathematics Summer Schools. It was established alongside the British Mathematical Olympiad Committee (BMOC) in 1991 with the support of the Edinburgh Mathematical Society, Institute of Mathematics and its Applications, the London Mathematical Society, and the Mathematical Association, each nominated two members. The BMOS replaced some of the Mathematical Association's activities. History In 1996, the United Kingdom Mathematics Trust (UKMT) was set up to manage competitions of this nature, though the BMOC remained in charge of the senior olympiads. Problems group The 'problems group' is a subsection of the BMOS which is responsible for supplying new and interesting problems for use domestic competitions and for submission to the IMO each year. References Mathematics organizations Mathematics education in the United Kingdom
https://en.wikipedia.org/wiki/Standard%20monomial%20theory
In algebraic geometry, standard monomial theory describes the sections of a line bundle over a generalized flag variety or Schubert variety of a reductive algebraic group by giving an explicit basis of elements called standard monomials. Many of the results have been extended to Kac–Moody algebras and their groups. There are monographs on standard monomial theory by and and survey articles by and One of important open problems is to give a completely geometric construction of the theory. History introduced monomials associated to standard Young tableaux. (see also ) used Young's monomials, which he called standard power products, named after standard tableaux, to give a basis for the homogeneous coordinate rings of complex Grassmannians. initiated a program, called standard monomial theory, to extend Hodge's work to varieties G/P, for P any parabolic subgroup of any reductive algebraic group in any characteristic, by giving explicit bases using standard monomials for sections of line bundles over these varieties. The case of Grassmannians studied by Hodge corresponds to the case when G is a special linear group in characteristic 0 and P is a maximal parabolic subgroup. Seshadri was soon joined in this effort by V. Lakshmibai and Chitikila Musili. They worked out standard monomial theory first for minuscule representations of G and then for groups G of classical type, and formulated several conjectures describing it for more general cases. proved their conjectures using the Littelmann path model, in particular giving a uniform description of standard monomials for all reductive groups. and and give detailed descriptions of the early development of standard monomial theory. Applications Since the sections of line bundles over generalized flag varieties tend to form irreducible representations of the corresponding algebraic groups, having an explicit basis of standard monomials allows one to give character formulas for these representations. Similarly one gets character formulas for Demazure modules. The explicit bases given by standard monomial theory are closely related to crystal bases and Littelmann path models of representations. Standard monomial theory allows one to describe the singularities of Schubert varieties, and in particular sometimes proves that Schubert varieties are normal or Cohen–Macaulay. . Standard monomial theory can be used to prove Demazure's conjecture. Standard monomial theory proves the Kempf vanishing theorem and other vanishing theorems for the higher cohomology of effective line bundles over Schubert varieties. Standard monomial theory gives explicit bases for some rings of invariants in invariant theory. Standard monomial theory gives generalizations of the Littlewood–Richardson rule about decompositions of tensor products of representations to all reductive algebraic groups. Standard monomial theory can be used to prove the existence of good filtrations on some representations of reductive alge
https://en.wikipedia.org/wiki/International%20Astrostatistics%20Association
The International Astrostatistics Association (IAA) is a non-profit professional organization for astrostatisticians. Astrostatistics as a discipline is composed of astrophysicists, statisticians, and those in computer information sciences who have an interest in the statistical analysis and data mining of astronomical data. The Association was founded as an independent organization in August 2012 by the Astrostatistics Committee and Network of the International Statistical Institute (ISI). The foremost objective of the IAA is to foster collaboration between statisticians and astrophysicists. The Association is managed by the IAA Council, composed of representatives from the ISI Astrostatistics Committee and the Astrostatistics Working Groups of the International Astronomical Union (IAU) and American Astronomical Society (AAS). The IAA has its convention in association with the biannual ISI World Statistics Congress. In April 2014, an independent group was created with the support of the IAA, the Cosmostatistics Initiative (COIN), chaired by Dr. Rafael S. de Souza. COIN is a worldwide endeavor aimed to create an interdisciplinary community around data-driven problems in Astronomy. It was designed to promote innovation in all aspects of academic scientific research. IAA Presidents and terms 2012–2017 Joseph Hilbe (USA) 2018–present Jogesh Babu (USA) See also List of astronomical societies References External links IAA homepage IAA Overview ISI committees Astrostatistics and Astroinformatics Portal : IAA home page COIN : Cosmostatistics Initiative Statistical societies Astronomy organizations Scientific organizations established in 2012
https://en.wikipedia.org/wiki/William%20Stone%20Weedon
William Stone Weedon (July 5, 1908 – May 13, 1984), was a scholar, university professor (philosophy, mathematics, logic, linguistic analysis), and U.S. Navy Officer. Early life and education Weedon was born in 1908 in Wilmington, Delaware, the only son of William Stone Weedon Sr. and Mary C. Weedon. His father, a chemist, died when his son William Jr. was only four. His young son William showed much promise in the arts and was able to sketch quite deftly what his eyes observed before the age of 10. He held a Ph.D. from University of Virginia as well as an M.S. from Harvard and Wesleyan Universities. At Harvard he studied under Alfred North Whitehead as a Special Scholar. University teaching Mr. Weedon taught many subjects at The University of Virginia and Wesleyan. Later on he would join the faculty at UVA and teach disciplines ranging from Mathematics to Philosophy. He was the recipient of the Algernon Sydney Award, the university's Raven Award, and the Thomas Jefferson Award. In 1963 Dr. Weedon assumed the professorship of 'University Professor' at UVA - an honor which enabled him to teach a broad range of disciplines throughout the university. Dr Weedon was a vocal proponent of developing seminars in the liberal arts at UVA, and he especially was interested in the largely unexplored connections between Platonism and Asian Philosophies. Professor Weedon taught some classes using the R. L. Moore method. He would give a list of axioms for some abstract operation and challenge students to prove something with no hints given. This technique sharpened one's reasoning skills. ''' Military career Weedon was an officer in the United States Navy, and so his scholarly life was often interrupted by war service; he left his posts at universities to serve his country during World War II as well as the Korean War. In 1942 he received the rank of lieutenant, the rank of lieutenant commander in 1948, and eventually achieving the rank of captain in 1959. He earned The Bronze Star in World War 2 and was said to have saved his ship from bombing by intercepting Japanese Coded messages. He had the unusual ability as a westerner at that time of being able to understand and speak a variety of Asian languages. This led him to a team that was involved in cryptanalysis during World War II for the purposes of breaking enemy codes. During the Korean War, he participated in negotiations that would bring an end to the active conflict. His service to the United States would continue as a consultant on the far east on behalf of the Department of Defense for some years afterwards. Personal life William Weedon married Elizabeth Dupont Bayard on June 25, 1934. They had four children and made their home in Charlottesville Virginia. In 1939, after their eldest daughter Ellen died unexpectedly at the age of 3, they created The Ellen Bayard Weedon Foundation in support of the Asian Arts. The Weedon Foundation is Non-Profit and regularly makes charit
https://en.wikipedia.org/wiki/Wellington%20Phoenix%20FC%20results%20by%20opposition%20%28A-M%29
This page details the fixtures, results and statistics between the Wellington Phoenix and their A-League opposition (from A to M) since the Phoenix joined the competition in the 2007–08 season. For results and statistics for opposition from N to Z, see Wellington Phoenix FC results by opposition (N-Z). All-time A-League results Includes finals results; does not include pre-season matches or FFA Cup matches. Overall record Home/away record All-time opposition goal scorers Goals scored against the Wellington Phoenix.Excludes pre-season matches. Adelaide United Statistics Results summary Leading goal scorers Discipline Matches Brisbane Roar Statistics Results summary Leading goal scorers Discipline Matches Central Coast Mariners Statistics Results summary Leading goal scorers Discipline Matches Gold Coast United Statistics Results summary Leading goal scorers Discipline Matches Melbourne City At the conclusion of the 2013/14 season, Melbourne Heart was re-branded to Melbourne City and changed their colours from red and white to blue and white. Statistics Results summary Leading goal scorers Discipline Matches Melbourne Victory Statistics Results summary Leading goal scorers Discipline Matches References External links results
https://en.wikipedia.org/wiki/Nanny%20Wermuth
Nanny Wermuth (born 4 December 1943) is the Professor emerita of Statistics, Chalmers University of Technology/University of Gothenburg. Her research interests are Multivariate statistical models and their properties, especially graphical Markov models, as well as their applications in the life sciences and in the natural sciences. Academic career Education 1967 First degree in Economics (Diplom-Volkswirtin), University of Munich 1972 Degree in Statistics (Doctor of Philosophy), Harvard University 1977 Degree in Medical Statistics (Professor), University of Mainz Professional positions 1972–1978 Research Assistant in Statistics; University of Dortmund, University of Mainz since 1978 Professor of Statistics and of Methods in Psychology, University of Mainz 1997–2000 Head of Research and Development, Center of Survey Research, Mannheim since 2003 Professor of Statistics, Department of Mathematical Sciences at Chalmers University of Technology and University of Gothenburg Selected services to the profession 1993–2001 Coordinating member of the European Science Foundation network HSSS 1993–2003 Editorial Advisor for the Springer Series of Statistics 1995–1996 President, German Region of the International Biometric Society 2000–2001 President, International Biometric Society 2001–2004 Chair of the Life Science Committee of the International Statistical Institute 2008–2009 President, Institute of Mathematical Statistics 2007–2010 Associate Editor of Bernoulli Selected recognitions 1968–1972 Stipends of the Fulbright Commission, of the International Peace Scholarship Fund and of Harvard University 1984–1985 Fulbright Scholar, Department of Statistics, Princeton University 1992 Max Planck-Research Prize, jointly with Sir David Cox, Oxford 2001 Short term Research Fellowship, Australian National University 2001–2002 Invited Research Fellow at Harvard’s Radcliffe Institute for Advanced Study 2011–2012 Senior Scientist Research Award, International Agency for Research on Cancer Professional affiliations She was elected as member of the International Statistical Institute (1982) and of the German Academy of Sciences (2002); as fellow of the American Statistical Association (1989) and of the Institute of Mathematical Statistics (2001). Personal life She has four sons with Dr. Dieter Wermuth - Jochen (1969) Martin (1974), Peter (1976) and Ulli (1981) References External links Academic website at Chalmers/University of Gothenburg entry at Mathematics Genealogy Project 1943 births Living people Presidents of the Institute of Mathematical Statistics Swedish statisticians Harvard Graduate School of Arts and Sciences alumni Elected Members of the International Statistical Institute Fellows of the American Statistical Association Fellows of the Institute of Mathematical Statistics Ludwig Maximilian University of Munich Johannes Gutenberg University Mainz alumni Women statisticians Mathematical statisticians
https://en.wikipedia.org/wiki/Georges%20Cuisenaire
Georges Cuisenaire (1891–1975), also known as Emile-Georges Cuisenaire, was a Belgian teacher who invented Cuisenaire rods, a mathematics teaching aid. Life Cuisenaire graduated from the Royal Conservatory of Music at Mons, where he was awarded first prize for violin. He was a primary school teacher at the Ville-Haute school in Thuin from 26 April 1912. In 1948 he became the founder and principal of the Industrial School of Thuin. Cuisenaire rods In 1945, following many years of research and experimentation, Cuisenaire created a game consisting of coloured cardboard strips of various lengths that he used to teach mathematics to young children. In 1951 the first edition of Numbers and Colours, the booklet explaining the method, appeared in Belgium. The "Cuisenaire Rod" method revolutionised the teaching of mathematics by being recognised by pedagogues and psychologists the world over as an instrument of exceptional efficacity. His method was adopted by thousands of teachers in over sixty countries. Honours Cuisenaire was made an officer of the Order of Leopold 11 January 1968. In 1973 UNESCO recommended the use of Cuisenaire learning aids and suggested the reform of mathematics education programmes based on his method. References External links The Cuisenaire Company: registered UK trademark holder, with background to Georges Cuisenaire 1891 births 1976 deaths 20th-century Belgian inventors 20th-century Belgian educators Mathematics educators
https://en.wikipedia.org/wiki/Linearised%20polynomial
In mathematics, a linearised polynomial (or q-polynomial) is a polynomial for which the exponents of all the constituent monomials are powers of q and the coefficients come from some extension field of the finite field of order q. We write a typical example as where each is in for some fixed positive integer . This special class of polynomials is important from both a theoretical and an applications viewpoint. The highly structured nature of their roots makes these roots easy to determine. Properties The map is a linear map over any field containing Fq. The set of roots of L is an Fq-vector space and is closed under the q-Frobenius map. Conversely, if U is any Fq-linear subspace of some finite field containing Fq, then the polynomial that vanishes exactly on U is a linearised polynomial. The set of linearised polynomials over a given field is closed under addition and composition of polynomials. If L is a nonzero linearised polynomial over with all of its roots lying in the field an extension field of , then each root of L has the same multiplicity, which is either 1, or a positive power of q. Symbolic multiplication In general, the product of two linearised polynomials will not be a linearized polynomial, but since the composition of two linearised polynomials results in a linearised polynomial, composition may be used as a replacement for multiplication and, for this reason, composition is often called symbolic multiplication in this setting. Notationally, if L1(x) and L2(x) are linearised polynomials we define when this point of view is being taken. Associated polynomials The polynomials and are q-associates (note: the exponents "qi" of L(x) have been replaced by "i" in l(x)). More specifically, l(x) is called the conventional q-associate of L(x), and L(x) is the linearised q-associate of l(x). q-polynomials over Fq Linearised polynomials with coefficients in Fq have additional properties which make it possible to define symbolic division, symbolic reducibility and symbolic factorization. Two important examples of this type of linearised polynomial are the Frobenius automorphism and the trace function In this special case it can be shown that, as an operation, symbolic multiplication is commutative, associative and distributes over ordinary addition. Also, in this special case, we can define the operation of symbolic division. If L(x) and L1(x) are linearised polynomials over Fq, we say that L1(x) symbolically divides L(x) if there exists a linearised polynomial L2(x) over Fq for which: If L1(x) and L2(x) are linearised polynomials over Fq with conventional q-associates l1(x) and l2(x) respectively, then L1(x) symbolically divides L2(x) if and only if l1(x) divides l2(x). Furthermore, L1(x) divides L2(x) in the ordinary sense in this case. A linearised polynomial L(x) over Fq of degree > 1 is symbolically irreducible over Fq if the only symbolic decompositions with Li over Fq are those for which one of the facto
https://en.wikipedia.org/wiki/Margaret%20Meyer
Margaret Theodora Meyer (September 1862 – 27 January 1924), also known as Maud Meyer was a British mathematician. She was one of the first directors of studies in mathematics, and one of the earliest members of the London Mathematical Society. In 1916, she was one of the first women to be elected a fellow of the Royal Astronomical Society. Biography Meyer was born in Strabane, Tyrone, Ireland, to a Presbyterian minister, Theodore Jonas Meyer, and his wife Jane Ann. She had an older brother, Sir William Stevenson Meyer, who served as first high commissioner for India. Meyer spent much of her childhood in Italy. She attended the North London Collegiate School for Girls, then enrolled at Girton College, Cambridge in 1879, graduating 15th wrangler in mathematics 1882. In 1907, she was awarded an ad eundem MA by Trinity College Dublin. She taught at Notting Hill High School, in London, from 1882 to 1888, and then became a resident lecturer in mathematics at Girton College, where she remained for 30 years. During World War I, Meyer undertook calculational work for the British War Office in her spare time. In 1918 she resigned from work at the college and worked for the British Air Ministry, which related to aircraft design and construction. Meyer had an interest in astronomy, as part of her degree concerned mathematical astronomy. She carried out much unpublished work on the subject. In 1916, she was one of the first women to be elected to the Royal Astronomical Society along with A. Grace Cook, Fiammetta Wilson, Ella Church, Mary Blagg and Irene Elizabeth Toye Warner. Other activities Meyer carved, and supervised students in the carving, of the oak paneling around the chancel of the college chapel at Girton College. She also had a passion for mountain climbing, and was a member and later president of the Ladies' Alpine Club. Death Meyer died, aged 61, in a collision with a bus while cycling in 1924. In her will, she bequeathed £2000 to Girton College for the benefit of women mathematics students, an additional £1000, and a collection of mathematics books. References 1862 births 1924 deaths Astronomers from Northern Ireland Women astronomers 19th-century British mathematicians Irish women scientists Alumni of Girton College, Cambridge Fellows of the Royal Astronomical Society Presidents of the Ladies' Alpine Club Steamboat ladies People from Strabane Scientists from County Tyrone 19th-century Irish mathematicians
https://en.wikipedia.org/wiki/Zden%C4%9Bk%20Frol%C3%ADk
Zdeněk Frolík (March 10, 1933 – May 3, 1989) was a Czech mathematician. His research interests included topology and functional analysis. In particular, his work concerned covering properties of topological spaces, ultrafilters, homogeneity, measures, uniform spaces. He was one of the founders of modern descriptive theory of sets and spaces. Two classes of topological spaces are given Frolík's name: the class P of all spaces such that is pseudocompact for every pseudocompact space , and the class C of all spaces such that is countably compact for every countably compact space . Frolík prepared his Ph.D. thesis under the supervision of Miroslav Katetov and Eduard Čech. Selected publications Generalizations of compact and Lindelöf spaces - Czechoslovak Math. J., 9 (1959), pp. 172–217 (in Russian, English summary) The topological product of countably compact spaces - Czechoslovak Math. J., 10 (1960), pp. 329–338 The topological product of two pseudocompact spaces - Czechoslovak Math. J., 10 (1960), pp. 339–349 Generalizations of the Gδ-property of complete metric spaces - Czechoslovak Math. J., 10 (1960), pp. 359–379 On the topological product of paracompact spaces - Bull. Acad. Polon., 8 (1960), pp. 747–750 Locally complete topological spaces - Dokl. Akad. Nauk SSSR, 137 (1961), pp. 790–792 (in Russian) Applications of complete families of continuous functions to the theory of Q-spaces - Czechoslovak Math. J., 11 (1961), pp. 115–133 Invariance of Gδ-spaces under mappings - Czechoslovak Math. J., 11 (1961), pp. 258–260 On almost real compact spaces - Bull. Acad. Polon., 9 (1961), pp. 247–250 On two problems of W.W. Comfort - Comment. Math. Univ. Carolin., 7 (1966), pp. 139–144 Non-homogeneity of βP- P - Comment. Math. Univ. Carolin., 7 (1966), pp. 705–710 Sums of ultrafilters - Bull. Amer. Math. Soc., 73 (1967), pp. 87–91 Homogeneity problems for extremally disconnected spaces - Comment. Math. Univ. Carolin., 8 (1967), pp. 757–763 Baire sets that are Borelian subspaces - Proc. Roy. Soc. A, 299 (1967), pp. 287–290 On the Suslin-graph theorem - Comment Math. Univ. Carolin., 9 (1968), pp. 243–249 A survey of separable descriptive theory of sets and spaces - Czechoslovak Math. J., 20 (1970), pp. 406–467 A measurable map with analytic domain and metrizable range is quotient - Bull. Amer. Math. Soc., 76 (1970), pp. 1112–1117 Luzin sets are additive - Comment Math. Univ. Carolin., 21 (1980), pp. 527–534 Refinements of perfect maps onto metrizable spaces and an application to Čech-analytic spaces - Topology Appl., 33 (1989), pp. 77–84 Decomposability of completely Suslin additive families - Proc. Amer. Math. Soc., 82 (1981), pp. 359–365 Applications of Luzinian separation principles (non-separable case) - Fund. Math., 117 (1983), pp. 165–185 Analytic and Luzin spaces (non-separable case) - Topology Appl., 19 (1985), pp. 129–156 See also Wijsman convergence References 1933 births 1989 deaths Charles University alumni 20th-century Czech mathematici
https://en.wikipedia.org/wiki/Walter%20Borho
Walter Borho (born 17 December 1945, in Hamburg) is a German mathematician, who works on algebra and number theory. Borho received his PhD in 1973 from the University of Hamburg under the direction of Ernst Witt with thesis Wesentliche ganze Erweiterungen kommutativer Ringe. He is a professor at the University of Wuppertal. Borho does research on representation theory, Lie algebras, ring theory and also on number theory (amicable numbers) and tilings. In 1986 he was an invited speaker at the International Congress of Mathematicians in Berkeley (Nilpotent orbits, primitive ideals and characteristic classes – a survey). Publications Borho, Don Zagier et al.: Lebendige Zahlen, Birkhäuser 1981 (containing Borho's Befreundete Zahlen [Amicable Numbers]) with Peter Gabriel, Rudolf Rentschler: Primideale in Einhüllenden auflösbarer Lie-Algebren, Springer Verlag, Lecture Notes in Mathematics, vol. 357, 1973 with Klaus Bongartz, D. Mertens, A. Steins: Farbige Parkette. Mathematische Theorie und Ausführung auf dem Computer [Colored tilings: mathematical theory and computer implementation], Birkhäuser 1988 with Jean-Luc Brylinski, Robert MacPherson: Nilpotent orbits, primitive ideals and characteristic classes. A geometric perspective in ring theory, Birkhäuser 1989 with Karsten Blankenagel, Axel vom Stein: References External links 20th-century German mathematicians 21st-century German mathematicians 1945 births Living people University of Hamburg alumni Academic staff of the University of Wuppertal
https://en.wikipedia.org/wiki/J%C3%A9r%C3%B4me%20Franel
Jérôme Franel (1859–1939) was a Swiss mathematician who specialised in analytic number theory. He is mainly known through a 1924 paper, in which he establishes the equivalence of the Riemann hypothesis to a statement on the size of the discrepancy in the Farey sequences, and which is directly followed (in the same journal) by a development on the same subject by Edmund Landau. Jérôme Franel was a citizen ("bourgeois") of Provence (Vaud, Switzerland). He was born on 29 November 1859 in Travers (Neuchâtel, Suisse) and died in Zürich on 21 November 1939. George Pólya said that he was an especially attractive kind of person and a very good teacher, but that, since he spent most of his time teaching, and reading French literature (for which he had a passion), he had no time left for research. After his retirement he worked on the Riemann hypothesis. Childhood and schools Jerôme Franel spent his first years with his 12 brothers and sisters in Travers. He graduated with a sciences highschool diploma from the "Ecole industrielle" in Lausanne. He then studied at the Politechnikum in Zürich, and in Berlin where he attended courses given by Weierstrass, Kronecker and Kummer, and finally in Paris where he attended courses by Hermite. On 15 September 1883 he was awarded a science bachelor's degree ("licence") from the Paris Academy. Career Franel taught then for two years at the "Ecole industrielle" in Lausanne. On 1 April 1886, then only 26 years old, he was appointed to the Chair of Mathematics in the French language at the Politechnikum in Zürich by the Federal Council of Switzerland. In 1896 he was a member of the organizing committee of the first International Congress of Mathematicians, which took place in Zürich in 1897. He delivered the introductory lecture to the congress, written by Henri Poincaré, but who was then unwell. In 1905 the University of Zürich awarded him an honorary doctorate, and the city of Zürich awarded him honorary citizenship ("Bourgeoisie"). Under his presidency (1905-1909) the school was entirely restructured, and it was probably through his insistence (in particular, through a 1907 speech) that the Polytechnikum finally obtained (in 1908) the right to award a doctoral degree like the University did. The first doctorates were awarded in 1909. He retired in 1929. References and notes Jérôme Franel's necrology, by Louis Kollros, in: Verhandlungen der Schweizerischen Naturforschenden Gesellschaft 120 (1940), 439-444. Read french document online External links 19th-century Swiss mathematicians 20th-century Swiss mathematicians Academic staff of ETH Zurich ETH Zurich alumni Humboldt University of Berlin alumni Number theorists 1859 births 1939 deaths
https://en.wikipedia.org/wiki/Point%E2%80%93line%E2%80%93plane%20postulate
In geometry, the point–line–plane postulate is a collection of assumptions (axioms) that can be used in a set of postulates for Euclidean geometry in two (plane geometry), three (solid geometry) or more dimensions. Assumptions The following are the assumptions of the point-line-plane postulate: Unique line assumption. There is exactly one line passing through two distinct points. Number line assumption. Every line is a set of points which can be put into a one-to-one correspondence with the real numbers. Any point can correspond with 0 (zero) and any other point can correspond with 1 (one). Dimension assumption. Given a line in a plane, there exists at least one point in the plane that is not on the line. Given a plane in space, there exists at least one point in space that is not in the plane. Flat plane assumption. If two points lie in a plane, the line containing them lies in the plane. Unique plane assumption. Through three non-collinear points, there is exactly one plane. Intersecting planes assumption. If two different planes have a point in common, then their intersection is a line. The first three assumptions of the postulate, as given above, are used in the axiomatic formulation of the Euclidean plane in the secondary school geometry curriculum of the University of Chicago School Mathematics Project (UCSMP). History The axiomatic foundation of Euclidean geometry can be dated back to the books known as Euclid's Elements (circa 300 B.C.). These five initial axioms (called postulates by the ancient Greeks) are not sufficient to establish Euclidean geometry. Many mathematicians have produced complete sets of axioms which do establish Euclidean geometry. One of the most notable of these is due to Hilbert who created a system in the same style as Euclid. Unfortunately, Hilbert's system requires 21 axioms. Other systems have used fewer (but different) axioms. The most appealing of these, from the viewpoint of having the fewest axioms, is due to G.D. Birkhoff (1932) which has only four axioms. These four are: the Unique line assumption (which was called the Point-Line Postulate by Birkhoff), the Number line assumption, the Protractor postulate (to permit the measurement of angles) and an axiom that is equivalent to Playfair's axiom (or the parallel postulate). For pedagogical reasons, a short list of axioms is not desirable and starting with the New math curricula of the 1960s, the number of axioms found in high school level textbooks has increased to levels that even exceed Hilbert's system. References External links The Point-Line-Plane Postulate as described in the Oracle Education Foundation's "ThinkQuest" online description of basic geometry postulates and theorems. The Point-Line-Plane Postulate as described in Professor Calkins' (Andrews University) online listing of basic geometry concepts. Foundations of geometry
https://en.wikipedia.org/wiki/Peter%20Littelmann
Peter Littelmann (born 10 December 1957) is a German mathematician at the University of Cologne working on algebraic groups and representation theory, who introduced the Littelmann path model and used it to solve several conjectures in standard monomial theory and other areas. References Home page External links Pictures from the Oberwolfach photo collection 20th-century German mathematicians Living people 21st-century German mathematicians 1957 births
https://en.wikipedia.org/wiki/Houses%20for%20Visiting%20Mathematicians
The Houses for Visiting Mathematicians (also known as the Mathematics Research Centre houses) are a set of five houses and two flats, built for academics attending mathematical conferences at the University of Warwick. The buildings are Grade II* listed and were built between 1968 and 1969 to the design of architect Bill Howell and were opened in June of that year by then Vice-Chancellor Jack Butterworth, Sir Christopher Zeeman and Bill Howell. Their construction was supported by a £50,000 grant from the Nuffield Foundation. In 1970, they received the RIBA Architecture Award. The houses comprise a combined living room/kitchen and large study bedroom on the ground floor, and smaller study bedrooms and a bathroom on the first floor. The curved walls of the downstairs study are lined with blackboards, built to the specification that they should be high enough for the mathematician to work but also "low enough for small children to use the bottom bit." See also Grade II* listed buildings in Coventry References Buildings and structures completed in 1969 Buildings and structures in Coventry Grade II* listed buildings in the West Midlands (county) Mathematics conferences University of Warwick
https://en.wikipedia.org/wiki/Joseph%20Barbato
Joseph Barbato (born 11 August 1994) is a French professional footballer who plays as a forward for Furiani. Career In January 2019, he returned to Furiani. Club statistics Notes References External links 1994 births Living people French men's footballers Men's association football forwards Ligue 1 players Ligue 2 players Championnat National players SC Bastia players US Colomiers Football players Borgo FC players AS Furiani-Agliani players FC Borgo players ÉF Bastia players Corsica men's international footballers Footballers from Corsica
https://en.wikipedia.org/wiki/Rosalind%20Tanner
Rosalind Cecilia Hildegard Tanner (née Young) (5 February 1900 – 24 November 1992) was a mathematician and historian of mathematics. She was the eldest daughter of the mathematicians Grace and William Young. She was born and lived in Göttingen in Germany (where her parents worked at the university) until 1908. During her life she used the name Cecily. Rosalind joined the University of Lausanne in 1917. She also helped her father's research between 1919 and 1921 at the University College Wales in Aberystwyth, and worked with Edward Collingwood, also of Aberystwyth, on a translation of Georges Valiron's course on Integral Functions. She received a L-És-sc (a bachelor's degree) from Lausanne in 1925. She then studied at Girton College, Cambridge, gaining a PhD in 1929 under the supervision of Professor E. W. Hobson for research on Stieltjes integration. She accepted a teaching post at Imperial College, London where she worked until 1967. After 1936, most of her research was in the history of mathematics, and she had a particular interest in Thomas Harriot, an Elizabethan mathematician. She set up the Harriot Seminars in Oxford and Durham. Rosalind married William Tanner in 1953; however, he died a few months after their marriage. In 1972 she and Ivor Grattan-Guinness published a second edition of her parents' book The Theory of Sets of Points, originally published in 1906. Rosalind Tanner died on 24 November 1992. References 1900 births 1992 deaths British historians of mathematics 20th-century British mathematicians 20th-century British historians 20th-century women mathematicians
https://en.wikipedia.org/wiki/Statistical%20thinking
Statistical thinking is a tool for process analysis. Statistical thinking relates processes and statistics, and is based on the following principles: All work occurs in a system of interconnected processes. Variation exists in all processes Understanding and reducing variation are keys to success. W. Edwards Deming promoted the concepts of statistical thinking, using two powerful experiments: 1. The Red Bead experiment, in which workers are tasked with running a more or less random procedure, yet the lowest "performing" workers are fired. The experiment demonstrates how the natural variability in a process can dwarf the contribution of individual workers' talent. 2. The Funnel experiment, again demonstrating that natural variability in a process can loom larger than it ought to. The take home message from the experiments is that before management adjusts a process—such as by firing seemingly underperforming employees, or by making physical changes to an apparatus—they should consider all sources of variation in the process that led to the performance outcome. Statistical thinking is a recognized method used as part of Six Sigma methodologies. See also Systems thinking References Statistical process control Six Sigma
https://en.wikipedia.org/wiki/Pepe%20Serer
José "Pepe" Pérez Serer (born 4 May 1966 in Quart de les Valls, Valencia, Spain) is a former footballer who was most recently the manager of Kairat in Almaty, Kazakhstan. Manager statistics Honours Barcelona UEFA Cup Winners' Cup: 1988–89 References 1966 births Living people Spanish men's footballers Spanish football managers Spanish expatriate football managers FC Kairat managers Expatriate football managers in Kazakhstan Men's association football defenders RCD Mallorca players
https://en.wikipedia.org/wiki/Principles%20of%20the%20Theory%20of%20Probability
Principles of the Theory of Probability is a 1939 book about probability by the philosopher Ernest Nagel. It is considered a classic discussion of its subject. Reception The philosopher Isaac Levi described Principles of the Theory of Probability as a well-known classic. References Bibliography Books 1939 non-fiction books American non-fiction books Books by Ernest Nagel Contemporary philosophical literature English-language books Books about philosophy of mathematics Probability books University of Chicago Press books
https://en.wikipedia.org/wiki/Demazure%20conjecture
In mathematics, the Demazure conjecture is a conjecture about representations of algebraic groups over the integers made by . The conjecture implies that many of the results of his paper can be extended from complex algebraic groups to algebraic groups over fields of other characteristics or over the integers. showed that Demazure's conjecture (for classical groups) follows from their work on standard monomial theory, and Peter Littelmann extended this to all reductive algebraic groups. References Representation theory Conjectures
https://en.wikipedia.org/wiki/Morphic%20word
In mathematics and computer science, a morphic word or substitutive word is an infinite sequence of symbols which is constructed from a particular class of endomorphism of a free monoid. Every automatic sequence is morphic. Definition Let f be an endomorphism of the free monoid A∗ on an alphabet A with the property that there is a letter a such that f(a) = as for a non-empty string s: we say that f is prolongable at a. The word is a pure morphic or pure substitutive word. Note that it is the limit of the sequence a, f(a), f(f(a)), f(f(f(a))), ... It is clearly a fixed point of the endomorphism f: the unique such sequence beginning with the letter a. In general, a morphic word is the image of a pure morphic word under a coding, that is, a morphism that maps letter to letter. If a morphic word is constructed as the fixed point of a prolongable k-uniform morphism on A∗ then the word is k-automatic. The n-th term in such a sequence can be produced by a finite state automaton reading the digits of n in base k. Examples The Thue–Morse sequence is generated over {0,1} by the 2-uniform endomorphism 0 → 01, 1 → 10. The Fibonacci word is generated over {a,b} by the endomorphism a → ab, b → a. The tribonacci word is generated over {a,b,c} by the endomorphism a → ab, b → ac, c → a. The Rudin–Shapiro sequence is obtained from the fixed point of the 2-uniform morphism a → ab, b → ac, c → db, d → dc followed by the coding a,b → 0, c,d → 1. The regular paperfolding sequence is obtained from the fixed point of the 2-uniform morphism a → ab, b → cb, c → ad, d → cd followed by the coding a,b → 0, c,d → 1. D0L system A D0L system (deterministic context-free Lindenmayer system) is given by a word w of the free monoid A∗ on an alphabet A together with a morphism σ prolongable at w. The system generates the infinite D0L word ω = limn→∞ σn(w). Purely morphic words are D0L words but not conversely. However, if ω = uν is an infinite D0L word with an initial segment u of length |u| ≥ |w|, then zν is a purely morphic word, where z is a letter not in A. See also Cutting sequence Lyndon word Hall word Sturmian word References Further reading Semigroup theory Formal languages Combinatorics on words
https://en.wikipedia.org/wiki/Cara%20Black%20career%20statistics
This is a list of the main career statistics of professional Zimbabwean tennis player Cara Black. Major finals Grand Slam tournament finals Doubles: 9 (5–4) Mixed doubles: 8 (5–3) By winning the 2010 Australian Open title, Black completed the mixed doubles Career Grand Slam. She became the sixth female player in history to achieve this. Year-end championships finals Doubles: 9 (3–6) Premier 5/Premier Mandatory finals Doubles: 31 (17–14) WTA career finals Singles: 2 (1–1) Doubles: 109 (60–49) ITF finals Singles Finals (6-5) Doubles (11–3) Grand Slam performance timelines Doubles Only Main Draw results in WTA Tour, Grand Slam Tournaments and Olympic Games are included in win–loss records. This table is current through the 2015 Wimbledon. Mixed doubles Black, Cara
https://en.wikipedia.org/wiki/Topological%20graph
In mathematics, a topological graph is a representation of a graph in the plane, where the vertices of the graph are represented by distinct points and the edges by Jordan arcs (connected pieces of Jordan curves) joining the corresponding pairs of points. The points representing the vertices of a graph and the arcs representing its edges are called the vertices and the edges of the topological graph. It is usually assumed that any two edges of a topological graph cross a finite number of times, no edge passes through a vertex different from its endpoints, and no two edges touch each other (without crossing). A topological graph is also called a drawing of a graph. An important special class of topological graphs is the class of geometric graphs, where the edges are represented by line segments. (The term geometric graph is sometimes used in a broader, somewhat vague sense.) The theory of topological graphs is an area of graph theory, mainly concerned with combinatorial properties of topological graphs, in particular, with the crossing patterns of their edges. It is closely related to graph drawing, a field which is more application oriented, and topological graph theory, which focuses on embeddings of graphs in surfaces (that is, drawings without crossings). Extremal problems for topological graphs A fundamental problem in extremal graph theory is the following: what is the maximum number of edges that a graph of n vertices can have if it contains no subgraph belonging to a given class of forbidden subgraphs? The prototype of such results is Turán's theorem, where there is one forbidden subgraph: a complete graph with k vertices (k is fixed). Analogous questions can be raised for topological and geometric graphs, with the difference that now certain geometric subconfigurations are forbidden. Historically, the first instance of such a theorem is due to Paul Erdős, who extended a result of Heinz Hopf and Erika Pannwitz. He proved that the maximum number of edges that a geometric graph with n > 2 vertices can have without containing two disjoint edges (that cannot even share an endpoint) is n. John Conway conjectured that this statement can be generalized to simple topological graphs. A topological graph is called "simple" if any pair of its edges share at most one point, which is either an endpoint or a common interior point at which the two edges properly cross. Conway's thrackle conjecture can now be reformulated as follows: A simple topological graph with n > 2 vertices and no two disjoint edges has at most n edges. The first linear upper bound on the number of edges of such a graph was established by Lovász et al. The best known upper bound, 1.3984n, was proved by Fulek and Pach. Apart from geometric graphs, Conway's thrackle conjecture is known to be true for x-monotone topological graphs. A topological graph is said to be x-monotone if every vertical line intersects every edge in at most one point. Alon and Erdős initiated the invest
https://en.wikipedia.org/wiki/1989%20L.League
Statistics of L. League in the 1989 season. Shimizu FC Ladies won the championship. JLSL League standings League awards Best player Top scorers Best eleven Best young player See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons L Japan Japan 1989 in Japanese women's sport
https://en.wikipedia.org/wiki/1990%20L.League
Statistics of L. League in the 1990 season. Yomiuri SC Ladies Beleza won the championship. JLSL League standings League awards Best player Top scorers Best eleven Best young player See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons L Japan Japan 1990 in Japanese women's sport
https://en.wikipedia.org/wiki/1991%20L.League
Statistics of L. League in the 1991 season. Yomiuri SC Ladies Beleza won the championship. JLSL League standings League awards Best player Top scorers Best eleven Best young player See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons L Japan Japan 1991 in Japanese women's sport
https://en.wikipedia.org/wiki/1992%20L.League
Statistics of L. League in the 1992 season. Yomiuri Nippon SC Ladies Beleza won the championship. JLSL League Standings League awards Best player Top scorers Best eleven Best young player JLSL Challenge League Promotion/relegation series Division 1 promotion/relegation series Shiroki FC Serena Promoted for Division 1 in 1993 Season. Tasaki Kobe Ladies Relegated to Division 2 in 1993 Season. See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons L Japan Japan 1992 in Japanese women's sport
https://en.wikipedia.org/wiki/1993%20L.League
Statistics of L. League in the 1993 season. Yomiuri Nippon SC Ladies Beleza won the championship. First stage Second stage Championship playoff Suzuyo Shimizu FC Lovely Ladies 0-2 Yomiuri Nippon SC Ladies Beleza Yomiuri Nippon SC Ladies Beleza won the championship. League standings League awards Best player Top scorers Best eleven Best young player JLSL Challenge League See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons L Japan Japan 1993 in Japanese women's sport
https://en.wikipedia.org/wiki/1994%20L.League
Statistics of L. League in the 1994 season. Matsushita Electric LSC Bambina won the championship. First stage Second stage Championship playoff Yomiuri-Seiyu Beleza 0-1 Matsushita Electric LSC Bambina Matsushita Electric LSC Bambina won the championship. League standings League awards Best player Top scorers Best eleven Best young player JLSL Challenge League Promotion/relegation series Division 1 promotion/relegation series Tasaki Perule FC Promoted for Division 1 in 1995 Season. Urawa Ladies FC Relegated to Division 2 in 1995 Season. See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons L Japan Japan 1994 in Japanese women's sport
https://en.wikipedia.org/wiki/1995%20L.League
Statistics of L. League in the 1995 season. Prima Ham FC Kunoichi won the championship. First stage Second stage League standings League awards Best player Top scorers Best eleven Best young player JLSL Challenge League See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons L Japan Japan 1995 in Japanese women's sport
https://en.wikipedia.org/wiki/1996%20L.League
Statistics of L. League in the 1996 season. Nikko Securities Dream Ladies won the championship. First stage Second stage League standings League awards Best player Top scorers Best eleven Best young player Promotion/relegation series JLSL Challenge match Urawa Ladies F.C. play to Division 1 promotion/relegation Series. Division 1 promotion/relegation Series OKI FC Winds stay Division 1 in 1997 Season. Urawa Ladies FC stay Division 2 in 1997 Season. See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons L Japan Japan 1996 in Japanese women's sport
https://en.wikipedia.org/wiki/1997%20L.League
Statistics of L. League in the 1997 season. Nikko Securities Dream Ladies won the championship. First stage Second stage Championship playoff Yomiuri-Seiyu Beleza 1-2 Nikko Securities Dream Ladies Nikko Securities Dream Ladies won the championship. League standings League awards Best player Top scorers Best eleven Best young player Promotion/relegation series Division 1 promotion/relegation series Takarazuka Bunnys Ladies SC stay Division 1 in 1998 Season. Mothers Kumamoto Rainbow Ladies stay Division 2 in 1998 Season. See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons L Japan Japan 1997 in Japanese women's sport
https://en.wikipedia.org/wiki/1998%20L.League
Statistics of L. League in the 1998 season. Nikko Securities Dream Ladies won the championship. First stage Second stage League standings League awards Best player Top scorers Best eleven Best young player See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons L Japan Japan 1998 in Japanese women's sport
https://en.wikipedia.org/wiki/1999%20L.League
Statistics of L. League in the 1999 season. Prima Ham FC Kunoichi won the championship. First stage Second stage Championship Playoff Prima Ham FC Kunoichi 3 - 1 NTV Beleza Prima Ham FC Kunoichi won the championship. League standings League awards Best player Top scorers Best eleven Best young player See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons L Japan Japan 1999 in Japanese women's sport
https://en.wikipedia.org/wiki/2000%20L.League
Statistics of L. League in the 2000 season. Nippon TV Beleza won the championship. First stage East West Second stage Championship playoff Position playoff League awards Best player Top scorers Best eleven Best young player See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons 1 L Japan Japan
https://en.wikipedia.org/wiki/2001%20L.League
Statistics of L. League in the 2001 season. Nippon TV Beleza won the championship. First stage East West Second stage Championship Playoff Position playoff League awards Best player Top scorers Best eleven Best young player See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons 1 L Japan Japan
https://en.wikipedia.org/wiki/2002%20L.League
Statistics of L. League in the 2002 season. Nippon TV Beleza won the championship. First stage East West Second stage Championship playoff Position playoff League awards Best player Top scorers Best eleven Best young player See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons 1 L Japan Japan
https://en.wikipedia.org/wiki/2003%20L.League
Statistics of L. League in the 2003 season. Tasaki Perule FC won the championship. First stage East West Second stage Championship playoff All Teames Stay Division 1 in 2004 Season. Position playoff Shimizudaihachi SC, JEF United Ichihara Ladies, Renaissance Kumamoto FC Relegated to Division 2 in 2004 Season. Division 1 Stay/Relegation playoff Ohara Gakuen JaSRA LSC, Takarazuka Bunnys Ladies SC Stay Division 1 in 2004 Season. Okayama Yunogo Belle, AS Elfen Sayama FC Relegated to Division 2 in 2004 Season. League awards Best player Top scorers Best eleven Best young player See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons 1 L Japan Japan
https://en.wikipedia.org/wiki/2004%20Nadeshiko%20League
Statistics of L. League in the 2004 season. Saitama Reinas FC won the championship. Division 1 Result League awards Best player Top scorers Best eleven Best young player Division 2 Result Best Player: Aya Miyama, Okayama Yunogo Belle See also Empress's Cup External links Nadeshiko League Official Site Nadeshiko League seasons 1 L Japan Japan
https://en.wikipedia.org/wiki/2005%20Nadeshiko%20League
Statistics of L. League in the 2005 season. Nippon TV Beleza won the championship. Division 1 Result League awards Best player Top scorers Best eleven Best young player Division 2 Result Best Player: Miwa Yonetsu, INAC Leonessa See also Empress's Cup External links Nadeshiko League Official Site Season at soccerway.com Nadeshiko League seasons 1 L Japan Japan
https://en.wikipedia.org/wiki/2006%20Nadeshiko%20League
Statistics of Nadeshiko.League in the 2006 season. Nippon TV Beleza won the championship. Division 1 First stage Second stage Championship playoff Position playoff League awards Best player Top scorers Best eleven Best young player Division 2 Result Best Player: Hiromi Katagiri, Albirex Niigata Ladies Promotion/relegation series Division 1 promotion/relegation series Ohara Gakuen JaSRA LSC Promoted to Division 1 in 2007 Season. Speranza FC Takatsuki Relegated to Division 2 in 2007 Season. See also Empress's Cup External links Nadeshiko League Official Site Season at soccerway.com Nadeshiko League seasons 1 L Japan Japan
https://en.wikipedia.org/wiki/2007%20Nadeshiko%20League
Statistics of Nadeshiko.League in the 2007 season. Nippon TV Beleza won the championship. Division 1 Result League awards Best player Top scorers Best eleven Best young player Division 2 Result Best Player: Aya Sameshima, TEPCO Mareeze Promotion/relegation series Division 1 promotion/relegation series Iga FC Kunoichi Stay Division 1 in 2008 Season. JEF United Chiba Ladies Stay Division 2 in 2008 Season. See also Empress's Cup External links Nadeshiko League Official Site Season at soccerway.com Nadeshiko League seasons 1 L Japan Japan
https://en.wikipedia.org/wiki/2008%20Nadeshiko%20League
Statistics of Nadeshiko.League in the 2008 season. Nippon TV Beleza won the championship. Division 1 Result League awards Best player Top scorers Best eleven Best young player Division 2 Result Best Player: Yuka Shimizu, JEF United Chiba Ladies Promotion/relegation series Division 1 promotion/relegation series Speranza FC Takatsuki Promoted for Division 1 in 2009 Season. Iga FC Kunoichi Relegated to Division 2 in 2009 Season. See also Empress's Cup External links Nadeshiko League Official Site Season at soccerway.com Nadeshiko League seasons 1 L Japan Japan
https://en.wikipedia.org/wiki/2009%20Nadeshiko%20League
Statistics of Nadeshiko.League in the 2009 season. Urawa Reds Ladies won the championship. Division 1 Result League awards Best player Top scorers Best eleven Best young player Division 2 Result Best Player: Yoshie Kasazaki, AS Elfen Sayama F.C. Promotion/relegation series Division 1 promotion/relegation series Fukuoka J. Anclas Promoted for Division 1 in 2010 Season. Speranza F.C. Takatsuki Relegated to Division 2 in 2010 Season. Division 2 Promotion series Block A Nippon Sport Science University L.S.C., Shizuoka Sangyo University Iwata Ladies, JFA Academy Fukushima L.F.C. Promoted for Division 2 in 2010 Season. Block B Tokiwagi Gakuen High School L.S.C., F.C. AGUILAS, A.S.C. Adooma Promoted for Division 2 in 2010 Season. See also Empress's Cup External links Nadeshiko League Official Site Season at soccerway.com Nadeshiko League seasons 1 L Japan Japan
https://en.wikipedia.org/wiki/2010%20Nadeshiko%20League
Statistics of Nadeshiko League in the 2010 season. NTV Beleza won the championship. As of 2010, by the reformation announced in November 2009, Division 1 and Division 2 was renamed as Nadeshiko League and Challenge League respectively. Also, the number of participating teams became 10 teams for Nadeshiko League from 8, and 12 teams for Challenge League, from 8, dividing into 2 sections of 6 teams. Nadeshiko League (Division 1) Result League awards Best player Top scorers Best eleven Best young player Challenge League (Division 2) Result East West Promotion/relegation series Division 1 promotion/relegation series Qualifiers Speranza F.C. Takatsuki play to Division 1 promotion/relegation Series Final. Final Iga F.C. Kunoichi Stay Division 1 in 2011 Season. Speranza F.C. Takatsuki Stay Division 2 in 2011 Season. Division 2 promotion/relegation series Qualifiers F.C. Takahashi Charme, Sfida Setagaya F.C. play to Division 2 promotion/relegation Series Final. Final F.C. Takahashi Charme, Sfida Setagaya F.C. Promoted for Division 2 in 2011 Season. Shimizudaihachi Pleiades Relegated to Regional League (Tokai League) in 2011 Season. Renaissance Kumamoto F.C. Relegated to Regional League (Kyushu, Q League) in 2011 Season. See also Empress's Cup References External links Nadeshiko League Official Site Season at soccerway.com Nadeshiko League seasons 1 L Japan Japan
https://en.wikipedia.org/wiki/2011%20Nadeshiko%20League
Statistics of Nadeshiko.League in the 2011 season. INAC Kobe Leonessa won the championship. Nadeshiko League Cup was cancelled due to the devastating damage from 2011 Tōhoku earthquake and tsunami on 11 March. Season opener became Week 5 (29 April) as the earthquake made Week 1 to 4 rescheduled chaotically after 11 June. The 4 games of Week 1 scheduled on 7/30, 7/31, 7/24, 6/11, and Week 2 on 7/24, 8/6, 6/12, 6/12. Such disorder continued until Week 4. Nadeshiko League (Division 1) Result League awards Best player Top scorers Best eleven Best young player Challenge League (Division 2) Result East Best Player(EAST): Mai Kyokawa, Tokiwagi Gakuen High School L.S.C. Top scorers(EAST): Mai Kyokawa, Tokiwagi Gakuen High School L.S.C. West Best Player(WEST): Chiho Takahashi, F.C. Takahashi Charme Top scorers(WEST): Akika Nishikawa, F.C. Takahashi Charme Promotion/relegation series Division 2 Promotion series Qualifiers Semi-final Final Japan Soccer College Ladies Promoted to Division 2 in 2012 Season. Ehime F.C. Ladies play to Division 2 promotion/relegation Series. Division 2 promotion/relegation series Ehime F.C. Ladies Promoted to Division 2 in 2012 Season. Norddea Hokkaido Relegated to Regional League (Hokkaido League) in 2012 Season. See also Empress's Cup References External links Nadeshiko League Official Site Season at soccerway.com Nadeshiko League seasons 1 L Japan Japan
https://en.wikipedia.org/wiki/Paul%20A.%20Catlin
Paul Allen Catlin ( – ) was a mathematician, professor of mathematics who worked in graph theory and number theory. He wrote a significant paper on the series of chromatic numbers and Brooks' theorem, titled Hajós graph coloring conjecture: variations and counterexamples. Career Originally from Bridgeport, Connecticut, Catlin majored in Mathematics with a B.A. degree from Carnegie Mellon University in 1970. Catlin held a Doctorate in Mathematics degree from Ohio State University. From 1972 to 1973, he was a research and teaching assistant at Ohio State University, where he earned the Master of Science degree in Mathematics. In 1976, he went to work at Wayne State University, where he concentrated the research on chromatic numbers and Brooks' theorem. As a result, Catlin published a significant paper in that series: Hajós graph coloring conjecture: variations and counterexamples., which showed that the conjecture raised by Hugo Hadwiger is further strengthened not only by but also by , which led to the joint paper written with Paul Erdős and Béla Bollobás titled Hadwiger's conjecture is true for almost every graph. He authored over fifty academic papers in number theory and graph theory. Many of his contributions and collaborations have been published in The Fibonacci Quarterly, in The Journal of Number Theory, in the Journal of Discrete Mathematics, and many other academic publications. He co-authored scholarly papers with Arthur M. Hobbs, Béla Bollobás and Paul Erdős, Hong-Jian Lai, Zheng-Yiao Han, and Yehong Shao, among others. He also published papers with G. Neil Robertson, with whom he also completed his dissertation thesis in 1976. Selected publications References 1948 births 1995 deaths 20th-century American mathematicians Number theorists Graph theorists Ohio State University Graduate School alumni Wayne State University faculty
https://en.wikipedia.org/wiki/Limited%20principle%20of%20omniscience
In constructive mathematics, the limited principle of omniscience (LPO) and the lesser limited principle of omniscience (LLPO) are axioms that are nonconstructive but are weaker than the full law of the excluded middle. They are used to gauge the amount of nonconstructivity required for an argument, as in constructive reverse mathematics. These principles are also related to weak counterexamples in the sense of Brouwer. Definitions The limited principle of omniscience states : LPO: For any sequence , , ... such that each is either or , the following holds: either for all , or there is a with . The second disjunct can be expressed as and is constructively stronger than the negation of the first, . The weak schema in which the former is replaced with the latter is called WLPO and represents particular instances of excluded middle. The lesser limited principle of omniscience states: LLPO: For any sequence , , ... such that each is either or , and such that at most one is nonzero, the following holds: either for all , or for all . Here and are entries with even and odd index respectively. It can be proved constructively that the law of the excluded middle implies LPO, and LPO implies LLPO. However, none of these implications can be reversed in typical systems of constructive mathematics. Terminology The term "omniscience" comes from a thought experiment regarding how a mathematician might tell which of the two cases in the conclusion of LPO holds for a given sequence . Answering the question "is there a with ?" negatively, assuming the answer is negative, seems to require surveying the entire sequence. Because this would require the examination of infinitely many terms, the axiom stating it is possible to make this determination was dubbed an "omniscience principle" by . Variants Logical versions The two principles can be expressed as purely logical principles, by casting it in terms of decidable predicates on the naturals. I.e. for which does hold. The lesser principle corresponds to a predicate version of that De Morgan's law that does not hold intuitionistically, i.e. the distributivity of negation of a conjunction. Analytic versions Both principles have analogous properties in the theory of real numbers. The analytic LPO states that every real number satisfies the trichotomy or or . The analytic LLPO states that every real number satisfies the dichotomy or , while the analytic Markov's principle states that if is false, then . All three analytic principles if assumed to hold for the Dedekind or Cauchy real numbers imply their arithmetic versions, while the converse is true if we assume (weak) countable choice, as shown in . See also Constructive analysis References External links Constructivism (mathematics)
https://en.wikipedia.org/wiki/Zsolt%20P%C3%B6l%C3%B6skei
Zsolt Pölöskei (born 19 February 1991) is a retired Hungarian football player. Club statistics Updated to games played as of 26 July 2018. References External links Profile at HLSZ Profile at MLSZ 1991 births Living people Footballers from Budapest Hungarian men's footballers Men's association football midfielders MTK Budapest FC players Fehérvár FC players Budapest Honvéd FC players Nemzeti Bajnokság I players Hungarian expatriate men's footballers Expatriate men's footballers in England Hungarian expatriate sportspeople in England
https://en.wikipedia.org/wiki/Compact%20semigroup
In mathematics, a compact semigroup is a semigroup in which the sets of solutions to equations can be described by finite sets of equations. The term "compact" here does not refer to any topology on the semigroup. Let S be a semigroup and X a finite set of letters. A system of equations is a subset E of the Cartesian product X∗ × X∗ of the free monoid (finite strings) over X with itself. The system E is satisfiable in S if there is a map f from X to S, which extends to a semigroup morphism f from X+ to S, such that for all (u,v) in E we have f(u) = f(v) in S. Such an f is a solution, or satisfying assignment, for the system E. Two systems of equations are equivalent if they have the same set of satisfying assignments. A system of equations if independent if it is not equivalent to a proper subset of itself. A semigroup is compact if every independent system of equations is finite. Examples A free monoid on a finite alphabet is compact. A free monoid on a countable alphabet is compact. A finitely generated free group is compact. A trace monoid on a finite set of generators is compact. The bicyclic monoid is not compact. Properties The class of compact semigroups is closed under taking subsemigroups and finite direct products. The class of compact semigroups is not closed under taking morphic images or infinite direct products. Varieties The class of compact semigroups does not form an equational variety. However, a variety of monoids has the property that all its members are compact if and only if all finitely generated members satisfy the maximal condition on congruences (any family of congruences, ordered by inclusion, has a maximal element). References Semigroup theory Formal languages Combinatorics on words
https://en.wikipedia.org/wiki/K.%20D.%20Tocher
Keith Douglas "Toch" Tocher (19 March 1921 – 30 December 1981) was a computer scientist known for contributions to computer simulation. Tocher received a first-class BSc in Mathematics in 1941 from University College London, a BSc in Statistics in 1946 from University of London, and a PhD in 1952 at Imperial College London. In 1958, he worked for United Steel Companies under Anthony Stafford Beer, and developed the first discrete-event simulation package, the General Simulation Program (GSP), a program that used a common structure to execute a range of simulations. He was appointed professor of operational research at the University of Southampton in 1980. He was awarded the silver medal of the Operational Research Society in 1967 and served as president from 1972–73. Tocher was also one of the creators of the SRT division algorithm that is used in the hardware of many modern computers. References External links Guide to the United Steel Companies Department of Operational Research and Cybernetics Handbooks, 1959-1960 1921 births 1981 deaths British computer scientists
https://en.wikipedia.org/wiki/New%20Horizon%20Scholars%20School%2C%20Thane
{ "type": "FeatureCollection", "features": [ { "type": "Feature", "properties": {}, "geometry": { "type": "Point", "coordinates": [ 72.97407746315004, 19.265578693719768 ] } } ] } New Horizon Scholars School is located in Kavesar near Anand Nagar Circle off State Highway 42 (Maharashtra) (commonly referred to as Ghodbunder Road) in Thane (West) in the Mumbai Metropolitan Region of India. It is a branch of the New Horizon Scholars School from the Navi Mumbai suburb Airoli. The school includes a pre-primary education section called Neo Kids. It has classes from Nursery to Grade 12. The school's Founder President is Dr. Subir Kumar Banerjee. The Chairperson is Ms. Suvra Banerjee. The current principal is Dr. Jyoti Nair . History The Chairman inaugurated the school on 16 October 2012, and the first academic year commenced in June 2013. Curriculum New Horizon Scholars School strictly follows the curriculum of India's Central Board of Secondary Education (CBSE). Evaluation The school has no exams in lower classes, including primary and pre-primary classes. Instead, it uses Continuous and Comprehensive Evaluation (CCE) for all classes, which consists of 'formative' and 'summative' evaluation. Activities The school offers a blend of scholastic and co-scholastic activities. All activities contribute to the personality development of children with an emphasis on public-speaking skills, music and other arts. Coaching is offered in chess, dance, aerobics, karate, and skating. Facilities include playgrounds and areas for sports such as football, basketball, volleyball, badminton, cricket and athletics, well-equipped Libraries, and Physics, Chemistry, Biology & IT laboratories. References External links 2012 establishments in Maharashtra Education in Thane Educational institutions established in 2012 Schools in Thane district http://cbseaff.nic.in/cbse_aff/schdir_Report/AppViewdir.aspx?affno=1130470
https://en.wikipedia.org/wiki/Hamdard%20University%20Bangladesh
Hamdard University Bangladesh () is a newly established private university in Bangladesh. Academic departments Faculty of Science, Engineering & Technology (FSET) Dept. of Mathematics Dept. of Electrical and Electronic Engineering Dept. of Computer Science and Engineering Faculty of Business Administration(FBA) Dept. of Business Administration (major in Marketing, Management, Finance, Accounting) Faculty of Arts & Social Science(FASS) Dept. of English Dept. of Economics Faculty of Unani and Ayurvedic Medicine (FAUM) Dept. of Unani Medicine Dept. of Ayurvedic Medicine Faculty of Health Sciences Dept. of Public Health Courses Undergraduate Bachelor of Science (Honours) in Mathematics Bachelor of Science (Honours) in Computer Science & Engineering Bachelor of Science (Honours) in Electrical & Electronics Engineering Bachelor of Business Administration (Major in Marketing) Bachelor of Business Administration (Management) Bachelor of Arts (Honours) in English Bachelor of Social Science (Honours) in Economics Bachelor of Unani Medicine and Surgery (BUMS) Bachelor of Ayurvedic Medicine and Surgery (BAMS) Graduate Master of Business Administration (MBA) Regular-39 credit Master of Business Administration (MBA) Regular-66 credit Executive MBA (EMBA)-Management Master of Public Health (MPH) Master of Science in Mathematics See also Hamdard Public College Jamia Hamdard Hamdard Public School References Universities and colleges in Bangladesh 2011 establishments in Bangladesh Educational institutions established in 2011
https://en.wikipedia.org/wiki/%C3%81lvaro%20%28footballer%2C%20born%202001%29
Álvaro de Oliveira Felicíssimo (born 27 May 2001), known as just Álvaro, is a Brazilian footballer who currently plays for Al Bataeh. Career statistics Club Notes References External links 2001 births Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football forwards UAE Pro League players UAE First Division League players América Futebol Clube (MG) players Shabab Al Ahli Club players Fujairah FC players Dibba Al Fujairah FC players Al Bataeh Club players Expatriate men's footballers in the United Arab Emirates Brazilian expatriate sportspeople in the United Arab Emirates
https://en.wikipedia.org/wiki/Defensive%20Runs%20Saved
In baseball statistics, defensive runs saved (DRS) measures the number of runs a player saved or cost his team on defense relative to an average player. Any positive number is above average, and the best fielders typically have a DRS figure of 15 to 20 for a season. The statistic was developed by Baseball Info Solutions and the data used in calculating it first became available for Major League Baseball (MLB) in 2003. Definition Fielding percentage is the statistic that has traditionally been used to measure defensive ability, but it fails to account for a fielder's defensive range. Fielders who can cover a large area on defense are able to make plays that most players would not have the chance to make. DRS was created to take range into account when measuring a player's defensive ability. In calculating DRS, points are either added or subtracted to a fielder's rating depending on whether or not they make a play on a ball that is hit towards them. For example, if a ball hit to the center fielder is expected to be caught 30 percent of the time, the fielder will lose .3 points if he does not catch it, or will gain .7 points if he does catch it. Each player's total points are later adjusted based on league averages, both with regards to average defensive performance, and with regards to how many runs a "point" equates to. Example The table below shows a comparison between the top 10 shortstops in terms of fielding percentage and the top 10 shortstops in terms of defensive runs saved from 2002 to 2019 in MLB. The table shows that only two players appear on both lists (Simmons and Hardy), exemplifying that there is a difference in what the two statistics measure. Leaders Note that DRS statistics are only available from the 2003 MLB season through the present. Thus, players of earlier eras who were noted for the defensive skills—such as third baseman Brooks Robinson and shortstop Ozzie Smith—were not evaluated in this manner. Also note that there is some variation in DRS as presented on baseball reference sites—for example, Baseball-Reference.com credits Adrián Beltré with a DRS figure of 201 for his career, while FanGraphs credits him with 200. The below figures are sourced from FanGraphs. Single season Through the end of the 2021 MLB season, the highest DRS recorded in a single season was by shortstop Andrelton Simmons, who had a DRS of 41 in 2017, while the lowest DRS recorded in a single season was by center fielder Matt Kemp, who had a DRS of -33 in 2010. Career Through the end of the 2021 MLB season, the highest cumulative DRS for a career is 200, by third baseman Adrián Beltré, while the lowest DRS for a career is -165 by shortstop Derek Jeter. Note that the totals for both Beltré and Jeter only reflect 2003 onward, even though both players began their MLB careers earlier. See also Ultimate zone rating References Fielding statistics
https://en.wikipedia.org/wiki/Luna%27s%20slice%20theorem
In mathematics, Luna's slice theorem, introduced by , describes the local behavior of an action of a reductive algebraic group on an affine variety. It is an analogue in algebraic geometry of the theorem that a compact Lie group acting on a smooth manifold X has a slice at each point x, in other words a subvariety W such that X looks locally like G×Gx W. (see slice theorem (differential geometry).) References Theorems in algebraic geometry
https://en.wikipedia.org/wiki/Slice%20theorem
In mathematics, the slice theorem refers to The slice theorem in differential geometry, or Luna's slice theorem, an analog in algebraic geometry.
https://en.wikipedia.org/wiki/Igusa%20variety
In mathematics, an Igusa curve is (roughly) a coarse moduli space of elliptic curves in characteristic p with a level p Igusa structure, where an Igusa structure on an elliptic curve E is roughly a point of order p of E(p) generating the kernel of V:E(p) → E. An Igusa variety is a higher-dimensional analogue of an Igusa curve. Igusa curves were studied by and Igusa varieties were introduced by . References Algebraic geometry Elliptic curves
https://en.wikipedia.org/wiki/Olaf%20Storaasli
Olaf O. Storaasli, Synective Labs VP, was a researcher at Oak Ridge National Laboratory (Computer Science and Mathematics Division's Future Technologies Group) and USEC following his NASA career. He led the hardware, software and applications teams' successful development of one of NASA's 1st parallel computers, the Finite element machine and developed rapid matrix equation algorithms tailored to high-performance computers (even harnessing FPGA accelerators) to solve science and engineering applications. He was PhD advisor and graduate instructor at UT, GWU and CNU and mentored 25 NHGS students. He is recognized by American Men and Women of Science, Marquis Who's Who, and NASA, Cray, Intel and Concordia College awards. NASA Awards include Viking Mars Lander design and Engineering Analysis (IPAD, RIM, HPC, FPGA, SPAR, FEM, Space Shuttle SRB and NASA Software-of-the-year). Education Storaasli received a B.A. in Physics, Mathematics & French (Concordia College, 1964), M.A. in Mathematics (USD,1966), Ph.D in Engineering Mechanics (NCSU, 1970) and post-doc fellowships: NTNU (1984–85), University of Edinburgh (2008). Research He develops, tests and documents parallel analysis software to speed matrix equation solution to simulate physical & biological behavior on advanced-computer architectures (e.g. NASA's GPS solver based on prior Finite element machine and rapid parallel analysis of Space Shuttle SRB redesign earned Cray's 1st GigaFLOP Performance Award at Supercomputing '89). Books Engineering Applications on NASA's FPGA-based Hypercomputer, 7th MAPLD, Washington, D.C., Sept 2004. Large-Scale Analysis, Design and Intelligent Synthesis Environments, Elsevier Sciences, 2000. Large-Scale Analysis & Design on High-Performance Computers & Workstations, Elsevier Sciences, 1998. Large-Scale Structural Analysis for High-Performance Computers & Workstations, Pergamon Press 1994. Parallel Computational Methods for Large-Scale Structural Analysis & Design, Pergamon Press 1993. Parallel Methods on Large-Scale Structural Analysis & Physics Applications, Pergamon Press 1991. References 1 Olaf Storaasli at the Mathematics Genealogy Project 2 State-of-the-Art in Heterogeneous Computing, Scientific Programming 18 pp. 1–33, IOS Press, 2010.(+PARA10) 3 High-Performance Mixed-Precision Linear Solver for FPGAs, IEEE Trans Computers 57/12, 1614–1623, 2008. 4 Accelerating Science Applications up to 100X with FPGAs, PARA08 Proc.Trondheim Norway, May 2008. 5 Computation Speed-up of Complex Durability Analysis of Large-Scale Composite Structures, AIAA 49th SDM Proc. 2008. 6 Accelerating Genome Sequencing 100-1000X MRSC Proc. Queen's University, Belfast, UK April 1–3, 2008. 7 Exploring Accelerating Science Applications with FPGAs, NCSA/RSSI Proc. Urbana, IL, July 20, 2007. 8 Performance Evaluation of FPGA-Based Biological Applications, Cray Users Group Proc. Seattle, May 2007. 9 Sparse Matrix-Vector Multiplication Design on FPGAs, IEEE 15th Symp on FCCM Proc., 349
https://en.wikipedia.org/wiki/Southern%20Nova%20Scotia
Southern Nova Scotia or the South Shore is a region of Nova Scotia, Canada. The area has no formal identity and is variously defined by geographic, county and other political boundaries. Statistics Canada, defines Southern Nova Scotia as an economic region, composed of Lunenburg County, Queens County, Shelburne County, Yarmouth County, and Digby County. According to Statistics Canada, the region had the highest decrease of population in Canada from 2009 to 2010, with a population decrease of 10.2 residents per thousand. The region also has the second-highest median age in Canada at 47.1 years old. Politically defined The South Shore is sometimes defined as part of the Halifax West, South Shore—St. Margaret's, and West Nova ridings at the federal level, or as the western rural part of the Halifax Regional Municipality, the Municipality of the District of Lunenburg, Queens County, and Shelburne County. There were five MLAs elected from this region in recent Nova Scotia provincial elections, when the region shifted from the Progressive Conservative Party to the more left-leaning New Democratic Party. It is generally considered to be a "swing" region that has changed political leanings in the recent past, and a key target for campaigning. History The South Shore was one of the first areas of North America to be colonized by Europeans following the French settlement at Port-Royal in 1605. The region, without good agricultural land, was only sparsely inhabited by the Acadians, although several settlements were established in present-day Shelburne County and the LaHave River valley. When the British took control of the region in 1713, they initiated a program of importing colonists from continental Europe, known as the Foreign Protestants, mostly from Germany and Switzerland. To this day the South Shore retains many German place names and surnames as well as a distinct accent compared to the New England settlers' influence in the Annapolis Valley or the Highland Scots' influence in northeastern Nova Scotia and Cape Breton Island. On December 19, 1906, the Halifax and Southwestern Railway opened between Halifax and Yarmouth, finishing a project that had begun in 1885, and bringing more reliable land transport to the region. Although the South Shore did not play a major role during the First World War, the area saw significant military activity during the Second World War and the ensuing Cold War, as Shelburne and Mill Cove became home to Royal Canadian Navy bases, and a Pinetree Line radar station was established by the Royal Canadian Air Force at Baccaro. In 1966, Canada's first satellite communications (SATCOM) earth station began operations at Mill Village. In the 1970s and 1980s, the Highway 103 arterial highway was built. During the 20th century, the South Shore became the centre of Nova Scotia's fishing industry, as fishermen in small boats operated from numerous tiny villages dotted along the coast. The larger communities also had fis
https://en.wikipedia.org/wiki/Adolph%20Winkler%20Goodman
Adolph Winkler Goodman (July 20, 1915 – July 30, 2004) was an American mathematician who contributed to number theory, graph theory and to the theory of univalent functions: The conjecture on the coefficients of multivalent functions named after him is considered the most interesting challenge in the area after the Bieberbach conjecture, proved by Louis de Branges in 1985. Life and work In 1948, he made a mathematical conjecture on coefficients of -valent functions, first published in his Columbia University dissertation thesis and then in a closely following paper. After the proof of the Bieberbach conjecture by Louis de Branges, this conjecture is considered the most interesting challenge in the field, and he himself and coauthors answered affirmatively to the conjecture for some classes of -valent functions. His researches in the field continued in the paper Univalent functions and nonanalytic curves, published in 1957: in 1968, he published the survey Open problems on univalent and multivalent functions, which eventually led him to write the two-volume book Univalent Functions. Apart from his research activity, He was actively involved in teaching: he wrote several college and high school textbooks including Analytic Geometry and the Calculus, and the five-volume set Algebra from A to Z. He retired in 1993, became a Distinguished Professor Emeritus in 1995, and died in 2004. Selected works Notes Biographical references References . . . . Additional sources 20th-century American mathematicians 21st-century American mathematicians Complex analysts Mathematical analysts Number theorists Graph theorists 1915 births 2004 deaths
https://en.wikipedia.org/wiki/Records%20and%20Statistics%20of%20the%20Primera%20Divisi%C3%B3n%20de%20F%C3%BAtbol%20Profesional
The following is a compilation of notable records and statistics of teams, players and seasons in Primera División. All time League Records Titles Most top-flight League titles: 17, C.D. FAS Most consecutive League titles: 7, Hércules (Amateur Era) 1927, 1928, 1929–30, 1930–31, 1931–32, 1932–33, 1933–34 Atlético Marte (Professional Era) 3- 1955, 1955–56 and 1956–57 Firpo (Professional Era) 3- 1990, 1991 and 1992–93 Top flight appearances Most Appearances: 64 C.D. FAS (1948–present) Records Team Most league goals scored in a season: 88, Atletico Marte (1978-1979) Fewest league goals scored in a season: 8, Juventud Olimpica Metalio (1999 Apertura) Most league goals conceded in a season: 111, Cojutepeque F.C. (1994–95) Fewest league goals conceded in a season:, () Biggest Win: C.D. Luis Angel Firpo 11-0 Cojutepeque F.C., 30 April 1995 Best undefeated streak: Atletico Marte 20 games (10 wins and 10 draws), 1985 season First team that bought another team spot in the Primera División : Atlético Constancia buying Once Municipal for 1 colon in 1958. Most consecutive games won at home: 31 games Once Municipal (2016/2017) and Santa Tecla F.C. (2017/2018) Individual Highest goal scorer of all time: Williams Reyes, 251 goals (2001-) First coach that has won a championship: Armando Chacón with Once Municipal in 1949. First foreign coach that's won a championship: Argentinian Alberto Cevasco with C.D. FAS in 1957-58. Most championship by a coach: Edwin Portillo won 7 titles with A.D. Isidro Metapan Most championship by a foreign coach: Chilean Hernán Carrasco Vivanco won 6 titles (Alianza-1965–66, 1966–67 and 1989–90, Atletico Marte -1968–69 and 1970, Aguila -1987–88) Most relegation by a team: 4, C.D. Dragon (1963/64, 1980–81, 1990–91, 2002-2003) and Once Municipal (1969–70, 1979–80, 2007–08 and 2012–13) Most goals scored in a game by one player : 7, Mario Aguila Zelaya with Firpo against Olimpic 7-0 (24 December 1950) Most goals by a top goalscorer: Argentinian Omar Muraco with 26 goals in 1958. Youngest player to play in the Primera División: 14 years old Ricardo Guevara Mora with Platense Oldest player in the Primera División: 43 years, 11 months and 1 day Magico Gonzales with San Salvador F.C. in 2002. First world cup champion player in the Primera División: Brazilian Zozimo played with C.D. Aguila in 1967–1969 (Champion with Brazil in Sweden 1958 and Chile 1962) First world cup player in the Primera División: Paraguayan Jorge Lino Romero played in the 1958 world cup with Atlante Records 1927–1997 Most league goals scored in a season (excluding playoffs): 83 goals, Alianza F.C. (1965–66) Fewest league goals scored in a season: 11, C.D. Sonsonate (1977–1978) Most league goals conceded in a season: 111, Cojutepeque F.C. (1994–1995) Fewest league goals conceded in a season: 6, C.D. FAS (1981) Biggest Win: C.D. Luis Angel Firpo 11-0 Cojutepeque F.C., 30 April 1995 Record away win: Highest scoring game: Most wins in a
https://en.wikipedia.org/wiki/Pavel%20Mach%C3%A1%C4%8Dek
Pavel Macháček (born 18 December 1977) is a Czech football defender currently playing for FK Bohemians Prague (Střížkov) in the Czech Republic. Career statistics Statistics accurate as of 30 June 2012 References External links 1977 births Living people Czech men's footballers Czech First League players Bohemians 1905 players FK Bohemians Prague (Střížkov) players Men's association football defenders
https://en.wikipedia.org/wiki/Vlastimil%20Karal
Vlastimil Karal (born 26 April 1983) is a Czech football defender currently playing for Bohemians Prague in the Czech 2. Liga. Career statistics Statistics accurate as of 30 June 2013 References External links 1983 births Living people Czech men's footballers Czech First League players Bohemians 1905 players FC Hradec Králové players FK Čáslav players FK Bohemians Prague (Střížkov) players Men's association football defenders
https://en.wikipedia.org/wiki/Sesquipower
In mathematics, a sesquipower or Zimin word is a string over an alphabet with identical prefix and suffix. Sesquipowers are unavoidable patterns, in the sense that all sufficiently long strings contain one. Formal definition Formally, let A be an alphabet and A∗ be the free monoid of finite strings over A. Every non-empty word w in A+ is a sesquipower of order 1. If u is a sesquipower of order n then any word w = uvu is a sesquipower of order n + 1. The degree of a non-empty word w is the largest integer d such that w is a sesquipower of order d. Bi-ideal sequence A bi-ideal sequence is a sequence of words fi where f1 is in A+ and for some gi in A∗ and i ≥ 1. The degree of a word w is thus the length of the longest bi-ideal sequence ending in w. Unavoidable patterns For a finite alphabet A on k letters, there is an integer M depending on k and n, such that any word of length M has a factor which is a sesquipower of order at least n. We express this by saying that the sesquipowers are unavoidable patterns. Sesquipowers in infinite sequences Given an infinite bi-ideal sequence, we note that each fi is a prefix of fi+1 and so the fi converge to an infinite sequence We define an infinite word to be a sesquipower if it is the limit of an infinite bi-ideal sequence. An infinite word is a sesquipower if and only if it is a recurrent word, that is, every factor occurs infinitely often. Fix a finite alphabet A and assume a total order on the letters. For given integers p and n, every sufficiently long word in A∗ has either a factor which is a p-power or a factor which is an n-sesquipower; in the latter case the factor has an n-factorisation into Lyndon words. See also ABACABA pattern References Semigroup theory Formal languages Combinatorics on words
https://en.wikipedia.org/wiki/Unavoidable%20pattern
In mathematics and theoretical computer science, a pattern is an unavoidable pattern if it is unavoidable on any finite alphabet. Definitions Pattern Like a word, a pattern (also called term) is a sequence of symbols over some alphabet. The minimum multiplicity of the pattern is where is the number of occurrence of symbol in pattern . In other words, it is the number of occurrences in of the least frequently occurring symbol in . Instance Given finite alphabets and , a word is an instance of the pattern if there exists a non-erasing semigroup morphism such that , where denotes the Kleene star of . Non-erasing means that for all , where denotes the empty string. Avoidance / Matching A word is said to match, or encounter, a pattern if a factor (also called subword or substring) of is an instance of . Otherwise, is said to avoid , or to be -free. This definition can be generalized to the case of an infinite , based on a generalized definition of "substring". Avoidability / Unavoidability on a specific alphabet A pattern is unavoidable on a finite alphabet if each sufficiently long word must match ; formally: if . Otherwise, is avoidable on , which implies there exist infinitely many words over the alphabet that avoid . By Kőnig's lemma, pattern is avoidable on if and only if there exists an infinite word that avoids . Maximal -free word Given a pattern and an alphabet . A -free word is a maximal -free word over if and match . Avoidable / Unavoidable pattern A pattern is an unavoidable pattern (also called blocking term) if is unavoidable on any finite alphabet. If a pattern is unavoidable and not limited to a specific alphabet, then it is unavoidable for any finite alphabet by default. Conversely, if a pattern is said to be avoidable and not limited to a specific alphabet, then it is avoidable on some finite alphabet by default. -avoidable / -unavoidable A pattern is -avoidable if is avoidable on an alphabet of size . Otherwise, is -unavoidable, which means is unavoidable on every alphabet of size . If pattern is -avoidable, then is -avoidable for all . Given a finite set of avoidable patterns , there exists an infinite word such that avoids all patterns of . Let denote the size of the minimal alphabet such that avoiding all patterns of . Avoidability index The avoidability index of a pattern is the smallest such that is -avoidable, and if is unavoidable. Properties A pattern is avoidable if is an instance of an avoidable pattern . Let avoidable pattern be a factor of pattern , then is also avoidable. A pattern is unavoidable if and only if is a factor of some unavoidable pattern . Given an unavoidable pattern and a symbol not in , then is unavoidable. Given an unavoidable pattern , then the reversal is unavoidable. Given an unavoidable pattern , there exists a symbol such that occurs exactly once in . Let represent the number of distinct symbols of pattern . If
https://en.wikipedia.org/wiki/Johann%20Vana
Johann Vanna (6 December 1908 – 4 November 1950) is an Austrian former footballer. Career statistics References 1908 births Year of death missing Men's association football midfielders Austrian men's footballers SK Rapid Wien players RC Strasbourg Alsace players
https://en.wikipedia.org/wiki/Recurrent%20word
In mathematics, a recurrent word or sequence is an infinite word over a finite alphabet in which every factor occurs infinitely many times. An infinite word is recurrent if and only if it is a sesquipower. A uniformly recurrent word is a recurrent word in which for any given factor X in the sequence, there is some length nX (often much longer than the length of X) such that X appears in every block of length nX. The terms minimal sequence and almost periodic sequence (Muchnik, Semenov, Ushakov 2003) are also used. Examples The easiest way to make a recurrent sequence is to form a periodic sequence, one where the sequence repeats entirely after a given number m of steps. Such a sequence is then uniformly recurrent and nX can be set to any multiple of m that is larger than twice the length of X. A recurrent sequence that is ultimately periodic is purely periodic. The Thue–Morse sequence is uniformly recurrent without being periodic, nor even eventually periodic (meaning periodic after some nonperiodic initial segment). All Sturmian words are uniformly recurrent. References An. Muchnik, A. Semenov, M. Ushakov, Almost periodic sequences, Theoret. Comput. Sci. vol.304 no.1-3 (2003), 1-33. Semigroup theory Formal languages Combinatorics on words
https://en.wikipedia.org/wiki/Good%20filtration
In mathematical representation theory, a good filtration is a filtration of a representation of a reductive algebraic group G such that the subquotients are isomorphic to the spaces of sections F(λ) of line bundles λ over G/B for a Borel subgroup B. In characteristic 0 this is automatically true as the irreducible modules are all of the form F(λ), but this is not usually true in positive characteristic. showed that the tensor product of two modules F(λ)⊗F(μ) has a good filtration, completing the results of who proved it in most cases and who proved it in large characteristic. showed that the existence of good filtrations for these tensor products also follows from standard monomial theory. References Representation theory Linear algebraic groups
https://en.wikipedia.org/wiki/Manin%20triple
In mathematics, a Manin triple (g, p, q) consists of a Lie algebra g with a non-degenerate invariant symmetric bilinear form, together with two isotropic subalgebras p and q such that g is the direct sum of p and q as a vector space. A closely related concept is the (classical) Drinfeld double, which is an even dimensional Lie algebra which admits a Manin decomposition. Manin triples were introduced by , who named them after Yuri Manin. classified the Manin triples where g is a complex reductive Lie algebra. Manin triples and Lie bialgebras If (g, p, q) is a finite-dimensional Manin triple then p can be made into a Lie bialgebra by letting the cocommutator map p → p ⊗ p be dual to the map q ⊗ q → q (using the fact that the symmetric bilinear form on g identifies q with the dual of p). Conversely if p is a Lie bialgebra then one can construct a Manin triple from it by letting q be the dual of p and defining the commutator of p and q to make the bilinear form on g = p ⊕ q invariant. Examples Suppose that a is a complex semisimple Lie algebra with invariant symmetric bilinear form (,). Then there is a Manin triple (g,p,q) with g = a⊕a, with the scalar product on g given by ((w,x),(y,z)) = (w,y) – (x,z). The subalgebra p is the space of diagonal elements (x,x), and the subalgebra q is the space of elements (x,y) with x in a fixed Borel subalgebra containing a Cartan subalgebra h, y in the opposite Borel subalgebra, and where x and y have the same component in h. References Lie algebras
https://en.wikipedia.org/wiki/Robert%20James%20Blattner
Robert James Blattner (6 August 1931 – 13 June 2015) was a mathematics professor at UCLA working on harmonic analysis, representation theory, and geometric quantization, who introduced Blattner's conjecture. Born in Milwaukee, Blattner received his bachelor's degree from Harvard University in 1953 and his Ph.D. from the University of Chicago in 1957. He joined the UCLA mathematics department in 1957 and remained on the staff until his retirement as professor emeritus in 1992. Blattner was a visiting scholar at the Institute for Advanced Study in 1964–65. In 2012 he became a fellow of the American Mathematical Society. References 1931 births 2015 deaths 20th-century American mathematicians 21st-century American mathematicians Harvard University alumni University of Chicago alumni University of California, Los Angeles faculty Institute for Advanced Study visiting scholars Fellows of the American Mathematical Society
https://en.wikipedia.org/wiki/Andrea%20Bertozzi
Andrea Louise Bertozzi (born 1965) is an American mathematician. Her research interests are in non-linear partial differential equations and applied mathematics. Education and career She earned her bachelor's and master's degrees from Princeton University, followed by her PhD from Princeton in 1991; her dissertation was titled Existence, Uniqueness, and a Characterization of Solutions to the Contour Dynamics Equation. Prior to joining UCLA in 2003, Bertozzi was an L. E. Dickson Instructor at the University of Chicago, and then Professor of Mathematics and Physics at Duke University. She spent one year at Argonne National Laboratory as the Maria Goeppert-Mayer Distinguished Scholar. She is a member of the faculty of the University of California, Los Angeles, as a professor of mathematics (since 2003) and Mechanical and Aerospace Engineering (since 2018) and Director of Applied Mathematics (since 2005). She is a member of the California NanoSystems Institute. Contributions Bertozzi has contributed to many areas of applied mathematics, including the theory of swarming behavior, aggregation equations and their solution in general dimension, the theory of particle-laden flows in liquids with free surfaces, data analysis/image analysis at the micro and nano scales, and the mathematics of crime. Her earlier fundamental work in fluids led to novel applications in image processing, most notably image inpainting, swarming models, and data clustering on graphs. Bertozzi coauthored the book Vorticity and Incompressible Flow, which was published in 2000 and remains one of her most cited works. Bertozzi now has over 200 publications on Web of Science, covering a range of topics including fluid dynamics, image processing, social sciences, and cooperative motion. Bertozzi's publications include over 100 collaborators in a wide range of disciplines including Mathematics, Applied Mathematics, Statistics, Computer Science, Chemistry, Physics, Mechanical and Aerospace Engineering, Medicine, Anthropology, Economics, Politics, and Criminology. Between 2010 and 2020, Bertozzi has been granted multiple patents related to her research, which center on image inpainting, data fusion mapping estimation, and most recently, on determining fluid reservoir connectivity using nanowire probes. Bertozzi has developed numerous novel mathematical theories throughout her career. While a Dickson Instructor at Univ. of Chicago, she developed the mathematical theory of thin film equations, fourth order degenerate parabolic equations that are used to describe lubrication theory for coating flows. She has also worked with Jeffrey Brantingham and other colleagues to apply mathematics to the patterns of urban crime, research which was the cover feature in the March 2, 2010 issue of Proceedings of the National Academy of Sciences. Bertozzi also spoke about the mathematics of crime at the 2010 annual meeting of the American Association for the Advancement of Science. Since 2017, Bert