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https://en.wikipedia.org/wiki/List%20of%20Cultural%20Properties%20of%20Nichinan%2C%20Tottori
This list is of the Cultural Properties of Japan located within the town of Nichinan in Tottori Prefecture. Statistics As of 18 March 2010, 14 Properties have been designated and a further 2 Properties registered. † One Special Natural Monument (denoted with an asterisk, smaller text, and brackets) is included within the count of Natural Monuments. Designated Cultural Properties Registered Cultural Properties See also Cultural Properties of Japan Hiba-Dōgo-Taishaku Quasi-National Park References External links Outline of the Cultural Administration of Japan Cultural Properties of Tottori Prefecture Cultural Properties of Nichinan Nichinan, Tottori Lists of Cultural Properties of Japan
https://en.wikipedia.org/wiki/Brede%20Moe
Brede Mathias Moe (born 15 December 1991) is a Norwegian professional footballer who plays as a defender for Bodø/Glimt. Career statistics Club Honours Bodø/Glimt Eliteserien: 2020, 2021 References 1991 births Living people People from Flatanger Norwegian men's footballers Men's association football defenders Eliteserien players Norwegian First Division players Ranheim Fotball players FK Bodø/Glimt players Rosenborg BK players Footballers from Trøndelag
https://en.wikipedia.org/wiki/Michael%20Karlsen
Michael Karlsen (born 3 February 1990) is a Norwegian footballer who plays as a striker for Ranheim IL. Career statistics Club References 1990 births Living people Norwegian men's footballers Norway men's youth international footballers Rosenborg BK players Ranheim Fotball players IL Hødd players Brattvåg IL players Eliteserien players Norwegian First Division players Norwegian Second Division players Footballers from Trondheim Men's association football midfielders
https://en.wikipedia.org/wiki/B.%20V.%20Rajarama%20Bhat
B. V. Rajarama Bhat is an Indian mathematician specialising in operator theory. He is a Professor of Mathematics in Indian Statistical Institute, Bangalore. Professor Bhat obtained his MSc and PhD degrees from the Indian Statistical Institute, Kolkata. He was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in 2007, the highest science award in India, in the mathematical sciences category. Other awards/honours Young Scientist Award of Indian National Science Academy in 1997 B. M. Birla Science prize for the year 1998 Books authored Lectures on Operator Theory, (Editor jointly with G. Elliott and P. Fillmore), Fields Institute for Research in Mathematical Sciences Monograph Series, Vol. 13, Amer. Math. Soc. 323pp. (1999). Cocycles of CCR flows, Memoirs of the American Mathematical Society, 149, no. 709 (2001) References External links 20th-century Indian mathematicians Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science
https://en.wikipedia.org/wiki/Siva%20Athreya
Siva Ramachandran Athreya (born 1971) is an Indian probability theorist specialising in statistical physics and population biology. He graduated in mathematics from St Stephen's College, Delhi, went to ISI in Kolkata and Bangalore where he completed his master's, obtained his PhD degree from University of Washington in 1998 under the supervision of Krzysztof Burdzy. He was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in 2012, the highest science award in India, in the mathematical sciences category. References 1971 births Living people Indian statisticians 21st-century Indian mathematicians Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science
https://en.wikipedia.org/wiki/Angelescu
Angelescu may refer to: Constantin Angelescu (1870–1948), a Romanian politician Emil Angelescu, a Romanian bobsledder Angelescu polynomials, in mathematics, generalizations of the Laguerre polynomials introduced by Angelescu (1938) given by the generating function
https://en.wikipedia.org/wiki/Superkoora
Superkoora (Arabic: سوبر كورة) is a pan-Arab internet-based sports statistics portal that proved to be the most searched website in Google's 2008 Zeitgeist or annual report from Egypt. Superkoora was also the very first Arab website ever listed by Google. It is the largest statistics portal of its kind in the region and is fast becoming a sought-after data and information source for sport media. History The online statistics portal was launched in August 2007 with the web domain superkoora.com providing sports results and statistics from all over the world. Statistics Superkoora.com contains regional and international football data and information not available on any other website. This free and accurate information includes: comparisons, data and figures on players, clubs, coaches and matches. The site also contains a unique list of historic goal scorers for all FIFA World Cups. As a result, it is often utilized or its data by large media organizations including Al Jazeera Sport. Superkoora2022.com is the newest site launched ahead of the FIFA World Cup Qatar 2022 to cover sport in that country and has been referred to by, among others, the most popular newspaper in the Arab World, London-based Asharq Al-Awsat. Contributors to Superkoora's English site include author and former BBC sports reporter, Keir Radnedge, Steph Clark, sports journalist and blogger, Ben Lyttleton and Will Scott. Superkoora was appointed the official media partner of the 2011 Golden Foot Award in Monaco. Founder Egypt-born, Abdelaziz Younis Abuhamar is the founder of superkoora.com. He is a bilingual journalist with 20 years of experience in the field of sports media. External links Superkoora.com Superkoora 2022 Superkoora Statistics Site References 2007 establishments in Egypt Internet properties established in 2007 Egyptian sport websites Arabic-language websites Arab mass media Mass media in Cairo
https://en.wikipedia.org/wiki/Adam%20Marcus%20%28mathematician%29
Adam Wade Marcus (born 1979) is an American mathematician. He holds the Chair of Combinatorial Analysis in the Institute of Mathematics at the École Polytechnique Fédérale de Lausanne. The team of Marcus, Daniel Spielman and Nikhil Srivastava was awarded the Pólya Prize in 2014 for their resolution of the Kadison–Singer problem and later the Michael and Sheila Held Prize in 2021 for their solution to long-standing conjectures in the study of Ramanujan graphs. History Marcus grew up in Marietta, Georgia and was a boarding student at the Darlington School in Rome, Georgia. He attended the Washington University in St. Louis for his undergraduate degree, where he was a Compton Fellow. He then completed his doctoral studies under the supervision of Prasad Tetali at the Georgia Institute of Technology. Following his graduation in 2008, he spent four years as a Gibbs Assistant Professor in Applied Mathematics at Yale University. In 2012, Marcus cofounded Crisply, an analytics company in Boston, Massachusetts, where he served as chief scientist until 2015. After leaving Crisply, Marcus spent five years as an assistant professor in the mathematics department and program in applied and computational mathematics at Princeton University before moving to EPFL in 2020. He is an alumnus of the Hampshire College Summer Studies in Mathematics. Awards During 2003–2004, Marcus was a Fulbright scholar in Hungary. In 2008, he was awarded the inaugural Dénes König Prize in Discrete Mathematics from the Society for Industrial and Applied Mathematics for his work in solving the Stanley–Wilf conjecture. A team consisting of Marcus, Daniel Spielman, and Nikhil Srivastava was awarded the 2014 Pólya Prize for their resolution of the Kadison–Singer problem. He was an invited speaker at the 2014 International Congress of Mathematicians in Seoul, South Korea. The team of Marcus, Spielman, and Srivastava was also awarded the 2021 Michael and Sheila Held Prize for their work in resolving the Kadison–Singer problem and their solution to long-standing conjectures in the study of Ramanujan graphs. Publications . . . References External links 21st-century American mathematicians Washington University in St. Louis mathematicians Combinatorialists Academic staff of the École Polytechnique Fédérale de Lausanne 1979 births Living people Washington University in St. Louis alumni Darlington School alumni Fulbright alumni Georgia Tech alumni Yale University faculty Princeton University faculty
https://en.wikipedia.org/wiki/Kenneth%20Falconer%20%28mathematician%29
Kenneth John Falconer FRSE (born 25 January 1952) is a British mathematician working in mathematical analysis and in particular on fractal geometry. He is Regius Professor of Mathematics in the School of Mathematics and Statistics at the University of St Andrews. Research Falconer is known for his work on the mathematics of fractals and in particular sets and measures arising from iterated function systems, especially self-similar and self-affine sets. Closely related is his research on Hausdorff and other fractal dimensions. He formulated Falconer's conjecture on the dimension of distance sets and conceived the notion of a digital sundial. In combinatorial geometry he established a lower bound of 5 for the chromatic number of the plane in the Lebesgue measurable case. Education and career Falconer was educated at Kingston Grammar School, Kingston upon Thames and Corpus Christi College, Cambridge. He graduated in 1974 and completed his PhD in 1979 under the supervision of Hallard Croft. He was a research fellow at Corpus Christi College, Cambridge from 1977 to 1980 before moving to Bristol University. He was appointed Professor of Pure Mathematics at the University of St Andrews in 1993 and was head of the School of Mathematics and Statistics from 2001 to 2004. He served on the council of the London Mathematical Society from 2000 to 2009 including as publications secretary from 2006 to 2009. Recognition Falconer was elected a Fellow of the Royal Society of Edinburgh in 1998. In 2020 he was awarded the Shephard Prize of the London Mathematical Society. Personal life Falconer was born 25 January 1952 at Bearsted Memorial Maternity Hospital outside Hampton Court Palace. His recreational interests include long-distance walking and hill walking. He was chair of the Long Distance Walkers Association from 2000 to 2003 and editor of their journal Strider from 1987 to 1992 and 2007–12. In 2021 he was appointed a Vice President of the LDWA. He has twice climbed all the Munros as well as all the Corbetts. References Selected publications External links Personal web page 1952 births Living people 20th-century British mathematicians 21st-century British mathematicians Fellows of Corpus Christi College, Cambridge Alumni of Corpus Christi College, Cambridge Fellows of the Royal Society of Edinburgh Academics of the University of St Andrews People educated at Kingston Grammar School British geometers Functional analysts
https://en.wikipedia.org/wiki/Meanings%20of%20minor%20planet%20names%3A%20240001%E2%80%93241000
240001–240100 |-id=021 | 240021 Radzo || || Jozef Radzo (born 1949) is a teacher of mathematics and physics at Gymnázium A. Bernoláka secondary school in Senec, Slovakia, where he established modern physics and chemistry laboratories. From 1973 to 1993, he worked in Gymnázium Šamor{í}n, where he encouraged S. Kürti's interest in astronomy. || |-id=022 | 240022 Demitra || || Pavol Demitra (1974–2011), Slovak ice-hockey player || |} 240101–240200 |-bgcolor=#f2f2f2 | colspan=4 align=center | |} 240201–240300 |-bgcolor=#f2f2f2 | colspan=4 align=center | |} 240301–240400 |-id=364 | 240364 Kozmutza || || Flóra Kozmutza (1905–1995) was a Hungarian educator, psychologist and high school teacher. || |-id=381 | 240381 Emilchyne || || Yemilchyne Raion (translit. Emil'chyns'kyi), a district in northern Ukraine, birthplace of Baikonur engineer Vladimir Khilchenko (born 1931) and folk singer Nina Matviyenko (born 1947) || |} 240401–240500 |-bgcolor=#f2f2f2 | colspan=4 align=center | |} 240501–240600 |-bgcolor=#f2f2f2 | colspan=4 align=center | |} 240601–240700 |-id=697 | 240697 Gemenc || 2005 GC || Gemenc, a forest and the only remaining tidal area of the Danube in Hungary. || |} 240701–240800 |-id=757 | 240757 Farkasberci || || Bertalan "Berci" Farkas (born 1949), the first Hungarian cosmonaut and the first Esperantist in space. || |} 240801–240900 |-id=871 | 240871 MOSS || 2006 DA || The Morocco Oukaimeden Sky Survey (MOSS) is an international amateur sky survey established in 2011. The Swiss–French–Moroccan partnership uses a 0.5-meter remote telescope at the Oukaïmeden Observatory , located in the Moroccan High Atlas mountain range (Src, Src, Src). || |} 240901–241000 |-bgcolor=#f2f2f2 | colspan=4 align=center | |} References 240001-241000
https://en.wikipedia.org/wiki/Samuel%20Kyere%20%28footballer%2C%20born%201992%29
Samuel Kyere (born 6 August 1992) is a Ghanaian football (defender) player whose last known club was Asante Kotoko. Career statistics Club References 1992 births Living people Ghanaian men's footballers Men's association football defenders Berekum Chelsea F.C. players Shirak SC players Armenian Premier League players Ghanaian expatriate men's footballers Expatriate men's footballers in Armenia
https://en.wikipedia.org/wiki/OjAlgo
oj! Algorithms or ojAlgo, is an open source Java library for mathematics, linear algebra and optimisation. It was first released in 2003 and is 100% pure Java source code and free from external dependencies. Its feature set make it particularly suitable for use within the financial domain. Capabilities Linear algebra in Java "high performance" multi-threaded feature-complete linear algebra package. Optimisation (mathematical programming) including LP, QP and MIP solvers. Finance related code (certainly usable in other areas as well): Extensive set of tools to work with time series - CalendarDateSeries, CoordinationSet & PrimitiveTimeSeries. Random numbers and stochastic processes - even multi-dimensional such - and the ability to drive these to do things like Monte Carlo simulations. A collection of Modern Portfolio Theory related classes - FinancePortfolio and its subclasses the Markowitz and Black-Litterman model implementations. Ability to download data from Yahoo Finance and Google Finance. It requires Java 8 since version v38. As of version 44.0, the finance specific code has been moved to its own project/module named ojAlgo-finance. Usage example Example of singular value decomposition: SingularValue<Double> svd = SingularValueDecomposition.make(matA); svd.compute(matA); MatrixStore<Double> U = svd.getQ1(); MatrixStore<Double> S = svd.getD(); MatrixStore<Double> V = svd.getQ2(); Example of matrix multiplication: PrimitiveDenseStore result = FACTORY.makeZero(matA.getRowDim(), matB.getColDim()); result.fillByMultiplying(matA, matB); References Java (programming language) libraries
https://en.wikipedia.org/wiki/Efficient%20Java%20Matrix%20Library
Efficient Java Matrix Library (EJML) is a linear algebra library for manipulating real/complex/dense/sparse matrices. Its design goals are; 1) to be as computationally and memory efficient as possible for both small and large matrices, and 2) to be accessible to both novices and experts. These goals are accomplished by dynamically selecting the best algorithms to use at runtime, clean API, and multiple interfaces. EJML is free, written in 100% Java and has been released under an Apache v2.0 license. EJML has three distinct ways to interact with it: 1) Procedural, 2) SimpleMatrix, and 3) Equations. The procedural style provides all capabilities of EJML and almost complete control over matrix creation, speed, and specific algorithms. The SimpleMatrix style provides a simplified subset of the core capabilities in an easy to use flow-styled object-oriented API, inspired by JAMA. The Equations style provides a symbolic interface, similar in spirit to Matlab and other CAS, that provides a compact way of writing equations. Capabilities EJML provides the following capabilities for dense matrices. Basic Operators (addition, multiplication, ... ) Matrix Manipulation (extract, insert, combine, ... ) Linear Solvers (linear, least squares, incremental, ... ) Decompositions (LU, QR, Cholesky, SVD, Eigenvalue, ...) Matrix Features (rank, symmetric, definitiveness, ... ) Random Matrices (covariance, orthogonal, symmetric, ... ) Different Internal Formats (row-major, block) Unit Testing Usage examples Equation style Computing the Kalman gain: eq.process("K = P*H'*inv( H*P*H' + R )"); Procedural style Computing Kalman gain: mult(H, P, c); multTransB(c, H, S); addEquals(S, R); if (!invert(S, S_inv)) throw new RuntimeException("Invert failed"); multTransA(H, S_inv, d); mult(P, d, K); SimpleMatrix style Example of singular value decomposition (SVD): SimpleSVD s = matA.svd(); SimpleMatrix U = s.getU(); SimpleMatrix W = s.getW(); SimpleMatrix V = s.getV(); Example of matrix multiplication: SimpleMatrix result = matA.mult(matB); DecompositionFactory Use of a DecompositionFactory to compute a Singular Value Decomposition with a Dense Double Row Major matrix (DDRM): SingularValueDecomposition_F64<DenseMatrix64F> svd = DecompositionFactory_DDRM.svd(true, true, true); if (!DecompositionFactory.decomposeSafe(svd, matA)) throw new DetectedException("Decomposition failed."); DenseMatrix64F U = svd.getU(null, false); DenseMatrix64F S = svd.getW(null); DenseMatrix64F V = svd.getV(null, false); Example of matrix multiplication: CommonOps_DDRM.mult(matA, matB, result); See also List of numerical libraries References External links Efficient Java Matrix Library (EJML) homepage Numerical libraries
https://en.wikipedia.org/wiki/Battle%20of%20Oslo%20%28football%29
The Battle of Oslo () or the Oslo Derby is the name given to football matches between Lyn Fotball and Vålerenga Fotball, both of them from Oslo, the capital of Norway. Official statistics Official statistics of honours won by Lyn and Vålerenga, as treated by the Football Association of Norway (NFF). Matches list League 1922–1937; 1946–1947 Note: The host of the matches between 1922 and 1937 and between 1946 and 1947 was unknown 1938–1939; 1949–present • Total: Lyn 33 wins, 16 draws, Vålerenga 20 wins. Cup • Total: Vålerenga 4, Lyn 1. Head-to-head Statistics The head-to-head statistics shows the results of Lyn and Vålerenga, when they played against each other in the Norwegian League or Cup. Ranking The head-to-head ranking table shows the results of Lyn and Vålerenga, when they played in the same league. • Total: Vålerenga 14 times higher, Lyn 11 times higher. Notes:1 The ranking table does not include the tables of Kretsserien, Østlandsligaen and the 1939–40 season of Norgesserien which was interrupted due to the World War II. 2 Both clubs played in the second tier. 3 In the 1960–61 season Vålerenga defeated Lyn in the bronze final. Records and statistics First competitive meeting: 4–1 win for Lyn, Kretsserien, 5 March 1922 First league meeting: Lyn 1–1 Vålerenga, Norgesserien, 8 August 1938 First Norwegian Cup meeting: Lyn 4–0 Vålerenga, semi-final, 1 October 1967 First away victory for Lyn: 3–0 vs Vålerenga, Norgesserien, 25 September 1938 First away victory for Vålerenga: 3–2 vs Lyn, Norgesserien, 4 September 1949 Highest scoring game: Vålerenga 6–4 Lyn, Hovedserien bronze final, 14 June 1961 Largest winning margin (Lyn): 7 goals – 7–0 vs Vålerenga, Kretsserien, 4 June 1924 Largest winning margin (Vålerenga): 5 goals – 6–1 vs Lyn, Hovedserien, 19 August 1962 Most consecutive wins (Vålerenga): 6, 4 September 1949 – 20 September 1958 Most consecutive wins (Lyn): 5, 16 August 1934 – 24 August 1937 Longest undefeated run (Lyn): 15 – 10 wins and 5 draws over 11 May 2002 to 21 May 2009 Longest undefeated run (Vålerenga): 9 – 7 wins and 2 draws over 22 August 1953 to 19 August 1962 Most games played against each other in a season: 3, in the 1967 season Doubles Lyn have achieved the double in six seasons (most recently in the 2008 season), while Vålerenga have managed to win both league matches in four seasons (most recently in the 1981 season). Lyn doubles Vålerenga doubles Top scorers This is the list of top scoring players in the derby (since 2002). 3 goals Odion Ighalo Bengt Sæternes 2 goals Henrik Dahl Christian Grindheim David Hanssen Kristofer Hæstad Espen Hoff Kim Holmen Peter Markstedt Lucas Pratto Luton Shelton Ole Bjørn Sundgot Players in both teams Women's football Official statistics Official statistics of honours won by Lyn and Vålerenga, as treated by the Football Association of Norway (NFF). Matches list League Cup Head-to-head Statistics The head-to-head statistics shows the resu
https://en.wikipedia.org/wiki/NCAA%20National%20Collegiate%20women%27s%20ice%20hockey%20tournament%20all-time%20team%20records
The following is a list of team records and statistics from those that have made appearances in the National Collegiate Women's Ice Hockey Championship. The championship has existed since the 2000–2001 season and groups include the university teams of Divisions I and II of the NCAA. These statistics are updated through the 2016 tournament. Tournament format history 2001–2004 4 teams (single-elimination) 2005–2021 8 teams (single-elimination) 2022–Present 11 teams (single-elimination) Most Championships Won By State The following list is of championships won ranked by state. Consolation game discontinued after 2005. Championships by conference References External links NCAA Division I women ice hockey page NCAA Ice Hockey, Division I Women's Records College women's ice hockey in the United States
https://en.wikipedia.org/wiki/Whish
Whish is a surname, and may refer to: C. M. Whish (1794–1833), English civil servant of the East India Company and author of the first western paper on the Kerala school of astronomy and mathematics J. L. Whish, his brother and also an English civil servant of the East India Company David Whish-Wilson (born 1966), Australian author Claudius Buchanan Whish (1827-1890), Australian sugar-planter Peter Whish-Wilson (born 1968), Australian politician See also Wish (disambiguation)
https://en.wikipedia.org/wiki/2009%20FIFA%20Confederations%20Cup%20statistics
These are the statistics for the 2009 FIFA Confederations Cup, an eight-team tournament running from 14 June 2009 through 28 June 2009. The tournament took place in South Africa. Goalscorers 5 goals Luís Fabiano 3 goals Fernando Torres David Villa Clint Dempsey 2 goals Kaká Mohamed Zidan Katlego Mphela Bernard Parker Giuseppe Rossi Dani Güiza Landon Donovan 1 goal Dani Alves Felipe Melo Juan Lúcio Maicon Robinho Homos Mohamed Shawky Daniele De Rossi Xabi Alonso Cesc Fàbregas Fernando Llorente Jozy Altidore Michael Bradley Charlie Davies Own goal Andrea Dossena (for Brazil) Source: FIFA Assists 3 assists Elano Maicon Mohamed Aboutrika Joan Capdevila 2 assists Kaká Tsepo Masilela Cesc Fàbregas Jonathan Spector 1 assist Twelve players Source: FIFA Scoring References External links 2009 FIFA Confederations Cup at FIFA.com Statistics
https://en.wikipedia.org/wiki/B%E1%BA%BFn%20Ngh%C3%A9
{ "type": "FeatureCollection", "features": [ { "type": "Feature", "properties": {}, "geometry": { "type": "Point", "coordinates": [ 10.7822, 106.7028 ] } } ] } Bến Nghé is a historic area of Saigon, Vietnam, which is today a ward of District 1. The area was developed in the 17th century. At the time the French Empire arrived in Saigon, Bến Nghé was a conglomeration of 40 villages along the Bến Nghé River. Notable buildings in the ward include the 1935 Jamia Al Muslimin Mosque at 66 Đông Du Street, also known as the Saigon Central Mosque, oldest and best known of the twelve mosques in Ho Chi Minh City. References Populated places in Ho Chi Minh City
https://en.wikipedia.org/wiki/Thomas%20Streicher
Thomas Streicher (born 1958) is an Austrian mathematician who is a Professor of Mathematics at Technische Universität Darmstadt. He received his PhD in 1988 from the University of Passau with advisor Manfred Broy. Work His research interests include categorical logic, domain theory and Martin-Löf type theory. In joint work with he constructed a model for intensional Martin-Löf type theory where identity types are interpreted as groupoids. This was the first model with non-trivial identity types, i.e. other than sets. Based on this work other models with non-trivial identity types were studied, including homotopy type theory which has been proposed as a foundation for mathematics in Vladimir Voevodsky's research program Univalent Foundations of Mathematics. Together with Martin Hofmann he received the 2014 LICS Test-of-Time Award for the paper: The groupoid model refutes uniqueness of identity proofs. Bibliography T. Streicher (1991), Semantics of Type Theory: Correctness, Completeness, and Independence Results, Birkhäuser Boston. M. Hofmann and T. Streicher (1996), The groupoid interpretation of type theory, in Sambin, Giovanni (ed.) et al., Twenty-five years of constructive type theory. Proceedings of a congress, Venice, Italy, October 19–21, 1995. T. Streicher (2006), Domain-theoretic Foundations of Functional Programming, World Scientific Pub Co Inc. References External links Official website at Technische Universität Darmstadt 20th-century German mathematicians Living people Academic staff of Technische Universität Darmstadt University of Passau alumni 21st-century German mathematicians 1958 births
https://en.wikipedia.org/wiki/N%20cell
N cell may refer to: N battery -cell (mathematics) The unit cube of dimension
https://en.wikipedia.org/wiki/Marie-Fran%C3%A7oise%20Roy
Marie-Françoise Roy (born 28 April 1950 in Paris) is a French mathematician noted for her work in real algebraic geometry. She has been Professor of Mathematics at the University of Rennes 1 since 1985 and in 2009 was made a Chevalier of the French Legion of Honour. In 2004, she received an Irène Joliot-Curie Prize. Research Roy works in real algebraic geometry in particular real spectra and, most recently, in complexity of algorithms in real algebraic geometry and also the applications. Education and career Marie-Françoise Roy got her education at École Normale Supérieure de jeunes filles and was an assistant professor at Université Paris Nord during 1973. She received her PhD at Université Paris Nord in 1980, supervised by Jean Bénabou. From 1981 she spent two years at Abdou Moumouni University in Niger. In 1985 she became a professor at University of Rennes 1 in Rennes, France. Service Roy was president of Société Mathématique de France from 2004 to 2007. In 1986, Roy was one of the founders of European Women in Mathematics (EWM), and was the convenor (president) of EWM 2009–2013. In 1987 she co-founded the French organization for women in mathematics, Femmes et Mathématiques, and became the organization's first president. Roy is scientific officer for Sub-Saharan Africa in Centre International de Mathématiques Pures et Appliquées, CIMPA]. Roy is president of Association d'Echanges Culturels Cesson Dankassari (Tarbiyya-Tatali) an organization working for joint activities in a commune Dan-Cassari in Niger and the French commune Cesson-Sévigné. Selected publications with Saugata Basu, Richard Pollack: Algorithms in real algebraic geometry. Springer 2003.pdf-file freely available on author's homepage with Jacek Bochnak, Michel Coste: Real algebraic geometry. 2.Edition, Springer, Ergebnisse der Mathematik Bd. 36, 1998 (first in French 1. Edition 1987). Three Problems in real algebraic geometry and their descendants. In: Engquist, Schmid: Mathematics unlimited- 2001 and beyond. Springer Verlag 2000, S. 991 (Hilberts 17th Problem, Algorithms, Topology of real algebraic varieties). Géométrie algébrique réelle. In: Jean-Paul Pier (Hrsg.): Development of Mathematics 1950-2000. Birkhäuser 2000. Introduction a la geometrie algebrique reelle, Cahiers Sem. Hist. Math., 1991, Online References External links Homepage International Center Scientific Research Homepage in Rennes 20th-century French mathematicians 21st-century French mathematicians 1950 births Living people French women mathematicians University of Paris alumni Algebraic geometers 20th-century women mathematicians 21st-century women mathematicians 20th-century French women 21st-century French women
https://en.wikipedia.org/wiki/2007%E2%80%9308%20Genoa%20CFC%20season
The 2007–08 Genoa C.F.C. season is the 1st since the promotion from the 2006-07 Serie B season. This article lists its season results, transfers, and statistics. Current squad Main transfers and loans Summer 2007 In Out Winter 2007–08 In Out Competitions Serie A League table Matches Goal scorers 19 goals Marco Borriello 4 goals Giuseppe Sculli 4 goals Julio César de León 3 goals Marco Di Vaio Luciano Figueroa Abdoulay Konko 2 goals Marco Rossi 1 goal Alessandro Lucarelli Matías Masiero Omar Milanetto Andrea Masiello Danilo References External links http://en.eufo.de/ Genoa CFC seasons Genoa
https://en.wikipedia.org/wiki/Orders%20of%20magnitude%20%28probability%29
This page lists events in order of increasing probability, grouped by orders of magnitude. These probabilities were calculated given assumptions detailed in the relevant articles and references. For example, the probabilities of obtaining the different poker hands assume that the cards are dealt fairly. References Probability Probability
https://en.wikipedia.org/wiki/2012%E2%80%9313%20Genoa%20CFC%20season
The 2012–13 Genoa C.F.C. season is the club's sixth consecutive Serie A season of the football. This article lists its season results, transfers and statistics. Current squad Main transfers and loans Summer 2012 In Out Winter 2012–13 In Out Competitions Serie A League table Matches Appearances and goals |- ! colspan="10" style="background:#dcdcdc; text-align:center"| Goalkeepers |- ! colspan="10" style="background:#dcdcdc; text-align:center"| Defenders |- ! colspan="10" style="background:#dcdcdc; text-align:center"| Midfielders |- ! colspan="10" style="background:#dcdcdc; text-align:center"| Forwards |- ! colspan="10" style="background:#dcdcdc; text-align:center"| Players transferred out during the season Goal scorers 12 goals Marco Borriello 5 goals Ciro Immobile 4 goals Boško Janković Andrea Bertolacci 3 goals Juraj Kucka 2 goals Antonio Floro Flores 1 goal Marco Rigoni Daniele Portanova Alexander Merkel Andreas Granqvist Matuzalém Luca Antonelli Eros Pisano Said Ahmed Said References External links http://eufo.de Genoa CFC seasons Genoa
https://en.wikipedia.org/wiki/Helmy%20Toulan
Helmy Toulan () (born 30 November 1949) is an Egyptian football coach and former player with Zamalek SC. He last coached Ceramica Cleopatra. Managerial statistics Honours As a player Zamalek SC Egypt Cup: 1974–75 As a manager Zamalek SC Egypt Cup: 2012–13 References External links Playersglobe.net 1949 births Living people Egyptian men's footballers Men's association football midfielders Egyptian Premier League players Zamalek SC players Egyptian football managers Zamalek SC managers Haras El Hodoud SC managers Al Masry SC managers Al-Ahly SC (Benghazi) managers Petrojet SC managers Tala'ea El Gaish SC managers Smouha SC managers Al Ittihad Alexandria Club managers ENPPI SC managers Egyptian expatriate football managers Expatriate football managers in the United Arab Emirates Egyptian expatriate sportspeople in the United Arab Emirates Expatriate football managers in Libya Egyptian expatriate sportspeople in Libya
https://en.wikipedia.org/wiki/Lie%20group%20action
In differential geometry, a Lie group action is a group action adapted to the smooth setting: G is a Lie group, M is a smooth manifold, and the action map is differentiable. Definition and first properties Let be a (left) group action of a Lie group G on a smooth manifold M; it is called a Lie group action (or smooth action) if the map is differentiable. Equivalently, a Lie group action of G on M consists of a Lie group homomorphism . A smooth manifold endowed with a Lie group action is also called a G-manifold. The fact that the action map is smooth has a couple of immediate consequences: the stabilizers of the group action are closed, thus are Lie subgroups of G the orbits of the group action are immersed submanifolds. Forgetting the smooth structure, a Lie group action is a particular case of a continuous group action. Examples For every Lie group G, the following are Lie group actions: the trivial action of G on any manifold the action of G on itself by left multiplication, right multiplication or conjugation the action of any Lie subgroup on G by left multiplication, right multiplication or conjugation the adjoint action of G on its Lie algebra . Other examples of Lie group actions include: the action of on M given by the flow of any complete vector field the actions of the general linear group and of its Lie subgroups on by matrix multiplication more generally, any Lie group representation on a vector space any Hamiltonian group action on a symplectic manifold the transitive action underlying any homogeneous space more generally, the group action underlying any principal bundle Infinitesimal Lie algebra action Following the spirit of the Lie group-Lie algebra correspondence, Lie group actions can also be studied from the infinitesimal point of view. Indeed, any Lie group action induces an infinitesimal Lie algebra action on M, i.e. a Lie algebra homomorphism . Intuitively, this is obtained by differentiating at the identity the Lie group homomorphism , and interpreting the set of vector fields as the Lie algebra of the (infinite-dimensional) Lie group . More precisely, fixing any , the orbit map is differentiable and one can compute its differential at the identity . If , then its image under is a tangent vector at x, and varying x one obtains a vector field on M. The minus of this vector field, denoted by , is also called the fundamental vector field associated with X (the minus sign ensures that is a Lie algebra homomorphism). Conversely, by Lie–Palais theorem, any abstract infinitesimal action of a (finite-dimensional) Lie algebra on a compact manifold can be integrated to a Lie group action. Moreover, an infinitesimal Lie algebra action is injective if and only if the corresponding global Lie group action is free. This follows from the fact that the kernel of is the Lie algebra of the stabilizer . On the other hand, in general not surjective. For instance, let be a principal G-bundle: the image
https://en.wikipedia.org/wiki/2013%E2%80%9314%20Colo-Colo%20season
The 2013-14 season was Club Social y Deportivo Colo-Colo's 83rd season in the Chilean Primera División. This article shows player statistics and all official matches that the club played during the 2013–14 season, which covers the period from 1 July 2013 to 30 June 2014. Competitions Torneo Apertura League table Results summary Result round by round Matches Torneo Clausura League table Results summary Result round by round Matches Copa Chile Group stage Knockout stage Copa Sudamericana First round Second round Squad Coaching staff Winter Transfers In Out References Colo-Colo seasons Colo-Colo
https://en.wikipedia.org/wiki/Richard%20Elman%20%28mathematician%29
Richard Steven Elman (born 21 March 1945) is an American mathematician at the University of California, Los Angeles, known for his work in algebra. He received his Ph.D. at the University of California, Berkeley in 1972, under the supervision of Tsit Yuen Lam. He is a fellow of the American Mathematical Society. Among his collaborators are Nikita Karpenko and Alexander Merkurjev. Selected publications as editor with Murray M. Schacher and Veeravalli S. Varadarajan: with Nikita Karpenko and Alexander Merkurjev: References External links Faculty page at UCLA Photo at MFO 1945 births Living people 20th-century American mathematicians 21st-century American mathematicians University of California, Los Angeles faculty Fellows of the American Mathematical Society UC Berkeley College of Letters and Science alumni
https://en.wikipedia.org/wiki/Slice%20theorem%20%28differential%20geometry%29
In differential geometry, the slice theorem states: given a manifold M on which a Lie group G acts as diffeomorphisms, for any x in M, the map extends to an invariant neighborhood of (viewed as a zero section) in so that it defines an equivariant diffeomorphism from the neighborhood to its image, which contains the orbit of x. The important application of the theorem is a proof of the fact that the quotient admits a manifold structure when G is compact and the action is free. In algebraic geometry, there is an analog of the slice theorem; it is called Luna's slice theorem. Idea of proof when G is compact Since G is compact, there exists an invariant metric; i.e., G acts as isometries. One then adapts the usual proof of the existence of a tubular neighborhood using this metric. See also Luna's slice theorem, an analogous result for reductive algebraic group actions on algebraic varieties References External links On a proof of the existence of tubular neighborhoods Theorems in differential geometry
https://en.wikipedia.org/wiki/Differential%20graded%20Lie%20algebra
In mathematics, in particular abstract algebra and topology, a differential graded Lie algebra (or dg Lie algebra, or dgla) is a graded vector space with added Lie algebra and chain complex structures that are compatible. Such objects have applications in deformation theory and rational homotopy theory. Definition A differential graded Lie algebra is a graded vector space over a field of characteristic zero together with a bilinear map and a differential satisfying the graded Jacobi identity: and the graded Leibniz rule: for any homogeneous elements x, y and z in L. Notice here that the differential lowers the degree and so this differential graded Lie algebra is considered to be homologically graded. If instead the differential raised degree the differential graded Lie algebra is said to be cohomologically graded (usually to reinforce this point the grading is written in superscript: ). The choice of cohomological grading usually depends upon personal preference or the situation as they are equivalent: a homologically graded space can be made into a cohomological one via setting . Alternative equivalent definitions of a differential graded Lie algebra include: a Lie algebra object internal to the category of chain complexes; a strict -algebra. A morphism of differential graded Lie algebras is a graded linear map that commutes with the bracket and the differential, i.e., and . Differential graded Lie algebras and their morphisms define a category. Products and coproducts The product of two differential graded Lie algebras, , is defined as follows: take the direct sum of the two graded vector spaces , and equip it with the bracket and differential . The coproduct of two differential graded Lie algebras, , is often called the free product. It is defined as the free graded Lie algebra on the two underlying vector spaces with the unique differential extending the two original ones modulo the relations present in either of the two original Lie algebras. Connection to deformation theory The main application is to the deformation theory over fields of characteristic zero (in particular over the complex numbers.) The idea goes back to Daniel Quillen's work on rational homotopy theory. One way to formulate this thesis (due to Vladimir Drinfeld, Boris Feigin, Pierre Deligne, Maxim Kontsevich, and others) might be: Any reasonable formal deformation problem in characteristic zero can be described by Maurer–Cartan elements of an appropriate differential graded Lie algebra. A Maurer-Cartan element is a degree −1 element, , that is a solution to the Maurer–Cartan equation: See also Differential graded algebra (DGA) Simplicial Lie algebra Homotopy Lie algebra References Further reading Jacob Lurie, Formal moduli problems, section 2.1 External links Differential algebra Lie algebras
https://en.wikipedia.org/wiki/DreamBox%20Learning
DreamBox Learning is an American online software provider that focuses on mathematics education at the elementary and middle school level. It provides pre-kindergarten through 8th-grade students with over 2,000 lessons presented as animated adventures, games, and challenges. In August 2023, it was announced that the company would be acquired by Discovery Education, a Charlotte-based education technology company backed by Clearlake Capital Group, for an undisclosed amount. On October 12, Discovery Education completed the purchase of DreamBox Learning. History In 2006, DreamBox Learning was founded in Bellevue, Washington by the CEO and serial entrepreneur Lou Gray, and former Microsoft employee Ben Slivka. In 2010, DreamBox Learning was acquired by the Charter School Growth Fund. The acquisition was sponsored by Netflix CEO Reed Hastings through a program-related investment. Jessie Woolley-Wilson became president and CEO of DreamBox Learning shortly after the acquisition. The software was designed for students outside the classroom to augment their mathematics education and school districts seeking to enhance their mathematics curriculum. In 2012, the firm offered free trial licensing of lessons aligned with the Common Core State Standards Initiative to all schools within the United States. The company released a free iOS app, DreamBox Math Learning program, in 2013. In 2014, the firm launched its Adaptive Math Curriculum for students in grades six through eight, with topics including basic functions, geometry, single-variable algebra, and ratios. Also in 2014, the International Society for Technology Education reported that DreamBox added the Spanish language support to its adaptive math software for students in grades K-8. In 2016, the company updated its K-8 math curriculum with the ability to create custom assignments for individual students. Funding DreamBox has raised money through at least the following funding rounds. US$7.1M Seed, October 2007 US$11M Series A, December 2011 – three investors: Reed Hastings, Kleiner Perkins, and GSV Capital. US$14.5M Series A, December 2013 – led by Reed Hastings and John Doerr. US$10M Series B, 2015 – led by Owl Ventures. US$130M Series C, July 2018 US$210M Series D, May 2023. DreamBox Learning is partnered with the education startup Clever Inc. In 2016, The Center for Education Policy Research at Harvard University performed a study that found a positive correlation between using DreamBox's adaptive learning and test scores, but could not state for certain that this was the result of using the computer program, despite attempting to control for student motivation or quality of instruction. References 2023 mergers and acquisitions Education companies of the United States Software companies of the United States Companies based in Bellevue, Washington Software companies established in 2006
https://en.wikipedia.org/wiki/Meanings%20of%20minor%20planet%20names%3A%20343001%E2%80%93344000
343001–343100 |-id=057 | 343057 Lucaravenni || || Luca Ravenni (1968–2015) was a software analyst and an amateur astronomer. In 1997 he graduated in mathematics with a thesis on gravity-assisted trajectories for space missions. He collaborated with the Torre Luciana Observatory. Name suggested by the Astronomical Observatory of the University of Siena. || |} 343101–343200 |-id=134 | 343134 Bizet || || Georges Bizet (1838 - 1875) was a French composer of the Romantic era. Bizet achieved few successes before his final work, Carmen, which has become one of the most popular and frequently performed works in the entire opera repertoire. || |-id=157 | 343157 Mindaugas || || Mindaugas (1200–1263), the first known Grand Duke of Lithuania and the King of Lithuania. || |-id=158 | 343158 Marsyas || || Marsyas, a Phrygian Satyr dared oppose Apollo in a musical duel. Marsyas lost when he could not play his flute upside-down. For his hubris he was tied to a tree, flayed, his blood turned into a stream. Marsyas is so named for its unusual retrograde orbit, that which opposes the motion of most solar system objects, Apollos included. || |} 343201–343300 |-id=230 | 343230 Corsini || || Enrico Maria Corsini (born 1969) is an astronomer and professor of astrophysics at Padua University in Italy. || |} 343301–343400 |-id=322 | 343322 Tomskuniver || 2010 CK || Tomsk State University is a recognized center of education and science. Founded on 1878 May 28 by a decree of Russian Emperor Alexander II, it was the first university in the Asian part of Russia. || |} 343401–343500 |-id=444 | 343444 Halluzinelle || || "Analoge Halluzinelle", a fictional female robot hologram in the satirical German science fiction TV-series Ijon Tichy: Space Pilot. The role is played by the actress Nora Tschirner. The story is based on The Star Diaries by Stanisław Lem. || |} 343501–343600 |-id=587 | 343587 Mamuna || || Nikolai Vladimirovich Mamuna (1956–2016) was an astronomer, teacher and leading lecturer of the Moscow Planetarium. He was artistic director of the Maximachev Planetarium, the author of a number of books and many journal publications, a science fiction writer, a radio and a TV host. || |} 343601–343700 |-id=664 | 343664 Nataliemainzer || || Natalie Mainzer (born 1978) is an American nurse who has cared for many patients suffering from COVID-19 during the global pandemic. || |} 343701–343800 |-id=743 | 343743 Kjurkchieva || || Diana Kjurkchieva (born 1952) is a professor in astronomy at the University of Shumen, Bulgaria and current President of the Bulgarian Astronomical Union. She works on the observation and modeling of variable stars, exoplanets and is the leading popularizer of astronomy science in Bulgaria. Name suggested by S. Ibryamov. || |} 343801–343900 |-bgcolor=#f2f2f2 | colspan=4 align=center | |} 343901–344000 |-id=000 | 344000 Astropolis || || The Kiev Club Astropolis, the largest association of amateur astronom
https://en.wikipedia.org/wiki/UEFA%20Women%27s%20Euro%202013%20statistics
These are the statistics for the UEFA Women's Euro 2013, which took place in Sweden. Goalscorers 5 goals Lotta Schelin 3 goals Nilla Fischer 2 goals Mia Brogaard Mariann Gajhede Knudsen Marie-Laure Delie Eugénie Le Sommer Louisa Nécib Wendie Renard Célia Okoyino da Mbabi Melania Gabbiadini Solveig Gulbrandsen Verónica Boquete Jennifer Hermoso Josefine Öqvist 1 goal Johanna Rasmussen Eniola Aluko Laura Bassett Toni Duggan Annica Sjölund Simone Laudehr Lena Lotzen Dzsenifer Marozsán Anja Mittag Dagný Brynjarsdóttir Margrét Lára Viðarsdóttir Ilaria Mauro Marit Fiane Christensen Ada Hegerberg Kristine Wigdahl Hegland Ingvild Isaksen Nelli Korovkina Elena Morozova Elena Terekhova Alexia Putellas Kosovare Asllani Marie Hammarström Own goal Raffaella Manieri (playing against Sweden) Irene Paredes (playing against Norway) Assists 4 assists Kosovare Asllani 2 assists Eugénie Le Sommer Louisa Nécib Adriana Martín Lotta Schelin Sara Thunebro 1 assist Julie Rydahl Bukh Katrine Pedersen Anita Asante Jill Scott Annika Kukkonen Élodie Thomis Fatmire Bajramaj Leonie Maier Dzsenifer Marozsán Anja Mittag Célia Okoyino da Mbabi Hallbera Guðný Gísladóttir Raffaella Manieri Patrizia Panico Kristine Hegland Ingrid Hjelmseth Ingvild Stensland Nelli Korovkina Elena Terekhova Sonia Bermúdez Verónica Boquete Lisa Dahlkvist Marie Hammarström Sofia Jakobsson Therese Sjögran Scoring Total number of matches played: 25 Total number of goals scored: 56 Average goals per match: 2.24 Total number of braces: 4 – Lotta Schelin for Sweden against Finland and Iceland, Delie for France against Russia, Okoyino da Mbabi for Germany against Iceland Total number of hat-tricks: 0 Total number of penalty kicks awarded: 6 Total number of penalty kicks scored: 2 – Margrét Lára Viðarsdóttir for Iceland against Norway, Louisa Nécib for France against Denmark Total number of penalty kicks missed: 4 – Lotta Schelin for Sweden against Denmark, Kosovare Asllani for Sweden against Denmark, Trine Rønning for Norway against Germany, Solveig Gulbrandsen for Norway against Germany Most goals scored by a team: 13 – Sweden Most goals scored by an individual: 5 – Lotta Schelin Most assists given by an individual: 4 – Kosovare Asllani Fewest goals scored by a team: 0 – Netherlands Fastest goal in a match from kickoff: 3rd minute – Marie Hammarström for Sweden against Iceland, Marit Fiane Christensen for Norway against Denmark Latest goal in a match without extra time: 90+3rd minute – Alexia Putellas for Spain against England, Jennifer Hermoso for Spain against Norway Stadiums Overall attendance: 216,888 Average attendance per match: 8,676 Highest attendance: 41,301 – Germany (1–0) Norway Lowest attendance: 2,157 – Russia (1–1) Spain Discipline Total number of yellow cards: 48 Average number of yellow cards per game: 1.92 Total number of red cards: 0 Average number of red cards per game: 0 Most fouls co
https://en.wikipedia.org/wiki/Oblate%20spheroidal%20wave%20function
In applied mathematics, oblate spheroidal wave functions (like also prolate spheroidal wave functions and other related functions) are involved in the solution of the Helmholtz equation in oblate spheroidal coordinates. When solving this equation, , by the method of separation of variables, , with: the solution can be written as the product of a radial spheroidal wave function and an angular spheroidal wave function by . Here , with being the interfocal length of the elliptical cross section of the oblate spheroid. The radial wave function satisfies the linear ordinary differential equation: . The angular wave function satisfies the differential equation: . It is the same differential equation as in the case of the radial wave function. However, the range of the radial coordinate is different from that of the angular coordinate . The eigenvalue of this Sturm–Liouville problem is fixed by the requirement that be finite for . For these two differential equations reduce to the equations satisfied by the associated Legendre polynomials. For , the angular spheroidal wave functions can be expanded as a series of Legendre functions. Such expansions have been considered by Müller. The differential equations given above for the oblate radial and angular wave functions can be obtained from the corresponding equations for the prolate spheroidal wave functions by the substitution of for and for . The notation for the oblate spheroidal functions reflects this relationship. There are different normalization schemes for spheroidal functions. A table of the different schemes can be found in Abramowitz and Stegun. Abramowitz and Stegun (and the present article) follow the notation of Flammer. Originally, the spheroidal wave functions were introduced by C. Niven, which lead to a Helmholtz equation in spheroidal coordinates. Monographs tying together many aspects of the theory of spheroidal wave functions were written by Strutt, Stratton et al., Meixner and Schafke, and Flammer. Flammer provided a thorough discussion of the calculation of the eigenvalues, angular wavefunctions, and radial wavefunctions for both the oblate and the prolate case. Computer programs for this purpose have been developed by many, including Van Buren et al., King and Van Buren, Baier et al., Zhang and Jin, and Thompson. Van Buren has recently developed new methods for calculating oblate spheroidal wave functions that extend the ability to obtain numerical values to extremely wide parameter ranges. These results are based on earlier work on prolate spheroidal wave functions. Fortran source code that combines the new results with traditional methods is available at http://www.mathieuandspheroidalwavefunctions.com. Tables of numerical values of oblate spheroidal wave functions are given in Flammer, Hanish et al., and Van Buren et al. Asymptotic expansions of angular oblate spheroidal wave functions for large values of have been derived by Müller., also similarly
https://en.wikipedia.org/wiki/SegReg
In statistics and data analysis, the application software SegReg is a free and user-friendly tool for linear segmented regression analysis to determine the breakpoint where the relation between the dependent variable and the independent variable changes abruptly. Features SegReg permits the introduction of one or two independent variables. When two variables are used, it first determines the relation between the dependent variable and the most influential independent variable, where after it finds the relation between the residuals and the second independent variable. Residuals are the deviations of observed values of the dependent variable from the values obtained by segmented regression on the first independent variable. The breakpoint is found numerically by adopting a series tentative breakpoints and performing a linear regression at both sides of them. The tentative breakpoint that provides the largest coefficient of determination (as a parameter for the fit of the regression lines to the observed data values) is selected as the true breakpoint. To assure that the lines at both sides of the breakpoint intersect each other exactly at the breakpoint, SegReg employs two methods and selects the method giving the best fit. SegReg recognizes many types of relations and selects the ultimate type on the basis of statistical criteria like the significance of the regression coefficients. The SegReg output provides statistical confidence belts of the regression lines and a confidence block for the breakpoint. The confidence level can be selected as 90%, 95% and 98% of certainty. To complete the confidence statements, SegReg provides an analysis of variance and an Anova table. During the input phase, the user can indicate a preference for or an exclusion of a certain type. The preference for a certain type is only accepted when it is statistically significant, even when the significance of another type is higher. ILRI provides examples of application to magnitudes like crop yield, watertable depth, and soil salinity. A list of publications in which SegReg is used can be consulted. Equations When only one independent variable is present, the results may look like: X < BP   ==>   Y = A1.X + B1 + RY X > BP   ==>   Y = A2.X + B2 + RY where BP is the breakpoint, Y is the dependent variable, X the independent variable, A the regression coefficient, B the regression constant, and RY the residual of Y. When two independent variables are present, the results may look like: X < BPX   ==>   Y = A1.X + B1 + RY X > BPX   ==>   Y = A2.X + B2 + RY Z < BPZ   ==>   RY = C1.Z + D1 Z > BPZ   ==>   RY = C2.Z + D2 where, additionally, BPX is BP of X, BPZ is BP of Z, Z is the second independent variable, C is the regression coefficient, and D the regression constant for the regression of RY on Z. Substituting the expressions of RY in the second set of equations into the first set yields: X < BPX and Z < BPZ   ==>   Y = A1.X + C1.Z +
https://en.wikipedia.org/wiki/Integral%20closure%20of%20an%20ideal
In algebra, the integral closure of an ideal I of a commutative ring R, denoted by , is the set of all elements r in R that are integral over I: there exist such that It is similar to the integral closure of a subring. For example, if R is a domain, an element r in R belongs to if and only if there is a finitely generated R-module M, annihilated only by zero, such that . It follows that is an ideal of R (in fact, the integral closure of an ideal is always an ideal; see below.) I is said to be integrally closed if . The integral closure of an ideal appears in a theorem of Rees that characterizes an analytically unramified ring. Examples In , is integral over . It satisfies the equation , where is in the ideal. Radical ideals (e.g., prime ideals) are integrally closed. The intersection of integrally closed ideals is integrally closed. In a normal ring, for any non-zerodivisor x and any ideal I, . In particular, in a normal ring, a principal ideal generated by a non-zerodivisor is integrally closed. Let be a polynomial ring over a field k. An ideal I in R is called monomial if it is generated by monomials; i.e., . The integral closure of a monomial ideal is monomial. Structure results Let R be a ring. The Rees algebra can be used to compute the integral closure of an ideal. The structure result is the following: the integral closure of in , which is graded, is . In particular, is an ideal and ; i.e., the integral closure of an ideal is integrally closed. It also follows that the integral closure of a homogeneous ideal is homogeneous. The following type of results is called the Briancon–Skoda theorem: let R be a regular ring and an ideal generated by elements. Then for any . A theorem of Rees states: let (R, m) be a noetherian local ring. Assume it is formally equidimensional (i.e., the completion is equidimensional.). Then two m-primary ideals have the same integral closure if and only if they have the same multiplicity. See also Dedekind–Kummer theorem Notes References Eisenbud, David, Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Mathematics, 150, Springer-Verlag, 1995, . Further reading Irena Swanson, Rees valuations. Commutative algebra Ring theory Algebraic structures
https://en.wikipedia.org/wiki/Riffle%20shuffle%20permutation
In the mathematics of permutations and the study of shuffling playing cards, a riffle shuffle permutation is one of the permutations of a set of items that can be obtained by a single riffle shuffle, in which a sorted deck of cards is cut into two packets and then the two packets are interleaved (e.g. by moving cards one at a time from the bottom of one or the other of the packets to the top of the sorted deck). Beginning with an ordered set (1 rising sequence), mathematically a riffle shuffle is defined as a permutation on this set containing 1 or 2 rising sequences. The permutations with 1 rising sequence are the identity permutations. As a special case of this, a -shuffle, for numbers and with , is a riffle in which the first packet has cards and the second packet has cards. Combinatorial enumeration Since a -shuffle is completely determined by how its first elements are mapped, the number of -shuffles is However, the number of distinct riffles is not quite the sum of this formula over all choices of and adding to (which would be ), because the identity permutation can be represented in multiple ways as a -shuffle for different values of and . Instead, the number of distinct riffle shuffle permutations of a deck of cards, for , is More generally, the formula for this number is ; for instance, there are 4503599627370444 riffle shuffle permutations of a 52-card deck. The number of permutations that are both a riffle shuffle permutation and the inverse permutation of a riffle shuffle is For , this is and for there are exactly 23427 invertible shuffles. Random distribution The Gilbert–Shannon–Reeds model describes a random probability distribution on riffle shuffles that is a good match for observed human shuffles. In this model, the identity permutation has probability of being generated, and all other riffle permutations have equal probability of being generated. Based on their analysis of this model, mathematicians have recommended that a deck of 52 cards be given seven riffles in order to thoroughly randomize it. Permutation patterns A pattern in a permutation is a smaller permutation formed from a subsequence of some values in the permutation by reducing these values to the range from 1 to while preserving their order. Several important families of permutations can be characterized by a finite set of forbidden patterns, and this is true also of the riffle shuffle permutations: they are exactly the permutations that do not have 321, 2143, and 2413 as patterns. Thus, for instance, they are a subclass of the vexillary permutations, which have 2143 as their only minimal forbidden pattern. Perfect shuffles A perfect shuffle is a riffle in which the deck is split into two equal-sized packets, and in which the interleaving between these two packets strictly alternates between the two. There are two types of perfect shuffle, an in shuffle and an out shuffle, both of which can be performed consistently by some well-trained
https://en.wikipedia.org/wiki/Gilbert%E2%80%93Shannon%E2%80%93Reeds%20model
In the mathematics of shuffling playing cards, the Gilbert–Shannon–Reeds model is a probability distribution on riffle shuffle permutations that has been reported to be a good match for experimentally observed outcomes of human shuffling, and that forms the basis for a recommendation that a deck of cards should be riffled seven times in order to thoroughly randomize it. It is named after the work of Edgar Gilbert, Claude Shannon, and J. Reeds, reported in a 1955 technical report by Gilbert and in a 1981 unpublished manuscript of Reeds. The model A riffle shuffle permutation of a sequence of elements is obtained by partitioning the elements into two contiguous subsequences, and then arbitrarily interleaving the two subsequences. For instance, this describes many common ways of shuffling a deck of playing cards, by cutting the deck into two piles of cards that are then riffled together. The Gilbert–Shannon–Reeds model assigns a probability to each of these permutations. In this way, it describes the probability of obtaining each permutation, when a shuffle is performed at random. The model may be defined in several equivalent ways, describing alternative ways of performing this random shuffle: Most similarly to the way humans shuffle cards, the Gilbert–Shannon–Reeds model describes the probabilities obtained from a certain mathematical model of randomly cutting and then riffling a deck of cards. First, the deck is cut into two packets. If there are a total of cards, then the probability of selecting cards in the first deck and in the second deck is defined as . Then, one card at a time is repeatedly moved from the bottom of one of the packets to the top of the shuffled deck, such that if cards remain in one packet and cards remain in the other packet, then the probability of choosing a card from the first packet is and the probability of choosing a card from the second packet is . A second, alternative description can be based on a property of the model, that it generates a permutation of the initial deck in which each card is equally likely to have come from the first or the second packet. To generate a random permutation according to this model, begin by flipping a fair coin times, to determine for each position of the shuffled deck whether it comes from the first packet or the second packet. Then split into two packets whose sizes are the number of tails and the number of heads flipped, and use the same coin flip sequence to determine from which packet to pull each card of the shuffled deck. A third alternative description is more abstract, but lends itself better to mathematical analysis. Generate a set of values from the uniform continuous distribution on the unit interval, and place them in sorted order. Then the doubling map from the theory of dynamical systems maps this system of points to a permutation of the points in which the permuted ordering obeys the Gilbert–Shannon–Reeds model, and the positions of the new points are agai
https://en.wikipedia.org/wiki/Ed%20Scheinerman
Edward R. Scheinerman is an American mathematician, working in graph theory and order theory. He is a professor of applied mathematics, statistics, and computer science at Johns Hopkins University. His contributions to mathematics include Scheinerman's conjecture, now proven, stating that every planar graph may be represented as an intersection graph of line segments. Scheinerman did his undergraduate studies at Brown University, graduating in 1980, and earned his Ph.D. in 1984 from Princeton University under the supervision of Douglas B. West. He joined the Johns Hopkins faculty in 1984, and since 2000 he has been an administrator there, serving as department chair, associate dean, vice dean for education, vice dean for graduate education, and vice dean for faculty (effective September 2019). He is a two-time winner of the Mathematical Association of America's Lester R. Ford Award for expository writing, in 1991 for his paper "Random intervals" with Joyce Justicz and Peter Winkler, and in 2001 for his paper "When Close is Close Enough". In 1992 he became a fellow of the Institute of Combinatorics and its Applications, and in 2012 he became a fellow of the American Mathematical Society. Selected publications Books Invitation to Dynamical Systems (Prentice Hall, 1996, reprinted by Dover Publications, 2012). Fractional Graph Theory (With Daniel Ullman, Wiley, 1997, reprinted by Dover Publications, 2011). Mathematics: A Discrete Introduction. (Brooks/Cole, 2000; 3rd edition, Cengage Learning, 2012). C++ for mathematicians : an introduction for students and professionals (Chapman & Hall/CRC, 2006). The Mathematics Lover's Companion: Masterpieces for Everyone (Yale University Press, 2017). Papers . . References External links Home page Year of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians Graph theorists Brown University alumni Princeton University alumni Johns Hopkins University faculty Fellows of the American Mathematical Society
https://en.wikipedia.org/wiki/Analytically%20unramified%20ring
In algebra, an analytically unramified ring is a local ring whose completion is reduced (has no nonzero nilpotent). The following rings are analytically unramified: pseudo-geometric reduced ring. excellent reduced ring. showed that every local ring of an algebraic variety is analytically unramified. gave an example of an analytically ramified reduced local ring. Krull showed that every 1-dimensional normal Noetherian local ring is analytically unramified; more precisely he showed that a 1-dimensional normal Noetherian local domain is analytically unramified if and only if its integral closure is a finite module. This prompted to ask whether a local Noetherian domain such that its integral closure is a finite module is always analytically unramified. However gave an example of a 2-dimensional normal analytically ramified Noetherian local ring. Nagata also showed that a slightly stronger version of Zariski's question is correct: if the normalization of every finite extension of a given Noetherian local ring R is a finite module, then R is analytically unramified. There are two classical theorems of that characterize analytically unramified rings. The first says that a Noetherian local ring (R, m) is analytically unramified if and only if there are a m-primary ideal J and a sequence such that , where the bar means the integral closure of an ideal. The second says that a Noetherian local domain is analytically unramified if and only if, for every finitely-generated R-algebra S lying between R and the field of fractions K of R, the integral closure of S in K is a finitely generated module over S. The second follows from the first. Nagata's example Let K0 be a perfect field of characteristic 2, such as F2. Let K be K0({un, vn : n ≥ 0}), where the un and vn are indeterminates. Let T be the subring of the formal power series ring K  generated by K and K2  and the element Σ(unxn+ vnyn). Nagata proves that T is a normal local noetherian domain whose completion has nonzero nilpotent elements, so T is analytically ramified. References Commutative algebra
https://en.wikipedia.org/wiki/William%20G.%20McCallum
William G. McCallum (born 1956 in Sydney, Australia) is a University Distinguished Professor of Mathematics and was Head of the Department of Mathematics at the University of Arizona from 2009 to 2013. Education and professional work He was educated at North Sydney Boys High School. He received his Ph.D. in Mathematics from Harvard University in 1984, under the supervision of Barry Mazur. After spending two years at the University of California, Berkeley, and one at the Mathematical Sciences Research Institute in Berkeley, he joined the faculty at the University of Arizona in 1987. In 1989 he joined the Harvard calculus consortium, and is the lead author of the consortium's multivariable calculus and college algebra texts. In 1993–94 he spent a year at the Institut des Hautes Études Scientifiques, and in 1995–96 he spent a year at the Institute for Advanced Study on a Centennial Fellowship from the American Mathematical Society. In 2006 he founded the Institute for Mathematics & Education at the University of Arizona. He was Director of the Institute until 2009 and again starting in 2013. In 2009–2010 he was one of the lead writers for the Common Core State Standards in Mathematics. His professional interests include arithmetical algebraic geometry and mathematics education. Selected honors and awards 2012: Fellow of the American Mathematical Society. 2012: The Mary P. Dolciani Award, administered by the Mathematical Association of America 2012: The American Mathematical Society Distinguished Public Service Award 2006: University of Arizona College of Science Galileo Circle Fellow. 2005: National Science Foundation’s Director's Award for Distinguished Teaching Scholars 1996: The University of Arizona College of Science Innovation in Teaching Award 1995: The American Mathematical Society Centennial Research Fellowship. Current projects Institute for Mathematics and Education Common Core State Standards in Mathematics Illustrative Mathematics Project Standards Progressions for the Common Core Tools for the Common Core Blog The Klein Project Mathematical Models at the University of Arizona References External links The U.S. Common Core State Standards, paper presented at ICME 12, Seoul, Korea (slides for this talk) Restoring and Balancing, in Usiskin, Anderson, and Zotto (eds), Future Curricular Trends in School Algebra and Geometry, Information Age Publishing (2010) Living people 1956 births Australian mathematicians University of Arizona faculty Harvard University alumni Fellows of the American Mathematical Society People educated at North Sydney Boys High School
https://en.wikipedia.org/wiki/Felix%20Leinen
Felix Leinen (born 15 May 1957) is a German professor, mathematician and politician of the Ecological Democratic Party (ÖDP.) Biography Leinen studied mathematics from 1976 to 1982 at the University of Mainz. He obtained a PhD (Dr. rer. nat.) in 1984 at the University of Freiburg. From 1984 to 1985 he worked as a Visiting assistant professor at Michigan State University, East Lansing. Since 1985 Leinen has worked at the University of Mainz. Since 1997 Leinen has been supernumerary professor at the Johannes Gutenberg-university. In the meantime, he made several professional visits to England, Italy and the USA. He volunteered in 1974–1984 supporting the Technisches Hilfswerk. Leinen is married and has four children. Political career Since 1995 he has been active in a citizens' initiative that fights against the conversion of the Laubenheimer Höhe area in Mainz-Laubenheim into a quarry. In 1999 he joined the Ecological Democratic Party and served as the deputy national chairman from 2008 to 2010. He heads the Federal Education Policy Working Group of the ÖDP. Leinen is treasurer of his party in Rhineland-Palatinate and ÖDP-chairman of the local chapter of Mainz-Hechtsheim. In the local elections of 2009, he succeeded in gaining a seat on Mainz City Council. References External links Publications by Felix Leinen 1957 births Living people Ecological Democratic Party politicians 20th-century German mathematicians 21st-century German mathematicians Academic staff of Johannes Gutenberg University Mainz Scientists from Wiesbaden University of Freiburg alumni Politicians from Wiesbaden
https://en.wikipedia.org/wiki/Mokhamad%20Syaifuddin
Mokhamad Syaifuddin (born in Surabaya, Indonesia, 9 August 1992) is an Indonesian professional footballer who plays as a defender for Liga 2 club Gresik United. Career statistics Club Honours Club Persebaya Surabaya Liga 2: 2017 East Java Governor Cup: 2020 International Indonesia U-23 Southeast Asian Games Silver medal: 2013 References External links Mokhamad Syaifuddin at Liga Indonesia 1992 births Living people Footballers from Surabaya Footballers from East Java Indonesian men's footballers Liga 1 (Indonesia) players Liga 2 (Indonesia) players Madura United F.C. players PSS Sleman players Persebaya Surabaya players Dewa United F.C. players Gresik United F.C. players Indonesia men's youth international footballers Men's association football defenders SEA Games silver medalists for Indonesia SEA Games medalists in football Competitors at the 2013 SEA Games
https://en.wikipedia.org/wiki/The%20Signal%20and%20the%20Noise
The Signal and the Noise: Why So Many Predictions Fail – but Some Don't is a 2012 book by Nate Silver detailing the art of using probability and statistics as applied to real-world circumstances. The book includes case studies from baseball, elections, climate change, the 2008 financial crash, poker, and weather forecasting. The book was the recipient of the 2013 Phi Beta Kappa Society book award in science. It has also been translated into several languages. Synopsis The book emphasizes Silver's skill, which is the practical art of mathematical model building using probability and statistics. Silver takes a big-picture approach to using statistical tools, combining sources of unique data (e.g., timing a minor league ball player's fastball using a radar gun), with historical data and principles of sound statistical analysis, many of which are violated by many pollsters and pundits who nonetheless have important media roles. The book includes richly detailed case studies from baseball, elections, climate change, the financial crash, poker, and weather forecasting. These different topics illustrate different statistical principles. For example, weather forecasting is used to introduce the idea of "calibration," or how well weather forecasts fit actual weather outcomes. There is much on the need for improved expressions of uncertainty in all statistical statements, reflecting ranges of probable outcomes and not just single "point estimates" like averages. Silver would like to see the media move away from vague terminology like "Obama has an edge in Ohio" or "Florida still a toss-up state" to probability statements, like "the probability of Obama winning the electoral college is 83%, while the expected fraction won by him of the popular vote is now 50.1% with an error range of ±2%". Such statements give odds on outcomes, including a 17% chance of Romney winning the electoral college. The shares of the popular vote similarly are ranges including outcomes in which Romney gets the most votes. What is highly probable is that the voting shares are in these ranges, but not whose share is highest; that's another probability question with closer odds. From such information, it's up to the consumer of such statements to use that information as best they can in dealing with an uncertain future in an age of information overload. That last idea frames Silver's entire narrative and motivates his pedagogical mission. Silver rejects much ideology taught with statistical method in colleges and universities today, specifically the "frequentist" approach of Ronald Fisher, originator of many classical statistical tests and methods. The problem Silver finds is a belief in perfect experimental, survey, or other designs, when data often comes from a variety of sources and idealized modeling assumptions rarely hold true. Often such models reduce complex questions to overly simple "hypothesis tests" using arbitrary "significance levels" to "accept or reject" a single
https://en.wikipedia.org/wiki/NSIA
NSIA may refer to: National Statistics and Information Authority (Afghanistan) Nigeria Sovereign Investment Authority Norwegian Safety Investigation Authority
https://en.wikipedia.org/wiki/Doris%20Schattschneider
Doris J. Schattschneider (née Wood) is an American mathematician, a retired professor of mathematics at Moravian College. She is known for writing about tessellations and about the art of M. C. Escher, for helping Martin Gardner validate and popularize the pentagon tiling discoveries of amateur mathematician Marjorie Rice, and for co-directing with Eugene Klotz the project that developed The Geometer's Sketchpad. Biography Schattschneider was born in Staten Island; her mother, Charlotte Lucile Ingalls Wood, taught Latin and was herself the daughter of a Staten Island school principal, and her father, Robert W. Wood, Jr., was an electrical engineer who worked for the New York City Bureau of Bridge Design. Her family moved to Lake Placid, New York during World War II, while her father served as an engineer for the U. S. Army; she began her schooling in Lake Placid, but returned to Staten Island after the war. She did her undergraduate studies in mathematics at the University of Rochester, and earned a Ph.D. in 1966 from Yale University under the joint supervision of Tsuneo Tamagawa and Ichirô Satake; her thesis, in abstract algebra, concerned semisimple algebraic groups. She taught at Northwestern University for a year and at the University of Illinois at Chicago Circle for three years before joining the faculty of Moravian College in 1968, where she remained for 34 years until her retirement. She was the first female editor of Mathematics Magazine, from 1981 to 1985. She was married for 54 years to the Rev. Dr. David A. Schattschneider (1939-2016), a church historian and Dean of Moravian Theological Seminary; their daughter Laura Ellen Schattschneider is a lawyer. Involvement with Marjorie Rice By February 1976, Marjorie Rice had discovered a new pentagon type and its variations in shape and drew up several tessellations by these pentagon tiles. She mailed her discoveries to Martin Gardner using her own home-made notation. He, in turn, sent Rice's work to Schattschneider, who was an expert in tiling patterns. Schattschneider was skeptical at first, saying that Rice's peculiar notation system seemed odd, like "hieroglyphics". But with careful examination, she was able to validate Rice's results. Schattschneider not only helped Martin Gardner popularize the pentagon tiling discoveries of Rice, but lauded her work as an exciting discovery by an amateur mathematician. In 1995, at a regional meeting of the Mathematical Association of America held in Los Angeles, Schattschneider convinced Rice and her husband to attend her lecture on Rice's work. Before concluding her talk, Schattschneider introduced the amateur mathematician who had advanced the study of tessellation. "And everybody in the room . . . gave her a standing ovation." Awards and honors Schattschneider won the Mathematical Association of America's Carl B. Allendoerfer Award for excellence in expository writing in Mathematics Magazine in 1979, for her article "Tiling the plane with cong
https://en.wikipedia.org/wiki/K.%20C.%20Nag
Keshab Chandra Nag or K.C. Nag () (10 July 1893 – 6 February 1987), was an Indian Bengali mathematician, author of various mathematics textbooks and educator. Early life K. C. Nag was born in Nagpara, Gurap, Hooghly, Bengal, British India (present-day West Bengal, India) on the holy day of Rath Yatra, 10 July 1893. His Father was Raghunath Nag and Mother Khiroda Sundari Debi. He lost his father at an early age of three. He was only cared for by his mother. Education Keshab Chandra Nag started his education in a Bengali Medium School at his village in Gurap. At that time that was the only school at Gurap. From Class VII he changed his school to Bhastara Yojneshshar Uccha Vidyalaya (Yojneshshar High School), 3 miles from his village. He would start walking early in the morning to reach his school and came back home at evening every day. In Class IX he got admitted to Kishenganj High School. In 1912, he passed the entrance examination with a First Class and joined Ripon College (now Surendranath College), Kolkata, in Science. In 1914, he passed the I.Sc examination with a First Class. After this due to severe financial crisis he had to discontinue his education and start earning money. Working life He started his career as Third Master in Bhastara Yojgeshshar Uccha Vidyalaya. He also did private tuitions when teaching there. His family was dependent on him but he resigned from his job to pursue higher studies. In 1917 he passed B.A with Mathematics and Sanskrit. He then received a job offer from Kishenganj High School as a Mathematics Teacher. He taught for some time in that school, after which he got another offer from Baharampur Krishnanath Collegiate School and joined the school as a mathematics teacher. In 1919 he got Diksha from Ma Sarada Devi. During that time the Maharaja of Kasimbazar (Cossimbazar) Manindra Chandra Nandi was a great admirer of Keshab Chandra. Maharaj allowed Keshab Chandra to use his vast library. In that library, he studied extensively about the history of India and especially the history of mathematics. At first, he lived in a mess at Rosa Road in Kolkata. From 1964 he started to live at his own house at Gobinda Ghoshal Lane in South Kolkata. Meeting with Ashutosh Mukhopadhyay In 1905 Sir Ashutosh Mukhopadhay established Mitra Institution (Branch) in Bhowanipore so that the students of South Kolkata can also get chance to study in that school. In 1906 Sir Ashutosh Mukhopadhay became the Vice Chancellor of Calcutta University and tried to bring various teachers from different parts of India to establish Calcutta University as one of the best universities of India. Similarly, he tried to bring teachers to Mitra Institution (Branch). Sir Ashutosh heard about Keshab Chandra, and he took him to Mitra Institution, Bhabanipur as a mathematics teacher. Due to his way of teaching mathematics Keshab Chandra came very close to Sir Ashutosh . Dr. Shyamaprasad Mukhopadhay son of Sir Ashutosh became a very good friend of Keshab Cha
https://en.wikipedia.org/wiki/2013%E2%80%9314%20Sporting%20CP%20season
The Sporting Clube de Portugal's 2013–14 season main competition is the Primeira Liga, known as the Liga ZON Sagres for sponsorship purposes. This article shows player statistics and all matches that the club plays during the 2013–14 season. Competitions Legend Primeira Liga Results by round Matches Taça de Portugal Taça da Liga Group stage Squad statistics Players Current squad Transfers In Out Out on loan References External links Official club website 2012-13 Portuguese football clubs 2013–14 season
https://en.wikipedia.org/wiki/Analytically%20irreducible%20ring
In algebra, an analytically irreducible ring is a local ring whose completion has no zero divisors. Geometrically this corresponds to a variety with only one analytic branch at a point. proved that if a local ring of an algebraic variety is a normal ring, then it is analytically irreducible. There are many examples of reduced and irreducible local rings that are analytically reducible, such as the local ring of a node of an irreducible curve, but it is hard to find examples that are also normal. gave such an example of a normal Noetherian local ring that is analytically reducible. Nagata's example Suppose that K is a field of characteristic not 2, and K  is the formal power series ring over K in 2 variables. Let R be the subring of K  generated by x, y, and the elements zn and localized at these elements, where is transcendental over K(x) . Then R[X]/(X 2–z1) is a normal Noetherian local ring that is analytically reducible. References Commutative algebra
https://en.wikipedia.org/wiki/Ole%20Christoffer%20Heieren%20Hansen
Ole Christoffer Heieren Hansen (born 26 February 1987) is a Norwegian footballer who plays as a defender for Kråkerøy. Heieren Hansen was born in Fredrikstad. Career statistics References 1987 births Living people Norwegian men's footballers Sarpsborg 08 FF players Norwegian First Division players Eliteserien players Footballers from Fredrikstad Men's association football defenders
https://en.wikipedia.org/wiki/Alan%20Edelman
Alan Stuart Edelman (born June 1963) is an American mathematician and computer scientist. He is a professor of applied mathematics at the Massachusetts Institute of Technology (MIT) and a Principal Investigator at the MIT Computer Science and Artificial Intelligence Laboratory (CSAIL) where he leads a group in applied computing. In 2004, he founded a business called Interactive Supercomputing which was later acquired by Microsoft. Edelman is a fellow of American Mathematical Society (AMS), Society for Industrial and Applied Mathematics (SIAM), Institute of Electrical and Electronics Engineers (IEEE), and Association for Computing Machinery (ACM), for his contributions in numerical linear algebra, computational science, parallel computing, and random matrix theory. He is one of the cocreators of the technical programming language Julia. Education Edelman received B.S. and M.S. degrees in mathematics from Yale University in 1984, and a Ph.D. in applied mathematics from MIT in 1989 under the direction of Lloyd N. Trefethen. Following a year at Thinking Machines Corporation, and at CERFACS in France, Edelman went to U.C. Berkeley as a Morrey Assistant Professor and Levy Fellow, 1990–93. He joined the MIT faculty in applied mathematics in 1993. Research Edelman's research interests include high-performance computing, numerical computation, linear algebra, and random matrix theory. In random matrix theory, Edelman is most famous for the Edelman distribution of the smallest singular value of random matrices (also known as Edelman's law), the invention of beta ensembles, and the introduction of the stochastic operator approach, and some of the earliest computational approaches. In high performance computing, Edelman is known for his work on parallel computing, as the co-founder of Interactive Supercomputing, as an inventor of the Julia programming language and for his work on the Future Fast Fourier transform. As the leader of the Julialab, he supervises work on scientific machine learning and compiler methodologies. In numerical linear algebra, Edelman is known for eigenvalues and condition numbers of random matrices, the geometry of algorithms with orthogonality constraints, the geometry of the generalized singular value decomposition (GSVD), and applications of Lie algebra to matrix factorizations. Awards A Sloan fellow, Edelman received a National Science Foundation (NSF) Faculty Career award in 1995. He has received numerous awards, among them the Gordon Bell Prize and Householder Prize (1990), the Chauvenet Prize (1998), the Edgerly Science Partnership Award (1999), the SIAM Activity Group on Linear Algebra Prize (2000), and the Lester R. Ford Award, (2005, with Gilbert Strang). In 2011, Edelman was selected a Fellow of SIAM, "for his contributions in bringing together mathematics and industry in the areas of numerical linear algebra, random matrix theory, and parallel computing." In 2015, he became a Fellow of the American Mathematical
https://en.wikipedia.org/wiki/Analytically%20normal%20ring
In algebra, an analytically normal ring is a local ring whose completion is a normal ring, in other words a domain that is integrally closed in its quotient field. proved that if a local ring of an algebraic variety is normal, then it is analytically normal, which is in some sense a variation of Zariski's main theorem. gave an example of a normal Noetherian local ring that is analytically reducible and therefore not analytically normal. References Commutative algebra
https://en.wikipedia.org/wiki/List%20of%20Swansea%20City%20A.F.C.%20records%20and%20statistics
Swansea City Association Football Club () is a Welsh professional football club based in the city of Swansea, south Wales, that play in the EFL Championship. They play their home matches at the Swansea.com Stadium. The club was founded in 1912 as Swansea Town and joined the Football League in 1921. The club changed their name in 1969, when it adopted the name Swansea City to reflect Swansea's new status as a city. The list encompasses the major honours won by Swansea City, records set by the club, their managers and their players, and details of their performance in European competition. The player records section itemises the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Swansea players on the international stage, and the highest transfer fees paid and received by the club. Attendance records at the Vetch Field and Swansea.com Stadium are also included. Honours Swansea City's honours include the following: The Football League English second tier (currently Football League Championship) Promoted (1): 1980–81 Play-off winners (1): 2010–11 English third tier (currently Football League One) Winners (3): 1924–25, 1948–49, 2007–08 Promoted (1): 1978–79 English fourth tier (currently Football League Two) Winners (1): 1999–2000 Promoted (3): 1969–70, 1977–78, 2004–05 Play-off winners (1): 1987–88 Domestic Cup Competition Football League Cup Winners (1): 2012–13 FA Cup Semi-finalists (2): 1925–26, 1963–64 Football League Trophy Winners (2): 1993–94, 2005–06 Welsh Cup Winners (10): 1912–13, 1931–32, 1949–50, 1960–61, 1965–66, 1980–81, 1981–82, 1982–83, 1988–89, 1990–91 Runners-up (8): 1914–15, 1925–26, 1937–38, 1939–40, 1948–49, 1955–56, 1956–57, 1968–69 FAW Premier Cup Winners (2): 2004–05, 2005–06 Runners-up (2): 2000–01, 2001–02 European Competition UEFA Cup Winners' Cup Qualification: 1961–62, 1966–67, 1981–82, 1982–83, 1983–84, 1989–90, 1991–92 UEFA Europa League Qualification: 2013-14 Domestic Youth Cup Competition FAW Welsh Youth Cup Winners (13): 1999, 2003, 2008, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019 Runners-up (6): 1990, 1991, 1994, 1996, 2004, 2009 Player records Appearances Youngest first-team player: Nigel Dalling, 15 years 289 days (against Southport, Fourth Division, 6 December 1974). Oldest first-team player: Tommy Hutchison, 43 years, 172 days (against Southend United, Third Division, 12 March 1991). Most appearances League matches only. To matches played 14 November 2017. Goalscorers Most goals in a season in all competitions: 40, by Cyril Pearce in 1931–32 Most league goals in a top-flight season: 34, by Bob Latchford in 1982–83 Most League goals in a season: 35, by Cyril Pearce in 1931–32 Most League goals in a 38-game season: 18, by Michu in 2012–13 Most goals in a competitive match: 5, by Jack Fowler against Charlton Athletic, Third Division (South), 27 December 1924. Most hat-tricks: 9, by Ja
https://en.wikipedia.org/wiki/Kent-Are%20Antonsen
Kent-Are Antonsen (born 12 February 1995) is a Norwegian footballer who plays as a midfielder for Tromsø. Antonsen was born in Storsteinnes. Career statistics Club References 1995 births Living people People from Balsfjord Norwegian men's footballers Norway men's youth international footballers Men's association football defenders Tromsø IL players Eliteserien players Norwegian First Division players Footballers from Troms og Finnmark
https://en.wikipedia.org/wiki/Dumitru%20Bogdan
Dumitru Bogdan (born 4 March 1989, Chișinău, Moldavian SSR) is a Moldavian football defender who plays for FC Academia Chișinău. Club statistics Total matches played in Moldavian First League: 70 matches - 5 goals References External links Profile at Divizia Nationala 1989 births Footballers from Chișinău Moldovan men's footballers Living people Men's association football defenders FC Iskra-Stal players FC Sfîntul Gheorghe players FC Academia Chișinău players FC Taraz players FC Kaisar players FC Tobol players
https://en.wikipedia.org/wiki/Andrei%20Tcaciuc
Andrei Tcaciuc (born 10 February 1982) is a Moldavian football midfielder who plays for FC Speranța Crihana Veche. Club statistics Total matches played in Moldavian First League: 117 matches – 12 goals References External links Profile at Divizia Nationala 1982 births People from Bender, Moldova Moldovan men's footballers FC Daugava players Moldovan expatriate men's footballers Expatriate men's footballers in Latvia Moldovan expatriate sportspeople in Latvia Living people Men's association football midfielders Footballers from Transnistria
https://en.wikipedia.org/wiki/Beyond%202011
Beyond 2011, also known as The Beyond 2011 Programme, was a project initiated by the UK Statistics Authority to look at the alternatives to running a UK census in 2021. In 2008, the Treasury Select Committee had expressed concerns about the increasing cost of running the census and inaccuracies in data gathered only every ten years. In 2010 the newly elected coalition government reiterated such concerns responding to a report by the UK Statistics Authority. The Beyond 2011 Programme was established in 2011 to look at alternatives to the traditional census approach. The UK Statistics Authority will coordinate activity with its counterparts in the devolved administrations of Scotland and Northern Ireland which have also set up reviews of the future approach to population data provision. In 2012 six options were identified by the Beyond 2011 Programme for further consideration, ranging from a full 10-year census to rolling or smaller scale annual surveys, some supplemented by administrative data capture. In 2014 the UK Statistics Authority announced its recommendation for the 2021 census in England and Wales. It proposed that in 2021 there should be a decennial census for England and Wales which would be conducted predominantly through online returns, supplemented by the further use of administrative and survey data. A parallel announcement for Scotland's 2021 census was made by the National Records for Scotland. Following agreement to the recommendations in January 2015 the UK Statistics Authority formally closed the Beyond 2011 Programme. It has been replaced by the Census Transformation Programme which has the purpose of taking forward and implementing the vision and recommended approaches. Background The decennial census has been the method of collecting United Kingdom-wide population-based statistics since 1801. Currently the UK census is governed by the Census Act 1920. However, prior to 1841 it was no more than a headcount. Since 1841, except in 1941 when no census took place due to the Second World War, detail was gathered about the household. Until the 1901 the enumerators were responsible for completing census enumerator sheets, transcribing the details included in household schedules completed by the head of the household. From the 1911 census onwards an individual census form, provided by and returned to an enumerator, was completed by the head of the household and became the primary source of demographic data. In 2001 census returns were for the first time sent out by post, but were collected by enumerators. The 2011 UK Census was the first time, individual census forms were issued through the Royal Mail and could also be returned by post, except in Scotland where instead they were collected by enumerators. Census forms could also be completed and submitted through the internet by the householder. In recent times, combined with other data, the ten-yearly census has provided the basis of socio-economic statistics used by all branche
https://en.wikipedia.org/wiki/Rodica%20Simion
Rodica Eugenia Simion (January 18, 1955 – January 7, 2000) was a Romanian-American mathematician. She was the Columbian School Professor of Mathematics at George Washington University. Her research concerned combinatorics: she was a pioneer in the study of permutation patterns, and an expert on noncrossing partitions. Biography Simion was one of the top competitors in the Romanian national mathematical olympiads. She graduated from the University of Bucharest in 1974, and immigrated to the United States in 1976. She did her graduate studies at the University of Pennsylvania, earning a Ph.D. in 1981 under the supervision of Herbert Wilf. After teaching at Southern Illinois University and Bryn Mawr College, she moved to George Washington University in 1987, and became Columbian School Professor in 1997. Recognition She is included in a deck of playing cards featuring notable women mathematicians published by the Association of Women in Mathematics. Research contributions Simion's thesis research concerned the concavity and unimodality of certain combinatorially defined sequences, and included what Richard P. Stanley calls "a very influential result" that the zeros of certain polynomials are all real. Next, with Frank Schmidt, she was one of the first to study the combinatorics of sets of permutations defined by forbidden patterns; she found a bijective proof that the stack-sortable permutations and the permutations formed by interleaving two monotonic sequences are equinumerous, and found combinatorial enumerations of many permutation classes. The "simsun permutations" were named after her and Sheila Sundaram, after their initial studies of these objects; a simsun permutation is a permutation in which, for all k, the subsequence of the smallest k elements has no three consecutive elements in decreasing order. Simion also did extensive research on noncrossing partitions, and became "perhaps the world's leading authority" on them. Other activities Simion was the main organizer of an exhibit about mathematics, Beyond Numbers, at the Maryland Science Center, based in part on her earlier experience organizing a similar exhibit at George Washington University. She was also a leader in George Washington University's annual Summer Program for Women in Mathematics. As well as being a mathematician, Simion was a poet and painter; her poem "Immigrant Complex" was published in a collection of mathematical poetry in 1979. Selected publications . . . . See also Cyclohedron References 1955 births 2000 deaths 20th-century Romanian mathematicians 20th-century American mathematicians Romanian emigrants to the United States American women mathematicians Combinatorialists University of Bucharest alumni University of Pennsylvania alumni Southern Illinois University faculty Bryn Mawr College faculty George Washington University faculty 20th-century American women scientists 20th-century women mathematicians
https://en.wikipedia.org/wiki/Marjorie%20Senechal
Marjorie Lee Senechal (née Wikler, born 1939) is an American mathematician and historian of science, the Louise Wolff Kahn Professor Emerita in Mathematics and History of Science and Technology at Smith College and editor-in-chief of The Mathematical Intelligencer. In mathematics, she is known for her work on tessellations and quasicrystals; she has also studied ancient Parthian electric batteries and published several books about silk. Biography Senechal was born in St. Louis, Missouri, the oldest of four children of Abraham Wikler, a United States Public Health Service physician. The family soon moved to Lexington, Kentucky, and Senechal grew up as a "narco brat" on the grounds of the Lexington Narcotic Hospital, a prison farm for drug addicts, where her father was associate director. She was educated at the Training School of the University of Kentucky, a small school with only one class in each grade; Senechal later wrote that the school's too-easy classwork, snobbish classmates, and anti-Jewish discrimination made her miserable. She left Lafayette High School after the 11th grade to begin her undergraduate studies as a pre-med at the University of Chicago, but soon switched to mathematics, graduating in 1960. While doing graduate studies at the Illinois Institute of Technology, she married mathematician Lester Senechal, and moved to Arizona with him before completing her own degree. Nevertheless, she finished her Ph.D. in 1965, under the supervision of Abe Sklar; her thesis concerned functional equations. Unable to get her own faculty position at Arizona because of the anti-nepotism rules then in place, she and her husband visited Brazil, supported by a Fulbright Scholarship. They then moved to Massachusetts, where she took the faculty position at Smith that she would keep for the rest of her career. She eventually divorced Senechal, and married photographer Stan Sherer in 1989. She retired in 2007; a festival in 2006 honoring her impending retirement included the performance of a musical play that she wrote with The Talking Band member Ellen Maddow, loosely centered around the theme of aperiodic tilings and the life of amateur mathematician Robert Ammann. Awards and honors Senechal won the Mathematical Association of America's Carl B. Allendoerfer Award for excellence in expository writing in Mathematics Magazine in 1982, for her article, "Which Tetrahedra Fill Space?" In 2008, her book American Silk 1830 – 1930 won the Millia Davenport Publication Award of the Costume Society of America. In 2012, she became a fellow of the American Mathematical Society. Books Crystalline Symmetries: An informal mathematical introduction (Alan Hilger, 1990) Quasicrystals and Geometry (Cambridge University Press, 1995) Long Life to Your Children! A portrait of High Albania (with S. Sherer, University of Massachusetts Press, 1997) Northampton's Century of Silk (City of Northampton, Massachusetts, 2004) American Silk 1830 – 1930: Entrepreneurs and Artifac
https://en.wikipedia.org/wiki/Nicolae%20Orlovschi
Nicolae Orlovschi (born 1 April 1985 in Bălți, Moldavian SSR) is a Moldavian football defender who plays for FC Dacia Chișinău. Club statistics Total matches played in Moldavian First League: 80 matches – 8 goals References External links Profile at Divizia Nationala Profile at FC Dacia Chișinău 1985 births Sportspeople from Bălți Moldovan men's footballers Living people Men's association football defenders Moldova men's youth international footballers Moldova men's international footballers
https://en.wikipedia.org/wiki/Alphonse%20Soppo
Alphonse Soppo (born 15 May 1985, in Yaoundé, Cameroon) is a Cameroonian football midfielder. Club statistics Total matches played in Moldavian First League: 144 matches - 2 goals References External links Profile at FC Dacia Chișinău 1985 births Footballers from Yaoundé Cameroonian men's footballers Cameroonian expatriate men's footballers Living people FC Dacia Chișinău players FC Nistru Otaci players FC Costuleni players FC Dinamo-Auto Tiraspol players FK Rudar Pljevlja players FK Zeta players Moldovan Super Liga players Montenegrin First League players Expatriate men's footballers in Moldova Cameroonian expatriate sportspeople in Moldova Expatriate men's footballers in Montenegro Cameroonian expatriate sportspeople in Montenegro Men's association football midfielders
https://en.wikipedia.org/wiki/Alexandru%20Costin
Alexandru Costin (born 21 October 1991, Chișinău, Moldavian SSR) is a Moldavian football defender who plays for FC Dacia Chișinău. Club statistics Total matches played in Moldavian First League: 10 matches (0 goals} References External links Profile at FC Dacia Chișinău 1991 births Footballers from Chișinău Moldovan men's footballers Living people Men's association football defenders FC Sfîntul Gheorghe players
https://en.wikipedia.org/wiki/Jude%20Ogada
Jude Iloba Ogada (born 15 December 1989, in Abuja, Nigeria) is a Nigerian football defender who last played for Dinamo-Auto Tiraspol. Club statistics Total matches played in Moldavian First League: 141 matches - 8 goals References External links Profile at FC Dacia Chișinău 1989 births Sportspeople from Abuja Nigerian men's footballers Living people Men's association football defenders CSF Bălți players FC Tiraspol players FC Dacia Chișinău players FC Dinamo-Auto Tiraspol players Moldovan Super Liga players Nigerian expatriate men's footballers Expatriate men's footballers in Moldova Nigerian expatriate sportspeople in Moldova
https://en.wikipedia.org/wiki/Yuriy%20Shevel
Yuriy Shevel (; born 29 January 1988) is a Ukrainian football forward. Club statistics Total matches played for FC Olimpia Bălți in Moldavian First League: 22 matches, 6 goals. References External links 1988 births Living people People from Vyshneve Ukrainian men's footballers Men's association football forwards FC Dynamo-2 Kyiv players FC Dynamo-3 Kyiv players Nyíregyháza Spartacus FC players Kaposvölgye VSC footballers FC Odesa players CSF Bălți players FC Dacia Chișinău players FC Guria Lanchkhuti players Dinamo Zugdidi players SC Tavriya Simferopol players Ukrainian expatriate men's footballers Expatriate men's footballers in Moldova Expatriate men's footballers in Georgia (country) Expatriate men's footballers in Hungary Ukrainian expatriate sportspeople in Hungary Ukrainian expatriate sportspeople in Moldova Ukrainian expatriate sportspeople in Georgia (country) Footballers from Kyiv Oblast FC Dynamo Kyiv players
https://en.wikipedia.org/wiki/Alexei%20Casian
Alexei Casian (born 1 October 1987) is a Moldavian football midfielder who represents Lane Xang Intra F.C. Club statistics He played in 2008-2011 totally in Moldovan National Division 56 matches, scoring 3 goals. In February 2014 he moved back to Uzbekistan Premier league club FK Andijan, where he has already performed in 2011, in summer of the same year he had terminated contract because of difficult situation of the club in the league. In autumn of the year Casian joined Lane Xang Intra F.C. and signed one-year deal with Laos premier league side, on 16 September he played in the game against all star Brazilian team for opening of new stadium in Laos. References External links Profile at FC Dacia Chișinău 1987 births People from Bender, Moldova Moldovan men's footballers Living people Men's association football midfielders FK Andijon players FC Dinamo-Auto Tiraspol players FC Iskra-Stal players Lanexang United F.C. players
https://en.wikipedia.org/wiki/Nicolas%20Mahut%20career%20statistics
This is a list of the main career statistics of professional tennis player Nicolas Mahut. Performance timelines Singles Doubles Current through the 2023 US Open. 1 Including appearances in Grand Slam, ATP Tour main draw matches, and Summer Olympics. 2 Including matches in Grand Slam, ATP Tour events, Summer Olympics, Davis Cup, World Team Cup and ATP Cup. * not held due to COVID-19 pandemic. Significant finals Grand Slam finals Doubles: 8 (5 titles, 3 runner-up) Year-end championships Doubles: 3 (2 titles, 1 runner-up) Masters 1000 finals Doubles: 12 (7 titles, 5 runner-ups) ATP World Tour career finals Singles: 6 (4 titles, 2 runner-ups) Doubles: 59 (37 titles, 22 runner-ups) Other finals ATP Challenger Tour and ITF Men's Circuit Singles: 27 (17 titles, 10 runner-ups) Doubles: 35 (26 titles, 9 runner-ups) ITF Junior's Circuit Singles: 4 (1 title, 3 runner-ups) Doubles: 11 (8 titles, 3 runner-up) Top 10 wins Mahut has a record against players who were, at the time the match was played, ranked in the top 10. Career Grand Slam seedings The tournaments won by Mahut are in boldface, while those where he was runner-up are in italics. Singles Doubles * See also Longest tennis match records Isner–Mahut match at the 2010 Wimbledon Championships France Davis Cup team List of France Davis Cup team representatives Sport in France References External links Nicolas Mahut at the ITF profile Mahut, Nicolas
https://en.wikipedia.org/wiki/Abe%20Sklar
Abe Sklar (November 25, 1925 – October 30, 2020) was an American mathematician and a professor of applied mathematics at the Illinois Institute of Technology (Illinois Tech) and the inventor of copulas in probability theory. Education and career Sklar was born in Chicago to Jewish parents who immigrated to the United States from Ukraine. He attended Von Steuben High School and later enrolled at the University of Chicago in 1942, when he was only 16. Sklar went on to become a student of Tom M. Apostol at the California Institute of Technology, where he earned his Ph.D. in 1956. His students at IIT have included geometers Clark Kimberling and Marjorie Senechal. In 1959, Sklar introduced the notion of and the name of "copulas" into probability theory and proved the theorem that bears his name, Sklar's theorem. That is, that multivariate cumulative distribution functions can be expressed in terms of copulas. This representation of distribution functions, which is valid in any dimension and unique when the margins are continuous, is the basis of copula modeling, a widespread data analytical technique used in statistics; this representation is often termed Sklar's representation. Schweizer–Sklar t-norms are also named after Sklar and Berthold Schweizer, who studied them together in the early 1960s. Bibliography References 1925 births 2020 deaths 20th-century American mathematicians 21st-century American mathematicians American people of Ukrainian-Jewish descent California Institute of Technology alumni Illinois Institute of Technology faculty University of Chicago alumni Probability theorists American mathematicians People from Chicago
https://en.wikipedia.org/wiki/%C3%89tale%20topos
In mathematics, the étale topos of a scheme X is the category of all étale sheaves on X. An étale sheaf is a sheaf on the étale site of X. Definition Let X be a scheme. An étale covering of X is a family , where each is an étale morphism of schemes, such that the family is jointly surjective that is . The category Ét(X) is the category of all étale schemes over X. The collection of all étale coverings of a étale scheme U over X i.e. an object in Ét(X) defines a Grothendieck pretopology on Ét(X) which in turn induces a Grothendieck topology, the étale topology on X. The category together with the étale topology on it is called the étale site on X. The étale topos of a scheme X is then the category of all sheaves of sets on the site Ét(X). Such sheaves are called étale sheaves on X. In other words, an étale sheaf is a (contravariant) functor from the category Ét(X) to the category of sets satisfying the following sheaf axiom: For each étale U over X and each étale covering of U the sequence is exact, where . Topos theory Sheaf theory
https://en.wikipedia.org/wiki/Ministry%20of%20Development%20Planning%20and%20Statistics
The Ministry of Development Planning and Statistics (Arabic: وزارة التخطيط التنموي والإحصاء) is a governmental agency in the State of Qatar. It was established through an Emiri Decision No (4) in 2013. History On 26 June 2013, the Emir Sheikh Tamim bin Hamad Al Thani issued the Emiri Order No. 4 of 2013 forming the Cabinet. In this order, Ministry of Development Planning and Statistics has been founded and Dr. Saleh Mohamed Salem Al Nabit has been appointed as Minister of Development Planning and Statistics. It was formed as a result of a merger between the General Secretariat for Development Planning (GSDP) and Qatar Statistics Authority (QSA). References Government ministries of Qatar Ministries established in 2013 2013 establishments in Qatar Urban planning in Qatar
https://en.wikipedia.org/wiki/Heavy-light%20decomposition
In combinatorial mathematics and theoretical computer science, heavy-light decomposition (also called heavy path decomposition) is a technique for decomposing a rooted tree into a set of paths. In a heavy path decomposition, each non-leaf node selects one "heavy edge", the edge to the child that has the greatest number of descendants (breaking ties arbitrarily). The selected edges form the paths of the decomposition. Decomposition into paths If the edges of a tree T are partitioned into a set of heavy edges and light edges, with one heavy edge from each non-leaf node to one of its children, then the subgraph formed by the heavy edges consists of a set of paths, with each non-leaf vertex belonging to exactly one path, the one containing its heavy edge. Leaf nodes of the tree that are not the endpoint of a heavy edge may be considered as forming paths of length zero. In this way, each vertex belongs to exactly one of the paths. Each path has a head vertex, its topmost vertex. Alternatively, the paths of heavy edges may be extended by including one light edge, the one from the head of the path to its parent. In this variation of the decomposition, some vertices belong to multiple paths, but every edge of T belongs to exactly one path. The path tree The paths of the decomposition may themselves be organized into a tree called the "path tree", "heavy path tree", or "compressed tree". Each node of the path tree corresponds to a path of the heavy path decomposition. If p is a path of the heavy path decomposition, then the parent of p in the path tree is the path containing the parent of the head of p. The root of the path tree is the path containing the root of the original tree. Alternatively, the path tree may be formed from the original tree by edge contraction of all the heavy edges. A "light" edge of a given tree is an edge that was not selected as part of the heavy path decomposition. If a light edge connects two tree nodes x and y, with x the parent of y, then x must have at least twice as many descendants as y. Therefore, on any root-to-leaf path of a tree with n nodes, there can be at most log2 n light edges. Equivalently, the path tree has height at most log2 n. Applications Heavy path decomposition was introduced by as part of the amortized analysis of their link/cut tree structure, and by as part of their data structure for lowest common ancestors, The link/cut tree data structure uses a partition of a dynamic tree into paths that is not necessarily the heavy path decomposition; its analysis uses a potential function measuring its distance from the heavy path decomposition, and the small height of the path tree implies that each data structure operation performs only a small number of steps that cannot be charged against improvements to this function. In the lowest common ancestor data structure, the decomposition is used to embed the input tree into a complete binary tree of logarithmic depth, allowing each query to be solved by cons
https://en.wikipedia.org/wiki/International%20Journal%20of%20Science%20and%20Mathematics%20Education
The International Journal of Science and Mathematics Education is a bimonthly peer-reviewed academic journal published by Springer Science+Business Media on behalf of the National Science Council of Taiwan. It covers science and mathematics education topics and research methods, particularly ones with cross-curricular dimensions or which explore the area from different cultural perspectives. The journal was established in 2004 with Fou-Lai Lin (National Taiwan Normal University). The current editor-in-chief is Hsin-Kai Wu (National Taiwan Normal University). Abstracting and indexing The journal is abstracted and indexed in: According to the Journal Citation Reports, the journal has a 2020 impact factor of 2.073. References External links Bimonthly journals Academic journals established in 2004 English-language journals Science education journals Springer Science+Business Media academic journals Mathematics education journals
https://en.wikipedia.org/wiki/Geometrically%20regular%20ring
In algebraic geometry, a geometrically regular ring is a Noetherian ring over a field that remains a regular ring after any finite extension of the base field. Geometrically regular schemes are defined in a similar way. In older terminology, points with regular local rings were called simple points, and points with geometrically regular local rings were called absolutely simple points. Over fields that are of characteristic 0, or algebraically closed, or more generally perfect, geometrically regular rings are the same as regular rings. Geometric regularity originated when Claude Chevalley and André Weil pointed out to that, over non-perfect fields, the Jacobian criterion for a simple point of an algebraic variety is not equivalent to the condition that the local ring is regular. A Noetherian local ring containing a field k is geometrically regular over k if and only if it is formally smooth over k. Examples gave the following two examples of local rings that are regular but not geometrically regular. Suppose that k is a field of characteristic p > 0 and a is an element of k that is not a pth power. Then every point of the curve xp + yp = a is regular. However over the field k[a1/p], every point of the curve is singular. So the points of this curve are regular but not geometrically regular. In the previous example, the equation defining the curve becomes reducible over a finite extension of the base field. This is not the real cause of the phenomenon: Chevalley pointed out to Zariski that the curve xp + y2 = a (with the notation of the previous example) is absolutely irreducible but still has a point that is regular but not geometrically regular. See also Regular scheme References Commutative algebra Algebraic geometry
https://en.wikipedia.org/wiki/R.%20K.%20Rubugunday
Raghunath Krishna Rubugunday (1918–2000) was an Indian mathematician specializing in number theory notable for his contribution to Waring's problem. Rubugunday was born in Madras in 1918. The famous mathematician K. Ananda Rau was an uncle on his father's side. He completed his B.A. Hons from Presidency College, Madras and Tripos from Cambridge in 1938. He returned to India and among other positions he was the Head of the Department of Mathematics at Saugar university. References 1918 births 2000 deaths 20th-century Indian mathematicians Indian number theorists Scientists from Chennai Presidency College, Chennai alumni Alumni of the University of Cambridge
https://en.wikipedia.org/wiki/Characteristic%20variety
In mathematical analysis, the characteristic variety of a microdifferential operator P is an algebraic variety that is the zero set of the principal symbol of P in the cotangent bundle. It is invariant under a quantized contact transformation. The notion is also defined more generally in commutative algebra. A basic theorem says a characteristic variety is involutive. References M. Sato, T. Kawai, and M. Kashiwara: Microfunctions and Pseudo-differential Equations. Lecture note in Math., No. 287, Springer, Berlin-Heidelberg-New York, pp. 265–529 (1973) Algebraic varieties Mathematical analysis
https://en.wikipedia.org/wiki/Mikhail%20Rakhmanov
Mikhail Alexeyevich Rakhmanov (; born May 27, 1992) is a Kazakhstani professional ice hockey winger who currently plays for Barys Astana of the Kontinental Hockey League (KHL). Career statistics Regular season International References External links 1992 births Living people Ice hockey people from Oskemen Barys Nur-Sultan players Snezhnye Barsy players Kazakhstani ice hockey right wingers Universiade silver medalists for Kazakhstan Universiade medalists in ice hockey Competitors at the 2017 Winter Universiade
https://en.wikipedia.org/wiki/Effaceable%20functor
In mathematics, an effaceable functor is an additive functor F between abelian categories C and D for which, for each object A in C, there exists a monomorphism , for some M, such that . Similarly, a coeffaceable functor is one for which, for each A, there is an epimorphism into A that is killed by F. The notions were introduced in Grothendieck's Tohoku paper. A theorem of Grothendieck says that every effaceable δ-functor (i.e., effaceable in each degree) is universal. References External links Meaning of “efface” in “effaceable functor” and “injective effacement” Functors
https://en.wikipedia.org/wiki/Beth%20Dawson
Elizabeth Knight Dawson (also published as Dawson-Saunders) is a biostatistician and biostatistics textbook author. Education and career Dawson completed a Ph.D. in educational psychology at the University of Illinois at Urbana–Champaign in 1977; her dissertation was The Sampling Distribution of The Canonical Redundancy Statistic. She worked as a professor in the Department of Medical Humanities of the Southern Illinois University School of Medicine, where she was granted tenure in 1981. By 1990 she was working as a senior psychometrician in the National Board of Medical Examiners, and by 1992 she had moved again to the American Board of Internal Medicine. After returning to the Southern Illinois University School of Medicine, she was chair of the 2000 Research in Medical Education Conference, and chair of the Council of Sections of the American Statistical Association. Book Dawson is the coauthor of the textbook Basic and Clinical Biostatistics (with Robert G. Trapp, Appleton & Lange, 1990). Recognition Dawson was elected as a Fellow of the American Statistical Association in 1994. References Year of birth missing (living people) Living people American statisticians Women statisticians University of Illinois College of Education alumni Southern Illinois University faculty Fellows of the American Statistical Association
https://en.wikipedia.org/wiki/Newport%20built-up%20area
The Newport Built-up area (previously known in official statistics as the Newport Urban Area) is an area of land defined by the United Kingdom Office for National Statistics (ONS) for population monitoring purposes. It is an urban conurbation and is not coterminous with the city boundaries. It consists of the urban area centred on Newport as well as contiguous settlements in the eastern and western valleys extending north of the city – including Cwmbran, Pontypool, Risca, Abercarn and Blackwood. It does however exclude physically detached urban areas within the city boundaries, such as Marshfield. The detailed methodology of the process used across the UK by ONS in 2011 is set out in 2011 Built-up Areas - Methodology and Guidance, published in June 2013. It is summarised as "..a ‘bricks and mortar’ approach, with areas defined as built-up land with a minimum area of 20 hectares (0.2 km2 / 0.077 mile2), while settlements within 200 metres of each other are linked. Built-up area sub-divisions are also identified to provide greater detail in the data, especially in the larger conurbations." The total population of the built-up area defined on this basis in 2011 was 306,844, making Newport the 23rd largest conurbation in England and Wales and the 2nd largest in Wales. Subdivisions The ONS provides sub-division statistics for the Newport Urban Area See also List of conurbations in the United Kingdom List of Welsh principal areas by population List of Welsh principal areas by area List of localities in Wales by population References Geography of Newport, Wales Urban areas of Wales Demographics of Wales
https://en.wikipedia.org/wiki/Promethea%20Pythaitha
Promethea Olympia Kyrene Pythaitha (born "Jasmine Smith" on March 13, 1991) is an American child genius with an IQ of 173. She started reading at age 1, began learning college-level calculus and was profiled by a CBS News 48 Hours special on "Whiz Kids!" at age 7, and at age 13 became the youngest student to complete work for a bachelor's degree from Montana State University in Mathematics. Early life and education Promethea was born to Georgia Smith, a Greek-born artist, and has two older siblings, Vanessa and Apollo. Her father, David Li, lives in San Jose, CA. For several months when Promethea was 4, she and her family were homeless and lived in their car in San Francisco. This was when her mother began to teach her advanced mathematics. At age 5, she was enrolled in Stanford University's Education Program for Gifted Youth. After being featured on a national CBS News special "Whiz Kids!", she was allowed to enroll as a regular student earning credit toward graduation at Montana State University. She audited her first M.S.U. course, calculus, at age 7. At age 13, she completed the course work necessary for a bachelor's degree in Mathematics, and at age 14 she officially graduated with that degree. Paying for college had always been a difficulty for the young student. Due to her young age, she was automatically disqualified for most university scholarships, and couldn't hold a job. A local family had paid for her tuition through the completion of her first degree. After her graduation, she spoke of her desire to continue her education, but due to her family's low income could not afford to continue with her studies. She wrote to Montana politicians, arguing that the state of Montana pledges a taxpayer funded education to other teenagers (throughout what is generally their high school years), but that she was being abandoned. Her alma mater offered to waive her tuition until she turned 16. In 2004, she changed her name, selecting names reflecting her aspirations and the ideals that she admired in ancient Greek history. Controversy In 2006, Promethea was awarded a $10,000 scholarship by the PanHellenic Scholarship Foundation. In January 2007, she was invited to speak in Chicago at a banquet to honor the Festival of the Three Hierarchs, a commemoration of the three founders of the Greek Orthodox Church. Her topic was to be the role of the church in education. During her research on the church founders, Promethea became convinced that the Church had committed genocide. In her speech, she demanded a separation of church and state, as well as the end of church control on education. The event was posted to YouTube and seen by Greeks around the world. Promethea received messages from passionate Greeks in America and Greece. Some sent her hate mail, but others commended her courage and sent books and offers of tuition. After her speech, she was invited to visit Greece for five days and was interviewed by Alpha TV. In 2011, she witnessed a shooting
https://en.wikipedia.org/wiki/North%20Wiltshire%2C%20Prince%20Edward%20Island
North Wiltshire is a municipality that holds community status in Prince Edward Island, Canada. It was incorporated in 1974. Demographics In the 2021 Census of Population conducted by Statistics Canada, North Wiltshire had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021. See also List of communities in Prince Edward Island References Communities in Queens County, Prince Edward Island Rural municipalities in Prince Edward Island
https://en.wikipedia.org/wiki/St.%20Nicholas%2C%20Prince%20Edward%20Island
St. Nicholas is a municipality that holds community status in Prince Edward Island, Canada. It was incorporated in 1991. Demographics In the 2021 Census of Population conducted by Statistics Canada, St. Nicholas had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021. See also List of communities in Prince Edward Island References Communities in Prince County, Prince Edward Island Rural municipalities in Prince Edward Island
https://en.wikipedia.org/wiki/York%2C%20Prince%20Edward%20Island
York is a municipality that holds community status in Prince Edward Island, Canada. It was incorporated in 1986. Demographics In the 2021 Census of Population conducted by Statistics Canada, York had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021. See also List of communities in Prince Edward Island References Communities in Queens County, Prince Edward Island Rural municipalities in Prince Edward Island
https://en.wikipedia.org/wiki/David%20Heron%20%28statistician%29
David Heron (28 April 1881 - 4 November 1969) was a Scottish statistician who was president of the Royal Statistical Society from 1947–1949. He was born in Perth and studied Mathematics and Natural Philosophy at the University of St Andrews. He was Karl Pearson's research assistant. Later he became a fellow at the Eugenics Laboratory of University College London. In 1906 he published "On the relation of fertility in man to social status". In 1915 he became chief statistician for the London Guarantee & Accident Company, an insurance company. During the Second World War, he was Director of Statistics for the Ministry of Food. He was married to Ethel Medwin from 1916 until her death in 1959. References External links "On the relation of fertility in man to social status" 1881 births Presidents of the Royal Statistical Society 1969 deaths
https://en.wikipedia.org/wiki/Auxiliary%20line
An auxiliary line (or helping line) is an extra line needed to complete a proof in plane geometry. Other common auxiliary constructs in elementary plane synthetic geometry are the helping circles. As an example, a proof of the theorem on the sum of angles of a triangle can be done by adding a straight line parallel to one of the triangle sides (passing through the opposite vertex). Although the adding of auxiliary constructs can often make a problem obvious, it's not at all obvious to discover the helpful construct among all the possibilities, and for this reason many prefer to use more systematic methods for the solution of geometric problems (such as the coordinate method, which requires much less ingenuity). References External links http://www.cut-the-knot.org/Generalization/MenelausByEinstein.shtml On Einstein's opinion regarding proofs that use the introduction of additional constructs Geometry
https://en.wikipedia.org/wiki/Saleh%2C%20Beni%20Suef
The village of Bani Saleh is one of the villages located in the center Fashn Beni Suef Arab Republic of Egypt. According to statistics for 2022-2023 April, the population of the city of Beni Suef, Egypt comprises 225.789 people. See also Beni Suef List of villages in Beni Suef Governorate References Villages in Egypt Populated places in Beni Suef Governorate
https://en.wikipedia.org/wiki/Local%20uniformization
In algebraic geometry, local uniformization is a weak form of resolution of singularities, stating roughly that a variety can be desingularized near any valuation, or in other words that the Zariski–Riemann space of the variety is in some sense nonsingular. Local uniformization was introduced by , who separated out the problem of resolving the singularities of a variety into the problem of local uniformization and the problem of combining the local uniformizations into a global desingularization. Local uniformization of a variety at a valuation of its function field means finding a projective model of the variety such that the center of the valuation is non-singular. This is weaker than resolution of singularities: if there is a resolution of singularities then this is a model such that the center of every valuation is non-singular. proved that if one can show local uniformization of a variety then one can find a finite number of models such that every valuation has a non-singular center on at least one of these models. To complete a proof of resolution of singularities it is then sufficient to show that one can combine these finite models into a single model, but this seems rather hard. (Local uniformization at a valuation does not directly imply resolution at the center of the valuation: roughly speaking; it only implies resolution in a sort of "wedge" near this point, and it seems hard to combine the resolutions of different wedges into a resolution at a point.) proved local uniformization of varieties in any dimension over fields of characteristic 0, and used this to prove resolution of singularities for varieties in characteristic 0 of dimension at most 3. Local uniformization in positive characteristic seems to be much harder. proved local uniformization in all characteristic for surfaces and in characteristics at least 7 for 3-folds, and was able to deduce global resolution of singularities in these cases from this. simplified Abhyankar's long proof. extended Abhyankar's proof of local uniformization of 3-folds to the remaining characteristics 2, 3, and 5. showed that it is possible to find a local uniformization of any valuation after taking a purely inseparable extension of the function field. Local uniformization in positive characteristic for varieties of dimension at least 4 is (as of 2019) an open problem. References (1998 2nd edition) External links Algebraic geometry Singularity theory
https://en.wikipedia.org/wiki/2013%E2%80%9314%20NK%20Hrvatski%20Dragovoljac%20season
The 2013–14 season is Hrvatski Dragovoljac's first season back in the Prva HNL since their promotion in 2012. This article shows player statistics and all official matches that the club will play during the 2013–14 season. Squad Competitions Prva HNL Results summary Results Table References NK Hrvatski Dragovoljac seasons Hrvatski Dragovoljac
https://en.wikipedia.org/wiki/Stephan%20Zwierschitz
Stephan Zwierschitz (born 17 September 1990) is an Austrian professional footballer who plays for Admira Wacker. Club statistics Updated to games played as of 16 June 2014. References External links Stephan Zwierschitz at ÖFB 1990 births Living people People from Mödling Austrian men's footballers Austria men's under-21 international footballers Men's association football defenders SKN St. Pölten players FC Admira Wacker Mödling players FK Austria Wien players Austrian Football Bundesliga players 2. Liga (Austria) players Footballers from Lower Austria
https://en.wikipedia.org/wiki/Procyclic
Procyclic may refer to: a term related to the profinite groups in mathematics Procyclic life stage, a life stage of the Trypanosoma parasite in African trypanosomiasis Procyclical and countercyclical are terms used to describe how an economic quantity is related to economic fluctuations.
https://en.wikipedia.org/wiki/Peter%20G.%20Moore
Professor Peter Gerald Moore (5 April 1928 – 14 June 2010) was an, academic, actuary and statistician. He was Professor of Statistics at London Business School, 1965–1993 and its principal from 1984 to 1989. Moore was a graduate of KCS Wimbledon, and subsequently at University College London where he took a first class honors degree in statistics. He also completed a PhD at UCL, including time spent studying at Princeton, NJ (US) as a Commonwealth Fund Harkness Fellow. Following National Service with the Royal Horse Artillery where he rose to the rank of Major, he joined the Territorial Army and was awarded the Territorial Decoration in 1963. He was a partner in consulting actuaries Duncan Fraser from 1974 to 1977. In 1984 he became the first president of the Institute of Actuaries from outside the insurance industry (1984-1986), subsequently also becoming the President of the Royal Statistical Society (1989-1991). A freeman of the city of London, he served as master of the Tallow Chandlers Company from 1994-1995. He was awarded the Guy medal (1970) and the Chambers Medal (1995) He served as a director of many FTSE 100 companies, government committees and helped establish the Hong Kong University of Science and Technology. He was a prolific writer, publishing many books on statistics and risk in management decisions. His books include: Standard Statistical Calculations 1965, Basic Operational Research 1971, Reason By Numbers 1980, The Anatomy of Decisions 1989, Moore received an honorary doctorate from Heriot-Watt University in 1985 His primary career legacy remains the London Business School. As a founding member of the faculty, he helped shape the curriculum and build the institution into a world leading provider of management education. In his roles as Vice Principal and Principal (now Dean) through the 1970s and 1980s, he grew the organisation, programs, student base and facilities. References 1928 births 2010 deaths Presidents of the Royal Statistical Society British statisticians Academics of London Business School
https://en.wikipedia.org/wiki/2013%E2%80%9314%20FK%20Pelister%20season
The 2013–14 season was a FK Pelister's 2nd consecutive season in First League. This article shows player statistics and all official matches that the club was played during the 2013–14 season. Current squad As of 29 January 2014 Competitions First League Results summary Results by round Results Table Macedonian Football Cup First round Second round Quarter-final Statistics Top scorers References FK Pelister seasons Pelister
https://en.wikipedia.org/wiki/2013%E2%80%9314%20FK%20Bregalnica%20%C5%A0tip%20season
The 2013–14 season is FK Bregalnica Štip's 4th consecutive season in First League. This article shows player statistics and all official matches that the club will play during the 2013–14 season. Squad As of 11 August 2013 Competitions First League Results summary Results Table Macedonian Cup Statistics Top scorers References FK Bregalnica Štip seasons Bregalnica Stip
https://en.wikipedia.org/wiki/2013%E2%80%9314%20Scottish%20Professional%20Football%20League
Statistics of the Scottish Professional Football League in season 2013–14. It was the first season of the competition, which had been formed in the summer of 2013 by the merger of the Scottish Premier League and the Scottish Football League. Scottish Premiership Scottish Championship Scottish League One Scottish League Two Award winners See also 2013–14 in Scottish football References Scottish Professional Football League seasons
https://en.wikipedia.org/wiki/Michael%20Barry%20%28Northern%20Mariana%20Islands%20footballer%29
Michael 'Bo' Barry (born 10 November 1995) is a footballer who plays for the Northern Mariana Islands national team. He was born in Cambodia. Career statistics International References External links Michael Barry at the Saint Leo University website 1995 births Living people Men's association football midfielders Northern Mariana Islands men's footballers Northern Mariana Islands men's international footballers
https://en.wikipedia.org/wiki/Sandi%20Klav%C5%BEar
Sandi Klavžar (born 5 February 1962) is a Slovenian mathematician working in the area of graph theory and its applications. He is a professor of mathematics at the University of Ljubljana. Education Klavžar received his Ph.D. from the University of Ljubljana in 1990, under the supervision of Wilfried Imrich and Tomaž Pisanski. Research Klavžar's research concerns graph products, metric graph theory, chemical graph theory, graph domination, and the Tower of Hanoi. Together with Wilfried Imrich and Richard Hammack, he is the author of the book Handbook of Product Graphs (CRC Press, 2011). Together with Andreas M. Hinz, Uroš Milutinović, and Ciril Petr, he is the author of the book The Tower of Hanoi – Myths and Maths (Springer, Basel, 2013). Awards and honors In 2007, Klavžar received the Zois award for exceptional contributions to science and mathematics. References External links Home page at the University of Ljubljana Living people 20th-century Slovenian mathematicians Graph theorists Mathematical chemistry University of Ljubljana alumni Academic staff of the University of Ljubljana 1962 births 21st-century Slovenian mathematicians
https://en.wikipedia.org/wiki/Weber%20problem
In geometry, the Weber problem, named after Alfred Weber, is one of the most famous problems in location theory. It requires finding a point in the plane that minimizes the sum of the transportation costs from this point to destination points, where different destination points are associated with different costs per unit distance. The Weber problem generalizes the geometric median, which assumes transportation costs per unit distance are the same for all destination points, and the problem of computing the Fermat point, the geometric median of three points. For this reason it is sometimes called the Fermat–Weber problem, although the same name has also been used for the unweighted geometric median problem. The Weber problem is in turn generalized by the attraction–repulsion problem, which allows some of the costs to be negative, so that greater distance from some points is better. Definition and history of the Fermat, Weber, and attraction-repulsion problems In the triangle case, the Fermat problem consists in locating a point with respect to three points in such a way that the sum of the distances between and each of the three other points is minimized. It was formulated by the famous French mathematician Pierre de Fermat before 1640, and it can be seen as the true beginning of both location theory, and space-economy. Torricelli found a geometrical solution to this problem around 1645, but it still had no direct numerical solution more than 325 years later. E. Weiszfeld published a paper in 1937 with an algorithm for the Fermat-Weber problem. As the paper was published in Tohoku Mathematical journal, and Weiszfeld immigrated to USA and changed his name to Vaszoni, his work was not widely known. Kuhn and Kuenne independently found a similar iterative solution for the general Fermat problem in 1962, and, in 1972, Tellier found a direct numerical solution to the Fermat triangle problem, which is trigonometric. Kuhn and Kuenne's solution applies to the case of polygons having more than three sides, which is not the case with Tellier's solution for reasons explained further on. The Weber problem consists, in the triangle case, in locating a point with respect to three points in such a way that the sum of the transportation costs between and each of the three other points is minimized. The Weber problem is a generalization of the Fermat problem since it involves both equal and unequal attractive forces (see below), while the Fermat problem only deals with equal attractive forces. It was first formulated, and solved geometrically in the triangle case, by Thomas Simpson in 1750. It was later popularized by Alfred Weber in 1909. Kuhn and Kuenne's iterative solution found in 1962, and Tellier's solution found in 1972 apply to the Weber triangle problem as well as to the Fermat one. Kuhn and Kuenne's solution applies also to the case of polygons having more than three sides. In its simplest version, the attraction-repulsion problem consists
https://en.wikipedia.org/wiki/Convex%20position
In discrete and computational geometry, a set of points in the Euclidean plane or a higher-dimensional Euclidean space is said to be in convex position or convex independent if none of the points can be represented as a convex combination of the others. A finite set of points is in convex position if all of the points are vertices of their convex hull. More generally, a family of convex sets is said to be in convex position if they are pairwise disjoint and none of them is contained in the convex hull of the others. An assumption of convex position can make certain computational problems easier to solve. For instance, the traveling salesman problem, NP-hard for arbitrary sets of points in the plane, is trivial for points in convex position: the optimal tour is the convex hull. Similarly, the minimum-weight triangulation of planar point sets is NP-hard for arbitrary point sets, but solvable in polynomial time by dynamic programming for points in convex position. The Erdős–Szekeres theorem guarantees that every set of points in general position (no three in a line) in two or more dimensions has at least a logarithmic number of points in convex position. If points are chosen uniformly at random in a unit square, the probability that they are in convex position is The McMullen problem asks for the maximum number such that every set of points in general position in a -dimensional projective space has a projective transformation to a set in convex position. Known bounds are . References Convex hulls
https://en.wikipedia.org/wiki/Forensic%20statistics
Forensic statistics is the application of probability models and statistical techniques to scientific evidence, such as DNA evidence, and the law. In contrast to "everyday" statistics, to not engender bias or unduly draw conclusions, forensic statisticians report likelihoods as likelihood ratios (LR). This ratio of probabilities is then used by juries or judges to draw inferences or conclusions and decide legal matters. Jurors and judges rely on the strength of a DNA match, given by statistics, to make conclusions and determine guilt or innocence in legal matters. In forensic science, the DNA evidence received for DNA profiling often contains a mixture of more than one person's DNA. DNA profiles are generated using a set procedure, however, the interpretation of a DNA profile becomes more complicated when the sample contains a mixture of DNA. Regardless of the number of contributors to the forensic sample, statistics and probabilities must be used to provide weight to the evidence and to describe what the results of the DNA evidence mean. In a single-source DNA profile, the statistic used is termed a random match probability (RMP). RMPs can also be used in certain situations to describe the results of the interpretation of a DNA mixture. Other statistical tools to describe DNA mixture profiles include likelihood ratios (LR) and combined probability of inclusion (CPI), also known as random man not excluded (RMNE). Computer programs have been implemented with forensic DNA statistics for assessing the biological relationships between two or more people. Forensic science uses several approaches for DNA statistics with computer programs such as; match probability, exclusion probability, likelihood ratios, Bayesian approaches, and paternity and kinship testing. Although the precise origin of this term remains unclear, it is apparent that the term was used in the 1980s and 1990s. Among the first forensic statistics conferences were two held in 1991 and 1993. Random match probability Random match possibilities (RMP) are used to estimate and express the rarity of a DNA profile. RMP can be defined as the probability that someone else in the population, chosen at random, would have the same genotype as the genotype of the contributor of the forensic evidence. RMP is calculated using the genotype frequencies at all the loci, or how common or rare the alleles of a genotype are. The genotype frequencies are multiplied across all loci, using the product rule, to calculate the RMP. This statistic gives weight to the evidence either for or against a particular suspect being a contributor to the DNA mixture sample. RMP can only be used as a statistic to describe the DNA profile if it is from a single source or if the analyst is able to differentiate between the peaks on the electropherogram from the major and minor contributors of a mixture. Since the interpretation of DNA mixtures with more than two contributors is very difficult for analysts to do withou
https://en.wikipedia.org/wiki/Roland%20Baracskai
Roland Baracskai (born 11 April 1992 in Budapest) is a Hungarian professional footballer who plays for Csákvár. Club statistics Updated to games played as of 9 December 2017. References MLSZ HLSZ 1992 births Living people Footballers from Budapest Hungarian men's footballers Hungary men's youth international footballers Men's association football forwards FC Felcsút players Fehérvár FC players Puskás Akadémia FC players Soproni VSE players Mezőkövesdi SE footballers Győri ETO FC players Nemzeti Bajnokság I players Nemzeti Bajnokság II players 21st-century Hungarian people
https://en.wikipedia.org/wiki/Zsolt%20Gajdos
Zsolt Gajdos (born 4 February 1993) is a Hungarian professional footballer who plays as a midfielder for Szeged-Csanád Grosics Akadémia. Club statistics Updated to games played as of 1 June 2014. References External links HLSZ 1993 births Living people Footballers from Zakarpattia Oblast Ukrainian people of Hungarian descent Hungarian men's footballers Men's association football midfielders Puskás Akadémia FC players Békéscsaba 1912 Előre footballers Aqvital FC Csákvár players Szolnoki MÁV FC footballers Szombathelyi Haladás footballers Nyíregyháza Spartacus FC players Zalaegerszegi TE players Szeged-Csanád Grosics Akadémia footballers Nemzeti Bajnokság I players Nemzeti Bajnokság II players