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https://en.wikipedia.org/wiki/Jerry%20Tamashiro
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Jerry Tamashiro (born 18 March 1971) is a former Peruvian-Japanese footballer who played as a forward.
Career statistics
Club
Notes
References
External links
Jerry Tamashiro Interview
1971 births
Living people
Peruvian men's footballers
Peru men's youth international footballers
Men's association football forwards
Major League Soccer players
Club Universitario de Deportes footballers
Carlos A. Mannucci players
Deportivo Municipal footballers
Club Alianza Lima footballers
Miami Fusion players
Juan Aurich footballers
Deportivo Coopsol players
Footballers from Lima
Peruvian people of Japanese descent
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https://en.wikipedia.org/wiki/1999%E2%80%932000%20Rochdale%20A.F.C.%20season
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The 1999–2000 Rochdale A.F.C. season was the club's 79th season in the Football League, and the 26th consecutive season in the fourth tier (League Division Three).
Statistics
|}
Competitions
Football League Third Division
FA Cup
League Cup (Worthington Cup)
League Trophy (Auto Windscreens Shield)
References
Rochdale A.F.C. seasons
1999–2000 Football League Third Division by team
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https://en.wikipedia.org/wiki/Sakuntala%20Panda
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Sakuntala Panda was an Indian writer who wrote in Odia language. She was the daughter of a very famous Mathematics teacher, Late Narayana Pati. She published 15 books of poetry, shortstories and travelogues. She also was the founder and editor of Odia women's monthly Sucharita. She was also editor of odia children's monthly Nandanakanan.
Biography
She was born on 10 November 1939 at Cuttack.
She founded a women's magazine in Odia 1975 and edited it for 28 years. She also edited a children's monthly, Nandankanan. She has published 15 books. She was a member of Odia advisory committee of the National Book Trust and the Kendra Sahitya Akademi. She was also a member of Odia Film Censor Board.
Published works
References
1939 births
2017 deaths
Women writers from Odisha
Writers from Odisha
Poets from Odisha
People from Cuttack
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https://en.wikipedia.org/wiki/Two-dimensional%20critical%20Ising%20model
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The two-dimensional critical Ising model is the critical limit of the Ising model in two dimensions. It is a two-dimensional conformal field theory whose symmetry algebra is the Virasoro algebra with the central charge .
Correlation functions of the spin and energy operators are described by the minimal model. While the minimal model has been exactly solved, see also, e.g., the article on Ising critical exponents, the solution does not cover other observables such as connectivities of clusters.
The minimal model
Space of states and conformal dimensions
The Kac table of the minimal model is:
This means that the space of states is generated by three primary states, which correspond to three primary fields or operators:
The decomposition of the space of states into irreducible representations of the product of the left- and right-moving Virasoro algebras is
where is the irreducible highest-weight representation of the Virasoro algebra with the conformal dimension .
In particular, the Ising model is diagonal and unitary.
Characters and partition function
The characters of the three representations of the Virasoro algebra that appear in the space of states are
where is the Dedekind eta function, and are theta functions of the nome , for example .
The modular S-matrix, i.e. the matrix such that , is
where the fields are ordered as .
The modular invariant partition function is
Fusion rules and operator product expansions
The fusion rules of the model are
The fusion rules are invariant under the symmetry .
The three-point structure constants are
Knowing the fusion rules and three-point structure constants, it is possible to write operator product expansions, for example
where are the conformal dimensions of the primary fields, and the omitted terms are contributions of descendant fields.
Correlation functions on the sphere
Any one-, two- and three-point function of primary fields is determined by conformal symmetry up to a multiplicative constant. This constant is set to be one for one- and two-point functions by a choice of field normalizations. The only non-trivial dynamical quantities are the three-point structure constants, which were given above in the context of operator product expansions.
with .
The three non-trivial four-point functions are of the type . For a four-point function , let and be the s- and t-channel Virasoro conformal blocks, which respectively correspond to the contributions of (and its descendants) in the operator product expansion , and of (and its descendants) in the operator product expansion . Let be the cross-ratio.
In the case of , fusion rules allow only one primary field in all channels, namely the identity field.
In the case of , fusion rules allow only the identity field in the s-channel, and the spin field in the t-channel.
In the case of , fusion rules allow two primary fields in all channels: the identity field and the energy field. In this case we write the conform
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https://en.wikipedia.org/wiki/Karl%20Broman
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Karl Broman is a professor at the University of Wisconsin–Madison (UWM) in the Biostatistics and Medical Informatics departments. He has been employed at UWM since 2007 and previously was employed at Johns Hopkins University from 1999 - 2007. Broman's original research focus was quantitative genetics, although he has also become known for his work on reproducible research. In 2016, Broman was named a Fellow of the American Statistical Association.
Research
Study of Bile Acids
In 2019 Karl Broman and a group of researchers published a study which found genetic variants in mice that impacted the bile acid levels in their guts.
Broman's other highly-cited papers include:
Broman, Karl W., et al. "Comprehensive human genetic maps: individual and sex-specific variation in recombination." The American Journal of Human Genetics 63.3 (1998): 861-869.
Broman, Karl W., et al. "R/qtl: QTL mapping in experimental crosses." Bioinformatics 19.7 (2003): 889-890.
Churchill, Gary A., et al. "The Collaborative Cross, a community resource for the genetic analysis of complex traits." Nature genetics 36.11 (2004): 1133.
Rstudio
Karl Broman created an R (programming language) package called 'R/qtlcharts'. This package is designed to interactively create visualizations of genetic data in high dimensions.
References
Year of birth missing (living people)
Living people
Johns Hopkins University alumni
University of Wisconsin–Madison faculty
R (programming language) people
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https://en.wikipedia.org/wiki/1926%E2%80%9327%20Rochdale%20A.F.C.%20season
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The 1926–27 season saw Rochdale compete for their 6th season in the Football League Third Division North.
Statistics
|}
Final league table
Competitions
Football League Third Division North
FA Cup
Lancashire Cup
Manchester Cup
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Rigidity%20%28K-theory%29
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In mathematics, rigidity of K-theory encompasses results relating algebraic K-theory of different rings.
Suslin rigidity
Suslin rigidity, named after Andrei Suslin, refers to the invariance of mod-n algebraic K-theory under the base change between two algebraically closed fields: showed that for an extension
of algebraically closed fields, and an algebraic variety X / F, there is an isomorphism
between the mod-n K-theory of coherent sheaves on X, respectively its base change to E. A textbook account of this fact in the case X = F, including the resulting computation of K-theory of algebraically closed fields in characteristic p, is in .
This result has stimulated various other papers. For example show that the base change functor for the mod-n stable A1-homotopy category
is fully faithful. A similar statement for non-commutative motives has been established by .
Gabber rigidity
Another type of rigidity relates the mod-n K-theory of an henselian ring A to the one of its residue field A/m. This rigidity result is referred to as Gabber rigidity, in view of the work of who showed that there is an isomorphism
provided that n≥1 is an integer which is invertible in A.
If n is not invertible in A, the result as above still holds, provided that K-theory is replaced by the fiber of the trace map between K-theory and topological cyclic homology. This was shown by .
Applications
used Gabber's and Suslin's rigidity result to reprove Quillen's computation of K-theory of finite fields.
References
Algebraic K-theory
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https://en.wikipedia.org/wiki/Cannon%E2%80%93Thurston%20map
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In mathematics, a Cannon–Thurston map is any of a number of continuous group-equivariant maps between the boundaries of two hyperbolic metric spaces extending a discrete isometric actions of the group on those spaces.
The notion originated from a seminal 1980s preprint of James Cannon and William Thurston "Group-invariant Peano curves" (eventually published in 2007) about fibered hyperbolic 3-manifolds.
Cannon–Thurston maps provide many natural geometric examples of space-filling curves.
History
The Cannon–Thurston map first appeared in a mid-1980s preprint of James W. Cannon and William Thurston called "Group-invariant Peano curves". The preprint remained unpublished until 2007, but in the meantime had generated numerous follow-up works by other researchers.
In their paper Cannon and Thurston considered the following situation. Let M be a closed hyperbolic 3-manifold that fibers over the circle with fiber S. Then S itself is a closed hyperbolic surface, and its universal cover can be identified with the hyperbolic plane . Similarly, the universal cover of M can be identified with the hyperbolic 3-space . The inclusion lifts to a -invariant inclusion . This inclusion is highly distorted because the action of on
is not geometrically finite.
Nevertheless, Cannon and Thurston proved that this distorted inclusion extends to a continuous -equivariant map
,
where and . Moreover, in this case the map j is surjective, so that it provides a continuous onto function from the circle onto the 2-sphere, that is, a space-filling curve.
Cannon and Thurston also explicitly described the map , via collapsing stable and unstable laminations of the monodromy pseudo-Anosov homeomorphism of S for this fibration of M. In particular, this description implies that the map j is uniformly finite-to-one, with the pre-image of every point of having cardinality at most 2g, where g is the genus of S.
After the paper of Cannon and Thurston generated a large amount of follow-up work, with other researchers analyzing the existence or non-existence of analogs of the map j in various other set-ups motivated by the Cannon–Thurston result.
Cannon–Thurston maps and Kleinian groups
Kleinian representations of surface groups
The original example of Cannon and Thurston can be thought of in terms of Kleinian representations of the surface group . As a subgroup of , the group H acts on by isometries, and this action is properly discontinuous. Thus one gets a discrete representation .
The group also acts by isometries, properly discontinuously and co-compactly, on the universal cover , with the limit set being equal to . The Cannon–Thurston result can be interpreted as saying that these actions of H on and induce a continuous H-equivariant map .
One can ask, given a hyperbolic surface S and a discrete representation , if there exists an induced continuous map .
For Kleinian representations of surface groups, the most general result in this direction is due to
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https://en.wikipedia.org/wiki/Ursescu%20theorem
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In mathematics, particularly in functional analysis and convex analysis, the Ursescu theorem is a theorem that generalizes the closed graph theorem, the open mapping theorem, and the uniform boundedness principle.
Ursescu Theorem
The following notation and notions are used, where is a set-valued function and is a non-empty subset of a topological vector space :
the affine span of is denoted by and the linear span is denoted by
denotes the algebraic interior of in
denotes the relative algebraic interior of (i.e. the algebraic interior of in ).
if is barreled for some/every while otherwise.
If is convex then it can be shown that for any if and only if the cone generated by is a barreled linear subspace of or equivalently, if and only if is a barreled linear subspace of
The domain of is
The image of is For any subset
The graph of is
is closed (respectively, convex) if the graph of is closed (resp. convex) in
Note that is convex if and only if for all and all
The inverse of is the set-valued function defined by For any subset
If is a function, then its inverse is the set-valued function obtained from canonically identifying with the set-valued function defined by
is the topological interior of with respect to where
is the interior of with respect to
Statement
Corollaries
Closed graph theorem
Uniform boundedness principle
Open mapping theorem
Additional corollaries
The following notation and notions are used for these corollaries, where is a set-valued function, is a non-empty subset of a topological vector space :
a convex series with elements of is a series of the form where all and is a series of non-negative numbers. If converges then the series is called convergent while if is bounded then the series is called bounded and b-convex.
is ideally convex if any convergent b-convex series of elements of has its sum in
is lower ideally convex if there exists a Fréchet space such that is equal to the projection onto of some ideally convex subset B of Every ideally convex set is lower ideally convex.
Related theorems
Simons' theorem
Robinson–Ursescu theorem
The implication (1) (2) in the following theorem is known as the Robinson–Ursescu theorem.
See also
Notes
References
Theorems involving convexity
Theorems in functional analysis
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https://en.wikipedia.org/wiki/Convex%20series
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In mathematics, particularly in functional analysis and convex analysis, a is a series of the form where are all elements of a topological vector space , and all are non-negative real numbers that sum to (that is, such that ).
Types of Convex series
Suppose that is a subset of and is a convex series in
If all belong to then the convex series is called a with elements of .
If the set is a (von Neumann) bounded set then the series called a .
The convex series is said to be a if the sequence of partial sums converges in to some element of which is called the .
The convex series is called if is a Cauchy series, which by definition means that the sequence of partial sums is a Cauchy sequence.
Types of subsets
Convex series allow for the definition of special types of subsets that are well-behaved and useful with very good stability properties.
If is a subset of a topological vector space then is said to be a:
if any convergent convex series with elements of has its (each) sum in
In this definition, is not required to be Hausdorff, in which case the sum may not be unique. In any such case we require that every sum belong to
or a if there exists a Fréchet space such that is equal to the projection onto (via the canonical projection) of some cs-closed subset of Every cs-closed set is lower cs-closed and every lower cs-closed set is lower ideally convex and convex (the converses are not true in general).
if any convergent b-series with elements of has its sum in
or a if there exists a Fréchet space such that is equal to the projection onto (via the canonical projection) of some ideally convex subset of Every ideally convex set is lower ideally convex. Every lower ideally convex set is convex but the converse is in general not true.
if any Cauchy convex series with elements of is convergent and its sum is in
if any Cauchy b-convex series with elements of is convergent and its sum is in
The empty set is convex, ideally convex, bcs-complete, cs-complete, and cs-closed.
Conditions (Hx) and (Hwx)
If and are topological vector spaces, is a subset of and then is said to satisfy:
: Whenever is a with elements of such that is convergent in with sum and is Cauchy, then is convergent in and its sum is such that
: Whenever is a with elements of such that is convergent in with sum and is Cauchy, then is convergent in and its sum is such that
If X is locally convex then the statement "and is Cauchy" may be removed from the definition of condition (Hwx).
Multifunctions
The following notation and notions are used, where and are multifunctions and is a non-empty subset of a topological vector space
The of is the set
is (respectively, , , , , , , ) if the same is true of the graph of in
The mulifunction is convex if and only if for all and all
The is the multifunction defined by For any subset
The is
The is For any su
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https://en.wikipedia.org/wiki/R%C3%BCdiger%20Wenzel
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Rüdiger Wenzel (born 3 June 1953) is a German retired professional footballer, who played as a forward. He scored 91 goals in 300 matches in the Bundesliga.
Career statistics
Honours
Fortuna Düsseldorf
DFB-Pokal: 1979–80
FC St. Pauli
Oberliga Nord: 1985–86
Individual
Goal of the Month: March 1989
References
External links
1953 births
Living people
Sportspeople from Lübeck
German men's footballers
Men's association football forwards
Bundesliga players
2. Bundesliga players
VfB Lübeck players
FC St. Pauli players
Eintracht Frankfurt players
Fortuna Düsseldorf players
West German men's footballers
Footballers from Schleswig-Holstein
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https://en.wikipedia.org/wiki/Projective%20tensor%20product
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In functional analysis, an area of mathematics, the projective tensor product of two locally convex topological vector spaces is a natural topological vector space structure on their tensor product. Namely, given locally convex topological vector spaces and , the projective topology, or π-topology, on is the strongest topology which makes a locally convex topological vector space such that the canonical map (from to ) is continuous. When equipped with this topology, is denoted and called the projective tensor product of and .
Definitions
Let and be locally convex topological vector spaces. Their projective tensor product is the unique locally convex topological vector space with underlying vector space having the following universal property:
For any locally convex topological vector space , if is the canonical map from the vector space of bilinear maps to the vector space of linear maps ; then the image of the restriction of to the continuous bilinear maps is the space of continuous linear maps .
When the topologies of and are induced by seminorms, the topology of is induced by seminorms constructed from those on and as follows. If is a seminorm on , and is a seminorm on , define their tensor product to be the seminorm on given by
for all in , where is the balanced convex hull of the set . The projective topology on is generated by the collection of such tensor products of the seminorms on and .
When and are normed spaces, this definition applied to the norms on and gives a norm, called the projective norm, on which generates the projective topology.
Properties
Throughout, all spaces are assumed to be locally convex. The symbol denotes the completion of the projective tensor product of and .
If and are both Hausdorff then so is ; if and are Fréchet spaces then is barelled.
For any two continuous linear operators and , their tensor product (as linear maps) is continuous.
In general, the projective tensor product does not respect subspaces (e.g. if is a vector subspace of then the TVS has in general a coarser topology than the subspace topology inherited from ).
If and are complemented subspaces of and respectively, then is a complemented vector subspace of and the projective norm on is equivalent to the projective norm on restricted to the subspace . Furthermore, if and are complemented by projections of norm 1, then is complemented by a projection of norm 1.
Let and be vector subspaces of the Banach spaces and , respectively. Then is a TVS-subspace of if and only if every bounded bilinear form on extends to a continuous bilinear form on with the same norm.
Completion
In general, the space is not complete, even if both and are complete (in fact, if and are both infinite-dimensional Banach spaces then is necessarily complete). However, can always be linearly embedded as a dense vector subspace of some complete locally convex TVS, which is generally denoted by .
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https://en.wikipedia.org/wiki/Injective%20tensor%20product
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In mathematics, the injective tensor product of two topological vector spaces (TVSs) was introduced by Alexander Grothendieck and was used by him to define nuclear spaces. An injective tensor product is in general not necessarily complete, so its completion is called the . Injective tensor products have applications outside of nuclear spaces. In particular, as described below, up to TVS-isomorphism, many TVSs that are defined for real or complex valued functions, for instance, the Schwartz space or the space of continuously differentiable functions, can be immediately extended to functions valued in a Hausdorff locally convex TVS with any need to extend definitions (such as "differentiable at a point") from real/complex-valued functions to -valued functions.
Preliminaries and notation
Throughout let and be topological vector spaces and be a linear map.
is a topological homomorphism or homomorphism, if it is linear, continuous, and is an open map, where has the subspace topology induced by
If is a subspace of then both the quotient map and the canonical injection are homomorphisms. In particular, any linear map can be canonically decomposed as follows: where defines a bijection.
The set of continuous linear maps (resp. continuous bilinear maps ) will be denoted by (resp. ) where if is the scalar field then we may instead write (resp. ).
The set of separately continuous bilinear maps (that is, continuous in each variable when the other variable is fixed) will be denoted by where if is the scalar field then we may instead write
We will denote the continuous dual space of by or and the algebraic dual space (which is the vector space of all linear functionals on whether continuous or not) by
To increase the clarity of the exposition, we use the common convention of writing elements of with a prime following the symbol (for example, denotes an element of and not, say, a derivative and the variables and need not be related in any way).
Notation for topologies
denotes the coarsest topology on making every map in continuous and or denotes endowed with this topology.
denotes weak-* topology on and or denotes endowed with this topology.
Note that every induces a map defined by is the coarsest topology on X′ making all such maps continuous.
denotes the topology of bounded convergence on and or denotes endowed with this topology.
denotes the topology of bounded convergence on or the strong dual topology on and or denotes endowed with this topology.
As usual, if is considered as a topological vector space but it has not been made clear what topology it is endowed with, then the topology will be assumed to be
denotes the Mackey topology on or the topology of uniform convergence on the convex balanced weakly compact subsets of and or denotes endowed with this topology. is the finest locally convex TVS topology on whose continuous dual space is equal to
denotes th
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https://en.wikipedia.org/wiki/The%20Mathematics%20of%20Games%20and%20Gambling
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The Mathematics of Games and Gambling is a book on probability theory and its application to games of chance. It was written by Edward Packel, and published in 1981 by the Mathematical Association of America as volume 28 of their New Mathematical Library series, with a second edition in 2006.
Topics
The book has seven chapters. Its first gives a survey of the history of gambling games in western culture, including brief biographies of two famous gamblers, Gerolamo Cardano and Fyodor Dostoevsky, and a review of the games of chance found in Dostoevsky's novel The Gambler. The next four chapters introduce the basic concepts of probability theory, including expectation, binomial distributions and compound distributions, and conditional probability, through games including roulette, keno, craps, chuck-a-luck, backgammon, and blackjack.
The sixth chapter of the book moves from probability theory to game theory, including material on tic-tac-toe, matrix representations of zero-sum games, nonzero-sum games such as the prisoner's dilemma, the concept of a Nash equilibrium, game trees, and the minimax method used by computers to play two-player strategy games.
A final chapter, "Odds and ends", includes analyses of bluffing in poker, horse racing, and lotteries.
The second edition adds material on online gambling systems, casino poker machines, and Texas hold 'em poker.
It also adds links to online versions of the games, and expands the material on game theory.
Audience and reception
The book is aimed at students, written for a general audience, and does not require any background in mathematics beyond high school algebra. However, many of its chapters include exercises, making it suitable for teaching high school or undergraduate-level courses using it. It is also suitable for readers interested in recreational mathematics. Although it could also be used to improve readers' ability at games of chance, it is not intended for that, as its overall message is that gambling games are best avoided.
Reviewer Sarah Boslaugh notes as a strength of a book the smooth interplay between its mathematical content and the context of the games it describes. Despite noting that the book's description of modern games is based on American practice, and doesn't address the way those games differ in Britain, reviewer Stephen Ainley calls the book "very enjoyable", adding that "it is hard to see how it could be done better or more readably". Reviewer J. Wade Davis calls it "accessible and very entertaining".
Recognition
The Basic Library List Committee of the Mathematical Association of America has listed this book as essential for inclusion in undergraduate mathematics libraries. It was the 1986 winner of the Beckenbach Book Prize.
References
Games of chance
Probability theory
Mathematics books
1981 non-fiction books
2006 non-fiction books
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https://en.wikipedia.org/wiki/1927%E2%80%9328%20Rochdale%20A.F.C.%20season
|
The 1927–28 season saw Rochdale compete for their 7th season in the Football League Third Division North.
Statistics
|}
Final league table
Competitions
Football League Third Division North
FA Cup
Lancashire Cup
Manchester Cup
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Thermodynamics%20and%20an%20Introduction%20to%20Thermostatistics
|
Thermodynamics and an Introduction to Thermostatistics is a textbook written by Herbert Callen that explains the basics of classical thermodynamics and discusses advanced topics in both classical and quantum frameworks. It covers the subject in an abstract and rigorous manner and contains discussions of applications. The textbook contains three parts, each building upon the previous. The first edition was published in 1960 and a second followed in 1985.
Overview
The first part of the book starts by presenting the problem thermodynamics is trying to solve, and provides the postulates on which thermodynamics is founded. It then develops upon this foundation to discuss reversible processes, heat engines, thermodynamics potentials, Maxwell's relations, stability of thermodynamics systems, and first-order phase transitions. As the author lays down the basics of thermodynamics, he then goes to discuss more advanced topics such as critical phenomena and irreversible processes.
The second part of the text presents the foundations of classical statistical mechanics. The concept of Boltzmann's entropy is introduced and used to describe the Einstein model, the two-state system, and the polymer model. Afterwards, the different statistical ensembles are discussed from which the thermodynamics potentials are derived. Quantum fluids and fluctuations are also discussed.
The last part of the text is a brief discussion on symmetry and the conceptual foundations of thermostatistics. In the final chapter, Callen advances his thesis that the symmetries of the fundamental laws of physics underlie the very foundations of thermodynamics and seeks to illuminate the crucial role thermodynamics plays in science.
Callen advises that a one-semester course for advanced undergraduates should cover the first seven chapters plus chapters 15 and 16 if time permits.
Second edition
Background
The second edition provides a descriptive account of the thermodynamics of critical phenomena, which progressed dramatically in the 1960s and 1970s. Drawing on feedback from students and instructors, Callen improved many explanations, explicitly solved examples, and added many exercises, many of which have complete or partial answers. He also provided an introduction to statistical mechanics with an emphasis on the core principles rather than the applications. However, he sought to neither separate thermodynamics and statistical mechanics completely nor subsume the former under the latter under the banner of "thermal physics." Indeed, thermal physics courses often emphasizes statistical mechanics at the expense of thermodynamics, despite its importance for industry, as a survey of business leaders conducted by the American Physical Society in 1971 suggested. Callen observed that thermodynamics had subsequently been de-emphasized.
Table of Contents
Part I: General Principles of Classical Thermodynamics
Introduction: The Nature of Thermodynamics and the Basis of Thermostatistics
C
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https://en.wikipedia.org/wiki/Ring%20lemma
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In the geometry of circle packings in the Euclidean plane, the ring lemma gives a lower bound on the sizes of adjacent circles in a circle packing.
Statement
The lemma states: Let be any integer greater than or equal to three. Suppose that the unit circle is surrounded by a ring of interior-disjoint circles, all tangent to it, with consecutive circles in the ring tangent to each other. Then the minimum radius of any circle in the ring is at least the unit fraction
where is the th Fibonacci number.
The sequence of minimum radii, from , begins
Generalizations to three-dimensional space are also known.
Construction
An infinite sequence of circles can be constructed, containing rings for each that exactly meet the bound of the ring lemma, showing that it is tight. The construction allows halfplanes to be considered as degenerate circles with infinite radius, and includes additional tangencies between the circles beyond those required in the statement of the lemma. It begins by sandwiching the unit circle between two parallel halfplanes; in the geometry of circles, these are considered to be tangent to each other at the point at infinity. Each successive circle after these first two is tangent to the central unit circle and to the two most recently added circles; see the illustration for the first six circles (including the two halfplanes) constructed in this way. The first circles of this construction form a ring, whose minimum radius can be calculated by Descartes' theorem to be the same as the radius specified in the ring lemma. This construction can be perturbed to a ring of finite circles, without additional tangencies, whose minimum radius is arbitrarily close to this bound.
History
A version of the ring lemma with a weaker bound was first proven by Burton Rodin and Dennis Sullivan as part of their proof of William Thurston's conjecture that circle packings can be used to approximate conformal maps. Lowell Hansen gave a recurrence relation for the tightest possible lower bound, and Dov Aharonov found a closed-form expression for the same bound.
Applications
Beyond its original application to conformal mapping, the circle packing theorem and the ring lemma play key roles in a proof by Keszegh, Pach, and Pálvölgyi that planar graphs of bounded degree can be drawn with bounded slope number.
References
Circle packing
Lemmas
Fibonacci numbers
Geometric inequalities
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https://en.wikipedia.org/wiki/List%20of%20Melbourne%20City%20FC%20%28A-League%20Women%29%20records%20and%20statistics
|
Melbourne City Women Football Club is an Australian professional soccer club based in Bundoora, Melbourne. The club was formed in 2015.
The list encompasses the honours won by Melbourne City Women. The player records section itemises the club's leading goalscorers and those who have made the most appearances in first-team competitions.
All figures are correct as of the match played on 22 March 2020.
Honours and achievements
W-League and Finals
W-League Premiership
Winners (2): 2015–16, 2019–20
W-League Championship
Winners (4): 2016, 2017, 2018, 2020
Player records
Appearances
Most league appearances: Steph Catley and Rebekah Stott, 62
Youngest first-team player: Lia Muldeary, 15 years, 112 days (against Newcastle Jets, W-League, 12 November 2017)
Oldest first-team player: Melissa Barbieri, 37 years, 271 days (against Sydney FC, W-League, 18 November 2017)
Most consecutive appearances: Lauren Barnes, 46 (from 8 January 2017 to 22 March 2020)
Most appearances
Competitive matches only, includes appearances as substitute. Numbers in brackets indicate goals scored.
Goalscorers
Youngest goalscorer: Melina Ayres, 16 years, 188 days (against Sydney FC, W-League, 18 October 2015)
Oldest goalscorer: Yukari Kinga, 35 years, 224 days (against Melbourne Victory, W-League, 12 December 2019)
Top goalscorers
Competitive matches only. Numbers in brackets indicate appearances made.
Managerial records
Club records
Matches
Firsts
First match: Sydney FC 0–6 Melbourne City, W-League, 18 October 2015
First home match at AAMI Park: Melbourne City 2–1 Melbourne Victory, W-League, 25 October 2015
First home match at CB Smith Reserve: Melbourne City 2–0 Adelaide United, W-League, 14 November 2015
Record wins
Record league win: 6–0 against Sydney FC, W-League, 18 October 2015
Record defeats
Record league defeat:
1–4 against Perth Glory, W-League, 27 October 2017
2–5 against Perth Glory, W-League, 25 November 2018
Record consecutive results
Record consecutive wins: 18, from 18 October 2015 to 4 December 2016
Record consecutive league wins: 18, from 18 October 2016 to 4 December 2016
Record consecutive defeats: 3, from 10 December 2016 to 27 December 2016
Record consecutive league defeats: 3, from 10 December 2016 to 27 December 2016
Record consecutive matches without a defeat: 18, from 18 October 2015 to 4 December 2016
Record consecutive league matches without a defeat: 18, from 18 October 2015 to 4 December 2016
Record consecutive matches without a win: 6, from 10 December 2016 to 15 January 2017
Record consecutive league matches without a win: 6, from 10 December 2016 to 15 January 2017
Goals
Most league goals scored in a season: 38 in 12 matches, W-League, 2015–16
Fewest league goals scored in a season: 19 in 12 matches, W-League, 2016–17
Most league goals conceded in a season: 15
in 12 matches, W-League, 2017–18
in 12 matches, W-League, 2018–19
Fewest league goals conceded in a season: 4
in 12 matches, W-League, 2015–16
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https://en.wikipedia.org/wiki/1928%E2%80%9329%20Rochdale%20A.F.C.%20season
|
The 1928–29 season saw Rochdale compete for their 8th season in the Football League Third Division North.
Statistics
|}
Final league table
Competitions
Football League Third Division North
FA Cup
Lancashire Cup
Manchester Cup
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/List%20of%20Adelaide%20United%20FC%20%28W-League%29%20records%20and%20statistics
|
Adelaide United Women Football Club is an Australian professional women's soccer club based in Hindmarsh, Adelaide. The club was formed in 2008.
The list encompasses the honours won by Adelaide United Women. The player records section itemises the club's leading goalscorers and those who have made the most appearances in first-team competitions.
All figures are correct as of the match played on 27 February 2020.
Player records
Appearances
Most league appearances: Racheal Quigley, 66
Youngest first-team player: Emily Condon, 15 years, 126 days (against Canberra United, W-League, 5 January 2014)
Oldest first-team player: Kristy Moore, 37 years, 305 days (against Newcastle Jets, W-League, 29 November 2014)
Most consecutive appearances: Georgia Campagnale, 41 (from 17 October 2015 to 1 December 2018)
Most appearances
Competitive matches only, includes appearances as substitute. Numbers in brackets indicate goals scored.
Goalscorers
Most goals in a season: 9
Adriana Jones (in the 2016–17 and 2018–19)
Youngest goalscorer: Emily Condon, 15 years, 132 days
Oldest goalscorer: Kristy Moore, 37 years 270 days
Top goalscorers
Competitive matches only. Numbers in brackets indicate appearances made
Managerial records
Club records
Matches
Firsts
First match: Queensland Roar 4–1 Adelaide United, W-League, 25 October 2008
First home match at Hindmarsh: Adelaide United 3–2 Newcastle Jets, W-League, 31 October 2008
First home match at Marden Sports Complex: Adelaide United 3–1 Newcastle Jets, W-League, 10 November 2007
Record wins
Record league win: 10–2 against Western Sydney Wanderers, W-League, 14 January 2017
Record defeats
Record league defeat:
0–6 against Central Coast Mariners, W-League, 6 December 2008
0–6 against Sydney FC, W-League, 11 November 2009
0–6 against Central Coast Mariners, W-League, 14 November 2009
1–7 against Newcastle Jets, W-League, 8 January 2011
Record consecutive results
Record consecutive wins: 3
from 19 October 2014 to 29 October 2014
from 14 January 2017 to 29 January 2017
Record consecutive league wins: 3
from 19 October 2014 to 29 October 2014
from 14 January 2017 to 29 January 2017
Record consecutive defeats: 19, from 28 November 2009 to 10 December 2011
Record consecutive league defeats: 19, from 28 November 2009 to 10 December 2011
Record consecutive matches without a defeat: 7, from 2 February 2018 to 6 December 2018
Record consecutive league matches without a defeat: 7, from 2 February 2018 to 6 December 2018
Record consecutive matches without a win: 34, from 15 November 2008 to 10 December 2011
Record consecutive league matches without a win: 34, from 15 November 2008 to 10 December 2011
Goals
Most league goals scored in a season: 31 in 12 matches, W-League, 2016–17
Fewest league goals scored in a season: 4 in 10 matches, W-League, 2010–11
Most league goals conceded in a season: 40 in 12 matches, W-League, 2012–13
Fewest league goals conceded in a season: 12 in 12 matches, W-L
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https://en.wikipedia.org/wiki/Stratified%20randomization
|
In statistics, stratified randomization is a method of sampling which first stratifies the whole study population into subgroups with same attributes or characteristics, known as strata, then followed by simple random sampling from the stratified groups, where each element within the same subgroup are selected unbiasedly during any stage of the sampling process, randomly and entirely by chance. Stratified randomization is considered a subdivision of stratified sampling, and should be adopted when shared attributes exist partially and vary widely between subgroups of the investigated population, so that they require special considerations or clear distinctions during sampling. This sampling method should be distinguished from cluster sampling, where a simple random sample of several entire clusters is selected to represent the whole population, or stratified systematic sampling, where a systematic sampling is carried out after the stratification process. Stratified random sampling is sometimes also known as "quota random sampling".
Steps for stratified random sampling
Stratified randomization is extremely useful when the target population is heterogeneous and effectively displays how the trends or characteristics under study differ between strata. When performing a stratified randomization, the following 8 steps should be taken:
Define a target population.
Define stratification variables and decide the number of strata to be created. The criteria for defining variables for stratification include age, socioeconomic status, nationality, race, education level and others and should be in line with the research objective. Ideally, 4-6 strata should be employed, as any increase in stratification variables will raise the probability for some of them to cancel out the impact of other variables.
Use a sampling frame to evaluate all the elements in the target population. Make changes afterwards based on coverage and grouping.
List all the elements and consider the sampling result. Each stratum should be mutually exclusive and add up to cover all members of the population, whilst each member of the population should fall into unique stratum, along with other members with minimum differences.
Make decisions over the random sampling selection criteria. This can be done manually or with a designed computer program.
Assign a random and unique number to all the elements followed by sorting these elements according to their number assigned.
Review the size of each stratum and numerical distribution of all elements in every strata. Determine the type of sampling, either proportional or disproportional stratified sampling.
Carry out the selected random sampling as defined in step 5. At minimum, one element must be chosen from each stratum so that the final sample includes representatives from every stratum. If two or more elements from each stratum are selected, error margins of the collected data can be calculated.
Stratified random assignment
Stratifi
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https://en.wikipedia.org/wiki/Group%20algebra
|
In mathematics, the group algebra can mean either
A group ring of a group over some ring.
A group algebra of a locally compact group.
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https://en.wikipedia.org/wiki/United%20States%20influenza%20statistics%20by%20flu%20season
|
US influenza statistics by flu season. From the Centers for Disease Control and Prevention page called "Disease Burden of Flu":
"Each year CDC estimates the burden of influenza in the U.S. CDC uses modeling to estimate the number of flu illnesses, medical visits, hospitalizations, and deaths related to flu that occurred in a given season. The methods used to calculate these estimates are described on CDC’s webpage, How CDC Estimates the Burden of Seasonal Flu in the U.S."
The tables below include the latest available years the CDC has provided on their website.
Hospitalizations and deaths
UI = uncertainty interval.
Row numbers are static. Other columns are sortable. This allows ranking of any column.
* 2019 to 2020 season is a preliminary estimate.
Symptomatic illnesses and medical visits
UI = uncertainty interval.
Row numbers are static. Other columns are sortable. This allows ranking of any column.
* 2019 to 2020 season is a preliminary estimate.
See also
Influenza pandemic
2009 swine flu pandemic
COVID-19 pandemic in the United States. Statistics section.
COVID-19 pandemic by country and territory. Flu statistics are often compared to coronavirus statistics.
COVID-19 pandemic cases. More statistics for comparison purposes.
COVID-19 pandemic deaths. More statistics for comparison purposes.
Influenza vaccine
Bird flu
Human flu
Swine flu
Horse flu
Dog flu
Freshers' flu
2012–2013 flu season
2017–2018 United States flu season
2019–2020 United States flu season
References
External links
United States
Disease outbreaks in the United States
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https://en.wikipedia.org/wiki/Government%20Degree%20College%20Phool%20Nagar
|
Government Associate College Phool Nagar is located in Phool Nagar, Punjab, Pakistan. It was established on 1 September 1974 and offers courses in mathematics, sciences, computer science, languages and history. A library was established in the college on 1 September 1989. The college was nationalized during the government of Pakistan Prime Minister Zulfikar Ali Bhutto.
Principal and vice principal
The current principal of the college is Rao Abdul Waheed Tabish (2017 to onwards). The vice principal is Abdul Ghani.
Departments
Following is the details of departments in Govt. Degree College Phool Nagar.
Department Of Mathematics
CTI
Department Of Statistics
Professor Mudassar Hussain (M.Phil Statistics)
Department Of Chemistry
Professor Usman Arshad (M.Phil Chemistry)
Department Of Biology
CTI
Department Of Physics
Professor Munir Ahmed (M.Phil Physics)
Department Of Psychology
Professor Abdul Waheed Tabish (M.Phil Psychology)
Department Of Islamiat
Professor Muhammad Zikriya M.Phil(Islamiat), PhD Scholar, MA(Education), MA(Arabic)
Dr.Muhammad Mansha Tayyab Ph.D Islamic Studies ,M.A (Arabic)
Department Of Urdu
Professor Rao Akbar Ali M.Phil(Urdu)
Department Of Education
CTI
Department Of English
Professor Habibullah
Naveed Ahmed
Department Of History
Professor Saleem Akhtar MA(Political Science)
Department Of Political Science
CTI
Department Of Sociology
CTI
Department Of Arabic
Professor Dr. Hafiz Abdul Ghani PhD(Islamiat)
Department Of Physical Education
Ali Yousaf
Department Of Economics
Professor Atif Javaid Rao M.Phil(Economics)
Professor Fahad Iqbal MA(Economics)
Department Of Library Science
Janaab Zahid Nawab MA(Library Science)
Teaching Subjects For Examination Of Intermediate
Compulsory Subjects:-
1- Urdu 2- English 3-Islamiat(Compulsory) 4- Pakistan Studies
Elective Subjects:-
Pre-Medical Group:-
1- Chemistry 2- Physics 3- Biology
Pre-Engineering Group
1- Chemistry 2- Physics 3- Mathematic
ICS
You have to select one of the following groups
G-1 Physics, Computer Science, Mathematic
G-2 Economics, Computer Science, Mathematic
G-3 Statistics, Computer Science, Mathematic
General Science Group:-
You have to select one of the following groups
G-1 Economica, Statistics, Mathematics
G-2 Physics, Statistics, Mathematics
I.Com:-
Accounting, Principle of Economics, Principle of Commerce, Business Math
Humanities Group:-
You have to select one of the following groups
G-1 Psychology, Sociology, Economics, History of Pakistan
G-2 Physical Education, Civics, Education
G-3 Library Science, Arabic, Islamiyat (Elective)
See also
Superior Group of Colleges
Punjab Group of Colleges
References
https://m.facebook.com/pages/category/Education/Government-Degree-College-for-Boys-Phool-Nagar-Kasur-949829955165596/
https://www.google.com/maps/place/Govt+Boys+College+Phool+Nagar,+Lahore,+Kasur,+Punjab,+Pakistan/@31.2158845,73.9357567,15z/data=!4m2!3m1!1s0x39185c7603b0b351:0x95f8b2703f6fc526?gl=pk
Scho
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https://en.wikipedia.org/wiki/Gentjan%20%C3%87o%C3%A7ja
|
Gentian Çoçja (born 18 March 1974) is an Albanian former footballer.
International statistics
References
1974 births
Living people
Albanian men's footballers
Albania men's international footballers
Men's association football midfielders
KF Vllaznia Shkodër players
Kategoria Superiore players
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https://en.wikipedia.org/wiki/A%20History%20of%20Folding%20in%20Mathematics
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A History of Folding in Mathematics: Mathematizing the Margins is a book in the history of mathematics on the mathematics of paper folding. It was written by Michael Friedman and published in 2018 by Birkhäuser as volume 59 of their Historical Studies series.
Topics
The book consists of six chapters, the first of which introduces the problem, sets it in the context of the investigation of the mathematical strength of straightedge and compass constructions, and introduces one of the major themes of the book, the relegation of paper folding to recreational mathematics as this sort of investigation fell out of favor among professional mathematicians, and its more recent resurrection as a serious topic of investigation. As a work of history, the book follows Hans-Jörg Rheinberger in making a distinction between epistemic objects, the not-yet-fully-defined subjects of scientific investigation,
and technical objects, the tools used in these investigations, and it links the perceived technicality of folding with its fall from mathematical favor.
The remaining chapters are organized chronologically, beginning in the 16th century and the second chapter. This chapter includes the work of Albrecht Dürer on polyhedral nets, arrangements of polygons in the plane that can be folded to form a given polyhedron, and of Luca Pacioli on the use of folding to replace the compass and straightedge in geometric constructions; it also discusses the history of paper, and paper folding in the context of bookbinding. The third chapter discusses the confluence of Arabic and European mathematics, into the 18th century, with topics including the symmetries of folded objects and the attempted use of folding to prove the parallel postulate. Although Eugenio Beltrami continued to use folded models to investigate non-Euclidean geometry into the 19th century, the fourth chapter of the book argues that other 19th-century uses of folding were more pedagogical, including the use of folded models to demonstrate mathematical concepts, their applications in chemistry, and the introduction of folding into kindergarten programs by Friedrich Fröbel. The late 19th century also saw the publication in India and then the west of the book Geometric Exercises in Paper Folding, by T. Sundara Row.
The final two chapters concern the 20th century and current topics of research in this area. They include work on formalizing paper folding as a form of axiomatic geometry beginning with Margherita Piazzola Beloch, the work of Wilhelm Ahrens in recreational mathematics, and the community of mathematical researchers coming together through the series of International Meetings of Origami Science and Technology (now known as the International Conference on Origami in Science, Math, and Education), and through works popularizing this area within mathematics such as the book Geometric Folding Algorithms by Erik Demaine and Joseph O'Rourke. Appendices include a translation of Beloch's work in this area, and
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https://en.wikipedia.org/wiki/1929%E2%80%9330%20Rochdale%20A.F.C.%20season
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The 1929–30 season saw Rochdale compete for their 9th season in the Football League Third Division North.
Statistics
|}
Final league table
Competitions
Football League Third Division North
FA Cup
Lancashire Cup
Manchester Cup
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/ILAS%20%28disambiguation%29
|
ILAS, ilas or variant, may refer to:
International Linear Algebra Society
Ilas, a barrio in Dao, Capiz, Philippines, composed of Ilas Sur and Ilas Norte
ILAS Air (ICAO airline code: ILC), see List of airline codes (I)
See also
ila (disambiguation)
isla (disambiguation)
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https://en.wikipedia.org/wiki/Juan%20Flores%20%28footballer%2C%20born%201964%29
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Juan Alberto Flores Maradiaga (born 8 March 1964) is a Honduran former football player.
Career statistics
Club
Notes
International
International goals
Scores and results list Honduras' goal tally first.
References
1964 births
Living people
Honduran men's footballers
Honduran expatriate men's footballers
Honduras men's international footballers
Men's association football forwards
Honduran football managers
C.D. Olimpia players
Santos Laguna footballers
Honduran expatriate sportspeople in Mexico
Expatriate men's footballers in Mexico
Liga MX players
People from Atlántida Department
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https://en.wikipedia.org/wiki/Andr%C3%A9s%20Catal%C3%A1n
|
Andrés Didyer Catalán Guemes (born 20 August 2000) is a Mexican professional footballer who plays as a defender.
Career statistics
Club
Honours
Mexico U17
CONCACAF U-17 Championship: 2017
References
2000 births
Living people
Mexico men's youth international footballers
Men's association football defenders
Atlético Morelia players
Liga Premier de México players
Liga MX players
Sportspeople from Cuernavaca
Footballers from Morelos
Mexican men's footballers
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https://en.wikipedia.org/wiki/Chisom%20Orji
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Chisom Martins Orji (born 5 April 2001) is a Nigerian international footballer who currently plays as a forward.
Career statistics
International
References
2001 births
Living people
Nigerian men's footballers
Nigeria men's international footballers
Men's association football forwards
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https://en.wikipedia.org/wiki/Remote%20point
|
In general topology, a remote point is a point that belongs to the Stone–Čech compactification of a Tychonoff space but that does not belong to the topological closure within of any nowhere dense subset of .
Let be the real line with the standard topology. In 1962, Nathan Fine and Leonard Gillman proved that, assuming the continuum hypothesis:
Their proof works for any Tychonoff space that is separable and not pseudocompact.
Chae and Smith proved that the existence of remote points is independent, in terms of Zermelo–Fraenkel set theory, of the continuum hypothesis for a class of topological spaces that includes metric spaces. Several other mathematical theorems have been proved concerning remote points.
References
General topology
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https://en.wikipedia.org/wiki/Roderick%20Reid
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Roderick Reid (born 10 January 1970) is a former Jamaican international footballer.
Career statistics
International
International goals
Scores and results list Jamaica's goal tally first.
References
1970 births
Living people
Jamaican men's footballers
Jamaica men's international footballers
Men's association football midfielders
Men's association football forwards
1991 CONCACAF Gold Cup players
1993 CONCACAF Gold Cup players
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https://en.wikipedia.org/wiki/1930%E2%80%9331%20Rochdale%20A.F.C.%20season
|
The 1930–31 season saw Rochdale compete for their 10th season in the Football League Third Division North.
Statistics
|}
Final league table
Competitions
Football League Third Division North
FA Cup
Lancashire Cup
Manchester Cup
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Dominique%20Haughton
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Dominique Marie-Annick Haughton is a French statistician whose research interests include business analytics, standards of living, and applications of statistics to music. She is a professor of mathematical sciences at Bentley University. She is also an associated researcher with the research center on Statistique, Analyse et Modélisation Multidisciplinaire at the University of Paris 1 Pantheon-Sorbonne.
Education and career
After studying for the baccalauréat at the Lycée Pierre de la Ramée in Saint-Quentin, in Northern France, and continued study at the Lycée privé Sainte-Geneviève, Haughton entered the Ecole Normale Supérieure in Paris in 1975, where she earned a master's degree in mathematics in 1976, a licenciate in English in 1977, and a Diplôme d'études approfondies in mathematics in 1977. After a year at Harvard University as a Sachs scholar, she entered the Ph.D. program at the Massachusetts Institute of Technology, and completed a Ph.D. in mathematics in 1983. Her dissertation, On the Choice of a Model to Fit Data from an Exponential Family, was supervised by Richard M. Dudley.
After working as an assistant professor at Swarthmore College, Temple University, and the University of Lowell, she joined the Bentley University faculty in 1991.
Books
Haughton is the co-author, with Mark-David McLaughlin, Kevin Mentzer, and Changan Zhang, of the book Movie Analytics: A Hollywood Introduction to Big Data (Springer, 2015). She is also the coauthor, with Jonathan Haughton, of Living Standards Analytics: Development through the Lens of Household Survey Data (Springer, 2011).
Recognition
Haughton was named a Fellow of the American Statistical Association in 2011 "for outstanding collaborative research, outreach, and training in business analytics; for analysis of international living standards data; and for service to the profession".
References
External links
Home page
Year of birth missing (living people)
Living people
American statisticians
French statisticians
Women statisticians
Massachusetts Institute of Technology School of Science alumni
Swarthmore College faculty
Temple University faculty
University of Massachusetts Lowell faculty
Bentley University faculty
Fellows of the American Statistical Association
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https://en.wikipedia.org/wiki/Emiliano%20Garc%C3%ADa
|
Emiliano García Escudero (born 25 November 2003) is a Mexican professional footballer who plays as a forward for Liga MX club Puebla.
Career statistics
Club
References
2003 births
Living people
Mexican men's footballers
Mexico men's youth international footballers
Spanish men's footballers
Men's association football forwards
Liga MX players
Club Puebla players
Villarreal CF players
Footballers from Mexico City
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https://en.wikipedia.org/wiki/Introduction%20to%203-Manifolds
|
Introduction to 3-Manifolds is a mathematics book on low-dimensional topology. It was written by Jennifer Schultens and published by the American Mathematical Society in 2014 as volume 151 of their book series Graduate Studies in Mathematics.
Topics
A manifold is a space whose topology, near any of its points, is the same as the topology near a point of a Euclidean space; however, its global structure may be non-Euclidean. Familiar examples of two-dimensional manifolds include the sphere, torus, and Klein bottle; this book concentrates on three-dimensional manifolds, and on two-dimensional surfaces within them. A particular focus is a Heegaard splitting, a two-dimensional surface that partitions a 3-manifold into two handlebodies. It aims to present the main ideas of this area, but does not include detailed proofs for many of the results that it states, in many cases because these proofs are long and technical.
The book has seven chapters. The first two are introductory, providing material about manifolds in general, the Hauptvermutung proving the existence and equivalence of triangulations for low-dimensional manifolds, the classification of two-dimensional surfaces, covering spaces, and the mapping class group. The third chapter begins the book's material on 3-manifolds, and
on the decomposition of manifolds into smaller spaces by cutting them along surfaces. For instance, the three-dimensional Schoenflies theorem states that cutting Euclidean space by a sphere can only produce two topological balls; an analogous theorem of J. W. Alexander states that at least one side of any torus in Euclidean space must be a solid torus. However, for more complicated manifolds, cutting along incompressible surfaces can be used to construct the JSJ decomposition of a manifold. This chapter also includes material on Seifert fiber spaces. Chapter four concerns knot theory, knot invariants, thin position, and the relation between knots and their invariants to manifolds via knot complements, the subspaces of Euclidean space on the other sides of tori.
Reviewer Bruno Zimmermann calls chapters 5 and 6 "the heart of the book", although reviewer Michael Berg disagrees, viewing chapter 4 on knot theory as more central. Chapter 5 discusses normal surfaces, surfaces that intersect the tetrahedra of a triangulation of a manifold in a controlled way. By parameterizing these surfaces by how many pieces of each possible type they can have within each tetrahedron of a triangulation, one can reduce many questions about manifolds such as the recognition of trivial knots and trivial manifolds to questions in number theory, on the existence of solutions to certain Diophantine equations. The book uses this tool to prove the existence and uniqueness of prime decompositions of manifolds. Chapter 6 concerns Heegaard splittings, surfaces which split a given manifold into two handlebodies. It includes the theorem of Reidemeister and Singer on common refinements ("stabilizations") o
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https://en.wikipedia.org/wiki/Lori%20Thombs
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Lori A. Thombs is an American statistician whose interests include social statistics, time series, and resampling. She is an associate professor of statistics at the University of Missouri, where she directs the Social Science Statistics Center, and president of the Southern Regional Council On Statistics.
Education and career
Thombs is a 1981 graduate of Baylor University, and completed a Ph.D. in statistics at Southern Methodist University in 1985. Her dissertation, Bootstrap Prediction Intervals for Autoregression, was supervised by William R. Schucany.
She joined the statistics department at the University of South Carolina, in Columbia, South Carolina, in 1985, and moved to the University of Missouri, in Columbia, Missouri, in 2003.
She was elected president of the Southern Regional Council On Statistics in 2018.
Books
Thombs is a coauthor, with Don Edwards and John D. Spurrier, of the books Elementary Statistics Laboratory Manual (in two versions, Wadsworth, 1995) and Statistics: Learning by Doing (Whittier, 1999). She is a coeditor, with Stanislav Kolenikov and Douglas Steinle, of Statistics in the Social Sciences: Current Methodological Developments (Wiley, 2010).
Recognition
Thombs was named a Fellow of the American Statistical Association in 2011.
References
External links
Home page
Year of birth missing (living people)
Living people
American statisticians
Women statisticians
Baylor University alumni
Southern Methodist University alumni
University of South Carolina faculty
University of Missouri faculty
Fellows of the American Statistical Association
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https://en.wikipedia.org/wiki/Pamela%20Liebeck
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Pamela Liebeck (née Lawrence, 1930–2012) was a British mathematician and mathematics educator, the author of two books on mathematics.
Life
Liebeck was born in Bromley on 11 July 1930, grew up in Surrey, and read mathematics at Somerville College, Oxford beginning in 1949. At Oxford, she also played on the cricket and tennis teams. After additional study at the University of Cambridge, she became a mathematics teacher. Her husband Hans Liebeck was also an Oxford mathematics student; they met through a shared love of playing chamber music, married in 1953, and moved together to Cape Town University in South Africa in 1955, where Liebeck taught mathematics part-time while raising two children and studying music.
In 1961, Liebeck and her husband returned to England. As their (now three) children grew old enough, she returned to teaching, first at the Madeley College of Education in Newcastle-under-Lyme (eventually part of Staffordshire University) and then at Keele University, where her husband had been posted since their return to England.
Her son, Martin W. Liebeck, became a mathematics professor at Imperial College London.
She died on 3 July 2012.
Books
Liebeck wrote two books on mathematics:
Vectors and Matrices (Pergamon, 1971)
How Children Learn Mathematics: A Guide for Parents and Teachers (Penguin, 1984)
References
External links
How Children Learn Mathematics at the Internet Archive
Vectors and Matrices at the Internet Archive
1930 births
2012 deaths
British mathematicians
British women mathematicians
Mathematics educators
Alumni of Somerville College, Oxford
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https://en.wikipedia.org/wiki/Ars%20Magnesia
|
Ars Magnesia (The Magnetic Art) was a book on magnetism by the Jesuit scholar Athanasius Kircher in 1631. It was his first published work, written while he was professor of ethics and mathematics, Hebrew and Syriac at the University of Würzburg. It was published in Würzburg by Elias Michael Zink.
Ideas discussed
The work is a 48-page pamphlet that appears to be a printed version of a lecture he had given some years previously while teaching at the Jesuit seminary in Heiligenstadt. It is a mixture of descriptions of Kircher’s own experiments and accounts drawn from classical authorities. He describes his own attempts to measure the force of a magnet by using a balance, relates how an eruption of Vesuvius caused magnetic needles to change direction, and wonders that a red-hot piece of iron is attracted by a magnet, although the magnet is not attracted by it. He also suggested that magnetism could serve as a basis for long-distance communication. He cited the works of Pliny and Plutarch and suggested conserving a magnet’s strength by wrapping it in dried woad leaves. He warned that leaving a magnet near a diamond or rubbing it with garlic would weaken it, but its strength could be regained by pouring boar’s blood over it.
Ars Magnesia also discussed how the powers of magnetism could be used to illustrate the miracles of the Bible. Years later in Rome, Kircher built machinery to demonstrate his propositions, allowing him to stage Jonah being swallowed by a whale by means of magnetism. He also constructed a glass sphere half-filled with water, containing a model of St. Peter with a magnet inside it, and another of Jesus with steel inside it, which could re-enact Jesus saving Peter as he walked on water.
To conclude, Kircher explained how the power of the magnet symbolized the divine authority of the Holy Trinity, the secular authority of an emperor, king, and prince, and the spiritual authority of priest, bishop, and preacher.
Later works on magnetism
Robert Boyle later wrote of magnetism that “the ingenious Kircher hath so largely prosecuted it in his voluminous Ars Magnetica (sic), yet he has not reaped his field so clean, but that a careful gleaner, may still find ears enough to make some sheaves.” Kircher returned to the subject of magnetism several times in his later studies, publishing Magnes sive de Arte Magnetica (1641) and Magneticum Naturae regnum (1667).
References
Magnetism
1631 in science
1631 books
Athanasius Kircher
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https://en.wikipedia.org/wiki/Franco%20Ayunta
|
Franco Ayunta (born 29 November 2002) is an Argentine footballer currently playing as a forward for Temperley.
Career statistics
Club
References
2002 births
Living people
Argentine men's footballers
Men's association football forwards
Primera Nacional players
Club Atlético Temperley footballers
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https://en.wikipedia.org/wiki/Andrey%20Soto
|
Andrey Josué Soto Ruiz (born 8 April 2003) is a Costa Rican footballer who currently plays as a midfielder for San Carlos.
Career statistics
Club
Notes
References
2003 births
Living people
Costa Rican men's footballers
Costa Rica men's youth international footballers
Men's association football forwards
A.D. San Carlos footballers
Liga FPD players
People from San Carlos (canton)
Sportspeople from Alajuela Province
21st-century Costa Rican people
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https://en.wikipedia.org/wiki/David%20Pech
|
David Pech (born 22 February 2002) is a Czech footballer who currently plays as a midfielder for Slavia Prague.
Career statistics
Club
Notes
References
External links
2002 births
Living people
Czech men's footballers
Czech Republic men's youth international footballers
Men's association football midfielders
FK Mladá Boleslav players
Czech First League players
People from Brandýs nad Labem-Stará Boleslav
Footballers from the Central Bohemian Region
SK Slavia Prague players
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https://en.wikipedia.org/wiki/Adam%20Saad%20%28footballer%2C%20born%202004%29
|
Adam Saad (born 8 February 2004) is a Ghanaian footballer who currently plays as a forward for Ghana Premier League side Dreams.
Career statistics
Club
Notes
References
2004 births
Living people
Ghanaian men's footballers
Men's association football forwards
Ghana Premier League players
Dreams F.C. (Ghana) players
Place of birth missing (living people)
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https://en.wikipedia.org/wiki/Energy-based%20generative%20neural%20network
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Energy-based generative neural networks is a class of generative models, which aim to learn explicit probability distributions of data in the form of energy-based models whose energy functions are parameterized by modern deep neural networks. Its name is due to the fact that this model can be derived from the discriminative neural networks. The parameter of the neural network in this model is trained in a generative manner by Markov chain Monte Carlo(MCMC)-based maximum likelihood estimation. The learning process follows an ''analysis by synthesis'' scheme, where within each learning iteration, the algorithm samples the synthesized examples from the current model by a gradient-based MCMC method, e.g., Langevin dynamics, and then updates the model parameters based on the difference between the training examples and the synthesized ones. This process can be interpreted as an alternating mode seeking and mode shifting process, and also has an adversarial interpretation. The first energy-based generative neural network is the generative ConvNet proposed in 2016 for image patterns, where the neural network is a convolutional neural network. The model has been generalized to various domains to learn distributions of videos, and 3D voxels. They are made more effective in their variants. They have proven useful for data generation (e.g., image synthesis, video synthesis, 3D shape synthesis, etc.), data recovery (e.g., recovering videos with missing pixels or image frames, 3D super-resolution, etc), data reconstruction (e.g., image reconstruction and linear interpolation ).
References
Neural networks
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https://en.wikipedia.org/wiki/Roy%20Korine
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Roy Korine (; born 10 September 2002) is an Israeli footballer who currently plays as a forward for Maccabi Netanya.
Early life
Korine was born in Herzliya, Israel.
Career statistics
Club
Notes
References
2002 births
Living people
Israeli men's footballers
Maccabi Netanya F.C. players
Hapoel Ramat Gan Givatayim F.C. players
Israeli Premier League players
Liga Leumit players
Footballers from Herzliya
Men's association football forwards
Israel men's youth international footballers
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https://en.wikipedia.org/wiki/Daniyar%20Usenov%20%28footballer%29
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Daniyar Bekturuly Usenov (, Daniiar Bektūrūly Üsenov; born 18 February 2001) is a Kazakhstani footballer currently playing as a midfielder for Caspiy.
Career statistics
Club
Notes
References
2001 births
Living people
Kazakhstani men's footballers
Men's association football midfielders
Kazakhstan Premier League players
FC Kairat players
People from Aktau
21st-century Kazakhstani people
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https://en.wikipedia.org/wiki/Bartosz%20Bajorek
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Bartosz Bajorek (born 22 January 2004) is a Polish footballer who plays as a forward for Unia Tarnów.
Career statistics
Club
Notes
References
2004 births
Living people
Polish men's footballers
Men's association football forwards
Stal Mielec players
Unia Tarnów (football) players
I liga players
III liga players
People from Staszów County
Footballers from Świętokrzyskie Voivodeship
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https://en.wikipedia.org/wiki/Dragan%20Stoisavljevi%C4%87
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Dragan Stoisavljevic (born 25 November 2003) is a Serbian footballer who plays as a forward for Voždovac.
Career statistics
Club
Notes
References
2003 births
Living people
Serbian men's footballers
Serbia men's youth international footballers
Men's association football forwards
Serbian SuperLiga players
FK Voždovac players
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https://en.wikipedia.org/wiki/Nansel%20Bussa
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Nansel Bussa (born 15 June 2003) is a Nigerian footballer who currently plays as a forward for Ifeanyi Ubah.
Career statistics
Club
Notes
References
2003 births
Living people
Nigerian men's footballers
Men's association football forwards
Ifeanyi Ubah F.C. players
Nigeria Professional Football League players
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https://en.wikipedia.org/wiki/Jamil%20Muhammad
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Jamil Muhammad Muhammad (born 12 November 2000) is a Nigerian footballer who currently plays as a midfielder for Kano Pillars.
Career statistics
Club
Notes
References
2000 births
Living people
Nigerian men's footballers
Nigeria men's youth international footballers
Men's association football midfielders
Kano Pillars F.C. players
Nigeria Professional Football League players
Footballers from Enugu
Nigeria men's under-20 international footballers
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https://en.wikipedia.org/wiki/Moy%E2%80%93Prasad%20filtration
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In mathematics, the Moy–Prasad filtration is a family of filtrations of p-adic reductive groups and their Lie algebras, named after Allen Moy and Gopal Prasad. The family is parameterized by the Bruhat–Tits building; that is, each point of the building gives a different filtration. Alternatively, since the initial term in each filtration at a point of the building is the parahoric subgroup for that point, the Moy–Prasad filtration can be viewed as a filtration of a parahoric subgroup of a reductive group.
The chief application of the Moy–Prasad filtration is to the representation theory of p-adic groups, where it can be used to define a certain rational number called the depth of a representation. The representations of depth r can be better understood by studying the rth Moy–Prasad subgroups. This information then leads to a better understanding of the overall structure of the representations, and that understanding in turn has applications to other areas of mathematics, such as number theory via the Langlands program.
For a detailed exposition of Moy-Prasad filtrations and the associated semi-stable points, see Chapter 13 of the book Bruhat-Tits theory: a new approach by Tasho Kaletha and Gopal Prasad.
History
In their foundational work on the theory of buildings, Bruhat and Tits defined subgroups associated to concave functions of the root system. These subgroups are a special case of the Moy–Prasad subgroups, defined when the group is split. The main innovations of Moy and Prasad were to generalize Bruhat–Tits's construction to quasi-split groups, in particular tori, and to use the subgroups to study the representation theory of the ambient group.
Examples
The following examples use the p-adic rational numbers and the p-adic integers . A reader unfamiliar with these rings may instead replace by the rational numbers and by the integers without losing the main idea.
Multiplicative group
The simplest example of a p-adic reductive group is , the multiplicative group of p-adic units. Since is abelian, it has a unique parahoric subgroup, . The Moy–Prasad subgroups of are the higher unit groups , where for simplicity is a positive integer: The Lie algebra of is , and its Moy–Prasad subalgebras are the nonzero ideals of :More generally, if is a positive real number then we use the floor function to define the th Moy–Prasad subgroup and subalgebra: This example illustrates the general phenomenon that although the Moy–Prasad filtration is indexed by the nonnegative real numbers, the filtration jumps only on a discrete, periodic subset, in this case, the natural numbers. In particular, it is usually the case that the th and th Moy–Prasad subgroups are equal if is only slightly larger than .
General linear group
Another important example of a p-adic reductive group is the general linear group ; this example generalizes the previous one because . Since is nonabelian (when ), it has infinitely many parahoric subgroups. One pa
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https://en.wikipedia.org/wiki/Geometric%20Exercises%20in%20Paper%20Folding
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Geometric Exercises in Paper Folding is a book on the mathematics of paper folding. It was written by Indian mathematician T. Sundara Row, first published in India in 1893, and later republished in many other editions. Its topics include paper constructions for regular polygons, symmetry, and algebraic curves. According to historian of mathematics Michael Friedman, it became "one of the main engines of the popularization of folding as a mathematical activity".
Publication history
Geometric Exercises in Paper Folding was first published by Addison & Co. in Madras in 1893. The book became known in Europe through a remark of Felix Klein in his book Vorträge über ausgewählte Fragen der Elementargeometrie (1895) and its translation Famous Problems Of Elementary Geometry (1897). Based on the success of Geometric Exercises in Paper Folding in Germany, the Open Court Press of Chicago published it in the US, with updates by Wooster Woodruff Beman and David Eugene Smith. Although Open Court listed four editions of the book, published in 1901, 1905, 1917, and 1941, the content did not change between these editions. The fourth edition was also published in London by La Salle, and both presses reprinted the fourth edition in 1958.
The contributions of Beman and Smith to the Open Court editions have been described as "translation and adaptation", despite the fact that the original 1893 edition was already in English. Beman and Smith also replaced many footnotes by references to their own work, replaced some of the diagrams by photographs, and removed some remarks specific to India. In 1966, Dover Publications of New York published a reprint of the 1905 edition, and other publishers of out-of-copyright works have also printed editions of the book.
Topics
Geometric Exercises in Paper Folding shows how to construct various geometric figures using paper-folding in place of the classical Greek Straightedge and compass constructions.
The book begins by constructing regular polygons beyond the classical constructible polygons of 3, 4, or 5 sides, or of any power of two times these numbers, and the construction by Carl Friedrich Gauss of the heptadecagon, it also provides a paper-folding construction of the regular nonagon, not possible with compass and straightedge. The nonagon construction involves angle trisection, but Rao is vague about how this can be performed using folding; an exact and rigorous method for folding-based trisection would have to wait until the work in the 1930s of Margherita Piazzola Beloch. The construction of the square also includes a discussion of the Pythagorean theorem. The book uses high-order regular polygons to provide a geometric calculation of pi.
A discussion of the symmetries of the plane includes congruence, similarity, and collineations of the projective plane; this part of the book also covers some of the major theorems of projective geometry including Desargues's theorem, Pascal's theorem, and Poncelet's closure theorem.
L
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https://en.wikipedia.org/wiki/Football%20records%20and%20statistics%20in%20Myanmar
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This page details football records in Myanmar.
Most successful teams
Top-performing clubs - league structures
Myanmar National League
The Invincibles
Unbeatable champions:
Shan United in 2022
MNL-2
Myanmar Womens League
Futsal League
Top-performing clubs - cup competitions
General Aung San Shield
Charity Cup
AFC Champions League
Participations
QS: Qualifying stage, G: Group round, R16: Round of 16, Q: Quarterfinals, S: Semifinal, R: Runner-up, W: Winner
AFC Cup
Participations
G: Group round, R16: Round 16, ZS: Zonal semi-finals, R: Runner-up, W: Winner
References
External links
mnl
afccup
MFF
Football in Myanmar
Association football records and statistics by country
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https://en.wikipedia.org/wiki/Statistics%20of%20the%20COVID-19%20pandemic%20in%20Brazil
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This article presents official statistics gathered during the COVID-19 pandemic in Brazil.
Statistics
Total confirmed cases
New cases, per month
Total confirmed cases, by region
Growth of confirmed cases
Total confirmed deaths
New deaths, per month
Total confirmed deaths, by region
Growth of confirmed deaths
Number of cases and deaths, on a logarithmic scale
Case fatality rate
The trend of case fatality rate for COVID-19 from 26 February, the day first case in the country was recorded.
Timeline table, by state
References
External links
https://covid.saude.gov.br/ – Ministry of Health Statistics Panel, updated daily
https://brasil.io/dataset/covid19/caso_full/ - Brasil.io, an aggregator of the data published by the Brazilian Ministry of Health
statistics
Brazil
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https://en.wikipedia.org/wiki/Sum%20of%20residues%20formula
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In mathematics, the residue formula says that the sum of the residues of a meromorphic differential form on a smooth proper algebraic curve vanishes.
Statement
In this article, X denotes a proper smooth algebraic curve over a field k. A meromorphic (algebraic) differential form has, at each closed point x in X, a residue which is denoted . Since has poles only at finitely many points, in particular the residue vanishes for all but finitely many points. The residue formula states:
Proofs
A geometric way of proving the theorem is by reducing the theorem to the case when X is the projective line, and proving it by explicit computations in this case, for example in .
proves the theorem using a notion of traces for certain endomorphisms of infinite-dimensional vector spaces. The residue of a differential form can be expressed in terms of traces of endomorphisms on the fraction field of the completed local rings which leads to a conceptual proof of the formula. A more recent exposition along similar lines, using more explicitly the notion of Tate vector spaces, is given by .
References
Algebraic geometry
Algebraic curves
Differential forms
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https://en.wikipedia.org/wiki/Anna%20Panorska
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Anna Katarzyna Panorska is a Polish mathematician and statistician who works as a professor in the department of mathematics and statistics at the University of Nevada, Reno.
Research
Panorska's research interests include studying extreme events in the stochastic processes used to model weather, water, and biology. She has also studied the effects of weather conditions on baseball performance, concluding that temperature has a larger effect than wind and humidity.
Education and career
Panorska studied mathematics at the University of Warsaw, completing a degree in 1986. After earning a master's degree in statistics at the University of Texas at El Paso in 1988, she returned to mathematics for her doctoral studies, completing a Ph.D. at the University of California, Santa Barbara in 1992. Her dissertation, Generalized Convolutions, was supervised by Svetlozar Rachev.
She became an assistant professor of mathematics at the University of Tennessee at Chattanooga in 1992, but left academia in 1997 to work as a biostatistician for BlueCross BlueShield of Tennessee. After visiting the University of California, Santa Barbara in 1999–2000, she took a research faculty position in 2000 at the Desert Research Institute, associated with the University of Nevada, Reno. In 2002 she became a regular faculty member in mathematics and statistics at the university, and in 2011 she was promoted to full professor.
References
External links
Home page
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
American statisticians
Polish mathematicians
Polish statisticians
Women statisticians
University of Warsaw alumni
University of Texas at El Paso alumni
University of California, Santa Barbara alumni
University of Tennessee at Chattanooga faculty
University of Nevada, Reno faculty
20th-century American women
21st-century American women
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https://en.wikipedia.org/wiki/Anna%20Maria%20Bigatti
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Anna Maria Bigatti is an Italian mathematician specializing in computational methods for commutative algebra. She is a ricercatore in the department of mathematics at the University of Genoa. She is one of the developers of CoCoA, a computer algebra system, and of its core library CoCoALib.
Education and career
Bigatti earned a laurea in mathematics in 1989 from the University of Genoa, and completed her Ph.D. in 1995 at the University of Turin. Her dissertation, Aspetti Combinatorici e Computazionali dell’Algebra Commutativa, was supervised by Lorenzo Robbiano. After postdoctoral study with Robbiano in Genoa, she took her present position as ricercatore in 1997.
Books
Bigatti is an author or co-author of three Italian textbooks, Elementi di matematica - Esercizi con soluzioni per scienze e farmacia (with Grazia Tamone, 2013), Matematica di base (with Lorenzo Robbiano, 2014), and Matematica di base - Esercizi svolti, testi d'esame, richiami di teoria (with Grazia Tamone, 2016). She is also a co-editor of several books in mathematical research including Monomial ideals, computations and applications (Lecture Notes in Mathematics, Springer, 2013) and Computations and Combinatorics in Commutative Algebra (Lecture Notes in Mathematics, Springer, 2017).
References
External links
Home page
Year of birth missing (living people)
Living people
Italian mathematicians
Italian women mathematicians
University of Genoa alumni
University of Turin alumni
Academic staff of the University of Genoa
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https://en.wikipedia.org/wiki/Star%20unfolding
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In computational geometry, the star unfolding of a convex polyhedron is a net obtained by cutting the polyhedron along geodesics (shortest paths) through its faces. It has also been called the inward layout of the polyhedron, or the Alexandrov unfolding after Aleksandr Danilovich Aleksandrov, who first considered it.
Description
In more detail, the star unfolding is obtained from a polyhedron by choosing a starting point on the surface of , in general position, meaning that there is a unique shortest geodesic from to each vertex of .
The star polygon is obtained by cutting the surface of along these geodesics, and unfolding the resulting cut surface onto a plane. The resulting shape forms a simple polygon in the plane.
The star unfolding may be used as the basis for polynomial time algorithms for various other problems involving geodesics on convex polyhedra.
Related unfoldings
The star unfolding should be distinguished from another way of cutting a convex polyhedron into a simple polygon net, the source unfolding. The source unfolding cuts the polyhedron at points that have multiple equally short geodesics to the given base point , and forms a polygon with at its center, preserving geodesics from . Instead, the star unfolding cuts the polyhedron along the geodesics, and forms a polygon with multiple copies of at its vertices. Despite their names, the source unfolding always produces a star-shaped polygon, but the star unfolding does not.
Generalizations of the star unfolding using a geodesic or quasigeodesic in place of a single base point have also been studied. Another generalization uses a single base point, and a system of geodesics that are not necessarily shortest geodesics.
Neither the star unfolding nor the source unfolding restrict their cuts to the edges of the polyhedron. It is an open problem whether every polyhedron can be cut and unfolded to a simple polygon using only cuts along its edges.
References
Polygons
Polyhedra
Computational geometry
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https://en.wikipedia.org/wiki/Soccer%20records%20and%20statistics%20in%20Australia
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This article concerns soccer records in Australia. Unless otherwise stated, records are taken from the National Soccer League or A-League Men. Where a different record exists for the top flight (National Soccer League 1977–2004, and A-League Men 2005–present), this is also given.
League
Records in this section refer to the Australian top division, as a combination of the A-League Men or National Soccer League.
Titles
Most Premiership titles: 5, South Melbourne
Most Championship titles: 5, Sydney FC
Most consecutive Premiership titles: 3, Melbourne City, 2020–21, 2021–22, 2022–23
Most consecutive Championship titles: 3, Sydney City: 1980, 1981, 1982
Representation
Most seasons overall: 29 seasons, Brisbane Roar
Fewest seasons overall: 1 season, Canterbury Marrickville, Collingwood Warriors, Mooroolbark, and Wollongong United
Wins
Most wins overall: 378, South Melbourne
Most consecutive wins: 10, Western Sydney Wanderers (13 January 2013 – 16 March 2013)
Most wins in a season: 20, South Melbourne (National Soccer League, 2000–01)
Fewest wins in a season: 1, New Zealand Knights (A-League, 2005–06)
Draws
Most draws overall: 194, Adelaide City
Most consecutive draws: 6, Wellington Phoenix (4 September 2009 to 17 October 2009)
Most draws in a season: 15, Wollongong City (National Soccer League, 1983)
Fewest draws in a season: 1, Canberra City (National Soccer League, 1984)
Losses
Most losses overall: 255, Wollongong Wolves
Most consecutive losses: 16, Canberra Cosmos (30 March 1998 to 10 January 1999)
Most losses in a season: 24, joint record:
Newcastle Breakers (National Soccer League, 1995–96)
Sydney United (National Soccer League, 1999–2000)
Fewest losses in a season: 1, Brisbane Roar (A-League, 2011–12)
Points
Most points overall: 1,317, South Melbourne
Most points in a season: 70 (16 wins, 2 draws), Melbourne Knights (National Soccer League, 1994–95)
Fewest points in a season: 6, New Zealand Knights (A-League, 2005–06)
Games without a win
Most consecutive league games without a win: 23, Canberra Cosmos (22 February 1998 to 24 January 1999)
Games without a defeat
Most consecutive league games without a defeat: 36, Brisbane Roar (18 September 2010 to 26 November 2011)
Goals
Most league goals scored in a season: 80, Wollongong Wolves (National Soccer League, 2000–01)
Most goals scored in total: 1,293, Marconi Stallions
Most consecutive games without scoring: 6, joint record:
Parramatta Eagles (11 December 1993 to 9 January 1994)
Preston Lions (11 October 1987 to 28 February 1988)
Preston Lions (12 July 1989 to 18 November 1989)
New Zealand Knights (10 September 2006 to 14 October 2006)
Newcastle Jets (4 December 2015 to 9 January 2016)
Scorelines
Record win: Marconi Stallions 9–0 Blacktown City (16 March 1980)
Highest scoring draw: Newcastle Breakers 5–5 Canberra Cosmos (16 February 1996)
Disciplinary
Most red cards in a career (individual): 13, Andrew Marth (Sunshine George Cross, Melbourne Knights and Carlton)
Transfers
Hig
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https://en.wikipedia.org/wiki/David%20Allen%20Hoffman
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David Allen Hoffman is an American mathematician whose research concerns differential geometry. He is an adjunct professor at Stanford University. In 1985, together with William Meeks, he proved that Costa's surface was embedded. He is a fellow of the American Mathematical Society since 2018, for "contributions to differential geometry, particularly minimal surface theory, and for pioneering the use of computer graphics as an aid to research." He was awarded the Chauvenet Prize in 1990 for his expository article "The Computer-Aided Discovery of New Embedded Minimal Surfaces". He obtained his Ph.D. from Stanford University in 1971 under the supervision of Robert Osserman.
Technical contributions
In 1973, James Michael and Leon Simon established a Sobolev inequality for functions on submanifolds of Euclidean space, in a form which is adapted to the mean curvature of the submanifold and takes on a special form for minimal submanifolds. One year later, Hoffman and Joel Spruck extended Michael and Simon's work to the setting of functions on immersed submanifolds of Riemannian manifolds. Such inequalities are useful for many problems in geometric analysis which deal with some form of prescribed mean curvature. As usual for Sobolev inequalities, Hoffman and Spruck were also able to derive new isoperimetric inequalities for submanifolds of Riemannian manifolds.
It is well known that there is a wide variety of minimal surfaces in the three-dimensional Euclidean space. Hoffman and William Meeks proved that any minimal surface which is contained in a half-space must fail to be properly immersed. That is, there must exist a compact set in Euclidean space which contains a noncompact region of the minimal surface. The proof is a simple application of the maximum principle and unique continuation for minimal surfaces, based on comparison with a family of catenoids. This enhances a result of Meeks, Leon Simon, and Shing-Tung Yau, which states that any two complete and properly immersed minimal surfaces in three-dimensional Euclidean space, if both are nonplanar, either have a point of intersection or are separated from each other by a plane. Hoffman and Meeks' result rules out the latter possibility.
Major publications
References
20th-century American mathematicians
Fellows of the American Mathematical Society
Year of birth missing (living people)
Living people
21st-century American mathematicians
Stanford University faculty
Stanford University alumni
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https://en.wikipedia.org/wiki/Christine%20B%C3%B6ckmann
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Christine Böckmann (née Hense, born 1955) is a German applied mathematician, numerical analyst, and expert on atmospheric lidar. She is an außerplanmäßiger Professor of mathematics at the University of Potsdam, and one of the Principal Investigators of EARLINET, the European Aerosol Research Lidar Network.
Böckmann studied mathematics at the Dresden University of Technology, earning a diploma in 1980 and completing her doctorate (Dr. rer. nat.) in 1984. Her dissertation, Ein ableitungsfreies Verfahren vom Gauß-Newton-Typ zur Lösung von nichtlinearen Quadratmittelproblemen mit separierten Variablen, was supervised by Hubert Schwetlick. She subsequently completed a habilitation at the University of Potsdam.
References
External links
1955 births
Living people
20th-century German mathematicians
German women mathematicians
Applied mathematicians
Numerical analysts
TU Dresden alumni
Academic staff of the University of Potsdam
21st-century German mathematicians
20th-century German women
21st-century German women
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https://en.wikipedia.org/wiki/Big-little-big%20lemma
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In the mathematics of paper folding, the big-little-big lemma is a necessary condition for a crease pattern with specified mountain folds and valley folds to be able to be folded flat. It differs from Kawasaki's theorem, which characterizes the flat-foldable crease patterns in which a mountain-valley assignment has not yet been made. Together with Maekawa's theorem on the total number of folds of each type, the big-little-big lemma is one of the two main conditions used to characterize the flat-foldability of mountain-valley assignments for crease patterns that meet the conditions of Kawasaki's theorem. Mathematical origami expert Tom Hull calls the big-little-big lemma "one of the most basic rules" for flat foldability of crease patterns.
Statement
The lemma concerns the angles made by consecutive pairs of creases at a single vertex of the crease pattern. It states that if any one of these angles is a local minimum (that is, smaller than the two angles on either side of it), then exactly one of the two creases bounding the angle must be a mountain fold and exactly one must be a valley fold.
Generalization and applications
A generalized version of the lemma holds for a sequence of equal angles at a single vertex, surrounded on both sides by a larger angle. For such a sequence, the number of mountain and valley folds bounding any of these angles must either be equal, or differ by one. It can be used as part of a linear time algorithm that tests whether a folding pattern with a single vertex can be folded flat, by repeatedly looking for sequences of angles that obey the lemma and pinching them off, until either getting stuck or reducing the input to two equal angles bounded by two creases of the same type as each other.
History
In their book Geometric Folding Algorithms, Erik Demaine and Joe O'Rourke credit the lemma to publications of Toshikazu Kawasaki in 1989, and Jacques Justin in 1994.
References
Paper folding
Lemmas
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https://en.wikipedia.org/wiki/Nuclear%20operator
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In mathematics, nuclear operators are an important class of linear operators introduced by Alexander Grothendieck in his doctoral dissertation. Nuclear operators are intimately tied to the projective tensor product of two topological vector spaces (TVSs).
Preliminaries and notation
Throughout let X,Y, and Z be topological vector spaces (TVSs) and L : X → Y be a linear operator (no assumption of continuity is made unless otherwise stated).
The projective tensor product of two locally convex TVSs X and Y is denoted by and the completion of this space will be denoted by .
L : X → Y is a topological homomorphism or homomorphism, if it is linear, continuous, and is an open map, where , the image of L, has the subspace topology induced by Y.
If S is a subspace of X then both the quotient map X → X/S and the canonical injection S → X are homomorphisms.
The set of continuous linear maps X → Z (resp. continuous bilinear maps ) will be denoted by L(X, Z) (resp. B(X, Y; Z)) where if Z is the underlying scalar field then we may instead write L(X) (resp. B(X, Y)).
Any linear map can be canonically decomposed as follows: where defines a bijection called the canonical bijection associated with L.
X* or will denote the continuous dual space of X.
To increase the clarity of the exposition, we use the common convention of writing elements of with a prime following the symbol (e.g. denotes an element of and not, say, a derivative and the variables x and need not be related in any way).
will denote the algebraic dual space of X (which is the vector space of all linear functionals on X, whether continuous or not).
A linear map L : H → H from a Hilbert space into itself is called positive if for every . In this case, there is a unique positive map r : H → H, called the square-root of L, such that .
If is any continuous linear map between Hilbert spaces, then is always positive. Now let R : H → H denote its positive square-root, which is called the absolute value of L. Define first on by setting for and extending continuously to , and then define U on by setting for and extend this map linearly to all of . The map is a surjective isometry and .
A linear map is called compact or completely continuous if there is a neighborhood U of the origin in X such that is precompact in Y.
In a Hilbert space, positive compact linear operators, say L : H → H have a simple spectral decomposition discovered at the beginning of the 20th century by Fredholm and F. Riesz:There is a sequence of positive numbers, decreasing and either finite or else converging to 0, and a sequence of nonzero finite dimensional subspaces of H (i = 1, 2, ) with the following properties: (1) the subspaces are pairwise orthogonal; (2) for every i and every , ; and (3) the orthogonal of the subspace spanned by is equal to the kernel of L.
Notation for topologies
σ(X, X′) denotes the coarsest topology on X making every map in X′ continuous and or denote
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https://en.wikipedia.org/wiki/Leona%20S.%20Aiken
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Leona Ruth Silver Aiken is an American President's Professor of psychology at Arizona State University.
She is the co-author of two widely used statistics textbooks, Applied Multiple Regression/Correlation Analysis for the Behavior Sciences and Multiple Regression: Testing and interpreting interactions.
Education and career
Aiken graduated from Virginia Commonwealth University in 1965, and completed a PhD in psychology at Purdue University in 1970. She joined the Temple University faculty in 1969, and moved to Arizona State University in 1985. At Arizona State, she was given the President's Professorship in 2010.
Research
In terms of substantive research, Aiken specializes in women's health protective behavior. This research involves the application of a two-stage process, the first stage being psychosocial modeling, followed by the second stage of model based intervention. An example of this two-stage process can be seen in one of her studies, where peer perception of middle schoolers was used to model high school success, followed by suggestions on how peer perception should be reflected on by both the students and their parents.
In terms of methodological research, Leona Aiken specializes in models containing continuous variable interactions, which includes analysis of variance, multiple regression analysis, multivariate analysis, and structural equation modeling.
Awards and honors
Aiken is fellow of the Association for Psychological Science, of the American Psychological Association in 4 divisions, and of the Western Psychological Association.
Leona Aiken is an elected member of the Society of Multivariate Experimental Psychology, and was president of the society in 2006.
References
External links
Year of birth missing (living people)
Living people
American women psychologists
21st-century American psychologists
Virginia Commonwealth University alumni
Purdue University alumni
Temple University faculty
Arizona State University faculty
Fellows of the Association for Psychological Science
Fellows of the American Psychological Association
American women academics
21st-century American women scientists
Quantitative psychologists
20th-century American women scientists
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https://en.wikipedia.org/wiki/Ptak%20space
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A locally convex topological vector space (TVS) is B-complete or a Ptak space if every subspace is closed in the weak-* topology on (i.e. or ) whenever is closed in (when is given the subspace topology from ) for each equicontinuous subset .
B-completeness is related to -completeness, where a locally convex TVS is -complete if every subspace is closed in whenever is closed in (when is given the subspace topology from ) for each equicontinuous subset .
Characterizations
Throughout this section, will be a locally convex topological vector space (TVS).
The following are equivalent:
is a Ptak space.
Every continuous nearly open linear map of into any locally convex space is a topological homomorphism.
A linear map is called nearly open if for each neighborhood of the origin in , is dense in some neighborhood of the origin in
The following are equivalent:
is -complete.
Every continuous biunivocal, nearly open linear map of into any locally convex space is a TVS-isomorphism.
Properties
Every Ptak space is complete. However, there exist complete Hausdorff locally convex space that are not Ptak spaces.
Let be a nearly open linear map whose domain is dense in a -complete space and whose range is a locally convex space . Suppose that the graph of is closed in . If is injective or if is a Ptak space then is an open map.
Examples and sufficient conditions
There exist Br-complete spaces that are not B-complete.
Every Fréchet space is a Ptak space. The strong dual of a reflexive Fréchet space is a Ptak space.
Every closed vector subspace of a Ptak space (resp. a Br-complete space) is a Ptak space (resp. a -complete space). and every Hausdorff quotient of a Ptak space is a Ptak space.
If every Hausdorff quotient of a TVS is a Br-complete space then is a B-complete space.
If is a locally convex space such that there exists a continuous nearly open surjection from a Ptak space, then is a Ptak space.
If a TVS has a closed hyperplane that is B-complete (resp. Br-complete) then is B-complete (resp. Br-complete).
See also
Notes
References
Bibliography
External links
Nuclear space at ncatlab
Topological vector spaces
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https://en.wikipedia.org/wiki/Masahiro%20Sakumoto
|
is a Japanese former Nippon Professional Baseball pitcher.
References
External links
Career statistics - NPB.jp
91 Masahiro Sakumoto PLAYERS2021 - Fukuoka SoftBank Hawks Official site
1974 births
Living people
Baseball people from Okinawa Prefecture
Japanese baseball players
Nippon Professional Baseball pitchers
Fukuoka Daiei Hawks players
Hanshin Tigers players
Yokohama BayStars players
Japanese baseball coaches
Nippon Professional Baseball coaches
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https://en.wikipedia.org/wiki/Yoshiie%20Tachibana
|
is a Japanese former Nippon Professional Baseball outfielder.
References
External links
Career statistics - NPB.jp
83 Yoshiie Tachibana PLAYERS2021 - Fukuoka SoftBank Hawks Official site
1958 births
Living people
Baseball people from Fukuoka Prefecture
Japanese baseball players
Nippon Professional Baseball outfielders
Crown Lighter Lions players
Seibu Lions players
Hanshin Tigers players
Jungo Bears players
Japanese baseball coaches
Nippon Professional Baseball coaches
|
https://en.wikipedia.org/wiki/Inductive%20tensor%20product
|
The finest locally convex topological vector space (TVS) topology on the tensor product of two locally convex TVSs, making the canonical map (defined by sending to ) continuous is called the inductive topology or the -topology. When is endowed with this topology then it is denoted by and called the inductive tensor product of and
Preliminaries
Throughout let and be locally convex topological vector spaces and be a linear map.
is a topological homomorphism or homomorphism, if it is linear, continuous, and is an open map, where the image of has the subspace topology induced by
If is a subspace of then both the quotient map and the canonical injection are homomorphisms. In particular, any linear map can be canonically decomposed as follows: where defines a bijection.
The set of continuous linear maps (resp. continuous bilinear maps ) will be denoted by (resp. ) where if is the scalar field then we may instead write (resp. ).
We will denote the continuous dual space of by and the algebraic dual space (which is the vector space of all linear functionals on whether continuous or not) by
To increase the clarity of the exposition, we use the common convention of writing elements of with a prime following the symbol (e.g. denotes an element of and not, say, a derivative and the variables and need not be related in any way).
A linear map from a Hilbert space into itself is called positive if for every In this case, there is a unique positive map called the square-root of such that
If is any continuous linear map between Hilbert spaces, then is always positive. Now let denote its positive square-root, which is called the absolute value of Define first on by setting for and extending continuously to and then define on by setting for and extend this map linearly to all of The map is a surjective isometry and
A linear map is called compact or completely continuous if there is a neighborhood of the origin in such that is precompact in
In a Hilbert space, positive compact linear operators, say have a simple spectral decomposition discovered at the beginning of the 20th century by Fredholm and F. Riesz:
There is a sequence of positive numbers, decreasing and either finite or else converging to 0, and a sequence of nonzero finite dimensional subspaces of () with the following properties: (1) the subspaces are pairwise orthogonal; (2) for every and every ; and (3) the orthogonal of the subspace spanned by is equal to the kernel of
Notation for topologies
denotes the coarsest topology on making every map in continuous and or denotes endowed with this topology.
denotes weak-* topology on and or denotes endowed with this topology.
Every induces a map defined by is the coarsest topology on making all such maps continuous.
denotes the topology of bounded convergence on and or denotes endowed with this topology.
denotes the topology of bounded conver
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https://en.wikipedia.org/wiki/Brazil%20national%20football%20team%20results%20%282010%E2%80%93present%29
|
This page details the match results and statistics of the Brazil national football team from 2010 to present.
Key
Key to matches
Att.=Match attendance
(H)=Home ground
(A)=Away ground
(N)=Neutral ground
Key to record by opponent
Pld=Games played
W=Games won
D=Games drawn
L=Games lost
GF=Goals for
GA=Goals against
Results
Brazil's score is shown first in each case.
Notes
Record by opponent
References
Brazil national football team results
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https://en.wikipedia.org/wiki/Knee%20of%20a%20curve
|
In mathematics, a knee of a curve (or elbow of a curve) is a point where the curve visibly bends, specifically from high slope to low slope (flat or close to flat), or in the other direction. This is particularly used in optimization, where a knee point is the optimum point for some decision, for example when there is an increasing function and a trade-off between the benefit (vertical y axis) and the cost (horizontal x axis): the knee is where the benefit is no longer increasing rapidly, and is no longer worth the cost of further increases – a cutoff point of diminishing returns.
In heuristic use, the term may be used informally, and a knee point identified visually, but in more formal use an explicit objective function is used, and depends on the particular optimization problem. A knee may also be defined purely geometrically, in terms of the curvature or the second derivative.
Definitions
The knee of a curve can be defined as a vertex of the graph. This corresponds with the graphical intuition (it is where the curvature has a maximum), but depends on the choice of scale.
The term "knee" as applied to curves dates at least to the 1910s,
and is found more commonly by the 1940s, being common enough to draw criticism. The unabridged Webster's Dictionary (1971 edition) gives definition 3h of knee as:
Criticism
Graphical notions of a "knee" of a curve, based on curvature, are criticized due to their dependence on the coordinate scale: different choices of scale result in different points being the "knee". This criticism dates at least to the 1940s, being found in , who criticize:
Applications
Elbow method
Maximum power point tracking
References
Curvature (mathematics)
Mathematical optimization
Operations research
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https://en.wikipedia.org/wiki/The%20Banach%E2%80%93Tarski%20Paradox%20%28book%29
|
The Banach–Tarski Paradox is a book in mathematics on the Banach–Tarski paradox, the fact that a unit ball can be partitioned into a finite number of subsets and reassembled to form two unit balls. It was written by Stan Wagon and published in 1985 by the Cambridge University Press as volume 24 of their Encyclopedia of Mathematics and its Applications book series. A second printing in 1986 added two pages as an addendum, and a 1993 paperback printing added a new preface.
In 2016 the Cambridge University Press published a second edition, adding Grzegorz Tomkowicz as a co-author, as volume 163 of the same series. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries.
Topics
The Banach–Tarski paradox, proved by Stefan Banach and Alfred Tarski in 1924, states that it is possible to partition a three-dimensional unit ball into finitely many pieces and reassemble them into two unit balls, a single ball of larger or smaller area, or any other bounded set with a non-empty interior. Although it is a mathematical theorem, it is called a paradox because it is so counter-intuitive; in the preface to the book, Jan Mycielski calls it the most surprising result in mathematics. It is closely related to measure theory and the non-existence of a measure on all subsets of three-dimensional space, invariant under all congruences of space, and to the theory of paradoxical sets in free groups and the representation of these groups by three-dimensional rotations, used in the proof of the paradox. The topic of the book is the Banach–Tarski paradox, its proof, and the many related results that have since become known.
The book is divided into two parts, the first on the existence of paradoxical decompositions and the second on conditions that prevent their existence. After two chapters of background material, the first part proves the Banach–Tarski paradox itself, considers higher-dimensional spaces and non-Euclidean geometry, studies the number of pieces necessary for a paradoxical decomposition, and finds analogous results to the Banach–Tarski paradox for one- and two-dimensional sets. The second part includes a related theorem of Tarski that congruence-invariant finitely-additive measures prevent the existence of paradoxical decompositions, a theorem that Lebesgue measure is the only such measure on the Lebesgue measurable sets, material on amenable groups, connections to the axiom of choice and the Hahn–Banach theorem. Three appendices describe Euclidean groups, Jordan measure, and a collection of open problems.
The second edition adds material on several recent results in this area, in many cases inspired by the first edition of the book. Trevor Wilson proved the existence of a continuous motion from the one-ball assembly to the two-ball assembly, keeping the sets of the partition disjoint at all times; this question had been posed by de Groot in the first edition of the bo
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https://en.wikipedia.org/wiki/Canadian%20Premier%20League%20records%20and%20statistics
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The following is a compilation of notable Canadian Premier League records and statistics for teams and players. The Canadian Premier League includes statistics from the CPL Finals in their season totals.
Champions
Canadian Premier League Finals
Award winners
Golden Boot
Golden Glove
Coach of the Year
Player of the Year
Best Under 21 Canadian Player of the Year
Defender of the Year
Player's Player of the Year
Career player records
Statistics below are for all-time leaders and include regular season and playoffs. Bold indicates active players. Team is the current team or for inactive players the last CPL team they played for. Current to end of 2023 Playoffs.
Goals
Assists
Clean sheets
Appearances
Hat-tricks
Club statistics
All-time regular season table
The all-time regular season table is a cumulative record of all match results, points and goals of every team that has played in the Canadian Premier League since its inception in 2019, excluding playoffs.
As of 2022 season
All-time regular season finishing positions
Best regular season records
Post-season active droughts
– Team is no longer playing in the Canadian Premier League.
Playoff appearances
Updated through 2023 Canadian Premier League season. This list does not include clubs that made the post-season as of that year.
Finals appearances
Updated through 2023 Canadian Premier League season. This list does not include the clubs that qualified as of that year.
Championships
Updated through 2023 Canadian Premier League season. This list does not include the club that won the championship as of that year.
CPL results in the Canadian Championship
Highest scoring games and largest victories
Largest victories
Highest scoring games
Transfer records
Highest transfer fees received
Attendance records
Highest Attendance; 17,611, Forge FC vs York9, April 27, 2019
Lowest Attendance; 0, 2020 Island Games
Seasonal average attendances
Best average season's attendance for each team in bold.
Notes
References
Canadian Premier League records and statistics
All-time football league tables
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https://en.wikipedia.org/wiki/1932%E2%80%9333%20Rochdale%20A.F.C.%20season
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The 1932–33 season saw Rochdale compete for their 12th season in the Football League Third Division North.
Statistics
|}
Final league table
Competitions
Football League Third Division North
FA Cup
Lancashire Cup
Manchester Cup
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Yuguo%20Chen
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Yuguo Chen is a professor of statistics at the University of Illinois at Urbana-Champaign. His work mainly focuses on Markov chain Monte Carlo algorithms and network analysis.
He received a B.S. in mathematics from University of Science and Technology of China in 1997 and a Ph.D. in statistics at Stanford University in 2001 under the supervision of Tze Leung Lai and Jun S. Liu. Prior to joining the University of Illinois, he was an assistant professor at the Institute of Statistics and Decision Sciences at Duke University from 2001 to 2005.
Chen was named a Fellow of the American Statistical Association in 2018.
Selected publications
"State and parameter estimation of hydrologic models using the constrained ensemble Kalman filter". Water Resources Research.
"Sequential Monte Carlo Methods for Statistical Analysis of Tables". Journal of the American Statistical Association 100:109–120.
References
External links
University of Illinois homepage
Living people
American statisticians
Stanford University alumni
University of Science and Technology of China alumni
University of Illinois Urbana-Champaign faculty
Year of birth missing (living people)
Fellows of the American Statistical Association
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https://en.wikipedia.org/wiki/Daniel%20Dugu%C3%A9
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Daniel Dugué was a French mathematician specializing in probability and statistics. He was born on 22 September 1912 in Saint-Louis in Senegal and died on 10 September 1987 in Paris, France.
Biography
After finishing high-school studies in Bordeaux, Daniel Dugué was admitted to ENS and with a degree agrégation de mathématiques when he was 21 years old, in 1933. He defended the doctoral dissertation in mathematics when he was 25 years old under the supervision of Georges Darmois and defended it before Émile Borel and Arnaud Denjoy. In the course of his thesis, Dugué proves several theorems in the theory of the maximum likelihood estimation combining results and tools from probability theory, such as those of Khinchin, Kolmogorov, and Doob with Fisher's theory of the maximum likelihood estimator. In 1937, Fisher invites Dugué to work with him in London, and Dugué spends two years as a Rockefeller fellow in London.
He subsequently contributed to the development of the rigorous theory of the maximum likelihood estimator. He also worked with Yuri Linnik on the decomposition of probability distributions.
Dugué succeeded Georges Darmois as a director of Paris Institute of Statistics in 1960 leading it until his retirement in 1981. He was married to Lucie Canaud and had four children, Catherine, Élisabeth, David and Marc. He died from illness in 1987.
Scientific prizes
Jérôme Ponti Prize (1946)
Montyon Prize (1947)
Scientific work
Application des propriétés de la limite au sens du calcul des probabilités à l’étude de diverses questions d’estimation, Thesis, Faculté des sciences de Paris, 1937.
Analycité et convexité des fonctions caractéristiques, in: Généralisations de la loi de probabilité de Laplace, 56 pages, Paris, Institut Henri-Poincaré, 1951.
Arithmétique des lois de probabilités, 50 pages, Paris, Gauthier-Villars, 1957.
Fonctions connexes de Polya, avec Maurice Girault, 302 pages, Paris, Institut Henri-Poincaré, 1957.
Statistique et psychologie, 4 fascicules de 48, 52, 25 et 38 pages, Paris, Institut Henri-Poincaré, 1957.
Sur certains exemples de décomposition en arithmétique des lois de probabilité, in: L'ennuple projectif et l'unification de théories de l'électromagnétisme de Weyl et de Veblen-Hoffmann, 39 pages, Paris, Institut Henri-Poincaré, 1951.
Sur la convergence presque complète des moyennes de variables aléatoires, 273 pages, Paris, Institut de statistique de l'université de Paris, 1957.
Algèbres de Boole, avec une introduction à la théorie algébrique des graphes orientés et aux sous-ensembles flous, par Michel Serfati, préface de Daniel Dugué, 183 pages, Paris, Centre de documentation universitaire, 1974.
Probabilités et statistiques en recherche scientifique, par Alex Rosengard, préface de Daniel Dugué, 311 pages, Paris, Dunod, 1972.
References
External links
Daniel Dugué discussing probability, interviewed by Monique Tosello on 23 July 1973, video from the Institut national de l'audiovisuel.
Academic staff o
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https://en.wikipedia.org/wiki/Fat%20Chance%3A%20Probability%20from%200%20to%201
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Fat Chance: Probability from 0 to 1 is an introductory undergraduate-level textbook on probability theory, centered on the metaphor of games of chance. It was written by Benedict Gross, Joe Harris, and Emily Riehl, based on a course for non-mathematicians taught to Harvard University undergraduates, and published by the Cambridge University Press in 2019. An associated online course has been offered to the public by Harvard.
Topics
Unusually for a probability theory book, this book does not use the phrase "random variable", instead referring to random processes as games. The first five chapters of the book concern counting problems, and include material on the exponential function, binomial coefficients, factorials, games of cards, dice, and coins, and the birthday paradox. After an interlude involving the binomial theorem, Pascal's triangle, and the Catalan numbers, the second part of the book concerns probability more directly. Its chapters concern the expected value, conditional probability and Bayes' theorem, events with unequal probabilities (biased coins and loaded dice), geometric probability, the law of large numbers, and normal distributions. The third part moves from probability to statistics, with topics including the central limit theorem and the meaning of false positives and false negatives in medical testing.
Audience and reception
Although the main purpose of the book is to be a textbook for college courses aimed at non-mathematicians, it can also be read independently by those interested in the topic. Reviewer Ludwig Paditz recommends the book to "readers without deeper knowledge in elementary statistics and probability". Reviewer Massimo Nespolo recommends as well that its readers take advantage of the associated online course offering.
References
Probability theory
Mathematics textbooks
2019 non-fiction books
Cambridge University Press books
Textbooks
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https://en.wikipedia.org/wiki/Tim%20Chartier
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Timothy P. Chartier (born 1969) is Joseph R. Morton Professor of Mathematics and Computer Science at Davidson College, known for his expertise in sports analytics and bracketology, for his popular mathematics books, and for the "mime-matics" shows combining mime and mathematics that he and his wife Tanya have staged.
The National Museum of Mathematics announced him as 2022-23 Distinguished Visiting Professor for the Public Dissemination of Mathematics, in June 2021.
Education and career
Chartier majored in applied mathematics at Western Michigan University, graduating in 1993, and stayed at Western Michigan for a master's degree in computational mathematics in 1996. He completed a PhD at the University of Colorado Boulder in 2001, with the dissertation Algebraic Multigrid Based on Element Interpolation (AMGe) and Spectral AMGe supervised by Steve McCormick. He has also studied mime, at the Centre du Silence in Colorado, at the Dell'Arte International School of Physical Theatre in California, and with Marcel Marceau.
After postdoctoral research at the University of Washington, he joined the Davidson College faculty in 2003. As well as his academic work, he is also a frequent consultant on sports analytics for ESPN, NASCAR, the National Basketball Association, and other groups.
Books
Chartier is the author of Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing (2014), which won the Euler Book Prize in 2020, and of When Life is Linear: From Computer Graphics to Bracketology (2015), which won the Beckenbach Book Prize in 2017.
He is also the author of X Games In Mathematics: Sports Training That Counts! (2020) and the coauthor, with Anne Greenbaum, of Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms (2012).
References
1969 births
Living people
21st-century American mathematicians
Western Michigan University alumni
University of Colorado Boulder alumni
Davidson College faculty
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https://en.wikipedia.org/wiki/Jan%20S.%20Hesthaven
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Jan S. Hesthaven is a Danish mathematician, currently Vice President for Academic Affairs at EPFL (École polytechnique fédérale de Lausanne). He is Professor of Mathematics, holds the Chair of Computational Mathematics and Simulation Science (MCSS), and was appointed Vice President for Academic Affairs at EPFL (starting in 2021). He is particularly known for contributions to the development, analysis and application of high-order accurate computational methods for time-dependent partial differential equations. He has also contributed substantially to the development of reduced order models and the application of neural networks and machine learning techniques to problems in science and engineering.
Career
Prof. Hesthaven obtained a Master of Science degree in computational physics from the Technical University of Denmark (DTU) in 1991. In 1995, he received a Ph.D. in Numerical Analysis from the Institute of Mathematical Modelling (DTU) and in 2009 he was awarded the degree of Dr.Techn. from DTU for substantial and lasting contributions that has helped to move his research area forward and penetrated into applications.
After graduation, he was appointed in 1995 as Visiting Assistant Professor at Brown University, then in 1999 as assistant professor and in 2003 he was promoted associate professor of applied mathematics with tenure at Brown University where in July 2005 he was promoted to professor of applied mathematics.
In 2006, he founded the Center for Computation and Visualization (CCV) at Brown University and was its director until 2013.
He served from Aug 2010 to June 2013 as founding deputy director of the Institute of Computational and Experimental Research in Mathematics ICERM, an NSF Mathematical Sciences Research Institute.
In 2013, he joined EPFL (École polytechnique fédérale de Lausanne) where he was appointed full professor of computational mathematics and simulation science, and shortly later, in February 2014, he founded the new unit of Scientific IT and Application Support (SCITAS)
Since 2016 he serves as Editor in Chief of SIAM Journal of Scientific Computing.
In February 2017, he became dean of the School of Basic Sciences (SB). In September 2020, he was appointed as Vice President for Academic Affairs at EPFL for a term starting in 2021.
Recognition
Brown University gave him their Philip J. Bray Award for Teaching Excellence in 2004.
He was elected as a SIAM Fellow in 2014. He was named to the 2023 class of Fellows of the American Mathematical Society, "for contributions to computational methods for PDEs, high-order accurate methods, and the reduced order method".
Books
Notes and references
External links
Year of birth missing (living people)
Living people
Danish mathematicians
Danish academic administrators
Technical University of Denmark alumni
Academic staff of the École Polytechnique Fédérale de Lausanne
Fellows of the American Mathematical Society
Fellows of the Society for Industrial and Applied M
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https://en.wikipedia.org/wiki/Helga%20Baum
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Helga Baum (née Dlubek, born 1954) is a German mathematician. She is professor for differential geometry and global analysis in the Institute for Mathematics of the Humboldt University of Berlin.
Education
Baum earned a doctorate (Dr. sc. nat.) in mathematics in 1980 at the Humboldt University of Berlin. Her dissertation, Spin-Strukturen und Dirac-Operatoren über Pseudoriemannschen Mannigfaltigkeiten, was supervised by .
Books
Baum of the author or coauthor of books including:
Conformal differential geometry: Q-curvature and conformal holonomy, with Andreas Juhl, Birkhäuser, 2010
Eichfeldtheorie: Eine Einführung in die Differentialgeometrie auf Faserbündeln [Gauge theory: An introduction into differential geometry on fibre bundles] (Springer, 2009; 2nd ed., 2014)
Twistor and Killing spinors on Riemannian manifolds, with Thomas Friedrich, Ralf Grunewald, and Ines Kath, Teubner, 1991
Spin-Strukturen und Dirac-Operatoren über pseudoriemannschen Mannigfaltigkeiten [Spin structures and Dirac operators on pseudo-Riemannian manifolds], Teubner, 1981
References
Living people
20th-century German mathematicians
German women mathematicians
Humboldt University of Berlin alumni
Academic staff of the Humboldt University of Berlin
21st-century German mathematicians
20th-century German women
21st-century German women
1954 births
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https://en.wikipedia.org/wiki/Restricted%20power%20series
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In algebra, the ring of restricted power series is the subring of a formal power series ring that consists of power series whose coefficients approach zero as degree goes to infinity. Over a non-archimedean complete field, the ring is also called a Tate algebra. Quotient rings of the ring are used in the study of a formal algebraic space as well as rigid analysis, the latter over non-archimedean complete fields.
Over a discrete topological ring, the ring of restricted power series coincides with a polynomial ring; thus, in this sense, the notion of "restricted power series" is a generalization of a polynomial.
Definition
Let A be a linearly topologized ring, separated and complete and the fundamental system of open ideals. Then the ring of restricted power series is defined as the projective limit of the polynomial rings over :
.
In other words, it is the completion of the polynomial ring with respect to the filtration . Sometimes this ring of restricted power series is also denoted by .
Clearly, the ring can be identified with the subring of the formal power series ring that consists of series with coefficients ; i.e., each contains all but finitely many coefficients .
Also, the ring satisfies (and in fact is characterized by) the universal property: for (1) each continuous ring homomorphism to a linearly topologized ring , separated and complete and (2) each elements in , there exists a unique continuous ring homomorphism
extending .
Tate algebra
In rigid analysis, when the base ring A is the valuation ring of a complete non-archimedean field , the ring of restricted power series tensored with ,
is called a Tate algebra, named for John Tate. It is equivalently the subring of formal power series which consists of series convergent on , where is the valuation ring in the algebraic closure .
The maximal spectrum of is then a rigid-analytic space that models an affine space in rigid geometry.
Define the Gauss norm of in by
This makes a Banach algebra over k; i.e., a normed algebra that is complete as a metric space. With this norm, any ideal of is closed and thus, if I is radical, the quotient is also a (reduced) Banach algebra called an affinoid algebra.
Some key results are:
(Weierstrass division) Let be a -distinguished series of order s; i.e., where , is a unit element and for . Then for each , there exist a unique and a unique polynomial of degree such that
(Weierstrass preparation) As above, let be a -distinguished series of order s. Then there exist a unique monic polynomial of degree and a unit element such that .
(Noether normalization) If is an ideal, then there is a finite homomorphism .
As consequence of the division, preparation theorems and Noether normalization, is a Noetherian unique factorization domain of Krull dimension n. An analog of Hilbert's Nullstellensatz is valid: the radical of an ideal is the intersection of all maximal ideals containing the ideal (we say the ring is Jacobson).
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https://en.wikipedia.org/wiki/List%20of%20Odisha%20FC%20records%20and%20statistics
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Odisha Football Club is an Indian professional football club based in Bhubaneswar, Odisha. The club was founded as Odisha FC in 2019. Odisha currently plays in the Indian Super League, one of the two co-existing premier football leagues in India along with I-League.
All stats are accurate as of match played on 23 February 2020.
Club
Update
As of 27 February 2021
Overview
Overall records
Head coaches
General
Note: When scores are mentioned, score of Odisha are given first.
First match: 1–2 (vs Jamshedpur, Indian Super League, 22 October 2019)
First win: 4–2 (vs Mumbai City, Indian Super League, 31 October 2019)
First goalscorer: Aridane Santana (vs Jamshedpur, Indian Super League, 22 October 2019)
First Indian goalscorer: Jerry Mawihmingthanga (vs Mumbai City, Indian Super League, 31 October 2019)
First goal in home ground: Carlos Delgado (vs Hyderabad, Indian Super League, 11 December 2019)
Biggest win (in Indian Super League):
4–2 (vs Mumbai City, 31 October 2019)
2–0 (vs Chennaiyin, 6 January 2020)
2–0 (vs Mumbai City, 11 January 2020)
Biggest loss (in Indian Super League):
1–6 (vs Mmbai City, 24 February 2021)
Club Captains
Appearances
Record appearance maker: 18 – Martín Pérez Guedes 18 – Narayan Das 18 – Xisco Hernández
Most appearances in Indian Super League: 18 – Martín Pérez Guedes 18 – Narayan Das 18 – Xisco Hernández
Most Appearances
As of 23 February 2020
(Players with their names in bold currently play for the club.)
Goals
All time top scorer: 9 - Aridane Santana
Most goals in Indian Super League: 9 - Aridane Santana
Most goals in a season: 9 - Aridane Santana
Most goals in a match: 3
Manuel Onwu (vs Kerala Blasters, Indian Super League, 23 February 2020)
Most Goals
As of 23 February 2020
(Players with their name in bold currently plays for the club.)
Hattricks
Other
Most Assists
As of 23 February 2020
(Players with their name in bold currently plays for the club.)
Most Clean Sheets
As of 23 February 2020
(Players with their name in bold currently plays for the club.)
See also
Odisha FC
2019–20 Odisha FC season
Indian Super League
Football in India
References
Odisha FC-related lists
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https://en.wikipedia.org/wiki/Dual%20system
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In mathematics, a dual system, dual pair, or duality over a field is a triple consisting of two vector spaces and over and a non-degenerate bilinear map .
Duality theory, the study of dual systems, is part of functional analysis. It is separate and distinct from dual-system theory in psychology.
Definition, notation, and conventions
Pairings
A or pair over a field is a triple which may also be denoted by consisting of two vector spaces and over (which this article assumes is either the real numbers or the complex numbers ) and a bilinear map , called the bilinear map associated with the pairing or simply the pairing's map/bilinear form.
For every , define
and for every define
Every is a linear functional on and every is a linear functional on .
Let
where each of these sets forms a vector space of linear functionals.
It is common practice to write instead of , in which case the pair is often denoted by rather than However, this article will reserve the use of for the canonical evaluation map (defined below) so as to avoid confusion for readers not familiar with this subject.
Dual pairings
A pairing is called a , a , or a over if the bilinear form is non-degenerate, which means that it satisfies the following two separation axioms:
separates/distinguishes points of : if is such that then ; or equivalently, for all non-zero , the map is not identically (i.e. there exists a such that );
separates/distinguishes points of : if is such that then ; or equivalently, for all non-zero the map is not identically (i.e. there exists an such that ).
In this case say that is non-degenerate, say that places and in duality (or in separated duality), and is called the duality pairing of the .
Total subsets
A subset of is called if for every ,
implies
A total subset of is defined analogously (see footnote).
Thus separates points of if and only if is a total subset of , and similarly for .
Orthogonality
The vectors and are called , written , if .
Two subsets and are orthogonal, written , if ; that is, if for all and .
The definition of a subset being orthogonal to a vector is defined analogously.
The orthogonal complement or annihilator of a subset is
.
Thus is a total subset of if and only if equals .
Polar sets
Throughout, will be a pairing over
The absolute polar or polar of a subset of is the set:
Dually, the absolute polar or polar of a subset of is denoted by and defined by
In this case, the absolute polar of a subset of is also called the absolute prepolar or prepolar of and may be denoted by
The polar is necessarily a convex set containing where if is balanced then so is and if is a vector subspace of then so too is a vector subspace of
If then the bipolar of denoted by is the set
Similarly, if then the bipolar of is
If is a vector subspace of then and this is also equal to the real polar of
Dual definitions and results
Given a pairi
|
https://en.wikipedia.org/wiki/Tze%20Leung%20Lai
|
Tze Leung Lai (June 28, 1945 – May 21, 2023) was a Chinese-American statistician of Hong Kong descent. He was the Ray Lyman Wilbur Professor of Statistics, as well as a professor of Biomedical Data Science and of the Institute of Computational and Mathematical Engineering (ICME) at Stanford University. He co-directed the Center for Innovative Study Design (CISD) at the Stanford University School of Medicine. He was the recipient of the COPSS Presidents' Award, one of the highest honors in statistics, in 1983.
He received his bachelor's degree from the University of Hong Kong in 1967. He received an M.A. in 1970 and a Ph.D. in 1971 in Mathematical Statistics from Columbia University.
He supervised 79 doctoral theses and 7 postdoctoral trainees.
He died on May 21, 2023.
Honors and awards
He received the COPSS Presidents' Award in 1983. He was also awarded a Guggenheim fellowship the same year.
He was a fellow of the American Statistical Association (1986), the Institute of Mathematical Statistics, and Academia Sinica (1994).
References
External links
Stanford homepage
American statisticians
Stanford University Department of Statistics faculty
Columbia Graduate School of Arts and Sciences alumni
Alumni of the University of Hong Kong
Fellows of the American Statistical Association
Fellows of the Institute of Mathematical Statistics
1945 births
2023 deaths
Members of Academia Sinica
|
https://en.wikipedia.org/wiki/Prix%20Paul%20Doistau%E2%80%93%C3%89mile%20Blutet
|
The Prix Paul Doistau–Émile Blutet is a biennial prize awarded by the French Academy of Sciences in the fields of mathematics and physical sciences since 1954. Each recipient receives 3000 euros. The prize is also awarded quadrennially in biology. The award is also occasionally awarded in other disciplines.
List of laureates
Mathematics
1958 Marc Krasner
1980 Jean-Michel Bony
1982 Jean-Pierre Ramis
1982 Gérard Maugin
1985 Dominique Foata
1986 Pierre-Louis Lions
1987 Pierre Bérard
1987 Lucien Szpiro
1999 Wendelin Werner
2001 Hélène Esnault
2004 Laurent Stolovitch
2006 Alice Guionnet
2008 Isabelle Gallagher
2010 Yves André
2012 Serge Cantat
2014 Sébastien Boucksom
2016 Hajer Bahouri
2018
Physical sciences
2002
2005 Mustapha Besbes
2007
2009 Hasnaa Chennaoui-Aoudjehane
2011 Henri-Claude Nataf
2013
2015 Philippe André
2019
Integrative biology
2000 Jérôme Giraudat
2004 Marie-Claire Verdus
2008 Hélène Barbier-Brygoo
2012 Olivier Hamant
Mechanical and computational science
2000 Annie Raoult
2002 Gilles Francfort
2002 Jean-Jacques Marigo
2006 Hubert Maigre
2006 Andreï Constantinescu
2008 Pierre Comte
2010 Nicolas Triantafyllidis
2012 Élisabeth Guazzelli
2014 Jacques Magnaudet
2019 Denis Sipp
Other disciplines
1967 Jacques Blamont
1975
1976 Martial Ducloy
1976 Arlette Nougarède
1981 Christian Bordé
1988
2019
References
Awards of the French Academy of Sciences
Awards established in the 1950s
Mathematics awards
|
https://en.wikipedia.org/wiki/Wolfgang%20Viechtbauer
|
Wolfgang Viechtbauer is a statistician. He is an associate professor of methodology and statistics at the Maastricht University in the Faculty of Health, Medicine and Life Sciences and Faculty of Psychology and Neuroscience. His most influential work has been focused on the field of meta-analysis and evidence synthesis.
Education
Viechtbauer completed a M.A. (2002) and a Ph.D. (2004) at the University of Illinois at Urbana–Champaign. His master's thesis was titled Bias of certain variance estimators in meta-analysis and his dissertation was titled Choosing between the fixed-, random-, and mixed-effects model in meta-analysis: an analysis of existing and new model selection methods. His doctoral advisor was David Budescu.
Career
Viechtbauer is an associate professor of methodology and statistics at the Maastricht University in the Faculty of Health, Medicine and Life Sciences and Faculty of Psychology and Neuroscience.
Selected works
References
External links
Living people
Year of birth missing (living people)
Place of birth missing (living people)
21st-century German mathematicians
Biostatisticians
German computer scientists
Academic staff of Maastricht University
University of Illinois Urbana-Champaign alumni
Nationality missing
|
https://en.wikipedia.org/wiki/Monique%20Jeanblanc
|
Monique Jeanblanc-Picqué (born 1947) is a French mathematician known for her work in mathematical finance; other topics in her research have included control theory and probability theory. She is a professor emerita at the University of Évry Val d'Essonne.
Education and career
Jeanblanc was a student at the Ecole Normale Supérieure de Cachan from 1966 to 1969, when she took a teaching position there. In 1992 she moved to the University of Évry.
Books
Jeanblanc is the author or coauthor of the books including
Enlargement of Filtration with Finance in View (with Anna Aksamit, Springer, 2017)
Mathematical Methods for Financial Markets (with Marc Yor and Marc Chesney, Springer, 2009)
Marchés financiers en temps continu: valorisation et équilibre (with Rose-Anne Dana, Economica, 1998), translated into English as Financial Markets in Continuous Time (Springer, 2003)
Recognition
In 2009, Jeanblanc was made a chevalier in the Legion of Honour.
References
External links
Home page
1947 births
Living people
French mathematicians
French women mathematicians
Knights of the Legion of Honour
|
https://en.wikipedia.org/wiki/COVID-19%20deaths
|
COVID-19 deaths may refer to:
, for information about the mortality of COVID-19
COVID-19 pandemic deaths, for statistics on COVID-19 deaths by region
COVID-19 pandemic death rates by country, for statistics on COVID-19 death rates by country
List of deaths due to COVID-19, for a list of notable people who have died from COVID-19
|
https://en.wikipedia.org/wiki/Andreas%20Kr%C3%B6hler
|
Andreas Kröhler (born 1 November 1966) is a former German football player who played as a forward. Krohler has played in the European Cup and Bundesliga with 1. FC Kaiserslautern.
Career statistics
References
External links
1966 births
Living people
German men's footballers
Men's association football forwards
1. FC Kaiserslautern players
1. FC Kaiserslautern II players
Wormatia Worms players
Bundesliga players
|
https://en.wikipedia.org/wiki/Delores%20Conway
|
Delores Ann Conway is an American statistician and economist known for her work on the statistics of real estate markets. She is Professor of Real Estate Economics and Statistics in the Simon Business School of the University of Rochester.
Education and career
Conway graduated in 1971 from the University of Wisconsin–Madison, with a bachelor's degree in mathematics, earning a second bachelor's degree in computer methods and statistics in 1972. She went to Stanford University for graduate study in statistics, earning a master's degree in 1975 and completing her Ph.D. in 1979. Her dissertation, Multivariate Distribution with Specified Marginals, was supervised by Ingram Olkin.
She became an assistant professor of business at the University of Chicago in 1979, as the first female faculty member in the University of Chicago Booth School of Business, and moved to the USC Marshall School of Business as an associate professor in 1985. At USC, she directed the Casden Real Estate Economics Forecast, beginning in 2004. She moved to the University of Rochester as associate dean in 2009.
Recognition
In 1997, Conway was elected as a Fellow of the American Statistical Association.
Personal life
After moving to Rochester, Conway married the president of the university, Joel Seligman.
References
External links
Year of birth missing (living people)
Living people
American statisticians
American economists
Women statisticians
American women economists
University of Wisconsin–Madison College of Letters and Science alumni
Stanford University alumni
University of Chicago faculty
University of Rochester faculty
Fellows of the American Statistical Association
21st-century American women
|
https://en.wikipedia.org/wiki/Diophantus%20and%20Diophantine%20Equations
|
Diophantus and Diophantine Equations is a book in the history of mathematics, on the history of Diophantine equations and their solution by Diophantus of Alexandria. It was originally written in Russian by Isabella Bashmakova, and published by Nauka in 1972 under the title Диофант и диофантовы уравнения. It was translated into German by Ludwig Boll as Diophant und diophantische Gleichungen (Birkhäuser, 1974) and into English by Abe Shenitzer as Diophantus and Diophantine Equations (Dolciani Mathematical Expositions 20, Mathematical Association of America, 1997).
Topics
In the sense considered in the book, a Diophantine equation is an equation written using polynomials whose coefficients are rational numbers. These equations are to be solved by finding rational-number values for the variables that, when plugged into the equation, make it become true. Although there is also a well-developed theory of integer (rather than rational) solutions to polynomial equations, it is not included in this book.
Diophantus of Alexandria studied equations of this type in the second century AD. Scholarly opinion has generally held that Diophantus only found solutions to specific equations, and had no methods for solving general families of equations. For instance, Hermann Hankel has written of the works of Diophantus that "not the slightest trace of a general, comprehensive method is discernible; each problem calls for some special method which refuses to work even for the most closely related problems". In contrast, the thesis of Bashmakova's book is that Diophantus indeed had general methods, which can be inferred from the surviving record of his solutions to these problems.
The opening chapter of the books tells what is known of Diophantus and his contemporaries, and surveys the problems published by Diophantus. The second chapter reviews the mathematics known to Diophantus, including his development of negative numbers, rational numbers, and powers of numbers, and his philosophy of mathematics treating numbers as dimensionless quantities, a necessary preliminary to the use of inhomogeneous polynomials. The third chapter brings in more modern concepts of algebraic geometry including the degree and genus of an algebraic curve, and rational mappings and birational equivalences between curves.
Chapters four and five concern conic sections, and the theorem that when a conic has at least one rational point it has infinitely many. Chapter six covers the use of secant lines to generate infinitely many points on a cubic plane curve, considered in modern mathematics as an example of the group law of elliptic curves. Chapter seven concerns Fermat's theorem on sums of two squares, and the possibility that Diophantus may have known of some form of this theorem. The remaining four chapters trace the influence of Diophantus and his works through Hypatia and into 19th-century Europe, particularly concentrating on the development of the theory of elliptic curves and their g
|
https://en.wikipedia.org/wiki/Agnes%20Berger
|
Agnes P. Berger (1916-2002) was a Hungarian-American mathematician who served as an associate professor of biostatistics at Columbia University's School of Public Health, as well as a statistical consultant at Mount Sinai.
Early years
Her first experiences with mathematics were thanks to the Hungarian publication Kömal (Kozepiskolai Matematikai Lapok), a monthly magazine for high school students that included math problems.
During her studies at the University of Budapest, she was a student of the prominent Hungarian mathematician Lipót Fejér, whom she would remember years later for his short, detailed classes and dramatic endings. Her parents were friends with the parents of contemporary mathematician Peter Lax.
She earned her doctorate.
Career
Berger collaborated with other statisticians such at Jerzy Neyman. She reviewed work of Joseph L. Fleiss, another statistical mathematician.
Family life and last years of life
Agnes Berger married Laszlo Berger, with whom she had a son, John Joseph Berger. She died at age 85 at Lenox Hill Hospital on March 27, 2002.
Some publications
With Abraham Wald, On Distinct Hypotheses. The Annals of Mathematical Statistics (1949), Volume 20, Number 1.
On Uniformly Consistent Tests. The Annals of Mathematical Statistics, Volume 22 (1951), Number 2.
Remark on Separable Spaces of Probability Measures. The Annals of Mathematical Statistics (1951), Volume 22, Number 1.
On orthogonal probability measures. Proceedings of the American Mathematical Society (1953), Volume 4, Number 5.
On Comparing Intensities of Association between Two Binary Characteristics in Two Different Populations. Journal of the American Statistical Association (1961), Volume 56, Number 296.
With Ruth Z. Gold, On Comparing Survival Times. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 4: Contributions to Biology and Problems of Medicine (1961), Number 67.
On comparing survival probabilities from discrete observations under unequal censoring. Statistics & Probability Letters (1983), Volume 1, Number 5.
With Ora E. Percus, On sampling by index cases. Statistics & Probability Letters (1985), Volume 3, Number 4.
With Guadalupe Gómez and Sylvan Wallenstein, A Homogeneity Test for Follow-up Studies. Mathematical Medicine and Biology (1988), Volume 5, Number 2.
References
External links
Columbia University faculty
Hungarian emigrants to the United States
1916 births
2002 deaths
American statisticians
Women statisticians
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https://en.wikipedia.org/wiki/Siddhartha%20Chib
|
Siddhartha Chib is an econometrician and statistician, the Harry C. Hartkopf Professor of Econometrics and Statistics at Washington University in St. Louis. His work is primarily in Bayesian statistics, econometrics, and Markov chain Monte Carlo methods.
Key papers include Albert and Chib (1993) which introduced an approach for binary and categorical response models based on latent variables that simplifies the Bayesian analysis of categorical response models; Chib and Greenberg (1995) which provided a derivation of the Metropolis-Hastings algorithm from first principles, guidance on implementation and extensions to multiple-block versions; Chib (1995) where a new method for calculating the marginal likelihood from the Gibbs output is developed; Chib and Jeliazkov (2001) where the method of Chib (1995) is extended to output of Metropolis-Hastings chains; Basu and Chib (2003) for a method for finding marginal likelihoods in Dirichlet process mixture models; Carlin and Chib (1995) which developed a model-space jump method for Bayesian model choice via Markov chain Monte Carlo methods; Chib (1998) which introduced a multiple-change point model that is estimated by the methods of Albert and Chib (1993) and Chib (1996) for hidden Markov processes; Kim, Shephard and Chib (1998) which introduced an efficient inference approach for univariate and multivariate stochastic volatility models; and Chib and Greenberg (1998) which developed the Bayesian analysis of the multivariate probit model.
He has also developed original methods for Bayesian inference in Tobit censored responses, discretely observed diffusions, univariate and multivariate ARMA processes, multivariate count responses, causal inference, hierarchical models of longitudinal data, nonparametric regression, and unconditional and conditional moment models.
Biography
He received a bachelor's degree from St. Stephen’s College, Delhi, in 1979, an M.B.A. from the Indian Institute of Management, Ahmedabad, in 1982, and a Ph.D. in economics from the University of California, Santa Barbara, in 1986. His advisors were Sreenivasa Rao Jammalamadaka and Thomas F. Cooley.
Honors and awards
He is a fellow of the American Statistical Association (2001), the International Society of Bayesian Analysis (2012), and the Journal of Econometrics (1996).
Selected publications
Albert, Jim; Chib, Siddhartha. "Bayesian Analysis of Binary and Polychotomous Response Data". Journal of the American Statistical Association, 88(2), 669–679, 1993.
Chib, Siddhartha; Greenberg, Edward. "Understanding the Metropolis–Hastings Algorithm". American Statistician, 49(4), 327–335, 1995
Chib, Siddhartha. "Marginal Likelihood from the Gibbs Output". Journal of the American Statistical Association, 90(4), 1313–1321, 1995.
Carlin, Brad; Chib, Siddhartha. "Bayesian Model Choice via Markov Chain Monte Carlo Methods". Journal of the Royal Statistical Society, Series B, 57(3), 473–484, 1995.
Chib, Siddhartha. "Calculating Posterior Distri
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https://en.wikipedia.org/wiki/Statistics%20in%20Biosciences
|
Statistics in Biosciences is a triannual peer-reviewed academic journal published by Springer Science+Business Media. It is the official journal of the International Chinese Statistical Association. It covers the development and application of statistical methods and their interface with other quantitative methods, such as computational and mathematical methods, in biological and life science, health science, and biopharmaceutical and biotechnological science. The journal publishes scientific papers in four formats: original articles, case studies and practice articles, review articles, and commentaries.
Abstracting and indexing
The journal is abstracted and indexed in the Emerging Sources Citation Index, Research Papers in Economics, and Scopus,
References
External links
Statistics journals
Academic journals established in 2009
Springer Science+Business Media academic journals
English-language journals
Triannual journals
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https://en.wikipedia.org/wiki/Yaca
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Yaca may refer to:
yaca, the concept of a namesake in Fijian tradition
yacA, a gene
See also
Yacas, a computer algebra system
Yacca (disambiguation)
Yacka (disambiguation)
Yaka (disambiguation)
IACA (disambiguation)
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https://en.wikipedia.org/wiki/Abdelmounaim%20Boutouil
|
Abdelmounaim Boutouil (; born 9 January 1998) is a Moroccan professional footballer who plays as a centre-back for South African Premier Division club Mamelodi Sundowns.
Career statistics
Club
.
Honours
Mamelodi Sundowns
Premier Soccer League: 2022–23
Morocco
African Nations Championship: 2020
Individual
African Nations Championship Team of the Tournament: 2020
References
1998 births
Living people
Moroccan men's footballers
Morocco men's youth international footballers
Moroccan expatriate men's footballers
AS FAR (football club) players
Kénitra AC players
Raja CA players
Royale Union Saint-Gilloise players
SCC Mohammédia players
Botola players
Men's association football defenders
Moroccan expatriate sportspeople in Belgium
Expatriate men's footballers in Belgium
2020 African Nations Championship players
Morocco men's A' international footballers
Moroccan expatriate sportspeople in South Africa
Expatriate men's soccer players in South Africa
Mamelodi Sundowns F.C. players
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https://en.wikipedia.org/wiki/John%20Aston%20%28statistician%29
|
Sir John Alexander David Aston is a British statistician, Chief Scientific Adviser (CSA) at the Home Office (2018–2020), and
Professor of Statistics, Statistical Laboratory, University of Cambridge. From 2021 he is the Harding Professor of Statistics in Public Life. And from July 2021 he has also served as a non-executive director on the board of the UK Statistics Authority.
Aston earned a bachelor's degree from the University of Cambridge, and a PhD in statistics from Imperial College London and McGill University in Montreal, Quebec. He was an academic at the University of Warwick and at Academia Sinica in Taiwan, before becoming a professor at the University of Cambridge.
Aston was one of the 23 attendees of the Scientific Advisory Group for Emergencies (Sage) during the early stage of the SARS-CoV2 pandemic owing to his CSA role at the time.
Personal life
He and his wife, Karri, have three children.
Honours
He was knighted in the 2021 Birthday Honours for services to statistics and public policymaking.
References
Living people
British statisticians
Alumni of the University of Cambridge
Alumni of Imperial College London
McGill University Faculty of Science alumni
Academics of the University of Warwick
Academics of the University of Cambridge
Year of birth missing (living people)
Place of birth missing (living people)
Knights Bachelor
Mathematical statisticians
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https://en.wikipedia.org/wiki/Dirichlet%20negative%20multinomial%20distribution
|
In probability theory and statistics, the Dirichlet negative multinomial distribution is a multivariate distribution on the non-negative integers. It is a multivariate extension of the beta negative binomial distribution. It is also a generalization of the negative multinomial distribution (NM(k, p)) allowing for heterogeneity or overdispersion to the probability vector. It is used in quantitative marketing research to flexibly model the number of household transactions across multiple brands.
If parameters of the Dirichlet distribution are , and if
where
then the marginal distribution of X is a Dirichlet negative multinomial distribution:
In the above, is the negative multinomial distribution and is the Dirichlet distribution.
Motivation
Dirichlet negative multinomial as a compound distribution
The Dirichlet distribution is a conjugate distribution to the negative multinomial distribution. This fact leads to an analytically tractable compound distribution.
For a random vector of category counts , distributed according to a negative multinomial distribution, the compound distribution is obtained by integrating on the distribution for p which can be thought of as a random vector following a Dirichlet distribution:
which results in the following formula:
where and are the dimensional vectors created by appending the scalars and to the dimensional vectors and respectively and is the multivariate version of the beta function. We can write this equation explicitly as
Alternative formulations exist. One convenient representation is
where and .
This can also be written
Properties
Marginal distributions
To obtain the marginal distribution over a subset of Dirichlet negative multinomial random variables, one only needs to drop the irrelevant 's (the variables that one wants to marginalize out) from the vector. The joint distribution of the remaining random variates is where is the vector with the removed 's. The univariate marginals are said to be beta negative binomially distributed.
Conditional distributions
If m-dimensional x is partitioned as follows
and accordingly
then the conditional distribution of on is where
and
.
That is,
Conditional on the sum
The conditional distribution of a Dirichlet negative multinomial distribution on is Dirichlet-multinomial distribution with parameters and . That is
.
Notice that the expression does not depend on or .
Aggregation
If
then, if the random variables with positive subscripts i and j are dropped from the vector and replaced by their sum,
Correlation matrix
For the entries of the correlation matrix are
Heavy tailed
The Dirichlet negative multinomial is a heavy tailed distribution. It does not have a finite mean for and it has infinite covariance matrix for . Therefore the moment generating function does not exist.
Applications
Dirichlet negative multinomial as a Pólya urn model
In the case when the parameters and are positive integers the Dirichlet
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https://en.wikipedia.org/wiki/2018%E2%80%9319%20Turkish%20Women%27s%20Volleyball%20League
|
The 2018–19 Turkish Women's Volleyball League is the 36th edition of the top-flight professional women's volleyball league in Turkey.
League table
Results
Head-to-Head results
Statistics
League stage
Play-Off Stage
Results
Week 1
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Week 2
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Week 3
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Week 4
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Week 5
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Week 6
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Week 7
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Week 8
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Week 9
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Week 10
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Week 11
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Week 12
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Week 13
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Week 14
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Week 15
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Week 16
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Week 17
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Week 18
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Week 19
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Week 20
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Week 21
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Week 22
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Play-outs
Play-offs
The eight teams that finished in the places 1 to 8 in the Regular season, compete in the Play-off (1-8).
Quarterfinals
Fifth place play-offs
Winners qualify for CEV Challenge Cup main phase.
2 matches were needed for win.
Semifinals
Winners qualify for CEV Champions League league round.
Seventh place matches
Fifth place matches
Third place matches
Winner qualify for CEV Champions League qualification round.
Loser qualify for CEV Cup main phase.
Final matches
5 matches were needed for win.
Final standing
Awards
Regular season
Best scorer
Olesia Rykhliuk (Beşiktaş)
Best setter
Ezgi Dilik (Eczacıbaşı VitrA)
Best outside spikers
Anne Buijs (Nilüfer Belediyespor)
Jana Kulan (Kameroğlu Beylikdüzü Vol. İht.)
Best middle blockers
Yasemin Güveli (Eczacıbaşı VitrA)
Ana Carolina da Silva (Nilüfer Belediyespor)
Best opposite spiker
Tijana Bošković (Eczacıbaşı VitrA)
Best libero
Pinar Eren (Beşiktaş)
Finals Series
MVP
Zhu Ting (VakıfBank)
Best spiker
Gözde Kırdar (VakıfBank)
Best blocker
Beyza Arıcı (Eczacıbaşı VitrA}
Best setter
Cansu Özbay (VakıfBank)
Best libero
Gizem Örge (VakıfBank)
Special award
Zehra Gunes (VakıfBank)
External links
2017–18 Vestel Venus Sultanlar Ligi
Turkey
Turkish Volleyball League
Turkish Volleyball League
2018 in Turkish women's sport
2019 in Turkish women's sport
Turkish Women's Volleyball League seasons
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https://en.wikipedia.org/wiki/2000%20Estonian%20census
|
2000 Population and Housing Census (PHC 2000) ( (REL 2000)) was a census that was carried out during 31 March 2000 – 9 April 2000 in Estonia by Statistics Estonia.
The total actual population recorded was 1,370,052 persons and 67.9% of them were Estonians. Compared to 1989 Estonia Census population was decreased by 195,000 persons (12.5%).
See also
Demographics of Estonia
References
External links
Results at Statistics Estonia
Censuses in Estonia
Demographics of Estonia
Ethnic groups in Estonia
2000 in Estonia
Estonia
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