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https://en.wikipedia.org/wiki/Metropolis-adjusted%20Langevin%20algorithm
In computational statistics, the Metropolis-adjusted Langevin algorithm (MALA) or Langevin Monte Carlo (LMC) is a Markov chain Monte Carlo (MCMC) method for obtaining random samples – sequences of random observations – from a probability distribution for which direct sampling is difficult. As the name suggests, MALA uses a combination of two mechanisms to generate the states of a random walk that has the target probability distribution as an invariant measure: new states are proposed using (overdamped) Langevin dynamics, which use evaluations of the gradient of the target probability density function; these proposals are accepted or rejected using the Metropolis–Hastings algorithm, which uses evaluations of the target probability density (but not its gradient). Informally, the Langevin dynamics drive the random walk towards regions of high probability in the manner of a gradient flow, while the Metropolis–Hastings accept/reject mechanism improves the mixing and convergence properties of this random walk. MALA was originally proposed by Julian Besag in 1994, (although the method Smart Monte Carlo was already introduced in 1978 ) and its properties were examined in detail by Gareth Roberts together with Richard Tweedie and Jeff Rosenthal. Many variations and refinements have been introduced since then, e.g. the manifold variant of Girolami and Calderhead (2011). The method is equivalent to using the Hamiltonian Monte Carlo (hybrid Monte Carlo) algorithm with only a single discrete time step. Further details Let denote a probability density function on , one from which it is desired to draw an ensemble of independent and identically distributed samples. We consider the overdamped Langevin Itô diffusion driven by the time derivative of a standard Brownian motion . (Note that another commonly-used normalization for this diffusion is which generates the same dynamics.) In the limit as , this probability distribution of approaches a stationary distribution, which is also invariant under the diffusion, which we denote . It turns out that, in fact, . Approximate sample paths of the Langevin diffusion can be generated by many discrete-time methods. One of the simplest is the Euler–Maruyama method with a fixed time step . We set and then recursively define an approximation to the true solution by where each is an independent draw from a multivariate normal distribution on with mean 0 and covariance matrix equal to the identity matrix. Note that is normally distributed with mean and covariance equal to times the identity matrix. In contrast to the Euler–Maruyama method for simulating the Langevin diffusion, which always updates according to the update rule MALA incorporates an additional step. We consider the above update rule as defining a proposal for a new state, This proposal is accepted or rejected according to the Metropolis-Hastings algorithm: set where is the transition probability density from to (no
https://en.wikipedia.org/wiki/Symmetry%20breaking%20%28disambiguation%29
Symmetry breaking is a concept in physics. The term may also refer to: a concept in biology: Symmetry breaking and cortical rotation a concept in mathematics: Symmetry-breaking constraints a concept in animal behavior: Symmetry breaking of escaping ants a concept in physics: Landau symmetry-breaking theory
https://en.wikipedia.org/wiki/Lorenzo%20Petrarca
Lorenzo Petrarca (born 24 July 1997 in Sant'Omero) is an Italian motorcycle racer. He competes in the CIV Supersport 600 Championship aboard a Kawasaki ZX-6R. Career statistics FIM CEV Moto3 Junior World Championship Races by year (key) (Races in bold indicate pole position, races in italics indicate fastest lap) Grand Prix motorcycle racing By season Races by year References External links 1997 births Living people Italian motorcycle racers Moto3 World Championship riders
https://en.wikipedia.org/wiki/KK%20Split%20in%20international%20competitions
KK Split history and statistics in FIBA Europe and Euroleague Basketball (company) competitions. 1970s 1971–72 FIBA European Champions Cup, 1st–tier The 1971–72 FIBA European Champions Cup was the 15th installment of the European top-tier level professional basketball club competition FIBA European Champions Cup (now called EuroLeague), running from November 4, 1971, to March 23, 1972. The trophy was won by Ignis Varese, who defeated Jugoplastika by a result of 70–69 at Yad Eliyahu Arena in Tel Aviv, Israel. Overall, Jugoplastika achieved in the present competition a record of 8 wins against 5 defeats, in five successive rounds. More detailed: First round Tie played on November 4, 1971, and on November 11, 1971. |} Second round Tie played on December 2, 1971, and on December 9, 1971. |} Quarterfinals Tie played on January 5, 1972, and on January 12, 1972. |} Tie played on January 19, 1972, and on February 3, 1972. |} Tie played on February 9, 1972, and on February 17, 1972. |} Group B standings: Semifinals Tie played on March 2, 1972, and on March 9, 1972. |} Final March 23, 1972 at Sports Palace at Yad Eliyahu in Tel Aviv, Israel. |} 1972–73 FIBA European Cup Winners' Cup, 2nd–tier The 1972–73 FIBA European Cup Winners' Cup was the 7th installment of FIBA's 2nd-tier level European-wide professional club basketball competition FIBA European Cup Winners' Cup (lately called FIBA Saporta Cup), running from October 18, 1972, to March 20, 1973. The trophy was won by Spartak Leningrad, who defeated Jugoplastika by a result of 77–62 at Alexandreio Melathron in Thessaloniki, Greece. Overall, Jugoplastika achieved in the present competition a record of 7 wins against 4 defeats, in two successive rounds. More detailed: First round Bye Second round Tie played on November 8, 1972, and on November 15, 1972. |} Top 12 Tie played on December 6, 1972, and on December 13, 1972. |} Quarterfinals Tie played on January 10, 1973, and on January 17, 1973. |} Tie played on January 24, 1973, and on January 31, 1973. |} Group B standings: Semifinals Tie played on February 28, 1973, and on March 7, 1973. |} Final March 20, 1973 at Alexandreio Melathron in Thessaloniki, Greece. |} 1973–74 FIBA Korać Cup, 3rd–tier The 1973–74 FIBA Korać Cup was the 3rd installment of the European 3rd-tier level professional basketball club competition FIBA Korać Cup, running from November 6, 1973, to April 11, 1974. The trophy was won by the title holder Birra Forst Cantù, who defeated Partizan by a result of 174–154 in a two-legged final on a home and away basis. Overall, Jugoplastika achieved in present competition a record of 5 wins against 5 defeats, in four successive rounds. More detailed: First round Tie played on November 6, 1973, and on November 13, 1973. |} Second round Tie played on November 27, 1973, and on December 4, 1973. |} Top 12 Tie played on January 8, 1974, and on January 15, 1974. |} Tie played on February 19,
https://en.wikipedia.org/wiki/Maurice%20L%27Abb%C3%A9
Maurice L'Abbé (1920 – July 21, 2006) was a Canadian academic and mathematician. Born in Ottawa, Ontario, L'Abbé obtained his license in mathematics in 1945 from the Université de Montréal, and a doctorate in mathematics from the Princeton University in 1951. He joined the faculty of science in the Université de Montréal becoming an associate professor in 1950 and full professor in 1956. He was director of the Université de Montréal's Department of Mathematics from 1957 to 1968. He was dean of the Faculty of Science from 1964 to 1968 and Vice-Rector for Research from 1968 to 1978. In 1968, he helped to establish the Centre de Recherches Mathématiques, the first mathematical research institute in Canada. Honours In 1993, he was made an Officer of the National Order of Quebec. In 1994, he was awarded the Prix Armand-Frappier. References 1920 births 2006 deaths Canadian mathematicians Canadian university and college faculty deans Officers of the National Order of Quebec Academics from Ottawa Princeton University alumni Université de Montréal alumni Academic staff of the Université de Montréal Presidents of the Canadian Mathematical Society
https://en.wikipedia.org/wiki/Algorismus%20%28Norse%20text%29
Algorismus is a short treatise on mathematics, written in Old Icelandic. It is the oldest text on mathematics in a Scandinavian language and survives in the early fourteenth-century manuscript Hauksbók, a large book written and compiled by Icelanders and taken to Norway during the later part of the 13th century by Haukur Erlendsson. It is probably a translation from Latin into Old Norse of some pages included in more ancient books such as Carmen de Algorismo by De Villa Dei of 1200, Liber Abaci by Fibonacci of 1202, and Algorismus Vulgaris by De Sacrobosco of 1230. References Icelandic literature Icelandic manuscripts Mathematics manuscripts Mathematics textbooks Old Norse literature 14th-century books
https://en.wikipedia.org/wiki/Marius%20Briceag
Marius Ionuţ Briceag (born 6 April 1992) is a Romanian professional footballer who plays as a left-back for Ekstraklasa club Korona Kielce. Career statistics Club Notes Honours Club Universitatea Craiova Cupa României: 2017–18 Supercupa României runner-up: 2018 Voluntari Cupa României runner-up: 2021–22 References External links 1992 births Living people Romanian men's footballers Liga I players Liga II players Ekstraklasa players FC Argeș Pitești players SCM Râmnicu Vâlcea players CS Universitatea Craiova players FC Voluntari players FC Steaua București players FC Universitatea Cluj players Korona Kielce players Men's association football defenders Footballers from Pitești Romanian expatriate men's footballers Expatriate men's footballers in Poland Romanian expatriate sportspeople in Poland
https://en.wikipedia.org/wiki/Coordinate%20systems%20for%20the%20hyperbolic%20plane
In the hyperbolic plane, as in the Euclidean plane, each point can be uniquely identified by two real numbers. Several qualitatively different ways of coordinatizing the plane in hyperbolic geometry are used. This article tries to give an overview of several coordinate systems in use for the two-dimensional hyperbolic plane. In the descriptions below the constant Gaussian curvature of the plane is −1. Sinh, cosh and tanh are hyperbolic functions. Polar coordinate system The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian system) is called the pole, and the ray from the pole in the reference direction is the polar axis. The distance from the pole is called the radial coordinate or radius, and the angle is called the angular coordinate, or polar angle. From the hyperbolic law of cosines, we get that the distance between two points given in polar coordinates is The corresponding metric tensor field is: The straight lines are described by equations of the form where r0 and θ0 are the coordinates of the nearest point on the line to the pole. Quadrant model system The Poincaré half-plane model is closely related to a model of the hyperbolic plane in the quadrant Q = {(x,y): x > 0, y > 0}. For such a point the geometric mean and the hyperbolic angle produce a point (u,v) in the upper half-plane. The hyperbolic metric in the quadrant depends on the Poincaré half-plane metric. The motions of the Poincaré model carry over to the quadrant; in particular the left or right shifts of the real axis correspond to hyperbolic rotations of the quadrant. Due to the study of ratios in physics and economics where the quadrant is the universe of discourse, its points are said to be located by hyperbolic coordinates. Cartesian-style coordinate systems In hyperbolic geometry rectangles do not exist. The sum of the angles of a quadrilateral in hyperbolic geometry is always less than 4 right angles (see Lambert quadrilateral). Also in hyperbolic geometry there are no equidistant lines (see hypercycles). This all has influences on the coordinate systems. There are however different coordinate systems for hyperbolic plane geometry. All are based on choosing a real (non ideal) point (the Origin) on a chosen directed line (the x-axis) and after that many choices exist. Axial coordinates Axial coordinates xa and ya are found by constructing a y-axis perpendicular to the x-axis through the origin. Like in the Cartesian coordinate system, the coordinates are found by dropping perpendiculars from the point onto the x and y-axes. xa is the distance from the foot of the perpendicular on the x-axis to the origin (regarded as positive on one side and negative on the other); ya is the distance from the foot of the perpendicular on the y-axis to the origin. Every point
https://en.wikipedia.org/wiki/Joe%20Irving
Joe Irving (born 8 June 1998) is a British motorcycle racer. Career statistics Grand Prix motorcycle racing By season Races by year References External links http://www.motogp.com/en/riders/Joe+Irving https://web.archive.org/web/20160205230631/http://www.britishsuperbike.com/support/2012/125gp.aspx 1998 births Living people British motorcycle racers Moto3 World Championship riders People from Holmfirth
https://en.wikipedia.org/wiki/Hafiza%20Rofa
Mohd Hafiza bin Rofa (born 8 July 1996) is a Malaysian professional motorcycle racer. Career statistics FIM CEV Moto3 Junior World Championship Races by year (key) (Races in bold indicate pole position, races in italics indicate fastest lap) Grand Prix motorcycle racing By season Races by year ARRC Underbone 150 Races by year (key) (Races in bold indicate pole position; races in italics indicate fastest lap) References External links http://www.motogp.com/en/riders/Hafiza+Rofa Living people 1996 births Malaysian motorcycle racers Moto3 World Championship riders
https://en.wikipedia.org/wiki/Herbert%20Gross
Herbert Irving Gross (April 2, 1929 – May 27, 2020) was an American Professor of mathematics (retired) and former senior lecturer at MIT’s Center for Advanced Engineering Study (CAES). He was best known as a pioneer in using distance learning for teaching mathematics. Biography Gross was born in Boston MA in 1929. He studied mathematics at Brandeis University and graduated in 1953 with a B.A. in mathematics. He then attended the Massachusetts Institute of Technology as a Ph. D. candidate and a Teaching Assistant in mathematics. In 1958, prior to having completed his studies at MIT, he left to become the founding mathematics department chairperson at Corning (NY) Community College where he remained for the next ten years. During that time he became Corning’s first educational television instructor, teaching calculus to high school students in Corning’s three high schools and published his first textbook (Mathematics: A Chronicle of Human Endeavor). He left Corning in 1968 to become the Senior Lecturer at MIT's Center for Advanced Engineering Study (CAES) where, from 1968 to 1973, he produced the critically acclaimed video course “Calculus Revisited”. In 1985 he produced Classic Arithmetic Course which was videotaped and since attracted many views and is considered to be a classic. In 2011 MIT's OpenCourseWare made the course available on its website where it has become a “cult classic” because of its “archaic” black-and-white- talking-head format. It has received over a million views on YouTube. In 1973 he left MIT to become the founding Mathematics Department Chairperson at Bunker Hill (Boston MA) Community College, where he remained until his retirement in 2003. After his retirement in 2003, he continued to develop his websites while working with elementary school teachers in an attempt to help them help their students internalize mathematics better. 1974 Gross was the founding president of the American Mathematics Association of Two Year Colleges (AMATYC). In 2014, at age 85 and under the sponsorship of Corning Inc., Gross developed a series of 40 arithmetic videos, designed to help elementary school teachers. Social engagement Gross chose to leave MIT to be able to move into the community college and prison environment. Gross: "In terms of a way of life there was something special to me about using my method of teaching math to help mathematically at-risk adults learn to overcome their fear of math and thus increases their chances for greater upward mobility." Gross often referred to the community colleges as “the statue of liberty for those who otherwise might have been educationally disenfranchised”. Gross was lauded by the principal of the Vocational School at the Harnett Correctional Institution for his work with the prisoners and his successful “Gateways to Mathematics” course (which was subtitled “Confidence through Competence”), turning even hard-core inmates around. Awards and honors In 2014, Gross' work was recognized by th
https://en.wikipedia.org/wiki/Global%20Digital%20Mathematics%20Library
The Global Digital Mathematics Library (GDML) is a project organized under the auspices of the International Mathematical Union (IMU) to establish a digital library focused on mathematics. A working group was convened in September 2014, following the 2014 International Congress of Mathematicians, by former IMU President Ingrid Daubechies and Chair Peter J. Olver of the IMU’s Committee on Electronic Information and Communication (CEIC). Currently the working group has eight members, namely: Thierry Bouche, Institut Fourier & Cellule MathDoc, Grenoble, France Bruno Buchberger, RISC, Hagenberg/Linz, Austria Patrick Ion, Mathematical Reviews/AMS, Ann Arbor, MI, US Michael Kohlhase, Jacobs University, Bremen, Germany Jim Pitman, University of California, Berkeley, CA, US Olaf Teschke, zbMATH/FIZ, Berlin, Germany Stephen M. Watt, University of Waterloo, Waterloo, ON, Canada Eric Weisstein, Wolfram Research, McAllen, TX, US Background In the spring of 2014, the Committee on Planning a Global Library of the Mathematical Sciences released a comprehensive study entitled “Developing a 21st Century Global Library for Mathematics Research.” This report states in its Strategic Plan section, “There is a compelling argument that through a combination of machine learning methods and editorial effort by both paid and volunteer editors, a significant portion of the information and knowledge in the global mathematical corpus could be made available to researchers as linked open data through the GDML." Workshop A workshop titled "Semantic Representation of Mathematical Knowledge" was held at the Fields Institute in Toronto during February 3–5, 2016. The goal of the workshop was to lay down the foundations of a prototype semantic representation language for the GDML. The workshop's organizers recognized that the extremely wide scope of mathematics as a whole made it unrealistic to map out the detailed concepts, structures, and operations needed and used in individual mathematical subjects. The workshop therefore limited itself to surveys of the status quo in mathematical representation languages including representation of prominent and fundamental theorems in certain areas that could serve as building blocks for additional mathematical results, and to discussing ways to best identify and design semantic components for individual disciplines of mathematics. The workshop organizers are presently preparing a report summarizing the workshop's conclusions and making recommendations for further progress towards a GDML. References See also Mathematical knowledge management Projects established in 2014 Digital library projects Mathematical projects Discipline-oriented digital libraries
https://en.wikipedia.org/wiki/Gabriel%20Ramos%20%28motorcyclist%29
Gabriel Ramos (born September 14, 1994) is a Venezuelan motorcycle racer. He was born in Maracay, Venezuela. Career statistics FIM CEV Moto3 Championship Races by year (key) (Races in bold indicate pole position; races in italics indicate fastest lap) Grand Prix motorcycle racing By season Races by year References External links Gabriel Ramos profile at MotoGP.com 1994 births Living people Sportspeople from Maracay Venezuelan motorcycle racers Moto3 World Championship riders 21st-century Venezuelan people
https://en.wikipedia.org/wiki/Chalermpol%20Polamai
Chalermpol Polamai (born 29 July 1982 in Pathumthani) is a Thai professional motorcycle racer. He races a Yamaha YZF-R6 in the MFJ All-Japan Road Race ST600 Championship. Career statistics Grand Prix motorcycle racing By season Races by year Supersport World Championship Races by year  * Season still in progress. External links 1982 births Living people Chalermpol Polamai Moto2 World Championship riders Chalermpol Polamai Chalermpol Polamai
https://en.wikipedia.org/wiki/Group%20actions%20in%20computational%20anatomy
Group actions are central to Riemannian geometry and defining orbits (control theory). The orbits of computational anatomy consist of anatomical shapes and medical images; the anatomical shapes are submanifolds of differential geometry consisting of points, curves, surfaces and subvolumes,. This generalized the ideas of the more familiar orbits of linear algebra which are linear vector spaces. Medical images are scalar and tensor images from medical imaging. The group actions are used to define models of human shape which accommodate variation. These orbits are deformable templates as originally formulated more abstractly in pattern theory. The orbit model of computational anatomy The central model of human anatomy in computational anatomy is a Groups and group action, a classic formulation from differential geometry. The orbit is called the space of shapes and forms. The space of shapes are denoted , with the group with law of composition ; the action of the group on shapes is denoted , where the action of the group is defined to satisfy The orbit of the template becomes the space of all shapes, . Several group actions in computational anatomy The central group in CA defined on volumes in are the diffeomorphism group which are mappings with 3-components , law of composition of functions , with inverse . Submanifolds: organs, subcortical structures, charts, and immersions For sub-manifolds , parametrized by a chart or immersion , the diffeomorphic action the flow of the position . Scalar images such as MRI, CT, PET Most popular are scalar images, , with action on the right via the inverse. . Oriented tangents on curves, eigenvectors of tensor matrices Many different imaging modalities are being used with various actions. For images such that is a three-dimensional vector then Tensor matrices Cao et al. examined actions for mapping MRI images measured via diffusion tensor imaging and represented via there principle eigenvector. For tensor fields a positively oriented orthonormal basis of , termed frames, vector cross product denoted then The Frénet frame of three orthonormal vectors, deforms as a tangent, deforms like a normal to the plane generated by , and . H is uniquely constrained by the basis being positive and orthonormal. For non-negative symmetric matrices, an action would become . For mapping MRI DTI images (tensors), then eigenvalues are preserved with the diffeomorphism rotating eigenvectors and preserves the eigenvalues. Given eigenelements , then the action becomes Orientation Distribution Function and High Angular Resolution HARDI Orientation distribution function (ODF) characterizes the angular profile of the diffusion probability density function of water molecules and can be reconstructed from High Angular Resolution Diffusion Imaging (HARDI). The ODF is a probability density function defined on a unit sphere, . In the field of information geometry, the space of ODF forms a Riemannian mani
https://en.wikipedia.org/wiki/Tetsuta%20Nagashima
is a Japanese motorcycle racer. He was the All Japan GP-Mono champion in 2011. Career statistics FIM CEV Moto2 European Championship Races by year (key) (Races in bold indicate pole position, races in italics indicate fastest lap) Grand Prix motorcycle racing By season By class Races by year (key) (Races in bold indicate pole position, races in italics indicate fastest lap) Superbike World Championship Races by year (key) (Races in bold indicate pole position) (Races in italics indicate fastest lap) References External links 1992 births Living people Japanese motorcycle racers Moto2 World Championship riders Sportspeople from Kanagawa Prefecture MotoGP World Championship riders LCR Team MotoGP riders Superbike World Championship riders
https://en.wikipedia.org/wiki/Michael%20Coletti%20%28motorcyclist%29
Michael Coletti (born 17 August 1995 in Italy) is an Italian motorcycle racer. Career statistics Grand Prix motorcycle racing By season Races by year References External links http://www.civ.tv/pilota/michael-coletti/ 1995 births Living people Italian motorcycle racers Moto3 World Championship riders
https://en.wikipedia.org/wiki/Bayesian%20estimation%20of%20templates%20in%20computational%20anatomy
Statistical shape analysis and statistical shape theory in computational anatomy (CA) is performed relative to templates, therefore it is a local theory of statistics on shape. Template estimation in computational anatomy from populations of observations is a fundamental operation ubiquitous to the discipline. Several methods for template estimation based on Bayesian probability and statistics in the random orbit model of CA have emerged for submanifolds and dense image volumes. The deformable template model of shapes and forms via diffeomorphic group actions Linear algebra is one of the central tools to modern engineering. Central to linear algebra is the notion of an orbit of vectors, with the matrices forming groups (matrices with inverses and identity) which act on the vectors. In linear algebra the equations describing the orbit elements the vectors are linear in the vectors being acted upon by the matrices. In computational anatomy the space of all shapes and forms is modeled as an orbit similar to the vectors in linear-algebra, however the groups do not act linear as the matrices do, and the shapes and forms are not additive. In computational anatomy addition is essentially replaced by the law of composition. The central group acting CA defined on volumes in are the diffeomorphisms which are mappings with 3-components , law of composition of functions , with inverse . Groups and group are familiar to the Engineering community with the universal popularization and standardization of linear algebra as a basic model A popular group action is on scalar images, , with action on the right via the inverse. For sub-manifolds , parametrized by a chart or immersion , the diffeomorphic action the flow of the position Several group actions in computational anatomy have been defined. Geodesic positioning via the Riemannian exponential For the study of deformable shape in CA, a more general diffeomorphism group has been the group of choice, which is the infinite dimensional analogue. The high-dimensional diffeomorphism groups used in computational anatomy are generated via smooth flows which satisfy the Lagrangian and Eulerian specification of the flow fields satisfying the ordinary differential equation: with the vector fields on termed the Eulerian velocity of the particles at position of the flow. The vector fields are functions in a function space, modelled as a smooth Hilbert space with the vector fields having 1-continuous derivative . For , with the inverse for the flow given by and the Jacobian matrix for flows in given as Flows were first introduced for large deformations in image matching; is the instantaneous velocity of particle at time . with the vector fields termed the Eulerian velocity of the particles at position of the flow. The modelling approach used in CA enforces a continuous differentiability condition on the vector fields by modelling the space of vector fields as a reproducing kernel Hilbert sp
https://en.wikipedia.org/wiki/Christophe%20Arciero
Christophe Arciero (born in France) is a French motorcycle racer. Career statistics Grand Prix motorcycle racing By season Races by year References External links Living people French motorcycle racers Moto3 World Championship riders Place of birth missing (living people) Year of birth missing (living people)
https://en.wikipedia.org/wiki/Luis%20V%C3%A1zquez%20Mart%C3%ADnez
Luis Vázquez Martínez is a Spanish applied mathematician. He is a professor of applied mathematics in the faculty of informatics of the Complutense University of Madrid. Vázquez was born on January 26, 1949, in Narayola, a town in the municipality of Camponaraya. He earned a licenciate in physical sciences from the Complutense University of Madrid in 1971, and a doctorate in physical sciences from the University of Zaragoza in 1975, under the supervision of Antonio Fernández-Rañada Menéndez de Luarca. After working as a Visiting Research Associate at Brown University, he returned to the Complutense University as an assistant professor in 1977. In 1995 the Shanghai University of Science and Technology gave him an honorary doctorate. Since 2005 has been a national corresponding member of the Spanish Royal Academy of Sciences. References Living people 1949 births 21st-century Spanish mathematicians University of Zaragoza alumni Academic staff of the Complutense University of Madrid 20th-century Spanish mathematicians Complutense University of Madrid alumni
https://en.wikipedia.org/wiki/List%20of%20Pakistan%20Super%20League%20records%20and%20statistics
This is a list of Pakistan Super League records of and statistics since the first ever season in 2016. The league, which is organised by the PCB, is a franchise Twenty20 cricket competition held previously in the UAE and now in Pakistan. Team records Result summary Source: ESPNcricinfo Last Update: 18 March 2023 Note: Tie&W and Tie&L indicates matches tied and then won or lost by "Super Over" The result percentage excludes no results and counts ties (irrespective of a tiebreaker) as half a win Highest totals Source: ESPNcricinfo Last Update: 18 March 2023 Lowest totals Source: ESPNcricinfo Last Update: 18 March 2023 Batting records Most runs Source: ESPNcricinfo Last Update: 18 March 2023 Highest individual score Source: ESPNcricinfo Last Update: 18 March 2023 Highest career average Source: ESPNcricinfo Last Update: 18 March 2023 Most 50+ Scores Source: ESPNcricinfo Last Update: 18 March 2023 Most Sixes Source: ESPNcricinfo Last Update: 18 March 2023 Most sixes in an innings Source: ESPNcricinfo Last Update: 18 March 2023 Highest strike rates Minimum of 125 balls faced Source: ESPNcricinfo Last Update: 18 March 2023 Highest strike rates in an inning Minimum of 125 balls faced Source: ESPNcricinfo Last Update: 18 March 2023 Most runs in a season Source: ESPNcricinfo Last Update: 18 March 2023 Fastest Centuries (100) Source: Inside Sport Last Update: 18 March 2023 Fastest Half Centuries (50) Source: Sports Info Last Update: 18 March 2023 Bowling records Most wickets Source: ESPNcricinfo Last Update: 18 March 2023 Best bowling figures in an innings Source: ESPNcricinfo Last Update: 18 March 2021 Best economy rates Minimum of 250 balls bowled Source: ESPNcricinfo Last Update: 18 March 2023 Best averages Minimum of 250 balls bowled Source: ESPNcricinfo Last Update: 18 March 2023 Best strike rates Minimum of 250 balls bowled Source: ESPNcricinfo Last Update: 18 March 2023 Most four-wickets (& over) hauls in an inning Minimum of 250 balls bowled Source: ESPNcricinfo Last Update: 18 March 2023 Best economy rate in an innings Source: ESPNcricinfo Last Update: 18 March 2023 Best strike rate in an innings Source: ESPNcricinfo Last Update: 18 March 2023 Most runs conceded in an innings Source: ESPNcricinfo Last Update: 18 March 2023 Most wickets in a season Source: ESPNcricinfo Last Update: 18 March 2023 Wicket-keeping records Most dismissals Source: ESPNcricinfo Last Updated: 18 March 2023 Most dismissals in a season Source: ESPNcricinfo Last Update: 18 March 2023 Most dismissals in an innings Source: ESPNcricinfo Last Update: 18 March 2023 Fielding records Most catches Source: ESPNcricinfo Last Update: 18 March 2023 Most catches in a season Source: ESPNcricinfo Last Update: 18 March 2023 Most catches in an innings Source: ESPNcricinfo Last Update: 18 March 2023 Partnership Records Highest Partnership by wicket Highest Partnership by Runs Awards Green cap and Hanif Mohammad awar
https://en.wikipedia.org/wiki/Romanian%20Statistical%20Yearbook
The Romanian Statistical Yearbook () is an annual publication of the National Institute of Statistics that presents data about the economic and social situation in Romania. The first yearbook appeared in 1902. The second, from 1912, came to over 800 pages, and presented data regarding the country's economic and social evolution over the previous decade. A third edition, covering the years 1915-1916, was begun in 1916 but did not appear until 1919, due to World War I. The next yearbook, covering 1922, came in 1923, and was followed by annual editions through 1940, a few of them describing two years. The 1931 edition was notable for incorporating data from the 1930 census and the 1931 election. For the first time, the 1931-1932, 1933 and 1934 editions included detailed data about the main exports from the 1929-1932 period, as well as statistics relating to the census of school-age children. The 1934 yearbook contained detailed information about agriculture, particularly in regard to the surface area devoted to fruit trees, the state of zootechnics and the number of tractors. The 1939-1940 yearbook was the final one before the communist regime resumed their publication after a 17-year gap. Annual statistical communiqués helped compensate for this absence in the 1945-1948 period. The next yearbook was published in 1957 and covered the years 1951-1955. Its authors noted that older data were adapted to current methodology, and that they were recalculated for the current national territory, which was smaller than that of Greater Romania. For the remainder of the regime's existence, which came to an end with the Romanian Revolution of 1989, yearbooks continued to appear annually. The editions of 1987, 1988 and 1989 were brochures of around 100 pages that indicated exponential growth in all areas of economic and social activity. The 1990 yearbook readopted the practice of including a number of indicators for the country's economic and social evolution. During the 1990s, the yearbook returned to a length of 700-1000 pages. Beginning in 1990, in the interests of transparency, relevance and credibility, the yearbook featured indicators previously hidden from public view. Examples include the use of economic resources, gross domestic product, national wealth, energy, housing and income, spending and consumption of the populace. The authors focused on aligning with international standards as well as including correct and comprehensive data for users of statistical information. The 2009 yearbook appeared in a special jubilee edition commemorating 150 years of official statistics in Romania. The yearbook includes the most recent data available in order to draw a picture of the economic situation and of the main economic indicators' evolution over the preceding few years. It is divided into twenty-three chapters: geography, meteorology and environment; population; workforce; income, spending and consumption; housing and public utilities; security and social as
https://en.wikipedia.org/wiki/David%20W.%20Henderson
David Wilson Henderson (February 23, 1939 – December 20, 2018) was a Professor Emeritus of Mathematics in the Department of Mathematics at Cornell University. His work ranges from the study of topology, algebraic geometry, history of mathematics and exploratory mathematics for teaching prospective mathematics teachers. His papers in the philosophy of mathematics place him with the intuitionist school of philosophy of mathematics. His practical geometry, which he put to work and discovered in his carpentry work, gives a perspective of geometry as the understanding of the infinite spaces through local properties. Euclidean geometry is seen in his work as extendable to the spherical and hyperbolic spaces starting with the study and reformulation of the 5th postulate. He was struck by an automobile in a pedestrian crosswalk on December 19, 2018, and died the next day from his injuries. References Bibliography Henderson, D. W. & Taimina, D. (2001). Crocheting the Hyperbolic Plane, Mathematical Intelligencer, vol.23, No. 2, 2001, pp. 17–28. Henderson, D. W. & Taimina, D. (2001). Essays in Mathematics? (Latvian), Skolotajs (Teacher journal), 4(28), 2001, Riga, pp. 27–31. Henderson, D. W. & Taimina, D. (2001). Geometry, The Hutchinson Encyclopedia of Mathematics. Henderson, D. W. & Taimina, D. (2004). Non-Euclidean Geometries, Encyclopædia Britannica. Henderson, D. W. & Taimina, D. (2005). Experiencing Geometry: Euclidean and non-Euclidean with History, Prentice Hall, Upper Saddle River, NJ. Taimina, D. & Henderson, W. (2005). How to Use History to Clarify Common Confusions in Geometry, MAA Notes volume No.68, p. 57-73. Taimina, D. & Henderson, D. W. (2005). Experiencing Geometry: Euclidean and Non-Euclidean with History, 3rd Edition.-Hall, Upper Saddle River, NJ. Taimina, D. & Henderson, D. W. (2020) " Experiencing Geometry: Euclidean and non-Euclidean with History", 4th Edition, open source Project Euclid https://projecteuclid.org/euclid.bia/1598805325 Taimina, D. & Henderson, D. W. (2006). Experiencing Meanings in Geometry, in Nathalie Sinclair, David Pimm, William Higginson eds, Mathematics and the Aesthetic, Springer, pp. 58–83. External links Personal webpage Papers, articles and talks David W. Henderson and Daina Taimina, Experiencing Meanings of Geometry, Chapter 3 in Aesthetics and Mathematics, (edited by David Pimm and M. Sinclair), Springer-Verlag. 2006, p.58-83.pdf. In Search of Meaning (Biography of David W. Henderson) Cornell University faculty 21st-century American mathematicians 2018 deaths Place of birth missing 1939 births 20th-century American mathematicians
https://en.wikipedia.org/wiki/Algebroid%20function
In mathematics, an algebroid function is a solution of an algebraic equation whose coefficients are analytic functions. So y(z) is an algebroid function if it satisfies where are analytic. If this equation is irreducible then the function is d-valued, and can be defined on a Riemann surface having d sheets. Analytic functions Equations
https://en.wikipedia.org/wiki/Koon%20Woon
Koon Woon is a Chinese-American poet, editor, student of mathematics, philosophy, and modal logic, and mentor based in Chinatown, Seattle, Washington. His poetry is internationally-anthologized. Early life Woon was born into a large family in a small village near Guangzhou, China, in 1949. Then, in 1960, he with his family immigrated to the United States. Education During the late 1960s to early 1970s, Woon attended the University of Washington, enrolled in courses in the Department of Mathematics and the Department of Philosophy. He then transferred to the University of Oregon, where John Wisdom was influential. After recovering from mental illness lasting two decades, he went to Antioch University Seattle and got a bachelor's degree. Then, Woon attended Fort Hays State University and got a master's degree. Literary work Woon has published two books of poetry, and self-published two memoirs. He edits Chrysanthemum and Five Willows Literary Review. Awards He is winner of a Pen Oak / Josephine Miles Award and an American Book Award. Publications Woon, K. (1998). The Truth in Rented Rooms. Los Angeles: Kaya Press. Woon, K. (2013). Water Chasing Water. Los Angeles: Kaya Press. Woon, K. (2016). Paper-son Poet: When rails were young.... Seattle: Goldfish Press. Woon, K. (2018). Rice Bowls: Previously Uncollected Words of Koon Woon. Seattle: Goldfish Press. References 1949 births Living people American male poets
https://en.wikipedia.org/wiki/Henry%20Hartness
Henry Hartness was an English professional football forward and half back who scored on his only appearance in the Scottish League for Heart of Midlothian. Career statistics References Year of birth missing Year of death missing Footballers from Newcastle upon Tyne English men's footballers Men's association football forwards Sunderland A.F.C. players Heart of Midlothian F.C. players Scotswood F.C. players Croydon Common F.C. players Scottish Football League players Southern Football League players
https://en.wikipedia.org/wiki/Apache%20Calcite
Apache Calcite is an open source framework for building databases and data management systems. It includes a SQL parser, an API for building expressions in relational algebra, and a query planning engine. As a framework, Calcite does not store its own data or metadata, but instead allows external data and metadata to be accessed by means of plug-ins. Several other Apache projects use Calcite. Hive uses Calcite for cost-based query optimization; Drill and Kylin use Calcite for SQL parsing and optimization; Samza and Storm use Calcite for streaming SQL. , Apex, Phoenix and Flink have projects under development that use Calcite. References Relational database management systems Calcite Software using the Apache license Free software programmed in Java (programming language)
https://en.wikipedia.org/wiki/Sixto%20R%C3%ADos
Sixto Ríos García (Pelahustán, Toledo, January 4, 1913 – Madrid, July 8, 2008), was a Spanish mathematician, known as the father of Spanish statistics. Biography The son of José María Ríos Moreiro and Maria Cristina Garcia Martin, he was taught by his parents, who were teachers. When the family moved to Madrid, he attended St. Maurice School and the IES San Isidro, being always the valedictorian. In 1932 he graduated with a degree in Mathematics from the Complutense University of Madrid, with the best marks and getting the award "Premio Extraodinario", later he obtained a Ph.D. in Mathematics. He was a student of Julio Rey Pastor and the Laboratory and Seminar of Mathematics (LSM). He recalled that Esteban Terradas influenced his entry to statistics. He became professor of mathematical analysis at the University of Valencia, as well as in Valladolid and Madrid. He also became Doctor Engineer Geographer, and professor at the Technical School of Aeronautical Engineering and the Faculty of Economics. He held the positions of Director of the School of Statistics at Complutense University of Madrid, Director of Consejo Superior de Investigaciones Científicas (CSIC) (Superior Council for Scientific Research), Director of the Department of Statistics at the Faculty of Mathematics at the Complutense University of Madrid, and president of the Spanish Statistics and Operations Research Society. He was a correspondent of the National Academy of Sciences of Argentina. Rios published a Spanish language description of the Von Neumann–Morgenstern utility theorem. He was a member of the editorial board of Statistical Abstracts and full member of the International Statistical Institute and the Institute of Mathematical Statistics. He conducted research with or directed theses of 16 professors, and some directors in statistical bureaus of Latin America. He conducted applied research for the Spanish industry and formed the School of Operations Research. He lectured at universities around the world and presented papers at international conferences and published in international journals, and helped to set up and direct research centers such as the School of Statistics at the University of Madrid, the Institute of Operations Research and Statistics at the Spanish National Research Council (CSIC) and its journal Works on Operations Research and Statistics, the School of Statistics at the Central University of Venezuela and the Department of Statistics and Operations Research at the Faculty of Sciences, with international courses sponsored by the Organization of American States (OAS) and UNESCO. Rios Garcia married Maria Jesus Insua Negrao and they had a son, Sixto Rios Ensua, who followed his father's profession. Publications He is the author of over 200 research works, publications and monographs, on mathematical analysis, probability and statistics and operations research, among them: Statistical Methods, (Ediciones del Castillo, SA, 1967), Special Mat
https://en.wikipedia.org/wiki/Abdullah%20Al-Oaisher
Abdullah Al-Oaisher (; born May 13, 1991) is a Saudi football player who plays for Al-Ettifaq as a goalkeeper. Career statistics Club Honours Club Al-Fateh Saudi Professional League: 2012–13 Saudi Super Cup: 2013 Al-Nassr Saudi Professional League: 2018–19 References External links 1991 births Living people Sportspeople from Al-Hasa Men's association football goalkeepers Saudi Arabian men's footballers Saudi Arabia men's international footballers Al Fateh SC players Al Nassr FC players Ohod Club players Al Shabab FC (Riyadh) players Al Wehda FC players Al-Ettifaq FC players Saudi Pro League players Saudi Arabian Shia Muslims
https://en.wikipedia.org/wiki/Bader%20Al-Nakhli
Bader Al-Nakhli (; born 20 May 1988) is a football (soccer) player who plays as a defender. Career statistics Honours Al Fateh Saudi Premier League: 2012-13 Saudi Super Cup: 2013 Al-Ittihad Saudi Crown Prince Cup: 2016–17 King Cup: 2018 Al-Khaleej First Division: 2021–22 References External links 1988 births Living people Saudi Arabian men's footballers Saudi Arabia men's international footballers Men's association football defenders Al Qadsiah FC players Al Nassr FC players Al Fateh SC players Al-Ittihad Club (Jeddah) players Al Batin FC players Al-Adalah FC players Al-Khaleej FC players Al-Rawdhah Club players Place of birth missing (living people) Saudi Pro League players Saudi First Division League players Saudi Second Division players Saudi Arabian Shia Muslims
https://en.wikipedia.org/wiki/Mohammed%20Al-Fuhaid
Mohammed Al-Fuhaid (; born January 8, 1990) is a Saudi professional footballer who plays as a midfielder for Al-Fateh. Career statistics Club Honours Al-Fateh SC Saudi Professional League: 2012–13 Saudi Super Cup: 2013 References External links 1990 births Living people Saudi Arabian men's footballers Sportspeople from Al-Hasa Men's association football midfielders Al Fateh SC players Saudi Pro League players Saudi Arabian Shia Muslims
https://en.wikipedia.org/wiki/Jan%20de%20Boer%20%28physicist%29
Jan de Boer (born 29 June 1967, in Doniawerstal) is a Dutch theoretical physicist specializing in string theory. After a double master's degree in mathematics and physics at the University of Groningen, De Boer obtained his PhD from Utrecht University in 1993 with the dissertation Extended conformal symmetry in non-critical string theory. He continued his studies at Stony Brook University and University of California, Berkeley. Since 2000 he has been professor of theoretical physics at the University of Amsterdam. From 1946 to 1981 an unrelated Jan de Boer (1911–2010) was professor of theoretical physics at the same department of the University of Amsterdam. His specialty was thermodynamics. Awards and fellowships 1984, First place and gold medal, 15th International Physics Olympiad 1984, Silver medal, 28th International Mathematics Olympiad 1995–1996, James Simons Fellowship, Stony Brook University 1996–1998, Miller Fellowship, Berkeley References 1967 births Living people Dutch string theorists Academic staff of the University of Amsterdam University of Groningen alumni Utrecht University alumni People from Skarsterlân
https://en.wikipedia.org/wiki/Calvin%20Zippin
Calvin Zippin (born July 17, 1926) is a cancer epidemiologist and biostatistician, and Professor Emeritus in the Department of Epidemiology and Biostatistics at the University of California School of Medicine in San Francisco (UCSF). He is a Fellow of the American Statistical Association, the American College of Epidemiology and the Royal Statistical Society of Great Britain. His doctoral thesis was the basis for the Zippin Estimator, a procedure for estimating wildlife populations using data from trapping experiments. He was a principal investigator in the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute (NCI) which assesses the magnitude and nature of the cancer problem in the United States. In 1961, he created training programs for cancer registry personnel, which he conducted nationally and internationally. He carried out research on the epidemiology and rules for staging of various cancers. He received a Lifetime Achievement and Leadership Award from the NCI in 2003. Early life and education Zippin was born on July 17, 1926, in Albany, New York, United States, the son of Samuel and Jennie (Perkel) Zippin. He received an AB degree magna cum laude in biology and mathematics, from the State University of New York at Albany in 1947. He was a research assistant at the Sterling-Winthrop Research Institute in Rensselaer, New York beginning in 1947. He was awarded a Doctor of Science degree in Biostatistics by the Johns Hopkins School of Hygiene and Public Health in Baltimore, Maryland in 1953. His thesis advisor was William G. Cochran a statistician known for Cochran’s theorem, Cochran-Mantel-Haenzel Test and author of standard biostatistical texts: “Experimental Designs” and “Sampling Techniques”. Zippin’s doctoral thesis, An Evaluation of the Removal Method of Estimating Animal Populations became the basis for the Zippin Estimator, and has been used for estimating populations of a wide variety of animal species. It is considered among the easiest and most accurate methods for estimating animal populations in the wild. Career At the Sterling-Winthrop Research Institute, Zippin performed various laboratory and statistical duties under Lloyd C. Miller, Ph.D., later Director of Revision (1950-1970) of the United States Pharmacopoeia. Dr. Miller encouraged Zippin to pursue a career in statistics which led to his graduate work at Johns Hopkins where he also held an appointment as a Research Assistant in Biostatistics from 1950 to 1953. Following graduate school, Zippin became an instructor in biostatistics (1953-1955) at the School of Public Health, University of California, Berkeley. He moved to the School of Medicine at the University of California, San Francisco where, at the level of assistant professor, he held appointments in the Cancer Research Institute and the Department of Preventive Medicine. With further advancement, in 1967 he became Professor of Epidemiology in the Cancer Research Institute, D
https://en.wikipedia.org/wiki/Yuudai%20Kamei
is a Japanese motorcycle racer. He currently races in the All Japan Road Race JSB1000 Championship aboard a CBR1000RR-R. Career statistics Grand Prix motorcycle racing By season Races by year (key) References External links Japanese motorcycle racers Living people 1996 births Moto3 World Championship riders
https://en.wikipedia.org/wiki/Sam%20Clarke%20%28motorcyclist%29
Sam Clarke (born 6 March 1996) is an Australian motorcycle racer. Career statistics Grand Prix motorcycle racing By season Races by year (key) References External links Profile on MotoGP.com Australian motorcycle racers 1996 births Living people Moto3 World Championship riders
https://en.wikipedia.org/wiki/1935%20S%C3%A3o%20Paulo%20FC%20season
The 1935 football season was São Paulo's 6th season since the club's founding in 1930. Statistics Scorers Overall {|class="wikitable" |- |Games played || 6 (Friendly match) |- |Games won || 4 (Friendly match) |- |Games drawn || 2 (Friendly match) |- |Games lost || 0 (Friendly match) |- |Goals scored || 14 |- |Goals conceded || 7 |- |Goal difference || +7 |- |Best result || 4–1 (A) v Portuguesa - Friendly match |- |Worst result || |- |Most appearances || |- |Top scorer || Luizinho (5) |- Friendlies External links official website Association football clubs 1935 season 1935 1935 in Brazilian football
https://en.wikipedia.org/wiki/1936%20S%C3%A3o%20Paulo%20FC%20season
The 1936 football season was São Paulo's 7th season since the club's founding in 1930. Statistics Scorers Overall {|class="wikitable" |- |Games played || 34 (21 Campeonato Paulista, 13 Friendly match) |- |Games won || 11 (7 Campeonato Paulista, 4 Friendly match) |- |Games drawn || 7 (2 Campeonato Paulista, 5 Friendly match) |- |Games lost || 16 (12 Campeonato Paulista, 4 Friendly match) |- |Goals scored || 44 |- |Goals conceded || 50 |- |Goal difference || -6 |- |Best result || 6–0 (H) v Paulista - Campeonato Paulista - 1937.01.03 |- |Worst result || 1–5 (A) v Portuguesa Santista - Campeonato Paulista - 1936.08.16 |- |Most appearances || |- |Top scorer || Chemp (6) |- Friendlies Official competitions Campeonato Paulista Record External links official website Association football clubs 1936 season 1936 1936 in Brazilian football
https://en.wikipedia.org/wiki/1937%20S%C3%A3o%20Paulo%20FC%20season
The 1937 football season was São Paulo's 8th season since the club's founding in 1930. Statistics Scorers Overall {|class="wikitable" |- |Games played || 31 (9 Campeonato Paulista, 22 Friendly match) |- |Games won || 12 (4 Campeonato Paulista, 8 Friendly match) |- |Games drawn || 1 (0 Campeonato Paulista, 1 Friendly match) |- |Games lost || 18 (5 Campeonato Paulista, 13 Friendly match) |- |Goals scored || 51 |- |Goals conceded || 51 |- |Goal difference || 0 |- |Best result || 7–0 (A) v Ypiranga-BA - Campeonato Paulista - 1937.11.18 |- |Worst result || 1–4 (A) v Galícia - Friendly match - 1937.11.211–4 (A) v Santos - Campeonato Paulista - 1937.09.12 |- |Most appearances || |- |Top scorer || Milani (13) |- Friendlies Official competitions Campeonato Paulista External links official website Association football clubs 1937 season 1937 1937 in Brazilian football
https://en.wikipedia.org/wiki/Delta-convergence
In mathematics, Delta-convergence, or Δ-convergence, is a mode of convergence in metric spaces, weaker than the usual metric convergence, and similar to (but distinct from) the weak convergence in Banach spaces. In Hilbert space, Delta-convergence and weak convergence coincide. For a general class of spaces, similarly to weak convergence, every bounded sequence has a Delta-convergent subsequence. Delta convergence was first introduced by Teck-Cheong Lim, and, soon after, under the name of almost convergence, by Tadeusz Kuczumow. Definition A sequence in a metric space is said to be Δ-convergent to if for every , . Characterization in Banach spaces If is a uniformly convex and uniformly smooth Banach space, with the duality mapping given by , , then a sequence is Delta-convergent to if and only if converges to zero weakly in the dual space (see ). In particular, Delta-convergence and weak convergence coincide if is a Hilbert space. Opial property Coincidence of weak convergence and Delta-convergence is equivalent, for uniformly convex Banach spaces, to the well-known Opial property Delta-compactness theorem The Delta-compactness theorem of T. C. Lim states that if is an asymptotically complete metric space, then every bounded sequence in has a Delta-convergent subsequence. The Delta-compactness theorem is similar to the Banach–Alaoglu theorem for weak convergence but, unlike the Banach-Alaoglu theorem (in the non-separable case) its proof does not depend on the Axiom of Choice. Asymptotic center and asymptotic completeness An asymptotic center of a sequence , if it exists, is a limit of the Chebyshev centers for truncated sequences . A metric space is called asymptotically complete, if any bounded sequence in it has an asymptotic center. Uniform convexity as sufficient condition of asymptotic completeness Condition of asymptotic completeness in the Delta-compactness theorem is satisfied by uniformly convex Banach spaces, and more generally, by uniformly rotund metric spaces as defined by J. Staples. Further reading William Kirk, Naseer Shahzad, Fixed point theory in distance spaces. Springer, Cham, 2014. xii+173 pp. G. Devillanova, S. Solimini, C. Tintarev, On weak convergence in metric spaces, Nonlinear Analysis and Optimization (B. S. Mordukhovich, S. Reich, A. J. Zaslavski, Editors), 43–64, Contemporary Mathematics 659, AMS, Providence, RI, 2016. References Theorems in functional analysis Nonlinear functional analysis Convergence (mathematics)
https://en.wikipedia.org/wiki/Cocompact%20embedding
In mathematics, cocompact embeddings are embeddings of normed vector spaces possessing a certain property similar to but weaker than compactness. Cocompactness has been in use in mathematical analysis since the 1980s, without being referred to by any name (Lemma 6),(Lemma 2.5),(Theorem 1), or by ad-hoc monikers such as vanishing lemma or inverse embedding. Cocompactness property allows to verify convergence of sequences, based on translational or scaling invariance in the problem, and is usually considered in the context of Sobolev spaces. The term cocompact embedding is inspired by the notion of cocompact topological space. Definitions Let be a group of isometries on a normed vector space . One says that a sequence converges to -weakly, if for every sequence , the sequence is weakly convergent to zero. A continuous embedding of two normed vector spaces, is called cocompact relative to a group of isometries on if every -weakly convergent sequence is convergent in . An elementary example: cocompactness for Embedding of the space into itself is cocompact relative to the group of shifts . Indeed, if , , is a sequence -weakly convergent to zero, then for any choice of . In particular one may choose such that , which implies that in . Some known embeddings that are cocompact but not compact , , relative to the action of translations on : . , , , relative to the actions of translations on . , , relative to the product group of actions of dilations and translations on . Embeddings of Sobolev space in the Moser–Trudinger case into the corresponding Orlicz space. Embeddings of Besov and Triebel–Lizorkin spaces. Embeddings of Strichartz spaces. References Compactness (mathematics) Convergence (mathematics) Functional analysis General topology Nonlinear functional analysis Normed spaces
https://en.wikipedia.org/wiki/Ilya%20Vorotnikov%20%28footballer%2C%20born%201986%29
Ilya Vorotnikov (born 1 February 1986) is a Kazakh footballer who plays as a centre back for FC Caspiy and Kazakhstan. Career statistics Club International Honours Alma-Ata Kazakhstan Cup (1): 2006 Atyrau Kazakhstan Cup (1): 2009 References External links 1986 births Living people Kazakhstani men's footballers Kazakhstan men's international footballers Kazakhstan Premier League players FC Irtysh Pavlodar players FC Atyrau players FC Kairat players FC Akzhayik players FC Taraz players FC Caspiy players Men's association football defenders Footballers from Almaty
https://en.wikipedia.org/wiki/Park%20Jeong-su
Park Jeong-su () is a South Korean footballer who plays as a defender. His most recent club was Seongnam FC. Club statistics Updated to end of 2021 season. References External links Profile at Kashiwa Reysol Profile at Yokohama F. Marinos 1994 births Living people South Korean men's footballers J1 League players J2 League players Yokohama F. Marinos players Kashiwa Reysol players Sagan Tosu players Seongnam FC players Men's association football defenders
https://en.wikipedia.org/wiki/Mary%20Fern%C3%A1ndez
Mary Fernández is an American computer scientist and activist for women and minorities in science, technology, engineering, and mathematics (STEM). She is the president of MentorNet, an organization that helps mentors and students develop mentoring relationships. Education Fernández enrolled in the engineering department at Brown University in the early 1980s. After taking an introductory computer science course taught by Andries van Dam, she changed her major to computer science. She earned her bachelor's and master's degrees from Brown, and her Ph.D. from Princeton University. Career Fernández joined AT&T as a senior technical staff member in 1995. She worked there for seventeen years, ending her career as the Assistant Vice President of Information and Software Systems Research. During her time there, she worked on technology to handle semi-structured XML, particularly the XQuery language. In 1998, Fernández joined MentorNet, an organization that matches mentors with STEM students and helps them develop mentoring relationships. She joined the board of directors of the organization in 2009, becoming the board chair in 2011. In 2013 she became CEO, and she transitioned to president in 2014 when MentorNet became a division of the Great Minds in STEM non-profit. Fernández served as the secretary and treasurer of ACM SIGMOD, and was the associate editor of ACM Transactions on Database Systems. She serves on the board of the Computing Research Association. In 2011, Fernández was awarded the Great Minds in STEM Technical Achievement in Industry Award. References American women computer scientists American computer scientists Brown University alumni Princeton University alumni AT&T people Scientists from New York (state) Place of birth missing (living people) Year of birth missing (living people) Living people 20th-century American scientists 21st-century American scientists 20th-century American women scientists 21st-century American women scientists
https://en.wikipedia.org/wiki/Mathematics%20and%20the%20Search%20for%20Knowledge
Mathematics and the Search for Knowledge is a 1985 book by Morris Kline about the role of mathematics when understanding of the physical world. It is preceded by Kline's work, Mathematics: The Loss of Certainty. In the book, Kline gives an outline of the development of physics, from ancient Greek astronomy to modern physics. He explains that modern physics (consisting of theories such as electromagnetism, relativity and quantum mechanics) differs from previous theories such as Newtonian mechanics in being purely mathematical models without any intuitive ways of being visualized. Further, unlike sensory perception, modern theories have provided predictions that have been verified and are immune to sensory illusions. Thus, Kline argues that it is mathematics that provides a true understanding of physical reality, rather than our senses. Bibliography Notes Books about mathematics 1985 non-fiction books
https://en.wikipedia.org/wiki/Qualitative%20theory%20of%20differential%20equations
In mathematics, the qualitative theory of differential equations studies the behavior of differential equations by means other than finding their solutions. It originated from the works of Henri Poincaré and Aleksandr Lyapunov. There are relatively few differential equations that can be solved explicitly, but using tools from analysis and topology, one can "solve" them in the qualitative sense, obtaining information about their properties. References Further reading Viktor Vladimirovich Nemytskii, Vyacheslav Stepanov, Qualitative theory of differential equations, Princeton University Press, Princeton, 1960. Original references Henri Poincaré, "Mémoire sur les courbes définies par une équation différentielle", Journal de Mathématiques Pures et Appliquées (1881, in French) (it was translated from the original Russian into French and then into this English version, the original is from the year 1892) Differential equations
https://en.wikipedia.org/wiki/National%20Institute%20of%20Statistics%20%28Mozambique%29
The National Institute of Statistics (Portuguese: Instituto Nacional de Estatística, INE) is an agency belonging to the Government of Mozambique and the principal agency for the collection of statistics in the country. It was created under Presidential Decree nº 9/96, of August 28, 1996. References Government agencies established in 1996 Government of Mozambique Mozambique
https://en.wikipedia.org/wiki/Milo%C5%A1%20Rus
Miloš Rus (born April 4, 1962) is a former Slovenian football goalkeeper and manager. Managerial statistics References External links Soccerway profile 1962 births Living people Yugoslav men's footballers Men's association football goalkeepers NK Olimpija Ljubljana (1945–2005) players NK Krka players NK IB 1975 Ljubljana managers NK Zagreb managers NK Celje managers J2 League managers Vegalta Sendai managers Yokohama FC managers Expatriate men's footballers in Austria Slovenian football managers Expatriate football managers in Croatia Slovenian expatriate sportspeople in Croatia Expatriate football managers in Japan Slovenian expatriate sportspeople in Japan Slovenian expatriate football managers Slovenian PrvaLiga managers
https://en.wikipedia.org/wiki/Hadamard%27s%20gamma%20function
In mathematics, Hadamard's gamma function, named after Jacques Hadamard, is an extension of the factorial function, different from the classical gamma function (it is an instance of a pseudogamma function.) This function, with its argument shifted down by 1, interpolates the factorial and extends it to real and complex numbers in a different way than Euler's gamma function. It is defined as: where denotes the classical gamma function. If is a positive integer, then: Properties Unlike the classical gamma function, Hadamard's gamma function is an entire function, i.e. it has no poles in its domain. It satisfies the functional equation with the understanding that is taken to be for positive integer values of . Representations Hadamard's gamma can also be expressed as where is the Lerch zeta function, and as where denotes the digamma function. References Gamma and related functions Analytic functions Special functions
https://en.wikipedia.org/wiki/Jostein%20Gundersen
Jostein Maurstad Gundersen (born 4 April 1996) is a Norwegian footballer who plays as a defender for Tromsø in the Tippeligaen. Career statistics References External links 1996 births Living people Norwegian men's footballers Tromsø IL players Eliteserien players Norwegian First Division players Men's association football defenders Footballers from Bergen
https://en.wikipedia.org/wiki/Doctrine%20of%20chances%20%28disambiguation%29
The term doctrine of chances is any of several things: The doctrine of chances, a rule of evidence in law The Doctrine of Chances, the first textbook on the mathematical theory of probability, published in 1718; The theory of probability, in 18th-century English, occurring in an influential posthumously published paper of the Reverend Thomas Bayes, "An Essay towards solving a Problem in the Doctrine of Chances.
https://en.wikipedia.org/wiki/Anders%20Nedreb%C3%B8
Anders Emil Nedrebø (born 19 August 1988) is a retired Norwegian footballer who played as a defender. His last club was Vålerenga which he left ahead of the 2017 season. Career statistics References 1988 births Living people Footballers from Bærum Bærum SK players Asker Fotball players Hamarkameratene players Vålerenga Fotball players Eliteserien players Norwegian First Division players Men's association football defenders Norwegian men's footballers
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20Joseph%20Liouville
Several concepts from mathematics and physics are named after the French mathematician Joseph Liouville. Euler–Liouville equation Liouville–Arnold theorem Liouville–Bratu–Gelfand equation Liouville–Green method Liouville's equation Liouville's formula Liouville function Liouville dynamical system Liouville field theory Liouville gravity Liouville integrability Liouville measure Liouville number Liouville one-form Liouville operator Liouville space Liouville surface Liouville–Neumann series Liouvillian function Riemann–Liouville integral Quantum Liouville equation Sturm–Liouville theory Liouville's theorem Liouville's theorem (complex analysis) Liouville's theorem (harmonic functions) Liouville's theorem (conformal mappings) Liouville's theorem (differential algebra) Liouville's theorem (diophantine approximation) Liouville's theorem (Hamiltonian) Lioville, Joseph
https://en.wikipedia.org/wiki/Complex%20random%20variable
In probability theory and statistics, complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable may take are complex numbers. Complex random variables can always be considered as pairs of real random variables: their real and imaginary parts. Therefore, the distribution of one complex random variable may be interpreted as the joint distribution of two real random variables. Some concepts of real random variables have a straightforward generalization to complex random variables—e.g., the definition of the mean of a complex random variable. Other concepts are unique to complex random variables. Applications of complex random variables are found in digital signal processing, quadrature amplitude modulation and information theory. Definition A complex random variable on the probability space is a function such that both its real part and its imaginary part are real random variables on . Examples Simple example Consider a random variable that may take only the three complex values with probabilities as specified in the table. This is a simple example of a complex random variable. The expectation of this random variable may be simply calculated: Uniform distribution Another example of a complex random variable is the uniform distribution over the filled unit circle, i.e. the set . This random variable is an example of a complex random variable for which the probability density function is defined. The density function is shown as the yellow disk and dark blue base in the following figure. Complex normal distribution Complex Gaussian random variables are often encountered in applications. They are a straightforward generalization of real Gaussian random variables. The following plot shows an example of the distribution of such a variable. Cumulative distribution function The generalization of the cumulative distribution function from real to complex random variables is not obvious because expressions of the form make no sense. However expressions of the form make sense. Therefore, we define the cumulative distribution of a complex random variables via the joint distribution of their real and imaginary parts: Probability density function The probability density function of a complex random variable is defined as , i.e. the value of the density function at a point is defined to be equal to the value of the joint density of the real and imaginary parts of the random variable evaluated at the point . An equivalent definition is given by where and . As in the real case the density function may not exist. Expectation The expectation of a complex random variable is defined based on the definition of the expectation of a real random variable: Note that the expectation of a complex random variable does not exist if or does not exist. If the complex random variable has a probability density function , then the expectation is given by . I
https://en.wikipedia.org/wiki/Effect%20algebra
Effect algebras are partial algebras which abstract the (partial) algebraic properties of events that can be observed in quantum mechanics. Structures equivalent to effect algebras were introduced by three different research groups in theoretical physics or mathematics in the late 1980s and early 1990s. Since then, their mathematical properties and physical as well as computational significance have been studied by researchers in theoretical physics, mathematics and computer science. History In 1989, Giuntini and Greuling introduced structures for studying unsharp properties, meaning those quantum events whose probability of occurring is strictly between zero and one (and is thus not an either-or event). In 1994, Chovanec and Kôpka introduced D-posets as posets with a partially defined difference operation. In the same year, the paper by Bennet and Foulis Effect algebras and unsharp quantum logics was published. While it was this last paper that first used the term effect algebra, it was shown that all three structures are equivalent. The proof of isomorphism of categories of D-posets and effect algebras is given for instance by Dvurecenskij and Pulmannova. Motivation The operational approach to quantum mechanics takes the set of observable (experimental) outcomes as the constitutive notion of a physical system. That is, a physical system is seen as a collection of events which may occur and thus have a measurable effect on the reality. Such events are called effects. This perspective already imposes some constrains on the mathematical structure describing the system: we need to be able to associate a probability to each effect. In the Hilbert space formalism, effects correspond to positive semidefinite self-adjoint operators which lie below the identity operator in the following partial order: if and only if is positive semidefinite. The condition of being positive semidefinite guarantees that expectation values are non-negative, and being below the identity operator yields probabilities. Now we can define two operations on the Hilbert space effects: and if , where denotes the identity operator. Note that is positive semidefinite and below since is, thus it is always defined. One can think of as the negation of . While is always positive semidefinite, it is not defined for all pairs: we have to restrict the domain of definition for those pairs of effects whose sum stays below the identity. Such pairs are called orthogonal; orthogonality reflects simultaneous measurability of observables. Definition An effect algebra is a partial algebra consisting of a set , constants and in , a total unary operation , a binary relation , and a binary operation , such that the following hold for all : commutativity: if , then and , associativity: if and , then and as well as orthosupplementation: and , and if such that , then , zero-one law: if , then . The unary operation is called orthosupplementation and the orthos
https://en.wikipedia.org/wiki/So%20Hirao
is a Japanese football player. He currently plays for J2 League side Thespakusatsu Gunma. Career statistics Last update: 2 December 2018. Reserves performance References External links Profile at Avispa Fukuoka 1996 births Living people Association football people from Osaka Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Gamba Osaka players Gamba Osaka U-23 players Avispa Fukuoka players FC Machida Zelvia players J.League U-22 Selection players Thespakusatsu Gunma players People from Tondabayashi, Osaka Men's association football forwards Men's association football fullbacks
https://en.wikipedia.org/wiki/Naif%20Hazazi%20%28footballer%2C%20born%201992%29
Naif Hazazi (, born 30 September 1992) is a Saudi Arabian football player who currently plays as a midfielder for Al-Raed. Career statistics International Statistics accurate as of match played 10 August 2019. Honours Al-Qadsiah MS League/First Division: 2014–15, runner-up 2019–20 References External links Living people 1992 births People from Khobar Men's association football midfielders Saudi Arabian men's footballers Saudi Arabia men's international footballers Al Qadsiah FC players Al Raed FC players Saudi First Division League players Saudi Pro League players
https://en.wikipedia.org/wiki/Star%20quad%20cable
Star-quad cable is a four-conductor cable that has a special quadrupole geometry which provides magnetic immunity when used in a balanced line. Four conductors are used to carry the two legs of the balanced line. All four conductors must be an equal distance from a common point (usually the center of a cable). The four conductors are arranged in a four-pointed star (forming a square). Opposite points of the star are connected together at each end of the cable to form each leg of the balanced circuit. Star quad cables often use filler elements to hold the conductor centers in a symmetric four-point arrangement about the cable axis. All points of the star must lie at equal distances from the center of the star. When opposite points are connected together they act as if they are one conductor located at the center of the star. This configuration places the geometric center of each of the two legs of the balanced circuit in the center of the star. To a magnetic field, both legs of the balanced circuit appear to be in the exact center of the star. This means that both legs of the balanced circuit will receive exactly the same interference from the magnetic field and a common-mode interference signal will be produced. This common-mode interference signal will be rejected by the balanced receiver. The magnetic immunity of star quad cable is a function of the accuracy of the star-quad geometry, the accuracy of the impedance balancing, and the common-mode rejection ratio of the balanced receiver. Star-quad cable typically provides a 10 dB to 30 dB reduction in magnetically-induced interference. Advantages When star-quad cable is used for a single balanced line, such as professional audio applications and two-wire telephony, two non-adjacent conductors are terminated together at both ends of the cable, and the other two conductors are also terminated together. Interference picked up by the cable arrives as a virtually perfect common mode signal, which is easily removed by a coupling transformer or differential amplifier. The combined benefits of twisting, differential signalling, and quadrupole pattern give outstanding noise immunity, especially advantageous for low-signal-level applications such as long microphone cables, even when installed very close to a power cable. It is particularly beneficial compared to twisted pair when AC magnetic field sources are in close proximity, for example a stage cable that can lie against an inline power transformer. Disadvantages The disadvantage is that star quad, in combining two conductors, typically has more capacitance than similar two-conductor twisted and shielded audio cable. High capacitance causes an increasing loss of high frequencies as distance increases. The high-frequency loss is due to the RC filter formed by the output impedance of the cable driver and the capacitance of the cable. In some cases an increase in distortion can occur in the cable driver if it has difficulty driving the higher cable ca
https://en.wikipedia.org/wiki/Matrix%20field
In abstract algebra, a matrix field is a field with matrices as elements. In field theory there are two types of fields: finite fields and infinite fields. There are several examples of matrix fields of different characteristic and cardinality. There is a finite matrix field of cardinality p for each prime p. One can find several finite matrix fields of characteristic p for any given prime number p. In general, corresponding to each finite field there is a matrix field. Since any two finite fields of equal cardinality are isomorphic, the elements of a finite field can be represented by matrices. Contrary to the general case for matrix multiplication, multiplication is commutative in a matrix field (if the usual operations are used). Since addition and multiplication of matrices have all needed properties for field operations except for commutativity of multiplication and existence of multiplicative inverses, one way to verify if a set of matrices is a field with the usual operations of matrix sum and multiplication is to check whether the set is closed under addition, subtraction and multiplication; the neutral element for matrix addition (that is, the zero matrix) is included; multiplication is commutative; the set contains a multiplicative identity (note that this does not have to be the identity matrix); and each matrix that is not the zero matrix has a multiplicative inverse. Examples 1. Take the set of all n × n matrices of the form with that is, matrices filled with zeroes except for the first row, which is filled with the same real constant . These matrices are commutative for multiplication: . The multiplicative identity is . The multiplicative inverse of a matrix with is given by It is easy to see that this matrix field is isomorphic to the field of real numbers under the map . 2. The set of matrices of the form where and range over the field of real numbers, forms a matrix field which is isomorphic to the field of complex numbers: corresponds to the real part of the number, while corresponds to the imaginary part. So the number , for example, would be represented as One can easily verify that : and also, by computing a matrix exponential, that Euler's identity, is valid: . See also Field theory Finite field Algebraic structure Galois theory Matrix ring Matrix group References Field (mathematics) Algebraic structures Matrices
https://en.wikipedia.org/wiki/A%20History%20of%20the%20Kerala%20School%20of%20Hindu%20Astronomy
A History of the Kerala School of Hindu Astronomy (in perspective) is the first definitive book giving a comprehensive description of the contribution of Kerala to astronomy and mathematics. The book was authored by K. V. Sarma who was a Reader in Sanskrit at Vishveshvaranand Institute of Sanskrit and Indological Studies, Panjab University, Hoshiarpur, at the time of publication of the book (1972). The book, among other things, contains details of the lives and works of about 80 astronomers and mathematicians belonging to the Kerala School. It has also identified 752 works belonging to the Kerala school. Even though C. M. Whish, an officer of East India Company, had presented a paper on the achievements of the mathematicians of Kerala School as early as 1842, western scholars had hardly taken note of these contributions. Much later in the 1940s, C. T. Rajagopal and his associates made some efforts to study and popularize the discoveries of Whish. Their work was lying scattered in several journals and as parts of books. Even after these efforts by C. T. Rajagopal and others, the view that Bhaskara II was the last significant mathematician pre-modern India had produced had prevailed among scholars, and surprisingly, even among Indian scholars. It was in this context K. V. Sarma published his book as an attempt to present in a succinct form the results of the investigations of C. T. Rajagopal and others and also the findings of his own investigations into the history of the Kerala school of astronomy and mathematics. Summary of the book The book is divided into six chapters. Chapter 1 gives an outline of the salient features of Kerala astronomy. Sarma emphasizes the spirit of inquiry, stress on observation and experimentation, concern for accuracy, and continuity of tradition as the important features of Kerala astronomy. Adherence to the Aryabhatan system, use of the katapayadi system for expressing numbers, the use of the Parahita and Drik systems for astronomical computations are some other important aspects of Kerala astronomy. Chapter 2 gives a brief account of the mathematical discoveries of Kerala mathematicians which anticipate many modern day discoveries in mathematics and astronomy. Among other topics, Sarma specifically mentions the following: Tycho Brahe's reduction to the ecliptic, Newton-Gauss interpolation formula, Taylor series for sine and cosine functions, power series for sine and cosine functions, Lhuier's formula for the circum-radius of a cyclic quadrilateral, Gregory's series for the inverse tangent, and approximations to the value of pi. Chapter 3 contains a discussion on the major trends in the Kerala literature on Jyotisha. This gives an indication of the range and depth of the topics discussed in the Kerala literature on Jyotisha. Chapter 4 is devoted to providing brief accounts of the Kerala authors of mathematical and astronomical works. There are accounts of as many as 80 authors beginning with the legendary Vararuc
https://en.wikipedia.org/wiki/Jan%20Vaerman
Jan Vaerman (1653–1731) was a Flemish mathematician. He worked as a school teacher first in Bruges and then, from 1693 to 1717, in Tielt. He wrote about French grammar, arithmetic, geometry, trigonometry and planimetrics. Works References 1653 births 1731 deaths Flemish mathematicians People from Aalst, Belgium
https://en.wikipedia.org/wiki/Pirmurod%20Burkhanov
Pirmurod Burkhanov (born 30 October 1977) is a retired Tajikistani International footballer. Career statistics International Statistics accurate as of 19 February 2016 International goals Goals for Senior National team Honours Club Regar-TadAZ Tajik League (5): 2001, 2002, 2003, 2004, 2006 Tajik Cup (3): 2000, 2001, 2006 Khujand Tajik Cup (1): 2008 References External links 1977 births Living people Tajikistani men's footballers Tajikistani expatriate men's footballers Tajikistan men's international footballers Men's association football forwards
https://en.wikipedia.org/wiki/System%20U
In mathematical logic, System U and System U− are pure type systems, i.e. special forms of a typed lambda calculus with an arbitrary number of sorts, axioms and rules (or dependencies between the sorts). They were both proved inconsistent by Jean-Yves Girard in 1972. This result led to the realization that Martin-Löf's original 1971 type theory was inconsistent as it allowed the same "Type in Type" behaviour that Girard's paradox exploits. Formal definition System U is defined as a pure type system with three sorts ; two axioms ; and five rules . System U− is defined the same with the exception of the rule. The sorts and are conventionally called “Type” and “Kind”, respectively; the sort doesn't have a specific name. The two axioms describe the containment of types in kinds () and kinds in (). Intuitively, the sorts describe a hierarchy in the nature of the terms. All values have a type, such as a base type (e.g. is read as “ is a boolean”) or a (dependent) function type (e.g. is read as “ is a function from natural numbers to booleans”). is the sort of all such types ( is read as “ is a type”). From we can build more terms, such as which is the kind of unary type-level operators (e.g. is read as “ is a function from types to types”, that is, a polymorphic type). The rules restrict how we can form new kinds. is the sort of all such kinds ( is read as “ is a kind”). Similarly we can build related terms, according to what the rules allow. is the sort of all such terms. The rules govern the dependencies between the sorts: says that values may depend on values (functions), allows values to depend on types (polymorphism), allows types to depend on types (type operators), and so on. Girard's paradox The definitions of System U and U− allow the assignment of polymorphic kinds to generic constructors in analogy to polymorphic types of terms in classical polymorphic lambda calculi, such as System F. An example of such a generic constructor might be (where k denotes a kind variable) . This mechanism is sufficient to construct a term with the type (equivalent to the type ), which implies that every type is inhabited. By the Curry–Howard correspondence, this is equivalent to all logical propositions being provable, which makes the system inconsistent. Girard's paradox is the type-theoretic analogue of Russell's paradox in set theory. References Further reading Lambda calculus Proof theory Type theory
https://en.wikipedia.org/wiki/Population%20proportion
In statistics, a population proportion, generally denoted by or the Greek letter , is a parameter that describes a percentage value associated with a population. For example, the 2010 United States Census showed that 83.7% of the American population was identified as not being Hispanic or Latino; the value of .837 is a population proportion. In general, the population proportion and other population parameters are unknown. A census can be conducted in order to determine the actual value of a population parameter, but often a census is not practical due to its costs and time consumption. A population proportion is usually estimated through an unbiased sample statistic obtained from an observational study or experiment. For example, the National Technological Literacy Conference conducted a national survey of 2,000 adults to determine the percentage of adults who are economically illiterate. The study showed that 72% of the 2,000 adults sampled did not understand what a gross domestic product is. The value of 72% is a sample proportion. The sample proportion is generally denoted by and in some textbooks by . Mathematical definition A proportion is mathematically defined as being the ratio of the quantity of elements (a countable quantity) in a subset to the size of a set : where is the count of successes in the population, and is the size of the population. This mathematical definition can be generalized to provide the definition for the sample proportion: where is the count of successes in the sample, and is the size of the sample obtained from the population. Estimation One of the main focuses of study in inferential statistics is determining the "true" value of a parameter. Generally, the actual value for a parameter will never be found, unless a census is conducted on the population of study. However, there are statistical methods that can be used to get a reasonable estimation for a parameter. These methods include confidence intervals and hypothesis testing. Estimating the value of a population proportion can be of great implication in the areas of agriculture, business, economics, education, engineering, environmental studies, medicine, law, political science, psychology, and sociology. A population proportion can be estimated through the usage of a confidence interval known as a one-sample proportion in the Z-interval whose formula is given below: where is the sample proportion, is the sample size, and is the upper critical value of the standard normal distribution for a level of confidence . Proof In order to derive the formula for the one-sample proportion in the Z-interval, a sampling distribution of sample proportions needs to be taken into consideration. The mean of the sampling distribution of sample proportions is usually denoted as and its standard deviation is denoted as: Since the value of is unknown, an unbiased statistic will be used for . The mean and standard deviation are rewritten respect
https://en.wikipedia.org/wiki/World%20Club%20Challenge%20records%20and%20statistics
Notable achievements, records, and statistics of the World Club Challenge are listed below: Records and statistics NOTE: The below statistics reflect records from all World Club Challenge matches from 1976 to present. They only include the finals of World Club Series 2015 and 2017 and of the 1997 World Club Championship. Match records Biggest win Highest scoring game Lowest scoring game Individual records Top try scorers Most tries in a game Most points in a game Most goals Drop goals Attendance Top 5 Attendances World Club Series only The World Club Series was the temporary name of the tournament following its temporary restructure between 2015 and 2017. Biggest win Highest scoring game Lowest scoring game Individual Top try scorers List of players who have scored 2 or more tries. Top goal scorers See also References World Club Challenge Rugby league records and statistics
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20George%20Airy
This is a list of things named after George Biddell Airy, a 19th-century mathematician and astronomer. Mathematics and related physics concepts Airy beam Airy condition Airy disc Airy distribution Airy differential equation Airy functions Ai(x) and Bi(x) Airy points. Airy stress functions Airy transform Airy wave theory. Airy zeta function Astronomy and geosciences Airy–Heiskanen model, see "Airy hypothesis". Airy, a crater on Mars. Airy-0, another smaller crater, whose location within Airy, defines the prime meridian of that planet. Airy (lunar crater) named in his honour. Airy ellipsoid Airy hypothesis Airy Mean Time Airy projection Airy Transit Circle Other Airy (software) References Airy Airy
https://en.wikipedia.org/wiki/2016%20Alberta%20municipal%20censuses
Alberta has provincial legislation allowing its municipalities to conduct municipal censuses between April 1 and June 30 inclusive. Due to the concurrency of Statistics Canada conducting the Canada 2016 Census in May 2016, the Government of Alberta offered municipalities the option to alter their 2016 municipal census timeframes to either March 1 through May 31 or May 1 through July 31. Municipalities choose to conduct their own censuses for multiple reasons such as to better inform municipal service planning and provision, to capitalize on per capita based grant funding from higher levels of government, or to simply update their populations since the last federal census. With the dissolution of the villages of Galahad and Strome on January 1, 2016, Alberta had 354 municipalities in 2016. Alberta Municipal Affairs recognized those conducted by 21 () of these municipalities. By municipal status, it recognized those conducted by 11 of Alberta's 18 cities, 5 of 108 towns, 2 of 90 villages, and 3 of 64 municipal districts. In addition to those recognized by Municipal Affairs, a census was planned by the Village of Forestburg for 2016 but was subsequently deferred to 2017. Some municipalities achieved population milestones as a result of their 2016 censuses. Airdrie became the eighth city in Alberta to exceed 60,000 residents, while Leduc surpassed 30,000 people and Cochrane grew beyond the 25,000 mark. Edmonton fell short of the 900,000-mark by 553 people, while Red Deer dipped back below 100,000 residents after surpassing that milestone in 2015. Municipal census results The following summarizes the results of the numerous municipal censuses conducted in 2016. Breakdowns Hamlets The following is a list of hamlet populations determined by 2016 municipal censuses conducted by Lac La Biche County and the Municipal District of Taber. Shadow population counts Alberta Municipal Affairs defines shadow population as "temporary residents of a municipality who are employed by an industrial or commercial establishment in the municipality for a minimum of 30 days within a municipal census year." Lac La Biche County conducted a shadow population count in 2016. The following presents the results of this count for comparison with its concurrent municipal census results. Notes See also 2013 Alberta municipal elections List of communities in Alberta References External links Alberta Municipal Affairs: Municipal Census & Population Lists Statistics Canada: Census Profile (2011 Census) 2016 municipal census links by municipality: Airdrie: 2016 Census Fact Sheets Beaumont: 2016 Beaumont Census Report Blackfalds: Census Report 2016 Calgary: 2016 Civic Census Results Camrose: Census 2016 Information & Results Chestermere: 2016 Municipal Census Staff Report Cochrane: 2016 Municipal Census Summary Report Edmonton 2016 Municipal Census Results Fort Saskatchewan 2016 Municipal Census Results Leduc: Census Information, Leduc Census 2016 Lethbridge: 2016 Census R
https://en.wikipedia.org/wiki/List%20of%20Asia%20Cup%20cricket%20records
This is an overall list of statistics and records of the Asia Cup, which was a One Day International tournament until 2016, since when it has alternated with Twenty20 International tournament. One Day Internationals Records and statistics Most runs Most wickets Most runs in the tournament Most wickets in the tournament Man of the tournament Man of the match (in final) Twenty20 Internationals Records and statistics Most runs Highest individual scores Highest average Most 50+ scores Other results General statistics by tournament Results of host teams See also List of Asia Cup centuries List of Asia Cup five-wicket hauls Women's Asia Cup References External links Asia Cup (ODI) Records on ESPNCricinfo Records Asia Cup
https://en.wikipedia.org/wiki/Sebasti%C3%A1n%20Britos
Sebastián Javier Britos Rodríguez (born January 2, 1988 in Minas) is a Uruguayan footballer currently playing as a goalkeeper for Atlante FC of the Ascenso MX. Career statistics Club Notes References 1988 births Living people Uruguayan men's footballers Uruguayan expatriate men's footballers Men's association football midfielders Uruguayan Primera División players Uruguayan Segunda División players Bolivian Primera División players Categoría Primera A players Ascenso MX players C.A. Bella Vista players Montevideo Wanderers F.C. players Liverpool F.C. (Montevideo) players Cortuluá footballers C.A. Cerro players Oriente Petrolero players El Tanque Sisley players Atlante F.C. footballers Uruguayan expatriate sportspeople in Bolivia Uruguayan expatriate sportspeople in Colombia Uruguayan expatriate sportspeople in Mexico Expatriate men's footballers in Bolivia Expatriate men's footballers in Colombia Expatriate men's footballers in Mexico People from Minas, Uruguay
https://en.wikipedia.org/wiki/Karsten%20Grove
Karsten Grove is a Danish-American mathematician working in metric and differential geometry, differential topology and global analysis, mainly in topics related to global Riemannian geometry, Alexandrov geometry, isometric group actions and manifolds with positive or nonnegative sectional curvature. Biography Grove studied mathematics at Aarhus University, where he obtained a Cand. Scient. (equivalent to a M.A.) in 1971 and Lic. Scient. (equivalent to a Ph.D.) in 1974. Between 1971 and 1972 he also acted as an instructor at Aarhus University. From 1972 to 1974 he had a postdoctoral position at the University of Bonn under the supervision of Wilhelm Klingenberg, despite not having yet formally concluded his doctoral degree. In 1974, Grove became an Assistant Professor at the University of Copenhagen and was promoted to Associate Professor in 1976, a position he held until 1987. He became a Professor at the University of Maryland in 1984, retiring from this position in 2009. Since 2007 he has held the endowed chair of "Rev. Howard J. Kenna, C.S.C. Professor" at the University of Notre Dame. Throughout his career, Grove has had 20 doctoral students, and 51 academic descendants. Grove was an invited speaker at the International Congress of Mathematicians in 1990 in Kyoto (Metric and Topological Measurements on manifolds). He is a fellow of the American Mathematical Society. Mathematical work One of Grove's most recognized mathematical contributions to Riemannian Geometry is the Diameter Sphere Theorem, proved jointly with Katsuhiro Shiohama in 1977, which states that a smooth closed Riemannian manifold with and is homeomorphic to a sphere. Subsequently, the critical point theory for distance functions developed as part of the proof of this result led to several important advances in the area. Another result obtained by Grove, in collaboration with Peter Petersen, is the finiteness of homotopy types of manifolds of a fixed dimension with lower sectional curvature bounds, upper diameter bound, and lower volume bound. References Year of birth missing (living people) Living people Differential geometers Danish mathematicians Aarhus University alumni Fellows of the American Mathematical Society Academic staff of the University of Copenhagen University of Notre Dame faculty
https://en.wikipedia.org/wiki/Whittle%20likelihood
In statistics, Whittle likelihood is an approximation to the likelihood function of a stationary Gaussian time series. It is named after the mathematician and statistician Peter Whittle, who introduced it in his PhD thesis in 1951. It is commonly used in time series analysis and signal processing for parameter estimation and signal detection. Context In a stationary Gaussian time series model, the likelihood function is (as usual in Gaussian models) a function of the associated mean and covariance parameters. With a large number () of observations, the () covariance matrix may become very large, making computations very costly in practice. However, due to stationarity, the covariance matrix has a rather simple structure, and by using an approximation, computations may be simplified considerably (from to ). The idea effectively boils down to assuming a heteroscedastic zero-mean Gaussian model in Fourier domain; the model formulation is based on the time series' discrete Fourier transform and its power spectral density. Definition Let be a stationary Gaussian time series with (one-sided) power spectral density , where is even and samples are taken at constant sampling intervals . Let be the (complex-valued) discrete Fourier transform (DFT) of the time series. Then for the Whittle likelihood one effectively assumes independent zero-mean Gaussian distributions for all with variances for the real and imaginary parts given by where is the th Fourier frequency. This approximate model immediately leads to the (logarithmic) likelihood function where denotes the absolute value with . Special case of a known noise spectrum In case the noise spectrum is assumed a-priori known, and noise properties are not to be inferred from the data, the likelihood function may be simplified further by ignoring constant terms, leading to the sum-of-squares expression This expression also is the basis for the common matched filter. Accuracy of approximation The Whittle likelihood in general is only an approximation, it is only exact if the spectrum is constant, i.e., in the trivial case of white noise. The efficiency of the Whittle approximation always depends on the particular circumstances. Note that due to linearity of the Fourier transform, Gaussianity in Fourier domain implies Gaussianity in time domain and vice versa. What makes the Whittle likelihood only approximately accurate is related to the sampling theorem—the effect of Fourier-transforming only a finite number of data points, which also manifests itself as spectral leakage in related problems (and which may be ameliorated using the same methods, namely, windowing). In the present case, the implicit periodicity assumption implies correlation between the first and last samples ( and ), which are effectively treated as "neighbouring" samples (like and ). Applications Parameter estimation Whittle's likelihood is commonly used to estimate signal parameters for signals that are buried in non-whi
https://en.wikipedia.org/wiki/Kristine%20Austgulen
Kristine Austgulen (born 4 November 1980) is a former Norwegian female basketball player. Virginia Commonwealth University statistics Source References 1980 births Living people Norwegian women's basketball players Forwards (basketball) Sportspeople from Bergen VCU Rams women's basketball players
https://en.wikipedia.org/wiki/Migu%20Music%20Awards
The Migu Music Awards () is a music awards founded by China Mobile to recognize most popular music artists and works based on the statistics of Chinese music streaming service Migu Music. Ceremonies Categories 2017 Migu Music Awards Album of the Year Best Male Singer Best Female Singer Best Ringback Music Selling Singer Most Popular Male Singer (Hong Kong/Taiwan) Most Popular Female Singer (Hong Kong/Taiwan) Most Popular Male Singer (Mainland China) Most Popular Female Singer (Mainland China) Most Popular Group Most Popular Singer-Songwriter Most Popular Stage Performance Most Improved Singer Most Improved Group Most Breakthrough Singer Most Appealing Singer Most Appealing Group Viewer's Choice Male Singer Viewer's Choice Female Singer Top 10 Songs of the Year References 2007 establishments in China Annual events in China Awards established in 2007 Chinese music awards Recurring events established in 2007
https://en.wikipedia.org/wiki/Andr%C3%A9s%20Ravecca
Andrés Ravecca Cadenas (born 2 January 1988 in Montevideo) is a Uruguayan footballer currently playing as a right-back for Deportivo Maldonado of the Uruguayan primera División. Career statistics Club Notes References 1988 births Living people Uruguayan men's footballers Men's association football defenders Footballers from Montevideo C.A. Cerro players Liverpool F.C. (Montevideo) players Deportivo Maldonado players Uruguayan Primera División players Uruguayan Segunda División players
https://en.wikipedia.org/wiki/D%C3%A1niel%20Gera
Dániel Gera (born 29 August 1995) is a professional Hungarian footballer who plays as a forward for Diósgyőr. Club career On 31 August 2022, Gera signed with Diósgyőr. Career statistics References External links 1995 births Footballers from Budapest Living people Hungarian men's footballers Hungary men's under-21 international footballers Men's association football midfielders MTK Budapest FC players Ferencvárosi TC footballers Puskás Akadémia FC players Diósgyőri VTK players Nemzeti Bajnokság I players Nemzeti Bajnokság II players
https://en.wikipedia.org/wiki/Brian%20C.%20Moyer
Brian C. Moyer is an American economist who is the Director of the U.S. National Center for Health Statistics. Moyer serves as senior advisor to the Centers for Disease Control and Prevention and to the Secretary of the U.S. Department of Health and Human Services; he also serves as the Statistical Official for the Department. Education Moyer received a bachelor's and master's degrees in economics from the University of Maryland and a Ph.D. in economics in 2002 from American University. Career Moyer spent more than 25 years with the U.S. Department of Commerce. He served as Director of the Bureau of Economic Analysis (BEA), where he led modernization efforts to improve official economic statistics, including the measures of gross domestic product (GDP). References American civil servants American economists Living people American University alumni University System of Maryland alumni Place of birth missing (living people) Year of birth missing (living people) United States Department of Commerce officials Centers for Disease Control and Prevention Trump administration personnel
https://en.wikipedia.org/wiki/Christian%20Ronaldo%20Sitepu
Christian Ronaldo Sitepu is a former Indonesian basketball player for Satria Muda Pertamina Jakarta and the Indonesia national basketball team. Career statistics Regular season Playoffs International References 1986 births Living people Indonesian men's basketball players People of Batak descent Power forwards (basketball) Sportspeople from Bogor ASEAN Basketball League players SEA Games silver medalists for Indonesia SEA Games medalists in basketball Competitors at the 2011 SEA Games Competitors at the 2015 SEA Games Competitors at the 2017 SEA Games Islamic Solidarity Games competitors for Indonesia
https://en.wikipedia.org/wiki/Danielle%20Macbeth
Danielle Monique Macbeth (born 1954, Edmonton) is a Canadian philosopher whose work focuses on the philosophy of mathematics, the philosophy of language, metaphysics, and the philosophy of logic. She is T. Wistar Brown Professor of Philosophy at Haverford College in Pennsylvania where she has taught since 1989. Macbeth also taught at the University of Hawaii from 1986–1989. Education and career Macbeth received a Bachelor of Science degree in Biochemistry at the University of Alberta in 1977 before beginning her philosophical studies. She then went on to receive a Bachelor of Arts degree in Philosophy and Religious Studies at McGill University in Montreal in 1980 and received her PhD from University of Pittsburgh in 1988. She wrote her dissertation under John Haugeland, and studied also with Wilfrid Sellars, John McDowell, and Robert Brandom. Macbeth has received numerous awards and fellowships including NEH Grants, and an ACLS Frederick Burkhardt Residential Fellowship. In 2002-2003, she was a Fellow at the Center for Advanced Study in Behavioral Sciences in Palo Alto, California. Macbeth is the author of two books, Frege’s Logic (2005) and Realizing Reason: A Narrative of Truth and Knowing (2014). Philosophical work Frege's Logic In Frege's Logic (2005), Macbeth proposes a new reading of Frege’s notation and logical project. Rather than treating Begriffsschrift (Frege's logic) as a notational variant of quantificational logic, Macbeth proposes that reasoning in Begriffsschrift is more like the diagrammatic reasoning of the geometrician or algebraicist. She argues that philosophers and mathematicians alike have failed to recognize the revolutionary powers of Begriffsschrift in its expressive and demonstrative capacities. Realizing Reason Realizing Reason, her most recent book, takes a Hegelian approach to the philosophy of mathematics and traces developments in philosophy, logic, mathematics, and physics beginning with Aristotle in order to illuminate how (pure) reason has come to be realized as a power of knowing. She focuses on three periods: Ancient Greece, early modern mathematics, physics, and philosophy (Descartes to Kant), and late nineteenth-century and early twentieth-century mathematics and physics. Macbeth argues that with her new reading of Frege, we can finally break out of the Kantian framework that remains in place even in twentieth-century analytic philosophy and thereby finally understand how contemporary mathematics enables real extensions of our knowledge on the basis of strictly deductive reasoning. Thus, she demonstrates how pure reason has finally been realized as a power of knowing. Macbeth has also published many articles on a wide range of topics in the history and philosophy of mathematics, the philosophy of language, the philosophy of mind, and pragmatism. Books Frege’s Logic (Cambridge, Mass.: Harvard University Press, 2005) Realizing Reason: A Narrative of Truth and Knowing (Oxford: Oxford University
https://en.wikipedia.org/wiki/OFC%20Nations%20Cup%20records%20and%20statistics
This is a list of records and statistics of the OFC Nations Cup. Debut of national teams Never qualified: , , , , Overall team records In this ranking 3 points are awarded for a win, 1 for a draw and 0 for a loss. As per statistical convention in football, matches decided in extra time are counted as wins and losses, while matches decided by penalty shoot-outs are counted as draws. Teams are ranked by total points, then by goal difference, then by goals scored. Medal table Comprehensive team results by tournament Legend – Champions – Runners-up – Third place – Fourth place – Semi-finals (in years without a 3rd/4th play-off) 5th — Fifth place 6th — Sixth place GS – Group stage — Qualified for an upcoming tournament — Qualified but withdrew — Did not qualify — Did not enter / Withdrew / Banned — Hosts For each tournament, the number of teams in each finals tournament (in brackets) are shown. General statistics by tournament Team: tournament position All-time Most championships 5, (1973, 1998, 2002, 2008, 2016) Most finishes in the top two 6, (1980, 1996, 1998, 2000, 2002, 2004) 6, (1973, 1998, 2000, 2002, 2008, 2016) Most finishes in the top four 9, (1973, 1996, 1998, 2000, 2002, 2004, 2008, 2012, 2016) Most second place finishers 3, (1973, 1980, 1996) Consecutive Most consecutive championships 2, (1980, 1996) Most consecutive finishes in the top two 6, (1980, 1996, 1998, 2000, 2002, 2004) Most consecutives finishes in the top four 7, (1998, 2000, 2002, 2004, 2008, 2012, 2016) Gaps Longest gap between successive titles 25 years, (1973–1998) Longest gap between successive appearances in the top two 16 years, (1996–2012) Longest gap between successive appearances in the top four 12 years, (1996–2008) Host team Best finish by host team Champions, (1973, 2002), (2004) Debuting teams Best finish by a debuting team Champions, (1973), (1980) Other Most finishes in the top two without ever being champion 2, (2008, 2012) Most finishes in the top four without ever being champion 5, (1996, 2000, 2004, 2012, 2016) Most finishes in the top four without ever finishing in the top two 4, (1973, 2000, 2002, 2008) Team: tournament progression All-time Progressed from the group stage the most times 9, (1973, 1996, 1998, 2000, 2002, 2004, 2008, 2012, 2016) Eliminated in the group stage the most times 4, (1980, 1998, 2012, 2016) Most appearances, never progressed from the group stage 2, (1998, 2000), (2012, 2016) Consecutive Most consecutive progressions from the group stage 8, (1996, 1998, 2000, 2002, 2004, 2008, 2012, 2016) Most consecutive eliminations from the group stage 2, (1998, 2000), (2012, 2016) Team: Matches played/goals scored All-time Most matches played 44, Most wins 32, Most losses 26, Most draws 5, , Most matches played without a win 6, Most goals scored 142, Most goals conceded 85, Fewest goals scored 1, , Fewe
https://en.wikipedia.org/wiki/Dominic%20Thiem%20career%20statistics
This is a list of the main career statistics of Austrian professional tennis player Dominic Thiem. To date, Thiem has won seventeen ATP singles titles, including at least one title on each surface (hard, clay and grass). He won the 2020 US Open title, and has reached three other Grand Slam finals at the 2018 French Open, 2019 French Open and 2020 Australian Open. He has also been in two Grand Slam semifinals at the 2016 French Open and 2017 French Open. He won the 2019 Indian Wells Masters and was a finalist at the 2017 and 2018 Madrid Open, semifinalist at the 2017 Italian Open, 2018 Paris Masters and 2019 Madrid Open and a quarterfinalist at the US Open in 2018 and at the French Open in 2020. Thiem achieved a career high singles ranking of world No. 3 on 2 March 2020. Career achievements At the 2014 US Open, Thiem advanced to the fourth round of a Grand Slam for the first time but lost in straight sets to sixth seed Tomáš Berdych. The following year, he reached his first ATP Masters 1000 quarterfinal at the Miami Open, where he lost to eventual runner-up Andy Murray in three sets. Later that year, Thiem won the first three ATP singles titles of his career at the Open de Nice Côte d'Azur, Croatia Open Umag and Swiss Open with wins over Leonardo Mayer, João Sousa and David Goffin in the finals. In February 2016, Thiem won his fourth ATP singles title at the Argentina Open, defeating top seed and defending champion Rafael Nadal en route after saving a match point in the third set. In the same month, he won his first ATP 500 title, and first title on hard court at the Abierto Mexicano Telcel, beating Bernard Tomic in the final. At the French Open, Thiem achieved his best Grand Slam result so far by advancing to the semifinals where he fell to the world No. 1 and eventual champion Novak Djokovic. He followed this up with his first title on grass at the MercedesCup, saving two match points against top seed Roger Federer en route. His strong performances throughout the year allowed him to qualify for the year-ending ATP World Tour Finals for the first time, where he scored his only win in the round-robin stage against Gaël Monfils. He finished with a career high year-end ranking of eighth. Thiem began 2017 by reaching the fourth round of the Australian Open for the first time but lost to Goffin in a rematch of their third round match from the previous year. After falling at the quarterfinal stage in three of his past five tournaments, he won his first title of the year and second ATP 500 title at the Rio Open without dropping a set. He then went on to reach his first Masters 1000 final in the Madrid Masters before losing to Rafael Nadal in a tight straight set battle. He would reach the semifinals of the French Open for the second year running beating Novak Djokovic in the process before losing in straight sets to Nadal. In 2020, Thiem won his first Grand Slam title at the 2020 US Open, defeating Alexander Zverev in a fifth-set tiebreak after b
https://en.wikipedia.org/wiki/John%20Freund
John Freund may refer to: John Christian Freund (1848–1924), co-publisher of The Music Trades magazine John E. Freund (1921–2004), author of university level textbooks on statistics John F. Freund (1918–2001), U.S. Army general
https://en.wikipedia.org/wiki/Bernard%20Tomic%20career%20statistics
This is a list of the main career statistics of professional Australian tennis player, Bernard Tomic. All statistics are according to the ATP Tour. To date, Tomic has reached one Grand Slam quarterfinal at the 2011 Wimbledon Championships and won four ATP singles titles including two consecutive titles at the Claro Open Colombia from 2014–2015. He was also a quarterfinalist at the 2015 BNP Paribas Open, the 2015 Shanghai Rolex Masters, the 2016 Western & Southern Open – Men's singles and part of the team which reached the semifinals of the 2015 Davis Cup. He also reached the fourth round of the Australian Open in 2012, 2015 and 2016. Tomic achieved a career high singles ranking of world No. 17 on 11 January 2016. Performance timelines Singles Current through to the 2023 French Open. Notes 2014 US Open counts as 1 win, 0 losses. David Ferrer received a walkover in the second round, after Tomic withdrew. 2015 Indian Wells Masters counts as 3 wins, 0 losses. Novak Djokovic received a walkover in the quarterfinals after Tomic withdrew with a back injury. Doubles ATP career finals Singles: 6 (4 titles, 2 runner-ups) Doubles: 1 (1 runner-up) ATP Challengers and ITF Futures finals Singles: 12 (7 titles, 5 runner-ups) Exhibition tournament finals Junior Grand Slam finals Singles: 2 (2 titles) Doubles: 1 (1 runner-up) Record against top 10 players Tomic's match record against players who have been ranked in the top 10. Only ATP Tour main draw and Davis Cup matches are considered. Players who have been ranked No. 1 are in boldface. Fernando Verdasco 6–1 Kevin Anderson 4–1 Tommy Haas 3–1 David Goffin 2–1 Fabio Fognini 2–2 Kei Nishikori 2–3 David Ferrer 2–4 Richard Gasquet 2–8 Félix Auger-Aliassime 1–0 James Blake 1–0 Nikolay Davydenko 1–0 Ernests Gulbis 1–0 Hubert Hurkacz 1–0 Lleyton Hewitt 1–0 Robin Söderling 1–0 Frances Tiafoe 1–0 Stanislas Wawrinka 1–1 Roberto Bautista Agut 1–2 Mardy Fish 1–2 Jack Sock 1–2 Marin Čilić 1–3 Radek Štěpánek 1–3 Marcos Baghdatis 0–1 Taylor Fritz 0–1 Juan Mónaco 0–1 Lucas Pouille 0–1 Andy Roddick 0–1 Denis Shapovalov 0–1 Janko Tipsarević 0–1 Pablo Carreño Busta 0–2 Juan Martín del Potro 0–2 Grigor Dimitrov 0–2 Gaël Monfils 0–2 Dominic Thiem 0–2 Mikhail Youzhny 0–2 John Isner 0–3 Rafael Nadal 0–3 Diego Schwartzman 0–3 Gilles Simon 0–3 Jo-Wilfried Tsonga 0–3 Roger Federer 0–4 Tomáš Berdych 0–5 Andy Murray 0–5 Milos Raonic 0–5 Novak Djokovic 0–6 * . Top-10 wins Tomic has an 8–40 (.167) record against players who were, at the time the match was played, ranked in the top 10. National representation Davis Cup (17–4) References Tomic, Bernard
https://en.wikipedia.org/wiki/Flemming%20Tops%C3%B8e
Flemming Topsøe (born 25 August 1938 in Aarhus, Denmark) is a Danish mathematician, and is emeritus in the mathematics department of the University of Copenhagen. He is the author of several mathematical science works, among them works about analysis, probability theory and information theory. He is the older brother of the engineer Henrik Topsøe (born 1944), son of the engineer Haldor Topsøe (1913–2013) and great-grandson of the crystallographer and chemist Haldor Topsøe (1842–1935). Topsøe completed his magister degree in mathematics at Aarhus University in 1962. After spending a year at the University of Cambridge in 1965–1966, he finished his PhD in 1971 at the University of Copenhagen. His thesis was titled Topology and Measure, and was later published by Springer. He was leader of the Danish Mathematical Society 1978–1982 and dynamic leader of Euromath 1983–1998, a great project about expansion of Internet-based services to mathematics societies in Europe and Russia. He received a Hlavka memorial medal in 1992 and a B. Bolzano honorary medal in 2006 of the Czechoslovak Academy of Sciences for his mathematical contributions. Books References External links 1938 births Living people People from Aarhus Academic staff of the University of Copenhagen Danish mathematicians Danish science writers
https://en.wikipedia.org/wiki/Wenzl
Wenzl may refer to: Wenzl (surname) Birman–Wenzl algebra, family of algebras
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20Stefan%20Banach
Stefan Banach was a Polish mathematician who made key contributions to mathematics. This article contains some of the things named in his memory. Mathematics Banach algebra Amenable Banach algebra Banach Jordan algebra Banach function algebra Banach *-algebra Banach algebra cohomology Banach bundle Banach bundle (non-commutative geometry) Banach fixed-point theorem Banach game Banach lattice Banach limit Banach manifold Banach measure Banach space Banach coordinate space Banach disks Banach norm Banach–Alaoglu theorem Banach–Mazur compactum Banach–Mazur game Banach–Mazur theorem Banach–Ruziewicz problem Banach-Saks theorem Banach-Schauder theorem Banach–Steinhaus theorem Banach–Stone theorem Banach–Tarski paradox Banach's matchbox problem Hahn–Banach theorem Other 16856 Banach Banach Journal of Mathematical Analysis International Stefan Banach Prize Stefan Banach Medal See also Banach
https://en.wikipedia.org/wiki/Mathematics%20education%20in%20the%20United%20Kingdom
Mathematics education in the United Kingdom is largely carried out at ages 5–16 at primary school and secondary school (basic numeracy is taught at an earlier age in the Early Years). Voluntary mathematics education in the UK takes place from 16 to 18, in sixth forms and other forms of further education. Whilst adults can study the subject at universities and higher education more widely. Mathematics education is not taught uniformly as exams and the syllabus vary across the countries of the United Kingdom, notably Scotland. The Programme for International Student Assessment coordinated by the OECD currently ranks the knowledge and skills of British 15-year-olds in mathematics and science above OECD averages. In 2011, the Trends in International Mathematics and Science Study (TIMSS) rated 13–14-year-old pupils in England and Wales 10th in the world for maths and 9th for science. History The School Certificate was established in 1918, for education up to 16, with the Higher School Certificate for education up to 18; these were both established by the Secondary Schools Examinations Council (SSEC), which had been established in 1917. 1950s The Association of Teachers of Mathematics was founded in 1950. 1960s The Joint Mathematical Council was formed in 1963 to improve the teaching of mathematics in UK schools. The Ministry of Education had been created in 1944, which became the Department of Education and Science in 1964. The Schools Council was formed in 1964, which regulated the syllabus of exams in the UK, and existed until 1984. The exam body Mathematics in Education and Industry in Trowbridge was formed in 1963, formed by the Mathematical Association; the first exam Additional Mathematics was first set in 1965. The Institute of Mathematics and its Applications was formed in 1964, and is the UK's chartered body for mathematicians, being based in Essex. Before calculators, many calculations would be done by hand with slide rules and log tables. 1970s Decimal Day, on 15 February 1971, allowed less time on numerical calculations at school. The Metric system curtailed lengthy calculations as well. 1980s Electronic calculators began to be owned at school from the early 1980s, becoming widespread from the mid-1980s. Parents and teachers believed that calculators would diminish abilities of mental arithmetic. Scientific calculators came to the aid for those working out logarithms and trigonometric functions. Since 1988, exams in Mathematics at age sixteen, except Scotland, have been provided by the GCSE. 1990s From the 1990s, mainly the late 1990s, computers became integrated into mathematics education at primary and secondary levels in the UK. The specialist schools programme was introduced in the mid-1990s in England. Fifteen new City Technology Colleges (CTCs) from the early 1990s often focussed on Maths. In 1996 the United Kingdom Mathematics Trust was formed to run the British Mathematical Olympiad, run by the British Mathematical Olym
https://en.wikipedia.org/wiki/Faddeev%E2%80%93LeVerrier%20algorithm
In mathematics (linear algebra), the Faddeev–LeVerrier algorithm is a recursive method to calculate the coefficients of the characteristic polynomial of a square matrix, , named after Dmitry Konstantinovich Faddeev and Urbain Le Verrier. Calculation of this polynomial yields the eigenvalues of as its roots; as a matrix polynomial in the matrix itself, it vanishes by the Cayley–Hamilton theorem. Computing the characteristic polynomial directly from the definition of the determinant is computationally cumbersome insofar as it introduces a new symbolic quantity ; by contrast, the Faddeev-Le Verrier algorithm works directly with coefficients of matrix . The algorithm has been independently rediscovered several times in different forms. It was first published in 1840 by Urbain Le Verrier, subsequently redeveloped by P. Horst, Jean-Marie Souriau, in its present form here by Faddeev and Sominsky, and further by J. S. Frame, and others. (For historical points, see Householder. An elegant shortcut to the proof, bypassing Newton polynomials, was introduced by Hou. The bulk of the presentation here follows Gantmacher, p. 88.) The Algorithm The objective is to calculate the coefficients of the characteristic polynomial of the matrix , where, evidently, = 1 and 0 = (−1)n det . The coefficients are determined by induction on , using an auxiliary sequence of matrices Thus, etc.,   ...; Observe terminates the recursion at . This could be used to obtain the inverse or the determinant of . Derivation The proof relies on the modes of the adjugate matrix, , the auxiliary matrices encountered.   This matrix is defined by and is thus proportional to the resolvent It is evidently a matrix polynomial in of degree . Thus, where one may define the harmless ≡0. Inserting the explicit polynomial forms into the defining equation for the adjugate, above, Now, at the highest order, the first term vanishes by =0; whereas at the bottom order (constant in , from the defining equation of the adjugate, above), so that shifting the dummy indices of the first term yields which thus dictates the recursion for =1,...,. Note that ascending index amounts to descending in powers of , but the polynomial coefficients are yet to be determined in terms of the s and . This can be easiest achieved through the following auxiliary equation (Hou, 1998), This is but the trace of the defining equation for by dint of Jacobi's formula, Inserting the polynomial mode forms in this auxiliary equation yields so that and finally This completes the recursion of the previous section, unfolding in descending powers of . Further note in the algorithm that, more directly, and, in comportance with the Cayley–Hamilton theorem, The final solution might be more conveniently expressed in terms of complete exponential Bell polynomials as Example Furthermore, , which confirms the above calculations. The characteristic polynomial of matrix is thus ; th
https://en.wikipedia.org/wiki/Harmonic%20Maass%20form
In mathematics, a weak Maass form is a smooth function on the upper half plane, transforming like a modular form under the action of the modular group, being an eigenfunction of the corresponding hyperbolic Laplace operator, and having at most linear exponential growth at the cusps. If the eigenvalue of under the Laplacian is zero, then is called a harmonic weak Maass form, or briefly a harmonic Maass form. A weak Maass form which has actually moderate growth at the cusps is a classical Maass wave form. The Fourier expansions of harmonic Maass forms often encode interesting combinatorial, arithmetic, or geometric generating functions. Regularized theta lifts of harmonic Maass forms can be used to construct Arakelov Green functions for special divisors on orthogonal Shimura varieties. Definition A complex-valued smooth function on the upper half-plane is called a weak Maass form of integral weight (for the group ) if it satisfies the following three conditions: (1) For every matrix the function satisfies the modular transformation law (2) is an eigenfunction of the weight hyperbolic Laplacian where (3) has at most linear exponential growth at the cusp, that is, there exists a constant such that as If is a weak Maass form with eigenvalue 0 under , that is, if , then is called a harmonic weak Maass form, or briefly a harmonic Maass form. Basic properties Every harmonic Maass form of weight has a Fourier expansion of the form where , and are integers depending on Moreover, denotes the incomplete gamma function (which has to be interpreted appropriately when ). The first summand is called the holomorphic part, and the second summand is called the non-holomorphic part of There is a complex anti-linear differential operator defined by Since , the image of a harmonic Maass form is weakly holomorphic. Hence, defines a map from the vector space of harmonic Maass forms of weight to the space of weakly holomorphic modular forms of weight It was proved by Bruinier and Funke (for arbitrary weights, multiplier systems, and congruence subgroups) that this map is surjective. Consequently, there is an exact sequence providing a link to the algebraic theory of modular forms. An important subspace of is the space of those harmonic Maass forms which are mapped to cusp forms under . If harmonic Maass forms are interpreted as harmonic sections of the line bundle of modular forms of weight equipped with the Petersson metric over the modular curve, then this differential operator can be viewed as a composition of the Hodge star operator and the antiholomorphic differential. The notion of harmonic Maass forms naturally generalizes to arbitrary congruence subgroups and (scalar and vector valued) multiplier systems. Examples Every weakly holomorphic modular form is a harmonic Maass form. The non-holomorphic Eisenstein series of weight 2 is a harmonic Maass form of weight 2. Zagier's Eisenstein series of weight 3/2 is a har
https://en.wikipedia.org/wiki/Kim%20Do-hyung
Kim Do-hyung (; born 6 October 1990) is a South Korean footballer who plays as a forward for Busan I'Park FC. Career statistics Club Notes References External links 1990 births Living people Footballers from Ulsan Dong-a University alumni South Korean men's footballers Men's association football forwards K League 1 players China League One players K League 2 players K3 League players Ulsan Hyundai FC players Busan IPark players Yanbian Funde F.C. players Chungju Hummel FC players Gimcheon Sangmu FC players Pohang Steelers players Daejeon Korail FC players Suwon FC players Hwaseong FC players South Korean expatriate men's footballers South Korean expatriate sportspeople in China Expatriate men's footballers in China
https://en.wikipedia.org/wiki/Antonio%20Sangiovanni
Antonio Sangiovanni (or San Giovanni) was a 17th-century Italian agronomist and mathematician. A nobleman from Vicenza, he wrote Seconda squara mobile, a noteworthy work in the field of geometry. Works References 17th-century births 17th-century deaths 17th-century Italian male writers 17th-century Italian mathematicians Italian agronomists
https://en.wikipedia.org/wiki/Discrete%20Analysis
Discrete Analysis is a mathematics journal covering the applications of analysis to discrete structures. Discrete Analysis is an arXiv overlay journal, meaning the journal's content is hosted on the arXiv. History Discrete Analysis was created by Timothy Gowers to demonstrate that a high-quality mathematics journal could be inexpensively produced outside of the traditional academic publishing industry. The journal is open access, and submissions are free for authors. The journal's 2018 MCQ is 1.21. References External links Open access journals Mathematics journals Academic journals established in 2016 Continuous journals Online-only journals English-language journals
https://en.wikipedia.org/wiki/List%20of%20Philippine%20Basketball%20Association%20career%20minutes%20played%20leaders
This is a list of Philippine Basketball Association players by total career minutes played. Statistics accurate as of January 16, 2023. See also List of Philippine Basketball Association players References External links Games Played
https://en.wikipedia.org/wiki/Anatoly%20Libgober
Anatoly Libgober (born 1949, in Moscow) is a Russian/American mathematician, known for work in algebraic geometry and topology of algebraic varieties. Early life Libgober was born in the Soviet Union, and immigrated to Israel in 1973 after active participation in the movement to change immigration policies in Soviet Union. He studied with Yuri Manin at Moscow University and with Boris Moishezon at Tel-Aviv University where he finished his PhD dissertation with Moishezon in 1977, doing his postdoctorate work at the [[Institute for Advanced Study]] (Princeton, N.J). He lectured extensively visiting, among others, l'Institut des hautes études scientifiques (Bures sur Ivette, France), the Max Planck Institute in Bonn (Germany), the Mathematical Sciences Research Institute (Berkeley), Harvard University and Columbia University. Currently he is Professor Emeritus at the University of Illinois at Chicago where he worked until his retirement in 2010. Professional profile Libgober's early work studies the diffeomorphism type of complete intersections in complex projective space. This later led to the discovery of relations between Hodge and Chern numbers. He introduced the technique of Alexander polynomial for the study of fundamental groups of the complements to plane algebraic curves. This led to Libgober's divisibility theorem and explicit relations between these fundamental groups, the position of singularities, and local invariants of singularities (the constants of quasi-adjunction). Later he introduced the characteristic varieties of the fundamental groups, providing a multivariable extension of Alexander polynomials, and applied these methods to the study of homotopy groups of the complements to hypersurfaces in projective spaces and the topology of arrangements of hyperplanes. In the early 90s he started work on interactions between algebraic geometry and physics, providing mirror symmetry predictions for the count of rational curves on complete intersections in projective spaces and developing the theory of elliptic genus of singular algebraic varieties. References 1949 births Living people Mathematicians from Moscow Tel Aviv University alumni 20th-century American mathematicians Soviet mathematicians Columbia University faculty 21st-century American mathematicians Soviet emigrants to Israel
https://en.wikipedia.org/wiki/K-regular%20sequence
In mathematics and theoretical computer science, a k-regular sequence is a sequence satisfying linear recurrence equations that reflect the base-k representations of the integers. The class of k-regular sequences generalizes the class of k-automatic sequences to alphabets of infinite size. Definition There exist several characterizations of k-regular sequences, all of which are equivalent. Some common characterizations are as follows. For each, we take R′ to be a commutative Noetherian ring and we take R to be a ring containing R′. k-kernel Let k ≥ 2. The k-kernel of the sequence is the set of subsequences The sequence is (R′, k)-regular (often shortened to just "k-regular") if the -module generated by Kk(s) is a finitely-generated R′-module. In the special case when , the sequence is -regular if is contained in a finite-dimensional vector space over . Linear combinations A sequence s(n) is k-regular if there exists an integer E such that, for all ej > E and 0 ≤ rj ≤ kej − 1, every subsequence of s of the form s(kejn + rj) is expressible as an R′-linear combination , where cij is an integer, fij ≤ E, and 0 ≤ bij ≤ kfij − 1. Alternatively, a sequence s(n) is k-regular if there exist an integer r and subsequences s1(n), ..., sr(n) such that, for all 1 ≤ i ≤ r and 0 ≤ a ≤ k − 1, every sequence si(kn + a) in the k-kernel Kk(s) is an R′-linear combination of the subsequences si(n). Formal series Let x0, ..., xk − 1 be a set of k non-commuting variables and let τ be a map sending some natural number n to the string xa0 ... xae − 1, where the base-k representation of x is the string ae − 1...a0. Then a sequence s(n) is k-regular if and only if the formal series is -rational. Automata-theoretic The formal series definition of a k-regular sequence leads to an automaton characterization similar to Schützenberger's matrix machine. History The notion of k-regular sequences was first investigated in a pair of papers by Allouche and Shallit. Prior to this, Berstel and Reutenauer studied the theory of rational series, which is closely related to k-regular sequences. Examples Ruler sequence Let be the -adic valuation of . The ruler sequence () is -regular, and the -kernel is contained in the two-dimensional vector space generated by and the constant sequence . These basis elements lead to the recurrence relations which, along with the initial conditions and , uniquely determine the sequence. Thue–Morse sequence The Thue–Morse sequence t(n) () is the fixed point of the morphism 0 → 01, 1 → 10. It is known that the Thue–Morse sequence is 2-automatic. Thus, it is also 2-regular, and its 2-kernel consists of the subsequences and . Cantor numbers The sequence of Cantor numbers c(n) () consists of numbers whose ternary expansions contain no 1s. It is straightforward to show that and therefore the sequence of Cantor numbers is 2-regular. Similarly the Stanley sequence 0, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31, 36, 37, 39, 40, ... of number
https://en.wikipedia.org/wiki/The%20Crest%20of%20the%20Peacock
The Crest of the Peacock: Non-European Roots of Mathematics is a book authored by George Gheverghese Joseph, and was first published by Princeton University Press in 1991. The book was brought out as a response to view of the history of mathematics epitomized by Morris Kline's statement that, comparing to what the Greeks achieved, "the mathematics of Egyptians and Babylonians is the scrawling of children just learning to write, as opposed to great literature", criticised by Joseph as "Eurocentric". The third edition of the book was released in 2011. The book is divided into 11 chapters. Chapter 1 provides a lengthy justification for the book. Chapter 2 is devoted to a discussion of the mathematics of Native Americans and Chapter 3 to the mathematics of ancient Egyptians. The next two chapters consider the mathematics of Mesopotamia, then there are two chapters on Chinese mathematics, three chapters on Indian mathematics, and the final chapter discusses Islamic mathematics. Plagiarism C. K. Raju accused Joseph and Dennis Almerida of plagiarism of his decade long scholastic work that began in 1998 for the Project of History of Indian Science, Philosophy and Culture funded by the Indian Academy of Sciences concerning Indian mathematics and its possible knowledge transfer. An ethics investigation of the research team of George Gheverghese Joseph and Dennis Almeida led to the dismissal of Dennis Almeida by University of Exeter and the University of Manchester posting an erratum and acknowledgement of C.K. Raju's work. G. G. Joseph denies the charges. Reviews A review of the first edition of the book: A review of the book by European Mathematical Information Service: A review of the book by David Pingree: For a critical assessment of some of the claims and arguments of the author: References Books about the history of mathematics Eurocentrism Geocultural perspectives Ethnocentrism Books involved in plagiarism controversies 1991 non-fiction books Princeton University Press books
https://en.wikipedia.org/wiki/Subterminal%20object
In category theory, a branch of mathematics, a subterminal object is an object X of a category C with the property that every object of C has at most one morphism into X. If X is subterminal, then the pair of identity morphisms (1X, 1X) makes X into the product of X and X. If C has a terminal object 1, then an object X is subterminal if and only if it is a subobject of 1, hence the name. The category of categories with subterminal objects and functors preserving them is not accessible. References External links Category theory
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20Hermann%20Minkowski
This is a list of things named after Hermann Minkowski (1864 - 1909), German mathematician: Mathematics Brunn–Minkowski theorem Hasse–Minkowski theorem Hermite–Minkowski theorem Minkowski addition Minkowski content Minkowski distance Minkowski functional Minkowski inequality Minkowski model Minkowski plane Minkowski problem Minkowski problem for polytopes Minkowski sausage Minkowski island Minkowski snowflake Minkowski space (number field) Minkowski's bound Minkowski's first inequality for convex bodies Minkowski's question mark function Minkowski's second theorem Minkowski's theorem in geometry of numbers Minkowski–Bouligand dimension Minkowski cover Minkowski–Hlawka theorem Minkowski–Steiner formula Smith–Minkowski–Siegel mass formula M-matrices Physics Abraham–Minkowski controversy Minkowski diagram Minkowski space Minkowski superspace Other Minkowski (crater) The main-belt asteroid 12493 Minkowski The character George Minkowski, from Lost. The character Renée Minkowski, from sci-fi audiodrama podcast Wolf 359. References Minkowski
https://en.wikipedia.org/wiki/Edson%20Guti%C3%A9rrez
Edson Antonio Gutiérrez Moreno (born 19 January 1996) is a Mexican professional footballer who plays as a right-back for Liga MX club Monterrey. Career statistics Club Honours Monterrey Liga MX: Apertura 2019 Copa MX: 2019–20 CONCACAF Champions League: 2019, 2021 References External links Living people 1996 births Mexican men's footballers People from Salamanca, Guanajuato Liga MX players Men's association football midfielders Men's association football defenders Celaya F.C. footballers C.F. Monterrey players
https://en.wikipedia.org/wiki/2015%20Cura%C3%A7ao%20Sekshon%20Pag%C3%A1
Statistics from the 2015 Curaçao Sekshon Pagá: Table Regular season Kaya 6 Kaya 4 Championship match See also Curaçao League First Division References External links Main Results 2015 1 1
https://en.wikipedia.org/wiki/1948%20Czechoslovak%20First%20League
Statistics of Czechoslovak First League in the 1948 season. Overview It was contested by 14 teams, and SK Slavia Prague led the league after 13 matches. However the season was interrupted due to league reorganisation and no championship was awarded. Josef Bican was the league's top scorer with 21 goals. Stadia and locations League standings Results Top goalscorers References Czechoslovakia - List of final tables (RSSSF) Czechoslovak First League seasons Czech 1948–49 in Czechoslovak football
https://en.wikipedia.org/wiki/Clarisse%20Le%20Bihan
Clarisse Agathe Le Bihan (born 14 December 1994) is a French professional footballer who plays as a midfielder for NWSL club Angel City. Career statistics International Scores and results list France's goal tally first. Score column indicates score after each Le Bihan goal. Honours France U19 Winner UEFA Women's Under-19 Championship: 2013 References External links 1994 births Living people People from Quimperlé Footballers from Finistère Women's association football forwards French women's footballers France women's youth international footballers France women's international footballers Division 1 Féminine players National Women's Soccer League players Montpellier HSC (women) players En Avant Guingamp (women) players Angel City FC players FISU World University Games gold medalists for France Universiade medalists in football UEFA Women's Euro 2017 players French expatriate women's footballers Expatriate women's soccer players in the United States French expatriate sportspeople in the United States