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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.
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Second round
Tie played on December 2, 1971, and on December 9, 1971.
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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.
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Group B standings:
Semifinals
Tie played on March 2, 1972, and on March 9, 1972.
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Final
March 23, 1972 at Sports Palace at Yad Eliyahu in Tel Aviv, Israel.
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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.
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Top 12
Tie played on December 6, 1972, and on December 13, 1972.
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Quarterfinals
Tie played on January 10, 1973, and on January 17, 1973.
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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.
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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.
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Second round
Tie played on November 27, 1973, and on December 4, 1973.
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Top 12
Tie played on January 8, 1974, and on January 15, 1974.
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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 |
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