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https://en.wikipedia.org/wiki/Exeter%20Mathematics%20School
Exeter Mathematics School is a maths school located in Exeter in the English county of Devon. It opened in September 2014 under the free schools initiative and is sponsored by Exeter College and the University of Exeter. It is intended to be a regional centre of excellence in mathematics for Cornwall, Devon, Dorset and Somerset. As a result, the school offers boarding facilities for pupils who live more than an hours drive away from the school. A total of 120 students are catered for at the school with some boarding from Monday to Friday during term time. The school is highly selective, with prospective students expected to have GCSE qualifications at grade 8-9 in Mathematics and Physics or Computer Science. Prospective students must also have five GCSEs in total at grade 5 or above including English at grade 6. The course structure of Exeter Mathematics School requires all students to study A-level Mathematics and Further Mathematics and either A-level Physics or Computer Science. Students may choose to study both, but one may be chosen and an additional A-level from a wider range of options, which are taught at Exeter College, may be taken as an alternative. References External links Boarding schools in Devon Education in Devon Educational institutions established in 2014 Free schools in England 2014 establishments in England Mathematics education in the United Kingdom Schools in Exeter University of Exeter
https://en.wikipedia.org/wiki/Aleksa%20Vidi%C4%87
Aleksa Vidić (; born 29 September 1994) is a Serbian professional footballer who plays as a defender for Shirak. Club career From 2013 till 2017 he played for Sloboda Užice. Career statistics References External links 1994 births Footballers from Užice Living people Serbian men's footballers Men's association football defenders FK Sloboda Užice players FK Mačva Šabac players FC Smolevichi players FC Minsk players FK Budućnost Podgorica players FK Zlatibor Čajetina players Shirak SC players Serbian First League players Belarusian Premier League players Montenegrin First League players Serbian expatriate men's footballers Expatriate men's footballers in Belarus Serbian expatriate sportspeople in Belarus Expatriate men's footballers in Montenegro Serbian expatriate sportspeople in Montenegro Expatriate men's footballers in Armenia
https://en.wikipedia.org/wiki/Vangelis%20Gotovos
Vangelis Gotovos (; born 13 August 1986) is a Greek professional footballer who plays as a defender for Gamma Ethniki club Panionios. Club statistics References 1986 births Living people Greek men's footballers Men's association football defenders Odysseas Anagennisi F.C. players Apollon Smyrnis F.C. players Footballers from Thessaloniki
https://en.wikipedia.org/wiki/Order%20polynomial
The order polynomial is a polynomial studied in mathematics, in particular in algebraic graph theory and algebraic combinatorics. The order polynomial counts the number of order-preserving maps from a poset to a chain of length . These order-preserving maps were first introduced by Richard P. Stanley while studying ordered structures and partitions as a Ph.D. student at Harvard University in 1971 under the guidance of Gian-Carlo Rota. Definition Let be a finite poset with elements denoted , and let be a chain elements. A map is order-preserving if implies . The number of such maps grows polynomially with , and the function that counts their number is the order polynomial . Similarly, we can define an order polynomial that counts the number of strictly order-preserving maps , meaning implies . The number of such maps is the strict order polynomial . Both and have degree . The order-preserving maps generalize the linear extensions of , the order-preserving bijections . In fact, the leading coefficient of and is the number of linear extensions divided by . Examples Letting be a chain of elements, we have and There is only one linear extension (the identity mapping), and both polynomials have leading term . Letting be an antichain of incomparable elements, we have . Since any bijection is (strictly) order-preserving, there are linear extensions, and both polynomials reduce to the leading term . Reciprocity theorem There is a relation between strictly order-preserving maps and order-preserving maps: In the case that is a chain, this recovers the negative binomial identity. There are similar results for the chromatic polynomial and Ehrhart polynomial (see below), all special cases of Stanley's general Reciprocity Theorem. Connections with other counting polynomials Chromatic polynomial The chromatic polynomial counts the number of proper colorings of a finite graph with available colors. For an acyclic orientation of the edges of , there is a natural "downstream" partial order on the vertices implied by the basic relations whenever is a directed edge of . (Thus, the Hasse diagram of the poset is a subgraph of the oriented graph .) We say is compatible with if is order-preserving. Then we have where runs over all acyclic orientations of G, considered as poset structures. Order polytope and Ehrhart polynomial The order polytope associates a polytope with a partial order. For a poset with elements, the order polytope is the set of order-preserving maps , where is the ordered unit interval, a continuous chain poset. More geometrically, we may list the elements , and identify any mapping with the point ; then the order polytope is the set of points with if . The Ehrhart polynomial counts the number of integer lattice points inside the dilations of a polytope. Specifically, consider the lattice and a -dimensional polytope with vertices in ; then we define the number of lattice points in ,
https://en.wikipedia.org/wiki/Wild%20problem
In the mathematical areas of linear algebra and representation theory, a problem is wild if it contains the problem of classifying pairs of square matrices up to simultaneous similarity. Examples of wild problems are classifying indecomposable representations of any quiver that is neither a Dynkin quiver (i.e. the underlying undirected graph of the quiver is a (finite) Dynkin diagram) nor a Euclidean quiver (i.e., the underlying undirected graph of the quiver is an affine Dynkin diagram). Necessary and sufficient conditions have been proposed to check the simultaneously block triangularization and diagonalization of a finite set of matrices under the assumption that each matrix is diagonalizable over the field of the complex numbers. See also Semi-invariant of a quiver References Linear algebra Representation theory
https://en.wikipedia.org/wiki/Hugo%20Norberto%20Castillo
Hugo Norberto Castillo Franco (born March 17, 1971 in Misiones, Argentina), known as Hugo Castillo, is an Argentine football manager and former player. Managerial statistics Managerial statistics External links 1971 births Living people Footballers from Misiones Province Argentine men's footballers Men's association football forwards Liga MX players C.F. Monterrey players Argentine football managers Atlas F.C. footballers Club América footballers Santos Laguna footballers Atlas F.C. managers Argentine expatriate men's footballers Argentine expatriate sportspeople in Mexico Expatriate men's footballers in Mexico
https://en.wikipedia.org/wiki/Bibhutibhushan%20Datta
Bibhutibhushan Datta (also Bibhuti Bhusan Datta; Bengali : বিভূতিভূষণ দত্ত, Bibhūtibhūṣaṇ Datta) (28 June 1888 – 6 October 1958) was a historian of Indian mathematics. Datta came from a poor Bengali family. He was a student of Ganesh Prasad, studied at University of Calcutta and secured the master's degree in mathematics in 1914 and doctorate degree in 1920 in applied mathematics. He taught at Calcutta University where he was lecturer at University Science College, and from 1924 to 1929 he was Rhashbehari Ghosh Professor of Applied Mathematics. During the 1920s and 1930s he created a reputation as an authority on the history of Indian mathematics. He was also deeply interested in Indian philosophy and religion. In 1929 he retired from his professorship and left the university in 1933, and became a sannyasin (an ascetic, a person who has renounced worldly pleasures) in 1938 under the name Swami Vidyaranya. History of Hindu Mathematics: A Source Book, written by him jointly with Avadhesh Narayan Singh (1901–1954) became a standard reference in the history of Indian mathematics. He also wrote a monograph on the Shulba Sutras. He published more than 70 research papers mostly related to history of Indian mathematics. In the last years of his life, as Swami Vidyaranya, he lived mainly at Pushkar (in Rajasthan). See also History of Hindu Mathematics: A Source Book External links Biography References Historians of mathematics Bengali mathematicians 1888 births 1958 deaths
https://en.wikipedia.org/wiki/Constant-recursive%20sequence
In mathematics and theoretical computer science, a constant-recursive sequence is an infinite sequence of numbers in which each number in the sequence is equal to a fixed linear combination of one or more of its immediate predecessors. The concept is variously known as a linear recurrence sequence, linear-recursive sequence, linear-recurrent sequence, a C-finite sequence, or a solution to a linear recurrence with constant coefficients. A prototypical example is the Fibonacci sequence , in which each number is the sum of the previous two. The power of two sequence is also constant-recursive because each number is the sum of twice the previous number. The square number sequence is also constant-recursive. However, not all sequences are constant-recursive; for example, the factorial sequence is not constant-recursive. All arithmetic progressions, all geometric progressions, and all polynomials are constant-recursive. Formally, a sequence of numbers is constant-recursive if it satisfies a recurrence relation where are constants. For example, the Fibonacci sequence satisfies the recurrence relation where is the th Fibonacci number. Constant-recursive sequences are studied in combinatorics and the theory of finite differences. They also arise in algebraic number theory, due to the relation of the sequence to polynomial roots; in the analysis of algorithms, as the running time of simple recursive functions; and in the theory of formal languages, where they count strings up to a given length in a regular language. Constant-recursive sequences are closed under important mathematical operations such as term-wise addition, term-wise multiplication, and Cauchy product. The Skolem–Mahler–Lech theorem states that the zeros of a constant-recursive sequence have a regularly repeating (eventually periodic) form. On the other hand, the Skolem problem, which asks for an algorithm to determine whether a linear recurrence has at least one zero, remains unsolved. Definition A constant-recursive sequence is any sequence of integers, rational numbers, algebraic numbers, real numbers, or complex numbers (written as as a shorthand) satisfying a formula of the form for all where are constants. (This equation is called a linear recurrence with constant coefficients of order d.) The order of the constant-recursive sequence is the smallest such that the sequence satisfies a formula of the above form, or for the everywhere-zero sequence. The d coefficients must be coefficients ranging over the same domain as the sequence (integers, rational numbers, algebraic numbers, real numbers, or complex numbers). For example for a rational constant-recursive sequence, and must be rational numbers. The definition above allows eventually-periodic sequences such as and . Some authors require that , which excludes such sequences. Examples Fibonacci and Lucas sequences The sequence 0, 1, 1, 2, 3, 5, 8, 13, ... of Fibonacci numbers is constant-recursive of order 2
https://en.wikipedia.org/wiki/Statsmodels
Statsmodels is a Python package that allows users to explore data, estimate statistical models, and perform statistical tests. An extensive list of descriptive statistics, statistical tests, plotting functions, and result statistics are available for different types of data and each estimator. It complements SciPy's stats module. Statsmodels is part of the Python scientific stack that is oriented towards data analysis, data science and statistics. Statsmodels is built on top of the numerical libraries NumPy and SciPy, integrates with Pandas for data handling, and uses Patsy for an R-like formula interface. Graphical functions are based on the Matplotlib library. Statsmodels provides the statistical backend for other Python libraries. Statsmodels is free software released under the Modified BSD (3-clause) license. References Free statistical software Python (programming language) scientific libraries
https://en.wikipedia.org/wiki/Raymond%20Ogden
Raymond William Ogden (born 19 September 1943) is a British applied mathematician. He is the George Sinclair Professor of Mathematics at the Department of Mathematics and Statistics of the University of Glasgow. Education Ogden earned his BA and PhD degrees from the University of Cambridge in 1970, under the supervision of Rodney Hill. His thesis was entitled On Constitutive Relations for Elastic and Plastic Materials. Work Ogden's research has been focused on the nonlinear theory of elasticity and its applications. His theoretical contributions include the derivation of exact solutions of nonlinear boundary value problems, for both compressible and incompressible materials, and an analysis of the linear and nonlinear stability of pre-stressed bodies and related studies of elastic wave propagation. In the field of applications, Ogden worked on modelling the elastic and inelastic behaviour of rubber-like solids. He has also made contributions to the biomechanics of soft biological tissues, the electroelasticity and magnetoelasticity of electromechanically sensitive elastomeric materials, and the effects on residual stress in materials that are capable of large elastic deformations. His book, Non-Linear Elastic Deformations, published in 1984 and reissued in 1999, has become a standard reference in this branch of solid mechanics. Awards and honours Ogden was awarded the ASME Koiter Medal in 2005 and the Prager Medal of the Society of Engineering Science in 2010. He was elected a Fellow of the Royal Society (FRS) in 2006. In 2016, the American Society of Mechanical Engineers (ASME) awarded Ogden the Timoshenko Medal. References Living people 1943 births Fellows of the Royal Society British mathematicians Academics of the University of Glasgow Alumni of the University of Cambridge
https://en.wikipedia.org/wiki/Segre%27s%20theorem
In projective geometry, Segre's theorem, named after the Italian mathematician Beniamino Segre, is the statement: Any oval in a finite pappian projective plane of odd order is a nondegenerate projective conic section. This statement was assumed 1949 by the two Finnish mathematicians G. Järnefelt and P. Kustaanheimo and its proof was published in 1955 by B. Segre. A finite pappian projective plane can be imagined as the projective closure of the real plane (by a line at infinity), where the real numbers are replaced by a finite field . Odd order means that is odd. An oval is a curve similar to a circle (see definition below): any line meets it in at most 2 points and through any point of it there is exactly one tangent. The standard examples are the nondegenerate projective conic sections. In pappian projective planes of even order greater than four there are ovals which are not conics. In an infinite plane there exist ovals, which are not conics. In the real plane one just glues a half of a circle and a suitable ellipse smoothly. The proof of Segre's theorem, shown below, uses the 3-point version of Pascal's theorem and a property of a finite field of odd order, namely, that the product of all the nonzero elements equals -1. Definition of an oval In a projective plane a set of points is called oval, if: (1) Any line meets in at most two points. If the line is an exterior (or passing) line; in case a tangent line and if the line is a secant line. (2) For any point there exists exactly one tangent at , i.e., . For finite planes (i.e. the set of points is finite) we have a more convenient characterization: For a finite projective plane of order (i.e. any line contains points) a set of points is an oval if and only if and no three points are collinear (on a common line). Pascal's 3-point version Theorem Let be an oval in a pappian projective plane of characteristic . is a nondegenerate conic if and only if statement (P3) holds: (P3): Let be any triangle on and the tangent at point to , then the points are collinear. Proof Let the projective plane be coordinatized inhomogeneously over a field such that is the tangent at , the x-axis is the tangent at the point and contains the point . Furthermore, we set (s. image) The oval can be described by a function such that: The tangent at point will be described using a function such that its equation is Hence (s. image) and I: if is a non degenerate conic we have and and one calculates easily that are collinear. II: If is an oval with property (P3), the slope of the line is equal to the slope of the line , that means: and hence (i): for all . With one gets (ii): and from we get (iii): (i) and (ii) yield (iv): and with (iii) at least we get (v): for all . A consequence of (ii) and (v) is . Hence is a nondegenerate conic. Remark: Property (P3) is fulfilled for any oval in a pappian projective plane of characteristic 2 with a n
https://en.wikipedia.org/wiki/Pallacanestro%20Treviso%20in%20international%20competitions
Pallacanestro Treviso history and statistics in FIBA Europe and Euroleague Basketball (company) competitions. European competitions Worldwide competitions External links FIBA Europe Euroleague ULEB Eurocup Pallacanestro Treviso Treviso
https://en.wikipedia.org/wiki/Ida%20Martha%20Metcalf
Ida Martha Metcalf (August 26, 1857 – October 24, 1952) was the second American woman to receive a PhD in mathematics. Early life Ida Metcalf was born in Texas to Charles A. and Martha C. (Williams) Metcalf. During her youth, her family moved about the south. After her father’s death, she moved to New England with her mother and siblings. By 1870, she was living in Massachusetts, where she taught school for many years. Education In 1883, Ida began studying at Boston University where she received a Bachelor’s in Philosophy (Ph.B.) in 1886. From 1888 to 1889, she was a graduate student at Cornell University, earning a master's degree in mathematics. After teaching at Bryn Mawr School in Baltimore, she returned to Cornell and receive her Ph.D. in 1893. Professional career For many years after receiving her Ph.D., Ida taught high school and worked in several financial firms and as a Civil Service Examiner. In 1912, she became a statistician in the Department of Finance for New York City, where she remained until her retirement in 1921. Later years After retirement, Ida continued to work intermittently as a Civil Service Examiner until 1939. Beginning with the onset of a serious illness in 1948, she lived in nursing homes until her death at the age of ninety-six. Theses 1886: The Origin and Development of Styles of Architecture PhB, Boston University. 1889: The Theory of Illumination by Reflected and Refracted Light Master's thesis, Cornell University. 1893: Geometric Duality in Space PhD dissertation, Cornell University (directed by James Edward Oliver). References External links Biographies of Women Mathematicians, Agnes Scott College American women mathematicians People from Texas Boston University alumni Cornell University alumni 1857 births 1952 deaths Bryn Mawr School people
https://en.wikipedia.org/wiki/List%20of%20NUTS%20regions%20in%20the%20European%20Union%20by%20GDP
This is a list of NUTS regions in the European Union by GDP. The European Union uses a classification for subnational territory called Nomenclature of Territorial Units for Statistics () (commonly abbreviated as NUTS). The NUTS 1 classification is applied to a group of regions, NUTS 2 for regions and NUTS 3 as subdivisions of regions. There are also two levels (NUTS 4 and 5) which relate to local administrative unit levels. Countries agree a NUTS classification with the European Commission. Geddes notes that NUTS level 2 is "particularly important", because they often exist as territorial-government divisions and are used for regional policies by countries. NUTS 1 typically has a population of 3-7 million; NUTS 2 0.8-3 million; and NUTS 3 150,000-800,000. As of 2015, there are 98 regions at NUTS 1 level, 276 regions at NUTS 2 level and 1,342 regions at NUTS 3 level (as a result, statistics at the NUTS level 3 are found as an external link to this article). The EU is based on the classification of NUTS 2 regions as: less developed regions, transition regions and more developed regions. The EU's Structural Funds and Cohesion Fund direct funding to NUTS level 2 regions based on their GDP (PPS) per capita in comparison to the EU average: less developed regions (less than 75%), transition regions (between 75% and 90% and more developed regions (over 90%). For the period 2014–20, EUR 351 billion will be invested in the EU's regions with most being directed to the less developed regions. NUTS level 1 (data in 2017) NUTS level 2 See also Economy of the European Union List of metropolitan areas in the European Union by GDP List of European regions by GDP References External links Annual GDP by NUTS 2 regions: Euro total; Euro per capita; PPS total; PPS per capita – Eurostat-Ref.: NAMA_10R_2GDP European Union
https://en.wikipedia.org/wiki/List%20of%20career%20achievements%20by%20Russell%20Westbrook
This page details the records, statistics, and career achievements of American professional basketball player Russell Westbrook. Westbrook plays the point guard position for the Los Angeles Clippers of the National Basketball Association (NBA). NBA career statistics Statistics are correct as of the 2016–17 season. Regular season Playoffs Career-highs Awards and accomplishments NBA Most Valuable Player: 2017 2x NBA scoring champion: 2015, 2017 5x NBA games played leader: 2009, 2010, 2011, 2012, 2013 9x All-NBA selection: First team: 2016, 2017 Second team: 2011, 2012, 2013, 2015, 2018 Third team: 2019, 2020 9x NBA All-Star: 2011, 2012, 2013, 2015, 2016, 2017, 2018, 2019, 2020 2x NBA All-Star Game MVP: 2015, 2016 NBA All-Rookie selection: First team: 2009 7x NBA Western Conference Player of the Month 15x NBA Western Conference Player of the Week 2x NBA Western Conference Rookie of the Month NBA Fan Award Best Style United States National game Olympic medalist: Gold: 2012 FIBA World Cup medalist: Gold: 2010 Olympic Basketball player of the year 2012 Best Comeback Athlete ESPY Award 2014 College Pac-10 Defensive Player of the Year: 2008 Best Dressed NBA player- 2017-2018 NBA achievements Regular season 1st Place All Time for triple-doubles in a career with 198. 1st Place All Time for triple-doubles in a single season with 42. 1st Place All Time for consecutive games with a triple double (11) (1/22/19-2/14/19). 1st Place All Time for 50-point triple-doubles in a single season with 3. 2nd Place All Time for points scored in a triple-double with 57 (3/29/2017 against Orlando Magic). Only player in NBA history to average a triple-double throughout three consecutive seasons. Only player in NBA history to average a triple double in four out of five seasons. Only player in NBA history to win the scoring title, MVP award, and average a triple-double in the same season. Only player in NBA history to win consecutive NBA All-Star Game MVP awards, without sharing either. Only player in NBA history to average 40 points, 12 rebounds, and 11 assists over a 5-game span. Only player in NBA history to win the scoring title and average at least 10 assists the following season. Only player in NBA history to have at least 100 points, 30 rebounds and 30 assists through his team's first three games of a season. Only player in NBA history to record a triple-double without missing a free throw or field goal (3/22/2017 against Philadelphia 76ers). Only player in NBA history to record five consecutive 30-point triple-doubles in a season. Only player in NBA history to have two streaks of seven consecutive triple-doubles in a single season. Only player in NBA history to record at least 50 points, 10 rebounds, and 10 assists three times in a single season. Only player in NBA history to record at least 45 points, 10 rebounds, and 10 assists four times in a single season. Only player in NBA history to record at least 40 points, 10 rebounds, and 10
https://en.wikipedia.org/wiki/Kenneth%20Walters
Kenneth Walters (1934 – 28 March 2022) was a British mathematician and rheologist. He was a Distinguished Research Professor at the Institute Of Mathematics, Physics and Computer Science of the Aberystwyth University. Education Walters earned his PhD from the University of Swansea in 1959 under the supervision of James G. Oldroyd. His thesis was entitled Some Elastico-Viscous Liquids with Continuous and Discrete Relaxation Spectra. Work Walters made contributions to rheology and the development of rheological science in the United Kingdom, and has conducted extensive studies of the behaviour of non-Newtonian fluids, particularly elastic liquids. He made advances in two major areas: the measurement of rheological properties, and the numerical solution of complex flows. In the first area, he extended the theory of viscometric flows, carried out a searching analysis of sources of error in the principal instruments in current use, and was involved in industrial applications arising in the manufacture of lubricants, detergents and paints. His book, Rheometry, is a standard work of reference and the book Numerical Simulation of Non-Newtonian Flow, of which he is joint author, is an influential text in this field of research. Awards and honours Prof. Walters was recognized extensively for his contributions to the rheological community by being awarded the Gold Medal from the British Society of Rheology in 1984 and the Weissenberg Award from the European Society of Rheology in 2002. Walters was elected a Fellow of the Royal Society (FRS) in 1991. In 1995 he was made a Foreign Associate of the National Academy of Engineering. He was an active member of the rheological community for many years. He served as President of the British Society of Rheology from 1974 to 1976, President of the European Society of Rheology from 1996 to 2000, and the Chairman of the International Committee on Rheology from 2000 to 2004. Personal life In 1961, Kenneth began dating Mary Eccles, an Aberystwyth student who had been Student ‘Rag Queen’ before they met. They were both committed Christians and married in 1963. Their mutual faith led them into lay leadership at St Michael's Anglican church in Aberystwyth. They had three children and seven grandchildren. Death Walters' death was announced on 30 March 2022. References 1934 births 2022 deaths British mathematicians Alumni of Swansea University Academics of Aberystwyth University Fellows of the Royal Society
https://en.wikipedia.org/wiki/Bronshtein%20and%20Semendyayev
Bronshtein and Semendyayev (often just Bronshtein or Bronstein, sometimes BS) is the informal name of a comprehensive handbook of fundamental working knowledge of mathematics and table of formulas originally compiled by the Russian mathematician Ilya Nikolaevich Bronshtein and engineer Konstantin Adolfovic Semendyayev. The work was first published in 1945 in Russia and soon became a "standard" and frequently used guide for scientists, engineers, and technical university students. Over the decades, high popularity and a string of translations, extensions, re-translations and major revisions by various editors led to a complex international publishing history centered around the significantly expanded German version. Legal hurdles following the fall of the Iron Curtain caused the development to split into several independent branches maintained by different publishers and editors to the effect that there are now two considerably different publications associated with the original title – and both of them are available in several languages. With some slight variations, the English version of the book was originally named A Guide-Book to Mathematics, but changed its name to Handbook of Mathematics. This name is still maintained up to the present by one of the branches. The other line is meanwhile named Users' Guide to Mathematics to help avoid confusion. Overview Bronshtein and Semendyayev is a comprehensive handbook of fundamental working knowledge of mathematics and table of formulas based on the Russian book (, literally: "Handbook of mathematics for engineers and students of technical universities") compiled by the Russian mathematician Ilya Nikolaevich Bronshtein () and engineer Konstantin Adolfovic Semendyayev (). The scope is the concise discussion of all major fields of applied mathematics by definitions, tables and examples with a focus on practicability and with limited formal rigour. The work also contains a comprehensive list of analytically solvable integrals, that is, those integrals which can be described in closed form with antiderivatives. History With Dmitrii Abramovich Raikov, Bronshtein authored a Russian handbook on elementary mathematics, mechanics and physics (), which was published in 1943. Around the same time in 1939/1940, Bronshtein, together with Semendyayev, also wrote their Russian handbook of mathematics for engineers and students of technical universities. Among other sources this work was influenced by the 1936 Russian translation of the 1931 edition of the much older German . Hot lead typesetting had already started when the Siege of Leningrad prohibited further development and the print matrices were relocated. After the war, they were considered lost, but could be found again years later, so that the first edition of could finally be published in 1945. The expanded German translation (literally: "Pocketbook of mathematics") by Viktor Ziegler was first published in 1958 by B. G. Teubner in Leipzig. It w
https://en.wikipedia.org/wiki/Conservative%20functor
In category theory, a branch of mathematics, a conservative functor is a functor such that for any morphism f in C, F(f) being an isomorphism implies that f is an isomorphism. Examples The forgetful functors in algebra, such as from Grp to Set, are conservative. More generally, every monadic functor is conservative. In contrast, the forgetful functor from Top to Set is not conservative because not every continuous bijection is a homeomorphism. Every faithful functor from a balanced category is conservative. References External links Category theory
https://en.wikipedia.org/wiki/Dwayne%20Jack
Dwayne Jack (born 19 January 1980) is a retired Trinidadian football player. Career statistics International International goals Scores and results list Trinidad and Tobago's goal tally first. References External links 1980 births Living people Trinidad and Tobago men's footballers Trinidad and Tobago men's international footballers Men's association football defenders 2007 CONCACAF Gold Cup players Tobago United F.C. players AC Port of Spain players San Juan Jabloteh F.C. players
https://en.wikipedia.org/wiki/Romauld%20Aguillera
Romauld Aguillera (born 2 February, 1979) is a retired Trinidadian football player. Career statistics International References External links Trinidad and Tobago men's footballers 1979 births Living people 2007 CONCACAF Gold Cup players Men's association football defenders Trinidad and Tobago men's international footballers
https://en.wikipedia.org/wiki/Giovanni%20Severini
Giovanni Severini (born April 23, 1993) is an Italian professional basketball player for Pallacanestro Cantù of the Italian Serie A2. Career statistics Lega Basket Serie A |- | style="text-align:left;"| 2009–10 | style="text-align:left;"| Siena | 1 || 0 || 1 || .0 || .0 || .0 || .0 || .0 || .0 || .0 || .0 |- | style="text-align:left;"| 2010–11 | style="text-align:left;"| Siena | 4 || 0 || 1.7 || .333 || 1.000 || .0 || .0 || .0 || .0 || .0 || .7 |- | style="text-align:left;"| 2011–12 | style="text-align:left;"| Siena | 1 || 0 || 1 || .0 || .0 || .0 || .0 || .0 || .0 || .0 || .0 |- | style="text-align:left;"| 2014–15 | style="text-align:left;"| Avellino | 3 || 0 || 1 || .0 || .0 || .0 || .3 || .0 || .0 || .0 || .0 |- | style="text-align:left;"| 2015–16 | style="text-align:left;"| Avellino | 21 || 1 || 4.5 || .263 || .250 || .500 || .5 || .1 || .2 || .0 || .6 |- class="sortbottom" | style="text-align:left;"| Career | style="text-align:left;"| | 30 || 1 || 3.6 || .171 || .300 || .250 || .4 || .1 || .1 || .0 || 0.5 External links Giovanni Severini at draftexpress.com Giovanni Severini at legabasket.it 1993 births Living people Italian men's basketball players Lega Basket Serie A players Mens Sana Basket players Pallacanestro Cantù players Shooting guards S.S. Felice Scandone players Sportspeople from Macerata
https://en.wikipedia.org/wiki/Peter%20Schr%C3%B6der
Peter Schröder is an American computer scientist and a professor of computer science at California Institute of Technology. Schröder is known for his contributions to discrete differential geometry and digital geometry processing. He is also a world expert in the area of wavelet based methods for computer graphics. In 2015, Schröder was elected as a Fellow of the Association for Computing Machinery for "contributions to computer graphics and geometry processing.". Biography Schröder received an M.S. from MIT's Media Lab in 1990, and a Ph.D. in computer science from Princeton University in 1994 under the supervision of Pat Hanrahan. In 1995, he joined the faculty of Caltech. He did his undergraduate work at the Technical University of Berlin in computer science and pure mathematics. Awards Schröder is the recipient of an NSF CAREER award, a Sloan Fellowship, a Packard Fellowship, and in 2015 was elected as a fellow of the Association for Computing Machinery. He is also the recipient of the ACM SIGGRAPH Computer Graphics Achievement Award in 2003. References Living people American computer scientists Fellows of the Association for Computing Machinery Year of birth missing (living people)
https://en.wikipedia.org/wiki/Apollon%20Patras%20B.C.%20in%20international%20competitions
Apollon Patras B.C. in international competitions is the history and statistics of Apollon Patras B.C. in FIBA Europe and Euroleague Basketball Company European-wide professional club basketball competitions. 1980s 1986–87 FIBA Korać Cup, 3rd–tier The 1986–87 FIBA Korać Cup was the 16th installment of the European 3rd-tier level professional basketball club competition FIBA Korać Cup, running from October 1, 1986 to March 25, 1987. The trophy was won by FC Barcelona, who defeated Limoges CSP in a two-legged final on a home and away basis. Overall, Apollon Patras achieved in present competition a record of 0 wins against 2 defeat, in one round. More detailed: First round Tie played on October 1, 1986 and on October 8, 1986. |} 1990s 1989–90 FIBA Korać Cup, 3rd–tier The 1989–90 FIBA Korać Cup was the 19th installment of the European 3rd-tier level professional basketball club competition FIBA Korać Cup, running from September 27, 1989 to March 28, 1990. The trophy was won by Ram Joventut, who defeated Scavolini Pesaro in a two-legged final on a home and away basis. Overall, Apollon Patras achieved in present competition a record of 0 wins against 2 defeats, in one round. More detailed: First round Tie played on September 27, 1989 and on October 4, 1989. |} 1996–97 FIBA EuroCup, 2nd–tier The 1996–97 FIBA EuroCup was the 31st installment of FIBA's 2nd-tier level European-wide professional club basketball competition FIBA EuroCup (lately called FIBA Saporta Cup), running from September 17, 1996 to April 15, 1997. The trophy was won by Real Madrid Teka, who defeated Riello Mash Verona by a result of 78–64 at Eleftheria Indoor Hall in Nicosia, Cyprus. Overall, Dexim Apollon Patras achieved in the present competition a record of 11 wins against 3 defeats, in three successive rounds. More detailed: First round Day 1 (September 17, 1996) |} Day 2 (September 24, 1996) |} Day 3 (October 1, 1996) |} Day 4 (October 8, 1996) |} Day 5 (October 15, 1996) |} Day 6 (November 5, 1996) |} Day 7 (November 12, 1996) |} Day 8 (November 19, 1996) |} Day 9 (December 3, 1996) |} Day 10 (December 10, 1996) |} Group F standings: Second round Tie played on January 14, 1997 and on January 21, 1997. |} Top 16 Tie played on February 11, 1997 and on February 18, 1997. |} 1997–98 FIBA EuroCup, 2nd–tier The 1997–98 FIBA EuroCup was the 32nd installment of FIBA's 2nd-tier level European-wide professional club basketball competition FIBA EuroCup (lately called FIBA Saporta Cup), running from September 16, 1997 to April 14, 1998. The trophy was won by Žalgiris, who defeated Stefanel Milano by a result of 82–67 at Hala Pionir in Belgrade, Yugoslavia. Overall, Apollon Achaia Clauss achieved in the present competition a record of 8 wins against 4 defeats, in two successive rounds. More detailed: First round Day 1 (September 16, 1997) |} Day 2 (September 23, 1997) |} Day 3 (September 30, 1997) |} Day 4 (October 7, 1997) |} Da
https://en.wikipedia.org/wiki/Panellinios%20B.C.%20in%20international%20competitions
Panellinios B.C. in international competitions is the history and statistics of Panellinios B.C. in FIBA Europe and Euroleague Basketball Company European-wide club basketball competitions. European competitions See also Greek basketball clubs in international competitions External links FIBA Europe EuroLeague ULEB EuroCup Panellinios Greek basketball clubs in European and worldwide competitions
https://en.wikipedia.org/wiki/Franco%20Lobos
César Franco Lobos Asman (born 22 February 1999) is a Chilean footballer who currently plays for Universidad de Chile as a forward. Career statistics Club External links Living people 1999 births Chilean men's footballers Chilean Primera División players Segunda División B players Club Universidad de Chile footballers RC Celta Fortuna players Unión La Calera footballers Chilean expatriate men's footballers Chilean expatriate sportspeople in Spain Expatriate men's footballers in Spain Men's association football forwards Footballers from Santiago
https://en.wikipedia.org/wiki/Iskander%20Taimanov
Iskander Asanovich Taimanov (born 20 December 1961, Искандер Асанович Тайманов) is a Russian mathematician whose research concerns geometry, calculus of variations, and soliton theory. He is the chair of the department of geometry and topology of Novosibirsk State University. He is a member of the Russian Academy of Sciences. He was a Ph.D. student of Sergey Petrovich Novikov. Some topics of his work are Morse–Novikov theory and Willmore surfaces. He is the author of the textbook Lectures on Differential Geometry. References External links Page at Novosibirsk State University 20th-century Russian mathematicians 21st-century Russian mathematicians Moscow State University alumni Textbook writers Academic staff of Novosibirsk State University 1961 births Living people
https://en.wikipedia.org/wiki/2016%20JAFA%20Division%20I%20football%20season
The 2016 Japan college football season, involves all play of college football in Japan organized by the Japan American Football Association (JAFA) at the Division I level. The statistics on that season can be found below. Conference standings Postseason Bowls Rice Bowl Playoffs References External links American Football in Japan Japan American Football Association (Japanese) NFL Japan Standings (Japanese) American football in Japan 2016 in Japanese sport 2016 in American football
https://en.wikipedia.org/wiki/Matthew%20Emerton
Matthew James Emerton (born 9 November 1971) is an Australian mathematician who is a professor of mathematics at the University of Chicago. His research interests include number theory, especially the theory of automorphic forms. Early life and education He earned his PhD in 1998 from Harvard University (where he studied under Barry Mazur and his PhD thesis was titled "2-Adic Modular Forms of Minimal Slope" ) and a BS (honors) from the University of Melbourne. Career After postdoctoral positions at the University of Michigan and the University of Chicago, Emerton joined the Northwestern University mathematics department as an assistant professor in 2001. He became an associate professor in 2005 and a full professor in 2008. He joined the University of Chicago faculty in 2011. Emerton introduced the notion of completed cohomology, which has proved to be a useful tool in the study of the p-adic theory of automorphic forms. Using this theory, together with the work of Colmez on the p-adic Langlands program, he posted a preprint in 2011 proving many cases of the Fontaine--Mazur conjecture. Awards Emerton was a Sloan fellow in 1997 and was an invited speaker at the 2014 ICM in Seoul where he gave a talk entitled "Completed cohomology and the p-adic Langlands program". Social media Emerton formally ranked among the top 0.25% users of MathOverflow, where he used to be a frequent contributor, known for his expository pieces on the Langlands program, his posts on algebraic geometry, and his posts on number theory. He has also been noted for his helpful comments on math blogs. References 1971 births Living people University of Chicago faculty Harvard University alumni Australian mathematicians University of Melbourne alumni
https://en.wikipedia.org/wiki/Yoshio%20Shimamoto
Yoshio Shimamoto was a nuclear physicist who also did work in mathematics and computer science. While at Brookhaven National Laboratory (1954-1987), he designed the logic for the MERLIN digital computer in 1958, and served as chairman of the Applied Mathematics Department from 1964 to 1975. Shimamoto researched in combinatorial mathematics, the economics of outer continental shelf oil and gas lease sales (on behalf of the U.S. Geological Survey), the architecture of supercomputers, and the linking of computers for parallel processing. During the 1970s, he worked with Heinrich Heesch and Karl Durre on methods for a computer-aided proof of the four color theorem, using computer programs to apply Heesch's notion of "discharging" to eliminate 4-colorable cases. A proof of the Four Color Theorem, which he presented in 1971, was later shown to be flawed, but it served as the basis for further work. Born in Hawaii in 1924, Shimamoto served with the U.S. Army Signal Corps and Strategic Bombing Survey in Japan, during World War II. He died in New Jersey on August 27, 2009. References 2009 deaths American mathematicians Nuclear physicists Brookhaven National Laboratory staff
https://en.wikipedia.org/wiki/Prior-free%20mechanism
A prior-free mechanism (PFM) is a mechanism in which the designer does not have any information on the agents' valuations, not even that they are random variables from some unknown probability distribution. A typical application is a seller who wants to sell some items to potential buyers. The seller wants to price the items in a way that will maximize his profit. The optimal prices depend on the amount that each buyer is willing to pay for each item. The seller does not know these amounts, and cannot even assume that the amounts are drawn from a probability distribution. The seller's goal is to design an auction that will produce a reasonable profit even in worst-case scenarios. PFMs should be contrasted with two other mechanism types: Bayesian-optimal mechanisms (BOM) assume that the agents' valuations are drawn from a known probability distribution. The mechanism is tailored to the parameters of this distribution (e.g., its median or mean value). Prior-independent mechanisms (PIM) assume that the agents' valuations are drawn from an unknown probability distribution. They sample from this distribution in order to estimate the distribution parameters. From the point-of-view of the designer, BOM is the easiest, then PIM, then PFM. The approximation guarantees of BOM and PIM are in expectation, while those of PFM are in worst-case. What can we do without a prior? A naive approach is to use statistics: ask the potential buyers what their valuations are and use their replies to calculate an empirical distribution function. Then, apply the methods of Bayesian-optimal mechanism design to the empirical distribution function. The problem with this naive approach is that the buyers may behave strategically. Since the buyers' answers affect the prices that they are going to pay, they may be incentivized to report false valuations in order to push the price down. The challenge in PFMD is to design truthful mechanisms. In truthful mechanisms, the agents cannot affect the prices they pay, so they have no incentive to report untruthfully. Several approaches for designing truthful prior-free mechanisms are described below. Deterministic empirical distribution For every agent , let be the empirical distribution function calculated based on the valuations of all agents except . Use the Bayesian-optimal mechanism with to calculate price and allocation for agent . Obviously, the bid of agent affects only the prices paid by other agents and not his own price; therefore, the mechanism is truthful. This "empirical Myerson mechanism" works in some cases but not in others. Here is a case in which it works quite well. Suppose we are in a digital goods auction. We ask the buyers for their valuation of the good, and get the following replies: 51 buyers bid "$1" 50 buyers bid "$3". For each of the buyers in group 1, the empirical distribution is 50 $1-buyers and 50 $3-buyers, so the empirical distribution function is "0.5 chance of $1 and 0.5 chance of $3
https://en.wikipedia.org/wiki/Deutsche%20Gesellschaft%20f%C3%BCr%20Qualit%C3%A4t
DGQ (in German: Deutsche Gesellschaft für Qualität e. V.; in English: German Association for Quality) is a membership organization, which was founded in 1952 by Technical Statistics Committee under Committee for Economical Production. Since 1972, DGQ is legally independent under its present name. The statutory purpose of the DGQ is to develop the expertise and methods in the field of quality management, to learn about the latest findings and promote their practical implementation. To this end, DGQ develops, communicates and promotes continuously in order to improve integrative management systems. With its 62 regional circles and four regional offices, DGQ provides a network of committed quality experts from companies and other organisations covering training sessions and seminars on quality, environmental and health & safety management. The monthly journal Qualität und Zuverlässigkeit (in English; Quality and Reliability) is an important means of communication with its members. DGQ e.V. is certified by DQS according to DIN EN ISO 9001: 2008 (Registration No. 3024-01). Structure Founded in 1989, DQS Research serves annually about 15 national and international research projects - from idea to implementation. In collaboration with more than 20 research institutions in Germany, the association carries out projects under the industrial research on the Federation of Industrial Research Associations, AiF (in German: Arbeitsgemeinschaft industrieller Forschungsvereinigungen) with financial support of the Federal Ministry for Economic Affairs and Energy. FQS e.V. focus on new approaches to improve quality, support research in the field of quality assurance, quality management and in neighbouring topics. They initiate research and development activities and promote the transfer of results into operational practice - for example, with the FQS workshops. The Personnel Certification division (in German: DGQ Personenzertifizierungsstelle) of DGQ is certified by the DAkkS according to DIN EN ISO 17024 / IEC (Registration No. D-ZP-19768-01-00). It meets internationally agreed requirements and issues certificates that certify the people skills. Aa part of the restructuring in 2007, DGQ Weiterbildung GmbH was established as a training division for non-profit and charity purpose. Today, more than 12,000 professionals and managers adopt each year the diverse educational offer, which includes about 800 courses, seminars, compact training, exams, study programs and e-learning. External Presence - Germany - DGQ and DIN (German Institute for Standardization) founded the first German certification body, DQS in 1985. The founding aim was mainly to promote the German economy. In 1986, DQS issued the first ISO9001 certificate in Germany and is currently one of the world's largest system certification bodies. In 1990, DQS became a charter and full member of IQNet. The main objective of this international certification network is building mutual recognition of cert
https://en.wikipedia.org/wiki/Structured%20expert%20judgment%3A%20the%20classical%20model
Expert Judgment (EJ) denotes a wide variety of techniques ranging from a single undocumented opinion, through preference surveys, to formal elicitation with external validation of expert probability assessments. Recent books are . In the nuclear safety area, Rasmussen formalized EJ by documenting all steps in the expert elicitation process for scientific review. This made visible wide spreads in expert assessments and teed up questions regarding the validation and synthesis of expert judgments. The nuclear safety community later took onboard expert judgment techniques underpinned by external validation . Empirical validation is the hallmark of science, and forms the centerpiece of the classical model of probabilistic forecasting . A European Network coordinates workshops. Application areas include nuclear safety, investment banking, volcanology, public health, ecology, engineering, climate change and aeronautics/aerospace. For a survey of applications through 2006 see and give exhortatory overviews. A recent large scale implementation by the World Health Organization is described in . A long running application at the Montserrat Volcano Observatory is described in . The classical model scores expert performance in terms of statistical accuracy (sometimes called calibration) and informativeness . These terms should not be confused with “accuracy and precision”. Accuracy “is a description of systematic errors” while precision “is a description of random errors”. In the classical model statistical accuracy is measured as the p-value or probability with which one would falsely reject the hypotheses that an expert's probability assessments were statistically accurate. A low value (near zero) means it is very unlikely that the discrepancy between an expert's probability statements and observed outcomes should arise by chance. Informativeness is measured as Shannon relative information (or Kullback Leibler divergence) with respect to an analyst-supplied background measure. Shannon relative information is used because it is scale invariant, tail insensitive, slow, and familiar. Parenthetically, measures with physical dimensions, such as the standard deviation, or the width of prediction intervals, raise serious problems, as a change of units (meters to kilometers) would affect some variables but not others. The product of statistical accuracy and informativeness for each expert is their combined score. With an optimal choice of a statistical accuracy threshold beneath which experts are unweighted, the combined score is a long run “strictly proper scoring rule”: an expert achieves his long run maximal expected score by and only by stating his true beliefs. The classical model derives Performance Weighted (PW) combinations. These are compared with Equally Weighted (EW) combinations, and recently with Harmonically Weighted (HW) combinations, as well as with individual expert assessments. While some mathematicians and decision analys
https://en.wikipedia.org/wiki/London%20Institute%20for%20Mathematical%20Sciences
The London Institute (officially the London Institute for Mathematical Sciences) is Britain’s only independent research centre in theoretical physics and mathematics. It was founded to be an alternative to universities, where scientists have to spend time on teaching and administrative duties. Instead, the Institute gives its researchers the freedom and support to devote themselves to research full-time. History In 2008, the Texan physicist Thomas Fink had the idea for creating an independent British institute for physics and maths. It was initially met with scepticism. The then head of Cambridge’s Cavendish Laboratory, Peter Littlewood, told him, “An institute cannot live on grants alone.” But Caltech's Tom Tombrello, who had mentored Fink on his Physics 11 course, encouraged the idea. The Institute was founded in 2011 and received its first grant, from DARPA, the following year. In 2015 it became eligible for funding from the EU scientific research agency. In 2019 it was awarded Independent Research Organisation status by UKRI, becoming the first independent research centre in the physical sciences to be allowed to compete with universities for funding from the seven Research Councils. In 2021 its researchers moved into the Royal Institution, occupying rooms that were once the private apartments of Sir Humphry Davy, Michael Faraday and John Tyndall, among others. After Russia invaded Ukraine in February 2022, the Institute created the Arnold and Landau Fellowships, named after the Ukrainian mathematician Vladimir Arnold and the Russian physicist Lev Landau. Consisting of ten three-year full-time positions, this is the biggest programme of its kind in the world. Research The London Institute does research in theoretical physics and mathematics. It does not have laboratories and does not conduct experiments. The Institute is committed to curiosity-driven, theoretical research as this has historically led to the most far-reaching breakthroughs, such as gravity and electromagnetism. In an article in The Times, it defined its work as “spotting the patterns within patterns”, which is a way to “unify seemingly disconnected fields” and open up new perspectives and subfields. Research at the London Institute spans four themes: Mathematics that unifies; The elegant universe; Life, learning and emergence; and the Theory of human enterprise. Its researchers have published papers on statistical physics in Nature Reviews Physics; algebraic geometry in the Journal of High Energy Physics; graph theory in the European Journal of Combinatorics; and network theory in Physical Review Letters. In 2021, the UK government announced the launch of Advanced Research and Invention Agency (ARIA), a new science agency designed to support projects that may create "a paradigm shift in science". As a roadmap for the new agency, the London Institute compiled a list of the 23 Mathematical Challenges of our time. Inspired by David Hilbert’s list of 23 challenges, 17 of w
https://en.wikipedia.org/wiki/Qvist%27s%20theorem
In projective geometry, Qvist's theorem, named after the Finnish mathematician , is a statement on ovals in finite projective planes. Standard examples of ovals are non-degenerate (projective) conic sections. The theorem gives an answer to the question How many tangents to an oval can pass through a point in a finite projective plane? The answer depends essentially upon the order (number of points on a line −1) of the plane. Definition of an oval In a projective plane a set of points is called an oval, if: Any line meets in at most two points, and For any point there exists exactly one tangent line through , i.e., }. When the line is an exterior line (or passant), if a tangent line and if the line is a secant line. For finite planes (i.e. the set of points is finite) we have a more convenient characterization: For a finite projective plane of order (i.e. any line contains points) a set of points is an oval if and only if and no three points are collinear (on a common line). Statement and proof of Qvist's theorem Qvist's theorem Let be an oval in a finite projective plane of order . (a) If is odd, every point is incident with 0 or 2 tangents. (b) If is even, there exists a point , the nucleus or knot, such that, the set of tangents to oval is the pencil of all lines through . Proof (a) Let be the tangent to at point and let be the remaining points of this line. For each , the lines through partition into sets of cardinality 2 or 1 or 0. Since the number is even, for any point , there must exist at least one more tangent through that point. The total number of tangents is , hence, there are exactly two tangents through each , and one other. Thus, for any point not in oval , if is on any tangent to it is on exactly two tangents. (b) Let be a secant, } and }. Because is odd, through any , there passes at least one tangent . The total number of tangents is . Hence, through any point for there is exactly one tangent. If is the point of intersection of two tangents, no secant can pass through . Because , the number of tangents, is also the number of lines through any point, any line through is a tangent. Example in a pappian plane of even order Using inhomogeneous coordinates over a field even, the set }, the projective closure of the parabola , is an oval with the point as nucleus (see image), i.e., any line , with , is a tangent. Definition and property of hyperovals Any oval in a finite projective plane of even order has a nucleus . The point set } is called a hyperoval or ()-arc. (A finite oval is an ()-arc.) One easily checks the following essential property of a hyperoval: For a hyperoval and a point the pointset } is an oval. This property provides a simple means of constructing additional ovals from a given oval. Example For a projective plane over a finite field even and , the set } is an oval (conic section) (see image), } is a hyperoval and } is another oval that is not a conic
https://en.wikipedia.org/wiki/History%20of%20Hindu%20Mathematics
History of Hindu Mathematics: A Source Book is a treatise on the history of Indian mathematics authored by Bibhutibhushan Datta and Awadhesh Narayan Singh and originally published in two parts in 1930's. The book has since been reissued in one volume by Asia Publishing House in 1962. The treatise has been a standard reference for the history of Indian mathematics for many years. History of the book Bibhutibhushan Datta, the senior author of the book, delivered a lecture titled "Contribution of the Ancient Hindus to Mathematics" on 20 December 1927 to the Allahabad University Mathematical Association. This address was published in the Bulletin of the Allahabad University Mathematical Association in two papers totalling 60 pages in length. Datta expanded this paper and wrote the treatise History of Hindu Mathematics in three volumes. Datta retired from academic life in 1933 and became an itinerant ascetic. At the time of retirement, the manuscript of the three-volume work was entrusted to his junior colleague Awadhesh Narayan Singh. Singh published the first two of these volumes as a joint publication. The first volume titled History of Hindu Mathematics. A Source Book (Part 1: Numerical notation and arithmetic) was published in 1935 and the second volume titled History of Hindu Mathematics. A Source Book (Part 2: Algebra) was published in 1938. The planned third volume was never published. Contents of the book This is basically a source book. Under various topics are collected translations of Sanskrit texts as found in Hindu mathematical texts. Part 1 Part 1 of the book is divided into chapters. Chapter 1 gives details of the various methods employed by the Hindus for denoting numbers. The chapter also contains details of the gradual evolution of the decimal place value notation in India. Chapter 2 deals with arithmetic in general and it contains the details of various methods for performing the arithmetical operations using a "board". The evolution of the operations of addition, subtraction, multiplication, division, squaring, cubing, and the extraction square root and cube root are all discussed in detail. Part 2 The whole of Part 2, running to about 307 pages, constitutes just one chapter numbered as Chapter 3 of the book. Some of the topics discussed in this chapter are linear equations with one unknown and with two unknowns, quadratic equations, linear indeterminate equations, solutions of equations of the form Nx2 + 1 = y2, indeterminate equations of higher degrees, and rational triangles. From reviews Reactions to the publication of the book were mixed: some were highly favorable and some were highly critical. For example, the reviewer in American Mathematical Monthly found the book "From the standpoint of authoritative subject matter and from that of book-making, it is a notable history", whereas the reviewer in Isis, a journal of the History of Science Society, found the book " . . . a mathematical panegyric on Hindu history. A h
https://en.wikipedia.org/wiki/KK%20Cibona%20in%20international%20competitions
KK Cibona history and statistics in FIBA Europe and Euroleague Basketball (company) competitions. European competitions Worldwide competitions Record KK Cibona has overall, from 1969–70 (first participation) to 2015–16 (last participation): 271 wins against 263 defeats plus 1 draws in 535 games for all the European club competitions. EuroLeague: 181–200 (381) FIBA Saporta Cup: 38–18 plus 1 draw (56) /// EuroCup Basketball: 1–21 (22) FIBA Korać Cup: 42–17 (59) /// FIBA Europe Cup: 10–7 (17) Also KK Cibona has a 12–4 record in the FIBA Intercontinental Cup. See also Yugoslav basketball clubs in European competitions External links FIBA Europe EuroLeague ULEB EuroCup Cibona
https://en.wikipedia.org/wiki/Football%20records%20and%20statistics%20in%20Algeria
This page details football records in Algeria. Most successful clubs overall External links Algeria - List of Champions - rsssf Algeria - List of Cup Finals - rsssf Football in Algeria Algeria
https://en.wikipedia.org/wiki/Alfred%20Oscar%20Coffin
Alfred Oscar Coffin (May 14, 1861 – 1933) was a professor of mathematics and Romance language. He is best known for being the first African American to obtain a PhD in biology. Coffin earned his bachelor's degree and master's degree at Fisk University. In 1889, he earned his PhD in biology at Illinois Wesleyan University. His thesis was titled 'The Origin of the Mound Builders'. In 1887, Coffin taught at Alcorn Agricultural and Mechanical College for two years in Mississippi. From 1889 to 1895, he worked as a professor of mathematics and Romance language at Wiley University at Marshall, Texas. He later worked as the booking agent for John William Boone. Early life Coffin was born May 14, 1861, in Pontotoc, Mississippi. References 1861 births 1933 deaths 20th-century African-American academics 20th-century American academics People from Pontotoc, Mississippi 19th-century African-American scientists 19th-century American mathematicians American biologists Illinois Wesleyan University alumni Fisk University alumni Academics from Mississippi American zoologists 19th-century African-American academics 19th-century American academics African-American mathematicians 20th-century African-American scientists
https://en.wikipedia.org/wiki/Successive%20approximation
Methods of successive approximation are a category of strategies in pure and applied mathematics. Successive approximation also may refer to: Successive approximation ADC, analog-to-digital-conversion method appropriate for signal processing Shaping, behaviorist-psychology strategy of conditioning subtle behaviors only after conditioning gross behaviors See also Homing (disambiguation), e.g. homing in on a goal Honing (disambiguation), e.g. honing down a cutting tool
https://en.wikipedia.org/wiki/Filippo%20Antonio%20Revelli
Filippo Antonio Revelli (1716 – 1801) was an Italian mathematician. Life He was professor of geometry for 26 years at the University of Turin. He had among his pupils Joseph-Louis Lagrange. His son Vincenzo Antonio Revelli (1764-1835) was a philosopher and painter. Works References 1716 births 1801 deaths 18th-century Italian mathematicians Academic staff of the University of Turin
https://en.wikipedia.org/wiki/Plymouth%20High%20School%20%28Indiana%29
Plymouth High School is a public high school located in Plymouth, Indiana, United States. Statistics In the 2020-21 school year, total enrollment is at 1,095 students. In the 2021-22 school year the ethnicity breakdown was: White - 66.2% Hispanic - 29.1% Black - 0.9% Asian - 1.0% Multi-racial - 2.6% Notable alumni Clifford L. Linedecker, American investigative journalist and author of true crime books Scott Skiles, former NBA basketball player and coach. Led Plymouth High School to the 1982 IHSAA State Basketball Championship. Morgan Uceny, retired American track and field athlete who participated in the 2012 Summer Olympics in London. See also List of high schools in Indiana References External links Official Website Buildings and structures in Marshall County, Indiana Public high schools in Indiana
https://en.wikipedia.org/wiki/Sporting%20B.C.%20in%20international%20competitions
Sporting B.C. in international competitions is the history and statistics of Sporting B.C. in FIBA Europe and Euroleague Basketball Company competitions. European competitions European games FIBA Korać Cup, 31-10-1979: AO Sporting Athinai - BG Bayreuth 66-59 (32-22) AO Sporting (coach: xxx): Dave Caligaris 22, Tom Kappos 4, Giorgos Skropolithas 8, Zakynthinos 18, Vasilopoulos 20, Kagidis 4. BG Bayreuth (coach: Stephen McMahon): Stephen McMahon 22, Michel 6, Gottfried Oliwa 8, Buzz Harnett 19, Georg Kämpf 4, Graf, Wagner, Martin. See also Greek basketball clubs in international competitions External links FIBA Europe EuroLeague ULEB EuroCup Greek basketball clubs in European and worldwide competitions European
https://en.wikipedia.org/wiki/Mohamed%20Ben%20Ammar
Mohamed Ben Ammar ( is a Tunisian football player, currently playing for Stade Africain Menzel Bourguiba. Career statistics Club Notes References External links Living people Tunisian men's footballers Men's association football forwards Tunisian Ligue Professionnelle 1 players Stade Tunisien players AS Marsa players CS Hammam-Lif players Stade Africain Menzel Bourguiba players Year of birth missing (living people) Place of birth missing (living people)
https://en.wikipedia.org/wiki/Zied%20Jebali
Zied Jebali (; born June 28, 1990) is a Tunisian football player, currently playing for AS Rejiche. Career statistics Club Notes References External links 1990 births Living people Tunisian men's footballers Men's association football goalkeepers Tunisian Ligue Professionnelle 1 players AS Marsa players Étoile Sportive du Sahel players AS Gabès players AS Rejiche players
https://en.wikipedia.org/wiki/Extended%20Mathematical%20Programming
Algebraic modeling languages like AIMMS, AMPL, GAMS, MPL and others have been developed to facilitate the description of a problem in mathematical terms and to link the abstract formulation with data-management systems on the one hand and appropriate algorithms for solution on the other. Robust algorithms and modeling language interfaces have been developed for a large variety of mathematical programming problems such as linear programs (LPs), nonlinear programs (NPs), Mixed Integer Programs (MIPs), mixed complementarity programs (MCPs) and others. Researchers are constantly updating the types of problems and algorithms that they wish to use to model in specific domain applications. Extended Mathematical Programming (EMP) is an extension to algebraic modeling languages that facilitates the automatic reformulation of new model types by converting the EMP model into established mathematical programming classes to solve by mature solver algorithms. A number of important problem classes can be solved. Specific examples are variational inequalities, Nash equilibria, disjunctive programs and stochastic programs. EMP is independent of the modeling language used but currently it is implemented only in GAMS. The new types of problems modeled with EMP are reformulated with the GAMS solver JAMS to well established types of problems and the reformulated models are passed to a suitable GAMS solver to be solved. The core of EMP is a file called where the annotations that are needed for the reformulations are added to the model. Equilibrium problems Equilibrium problems model questions arising in the study of economic equilibria in a mathematically abstract form. Equilibrium problems include Variational Inequalities, problems with Nash Equilibria, and Multiple Optimization Problems with Equilibrium Constraints (MOPECs). Use EMP's keywords to reformulate these problems as mixed complementarity problems (MCPs), a class of problems for which mature solver technology exists. Solve the newly reformulated EMP keyword version of the problem with the PATH solver or other GAMS MCP solvers. Examples of the use of EMP to solve equilibrium problems include the computation of Cournot–Nash–Walras equilibria.., modeling water allocation, long-term planning of transmission line expansion of the electrical grid, modeling risk-averse agents in hydro-thermal electricity markets with uncertain inflows into hydro reservoirs and modeling variational inequalities in energy markets Hierarchical optimization Hierarchical optimization problems are mathematical programs with an additional optimization problem in their constraints. A simple example is the bilevel programming problem that optimizes an upper level objective over constraints that include another lower level optimization problem. Bilevel programming is used in many areas. One example is the design of optimal tax instruments. The tax instrument is modeled in the upper level and the clearing market is modeled in
https://en.wikipedia.org/wiki/Guillaume%20Le%20Blond
Guillaume Le Blond (1704 – May 24, 1781) was a French mathematician. He was born in Paris. He was a professor of mathematics at the grand stable of the King (1736) and then the Enfants de France (1756). Leblond kept this job until 1778, when he became secretary of the cabinet of Madame Victoire. Le Blond wrote the following works, some of which have been translated into German. His work "Éléments de fortification" was translated to Ottoman Turkish language in 1834 as "Usûl-i İstihkâmât"(Method of Fortifications) by Ishak Efendi. Essai sur la castramétation, 1748, in-8°) ; Éléments de tactique, 1758, in-4° ; Artillerie raisonnée contenant l’usage des différentes bouches à feu, 1761, in-8° ; l’Arithmétique et la géométrie de l’officier, 1768, 2 vol. in-8° ; Traité de l’attaque des places, 1780, in-8° ; Éléments de fortification, 1739, in-8°. He also produced editions of Mémoires d’artillerie by Pierre Surirey de Saint-Remy and the Géométrie by Joseph Sauveur and collaborated on the Encyclopédie. References Sources Pierre Larousse, Grand Dictionnaire universel du XIXe siècle, vol. 10, Paris, Administration du grand Dictionnaire universel, (p. 288). Scientists from Paris 1704 births 1781 deaths 18th-century French mathematicians Contributors to the Encyclopédie (1751–1772)
https://en.wikipedia.org/wiki/Walter%20Neumann
Walter David Neumann (born 1 January 1946) is a British mathematician who works in topology, geometric group theory, and singularity theory. He is an emeritus professor at Barnard College, Columbia University. Neumann obtained his Ph.D. under the joint supervision of Friedrich Hirzebruch and Klaus Jänich at the University of Bonn in 1969. He is a son of the mathematicians Bernhard Neumann and Hanna Neumann. His brother Peter M. Neumann was also a mathematician. He is in the Inaugural Class of Fellows of the American Mathematical Society. References External links Google Scholar Profile Home page at Columbia 20th-century British mathematicians Topologists 1946 births Fellows of the American Mathematical Society Living people
https://en.wikipedia.org/wiki/Sum%20of%20squares%20function
In number theory, the sum of squares function is an arithmetic function that gives the number of representations for a given positive integer as the sum of squares, where representations that differ only in the order of the summands or in the signs of the numbers being squared are counted as different, and is denoted by . Definition The function is defined as where denotes the cardinality of a set. In other words, is the number of ways can be written as a sum of squares. For example, since where each sum has two sign combinations, and also since with four sign combinations. On the other hand, because there is no way to represent 3 as a sum of two squares. Formulae k = 2 The number of ways to write a natural number as sum of two squares is given by . It is given explicitly by where is the number of divisors of which are congruent to 1 modulo 4 and is the number of divisors of which are congruent to 3 modulo 4. Using sums, the expression can be written as: The prime factorization , where are the prime factors of the form and are the prime factors of the form gives another formula , if all exponents are even. If one or more are odd, then . k = 3 Gauss proved that for a squarefree number , where denotes the class number of an integer . There exist extensions of Gauss' formula to arbitrary integer . k = 4 The number of ways to represent as the sum of four squares was due to Carl Gustav Jakob Jacobi and it is eight times the sum of all its divisors which are not divisible by 4, i.e. Representing , where m is an odd integer, one can express in terms of the divisor function as follows: k = 6 The number of ways to represent as the sum of six squares is given by where is the Kronecker symbol. k = 8 Jacobi also found an explicit formula for the case : Generating function The generating function of the sequence for fixed can be expressed in terms of the Jacobi theta function: where Numerical values The first 30 values for are listed in the table below: See also Jacobi's four-square theorem Gauss circle problem References External links Arithmetic functions Squares in number theory Integer factorization algorithms
https://en.wikipedia.org/wiki/Vadim%20Mogilnitsky
Vadim Anatolyevich Moghilnitsky (; 21 September 1935, Odessa — 3 August 2012, Chelyabinsk) — mathematics teacher, musicologist, translator, poet. The author of the first Russian biography of Russian pianist Sviatoslav Richter. Sister - Moghilnitskaya Galina Anatolyevna, Ukrainian pedagog, publicist and poet. Vadim Moghilnitsky was born in Odessa in the family of mathematics teachers Anatoly Alexandrovich Moghilnitsky and Asya Ivanovna Zvintarnaya. Graduated from Odessa University. Since 1965 lived in Chelyabinsk where he taught mathematics in South Ural State University. Vadim Moghilnitsky is the author of two books about Sviatoslav Richter: "Richter" (first Russian biography of the pianist, 2000) and "Richter-ensemblist" (2012). Also Vadim Moghilnitsky is the translator of Vladislav Dulemba's "Chopin", the biography of Chopin (from Polish into Russian, 2001). Vadim Moghilnitsky is the author of more than 200 pieces of poetry in Russian and Ukrainian languages. In 2015 the collection of selected poetry by Vadim Moghilnitsky was published: "Бессонные пути" ("Sleepless paths"). Bibliography Mathematics books В.И. Заляпин, Ю.Г. Малиновский, В.А. Могильницкий. МАТЕМАТИКА. В помощь поступающим., Челябинск, Изд. Татьяны Лурье, 2000, 320с. В.И. Заляпин, Ю.Г. Малиновский, В.А. Могильницкий. Компьютерное тестирование., Челябинск, Изд. ВЕРСИЯ, 1997, 64с. В.А. Могильницкий. Введение в анализ. Учебное пособие, ч.1(1999)Б –100с., ч.2(1997), 75с., Изд. ЮУрГУ В.А. Могильницкий. Элементы комплексного анализа : Учеб. пособие . Челябинск, ЧПИ им. Ленинского комсомола, 1989, 100с. Musicology Вадим Могильницкий. Святослав Рихтер. — Урал LTD, 2000. — Вадим Могильницкий. Шопен. — Урал LTD, 2001. — Вадим Могильницкий. Рихтер-ансамблист. — Издательский дом Игоря Розина, 2012. — Poetry Вадим Могильницкий. Бессонные пути. — Издательский дом Игоря Розина, 2015 — Links Страница, посвященная Вадиму Могильницкому, на сайте издательства Игоря Розина "Абрам Давидович Кацман - ученый, педагог, человек", Заляпин, В. И. "Поэзия и проза лучшего на свете ремесла" (Журнал "Юность" №7, 1963) Айвар Валеев - "Математик написал книгу о музыканте" (Журнал "Эксперт Урал" №6 (6), 2000) Лидия Панфилова - "Могильницкий написал книгу о музыканте Рихтере" (газета "Челябинский рабочий" от 19 апреля 2000) Анна Соболева - "Ломка критических стульев" (рецензия на книгу Вадима Могильницкого "Святослав Рихтер") 20th-century Russian writers Russian male poets 1935 births 2012 deaths 20th-century Russian male writers
https://en.wikipedia.org/wiki/Guillermo%20Celis
Guillermo León Celis Montiel (born 8 May 1993) is a Colombian professional footballer who plays as a midfielder for Categoria Primera A club Deportes Tolima. Club statistics Notes Honours Club Junior Copa Colombia: 2015 Benfica Primeira Liga: 2016–17 Supertaça Cândido de Oliveira: 2016 International Colombia Copa América: Third place 2016 References External links 1993 births Living people People from Sincelejo Colombian men's footballers Colombian expatriate men's footballers Men's association football midfielders Barranquilla F.C. footballers Atlético Junior footballers S.L. Benfica footballers Vitória S.C. players Club Atlético Colón footballers Categoría Primera A players Argentine Primera División players Primeira Liga players Colombia men's under-20 international footballers Colombia men's international footballers Copa América Centenario players Colombian expatriate sportspeople in Portugal Colombian expatriate sportspeople in Argentina Expatriate men's footballers in Portugal Expatriate men's footballers in Argentina
https://en.wikipedia.org/wiki/D%C3%A1vid%20Banai
Dávid Banai (born 9 May 1994 in Budapest) is a Hungarian football player who currently plays for Újpest. Club statistics Updated to games played as of 27 June 2020. References External links 1994 births Living people Footballers from Budapest Hungarian men's footballers Újpest FC players Nemzeti Bajnokság I players Men's association football goalkeepers 21st-century Hungarian people
https://en.wikipedia.org/wiki/3x%20%2B%201%20semigroup
In algebra, the 3x + 1 semigroup is a special subsemigroup of the multiplicative semigroup of all positive rational numbers. The elements of a generating set of this semigroup are related to the sequence of numbers involved in the still open Collatz conjecture or the "3x + 1 problem". The 3x + 1 semigroup has been used to prove a weaker form of the Collatz conjecture. In fact, it was in such context the concept of the 3x + 1 semigroup was introduced by H. Farkas in 2005. Various generalizations of the 3x + 1 semigroup have been constructed and their properties have been investigated. Definition The 3x + 1 semigroup is the multiplicative semigroup of positive rational numbers generated by the set The function T : Z → Z, where Z is the set of all integers, as defined below is used in the "shortcut" definition of the Collatz conjecture: The Collatz conjecture asserts that for each positive integer n, there is some iterate of T with itself which maps n to 1, that is, there is some integer k such that T(k)(n) = 1. For example if n = 7 then the values of T(k)(n) for k = 1, 2, 3,... are 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1 and T(11)(7) = 1. The relation between the 3x + 1 semigroup and the Collatz conjecture is that the 3x + 1 semigroup is also generated by the set The weak Collatz conjecture The weak Collatz conjecture asserts the following: "The 3x + 1 semigroup contains every positive integer." This was formulated by Farkas and it has been proved to be true as a consequence of the following property of the 3x + 1 semigroup: The 3x + 1 semigroup S equals the set of all positive rationals in lowest terms having the property that b ≠ 0 (mod 3). In particular, S contains every positive integer. The wild semigroup The semigroup generated by the set which is also generated by the set is called the wild semigroup. The integers in the wild semigroup consists of all integers m such that m ≠ 0 (mod 3). See also Wild number References Semigroup theory Arithmetic dynamics Integer sequences Number theory
https://en.wikipedia.org/wiki/National%20Mortality%20Followback%20Survey
The National Mortality Followback Survey is a survey conducted multiple times in the United States as part of a program that was started by the National Center for Health Statistics in the 1960s. The survey gathers information on Americans who died in a given year from their death certificates and family members (or others who are familiar with the decedent's life history.) The first NMFS was conducted in 1961, and focused on, among other topics, institutional and hospital care people received in the last year of their life. Subsequent surveys were conducted in 1962-3, 1964-5, 1966-8, 1986, and 1993. As of 2009, it is conducted by the National Vital Statistics System. References Health surveys
https://en.wikipedia.org/wiki/Leslie%20Sydney%20Dennis%20Morley
Leslie Sydney Dennis Morley (23 May 1924 — 16 June 2011) FRS FREng FRAeS was a Professorial Research fellow at the Brunel Institute of Computational Mathematics (BICOM) in London and the author of the book Skew plates and structures. Awards and honours Morley was elected a Fellow of the Royal Society (FRS) in 1992. His certificate of election reads: Morley was also elected a fellow of the Royal Academy of Engineering and Royal Aeronautical Society. References Fellows of the Royal Society 1924 births 2011 deaths
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20Arnold%20Sommerfeld
Physics and mathematics Arnold Sommerfeld was a German theoretical physicist whom the following is named after: Sommerfeld coefficient Sommerfeld constant (α) Sommerfeld expansion Sommerfeld effect Sommerfeld identity Sommerfeld number Sommerfeld parameter Sommerfeld radiation condition Sommerfeld's approximation Sommerfeld–Goubau line Sommerfeld–Kossel displacement law Sommerfeld–Runge method Sommerfeld–Watson representation Sommerfeld–Wilson ratio Sommerfeld–Zenneck surface wave Bohr–Sommerfeld model Sommerfeld–Wilson quantization Drude–Sommerfeld model Gamow–Sommerfeld factor Grimm–Sommerfeld rule Orr–Sommerfeld equation Rayleigh–Sommerfeld diffraction theory Astronomical objects Sommerfeld crater 32809 Sommerfeld, minor planet Arnold Sommerfeld Sommerfeld
https://en.wikipedia.org/wiki/Koichi%20Sekikawa
is a former Nippon Professional Baseball outfielder. External links Career statistics - NPB.jp 88 Koichi Sekikawa PLAYERS2021 - Fukuoka SoftBank Hawks Official site 1969 births Living people Baseball people from Tokyo Japanese baseball players Komazawa University alumni Nippon Professional Baseball outfielders Hanshin Tigers players Chunichi Dragons players Tohoku Rakuten Golden Eagles players Japanese baseball coaches Nippon Professional Baseball coaches
https://en.wikipedia.org/wiki/Shinji%20Kurano
is a former Nippon Professional Baseball pitcher. External links Career statistics - NPB.jp 1974 births Living people Baseball people from Mie Prefecture Aoyama Gakuin University alumni Japanese baseball players Nippon Professional Baseball pitchers Fukuoka Daiei Hawks players Fukuoka SoftBank Hawks players Japanese baseball coaches Nippon Professional Baseball coaches
https://en.wikipedia.org/wiki/Near%20East%20B.C.%20in%20international%20competitions
Near East B.C. in international competitions is the history and statistics of Near East B.C. in FIBA Europe and Euroleague Basketball Company competitions. European competitions See also Greek basketball clubs in international competitions External links FIBA Europe EuroLeague ULEB EuroCup Greek basketball clubs in European and worldwide competitions
https://en.wikipedia.org/wiki/KK%20Olimpija%20in%20international%20competitions
KK Olimpija history and statistics in FIBA Europe and Euroleague Basketball (company) competitions. European competitions Worldwide competitions Record KK Olimpija has overall, from 1958 (first participation) to 2015–16 (last participation): 236 wins against 260 defeats in 496 games for all the European club competitions. EuroLeague: 151–185 (336) FIBA Saporta Cup: 43–32 (75) /// EuroCup Basketball: 21–27 (48) FIBA Korać Cup: 21–16 (37) See also Yugoslav basketball clubs in European competitions External links FIBA Europe EuroLeague ULEB EuroCup KK Olimpija Olimpija
https://en.wikipedia.org/wiki/Carl%20Pearcy
Carl Mark Pearcy, Jr. (born August 25, 1935) is an American mathematician whose research has been concentrated on operator theory and operator algebras. He has coauthored several books, including "Introduction to operator theory I", Introduction to analysis", and "Measure and integration", all published by Springer and coauthored by Arlen Brown (and Hari Bercovici in the case of Measure and integration). Pearcy had 31 Ph. D. students at Michigan and TAMU , several of whom are outstanding mathematicians. Pearcy's bibliography contains more than 150 papers, and his research has concerned the invariant subspace problem and the theory of dual algebras. Pearcy was born in Beaumont, Texas and raised in Galveston, Texas and educated at Texas A&M University, the University of Chicago, and Rice University. His Ph. D. was taken from Rice University in 1960 under Arlen Brown. In 1963 Pearcy became a Hildebrandt Instructor at the University of Michigan. He was promoted to Professor in 1968 and remained there until 1990, when he retired and was named Professor of Mathematics at Texas A and M University. Pearcy retired from that position in 2012. References External links Pearcy's papers 20th-century American mathematicians Living people Texas A&M University alumni Rice University alumni University of Chicago alumni University of Michigan faculty 21st-century American mathematicians 1935 births People from Beaumont, Texas
https://en.wikipedia.org/wiki/Presidential%20Award%20for%20Excellence%20in%20Science%2C%20Mathematics%2C%20and%20Engineering%20Mentoring
The Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring (PAESMEM) is a Presidential award established by the United States White House in 1995. The program is administered by the National Science Foundation (NSF) on behalf of the White House Office of Science and Technology Policy (OSTP) to reward outstanding mentoring by individuals and organizations. PAESMEM is the highest national mentoring award bestowed by the White House. A Few Selected Recipients 1996 – Richard A. Tapia 1997 – Geraldine L. Richmond 1998 – Nina Roscher 2000 – Maria Elena Zavala 2003 – Individual – Linda B. Hayden, Margaret Werner-Washburne Organisation – Karl W. Reid (National Society of Black Engineers) 2004 - Organization - Society for Advancement of Chicanos and Native Americans in Science 2005 – Lenore Blum, Rosemary Gillespie, Cheryl B. Schrader 2007 Individual – Jerzy Leszczynski, Kennedy Reed, Kenneth Sajwan, Laura Bottomley, Lesia Crumpton-Young, Mary Anne Nelson, Patricia DeLeon, Steven Oppenheimer Organisation – Medeva Ghee (The Leadership Alliance & The Partnership for Minority Science Education) 2008 – Richard Zare, Susan M. Kauzlarich 2009 – Maja Matarić 2011 – Juan E. Gilbert, Jo Handelsman, Mary Lou Soffa 2014 – Erika Tatiana Camacho, Keivan Stassun 2015 Organisation – EDGE Foundation 2018 – Ulrica Wilson 2020 - Overtoun Jenda STEM mentoring Mentoring in the STEM fields has been shown to assist with student retention, a significant problem in the STEM pipeline. References External links Official site National Science Foundation Program page National Science Foundation Mentorships American science and technology awards
https://en.wikipedia.org/wiki/Olive%20Jean%20Dunn
Olive Jean Dunn (1 September 1915 – 12 January 2008) was an American mathematician and statistician, and professor of biostatistics at the University of California Los Angeles (UCLA). She described methods for computing confidence intervals and also codified the Bonferroni correction's application to confidence intervals. She authored the textbook Basic Statistics: A Primer for the Biomedical Sciences in 1977. Education and career Dunn studied mathematics at the UCLA, earning a BA in 1936 and an MA in 1951. She was awarded a PhD in mathematics in 1956 at UCLA, supervised by Paul G. Hoel. The title of Dunn's doctoral dissertation was Estimation problems for dependent regression. In 1956, she was appointed assistant professor of statistics at Iowa State College. Dunn returned to UCLA in 1959 as assistant professor of biostatistics and assistant professor of preventive medicine and health, later becoming full professor and serving in that role until her retirement. Dunn served on the editorial boards of several journals. Contributions to statistical methods and textbooks Some of Dunn's 1958 and 1959 work led to the conjecture of the Gaussian correlation inequality, which was only proved by German mathematician Thomas Royen in 2014 and was only widely recognized as proved in 2017. Dunn's doctoral dissertation work formed the basis for her continuing development of methods for confidence intervals in biostatistics, and the development of a method for correcting for multiple testing. From the notes to her 1959 publication on confidence intervals:"Most of the research for this paper was part of my doctoral dissertation. The idea of writing an article for the research worker who uses statistical methods was suggested to me by one of the non-statisticians on my doctoral committee at the time of my final examination. In working on the various confidence intervals for k means, I thought of the Bonferroni inequality ones quite early, but since they were so simple I thought they couldn't possibly be of any use. I spent a long time trying to prove that the confidence intervals which would be used in the case of independent variables could also be used or dependent variables. After failing to find a general proof for this, I finally noticed that the simple Bonferroni intervals were nearly as short."The first edition of her textbook, Basic statistics: a primer for the biomedical sciences, was published in 1964 Later editions were co-authored with another professor from UCLA, Virginia A. Clark. Dunn and Clark also co-authored Applied statistics: an analysis of variance and regression, which has also had several editions, with Ruth Mickey joining the authors. Honors Dunn became a Fellow of the American Statistical Association in 1968. She was also a fellow of the American Association for the Advancement of Science (AAAS) and the American Public Health Association. In October 1974, Dunn was honored as the annual UCLA annual Woman of Science, awarded to "
https://en.wikipedia.org/wiki/Globo%C4%8Dica%2C%20Struga
Globočica () is a village in Municipality of Struga, North Macedonia. Demographics According to statistics gathered by Vasil Kanchov in 1900, Globočica was populated by 300 Bulgarian Exarchists. According to Dimitar Mishev, the village had 360 Bulgarian Exarchist residents. During the years 1961–1964, inhabitants of Globochica moved to Struga; in 1903, the Cartographic Society of Sofia registered the village as inhabited by Albanians, as with all of the villages in Malësia. Nowadays, people descended from this village have been assimilated and identify as Macedonians. References Villages in Struga Municipality Albanian communities in North Macedonia
https://en.wikipedia.org/wiki/Selci%2C%20Struga
Selci is a village in Municipality of Struga, North Macedonia. In the 19th century Selci was a Bulgarian village in Debar kaza of the Ottoman Empire. According to the statistics of Vasil Kanchov ("Macedonia. Ethnography and Statistics") in 1900 there were 1,050 Bulgarian inhabitants, all Christians. The entire Christian population of the village is under the rule of Bulgarian Exarchate. According to the Secretary of the Exarchate Dimitar Mishev ("La Macédoine et sa Population Chrétienne”) in 1905 there were 1,144 Bulgarian Exarchists in Selce and a Bulgarian school operated in the village. According to statistics from the newspaper Debarski Glas in 1911 in Selci there were 150 Bulgarian Exarchate houses. According to the 2002 census, the village was without inhabitants. As of the 2021 census, Selci had 6 residents with the following ethnic composition: Macedonians 5 Persons for whom data are taken from administrative sources 1 References Villages in Struga Municipality
https://en.wikipedia.org/wiki/Podgorci%2C%20Struga
Podgorci (, ) is a small village in the municipality of Struga, North Macedonia. History In 1900, Vasil Kanchov gathered and compiled statistics on demographics in the area and reported that the village of Podgorci was inhabited by about 600 Bulgarian Christians and 550 Bulgarian Muslims. The "La Macédoine et sa Population Chrétienne" survey by Dimitar Mishev (D. Brankov) concluded that the Christian part of the local population in 1905 was composed of 288 Exarchist Bulgarians and 352 Patriarchist Bulgarians. There were Bulgarian and Serbian schools in the beginning of 20th century According to the 1943 Albanian census, Podgorci was inhabited by 700 Muslim Albanians, 563 Orthodox Macedonians and 30 Orthodox Aromanians. Demographics Podgorci has been inhabited by Orthodox Christian Macedonians and a Torbeš population. Population As of the 2021 census, Podgorci had 2,430 residents with the following ethnic composition: Turks 857 Others (including Torbeš) 642 Albanians 583 Macedonians 243 Persons for whom data are taken from administrative sources 87 Bosniaks 18 2002 Population: 2,160 Macedonians 376 Albanians 573 Turks 564 Vlachs 7 Serbs 41 Other 599 Languages Languages spoken among the population of Podgorci: Macedonian 1995 Albanian 89 Turkish 22 Bosnian 1 Rest 53 References External links Villages in Struga Municipality Torbeši settlements Albanian communities in North Macedonia
https://en.wikipedia.org/wiki/Oktisi
Oktisi (, ) is a village in the municipality of Struga, North Macedonia. History In 1900, Vasil Kanchov gathered and compiled statistics on demographics in the area and reported that the village of Oktisi was inhabited by about 840 Bulgarian Christians and 550 Bulgarian Muslims. The "La Macédoine et sa Population Chrétienne" survey by Dimitar Mishev (D. Brankov) concluded that the Christian part of the local population in 1905 was composed of 1016 Bulgarian Exarchists. There was a Bulgarian school in the beginning of 20th century Oktis Basilica The Oktis Basilica was a paleochristian basilica in the northern part of the village of Oktis, but the church of the village (St. Nicholas) was built on the foundations of this basilica in 1927. In 1954, the Archaeological Museum of Macedonia undertook excavations of the basilica, which continued until 1994 under Dimçe Koço. The basilica has dimensions of 27.20 x 24.10 m., and consists of a narthex, exonarthex, side annexes and an intersection. It was constructed in a single phase. The floors of the central ship, the narthex, the crossroads, and the northern annex are filled with mosaics, decorated with geometric elements and fauna as well as a few preserved parts of the animal world. The Oktis Basilica is believed to originate in the 5th century as a sacred temple for the inhabitants of that early Christian period, which are hypothesised to be part of the wider ancestral population of the Albanians. The archaeological materials found in the excavations of the site are preserved in the People's Museum of Struga. It is possible that the mosaic in the narthex of the basilica represents the awareness of Christian unity among the early Albanian Byzantine Christian communities. Demographics Oktisi has traditionally been inhabited by Orthodox Macedonians and a Torbeš population. As of the 2021 census, Oktisi had 1,925 residents with the following ethnic composition: Turks 762 Macedonians 409 Others (including Torbeš) 342 Albanians 241 Persons for whom data are taken from administrative sources 171 According to the 2002 census, the village had a total of 2,479 inhabitants. Ethnic groups in the village include: Turks 1,071 Macedonians 955 Albanians 346 Romani 1 Serbs 1 Bosniaks 15 Others 91 References External links Villages in Struga Municipality Torbeši settlements Albanian communities in North Macedonia
https://en.wikipedia.org/wiki/Amplitude%20%28disambiguation%29
Amplitude is a measure of a periodic variable in classical physics. Amplitude may also refer to: In mathematics and physics Jacobi amplitude of Jacobi elliptic functions Probability amplitude, in quantum mechanics Scattering amplitude, in quantum mechanics Complex amplitude Video games Amplitude Studios, a video game developer Amplitude (2003 video game), a 2003 music video game for the PlayStation 2 Amplitude (2016 video game), a 2016 reboot of the 2003 video game for the PlayStation 3 and PlayStation 4 Organizations Amplitude (company), an American public company which provides analytics products Other uses Amplitude (political party), a Chilean political party A term in gymnastics expressing the degree of execution of a gymnastic element A type of throw in Greco-Roman or freestyle wrestling
https://en.wikipedia.org/wiki/John%20Clayton%20Taylor
John Clayton Taylor (born 4 August 1930) is a British mathematical physicist. He is an Emeritus Professor of Mathematical Physics at the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge and an Emeritus Fellow of Robinson College. He is the father of mathematician Richard Taylor. Education Taylor earned his PhD from the University of Cambridge in 1956, under the supervision of Richard J. Eden and Abdus Salam. His thesis was entitled Renormalisation and Related Topics in Quantum Field Theory. Research Taylor has made contributions to quantum field theory and the physics of elementary particles. His contributions include: the discovery (also made independently by Lev Landau) of singularities in the analytical structure of the Feynman integrals for processes in quantum field theory, the PCAC nature of radioactive decay of the pion and the discovery in 1971 of the so-called Slavnov–Taylor identities, which control symmetry and renormalisation of gauge theories. With various collaborators, in 1980 he discovered that real and virtual infrared divergences do not cancel in QCD as they do in QED. They also showed how these infrared divergences exponentiate. In addition, they contributed to the resummation programme in thermal QCD, simplifying the "hard" part of the effective action. Later, they studied complications arising from the non-polynomial nature of the QCD Hamiltonian in the (unitary) Coulomb gauge. Books Gauge Theories of Weak Interactions (1976) Hidden Unity in Nature's Laws (2001) Gauge Theories in the Twentieth Century (2001) Awards and honours Taylor was elected a Fellow of the Royal Society (FRS) in 1981. His certificate of election reads: References 1930 births Living people Fellows of Robinson College, Cambridge Fellows of the Royal Society British mathematicians British physicists
https://en.wikipedia.org/wiki/Antoine%20Cavalleri
Antoine Cavalleri (1698–1765) was a Jesuit professor of mathematics at Cahors during much of the French Enlightenment in the 18th century, until late in the reign of Louis XV of France. Intellectual climate of the age During the early years of the 18th century Isaac Newton's work on gravity was still incompletely accepted in France and Descartes' vortex theory had not yet been conclusively superseded. One result was the difficulty of formulating and establishing a coherent and compelling explanatory theory of tidal action. The French Académie Royale des Sciences both supported practical research into tidal effects, and offered a prize for the best essay to establish the topic on a sound mathematical and theoretical footing. Three essays were selected for prizes, all of them by supporters of Newtonian theory. They were Daniel Bernoulli, Leonhard Euler, and Colin Maclaurin. However, it was rumoured by Pierre Louis Maupertuis that the reason that Cavalleri was added to the list of winners was that one influential judge among those selecting the winning essays was René Antoine Ferchault de Réaumur, who favoured Decartes' vortex theory, and who insisted that at least one winner should be a supporter of that view, though by that time it was rapidly losing ground and leading workers in the field already were rejecting it. As a sop for Réaumur, his colleagues consented to include an arbitrary choice of essay supporting the vorticist view. Cavalleri not only was fairly prominent in his own right, but had recently won two prizes from the Académie de Bordeaux for his essays: "Opacité et diaphanéité des corps" in 1738 and "Chaleur et froideur des eaux minérales" in 1739, so he was a convenient choice. Cavalleri's obscurity Though competent, Cavalleri is little remembered. He was perhaps doubly unfortunate; firstly, in an age that produced figures such as the Bernoulli family, Euler, Lacaille, D'Alembert, Reaumur, and Lagrange, even a prominent professor of mathematics is easy to overlook. Secondly, Cavalleri's essay on tides, though penetrating in that he recognised debatable points in both Cartesian and Newtonian theory, amounted to the last substantial support for the Cartesian theory of vortices; in effect a futile rearguard action. It is true that Fontenelle has been referred to as the last defender of the vortices, but unlike Cavalleri he wrote as an interpreter and populariser, rather than as an analyst or formulator of material theory. On the one hand Cavalleri's objection to Descartes' theory was mainly that it effectively dismissed the obvious tidal influence of the sun. On the other he rejected Newton's theory of remote gravitational attraction. The latter idea might seem naive, but even in 21st century theoretical physics there are echoes of dissatisfaction with the concept of action at a distance. He tried to construct a theoretical basis for an inverse square law of gravitational attraction arising from Cartesian vortices. Newton however, h
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20Pafnuty%20Chebyshev
Mathematics Chebyshev center Chebyshev constants Chebyshev cube root Chebyshev distance Chebyshev equation Chebyshev's equioscillation theorem Chebyshev filter, a family of analog filters in electronics and signal processing Chebyshev function in number theory Chebyshev integral Chebyshev iteration Chebyshev method Chebyshev nodes Chebyshev polynomials and the "Chebyshev form" Chebyshev norm Discrete Chebyshev polynomials Discrete Chebyshev transform Chebyshev rational functions Chebyshev–Gauss quadrature Chebyshev–Markov–Stieltjes inequalities Chebyshev's bias Chebyshev's inequality in probability and statistics Chebyshev–Cantelli inequality Multidimensional Chebyshev's inequality Chebyshev pseudospectral method Chebyshev space Chebyshev's sum inequality Chebyshev's theorem (disambiguation) Mechanics Chebyshev linkage, a straight line generating linkage Chebyshev's Lambda Mechanism and Translating Table Linkage Chebychev–Grübler–Kutzbach criterion for the mobility analysis of linkages Roberts–Chebyshev theorem on the generation of cognate coupler-curves. Other Chebyshev (crater) 2010 Chebyshev, asteroid Chebyshev
https://en.wikipedia.org/wiki/Moduli%20stack%20of%20elliptic%20curves
In mathematics, the moduli stack of elliptic curves, denoted as or , is an algebraic stack over classifying elliptic curves. Note that it is a special case of the moduli stack of algebraic curves . In particular its points with values in some field correspond to elliptic curves over the field, and more generally morphisms from a scheme to it correspond to elliptic curves over . The construction of this space spans over a century because of the various generalizations of elliptic curves as the field has developed. All of these generalizations are contained in . Properties Smooth Deligne-Mumford stack The moduli stack of elliptic curves is a smooth separated Deligne–Mumford stack of finite type over , but is not a scheme as elliptic curves have non-trivial automorphisms. j-invariant There is a proper morphism of to the affine line, the coarse moduli space of elliptic curves, given by the j-invariant of an elliptic curve. Construction over the complex numbers It is a classical observation that every elliptic curve over is classified by its periods. Given a basis for its integral homology and a global holomorphic differential form (which exists since it is smooth and the dimension of the space of such differentials is equal to the genus, 1), the integralsgive the generators for a -lattice of rank 2 inside of pg 158. Conversely, given an integral lattice of rank inside of , there is an embedding of the complex torus into from the Weierstrass P function pg 165. This isomorphic correspondence is given byand holds up to homothety of the lattice , which is the equivalence relationIt is standard to then write the lattice in the form for , an element of the upper half-plane, since the lattice could be multiplied by , and both generate the same sublattice. Then, the upper half-plane gives a parameter space of all elliptic curves over . There is an additional equivalence of curves given by the action of thewhere an elliptic curve defined by the lattice is isomorphic to curves defined by the lattice given by the modular actionThen, the moduli stack of elliptic curves over is given by the stack quotientNote some authors construct this moduli space by instead using the action of the Modular group . In this case, the points in having only trivial stabilizers are dense. Stacky/Orbifold points Generically, the points in are isomorphic to the classifying stack since every elliptic curve corresponds to a double cover of , so the -action on the point corresponds to the involution of these two branches of the covering. There are a few special points pg 10-11 corresponding to elliptic curves with -invariant equal to and where the automorphism groups are of order 4, 6, respectively pg 170. One point in the Fundamental domain with stabilizer of order corresponds to , and the points corresponding to the stabilizer of order correspond to pg 78. Representing involutions of plane curves Given a plane curve by its Weierstrass equationand a
https://en.wikipedia.org/wiki/Austrian%20Statistical%20Society
The Austrian Statistical Society (Österreichischen Statistischen Gesellschaft) is a national scientific organization. It publishes the Austrian Journal of Statistics (), formerly known as the Österreichische Zeitschrift für Statistik (). Journal The official journal of the society is the Austrian Journal of Statistics (), a quarterly peer-reviewed open access scientific journal published under a Creative Commons Attribution License (CC-BY). It was established in 1972 and covers the use of statistical methods in all kind of theoretical and applied disciplines. Special emphasis is put on methods and results in official statistics. Editors The following persons have been editors-in-chief of the journal: 2014–2016 Matthias Templ 2004–2013 Herwig Friedl 2002–2012 Rudolf Dutter References External links 1951 establishments in Austria Statistical societies
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20George%20Gabriel%20Stokes
Sir George Stokes (1819–1903) was an Anglo-Irish mathematical physicist whose career left a prolific body of work in mathematics and physics. Below is a collection of some of the things named after him. Physics Campbell–Stokes recorder Coriolis–Stokes force Stokes equation Stokes formula Stokes' law of sound attenuation Stokes line Stokes–Einstein (Stokes–Einstein–Sutherland) equation (translational diffusion) Stokes–Einstein–Debye equation (rotational diffusion) Fluid dynamics Stokes approximation Navier–Stokes equations Stokes first problem Stokes second problem Stokes drift Stokes expansion, see section about Stokes expansion Stokes flow Stokes number Stokes' paradox Stokes radius Stokes stream function Stokes wave Stokes (unit) Stokes' law Stokeslet Optics Stokes operators (quantum) Stokes parameters Stokes relations Stokes shift Stokes vector Stokes lens Mathematics Navier–Stokes equations, see section on fluid dynamics Navier–Stokes existence and smoothness Stokes' theorem Kelvin–Stokes theorem Generalized Stokes theorem Stokes operator Stokes phenomenon Astronomical features Stokes (lunar crater) Stokes (Martian crater) Stokes Stokes
https://en.wikipedia.org/wiki/Alberto%20Pappiani
Alberto Pappiani (1709–1790) was an Italian mathematician, astronomer, and theologian. He was a Piarist priest and teacher of philosophy and mathematics in the Florentine College. In 1758 he became president of the Academy of Dogmatic Theologians in Florence. Works References 1709 births 1790 deaths 18th-century Italian astronomers 18th-century Italian mathematicians 18th-century Italian Roman Catholic theologians Piarists
https://en.wikipedia.org/wiki/Joseph-Fran%C3%A7ois%20Marie
Joseph-François Marie (1738 – 1801) was a French mathematician. He was an abbot and professor of mathematics at the Collège Mazarin. Works References French abbots 18th-century French mathematicians 1801 deaths 1738 births
https://en.wikipedia.org/wiki/David%20Salesin
David Salesin is an American computer scientist. He has worked in computer graphics, three-dimensional and four-dimensional mathematics, and photorealistic rendering. Until 2019, he was the Director of Snap Inc. Research Team, an affiliate professor in the Department of Computer Science & Engineering of the University of Washington in Seattle, and previously director of the Adobe Creative Technologies Lab. He is currently a Principal Scientist at Google. Salesin graduated from Brown University in 1983, and did graduate work at Stanford. Salesin received a National Young Investigator award from the National Science Foundation in 1993, and in 1995 was named a Presidential Faculty Fellow, receiving a National Science Foundation grant. Computer Animation Rendering André and Wally B. (1984) models: André/Wally Young Sherlock Holmes (1985) computer animation: Industrial Light & Magic Luxo Jr. (1986) rendering Tin Toy (1988) dynamics Toy Story (1995) renderman software development References External links http://www.adobe.com/technology/people/san-francisco/david-salesin.html http://salesin.cs.washington.edu/cv.html Year of birth missing (living people) Living people American computer scientists Brown University alumni University of Washington faculty
https://en.wikipedia.org/wiki/Kim%20Hyun-hun
Kim Hyun-hun (; born 30 April 1991) is a South Korean footballer who plays as centre back for Suwon FC in K League 1. Club statistics As of 23 February 2022. References External links Profile at Avispa Fukuoka 1991 births Living people Men's association football defenders South Korean men's footballers South Korean expatriate men's footballers J1 League players J2 League players China League One players K League 1 players K League 2 players JEF United Chiba players Avispa Fukuoka players Yunnan Flying Tigers F.C. players Gyeongnam FC players Gyeongju Citizen FC players Seoul E-Land FC players Gwangju FC players Suwon FC players Expatriate men's footballers in Japan South Korean expatriate sportspeople in Japan Expatriate men's footballers in China South Korean expatriate sportspeople in China
https://en.wikipedia.org/wiki/Science%20%26%20Education
Science & Education: Contributions from History, Philosophy, and Sociology of Science and Mathematics is a peer-reviewed academic journal published by Springer Science+Business Media. It covers the roles and uses of history and philosophy of science and sociology of science in the teaching of science and mathematics. , the editor-in-chief is Sibel Erduran, who succeeded Kostas Kampourakis (University of Geneva), who in turn succeeded founding editor Michael R. Matthews (University of New South Wales). According to the Journal Citation Reports, the journal has a 2017 impact factor of 1.265. References External links Education journals Philosophy journals English-language journals Springer Science+Business Media academic journals Academic journals established in 1992 Science education journals
https://en.wikipedia.org/wiki/Cone%20condition
In mathematics, the cone condition is a property which may be satisfied by a subset of a Euclidean space. Informally, it requires that for each point in the subset a cone with vertex in that point must be contained in the subset itself, and so the subset is "non-flat". Formal definitions An open subset of a Euclidean space is said to satisfy the weak cone condition if, for all , the cone is contained in . Here represents a cone with vertex in the origin, constant opening, axis given by the vector , and height . satisfies the strong cone condition if there exists an open cover of such that for each there exists a cone such that . References Euclidean geometry
https://en.wikipedia.org/wiki/Ralph%20McKenzie
Ralph Nelson Whitfield McKenzie (born October 20, 1941) is an American mathematician, logician, and abstract algebraist. He received his doctorate from the University of Colorado Boulder in 1967. He is a fellow of the American Mathematical Society. Selected works McKenzie with David Hobby: The structure of finite algebras, AMS 1988 McKenzie with Ralph Freese: Commutator Theory for Congruence Modular Varieties, London Math. Society Lecture Notes, Cambridge University Press 1987 References Living people 1941 births 20th-century American mathematicians People from Cisco, Texas Fellows of the American Mathematical Society 21st-century American mathematicians
https://en.wikipedia.org/wiki/Worldly%20cardinal
In mathematical set theory, a worldly cardinal is a cardinal κ such that the rank Vκ is a model of Zermelo–Fraenkel set theory. Relationship to inaccessible cardinals By Zermelo's theorem on inaccessible cardinals, every inaccessible cardinal is worldly. By Shepherdson's theorem, inaccessibility is equivalent to the stronger statement that (Vκ, Vκ+1) is a model of second order Zermelo-Fraenkel set theory. Being worldly and being inaccessible are not equivalent; in fact, the smallest worldly cardinal has countable cofinality and therefore is a singular cardinal. The following are in strictly increasing order, where ι is the least inaccessible cardinal: The least worldly κ. The least worldly κ and λ (κ<λ, and same below) with Vκ and Vλ satisfying the same theory. The least worldly κ that is a limit of worldly cardinals (equivalently, a limit of κ worldly cardinals). The least worldly κ and λ with Vκ ≺Σ2 Vλ (this is higher than even a κ-fold iteration of the above item). The least worldly κ and λ with Vκ ≺ Vλ. The least worldly κ of cofinality ω1 (corresponds to the extension of the above item to a chain of length ω1). The least worldly κ of cofinality ω2 (and so on). The least κ>ω with Vκ satisfying replacement for the language augmented with the (Vκ,∈) satisfaction relation. The least κ inaccessible in Lκ(Vκ); equivalently, the least κ>ω with Vκ satisfying replacement for formulas in Vκ in the infinitary logic L∞,ω. The least κ with a transitive model M⊂Vκ+1 extending Vκ satisfying Morse–Kelley set theory. (not a worldly cardinal) The least κ with Vκ having the same Σ2 theory as Vι. The least κ with Vκ and Vι having the same theory. The least κ with Lκ(Vκ) and Lι(Vι) having the same theory. (not a worldly cardinal) The least κ with Vκ and Vι having the same Σ2 theory with real parameters. (not a worldly cardinal) The least κ with Vκ ≺Σ2 Vι. The least κ with Vκ ≺ Vι. The least infinite κ with Vκ and Vι satisfying the same L∞,ω statements that are in Vκ. The least κ with a transitive model M⊂Vκ+1 extending Vκ and satisfying the same sentences with parameters in Vκ as Vι+1 does. The least inaccessible cardinal ι. References External links Worldly cardinal in Cantor's attic Large cardinals
https://en.wikipedia.org/wiki/Quillen%20metric
In mathematics, and especially differential geometry, the Quillen metric is a metric on the determinant line bundle of a family of operators. It was introduced by Daniel Quillen for certain elliptic operators over a Riemann surface, and generalized to higher-dimensional manifolds by Jean-Michel Bismut and Dan Freed. The Quillen metric was used by Quillen to give a differential-geometric interpretation of the ample line bundle over the moduli space of vector bundles on a compact Riemann surface, known as the Quillen determinant line bundle. It can be seen as defining the Chern–Weil representative of the first Chern class of this ample line bundle. The Quillen metric construction and its generalizations were used by Bismut and Freed to compute the holonomy of certain determinant line bundles of Dirac operators, and this holonomy is associated to certain anomaly cancellations in Chern–Simons theory predicted by Edward Witten. The Quillen metric was also used by Simon Donaldson in 1987 in a new inductive proof of the Hitchin–Kobayashi correspondence for projective algebraic manifolds, published one year after the resolution of the correspondence by Shing-Tung Yau and Karen Uhlenbeck for arbitrary compact Kähler manifolds. Determinant line bundle of a family of operators Suppose are a family of Fredholm operators between Hilbert spaces, varying continuously with respect to for some topological space . Since each of these operators is Fredholm, the kernel and cokernel are finite-dimensional. Thus there are assignments which define families of vector spaces over . Despite the assumption that the operators vary continuously in , these assignments of vector spaces do not form vector bundles over the topological space , because the dimension of the kernel and cokernel may jump discontinuously for a family of differential operators. However, the index of a differential operator, the dimension of the kernel subtracted by the dimension of the cokernel, is an invariant up to continuous deformations. That is, the assignment is a constant function on . Since it is not possible to take a difference of vector bundles, it is not possible to combine the families of kernels and cokernels of into a vector bundle. However, in the K-theory of , formal differences of vector bundles may be taken, and associated to the family is an element This virtual index bundle contains information about the analytical properties of the family , and its virtual rank, the difference of dimensions, may be computed using the Atiyah–Singer index theorem, provided the operators are elliptic differential operators. Whilst the virtual index bundle is not a genuine vector bundle over the parameter space , it is possible to pass to a genuine line bundle constructed out of . For any , the determinant line of is defined as the one-dimensional vector space One defines the determinant line bundle of the family as the fibrewise determinant of the virtual index bundle, which over e
https://en.wikipedia.org/wiki/Ryo%20Takahashi%20%28footballer%2C%20born%201993%29
is a Japanese footballer who plays as a left winger or a left back for Fagiano Okayama in the J2 League. Career statistics Club References External links Profile at Shonan Bellmare Profile at Nagoya Grampus 1993 births Living people Meiji University alumni Association football people from Gunma Prefecture Japanese men's footballers J1 League players J2 League players Nagoya Grampus players Shonan Bellmare players Matsumoto Yamaga FC players Fagiano Okayama players Men's association football midfielders
https://en.wikipedia.org/wiki/Francis%20Rasolofonirina
Francis Rasolofonirina is a Malagasy-born Mauritian football player. Career statistics International Statistics accurate as of match played 28 March 2017 International goals References External links Living people Mauritius men's international footballers Mauritian men's footballers Mauritian Premier League players Petite Rivière Noire FC players 1986 births People from Toliara Mauritian people of Malagasy descent Sportspeople of Malagasy descent Men's association football defenders
https://en.wikipedia.org/wiki/Continental%20Classroom
Continental Classroom is a U.S. educational television program that was broadcast on the NBC network five days a week in the early morning from 1958 to 1963, covering physics, chemistry, mathematics, and American government. It was targeted at teachers and college students and many institutions offered college credit for courses of which the broadcasts were the main component. The physics course was the first course in the subject available for credit nationwide and the government course was the first nationally broadcast TV course in social studies; the mathematics course has been called the first MOOC (massive open online course) in statistics. Background, production and format The idea for the course came from the drive to upgrade science education in the US after the Soviet Union's successful launch of Sputnik in 1957. Learning of a plan by the New York State Commissioner of Education, James Allen, to spend $600,000 on a refresher course for science teachers, Edward Stanley, Director of Public Affairs and Education at NBC, decided the network could do the same nationwide for not much more money. The American Association of Colleges for Teacher Education was also planning a pilot project on using television in teacher training. Major funding for the program came from the Ford Foundation and from various corporations. The title came from a phrase Stanley used to explain the idea to James Killian, science advisor to President Eisenhower. Physics for the nuclear age was the topic of the first year's course, which was broadcast from 6:30 to 7:00 in the morning Monday through Friday. The second course, in chemistry, was preceded by a rebroadcast of the physics course at 6:00 am. Courses in mathematics and American government followed. The Ford Foundation withdrew its funding for the fourth season, and the network subsequently canceled the program. The fifth season was a rebroadcast of the fourth, the last program airing on May 17, 1963. Lecturers were paid $40,000 for a year of at least 130 half-hour lectures, and could have one or more paid assistants. They were given use of an apartment in Manhattan and their children were placed by NBC in good schools. They worked from outlines, rather than memorizing scripts. Each lecture was recorded in a four-hour studio session some two weeks ahead of the air date, usually in the afternoon by instructor preference. The first two seasons used three cameras; after the loss of the Ford Foundation support, this was reduced to two. The total budget was between $1.2 and $1.5 million a year. The program attracted more viewers and a wider variety of viewers than NBC had expected: 400,000 for the physics course, 600,000 for chemistry, and one and a half million for American government, and including high-school classes (two of them for blind students), more than 800 engineers in the San Francisco Bay Area, nuns, 500 inmates of San Quentin State Prison in California, parents of students studying science, and other
https://en.wikipedia.org/wiki/Fulton%20County%20Health%20Center
Fulton County Health Center (FCHC) is a rural critical access hospital. It serves the community of Fulton County, and is located in Wauseon Ohio. Patient care statistics U.S. News & World Report collates the number of patients seen by the hospital annually, as follows: Facilities Hospital The FCHC facility is equipped as a general medical and surgery hospital, with the following special units: Emergency department with 20 beds. Helipad for medical evacuation. Vascular diagnostic imaging and a heart catheterization system. Wound care and hyperbaric oxygen therapy (HBOT). Oncology treatment center. Critical care unit. Obstetrics and birthing center. Sleep medicine. Health center The FCHC campus covers 28 acres. On the grounds are additional facilities that together comprise a complete health care center for the community. They include: Fulton Manor and Fulton Suites, a nursing home. FulCare Behavioral Health, a mental health facility. Dialysis center operated by DaVita Inc. Free Care Clinic at FCHC Medical Office Building. Community A fitness center is located within a rehabilitation facility in Wauseon's historic downtown business district, near the original Wauseon City Hospital. The hospital's sleep lab has been expanded off-campus to Swanton, Ohio with two more beds, which doubles the capacity of FCHC's sleep medicine department. History FCHC has published a newsletter since 2009 named "Health Centering," which is mailed quarterly to residents in the community. PDF versions are available on the website, and these past issues contain a rich history of the hospital. Early history 1903: Wauseon's first City Hospital was built originally as Wauseon High School in 1868. When the school moved, the building was converted and used as a hospital in 1903. The old hospital still stands today and houses the Fulton County Ohio Historical Society. 1930: Detwiler Memorial Hospital was built in 1929 and opened in 1930. After a new hospital was built across the road, the county then converted the hospital into a nursing home called Detwiler Manor. Later, the manor moved across the road to facilities on the current hospital campus. The beautiful historic brick building was renovated, once again re-purposed, and now houses the Fulton County's Job & Family Services offices. Today's campus The government of Fulton County, Ohio, owns the campus property. 1973: The current hospital facility opened in 1973, and was very progressive in design, featuring single-patient private rooms. Private rooms, while initially expensive to build, keep patients safer from hospital-acquired infections like MRSA. While originally built a size large enough to house 106 beds, changing community needs has resulted in FCHC now having only a maximum 25 bed in-patient capacity, complying with federal Critical Access Hospital (CAH) guidelines. Many of the former patient rooms have been converted to other uses. 1996: The 1990s saw the former hospital acro
https://en.wikipedia.org/wiki/KK%20Zadar%20in%20international%20competitions
KK Zadar history and statistics in FIBA Europe and Euroleague Basketball (company) competitions. European competitions Record KK Zadar has overall from 1965–66 (first participation) to 2010–11 (last participation): 180 wins against 187 defeats plus 2 draws in 369 games for all the European club competitions. EuroLeague: 44–76 (120) FIBA Saporta Cup: 33–26 plus 1 draw (60) /// EuroCup Basketball: 35–32 (67) FIBA Korać Cup: 59–38 plus 1 draw (98) /// FIBA EuroChallenge: 9–15 (24) See also Yugoslav basketball clubs in European competitions External links FIBA Europe EuroLeague ULEB EuroCup KK Zadar Zadar
https://en.wikipedia.org/wiki/Normal%20plane%20%28geometry%29
A normal plane is any plane containing the normal vector of a surface at a particular point. The normal plane also refers to the plane that is perpendicular to the tangent vector of a space curve; (this plane also contains the normal vector) see Frenet–Serret formulas. Normal section The normal section of a surface at a particular point is the curve produced by the intersection of that surface with a normal plane. The curvature of the normal section is called the normal curvature. If the surface is bow or cylinder shaped, the maximum and the minimum of these curvatures are the principal curvatures. If the surface is saddle shaped the maxima of both sides are the principal curvatures. The product of the principal curvatures is the Gaussian curvature of the surface (negative for saddle shaped surfaces). The mean of the principal curvatures is the mean curvature of the surface; if (and only if) the mean curvature is zero, the surface is called a minimal surface. See also Earth normal section Normal bundle Normal curvature Osculating plane Principal curvature Tangent plane (geometry) References Geometrical optics Surfaces Differential geometry
https://en.wikipedia.org/wiki/Lorenzo%20Ramero
Lorenzo Ramero is an Italian mathematician living in France, specialized in algebraic and arithmetic geometry. He is currently a professor of mathematics at the University of Lille. Ramero obtained his Laurea in Matematica from the University of Pisa and his Diploma from the Scuola Normale Superiore di Pisa in 1989. He completed his Ph.D. at the Massachusetts Institute of Technology in 1994 under the supervision of Alexander Beilinson, with a thesis titled An -adic Fourier transform over local fields. Together with Ofer Gabber, Ramero developed the algebraic geometry based on almost rings extending earlier ideas of Gerd Faltings on "almost mathematics". This theory extends already classical algebraic geometry formalism of Alexander Grothendieck's school in order to treat new phenomena in p-adic Hodge theory. This work is systematized in their monograph Almost ring theory. More foundational material was developed after the first book, and especially an extended theory of perfectoid rings and perfectoid spaces which generalizes the recent work of Peter Scholze. These aspects were recapitulated in the book "Foundations for Almost Ring Theory". References External links Personal website PhD thesis at MIT 21st-century Italian mathematicians Living people Massachusetts Institute of Technology alumni 20th-century Italian mathematicians French mathematicians Algebraic geometers University of Pisa alumni Scuola Normale Superiore di Pisa alumni Year of birth missing (living people)
https://en.wikipedia.org/wiki/Demushkin
Demushkin, Dyemushkin or Dyomushkin () may refer to Demushkin group in mathematical group theory Dmitry Demushkin (born 1979), Russian politician and public figure
https://en.wikipedia.org/wiki/Richard%20Kenyon
Richard W. Kenyon (born 1964) is an American mathematician known for his contributions in combinatorics and probability theory. He is the Erastus L. DeForest Professor of Mathematics at Yale University. Kenyon graduated from Rice University and then earned his PhD under supervision of William Thurston at Princeton University. He won the Rollo Davidson Prize in 2001 and the Loève Prize in 2007. In 2014 Kenyon was chosen as a Simons Investigator and inducted into the American Academy of Arts and Sciences. In 2018, he was an invited speaker at the International Congress of Mathematicians in Rio de Janeiro. References External links Website at Yale University 1964 births Living people 20th-century American mathematicians Rice University alumni Princeton University alumni Yale University faculty Probability theorists Simons Investigator 21st-century American mathematicians
https://en.wikipedia.org/wiki/Alice%20Guionnet
Alice Guionnet (born 24 May 1969) is a French mathematician known for her work in probability theory, in particular on large random matrices. Biography Guionnet entered the École Normale Supérieure (Paris) in 1989. She earned her PhD in 1995 under the supervision of Gérard Ben Arous at University of Paris-Sud. Focuses of her academic research can be viewed in her thesis, Dynamique de Langevin d'un verre de spins (Langevin Dynamics of spin glass). She has held positions at the Courant Institute, Berkeley, MIT, and ENS (Paris). She is currently a Director of Research at ENS de Lyon. Works Alice Guionnet is known for her work on large random matrices. In this context, she established principles of large deviations for the empirical measurements of the eigenvalues of large random matrices with Gérard Ben Arous and Ofer Zeitouni, applied the theory of concentration of measure, initiated the rigorous study of matrices with a heavy tail, and obtained the convergence of spectral measurement of non-normal matrices. She developed the analysis of Dyson-Schwinger equations to obtain topological asymptotic expansions, and studied changes in beta-models and random tilings. In collaboration with Alessio Figalli, she introduced the concept of approximate transport to demonstrate the universality of local fluctuations. Alice Guionnet also demonstrated significant results in free probabilities by comparing Voiculescu entropies, building with Vaughan Jones and Dimitri Shlyakhtenko a round of subfactors from planar algebras of any index, and establishing isomorphisms between the algebras of von Neumann generated by q-Gaussian variables by constructing free transport. Distinctions The Mathematical Research Institute of Oberwolfach awarded her the Oberwolfach Prize in 1998. In 2003 she was awarded the Rollo Davidson Prize for her work in probability. In 2006, the French Academy of Sciences awarded her the Prix Paul Doistau–Émile Blutet. For her contributions, she won the 2009 Loève Prize. In 2012 she became a Simons Investigator. She was elected to the French Academy of Sciences in 2017. She is also a Fellow of the Institute of Mathematical Statistics. Guinnet is the 2018 winner of the Blaise Pascal Medal in Mathematics of the European Academy of Sciences. She became a member of the Academia Europaea in 2017. She has been a Knight of the Legion of Honour since 2012. In 2022 she was elected as an international member to the National Academy of Sciences (NAS) and International Honorary Member of the American Academy of Arts and Sciences (AAAS). Publications with Greg W. Anderson and Ofer Zeitouni, Introduction to Random Matrices, Cambridge University Press, 2009 Large Random Matrices - Readings on Macroscopic Asymptotics, Springer, 2009 (Reading Notes in Mathematics, Summer School of Probability of Saint-Flour 2006) "Central limit theorem for nonlinear filtering and interacting particle systems", Annals of Applied probability 9, p. 275-297, 1999 Dyna
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20Emmy%20Noether
Emmy Noether was a German mathematician who flourished in the early 20th century. This article is dedicated to the things named after her achievements. Mathematics "Noetherian" Noetherian Noetherian group Noetherian module Noetherian ring Noetherian space Noetherian induction Noetherian scheme Other Astronomy The crater Nöther on the far side of the Moon is named after her. The 7001 Noether asteroid also is named for her. References Sources nother
https://en.wikipedia.org/wiki/BC%20Brno%20in%20international%20competitions
BC Brno history and statistics in FIBA Europe and Euroleague Basketball (company) competitions. European competitions Worldwide competitions Record BC Brno has overall, from 1958–59 (first participation) to 2006–07 (last participation): 85 wins against 93 defeats in 178 games for all the European club competitions. EuroLeague: 48–45 (93) FIBA Saporta Cup: 22–25 (47) FIBA Korać Cup: 5–9 (14) FIBA EuroCup Challenge: 10–14 (24) See also Czechoslovak basketball clubs in European competitions External links FIBA Europe Euroleague ULEB Eurocup Sport in Brno Basketball in the Czech Republic Basketball clubs in international competitions
https://en.wikipedia.org/wiki/Suicide%20in%20Iran
Suicide in Iran is believed to be a growing concern in recent years. According to statistics most of the people who commit suicide are between the ages of 15 and 35. Economic problems, mental illnesses, cultural obligations, political issues, and social pressures are the major factors for suicide commission in Iran. Per Iranian Legal Medicine Organization statistics are classified to avoid negative atmosphere. Definitions The word "suicide" in Persian dictionaries like Moeen, Dehkhoda, and Amid, has been defined as "killing self by any means". The Oxford English Dictionary records the first use of the word "suicide" by Walter Charleton in 1651. Apparently the word suicide in French was used by Pierre Desfontaines for the first time. Later, this word was accepted by the French Academy of Sciences. Ali EslamiNasab, considers the combination of two Latin words sui (self=) and cide (killing=Persian:کُشتن) a correct term for suicide (self-killing=Persian: خودکشی khudkushi). The concept of suicide in the Moaser Persian Dictionary is defined as "the intentional termination of life by one's own intention and own hands". The first sociological analysis of suicide has been put forward by the French sociologist, Émile Durkheim. He states in his 1897 book suicide that "suicide is any type of death which is a direct or indirect cause of the victim's own positive or negative acts that he/she was aware of in advance". Durkheim categorized suicides into the following four types all of which are related to the relationship of the individual to society: 1- Egoistic suicide that is the cause of individualism and the separation from the society; 2- Altruistic suicide that occurs when the individual has a deep attachment to the society; 3- Anomic suicide which is the cause of anomie and lawlessness in the society; and 4- Fatalistic suicide that occurs when the wills, emotions and incentives of the members of the society is under the restrict control of the society. In the late 19th century, Sigmund Freud was the first to review suicide from a psychological point of view. He considered suicide as "the ultimate anger towards self caused by the unconscious". Freud, divided human instincts into two categories: death instinct (Thanatos) and life instinct (Eros). He believed that the death instinct starts immediately after birth and intends to return in the future. This instinct is the cause of extinction, grudge, and termination of generation (reproduction). On the other hand, the life instinct is the cause of friendship, love, and reproduction. Gradually, Freud developed his theory of death instinct, which is in opposition to libido. Erwin Stengel is the first person to differentiate between suicide and suicide intention from a psychological point of view. After some research, he dedicated an independent branch of psychology to the suicide intention. Research has suggested that unlike suicide the intention of suicide has other goals than just simple "self destruct
https://en.wikipedia.org/wiki/Virtus%20Pallacanestro%20Bologna%20in%20international%20competitions
Virtus Pallacanestro Bologna history and statistics in FIBA Europe and Euroleague Basketball (company) competitions. European competitions Worldwide competitions Record Virtus Pallacanestro Bologna has overall from 1960 to 1961 (first participation) to 2008-09 (last participation): 259 wins against 158 defeats in 417 games for all the European club competitions. (1st–tier) FIBA European Champions Cup or FIBA European League or FIBA Euroleague or Euroleague: 169–115 in 284 games. (2nd–tier) FIBA European Cup Winner's Cup or FIBA Saporta Cup: 48–25 in 73 games. (2nd–tier) ULEB Cup: 3–7 in 10 games. (3rd–tier) FIBA Korać Cup: 14–4 in 18 games. (3rd–tier) FIBA EuroCup or FIBA EuroChallenge: 25–7 in 32 games. Also Virtus has a 4 (w) – 2 (d) record in the McDonald's Championship. External links FIBA Europe Euroleague ULEB Eurocup Virtus Bologna Sport in Bologna
https://en.wikipedia.org/wiki/Maryna%20Viazovska
Maryna Sergiivna Viazovska (, ; born 2 December 1984) is a Ukrainian mathematician known for her work in sphere packing. She is a full professor and Chair of Number Theory at the Institute of Mathematics of the École Polytechnique Fédérale de Lausanne in Switzerland. She was awarded the Fields Medal in 2022. Education and career Viazovska was born in Kyiv, the oldest of three sisters. Her father was a chemist who worked at the Antonov aircraft factory and her mother an engineer. She attended a specialized secondary school for high-achieving students in science and technology, Kyiv Natural Science Lyceum No. 145. An influential teacher there, Andrii Knyazyuk, had previously worked as a professional research mathematician before becoming a secondary school teacher. Viazovska competed in domestic mathematics Olympiads when she was at high school, placing 13th in a national competition where 12 students were selected to a training camp before a six-member team for the International Mathematical Olympiad was chosen. As a student at Taras Shevchenko National University of Kyiv, she competed at the International Mathematics Competition for University Students in 2002, 2003, 2004, and 2005, and was one of the first-place winners in 2002 and 2005. She co-authored her first research paper in 2005. Viazovska earned a master's from the University of Kaiserslautern in 2007, PhD from the Institute of Mathematics of the National Academy of Sciences of Ukraine in 2010, and a doctorate (Dr. rer. nat.) from the University of Bonn in 2013. Her doctoral dissertation, Modular Functions and Special Cycles, concerns analytic number theory and was supervised by Don Zagier and Werner Müller. She was a postdoctoral researcher at the Berlin Mathematical School and the Humboldt University of Berlin and a Minerva Distinguished Visitor at Princeton University. Since January 2018 she has held the Chair of Number Theory as a full professor at the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland after a short stint as tenure-track assistant professor. Contributions In 2016, Viazovska solved the sphere-packing problem in dimension 8. Her dimension 8 solution quickly led to collaboration with others, and a solution in dimension 24. Previously, the problem had been solved only for three or fewer dimensions, and the proof of the three-dimensional version (the Kepler conjecture) involved long computer calculations. In contrast, Viazovska's proof for 8 and 24 dimensions is "stunningly simple". As well as for her work on sphere packing, Viazovska is also known for her research on spherical designs with Bondarenko and Radchenko. With them she proved a conjecture of Korevaar and Meyers on the existence of small designs in arbitrary dimensions. This result was one of the contributions for which her co-author Andriy Bondarenko won the Vasil A. Popov Prize for approximation theory in 2013. Recognition In 2016, Viazovska received the Salem Prize and, in 2017, the Clay Res
https://en.wikipedia.org/wiki/Colombia%20national%20football%20team%20records%20and%20statistics
The following is a list of the Colombia national football team's competitive records and statistics. Individual records Player records Players in bold are still active with Colombia. Most capped players Most capped goalkeepers Top goalscorers Manager records Team records Competition records FIFA World Cup 1.Played Intercontinental playoffs. Copa América Champions   Runners-up   Third place   Fourth place FIFA Confederations Cup Head-to-head record This is a list of the official games played by Colombia national football team up to and including the match against Argentina on 1 February 2022. AFC CAF CONCACAF CONMEBOL OFC UEFA Full Confederation record References Colombia national football team records and statistics National association football team records and statistics
https://en.wikipedia.org/wiki/Mary%20Wynne%20Warner
Mary Wynne Warner (née Davies; 22 June 1932 – 1 April 1998) was a Welsh mathematician, specializing in fuzzy mathematics. Her obituary in the Bulletin of the London Mathematical Society noted that fuzzy topology was "the field in which she was one of the pioneers and recognized as one of the leading figures for the past thirty years." Early life and education Mary Wynne Davies was born in Carmarthen, Wales, the elder daughter of Sydney and Esther Davies (née Jones), where the family resided until she was six years old. She was raised and received the first ten years of her education in Llandovery, where her father was a schoolmaster at the local grammar school. Attaining ten Distinctions in her School Certificate exams, she received the remainder of her secondary education at Howell's Boarding School, Denbigh in order to facilitate her study of physics. Both a Draper's Company Exhibition and an Open Scholarship were awarded to Warner following academic distinction at Howell's. This facilitated her undergraduate study of mathematics at Somerville College, Oxford, commencing in 1951 and from which she graduated in 1953 with a second-class degree. Warner had acquired various academic prizes at both the college and university level during her undergraduate degree, allowing her to progress to doctoral work in Oxford via a Research Scholarship. In 1956 her earliest research paper, 'A note on Borsuk's antipodal point theorem in the Oxford Quarterly Journal of Mathematics was published under the supervision of the Waynflete Chair of Pure Mathematics, J.H.C Whitehead. During this period, Warner was initiated into his notable and prolific algebraic topology research group. Amid her academic study, Warner began a romantic relationship with Gerald Warner, who had read history at Oxford, and after graduating in 1954 had embarked upon a career in the Diplomatic Service's Intelligence Branch. She would marry Warner in 1956 before his assignment to Beijing, China. The transient nature of his occupation disrupted her ability to participate formally in academia and terminated her doctoral studies at Oxford, but she continued to dedicate herself to mathematical research to the extent that the demands of being a diplomat's wife would allow. Career and legacy The trajectory of Warner's career was shaped by her husband's overseas diplomatic assignments. Whilst stationed in Beijing between 1956 and 1958 Warner continued her involvement with Oxford's Whitehead research group, working alongside prominent Chinese topologist Chang Su-chen until escalating political tensions forced them to terminate communication in 1958. The family subsequently returned to London, England for a period between 1958 and 1960 during which Mary lectured part-time at Bedford College; this was followed by a year overseas in Rangoon, Burma. Under her instruction and direction as Senior Lecturer in Mathematics at Rangoon University, its first MSc Mathematics program was developed. Prior t
https://en.wikipedia.org/wiki/2007%E2%80%9308%20in%20Swiss%20football
Statistics of the Swiss Super League for the 2007–08 football season. Statistics of the Swiss Challenge League for the 2007–08 football season. Statistics of the Swiss 1. Liga for the 2007–08 football season. Statistics of the 2. Liga Interregional for the 2007–08 football season. Super League Challenge League 1. Liga Group 1 Group 2 Group 3 Play-off to Challenge League 1st round Final round Relegation play-off References Worldfootball.net