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https://en.wikipedia.org/wiki/Harish-Chandra%20homomorphism | In mathematical representation theory, a Harish-Chandra homomorphism is a homomorphism from a subalgebra of the universal enveloping algebra of a semisimple Lie algebra to the universal enveloping algebra of a subalgebra. A particularly important special case is the Harish-Chandra isomorphism identifying the center of the universal enveloping algebra with the invariant polynomials on a Cartan subalgebra.
In the case of the K-invariant elements of the universal enveloping algebra for a maximal compact subgroup K, the Harish-Chandra homomorphism was studied by .
References
Representation theory of Lie groups |
https://en.wikipedia.org/wiki/Julio%20Maceiras | Julio Maceiras Fauque (22 April 1926 - 6 September 2011) was a Uruguayan football goalkeeper who played for Uruguay in the 1954 FIFA World Cup. He also played for Danubio F.C.
Career statistics
International
References
External links
1926 births
2011 deaths
Uruguayan men's footballers
Uruguay men's international footballers
Men's association football goalkeepers
Uruguayan Primera División players
Danubio F.C. players
1954 FIFA World Cup players
Copa América-winning players |
https://en.wikipedia.org/wiki/1934%E2%80%9335%20Galatasaray%20S.K.%20season | The 1934–35 season was Galatasaray SK's 31st in existence and the club's 23rd consecutive season in the Istanbul Football League.
Squad statistics
Squad changes for the 1934–35 season
In:
Competitions
Istanbul Football League
Standings
Matches
Kick-off listed in local time (EEST)
İstanbul Shield
Friendly Matches
References
Atabeyoğlu, Cem. 1453–1991 Türk Spor Tarihi Ansiklopedisi. page(127).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
Tekil, Süleyman. Dünden bugüne Galatasaray, (1983), page(66-72, 141, 160-161, 180-181). Arset Matbaacılık Kol.Şti.
Futbol vol.2. Galatasaray. Page: 587. Tercüman Spor Ansiklopedisi. (1981)Tercüman Gazetecilik ve Matbaacılık AŞ.
Ulus Newspaper Archive. May, August 1935.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1934–35 season
1930s in Istanbul |
https://en.wikipedia.org/wiki/L%C3%BCroth%20quartic | In mathematics, a Lüroth quartic is a nonsingular quartic plane curve containing the 10 vertices of a complete pentalateral. They were introduced by . showed that the Lüroth quartics form an open subset of a degree 54 hypersurface, called the Lüroth hypersurface, in the space P14 of all quartics. proved that the moduli space of Lüroth quartics is rational.
References
Algebraic curves |
https://en.wikipedia.org/wiki/Atiyah%20algebroid | In mathematics, the Atiyah algebroid, or Atiyah sequence, of a principal -bundle over a manifold , where is a Lie group, is the Lie algebroid of the gauge groupoid of . Explicitly, it is given by the following short exact sequence of vector bundles over :
It is named after Michael Atiyah, who introduced the construction to study the existence theory of complex analytic connections. It plays a crucial example in the integrability of (transitive) Lie algebroids, and it has applications in gauge theory and geometric mechanics.
Definitions
As a sequence
For any fiber bundle over a manifold , the differential of the projection defines a short exact sequence
of vector bundles over , where the vertical bundle is the kernel of .
If is a principal -bundle, then the group acts on the vector bundles in this sequence. Moreover, since the vertical bundle is isomorphic to the trivial vector bundle , where is the Lie algebra of , its quotient by the diagonal action is the adjoint bundle . In conclusion, the quotient by of the exact sequence above yields a short exact sequence of vector bundles over , which is called the Atiyah sequence of .
As a Lie algebroid
Recall that any principal -bundle has an associated Lie groupoid, called its gauge groupoid, whose objects are points of , and whose morphisms are elements of the quotient of by the diagonal action of , with source and target given by the two projections of . By definition, the Atiyah algebroid of is the Lie algebroid of its gauge groupoid.
It follows that , while the anchor map is given by the differential , which is -invariant. Last, the kernel of the anchor is isomorphic precisely to .
The Atiyah sequence yields a short exact sequence of -modules by taking the space of sections of the vector bundles. More precisely, the sections of the Atiyah algebroid of is the Lie algebra of -invariant vector fields on under Lie bracket, which is an extension of the Lie algebra of vector fields on by the -invariant vertical vector fields. In algebraic or analytic contexts, it is often convenient to view the Atiyah sequence as an exact sequence of sheaves of local sections of vector bundles.
Examples
the Atiyah algebroid of the principal -bundle is the Lie algebra
the Atiyah algebroid of the principal -bundle is the tangent algebroid
given a transitive -action on , the Atiyah algebroid of the principal bundle , with structure group the isotropy group of the action at an arbitrary point, is the action algebroid
the Atiyah algebroid of the frame bundle of a vector bundle is the general linear algebroid (sometimes also called Atiyah algebroid of )
Properties
Transitivity and integrability
The Atiyah algebroid of a principal -bundle is always
transitive (so its unique orbit is the entire and its isotropy Lie algebra bundle is the associated bundle )
integrable (to the gauge groupoid of )
Note that these two properties are independent. Integrable Lie algebroids does not |
https://en.wikipedia.org/wiki/Submodular%20set%20function | In mathematics, a submodular set function (also known as a submodular function) is a set function that, informally, describes the relationship between a set of inputs and an output, where adding more of one input has a decreasing additional benefit (diminishing returns). The natural diminishing returns property which makes them suitable for many applications, including approximation algorithms, game theory (as functions modeling user preferences) and electrical networks. Recently, submodular functions have also found immense utility in several real world problems in machine learning and artificial intelligence, including automatic summarization, multi-document summarization, feature selection, active learning, sensor placement, image collection summarization and many other domains.
Definition
If is a finite set, a submodular function is a set function , where denotes the power set of , which satisfies one of the following equivalent conditions.
For every with and every we have that .
For every we have that .
For every and such that we have that .
A nonnegative submodular function is also a subadditive function, but a subadditive function need not be submodular.
If is not assumed finite, then the above conditions are not equivalent. In particular a function
defined by if is finite and if is infinite
satisfies the first condition above, but the second condition fails when and are infinite sets with finite intersection.
Types and examples of submodular functions
Monotone
A set function is monotone if for every we have that . Examples of monotone submodular functions include:
Linear (Modular) functions Any function of the form is called a linear function. Additionally if then f is monotone.
Budget-additive functions Any function of the form for each and is called budget additive.
Coverage functions Let be a collection of subsets of some ground set . The function for is called a coverage function. This can be generalized by adding non-negative weights to the elements.
Entropy Let be a set of random variables. Then for any we have that is a submodular function, where is the entropy of the set of random variables , a fact known as Shannon's inequality. Further inequalities for the entropy function are known to hold, see entropic vector.
Matroid rank functions Let be the ground set on which a matroid is defined. Then the rank function of the matroid is a submodular function.
Non-monotone
A submodular function that is not monotone is called non-monotone.
Symmetric
A non-monotone submodular function is called symmetric if for every we have that .
Examples of symmetric non-monotone submodular functions include:
Graph cuts Let be the vertices of a graph. For any set of vertices let denote the number of edges such that and . This can be generalized by adding non-negative weights to the edges.
Mutual information Let be a set of random variables. Then for any we have that is a submodular fu |
https://en.wikipedia.org/wiki/Haitham%20Al-Shboul | Haitham Al-Shboul () is a retired Jordanian footballer and football manager. He is a former head coach of Jordanian club Al-Faisaly.
Managerial statistics
Honors and Participation in International Tournaments
In AFC Asian Cups
2004 Asian Cup
In Pan Arab Games
1999 Pan Arab Games
In Arab Nations Cup
2002 Arab Nations Cup
In WAFF Championships
2000 WAFF Championship
2002 WAFF Championship
2004 WAFF Championship
International goals
References
External links
1974 births
Living people
Jordanian men's footballers
Jordan men's international footballers
Men's association football midfielders
Al-Faisaly SC players
Al-Shorta SC managers
Jordanian football managers
Footballers from Amman
Jordanian expatriate football managers |
https://en.wikipedia.org/wiki/1935%E2%80%9336%20Galatasaray%20S.K.%20season | The 1935–36 season was Galatasaray SK's 32nd in existence and the club's 24th consecutive season in the Istanbul Football League.
Squad statistics
Squad changes for the 1935–36 season
In:
Out:
Competitions
Istanbul Football League
Standings
Matches
Kick-off listed in local time (EEST)
Friendly Matches
References
Tekil, Süleyman. Dünden bugüne Galatasaray, (1983), page(72-75, 141, 160-161, 181-182). Arset Matbaacılık Kol.Şti.
Futbol vol.2. Galatasaray. Page: 564, 587. Tercüman Spor Ansiklopedisi. (1981)Tercüman Gazetecilik ve Matbaacılık AŞ.
Ulus Newspaper Archives November 1935, January 1936, July 1936
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1935–36 season
1930s in Istanbul |
https://en.wikipedia.org/wiki/Leonard%20Roth | Leonard Roth (29 August 1904 Edmonton, London, England – 28 November 1968 Pittsburgh, Pennsylvania) was a mathematician working in the Italian school of algebraic geometry. He introduced an example of a unirational variety that was not rational (though his proof that it was not rational was incomplete).
Roth was educated at Latymer Upper School, Dulwich College and Clare College, Cambridge, where he graduated as a Wrangler in 1926. His sister was Queenie Roth, literary critic and wife of F. R. Leavis.
Publications
References
Further reading
20th-century English mathematicians
1904 births
1968 deaths
Alumni of Clare College, Cambridge
British Jews
People from Edmonton, London
British emigrants to the United States |
https://en.wikipedia.org/wiki/Premier%20League%20records%20and%20statistics | The Premier League is an English professional league for association football clubs. At the top of the English football league system, it is the country's primary football competition and is contested by 20 clubs. The competition was formed in February 1992 following the decision of clubs in the Football League First Division to break away from The Football League, in order to take advantage of a lucrative television rights deal.
Team records
Titles
Most titles: 13, Manchester United
Most consecutive title wins: 3
Manchester United (1998–99, 1999–2000, 2000–01)
Manchester United (2006–07, 2007–08, 2008–09)
Manchester City (2020–21, 2021–22, 2022–23)
Biggest title-winning margin: 19 points, 2017–18; Manchester City (100 points) over Manchester United (81 points)
Smallest title-winning margin: 0 points and +8 goal difference – 2011–12; Manchester City (+64) over Manchester United (+56). Both finished on 89 points, but Manchester City won the title with a superior goal difference, the only time that goal difference has decided the Premier League title.
Earliest title win with the most games remaining: 7 games: Liverpool (2019–20)
Points
Most points in a season: 100, Manchester City (2017–18)
Most home points in a season: 55
Chelsea (2005–06)
Manchester United (2010–11)
Manchester City (2011–12)
Liverpool (2019–20)
Most away points in a season: 50, Manchester City (2017–18)
Most points without winning the league: 97, Liverpool (2018–19)
Fewest points in a season: 11, Derby County (2007–08)
Most points while bottom of the league:
42 games: 40, Nottingham Forest (1992–93)
38 games: 34, Nottingham Forest (1996–97)
Fewest home points in a season: 7, Sunderland (2005–06)
Fewest away points in a season: 3, Derby County (2007–08)
Fewest points in a season while winning the league: 75, Manchester United (1996–97)
Most points in a season while being relegated:
42 games: 49, Crystal Palace (1992–93)
38 games: 42, West Ham United (2002–03)
Fewest points in a season while avoiding relegation: 34, West Bromwich Albion (2004–05)
Most points in a season by a team promoted in the previous season:
42 games: 77, Newcastle United (1993–94) and Nottingham Forest (1994–95)
38 games: 66, Ipswich Town (2000–01)
Most days spent on top of the league: 274
Chelsea (2014–15)
Liverpool (2019–20)
Most days spent on top of the league without winning the title: 248
Arsenal (2022–23)
Wins
Most wins in total: 731, Manchester United
Most wins in a season: 32
Manchester City (2017–18, 2018–19)
Liverpool (2019–20)
Most home wins in a season: 18
Chelsea (2005–06)
Manchester United (2010–11)
Manchester City (2011–12, 2018–19)
Liverpool (2019–20)
Most away wins in a season: 16, Manchester City (2017–18)
Fewest wins in a season: 1, Derby County (2007–08)
Fewest home wins in a season: 1
Sunderland (2005–06)
Derby County (2007–08)
Fewest away wins in a season: 0
Leeds United (1992–93)
Coventry City (1999–2000)
Wolverhampton Wanderers (2003–04)
Norwich City (2004–05)
Derby County (2007–08 |
https://en.wikipedia.org/wiki/1936%E2%80%9337%20Galatasaray%20S.K.%20season | The 1936–37 season was Galatasaray SK's 33rd in existence and the club's 25th consecutive season in the Istanbul Football League.
Squad statistics
Squad changes for the 1936–37 season
In:
Competitions
Istanbul Football League
Classification
Matches
Kick-off listed in local time (EEST)
Milli Küme
Classification
Matches
Friendly Matches
Ankara Stadyum Kupası
References
Atabeyoğlu, Cem. 1453-1991 Türk Spor Tarihi Ansiklopedisi. page(142-143).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
Tekil, Süleyman. Dünden bugüne Galatasaray, (1983), page(75-76, 113-116, 182). Arset Matbaacılık Kol.Şti.
Futbol vol.2. Galatasaray. Page: 564, 585. Tercüman Spor Ansiklopedisi. (1981)Tercüman Gazetecilik ve Matbaacılık AŞ.
1937 Milli Küme Maçları. Türk Futbol Tarihi vol.1. page(80). (June 1992) Türkiye Futbol Federasyonu Yayınları.
Cumhuriyet Newspaper Archives. March 1937.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1936–37 season
1930s in Istanbul |
https://en.wikipedia.org/wiki/1937%E2%80%9338%20Galatasaray%20S.K.%20season | The 1937–38 season was Galatasaray SK's 34th in existence and the club's 26th consecutive season in the Istanbul Football League.
Squad statistics
Squad changes for the 1937–38 season
In:
Competitions
Istanbul Football League
Classification
Matches
Kick-off listed in local time (EEST)
İstanbul Shield
Matches
Milli Küme
Classification
Matches
Friendly Matches
References
Atabeyoğlu, Cem. 1453–1991 Türk Spor Tarihi Ansiklopedisi. page(143-144).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
Tekil, Süleyman. Dünden bugüne Galatasaray, (1983), page(76-87, 117-120, 161-162, 183). Arset Matbaacılık Kol.Şti.
Futbol vol.2. Galatasaray. pp. 564–565, 585. Tercüman Spor Ansiklopedisi. (1981)Tercüman Gazetecilik ve Matbaacılık AŞ.
1938 Milli Küme Maçları. Türk Futbol Tarihi vol.1. page(80). (June 1992) Türkiye Futbol Federasyonu Yayınları.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1937–38 season
1930s in Istanbul
Galatasaray Sports Club 1937–38 season |
https://en.wikipedia.org/wiki/Valentiner | Valentiner may refer to :
Herman Valentiner, Danish mathematician, who introduced the
Valentiner group in mathematics
Karl Wilhelm Valentiner, astronomer
Max Valentiner, U-boat captain
Wilhelm Valentiner, art historian
See also
Valentine (disambiguation) |
https://en.wikipedia.org/wiki/Dominik%20Rie%C4%8Dick%C3%BD | Dominik Riečický (born 9 June 1992) is a Slovak ice hockey goaltender who currently plays with HC Košice of the Slovak Extraliga.
Career statistics
Regular season and playoffs
Awards and honors
References
External links
1992 births
Living people
Ice hockey people from Košice
HC Košice players
HC Prešov players
HK Spišská Nová Ves players
HC 07 Detva players
MHC Martin players
Slovak ice hockey goaltenders |
https://en.wikipedia.org/wiki/Busemann%E2%80%93Petty%20problem | In the mathematical field of convex geometry, the Busemann–Petty problem, introduced by , asks whether it is true that a symmetric convex body with larger central hyperplane sections has larger volume. More precisely, if K, T are symmetric convex bodies in Rn such that
for every hyperplane A passing through the origin, is it true that Voln K ≤ Voln T?
Busemann and Petty showed that the answer is positive if K is a ball. In general, the answer is positive in dimensions at most 4, and negative in dimensions at least 5.
History
showed that the Busemann–Petty problem has a negative solution in dimensions at least 12, and this bound was reduced to dimensions at least 5 by several other authors. pointed out a particularly simple counterexample: all sections of the unit volume cube have measure at most , while in dimensions at least 10 all central sections of the unit volume ball have measure at least . introduced intersection bodies, and showed that the Busemann–Petty problem has a positive solution in a given dimension if and only if every symmetric convex body is an intersection body. An intersection body is a star body whose radial function in a given direction u is the volume of the hyperplane section u⊥ ∩ K for some fixed star body K.
used Lutwak's result to show that the Busemann–Petty problem has a positive solution if the dimension is 3. claimed incorrectly that the unit cube in R4 is not an intersection body, which would have implied that the Busemann–Petty problem has a negative solution if the dimension is at least 4. However showed that a centrally symmetric star-shaped body is an intersection body if and only if the function 1/||x|| is a positive definite distribution, where ||x|| is the homogeneous function of degree 1 that is 1 on the boundary of the body, and used this to show that the unit balls l, 1 < p ≤ ∞ in n-dimensional space with the lp norm are intersection bodies for n = 4 but are not intersection bodies for n ≥ 5, showing that Zhang's result was incorrect. then showed that the Busemann–Petty problem has a positive solution in dimension 4.
gave a uniform solution for all dimensions.
See also
Shephard's problem
References
Convex geometry |
https://en.wikipedia.org/wiki/Slater%27s%20condition | In mathematics, Slater's condition (or Slater condition) is a sufficient condition for strong duality to hold for a convex optimization problem, named after Morton L. Slater. Informally, Slater's condition states that the feasible region must have an interior point (see technical details below).
Slater's condition is a specific example of a constraint qualification. In particular, if Slater's condition holds for the primal problem, then the duality gap is 0, and if the dual value is finite then it is attained.
Formulation
Consider the optimization problem
where are convex functions. This is an instance of convex programming.
In words, Slater's condition for convex programming states that strong duality holds if there exists an such that is strictly feasible (i.e. all constraints are satisfied and the nonlinear constraints are satisfied with strict inequalities).
Mathematically, Slater's condition states that strong duality holds if there exists an (where relint denotes the relative interior of the convex set
) such that
(the convex, nonlinear constraints)
Generalized Inequalities
Given the problem
where is convex and is -convex for each . Then Slater's condition says that if there exists an such that
and
then strong duality holds.
References
Convex optimization |
https://en.wikipedia.org/wiki/Keller%27s%20conjecture | In geometry, Keller's conjecture is the conjecture that in any tiling of -dimensional Euclidean space by identical hypercubes, there are two hypercubes that share an entire -dimensional face with each other. For instance, in any tiling of the plane by identical squares, some two squares must share an entire edge, as they do in the illustration.
This conjecture was introduced by , after whom it is named. A breakthrough by showed that it is false in ten or more dimensions, and after subsequent refinements, it is now known to be true in spaces of dimension at most seven and false in all higher dimensions. The proofs of these results use a reformulation of the problem in terms of the clique number of certain graphs now known as Keller graphs.
The related Minkowski lattice cube-tiling conjecture states that whenever a tiling of space by identical cubes has the additional property that the cubes' centers form a lattice, some cubes must meet face-to-face. It was proved by György Hajós in 1942.
, , and give surveys of work on Keller's conjecture and related problems.
Statement
A tessellation or tiling of a Euclidean space is, intuitively, a family of subsets that cover the whole space without overlapping. More formally,
a family of closed sets, called tiles, forms a tiling if their union is the whole space and every two distinct sets in the family have disjoint interiors. A tiling is said to be monohedral if all of the tiles have the same shape (they are congruent to each other). Keller's conjecture concerns monohedral tilings in which all of the tiles are hypercubes of the same dimension as the space. As formulates the problem, a cube tiling is a tiling by congruent hypercubes in which the tiles are additionally required to all be translations of each other without any rotation, or equivalently, to have all of their sides parallel to the coordinate axes of the space. Not every tiling by congruent cubes has this property; for instance, three-dimensional space may be tiled by two-dimensional sheets of cubes that are twisted at arbitrary angles with respect to each other. In formulating the same problem, instead considers all tilings of space by congruent hypercubes and states, without proof, that the assumption that cubes are axis-parallel can be added without loss of generality.
An -dimensional hypercube has faces of dimension that are, themselves, hypercubes; for instance, a square has four edges, and a three-dimensional cube has six square faces. Two tiles in a cube tiling (defined in either of the above ways) meet face-to-face if there is an ()-dimensional hypercube that is a face of both of them. Keller's conjecture is the statement that every cube tiling has at least one pair of tiles that meet face-to-face in this way.
The original version of the conjecture stated by Keller was for a stronger statement: every cube tiling has a column of cubes all meeting face-to-face. This version of the problem is true or false for the same dimensions |
https://en.wikipedia.org/wiki/Radial%20set | In mathematics, a subset of a linear space is radial at a given point if for every there exists a real such that for every
Geometrically, this means is radial at if for every there is some (non-degenerate) line segment (depend on ) emanating from in the direction of that lies entirely in
Every radial set is a star domain although not conversely.
Relation to the algebraic interior
The points at which a set is radial are called .
The set of all points at which is radial is equal to the algebraic interior.
Relation to absorbing sets
Every absorbing subset is radial at the origin and if the vector space is real then the converse also holds. That is, a subset of a real vector space is absorbing if and only if it is radial at the origin.
Some authors use the term radial as a synonym for absorbing.
See also
References
Convex analysis
Functional analysis
Linear algebra
Topology |
https://en.wikipedia.org/wiki/Li%20Fubao | Li Fubao is a Chinese football player who played for China in the 1980 Asian Cup.
Career statistics
International statistics
References
External links
Team China Stats
Chinese men's footballers
China men's international footballers
1980 AFC Asian Cup players
1954 births
Living people
Asian Games bronze medalists for China
Asian Games medalists in football
Men's association football forwards
Men's association football midfielders
Footballers at the 1978 Asian Games
Medalists at the 1978 Asian Games
Jiangsu F.C. players
People from Zhangjiakou |
https://en.wikipedia.org/wiki/Xu%20Yonglai | Xu Yonglai (; born August 16, 1954) is a Chinese football player who played for China in the 1980 Asian Cup.
Career statistics
International statistics
References
External links
Team China Stats
Chinese men's footballers
China men's international footballers
1980 AFC Asian Cup players
Shandong Taishan F.C. players
Qingdao Hainiu F.C. (1990) managers
Living people
1954 births
Men's association football forwards
Chinese football managers |
https://en.wikipedia.org/wiki/Bad%20Behaviour | Bad Behaviour may refer to:
Bad behaviour (mathematics), a pathological phenomenon; properties atypically bad or counterintuitive
Bad Behavior, a 1988 short story collection by American writer Mary Gaitskill
Bad Behaviour (1993 film), 1993 British comedy film
Bad Behaviour (2010 film)
Bad Behaviour (2023 film), 2023 New Zealand dark comedy film
Bad Behaviour (TV series), 2023 Australian television drama series
Bad Behaviour (song), by Jedward
Bad Behaviour Tour, by Jedward
Misbehaviour
See also
Behavior (disambiguation)
Bad (disambiguation)
Behaving Badly (disambiguation)
Good behaviour (disambiguation) |
https://en.wikipedia.org/wiki/Thomas%20Zink | Thomas Zink (born 14 April 1949 in Berlin) is a German mathematician. He currently holds a chair for arithmetic algebraic geometry at the University of Bielefeld.
He has been doing research at the Institute for Advanced Study in Princeton, at the University of Toronto and at the University of Bonn among others.
In 1992, he was awarded the Gottfried Wilhelm Leibniz Prize of the Deutsche Forschungsgemeinschaft joint with Christopher Deninger (Westfälische Wilhelms-Universität of Münster), Michael Rapoport (University of Wuppertal) and Peter Schneider (University of Cologne). The four researchers succeeded to apply modern methods of algebraic geometry to the solution of diophantine equations.
Furthermore, he is a member of the German Academy of Sciences Leopoldina (Halle an der Saale).
External links
Homepage of Thomas Zink
List of all Leibniz price laureates (DFG) (PDF; 7,52 MB)
1949 births
Living people
20th-century German mathematicians
Gottfried Wilhelm Leibniz Prize winners
21st-century German mathematicians |
https://en.wikipedia.org/wiki/Duality%20gap | In optimization problems in applied mathematics, the duality gap is the difference between the primal and dual solutions. If is the optimal dual value and is the optimal primal value then the duality gap is equal to . This value is always greater than or equal to 0 (for minimization problems). The duality gap is zero if and only if strong duality holds. Otherwise the gap is strictly positive and weak duality holds.
In general given two dual pairs separated locally convex spaces and . Then given the function , we can define the primal problem by
If there are constraint conditions, these can be built into the function by letting where is the indicator function. Then let be a perturbation function such that . The duality gap is the difference given by
where is the convex conjugate in both variables.
In computational optimization, another "duality gap" is often reported, which is the difference in value between any dual solution and the value of a feasible but suboptimal iterate for the primal problem. This alternative "duality gap" quantifies the discrepancy between the value of a current feasible but suboptimal iterate for the primal problem and the value of the dual problem; the value of the dual problem is, under regularity conditions, equal to the value of the convex relaxation of the primal problem: The convex relaxation is the problem arising replacing a non-convex feasible set with its closed convex hull and with replacing a non-convex function with its convex closure, that is the function that has the epigraph that is the closed convex hull of the original primal objective function.
References
Linear programming
Convex optimization |
https://en.wikipedia.org/wiki/Enneahedron | In geometry, an enneahedron (or nonahedron) is a polyhedron with nine faces. There are 2606 types of convex enneahedron, each having a different pattern of vertex, edge, and face connections. None of them are regular.
Examples
The most familiar enneahedra are the octagonal pyramid and the heptagonal prism. The heptagonal prism is a uniform polyhedron, with two regular heptagon faces and seven square faces. The octagonal pyramid has eight isosceles triangular faces around a regular octagonal base. Two more enneahedra are also found among the Johnson solids: the elongated square pyramid and the elongated triangular bipyramid. The three-dimensional associahedron, with six pentagonal faces and three quadrilateral faces, is an enneahedron. Five Johnson solids have enneahedral duals: the triangular cupola, gyroelongated square pyramid, self-dual elongated square pyramid, triaugmented triangular prism (whose dual is the associahedron), and tridiminished icosahedron.
Another enneahedron is the diminished trapezohedron with a square base, and 4 kite and 4 triangle faces.
The Herschel graph represents the vertices and edges of the Herschel enneahedron above, with all of its faces quadrilaterals. It is the simplest polyhedron without a Hamiltonian cycle, the only enneahedron in which all faces have the same number of edges, and one of only three bipartite enneahedra.
The smallest pair of isospectral polyhedral graphs are enneahedra with eight vertices each.
Space-filling enneahedra
Slicing a rhombic dodecahedron in half through the long diagonals of four of its faces results in a self-dual enneahedron, the square diminished trapezohedron, with one large square face, four rhombus faces, and four isosceles triangle faces. Like the rhombic dodecahedron itself, this shape can be used to tessellate three-dimensional space. An elongated form of this shape that still tiles space can be seen atop the rear side towers of the 12th-century Romanesque Basilica of Our Lady (Maastricht). The towers themselves, with their four pentagonal sides, four roof facets, and square base, form another space-filling enneahedron.
More generally, found at least 40 topologically distinct space-filling enneahedra.
Topologically distinct enneahedra
There are 2606 topologically distinct convex enneahedra, excluding mirror images. These can be divided into subsets of 8, 74, 296, 633, 768, 558, 219, 50, with 7 to 14 vertices respectively. A table of these numbers, together with a detailed description of the nine-vertex enneahedra, was first published in the 1870s by Thomas Kirkman.
References
External links
Enumeration of Polyhedra by Steven Dutch
Polyhedra |
https://en.wikipedia.org/wiki/Ivan%20Cherednik | Ivan Cherednik (Иван Владимирович Чередник) is a Russian-American mathematician. He introduced double affine Hecke algebras, and used them to prove Macdonald's constant term conjecture in . He has also dealt with algebraic geometry, number theory and Soliton equations. His research interests include representation theory, mathematical physics, and algebraic combinatorics. He is currently the Austin M. Carr Distinguished Professor of mathematics at the University of North Carolina at Chapel Hill.
In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin.
See also
Dyson conjecture
Macdonald polynomials
Yangian
Publications
References
University of North Carolina page about Ivan Cherednik
Cherednik on Math-Net.Ru
Russian mathematicians
20th-century American mathematicians
21st-century American mathematicians
University of North Carolina at Chapel Hill faculty
Algebraists
Living people
1951 births |
https://en.wikipedia.org/wiki/Geography%20of%20Madurai | Madurai is a city in the Indian state of Tamil Nadu and administrative headquarters of Madurai District. It is the third largest municipal corporation in Tamil Nadu.
Topology
The average elevation of the city is
Divisions
For the administration purpose the city is divided into four zones by the municipal corporation administration. Madurai East zone, Madurai West zone, Madurai North zone, Madurai South zone.
Climate
Civic amenities
Drinking water for the city is mostly dependent on Vaigai river. |
https://en.wikipedia.org/wiki/Faroese%20Dane | A Faroese Dane is a resident of Denmark with a Faroese ethnic background.
Statistics
In 2006, 21,687 people of Faroese descent were recorded in Denmark, a figure almost half the population of the Faroe Islands.
On average each year, not fewer than 240 Faroese move to Denmark from Faroe Islands, which is about 0.5% of the Faroese population.
See also
Faroe Islanders
References
Faroese people
Ethnic groups in Denmark
Faroese diaspora
Scandinavian diaspora
Danish people of Faroese descent |
https://en.wikipedia.org/wiki/Bijaganita | Bijaganita (IAST: ) was treatise on algebra by the Indian mathematician Bhāskara II. It is the second volume of his main work Siddhānta Shiromani ("Crown of treatises") alongside Lilāvati, Grahaganita and Golādhyāya.
Meaning
Bijaganita, which literally translates to "mathematics () using seeds ()", is one of the two main branches of mediaeval Indian mathematics, the other being , or "mathematics using algorithms. It derives its name from the fact that it employs algebraic equations () that are compared to plant seeds () due to their capacity to generate solutions to mathematical problems."
Contents
The book is divided into six parts, mainly indeterminate equations, quadratic equations, simple equations, surds. The contents are:
Introduction
On Simple Equations
On Quadratic Equations
On Equations involving indeterminate Questions of the 1st Degree
On Equations involving indeterminate Questions of the 2nd Degree
On Equations involving Rectangles
In Bijaganita Bhāskara II refined Jayadeva's way of generalization of Brahmagupta's approach to solving indeterminate quadratic equations, including Pell's equation which is known as chakravala method or cyclic method. Bijaganita is the first text to recognize that a positive number has two square roots
Translations
The translations or editions of the Bijaganita into English include:
1817. Henry Thomas Colebrooke, Algebra, with Arithmetic and mensuration, from the Sanscrit of Brahmegupta and Bháscara
1813. Ata Allah ibn Ahmad Nadir Rashidi; Samuel Davis
1813. Strachey, Edward, Sir, 1812–1901
Bhaskaracharya's Bijaganita and its English and Marathi Translation by Prof. S. K. Abhyankar
Two notable Scholars from Varanasi Sudhakar Dwivedi and Bapudeva Sastri studied Bijaganita in the nineteenth century.
See also
Indian mathematics
Timeline of algebra and geometry
References
Bibliography
External links
Hindi translation by Durga Prasad
Indian mathematics
Social history of India
History of science and technology in India
History of algebra
12th-century books
Sanskrit texts |
https://en.wikipedia.org/wiki/Baseball%20Register | The Baseball Register, also known as the Official Baseball Register, was an annual almanac of baseball player statistics, published by The Sporting News. It was published in May after player changes had been made, at the start of the season. It ceased publication with its 2007 edition. In its first years of publication, from 1940 until 1965, it bore the subtitle "The Game's Four Hundred".
References
Official Baseball Register, 1974 edition, Joe Marcin, Mike Douchant, editors.
Annual magazines published in the United States
Sports magazines published in the United States
Defunct magazines published in the United States
Major League Baseball books
Magazines established in 1940
Magazines disestablished in 2007
Magazines published in North Carolina |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20FC%20Dynamo%20Kyiv%20season | This article covers the results and statistics of Dynamo Kyiv during the 2011–12 season. During the season, Dynamo Kyiv competed in the Ukrainian Premier League, Ukrainian Cup, Ukrainian Super Cup, UEFA Champions League and in the UEFA Europa League.
Squad
Transfers
In
Loans in
Out
Loans out
Released
Competitions
Overview
Super Cup
Premier League
Results summary
Results by round
Results
League table
Ukrainian Cup
UEFA Champions League
Qualifying rounds
UEFA Europa League
Qualifying rounds
Group stage
Squad statistics
Appearances and goals
|-
|colspan="16"|Players away from Dynamo Kyiv on loan:
|-
|colspan="16"|Players who left Dynamo Kyiv during the season:
|}
Goal scorers
Clean sheets
Disciplinary record
References
External links
FC Dynamo Kyiv official website
FC Dynamo Kyiv on soccerway.com
FC Dynamo Kyiv seasons
Dynamo Kyiv
Dynamo Kyiv |
https://en.wikipedia.org/wiki/Knorre | Knorre is a surname. Notable people with the surname include:
Ernst Friedrich Knorre (1759–1810), German-born astronomer and professor of mathematics who lived and worked in present-day Estonia
Karl Friedrich Knorre (1801–1883), son of Ernst Friedrich, Russian astronomer of German ethnic origin
Viktor Knorre (1840–1919), son of Karl Friedrich, Russian astronomer of German ethnic origin
Dmitrii Knorre (born 1926), Russian chemist and biochemist |
https://en.wikipedia.org/wiki/Robert%20Wayne%20Thomason | Robert Wayne Thomason (5 November 1952 in Tulsa, Oklahoma, U.S. – 5 November 1995 in Paris, France) was an American mathematician who worked on algebraic K-theory. His results include a proof that all infinite loop space machines are in some sense equivalent, and progress on the Quillen–Lichtenbaum conjecture.
Thomason did his undergraduate studies at Michigan State University, graduating with a B.S. in mathematics in 1973. He completed his Ph.D. at Princeton University in 1977, under the supervision of John Moore. From 1977 to 1979 he was a C. L. E. Moore instructor at the Massachusetts Institute of Technology, and from 1979 to 1982 he was a Dickson Assistant Professor at the University of Chicago. After spending a year at the Institute for Advanced Study, he was appointed as faculty at Johns Hopkins University in 1983.
Thomason suffered from diabetes; in early November 1995, just shy of his 43rd birthday, he went into diabetic shock and died in his apartment in Paris.
Publications
Erratum
References
External links
20th-century American mathematicians
1952 births
1995 deaths
Mathematicians from Oklahoma
Princeton University alumni
Deaths from diabetes
Massachusetts Institute of Technology School of Science faculty
University of Chicago faculty
Topologists
People from Tulsa, Oklahoma
Michigan State University alumni
Institute for Advanced Study people
Johns Hopkins University faculty
Sloan Research Fellows |
https://en.wikipedia.org/wiki/Inverse%20probability%20weighting | Inverse probability weighting is a statistical technique for calculating statistics standardized to a pseudo-population different from that in which the data was collected. Study designs with a disparate sampling population and population of target inference (target population) are common in application. There may be prohibitive factors barring researchers from directly sampling from the target population such as cost, time, or ethical concerns. A solution to this problem is to use an alternate design strategy, e.g. stratified sampling. Weighting, when correctly applied, can potentially improve the efficiency and reduce the bias of unweighted estimators.
One very early weighted estimator is the Horvitz–Thompson estimator of the mean. When the sampling probability is known, from which the sampling population is drawn from the target population, then the inverse of this probability is used to weight the observations. This approach has been generalized to many aspects of statistics under various frameworks. In particular, there are weighted likelihoods, weighted estimating equations, and weighted probability densities from which a majority of statistics are derived. These applications codified the theory of other statistics and estimators such as marginal structural models, the standardized mortality ratio, and the EM algorithm for coarsened or aggregate data.
Inverse probability weighting is also used to account for missing data when subjects with missing data cannot be included in the primary analysis.
With an estimate of the sampling probability, or the probability that the factor would be measured in another measurement, inverse probability weighting can be used to inflate the weight for subjects who are under-represented due to a large degree of missing data.
Inverse Probability Weighted Estimator (IPWE)
The inverse probability weighting estimator can be used to demonstrate causality when the researcher cannot conduct a controlled experiment but has observed data to model. Because it is assumed that the treatment is not randomly assigned, the goal is to estimate the counterfactual or potential outcome if all subjects in population were assigned either treatment.
Suppose observed data are drawn i.i.d (independent and identically distributed) from unknown distribution P, where
covariates
are the two possible treatments.
response
We do not assume treatment is randomly assigned.
The goal is to estimate the potential outcome, , that would be observed if the subject were assigned treatment . Then compare the mean outcome if all patients in the population were assigned either treatment: . We want to estimate using observed data .
Estimator Formula
Constructing the IPWE
where
construct or using any propensity model (often a logistic regression model)
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of t |
https://en.wikipedia.org/wiki/Projection%20body | In convex geometry, the projection body of a convex body in n-dimensional Euclidean space is the convex body such that for any vector , the support function of in the direction u is the (n – 1)-dimensional volume of the projection of K onto the hyperplane orthogonal to u.
Hermann Minkowski showed that the projection body of a convex body is convex. and used projection bodies in their solution to Shephard's problem.
For a convex body, let denote the polar body of its projection body. There are two remarkable affine isoperimetric inequality for this body. proved that for all convex bodies ,
where denotes the n-dimensional unit ball and is n-dimensional volume, and there is equality precisely for ellipsoids. proved that for all convex bodies ,
where denotes any -dimensional simplex, and there is equality precisely for such simplices.
The intersection body IK of K is defined similarly, as the star body such that for any vector u the radial function of IK from the origin in direction u is the (n – 1)-dimensional volume of the intersection of K with the hyperplane u⊥.
Equivalently, the radial function of the intersection body IK is the Funk transform of the radial function of K.
Intersection bodies were introduced by .
showed that a centrally symmetric star-shaped body is an intersection body if and only if the function 1/||x|| is a positive definite distribution, where ||x|| is the homogeneous function of degree 1 that is 1 on the boundary of the body, and used this to show that the unit balls l, 2 < p ≤ ∞ in n-dimensional space with the lp norm are intersection bodies for n=4 but are not intersection bodies for n ≥ 5.
See also
Busemann–Petty problem
Shephard's problem
References
Convex geometry |
https://en.wikipedia.org/wiki/Tschuprow%27s%20T | In statistics, Tschuprow's T is a measure of association between two nominal variables, giving a value between 0 and 1 (inclusive). It is closely related to Cramér's V, coinciding with it for square contingency tables.
It was published by Alexander Tschuprow (alternative spelling: Chuprov) in 1939.
Definition
For an r × c contingency table with r rows and c columns, let be the proportion of the population in cell and let
and
Then the mean square contingency is given as
and Tschuprow's T as
Properties
T equals zero if and only if independence holds in the table, i.e., if and only if . T equals one if and only there is perfect dependence in the table, i.e., if and only if for each i there is only one j such that and vice versa. Hence, it can only equal 1 for square tables. In this it differs from Cramér's V, which can be equal to 1 for any rectangular table.
Estimation
If we have a multinomial sample of size n, the usual way to estimate T from the data is via the formula
where is the proportion of the sample in cell . This is the empirical value of T. With the Pearson chi-square statistic, this formula can also be written as
See also
Other measures of correlation for nominal data:
Cramér's V
Phi coefficient
Uncertainty coefficient
Lambda coefficient
Other related articles:
Effect size
References
Liebetrau, A. (1983). Measures of Association (Quantitative Applications in the Social Sciences). Sage Publications
Summary statistics for contingency tables |
https://en.wikipedia.org/wiki/Ahmad%20Darwish | Ahmad Darwish was a Syrian professional footballer. He played for Syria in the editions 1980 Asian Cup and 1984 Asian Cup.
References
Statistics
Living people
Syrian men's footballers
1980 AFC Asian Cup players
1984 AFC Asian Cup players
Men's association football midfielders
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Geoffrey%20Colin%20Shephard | Geoffrey Colin Shephard is a mathematician who works on convex geometry and reflection groups. He asked Shephard's problem on the volumes of projected convex bodies, posed another problem on polyhedral nets, proved the Shephard–Todd theorem in invariant theory of finite groups, began the study of complex polytopes, and classified the complex reflection groups.
Shephard earned his Ph.D. in 1954 from Queens' College, Cambridge, under the supervision of J. A. Todd. He was a professor of mathematics at the University of East Anglia until his retirement.
Selected publications
References
External links
Photo from Oberwolfach
Year of birth missing (living people)
Living people
20th-century British mathematicians
21st-century British mathematicians
Alumni of Queens' College, Cambridge
Academics of the University of East Anglia |
https://en.wikipedia.org/wiki/Li%20Huayun | Li Huayun is a Chinese football forward who played for China in the 1984 Asian Cup. He also played for Liaoning.
Career statistics
International statistics
External links
Team China Stats
1963 births
Living people
Men's association football forwards
Chinese men's footballers
China men's international footballers
1984 AFC Asian Cup players |
https://en.wikipedia.org/wiki/Wu%20Yuhua | Wu Yuhua is a Chinese football midfielder who played for China in the 1984 Asian Cup. He also played for Guangdong.
Career statistics
International statistics
External links
Team China Stats
Player profile at Sodasoccer.com
Chinese men's footballers
1960 births
Living people
Men's association football midfielders
Footballers from Guangzhou
China men's international footballers |
https://en.wikipedia.org/wiki/Quantum%20non-equilibrium | Quantum non-equilibrium is a concept within stochastic formulations of the De Broglie–Bohm theory of quantum physics.
Overview
In quantum mechanics, the Born rule states that the probability density of finding a system in a given state, when measured, is proportional to the square of the amplitude of the system's wavefunction at that state, and it constitutes one of the fundamental axioms of the theory.
This is not the case for the De Broglie–Bohm theory, where the Born rule is not a basic law. Rather, in this theory the link between the probability density and the wave function has the status of a hypothesis, called the quantum equilibrium hypothesis, which is additional to the basic principles governing the wave function, the dynamics of the quantum particles and the Schrödinger equation. (For mathematical details, refer to the derivation by Peter R. Holland.)
Accordingly, quantum non-equilibrium describes a state of affairs where the Born rule is not fulfilled; that is, the probability to find the particle in the differential volume at time t is unequal to
Recent advances in investigations into properties of quantum non-equilibrium states have been performed mainly by theoretical physicist Antony Valentini, and earlier steps in this direction were undertaken by David Bohm, Jean-Pierre Vigier, Basil Hiley and Peter R. Holland. The existence of quantum non-equilibrium states has not been verified experimentally; quantum non-equilibrium is so far a theoretical construct. The relevance of quantum non-equilibrium states to physics lies in the fact that they can lead to different predictions for results of experiments, depending on whether the De Broglie–Bohm theory in its stochastic form or the Copenhagen interpretation is assumed to describe reality. (The Copenhagen interpretation, which stipulates the Born rule a priori, does not foresee the existence of quantum non-equilibrium states at all.) That is, properties of quantum non-equilibrium can make certain classes of Bohmian theories falsifiable according to the criterion of Karl Popper.
In practice, when performing Bohmian mechanics computations in quantum chemistry, the quantum equilibrium hypothesis is simply considered to be fulfilled, in order to predict system behaviour and the outcome of measurements.
Relaxation to equilibrium
The causal interpretation of quantum mechanics has been set up by de Broglie and Bohm as a causal, deterministic model, and it was extended later by Bohm, Vigier, Hiley, Valentini and others to include stochastic properties.
Bohm and other physicists, including Valentini, view the Born rule linking to the probability density function as representing not a basic law, but rather as constituting a result of a system having reached quantum equilibrium during the course of the time development under the Schrödinger equation. It can be shown that, once an equilibrium has been reached, the system remains in such equilibrium over the course of its further evoluti |
https://en.wikipedia.org/wiki/Yang%20Zhaohui | Yang Zhaohui is a Chinese football midfielder who played for China in the 1984 Asian Cup. He also played for Beijing Guoan F.C.
Career statistics
International statistics
External links
Team China Stats
Player profile at Sodasoccer.com
1962 births
Living people
Chinese men's footballers
Footballers from Beijing
Men's association football midfielders
China men's international footballers
Beijing Guoan F.C. players |
https://en.wikipedia.org/wiki/Tree%20of%20primitive%20Pythagorean%20triples | In mathematics, a tree of primitive Pythagorean triples is a data tree in which each node branches to three subsequent nodes with the infinite set of all nodes giving all (and only) primitive Pythagorean triples without duplication.
A Pythagorean triple is a set of three positive integers a, b, and c having the property that they can be respectively the two legs and the hypotenuse of a right triangle, thus satisfying the equation ; the triple is said to be primitive if and only if the greatest common divisor of a, b, and c is one. Primitive Pythagorean triple a, b, and c are also pairwise coprime. The set of all primitive Pythagorean triples has the structure of a rooted tree, specifically a ternary tree, in a natural way. This was first discovered by B. Berggren in 1934.
F. J. M. Barning showed that when any of the three matrices
is multiplied on the right by a column vector whose components form a Pythagorean triple, then the result is another column vector whose components are a different Pythagorean triple. If the initial triple is primitive, then so is the one that results. Thus each primitive Pythagorean triple has three "children". All primitive Pythagorean triples are descended in this way from the triple (3, 4, 5), and no primitive triple appears more than once. The result may be graphically represented as an infinite ternary tree with (3, 4, 5) at the root node (see classic tree at right). This tree also appeared in papers of A. Hall in 1970 and A. R. Kanga in 1990. In 2008 V. E. Firstov showed generally that only three such trichotomy trees exist and give explicitly a tree similar to Berggren's but starting with initial node (4, 3, 5).
Proofs
Presence of exclusively primitive Pythagorean triples
It can be shown inductively that the tree contains primitive Pythagorean triples and nothing else by showing that starting from a primitive Pythagorean triple, such as is present at the initial node with (3, 4, 5), each generated triple is both Pythagorean and primitive.
Preservation of the Pythagorean property
If any of the above matrices, say A, is applied to a triple (a, b, c)T having the Pythagorean property a2 + b2 = c2 to obtain a new triple (d, e, f)T = A(a, b, c)T, this new triple is also Pythagorean. This can be seen by writing out each of d, e, and f as the sum of three terms in a, b, and c, squaring each of them, and substituting c2 = a2 + b2 to obtain f2 = d2 + e2. This holds for B and C as well as for A.
Preservation of primitivity
The matrices A, B, and C are all unimodular—that is, they have only integer entries and their determinants are ±1. Thus their inverses are also unimodular and in particular have only integer entries. So if any one of them, for example A, is applied to a primitive Pythagorean triple (a, b, c)T to obtain another triple (d, e, f)T, we have (d, e, f)T = A(a, b, c)T and hence (a, b, c)T = A−1(d, e, f)T. If any prime factor were shared by any two of (and hence all three of) d, e, and f then by thi |
https://en.wikipedia.org/wiki/Ince%20equation | In mathematics, the Ince equation, named for Edward Lindsay Ince, is the differential equation
When p is a non-negative integer, it has polynomial solutions called Ince polynomials. In particular, when , then it has a closed-form solution
where is a constant.
See also
Whittaker–Hill equation
Ince–Gaussian beam
References
Ordinary differential equations |
https://en.wikipedia.org/wiki/2009%20Swedish%20Football%20Division%202 | Statistics of Swedish football Division 2 in season 2009.
League standings
Norrland
Division 2 Norra Svealand
Division 2 Östra Svealand
Division 2 Östra Götaland
Division 2 Västra Götaland
Division 2 Södra Götaland
Player of the year awards
Ever since 2003 the online bookmaker Unibet have given out awards at the end of the season to the best players in Division 2. The recipients are decided by a jury of sportsjournalists, coaches and football experts. The names highlighted in green won the overall national award.
References
Sweden - List of final tables (Clas Glenning)
Swedish Football Division 2 seasons
4
Sweden
Sweden |
https://en.wikipedia.org/wiki/2010%20Swedish%20Football%20Division%202 | Statistics of Swedish football Division 2 for the 2010 season.
League standings
Norrland 2010
Norra Svealand 2010
Södra Svealand 2010
Östra Götaland 2010
Västra Götaland 2010
Södra Götaland 2010
Player of the year awards
Ever since 2003 the online bookmaker Unibet have given out awards at the end of the season to the best players in Division 2. The recipients are decided by a jury of sportsjournalists, coaches and football experts. The names highlighted in green won the overall national award.
References
Sweden - List of final tables (Clas Glenning)
Swedish Football Division 2 seasons
4
Sweden
Sweden |
https://en.wikipedia.org/wiki/List%20of%20Proton%20launches%20%282010%E2%80%932019%29 | This is a list of launches made by the Proton-M rocket between 2010 and 2019. All launches were conducted from the Baikonur Cosmodrome.
Launch statistics
Rocket configurations
Launch sites
Launch outcomes
Launch history
References
Universal Rocket (rocket family)
Proton2010
Proton launches |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20FC%20Thun%20season | This article covers the results and statistics of FC Thun during the 2011–12 season. During the season Thun will compete in the Swiss Super League, Swiss Cup and in the UEFA Europa League.
Match results
Legend
Swiss Super League
Swiss Cup
UEFA Europa League
Second qualifying round
Thun won 2–1 on aggregate
Third qualifying round
Thun win on away goals rule
Play-off round
Thun lost 5–1 on aggregate
Squad statistics
Appearances for competitive matches only
Transfers
In
Out
External links
FC Thun official website
FC Thun on soccerway.com
Thun season
FC Thun seasons
Thun |
https://en.wikipedia.org/wiki/Frank%20Smithies | Frank Smithies FRSE (1912–2002) was a British mathematician who worked on integral equations, functional analysis, and the history of mathematics.
He was elected as a fellow of the Royal Society of Edinburgh in 1961.
He was an alumnus and an academic of Cambridge University.
Publications
References
External links
20th-century British mathematicians
Fellows of the Royal Society of Edinburgh
1912 births
2002 deaths
Mathematical analysts
Alumni of the University of Cambridge
Academics of the University of Cambridge
Scientists from Edinburgh
British historians of mathematics |
https://en.wikipedia.org/wiki/Cherednik | Cherednik or Cherednyk (Чередник) is a Russian surname. Notable people with the surname include:
Ivan Cherednik Mathematician
Cherednik algebra
Oleksiy Cherednyk Football player
Yuri Cherednik, Volleyball player
Russian-language surnames |
https://en.wikipedia.org/wiki/M/G/1%20queue | In queueing theory, a discipline within the mathematical theory of probability, an M/G/1 queue is a queue model where arrivals are Markovian (modulated by a Poisson process), service times have a General distribution and there is a single server. The model name is written in Kendall's notation, and is an extension of the M/M/1 queue, where service times must be exponentially distributed. The classic application of the M/G/1 queue is to model performance of a fixed head hard disk.
Model definition
A queue represented by a M/G/1 queue is a stochastic process whose state space is the set {0,1,2,3...}, where the value corresponds to the number of customers in the queue, including any being served. Transitions from state i to i + 1 represent the arrival of a new customer: the times between such arrivals have an exponential distribution with parameter λ. Transitions from state i to i − 1 represent a customer who has been served, finishing being served and departing: the length of time required for serving an individual customer has a general distribution function. The lengths of times between arrivals and of service periods are random variables which are assumed to be statistically independent.
Scheduling policies
Customers are typically served on a first-come, first-served basis, other popular scheduling policies include
processor sharing where all jobs in the queue share the service capacity between them equally
last-come, first served without preemption where a job in service cannot be interrupted
last-come, first served with preemption where a job in service is interrupted by later arrivals, but work is conserved
generalized foreground-background (FB) scheduling also known as least-attained-service where the jobs which have received least processing time so far are served first and jobs which have received equal service time share service capacity using processor sharing
shortest job first without preemption (SJF) where the job with the smallest size receives service and cannot be interrupted until service completes
preemptive shortest job first where at any moment in time the job with the smallest original size is served
shortest remaining processing time (SRPT) where the next job to serve is that with the smallest remaining processing requirement
Service policies are often evaluated by comparing the mean sojourn time in the queue. If service times that jobs require are known on arrival then the optimal scheduling policy is SRPT.
Policies can also be evaluated using a measure of fairness.
Queue length
Pollaczek–Khinchine method
The probability generating function of the stationary queue length distribution is given by the Pollaczek–Khinchine transform equation
where g(s) is the Laplace transform of the service time probability density function. In the case of an M/M/1 queue where service times are exponentially distributed with parameter μ, g(s) = μ/(μ + s).
This can be solved for individual state probabilities either using by dir |
https://en.wikipedia.org/wiki/Sania%20Mirza%20career%20statistics | This is a list of the main career statistics of Indian professional tennis player Sania Mirza.
Performance timelines
Singles
Doubles
Mixed doubles
Significant finals
Grand Slam tournaments
Women's doubles: 4 (3 titles, 1 runner-up)
Mixed doubles: 8 (3 titles, 5 runner-ups)
Olympic Games
Mixed doubles
Year-end championships
Doubles: 2 (2 titles)
Premier Mandatory & Premier 5 tournaments
Doubles: 18 (9 titles, 9 runner-ups)
WTA career finals
Singles: 4 (1 title, 3 runner-ups)
Doubles: 66 (43 titles, 23 runner-ups)
ITF Circuit finals
Singles: 19 (14–5)
Doubles: 13 (4–9)
ITF Junior career
Grand Slam finals
Girls' doubles: 1 (1 title)
Junior Circuit finals
Singles (10–4)
Doubles (13–6)
Fed Cup
Other finals
Singles
Doubles
Mixed doubles
WTA ranking
Doubles
Grand Slam seedings
The tournaments won by Sania are in boldface, and advances into finals by Sania are in italics.
Women's doubles
*
Mixed doubles
Career earnings
Year-end rankings
SanTina Streaks
14-match win streak 2015
Sania Mirza and Martina Hingis joined forces during March 2015. They saw immediate success winning first three tournaments together.
41-match win streak 2015–2016
Sania Mirza and Martina Hingis were chasing the longest winning streak since 1990 at 44 match wins set by Jana Novotná and Helena Suková but fell 3 matches short.
Doubles Head to Head
Partnerships
Sania Mirza had changed lot of partnerships before stopping singles play but once becoming a doubles specialist she became cautious and kept long partnerships in both Women's and Mixed doubles. Martina Hingis is the 70th women's doubles partner of Sania's career. Sania has also teamed with 14 players in Grandslam Mixed Doubles. She's currently playing Mixed Doubles with Ivan Dodig of Croatia.
Partners in Women's doubles
Records with Title Partners in Women's doubles
Partners in Mixed doubles
These lists only consists of players who played with Sania Mirza in WTA(& ITF) recognized tournaments which include the Olympics, Grand Slams, WTA Year-end championship, Premier tournaments, Fed Cup Ties, and WTA Challengers. They do not include the players who played with her in the other unrecognised multi-sport events and leagues such as IPTL. ITF Junior partners are also not included. The order of the players in the list is based on their first partnering with Sania Mirza. Leander Paes had also earlier played with Sania Mirza in 2006, 2010 in Asian Games and Commonwealth Games.
Sania has won one or more title(s) with players whose names are in bold and the current partners names are in italic.
Other partners
India – Asian Games/Commonwealth Games/Other events
Mahesh Bhupathi
Leander Paes
Vishnu Vardhan
Shikha Uberoi
Rushmi Chakravarthi
Prarthana Thombare
Saketh Myneni
International Premier Tennis League
Rohan Bopanna
Roger Federer
Ivan Dodig
Exhibition match
Kim Clijsters
References
http://www.itftennis.com/procircuit/players/player/profile.aspx?playeri |
https://en.wikipedia.org/wiki/List%20of%20formal%20systems | This is a list of formal systems, also known as logical calculi.
Mathematical
Domain relational calculus, a calculus for the relational data model
Functional calculus, a way to apply various types of functions to operators
Join calculus, a theoretical model for distributed programming
Lambda calculus, a formulation of the theory of reflexive functions that has deep connections to computational theory
Matrix calculus, a specialized notation for multivariable calculus over spaces of matrices
Modal μ-calculus, a common temporal logic used by formal verification methods such as model checking
Pi-calculus, a formulation of the theory of concurrent, communicating processes that was invented by Robin Milner
Predicate calculus, specifies the rules of inference governing the logic of predicates
Propositional calculus, specifies the rules of inference governing the logic of propositions
Refinement calculus, a way of refining models of programs into efficient programs
Rho calculus, introduced as a general means to uniformly integrate rewriting and lambda calculus
Tuple calculus, a calculus for the relational data model, inspired the SQL language
Umbral calculus, the combinatorics of certain operations on polynomials
Vector calculus (also called vector analysis), comprising specialized notations for multivariable analysis of vectors in an inner-product space
Other formal systems
Music is a formal system too. Please have editors illuminate on this.
See also
Formal systems |
https://en.wikipedia.org/wiki/Claude%20Ambrose%20Rogers | Claude Ambrose Rogers FRS (1 November 1920 – 5 December 2005) was an English mathematician who worked in analysis and geometry.
Research
Much of his work concerns the Geometry of Numbers, Hausdorff Measures, Analytic Sets, Geometry and Topology of Banach Spaces, Selection Theorems and Finite-dimensional Convex Geometry. In the theory of Banach spaces and summability, he proved the Dvoretzky–Rogers lemma and the Dvoretzky–Rogers theorem, both with Aryeh Dvoretzky. He constructed a counterexample to a conjecture related to the Busemann–Petty problem. In the geometry of numbers, the Rogers bound is a bound for dense packings of spheres.
Awards and honours
Rogers was elected a Fellow of the Royal Society (FRS) in 1959. He won the London Mathematical Society's De Morgan Medal in 1977.
Personal life
Rogers was married to children's writer Joan North. They had two daughters, Jane and Petra.
References
1920 births
2005 deaths
20th-century English mathematicians
21st-century English mathematicians
Functional analysts
Measure theorists
British geometers
Fellows of the Royal Society |
https://en.wikipedia.org/wiki/Shigeo%20Sasaki | Shigeo Sasaki () (18 November 1912 Yamagata Prefecture, Japan – 14 August 1987 Tokyo) was a Japanese mathematician working on differential geometry who introduced Sasaki manifolds. He retired from Tohoku University's Mathematical Institute in April 1976.
Publications
References
20th-century Japanese mathematicians
1912 births
1987 deaths |
https://en.wikipedia.org/wiki/Walter%20Ledermann | Walter Ledermann FRSE (18 March 1911, Berlin, Germany – 22 May 2009, London, England) was a German and British mathematician who worked on matrix theory, group theory, homological algebra, number theory, statistics, and stochastic processes. He was elected to the Royal Society of Edinburgh in 1944.
Education
Ledermann studied at the Köllnisches Gymnasium and Leibniz Gymnasium in Berlin, from which he graduated in 1928 at the age of 17. He went on to study at the University of Berlin, but due to the rise of Hitler and antisemitism, was forced to flee Germany shortly after he completed his undergraduate studies in 1934. Through the International Student Service in Geneva, he was able to obtain a scholarship to study at the University of St Andrews in Scotland. His doctoral work at St Andrews was supervised by Herbert Turnbull. He was awarded his PhD in 1936. Whilst working at the University of Edinburgh with Professor Sir Godfrey Thomson, Ledermann was granted a DSc in 1940 for his work with Thomson on intelligence testing.
Career
He taught at the universities of Dundee, St Andrews, Manchester, and finally Sussex. At Sussex, Ledermann was appointed professor in 1965, where he continued to teach until he was 89. He wrote various mathematics textbooks.
Publications
; 2nd edn. 1953; 3rd edn. 1957; 4th rev. edn. 1961
; also published 1966 (New York, Dover)
; 2nd edn. 1996 Addison-Wesley
; 2nd edn. 1987
; 10 editions from 1980 to 1991
References
Further reading
Interview with Walter Ledermann – Gap system.org
1911 births
2009 deaths
Scientists from Berlin
Jewish emigrants from Nazi Germany to the United Kingdom
Alumni of the University of St Andrews
20th-century German mathematicians
21st-century German mathematicians
20th-century British mathematicians
21st-century British mathematicians
Academics of the University of Edinburgh
Academics of the University of Dundee
Academics of the University of St Andrews
Academics of the University of Manchester
Academics of the University of Sussex
Fellows of the Royal Society of Edinburgh |
https://en.wikipedia.org/wiki/Wilhelm%20Klingenberg | Wilhelm Paul Albert Klingenberg (28 January 1924 – 14 October 2010) was a German mathematician who worked on differential geometry and in particular on closed geodesics.
Life
Klingenberg was born in 1924 as the son of a Protestant minister. In 1934 the family moved to Berlin; he joined the Wehrmacht in 1941. After the war, he studied mathematics at the University of Kiel, where he finished his Ph.D. in 1950 with , with a thesis in affine differential geometry.
After some time as an assistant of Friedrich Bachmann, he worked in the group of Wilhelm Blaschke at the University of Hamburg, where he defended his Habilitation in 1954. He then visited Sapienza University of Rome, working in the group of Francesco Severi and Beniamino Segre, after which he obtained a faculty position at the University of Göttingen (with Kurt Reidemeister), where he stayed until 1963.
In 1954–55 Klingenberg spent a year at Indiana University Bloomington; during this time he also visited Marston Morse at Princeton University. In 1956–58 he accepted invitations to the Institute for Advanced Study in Princeton, New Jersey. In 1962 he visited the University of California, Berkeley as a guest of Shiing-Shen Chern, who he knew from his time in Hamburg. Later he became a full (C4-) professor at the University of Mainz, and in 1966 a full (C4-) professor at the University of Bonn, a position he kept till his retirement in 1989.
Klingenberg married Christine Klingenberg née Kob in 1953 and has two sons and a daughter.
In 1966 he was an invited speaker at the quadrennial International Congress of Mathematicians in Moscow; his talk was on "Morse theory in the space of closed curves".
Work
Klingenberg's area of work was geometry, especially differential geometry and Riemannian geometry. Besides many articles he published several books. One of his major achievements was the proof of the sphere theorem in joint work with Marcel Berger in 1960: The sphere theorem states that a complete, simply connected Riemannian manifold with sectional curvature contained in the interval (1, 4] is homeomorphic to the sphere.
Publications
See also
Global differential geometry of surfaces
References
External links
Oberwolfach photos of Wilhelm Klingenberg
20th-century German mathematicians
21st-century German mathematicians
Differential geometers
1924 births
2010 deaths
People from Rostock
Academic staff of the University of Göttingen
Academic staff of Johannes Gutenberg University Mainz
Academic staff of the University of Bonn
German military personnel of World War II
University of Kiel alumni |
https://en.wikipedia.org/wiki/Burkill%20integral | In mathematics, the Burkill integral is an integral introduced by for calculating areas. It is a special case of the Kolmogorov integral.
References
Definitions of mathematical integration |
https://en.wikipedia.org/wiki/Kolmogorov%20integral | In mathematics, the Kolmogorov integral (or Kolmogoroff integral) is a generalized integral introduced by including the Lebesgue–Stieltjes integral, the Burkill integral, and the Hellinger integral as special cases. The integral is a limit over a directed family of partitions, when the resulting limiting value is independent of the tags of each partition segment.
References
Definitions of mathematical integration |
https://en.wikipedia.org/wiki/Hellinger%20integral | In mathematics, the Hellinger integral is an integral introduced by that is a special case of the Kolmogorov integral. It is used to define the Hellinger distance in probability theory.
References
Definitions of mathematical integration |
https://en.wikipedia.org/wiki/Hans%20Frederick%20Blichfeldt | Hans Frederick Blichfeldt (1873–1945) was a Danish-American mathematician at Stanford University, known for his contributions to group theory, the representation theory of finite groups, the geometry of numbers, sphere packing, and quadratic forms. He is the namesake of Blichfeldt's theorem.
Life
Blichfeldt was one of five children of a Danish farming couple, Erhard Christoffer Laurentius Blichfeldt and Nielsine Maria Schlaper; many of his father's ancestors were ministers. He was born on January 9, 1873, in Iller, a village in the Sønderborg Municipality of Denmark. In 1881, the family moved to Copenhagen. In 1888, he passed with high honors the entrance examinations for the University of Copenhagen, but his family was unable to afford sending him to the university. Instead, later the same year, they moved again to the US. He worked for several years as a lumberman, a railway worker, a traveling surveyor, and then as a government draftsman in Bellingham, Washington.
In 1894, he became a student at Stanford University, which admitted its first students in 1891 and did not charge tuition at the time. He did not have a high school diploma, so he had to be admitted as a special student, with a letter of support from his drafting supervisor. By 1895 he had become a regular student, and he earned a bachelor's degree there in 1896, one of three graduating mathematics students that year. He stayed for a master's degree in 1897, and in the same year was appointed an instructor at Stanford. It was customary to travel to Europe for doctoral study in mathematics, and with financial support from Stanford professor Rufus L. Green he traveled to Leipzig University and completed a Ph.D. there in 1898. His doctoral dissertation, On a Certain Class of Groups of Transformation in Three-dimensional Space, was supervised by Sophus Lie, and he graduated summa cum laude. Eric Temple Bell suggests that he may have chosen to work with Lie, among other famous mathematicians of the time, because of their shared Scandinavian heritage, and by doing so he set the course of his life's work.
Returning to Stanford, he became a full professor by 1913, and department chair from 1927 until his retirement in 1938. He also visited the University of Chicago in 1911 and Columbia University in 1924 and 1925, represented the US at the International Congress of Mathematicians in 1932 and 1936, and served as vice-president of the American Mathematical Society in 1912.
Blichfeldt remained unmarried throughout his life. He died on November 16, 1945, in Palo Alto, California, of complications following an operation for a heart attack.
Contributions
Blichfeldt made his first mathematical publication, on Heronian triangles, as an undergraduate in 1896.
Blichfeldt's work in group theory includes an improved bound for the Jordan–Schur theorem, that finite linear groups have normal abelian subgroups of index bounded by a function of their dimension, and a result relating the order of a perm |
https://en.wikipedia.org/wiki/Gabriel%20Xavier%20Paul%20Koenigs | Gabriel Xavier Paul Koenigs (17 January 1858 in Toulouse, France – 29 October 1931 in Paris, France) was a French mathematician who worked on analysis and geometry. He was elected as Secretary General of the Executive Committee of the International Mathematical Union after the first world war, and used his position to exclude countries with whom France had been at war from the mathematical congresses.
He was awarded the Poncelet Prize for 1893.
Publications
Koenigs G. Recherches sur les intégrals de certaines équations fontionnelles. Ann. École Normale, Suppl., 1884, (3)1.
See also
Koenigs function
Schröder's equation
References
French mathematicians
Members of the French Academy of Sciences
1858 births
1931 deaths |
https://en.wikipedia.org/wiki/Deviation%20risk%20measure | In financial mathematics, a deviation risk measure is a function to quantify financial risk (and not necessarily downside risk) in a different method than a general risk measure. Deviation risk measures generalize the concept of standard deviation.
Mathematical definition
A function , where is the L2 space of random variables (random portfolio returns), is a deviation risk measure if
Shift-invariant: for any
Normalization:
Positively homogeneous: for any and
Sublinearity: for any
Positivity: for all nonconstant X, and for any constant X.
Relation to risk measure
There is a one-to-one relationship between a deviation risk measure D and an expectation-bounded risk measure R where for any
.
R is expectation bounded if for any nonconstant X and for any constant X.
If for every X (where is the essential infimum), then there is a relationship between D and a coherent risk measure.
Examples
The most well-known examples of risk deviation measures are:
Standard deviation ;
Average absolute deviation ;
Lower and upper semideviations and , where and ;
Range-based deviations, for example, and ;
Conditional value-at-risk (CVaR) deviation, defined for any by , where is Expected shortfall.
See also
Unitized risk
References
Financial risk modeling |
https://en.wikipedia.org/wiki/List%20of%20the%20busiest%20airports%20in%20China | China's busiest airports are a series of lists ranking the 100 busiest airports in Mainland China according to the number of total passengers, including statistics for total aircraft movements and total cargo movements, following the official register yearly since 2000. The data here presented are provided by the Civil Aviation Administration of China (CAAC) and these statistics do not include the results for the special administrative regions of Hong Kong and Macau, or the disputed region of Taiwan. Both Hong Kong and Macau have their own civil aviation regulators (the Civil Aviation Department and the Civil Aviation Authority respectively); Taiwan also has its own civil aviation regulator (the Aviation Safety Council).
The lists are presented in chronological order starting from the latest year. The number of total passengers is measured in persons and includes any passenger that arrives or departs from, or transits through, every airport in the country. The number of total aircraft movements is measured in airplane-times and includes the departures and arrivals of any kind of aircraft in schedule or charter conditions. The number of total cargo movements in metric tonnes and includes all the movements of cargo and mail that arrives or departs from the airport.
At a glance
2022 final statistics
The 100 busiest airports in China in 2022 ordered by total passenger traffic, according to CAAC statistics.
2021 final statistics
The 100 busiest airports in China in 2021 ordered by total passenger traffic, according to CAAC statistics.
2020 final statistics
The 100 busiest airports in China in 2020 ordered by total passenger traffic, according to CAAC statistics.
2019 final statistics
The 100 busiest airports in China in 2019 ordered by total passenger traffic, according to CAAC statistics.
2018 final statistics
The 100 busiest airports in China in 2018 ordered by total passenger traffic, according to CAAC statistics.
2017 final statistics
The 100 busiest airports in China in 2017 ordered by total passenger traffic, according to the CAAC.
2016 final statistics
The 100 busiest airports in China in 2016 ordered by total passenger traffic, according to the CAAC report.
2015 final statistics
The 100 busiest airports in China in 2015 ordered by total passenger traffic, according to the CAAC report.
2014 final statistics
The 100 busiest airports in China in 2014 ordered by total passenger traffic, according to the CAAC report.
2013 final statistics
The 100 busiest airports in China in 2013 ordered by total passenger traffic, according to the CAAC report.
2012 final statistics
The 100 busiest airports in China in 2012 ordered by total passenger traffic, according to the CAAC report.
2011 final statistics
The 100 busiest airports in China in 2011 ordered by total passenger traffic, according to the CAAC report.
2010 final statistics
The 100 busiest airports in China in 2010 ordered by total passenger traffic, according to the |
https://en.wikipedia.org/wiki/Taira%20Honda | was a Japanese mathematician working on number theory who proved the Honda–Tate theorem classifying abelian varieties over finite fields.
References
20th-century Japanese mathematicians
Number theorists
1932 births
1975 deaths |
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20Peter%20Gustav%20Lejeune%20Dirichlet | The German mathematician Peter Gustav Lejeune Dirichlet (1805–1859) is the eponym of many things.
Mathematics
Theorems named Dirichlet's theorem:
Dirichlet's approximation theorem (diophantine approximation)
Dirichlet's theorem on arithmetic progressions (number theory, specifically prime numbers)
Dirichlet's unit theorem (algebraic number theory and rings)
Dirichlet algebra
Dirichlet beta function
Dirichlet boundary condition (differential equations)
Neumann–Dirichlet method
Dirichlet characters (number theory, specifically zeta and L-functions. 1831)
Dirichlet conditions (Fourier series)
Dirichlet convolution (number theory and arithmetic functions)
Dirichlet density (number theory)
Dirichlet average
Dirichlet distribution (probability theory)
Dirichlet-multinomial distribution
Dirichlet negative multinomial distribution
Generalized Dirichlet distribution (probability theory)
Grouped Dirichlet distribution
Inverted Dirichlet distribution
Matrix variate Dirichlet distribution
Dirichlet divisor problem (currently unsolved) (Number theory)
Dirichlet eigenvalue
Dirichlet's ellipsoidal problem
Dirichlet eta function (number theory)
Dirichlet form
Dirichlet function (topology)
Dirichlet hyperbola method
Dirichlet integral
Dirichlet kernel (functional analysis, Fourier series)
Dirichlet L-function
Dirichlet principle
Dirichlet problem (partial differential equations)
Dirichlet process
Dependent Dirichlet process
Hierarchical Dirichlet process
Imprecise Dirichlet process
Dirichlet ring (number theory)
Dirichlet series (analytic number theory)
Dirichlet series inversion
General Dirichlet series
Dirichlet space
Dirichlet stability criterion (dynamical systems)
Dirichlet tessellation, Dirichlet cell, Dirichlet polygon also called a Voronoi diagram (geometry)
Dirichlet's test (analysis)
Dirichlet's energy
Pigeonhole principle/Dirichlet's box (or drawer) principle (combinatorics)
Latent Dirichlet allocation
Class number formula
Physics
Dirichlet membrane
Non-mathematical
11665 Dirichlet
Dirichlet (crater)
Dirichlet–Jackson Basin
Dirichlet |
https://en.wikipedia.org/wiki/Gordon%20Thomas%20Whyburn | Gordon Thomas Whyburn (7 January 1904 Lewisville, Texas – 8 September 1969 Charlottesville, Virginia) was an American mathematician who worked on topology.
Whyburn studied at the University of Texas in Austin, where he received a bachelor's degree in chemistry in 1925. Under the influence of his teacher Robert Lee Moore, Whyburn continued to study at Austin but changed to mathematics and earned a master's degree in mathematics in 1926 and then a PhD in 1927. After two years as an adjunct professor at U. of Texas, with the aid of a Guggenheim fellowship Whyburn spent the academic year 1929/1930 in Vienna with Hans Hahn and in Warsaw with Kuratowski and Sierpinski. After the fellowship expired, Whyburn became a professor at Johns Hopkins University. From 1934 he was a professor at the University of Virginia, where he modernized the mathematics department and spent the rest of his career. He was chair of the department until his first heart attack in 1966; Edward J. McShane joined the department in 1935, and Gustav A. Hedlund was a member of the department from 1939 to 1948. In the academic year 1952/1953 Whyburn was a visiting professor at Stanford University. In 1953–1954 he served as president of the American Mathematical Society.
Whyburn was awarded the Chauvenet Prize in 1938 for his paper "On the Structure of Continua", and was elected a member of the National Academy of Sciences in 1951. His doctoral students include John L. Kelley and Alexander Doniphan Wallace.
His brother William Marvin Whyburn (1901–1972) was a mathematics professor at UCLA and became known for his work on ordinary differential equations.
Publications
References
20th-century American mathematicians
Members of the United States National Academy of Sciences
Presidents of the American Mathematical Society
Topologists
University of Texas at Austin College of Natural Sciences alumni
University of Virginia faculty
1904 births
1969 deaths
Mathematicians from Texas
People from Lewisville, Texas
Burials at the University of Virginia Cemetery |
https://en.wikipedia.org/wiki/Zarhin%20trick | In mathematics, the Zarhin trick is a method for eliminating the polarization of abelian varieties A by observing that the abelian variety A4 × Â4 is principally polarized. The method was introduced by in his proof of the Tate conjecture over global fields of positive characteristic.
References
Abelian varieties |
https://en.wikipedia.org/wiki/Erick%20Ozuna | Erick Junior Ozuna López (born October 5, 1990) is a Dominican Republic footballer who plays as a striker for Universidad O&M and the Dominican Republic national team.
Career statistics
International goals
Scores and results list the Dominican Republic's goal tally first.
References
External links
1990 births
Living people
Dominican Republic men's footballers
Club Barcelona Atlético players
Tempête FC players
C.D. Árabe Unido players
Dominican Republic men's international footballers
Dominican Republic expatriate men's footballers
Expatriate men's footballers in Haiti
Expatriate men's footballers in Panama
Liga Panameña de Fútbol players
Liga Dominicana de Fútbol players
Ligue Haïtienne players
Men's association football forwards |
https://en.wikipedia.org/wiki/Howard%20Hawks%20Mitchell | Howard Hawks Mitchell (January 13, 1885, Marietta, Ohio – 1943) was an American mathematician who worked on group theory and number theory and who introduced Mitchell's group.
In 1910 he received a PhD from Princeton University as Oswald Veblen's first doctoral student. During the academic year 1910/1911 Mitchell was an instructor at Yale University. At the University of Pennsylvania he was an instructor from 1911 to 1914 and then a professor until his death in 1943 at age 58 from coronary thrombosis.
Mitchell was elected to the American Philosophical Society in 1925. His doctoral students include Leonard Carlitz.
Selected works
References
Rank and File American Mathematicians (pdf) by David Zitarelli
20th-century American mathematicians
Princeton University alumni
University of Pennsylvania faculty
1885 births
1943 deaths
Members of the American Philosophical Society |
https://en.wikipedia.org/wiki/Size%20%28statistics%29 | In statistics, the size of a test is the probability of falsely rejecting the null hypothesis. That is, it is the probability of making a type I error. It is denoted by the Greek letter α (alpha).
For a simple hypothesis,
In the case of a composite null hypothesis, the size is the supremum over all data generating processes that satisfy the null hypotheses.
A test is said to have significance level if its size is less than or equal to .
In many cases the size and level of a test are equal.
References
Statistical hypothesis testing |
https://en.wikipedia.org/wiki/Loch%20Ness%20monster%20surface | In mathematics, the Loch Ness monster is a surface with infinite genus but only one end. It appeared named this way already in a 1981 article by . The surface can be constructed by starting with a plane (which can be thought of as the surface of Loch Ness) and adding an infinite number of handles (which can be thought of as loops of the Loch Ness monster).
See also
Cantor tree surface
Jacob's ladder surface
References
Surfaces
Loch Ness Monster |
https://en.wikipedia.org/wiki/Sigma-martingale | In mathematics and information theory of probability, a sigma-martingale is a semimartingale with an integral representation. Sigma-martingales were introduced by C.S. Chou and M. Emery in 1977 and 1978. In financial mathematics, sigma-martingales appear in the fundamental theorem of asset pricing as an equivalent condition to no free lunch with vanishing risk (a no-arbitrage condition).
Mathematical definition
An -valued stochastic process is a sigma-martingale if it is a semimartingale and there exists an -valued martingale M and an M-integrable predictable process with values in such that
References
Martingale theory |
https://en.wikipedia.org/wiki/List%20of%20Motherwell%20F.C.%20records%20and%20statistics | Motherwell Football Club is a Scottish professional association football club from the North Lanarkshire town of Motherwell, competing in the Scottish Premiership. This is an overview of all the statistics and records involving Motherwell since its official formation on 17 May 1886.
Honours
Sources:
Records and statistics
Firsts
First match: Motherwell 3-2 Hamilton Academical (17 May 1886)
First match played at Roman Road: Motherwell 3-2 Hamilton Academical (17 May 1886)
First match played at Dalziel Park: Motherwell 3-3 Rangers (9 March 1889)
First match played at Fir Park: Motherwell 1-8 Celtic (3 August 1895)
First match played (as a professional side): Motherwell 4-1 Hamilton Academical (5 August 1893)
First match played in league (as a professional side): Motherwell 4-1 Clyde (12 August 1893)
First match played in Scottish Premier Division: Motherwell 1-1 Ayr United (30 August 1975)
First match played in SPL: Motherwell 1-0 St Johnstone (1 August 1998)
First match played in Scottish Premiership: Hibernian 0-1 Motherwell (4 August 2013)
First match played in Scottish Cup: Cambuslang 6-1 Motherwell (11 September 1886)
First match played in Scottish League Cup: Motherwell 0-1 Queen of the South (21 September 1946)
First match played in Lanarkshire Cup (as Motherwell): Motherwell 3-3 Albion Rovers (20 November 1886)
First match played in Texaco Cup/Anglo-Scottish Cup: Motherwell 1-0 Stoke City (14 September 1970)
First win in SPL: Motherwell 1-0 St Johnstone (1 August 1998)
First draw in SPL: Motherwell 1-1 Dunfermline Athletic (22 August 1998)
First defeat in SPL: Rangers 2-1 Motherwell (15 August 1998)
First win in Scottish Premiership: Hibernian 0-1 Motherwell (4 August 2013)
First defeat in Scottish Premiership: Motherwell 1-3 Aberdeen (12 August 2013)
First match played in Europe: 1991–92 European Cup Winners' Cup vs GKS Katowice (18 September 1991)
First goal scored in SPL: Jered Stirling vs St Johnstone (1 August 1998)
First goal scored in Scottish Premiership: Henri Anier vs Hibernian (4 August 2013)
First goal scored in Europe: Steve Kirk vs GKS Katowice (1 October 1991)
First hat-trick scored in SPL: John Spencer vs Aberdeen (20 October 1999)
First hat-trick scored in Europe: Jamie Murphy vs Flamurtari (23 July 2009)
Individual
Most Capped player (Scotland): Stephen O'Donnell (25 caps)
Most Capped player (Other): Stephen Craigan (54 caps for Northern Ireland)
Youngest Player: William Hunter 17 years (1958)
5,000th SPL Goal: Scott McDonald versus Falkirk (Season 2005-2006)
Most Clean Sheets in a season (All Competitions): Darren Randolph (20 clean sheets, Season 2010-2011)
Appearances
Most League appearances: Bob Ferrier, 626, 1917–1937
Most League appearances since World War Two: Steven Hammell, 583, 1999–2006, 2008–2018
Most SPL appearances: Steven Hammell, 399, 1999–2006, 2008–2013
Most Premiership appearances: John Sutton, 38, 2013–present
Most European appearances: Steven Hammell, 19, 2008 |
https://en.wikipedia.org/wiki/Jacob%27s%20ladder%20surface | In mathematics, Jacob's ladder is a surface with infinite genus and two ends. It was named after Jacob's ladder by Étienne , because the surface can be constructed as the boundary of a ladder that is infinitely long in both directions.
See also
Cantor tree surface
Loch Ness monster surface
References
Surfaces |
https://en.wikipedia.org/wiki/Predictable%20process | In stochastic analysis, a part of the mathematical theory of probability, a predictable process is a stochastic process whose value is knowable at a prior time. The predictable processes form the smallest class that is closed under taking limits of sequences and contains all adapted left-continuous processes.
Mathematical definition
Discrete-time process
Given a filtered probability space , then a stochastic process is predictable if is measurable with respect to the σ-algebra for each n.
Continuous-time process
Given a filtered probability space , then a continuous-time stochastic process is predictable if , considered as a mapping from , is measurable with respect to the σ-algebra generated by all left-continuous adapted processes.
This σ-algebra is also called the predictable σ-algebra.
Examples
Every deterministic process is a predictable process.
Every continuous-time adapted process that is left continuous is obviously a predictable process.
See also
Adapted process
Martingale
References
Stochastic processes |
https://en.wikipedia.org/wiki/Cantor%20tree | In mathematical set theory, the Cantor tree is either the full binary tree of height ω + 1, or a topological space related to this by joining its points with intervals, that was introduced by Robert Lee Moore in the late 1920s as an example of a non-metrizable Moore space .
References
Trees (set theory)
Topological spaces |
https://en.wikipedia.org/wiki/Translation%20surface | In mathematics a translation surface is a surface obtained from identifying the sides of a polygon in the Euclidean plane by translations. An equivalent definition is a Riemann surface together with a holomorphic 1-form.
These surfaces arise in dynamical systems where they can be used to model billiards, and in Teichmüller theory. A particularly interesting subclass is that of Veech surfaces (named after William A. Veech) which are the most symmetric ones.
Definitions
Geometric definition
A translation surface is the space obtained by identifying pairwise by translations the sides of a collection of plane polygons.
Here is a more formal definition. Let be a collection of (not necessarily convex) polygons in the Euclidean plane and suppose that for every side of any there is a side of some with and for some nonzero vector (and so that . Consider the space obtained by identifying all with their corresponding through the map .
The canonical way to construct such a surface is as follows: start with vectors and a permutation on , and form the broken lines and starting at an arbitrarily chosen point. In the case where these two lines form a polygon (i.e. they do not intersect outside of their endpoints) there is a natural side-pairing.
The quotient space is a closed surface. It has a flat metric outside the set images of the vertices. At a point in the sum of the angles of the polygons around the vertices which map to it is a positive multiple of , and the metric is singular unless the angle is exactly .
Analytic definition
Let be a translation surface as defined above and the set of singular points. Identifying the Euclidean plane with the complex plane one gets coordinates charts on with values in . Moreover, the changes of charts are holomorphic maps, more precisely maps of the form for some . This gives the structure of a Riemann surface, which extends to the entire surface by Riemann's theorem on removable singularities. In addition, the differential where is any chart defined above, does not depend on the chart. Thus these differentials defined on chart domains glue together to give a well-defined holomorphic 1-form on . The vertices of the polygon where the cone angles are not equal to are zeroes of (a cone angle of corresponds to a zero of order ).
In the other direction, given a pair where is a compact Riemann surface and a holomorphic 1-form one can construct a polygon by using the complex numbers where are disjoint paths between the zeroes of which form an integral basis for the relative cohomology.
Examples
The simplest example of a translation surface is obtained by gluing the opposite sides of a parallelogram. It is a flat torus with no singularities.
If is a regular -gon then the translation surface obtained by gluing opposite sides is of genus with a single singular point, with angle .
If is obtained by putting side to side a collection of copies of the unit square then any translati |
https://en.wikipedia.org/wiki/Environmental%20protection%20expenditure%20accounts | Environmental protection expenditure accounts (EPEA) are a statistical framework that describes environmental activities in monetary terms and organises these statistics into a full set of accounts, just like that of the national accounts. The EPEA is part of the System of Integrated Environmental and Economic Accounting which, in March 2012, was adopted as a statistical standard by the United Nations Statistical Commission.
The EPEA results in a net national total expenditure for environmental protection of an economy. The statistics are usually presented by economic sectors (government, industries, households) and by what environmental domain has been protected, i.e. water, air, biodiversity etc.
The main types of statistics that feed into the framework are investment statistics, statistics on current outlays, government statistics on subsidies and investment grants, all with bearing on protection of the environment.
The statistics cover actual outlays. This means that, for example, losses of income are not seen in the statistics with the exception of specific transfers (or subsidies) that are designed to compensate any economic losses. Neither do the statistics cover all activities that might have a beneficial environmental impact. There is a distinction between the purpose of the activity and the effect of the activity. For example, new production equipment that is installed solely for the purpose of increasing productivity and reducing costs may use energy and materials more efficiently, and as a side effect reduce environmental discharges. The expenditure for this new equipment would not be included in EPE.
The main aim of the statistics is to provide indicators to show the response of society to reduce pollution. The statistics can be used in different types of analysis. One type of analysis determines whether the "polluter pays" principle holds, i.e. whether those who pollute are also the ones who pay for remediation and clean-up. It can also be used to analyse the effects on enterprise competitiveness, for cost-effective analysis related to propositions of new regulations and policies.
Scope
In order to create the statistics on environmental protection expenditure (EPE) an international definition has been agreed upon.
"Environmental protection groups together all actions and activities that are aimed at the prevention,
reduction and elimination of pollution as well as any other degradation of the environment. This includes measures taken in order to restore the environment after it has been degraded due to the pressures from human activities".1994 SERIEE §2006 and SEEA Central Framework chapter 4
This definition delimitates the area so that hygiene and security are excluded as well as management of natural resources.
The full sequence of EPEA are compiled through five different tables that interact with one another. The tables are established, just like the national accounts on a double-entry bookkeeping system. They wer |
https://en.wikipedia.org/wiki/Fred%20Van%20Oystaeyen | Fred Van Oystaeyen (born 1947), also Freddy van Oystaeyen, is a mathematician and emeritus professor of mathematics at the University of Antwerp. He has pioneered work on noncommutative geometry, in particular noncommutative algebraic geometry.
Biography
In 1972, Fred Van Oystaeyen obtained his Ph.D. from the Vrije Universiteit of Amsterdam. In 1975 he became professor at the University of Antwerp, Department of Mathematics and Computer Science.
Van Oystaeyen has well over 200 scientific papers and several books. One of his recent books, Virtual Topology and Functor Geometry, provides an introduction to noncommutative topology.
At the occasion of his 60th birthday, a conference in his honour was held in Almería, September 18 to 22, 2007; on March 25, 2011, he received his first honorary doctorate from that same university, Universidad de Almería.
At the campus of Universidad de Almería the street "Calle Fred Van Oystaeyen" (previously "Calle los Gallardos") is named after him.
In 2019, he will receive another honorary doctorate from the Vrije Universiteit Brussel.
Books
Hidetoshi Marubayashi, Fred Van Oystaeyen: Prime Divisors and Noncommutative Valuation Theory, Springer, 2012,
Fred Van Oystaeyen: Virtual topology and functor geometry, Chapman & Hall, 2008,
Constantin Nastasescu, Freddy van Oystaeyen: Methods of graded rings, Lecture Notes in Mathematics 1836, Springer, February 2004,
Freddy van Oystaeyen: Algebraic geometry for associative algebras, M. Dekker, New York, 2000,
F. van Oystaeyen, A. Verschoren: Relative invariants of rings: the noncommutative theory, M. Dekker, New York, 1984,
F. van Oystaeyen, A. Verschoren: Relative invariants of rings: the commutative theory, M. Dekker, New York, 1983,
Freddy M.J. van Oystaeyen, Alain H.M.J. Verschoren: Non-commutative algebraic geometry: an introduction, Springer-Verlag, 1981,
F. van Oystaeyen, A. Verschoren: Reflectors and localization : application to sheaf theory, M. Dekker, New York, 1979,
F. van Oystaeyen: Prime spectra in non-commutative algebra, Springer-Verlag, 1975,
References
External links
Fred Van Oystaeyen, Universiteit Antwerpen - Academic bibliography - Research
Fred Van Oystaeyen, publication list at Scientific Commons
Fred Van Oystaeyen: On the Reality of Noncommutative Space, neverendingbooks.org
1947 births
Living people
Belgian mathematicians
Vrije Universiteit Amsterdam alumni
Academic staff of the University of Antwerp |
https://en.wikipedia.org/wiki/Dewayne%20Bunch%20%28Kentucky%20politician%29 | DeWayne Bunch (February 22, 1962 – July 11, 2012) was a teacher and a Republican politician in Kentucky.
Biography
Bunch taught mathematics and science at Whitley County High School in Williamsburg, Kentucky. He also was a member of the Kentucky National Guard for 23 years and served a tour of duty in Iraq. In 2010 he was elected to the Kentucky House of Representatives, defeating incumbent Charlie Siler to represent the 82nd district (Whitley County and part of Laurel County).
Bunch resigned his seat in the Kentucky House on October 26, 2011, following his head injury, and Kentucky Governor Steven Beshear called for a special election to be held December 20, 2011, to fill the rest of Bunch's term, which was to end December 31, 2012. DeWayne Bunch's wife Regina, a special education teacher at Whitley County Middle School, announced that she would seek to succeed him in office, running as a Republican. Local party leaders named Regina Bunch as their candidate. As of November 16, 2011, Democratic Party leaders in Whitley County said they were unlikely to nominate a candidate to oppose her.
Head injury and death
On April 12, 2011, while attempting to break up a fight in the school cafeteria, Bunch was knocked down and hit his head on the floor, which the local sheriff described as being hard "like slate". In the immediate aftermath of the incident he was reported to be in "extremely critical condition", after being rushed to the University of Kentucky Medical Center in Lexington, where he was treated for more than two weeks, before being transferred to the Shepherd Center, a specialized facility in Atlanta for the treatment and rehabilitation of brain and spinal cord injuries. By June, he was communicating with his family, and had regained certain abilities, but as of October 2011, he was still a patient at the Shepherd Center.
Bunch died on July 11, 2012, from the injuries sustained the year before, aged 50.
References
1962 births
2012 deaths
Schoolteachers from Kentucky
Republican Party members of the Kentucky House of Representatives
People from Whitley County, Kentucky
People with traumatic brain injuries |
https://en.wikipedia.org/wiki/R.%20Michael%20Canjar | Robert Michael "Mike" Canjar (September 9, 1953 – May 7, 2012) was a Professor in the Department of Mathematics and Computer Science at University of Detroit Mercy (UDM). He started there in 1995, and served as department Chairman from 1995–2002. He was promoted to Full Professor in 2001. He previously taught at several universities, including the University of Baltimore. He lived in Livonia, part of metropolitan Detroit, Michigan.
Education
Mike Canjar attended the University of Detroit (now University of Detroit Mercy) where he received his Bachelor of Engineering degree in 1973. He earned a Master of Engineering degree in 1974. He received a Ph.D. in Mathematics from the University of Michigan in 1982, specializing in Mathematical Logic.
Academia
Canjar was Professor of the Department of Mathematics and Computer Science of the University of Detroit Mercy, where he also served as departmental Chairman from 1995–2002. He was with UDM since 1995.
He previously taught at a number of universities, including the University of Baltimore where he'd served as Chairman of the Department of Mathematics, Computer Science, and Statistics. He published a number of articles in mathematical journals on Mathematical Logic and Set Theory. He was also interested in Computer Science, particularly in object-oriented programming and Windows programming, developing courses in those areas.
Canjar has served as president of the Professors' Union of the University of Detroit Mercy.
Gambling theory
Using the pen name MathProf, Mike Canjar was a regular contributor to various websites dedicated to the study of casino games and advantage play, most often to Stanford Wong's Blackjack website where he won a record number 16 times the award for Post of The Month.
MathProf was considered one of the most prominent contributors to the study of casino Blackjack and the related subjects of bankroll management, risk of ruin, kurtosis and skewness, cut card effects, large deviations, and others.
Personal life
Robert Michael Canjar was born in Detroit, Michigan, in 1953, the only child of his parents, Lawrence N. Canjar and Lillian Patricia "Pat" McDonald. His father was Dean of Engineering at the University of Detroit. His mother, who had received a master's degree in Clinical Psychology from the University of Detroit, was a practicing clinical psychologist.
Mike Canjar and Elaine Bell, who has a master's degree in Computer Science and serves as Director of Institutional Research at the UDM, were married on August 8, 2010.
In 2011, Canjar, who was raised as a Roman Catholic, became a member of the Disciples of Christ Memorial Christian Church.
During his April 2010 annual physical exam, he was diagnosed with having inoperable prostate cancer at an already advanced stage, with distant metastasis, and began chemotherapy treatment. Mike Canjar died on May 7, 2012.
References
External links
"Why Optimal Betting is not Optimal" by R. Michael Canjar, 2nd Annual Skaff Memor |
https://en.wikipedia.org/wiki/Switzerland%27s%20Land%20Use%20Statistics | The Land Use Statistics of the Federal Statistical Office collect information in 12-year intervals about Switzerland's land use and land cover based on aerial photographs of the Federal Office of Topography (swisstopo). In addition to statistics, the Land Use Statistics also provides basic geodata in hectare resolution for Geographical Information Systems (GIS) of the Confederation, the cantons, research institutes and higher education institutions. Furthermore, it provides inputs for national programmes and indicator systems.
Legal basis
The legal bases for the Land Use Statistics are Arts. 65, 73, 75, 77 and 104 of the Federal Constitution, Article 3 of the Federal Statistics Act, the Federal Council's decision of 17 February 1982 and the Ordinance of 30 June 1993 on the Conduct of Federal Statistical Surveys (SR 431.012.1), status 2004.
Type of survey
The Land Use Statistics are compiled by means of aerial point sampling of aerial photographs of the Federal Office of Topography. Some 4.1 million sample points at intervals of 100x100m are made.
Features registered
All of Switzerland's surface area is covered at the levels of Switzerland, cantons, districts, communes, hectares and various spatial units. The registered features are divided into 72 land use and land cover categories in the areas of settlements (buildings and industrial areas, traffic areas, recreational facilities, mines, landfills, construction sites), agriculture (arable land, meadows, pastures, fruit cultivation, vineyards and horticulture), stocked areas (forest, shrub forest, woodland), unproductive areas (watercourses, unproductive vegetation, rocks, sand, boulders, glaciers, firn).
Date survey conducted
The Land Use Statistics have been compiled every 12 years since 1979. This statistic is produced the year after the aerial photographs are taken and is available two years after they are taken. The aerial photographs of the Federal Office of Topography are taken in a six-year cycle (1979/85, 1992/97, 2004/09).
Footnotes and references
Federal Statistical Office, Swiss Land Use Statistics, Fact Sheet (German)
External links
Federal Statistical Office (FSO), History of the Land Use Statistics, Land Use Statistics to date (German)
Geography of Switzerland |
https://en.wikipedia.org/wiki/Electoral%20Calculus | Electoral Calculus is a political forecasting web site that attempts to predict future United Kingdom general election results. It considers national factors and local demographics.
Main features
The site was developed by Martin Baxter, who was a financial analyst specialising in mathematical modelling.
The site includes maps, predictions and analysis articles. It has separate sections for elections in Scotland and Northern Ireland.
From April 2019, the headline prediction covered the Brexit Party and Change UK – The Independent Group. Change UK was later removed from the headline prediction ahead of the 2019 general election as their poll scores were not statistically significant.
Methodology
The site is based around the employment of scientific techniques on data about the United Kingdom's electoral geography, which can be used to calculate the uniform national swing. It takes account of national polls and trends but excludes local issues.
The calculations were initially based on what is termed the Transition Model, which is derived from the additive uniform national swing model. This uses national swings in a proportional manner to predict local effects. The Strong Transition Model was introduced in October 2007, and considers the effects of strong and weak supporters. The models are explained in detail on the web site.
Predictions
Across the eight general elections from 1992 to 2019:
EC correctly predicted the party to win the most seats in seven out of eight (all except 1992).
EC correctly predicted the majority party or lack of a majority, in five (1997, 2001, 2005, 2010 no majority and 2019).
The mean polling error for the two largest parties was 4.8%.
Reception
It was listed by The Guardian in 2004 as one of the "100 most useful websites", being "the best" for predictions. In 2012 it was described by PhD student Chris Prosser at the University of Oxford as "probably the leading vote/seat predictor on the internet". Its detailed predictions for individual seats have been noted by Paul Evans on the localdemocracy.org.uk blog. Academic Nick Anstead noted in his observations from a 2010 Personal Democracy Forum event, that Mick Fealty of Slugger O'Toole considered Electoral Calculus to be "massively improved" in comparison with the swingometer.
With reference to the 2010 United Kingdom general election, it was cited by journalists Andrew Rawnsley and Michael White in The Guardian. John Rentoul in The Independent referred to the site after the election.
The founder of Electoral Calculus, Martin Baxter, and its sole employee, Marwan Riach, have regularly appeared on UK and international media to offer polling expertise to their audience.
References
External links
Electoral Calculus
British political websites
Elections in the United Kingdom
Electoral geography
Opinion polling in the United Kingdom
Psephology
Mathematical modeling |
https://en.wikipedia.org/wiki/Joachim%20von%20zur%20Gathen | Joachim von zur Gathen (born 1950) is a German and computer scientist. His research spans several areas in mathematics and computer science, including computational complexity, cryptography, finite fields, and computer algebra.
Biography
Joachim von zur Gathen has a Diploma in Mathematik from ETH Zürich, and graduated as Dr. phil. from Universität Zürich in 1980 under the supervision of Volker Strassen. The title of his Ph.D. thesis is "Sekantenräume von Kurven". In 1981 he accepted a position in the Department of Computer Science at the University of Toronto, eventually becoming a Full Professor. In 1994, he moved to the Department of Mathematics at Universität Paderborn. Since 2004, he has been a professor at the B-IT and the Department of Computer Science at the Universität Bonn. He is the founding editor-in-chief of the Birkhäuser (now Springer) journal Computational Complexity.
A symposium at B-IT in 2010 was held in honor of his 60th birthday, and a special issue of the Journal of Symbolic Computation was published as a festschrift for the event.
Selected publications
Translated into Japanese. Chinese edition.
References
External links
Homepage at the b-it
1950 births
Living people
20th-century German mathematicians
German computer scientists
Theoretical computer scientists
21st-century German mathematicians |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20HB%20K%C3%B8ge%20season | This article shows statistics of individual players for the football club HB Køge. It also lists all matches that HB Køge will play in the 2011–12 season.
Players
Squad information
This section show the squad as currently, considering all players who are confirmedly moved in and out.
References
External links
HB Køge official website
HB Køge seasons
Hb Koge |
https://en.wikipedia.org/wiki/1928%E2%80%9329%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1928–29 season.
League standings
Uppsvenska 1928–29
Östsvenska 1928–29
Mellansvenska 1928–29
Nordvästra 1928–29
Södra Mellansvenska 1928–29
Sydöstra 1928–29
Västsvenska 1928–29
Sydsvenska 1928–29
Footnotes
References
Swedish Football Division 3 seasons
3
Sweden |
https://en.wikipedia.org/wiki/MyMathLab | MyMathLab is an online interactive and educational system designed by Pearson Education to accompany its published math textbooks. It covers courses from basic math through calculus and statistics, as well as math for business, engineering and future educators. Pearson designed MyMathLab to respond to the needs of instructors and students who wanted more opportunity for practice, immediate feedback, and automated grading.
MyLab and Mastering
Pearson's MyLab and Mastering series consists of more than 70 online interactive and educational system in a variety of different subjects. Some features of MyMathLab (and MyStatLab) specifically for students are homework, quizzes, tests, full eText, and multimedia tutorials. For instructors' benefits, MyMathLab records and evaluates students' learning progress and time spent on assignments. Instructors may set up a customized MyMathLab course.
Effectiveness
A report of the effectiveness of MyLab and Mastering, and how to plan and implement a course has been published by Pearson.
Fayetteville State University conducted a study on whether using an online interactive system such as MyMathLab would increase a student's academic performance compared to the traditional paper-based homework system. The study was done in a college algebra course. The result showed that those who pass the course using MyMathLab is 70% while using traditional homework system is 49%. However, the study neglected to factor in students preemptively dropping the course out of frustration and the increased amount of time students were forced to spend on a topic due to poor user interface design and incorrect answer parsing. When comparing outcomes between three semesters of a college algebra course taught using MyMathlab and one semester taught with a mix of OER and other low-cost alternatives using the same instructors, a Georgia College & State University study found that students who used the OER and low-cost alternatives were more likely to earn a C or higher and less likely to withdraw from the course than those who used MyMathLab. A study done by North Georgia College and State University shows that most students found MyMathLab's video tutoring feature useful. Some students argue that most of MyMathLab's videos only cover basic concepts when they demand more videos on advanced materials. Another review claims that some tutors are not as easily understood as others. "MyMathLab" has also fallen under additional criticism for wording problems in a way that students cannot easily understand.
Users have complained that content in MyMathLab is not accessible using screen readers.
Features
Pearson’s MyMathLab consists of several features that aid instructors and students. The homework and practice exercises take advantage of an algorithm to generate problems, so students can have limitless options to practice problems. Another core feature of MyMathLab is the eText book. The eText book can be viewed through a traditional computer |
https://en.wikipedia.org/wiki/1929%E2%80%9330%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1929–30 season.
League standings
Uppsvenska 1929–30
Östsvenska 1929–30
Mellansvenska 1929–30
Nordvästra 1929–30
Södra Mellansvenska 1929–30
Sydöstra 1929–30
Västsvenska 1929–30
Sydsvenska 1929–30
Footnotes
References
Swedish Football Division 3 seasons
3
Sweden |
https://en.wikipedia.org/wiki/1930%E2%80%9331%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1930–31 season.
League standings
Uppsvenska 1930–31
Östsvenska 1930–31
Mellansvenska 1930–31
Nordvästra 1930–31
Södra Mellansvenska 1930–31
Sydöstra 1930–31
Västsvenska 1930–31
Sydsvenska 1930–31
Footnotes
References
Swedish Football Division 3 seasons
3
Sweden |
https://en.wikipedia.org/wiki/Covariance%20operator | In probability theory, for a probability measure P on a Hilbert space H with inner product , the covariance of P is the bilinear form Cov: H × H → R given by
for all x and y in H. The covariance operator C is then defined by
(from the Riesz representation theorem, such operator exists if Cov is bounded). Since Cov is symmetric in its arguments, the covariance operator is
self-adjoint. When P is a centred Gaussian measure, C is also a nuclear operator. In particular, it is a compact operator of trace class, that is, it has finite trace.
Even more generally, for a probability measure P on a Banach space B, the covariance of P is the bilinear form on the algebraic dual B#, defined by
where is now the value of the linear functional x on the element z.
Quite similarly, the covariance function of a function-valued random element (in special cases is called random process or random field) z is
where z(x) is now the value of the function z at the point x, i.e., the value of the linear functional evaluated at z.
See also
Bilinear forms
Covariance and correlation
Probability theory
Hilbert spaces |
https://en.wikipedia.org/wiki/1931%E2%80%9332%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1931–32 season.
League standings
Uppsvenska 1931–32
Östsvenska 1931–32
Mellansvenska 1931–32
Nordvästra 1931–32
Södra Mellansvenska 1931–32
Sydöstra 1931–32
Västsvenska 1931–32
Sydsvenska 1931–32
Footnotes
References
Swedish Football Division 3 seasons
3
Sweden |
https://en.wikipedia.org/wiki/1932%E2%80%9333%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1932–33 season.
League standings
Uppsvenska 1932–33
Östsvenska 1932–33
Mellansvenska 1932–33
Nordvästra 1932–33
Södra Mellansvenska 1932–33
Sydöstra 1932–33
Västsvenska 1932–33
Sydsvenska 1932–33
Footnotes
References
Swedish Football Division 3 seasons
3
Sweden |
https://en.wikipedia.org/wiki/Formation%20%28group%20theory%29 | In group theory, a branch of mathematics, a formation is a class of groups closed under taking images and such that if G/M and G/N are in the formation then so is G/M∩N. introduced formations to unify the theory of Hall subgroups and Carter subgroups of finite solvable groups.
Some examples of formations are the formation of p-groups for a prime p, the formation of π-groups for a set of primes π, and the formation of nilpotent groups.
Special cases
A Melnikov formation is closed under taking quotients, normal subgroups and group extensions. Thus a Melnikov formation M has the property that for every short exact sequence
A and C are in M if and only if B is in M.
A full formation is a Melnikov formation which is also closed under taking subgroups.
An almost full formation is one which is closed under quotients, direct products and subgroups, but not necessarily extensions. The families of finite abelian groups and finite nilpotent groups are almost full, but neither full nor Melnikov.
Schunck classes
A Schunck class, introduced by , is a generalization of a formation, consisting of a class of groups such that a group is in the class if and only if every primitive factor group is in the class. Here a group is called primitive if it has a self-centralizing normal abelian subgroup.
References
Group theory |
https://en.wikipedia.org/wiki/1933%E2%80%9334%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1933–34 season.
League standings
Uppsvenska 1933–34
Östsvenska 1933–34
Mellansvenska 1933–34
Nordvästra 1933–34
Södra Mellansvenska 1933–34
Sydöstra 1933–34
Västsvenska 1933–34
Sydsvenska 1933–34
Footnotes
References
Swedish Football Division 3 seasons
3
Sweden |
https://en.wikipedia.org/wiki/Log-Cauchy%20distribution | In probability theory, a log-Cauchy distribution is a probability distribution of a random variable whose logarithm is distributed in accordance with a Cauchy distribution. If X is a random variable with a Cauchy distribution, then Y = exp(X) has a log-Cauchy distribution; likewise, if Y has a log-Cauchy distribution, then X = log(Y) has a Cauchy distribution.
Characterization
The log-Cauchy distribution is a special case of the log-t distribution where the degrees of freedom parameter is equal to 1.
Probability density function
The log-Cauchy distribution has the probability density function:
where is a real number and . If is known, the scale parameter is . and correspond to the location parameter and scale parameter of the associated Cauchy distribution. Some authors define and as the location and scale parameters, respectively, of the log-Cauchy distribution.
For and , corresponding to a standard Cauchy distribution, the probability density function reduces to:
Cumulative distribution function
The cumulative distribution function (cdf) when and is:
Survival function
The survival function when and is:
Hazard rate
The hazard rate when and is:
The hazard rate decreases at the beginning and at the end of the distribution, but there may be an interval over which the hazard rate increases.
Properties
The log-Cauchy distribution is an example of a heavy-tailed distribution. Some authors regard it as a "super-heavy tailed" distribution, because it has a heavier tail than a Pareto distribution-type heavy tail, i.e., it has a logarithmically decaying tail. As with the Cauchy distribution, none of the non-trivial moments of the log-Cauchy distribution are finite. The mean is a moment so the log-Cauchy distribution does not have a defined mean or standard deviation.
The log-Cauchy distribution is infinitely divisible for some parameters but not for others. Like the lognormal distribution, log-t or log-Student distribution and Weibull distribution, the log-Cauchy distribution is a special case of the generalized beta distribution of the second kind. The log-Cauchy is actually a special case of the log-t distribution, similar to the Cauchy distribution being a special case of the Student's t distribution with 1 degree of freedom.
Since the Cauchy distribution is a stable distribution, the log-Cauchy distribution is a logstable distribution. Logstable distributions have poles at x=0.
Estimating parameters
The median of the natural logarithms of a sample is a robust estimator of . The median absolute deviation of the natural logarithms of a sample is a robust estimator of .
Uses
In Bayesian statistics, the log-Cauchy distribution can be used to approximate the improper Jeffreys-Haldane density, 1/k, which is sometimes suggested as the prior distribution for k where k is a positive parameter being estimated. The log-Cauchy distribution can be used to model certain survival processes where significant outliers or extreme resu |
https://en.wikipedia.org/wiki/Quasi-relative%20interior | In topology, a branch of mathematics, the quasi-relative interior of a subset of a vector space is a refinement of the concept of the interior. Formally, if is a linear space then the quasi-relative interior of is
where denotes the closure of the conic hull.
Let is a normed vector space, if is a convex finite-dimensional set then such that is the relative interior.
See also
References
Topology |
https://en.wikipedia.org/wiki/Unscented%20transform | The unscented transform (UT) is a mathematical function used to estimate the result of applying a given nonlinear transformation to a probability distribution that is characterized only in terms of a finite set of statistics. The most common use of the unscented transform is in the nonlinear projection of mean and covariance estimates in the context of nonlinear extensions of the Kalman filter. Its creator Jeffrey Uhlmann explained that "unscented" was an arbitrary name that he adopted to avoid it being referred to as the “Uhlmann filter” though others have indicated that "unscented" is a contrast to "scented" intended as a euphemism for "stinky"
Background
Many filtering and control methods represent estimates of the state of a system in the form of a mean vector and an associated error covariance matrix. As an example, the estimated 2-dimensional position of an object of interest might be represented by a mean position vector, , with an uncertainty given in the form of a 2x2 covariance matrix giving the variance in , the variance in , and the cross covariance between the two. A covariance that is zero implies that there is no uncertainty or error and that the position of the object is exactly what is specified by the mean vector.
The mean and covariance representation only gives the first two moments of an underlying, but otherwise unknown, probability distribution. In the case of a moving object, the unknown probability distribution might represent the uncertainty of the object's position at a given time. The mean and covariance representation of uncertainty is mathematically convenient because any linear transformation can be applied to a mean vector and covariance matrix as and . This linearity property does not hold for moments beyond the first raw moment (the mean) and the second central moment (the covariance), so it is not generally possible to determine the mean and covariance resulting from a nonlinear transformation because the result depends on all the moments, and only the first two are given.
Although the covariance matrix is often treated as being the expected squared error associated with the mean, in practice the matrix is maintained as an upper bound on the actual squared error. Specifically, a mean and covariance estimate is conservatively maintained so that the covariance matrix is greater than or equal to the actual squared error associated with . Mathematically this means that the result of subtracting the expected squared error (which is not usually known) from is a semi-definite or positive-definite matrix. The reason for maintaining a conservative covariance estimate is that most filtering and control algorithms will tend to diverge (fail) if the covariance is underestimated. This is because a spuriously small covariance implies less uncertainty and leads the filter to place more weight (confidence) than is justified in the accuracy of the mean.
Returning to the example above, when the covariance is zero it i |
https://en.wikipedia.org/wiki/Midpoint%20polygon | In geometry, the midpoint polygon of a polygon is the polygon whose vertices are the midpoints of the edges of . It is sometimes called the Kasner polygon after Edward Kasner, who termed it the inscribed polygon "for brevity".
Examples
Triangle
The midpoint polygon of a triangle is called the medial triangle. It shares the same centroid and medians with the original triangle. The perimeter of the medial triangle equals the semiperimeter of the original triangle, and the area is one quarter of the area of the original triangle. This can be proven by the midpoint theorem of triangles and Heron's formula. The orthocenter of the medial triangle coincides with the circumcenter of the original triangle.
Quadrilateral
The midpoint polygon of a quadrilateral is a parallelogram called its Varignon parallelogram. If the quadrilateral is simple, the area of the parallelogram is one half the area of the original quadrilateral. The perimeter of the parallelogram equals the sum of the diagonals of the original quadrilateral.
See also
Circulant matrix
Midpoint-stretching polygon
Varignon's theorem
References
Further reading
External links
Polygons |
https://en.wikipedia.org/wiki/1934%E2%80%9335%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1934–35 season.
League standings
Uppsvenska Östra 1934–35
Uppsvenska Västra 1934–35
Östsvenska 1934–35
Mellansvenska 1934–35
Nordvästra 1934–35
Södra Mellansvenska 1934–35
Sydöstra 1934–35
Västsvenska Norra 1934–35
Västsvenska Södra 1934–35
Sydsvenska 1934–35
Footnotes
References
Swedish Football Division 3 seasons
3
Sweden |
https://en.wikipedia.org/wiki/1935%E2%80%9336%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1935–36 season.
League standings
Uppsvenska Östra 1935–36
Uppsvenska Västra 1935–36
Östsvenska 1935–36
Mellansvenska 1935–36
Nordvästra 1935–36
Södra Mellansvenska 1935–36
Sydöstra 1935–36
Västsvenska Norra 1935–36
Västsvenska Södra 1935–36
Sydsvenska 1935–36
Footnotes
References
Swedish Football Division 3 seasons
3
Sweden |
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