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https://en.wikipedia.org/wiki/Gr%C3%A9gory%20Miermont | Grégory Miermont (born 16 July 1979) is a French mathematician working on probability, random trees and random maps.
Biography
After high school, Miermont trained for two years at Classe préparatoire aux grandes écoles at the end of which he was admitted at the École normale supérieure in Paris. He studied there from 1998 to 2002, spending the 2001–2002 year as a visiting student in Berkeley. He received his doctorate at Pierre and Marie Curie University in 2003, under the supervision of Jean Bertoin. Then, he became a CNRS researcher in 2004 at University of Paris-Sud and École normale supérieure, and was promoted to the rank of professor in 2009. Since 2012 he is a professor at the École normale supérieure de Lyon.
Work
Miermont worked on the theory of probability, more precisely on the geometry and scaling limits of random planar maps, and on fragmentation related to random trees.
Awards and honors
Diplomas, titles and awards
2003: PhD Thesis (advisor J. Bertoin)
2008: Habilitation dissertation
2007: Prize of the Fondation des Sciences Mathématiques de Paris
2009: Rollo Davidson Prize
2012: Prize of the European Mathematical Society
2014: Doeblin Prize
2015: Medallion lecturer: Compact Brownian Surfaces
Selected writings
G. Miermont, Self-similar fragmentations derived from the stable tree. I. Splitting at heights, Probab. Theory Related Fields, 127 (2003), pp. 423–454 .
B. Haas and G. Miermont, The genealogy of self-similar fragmentations with negative index as a continuum random tree, Electron. J. Probab., 9 (2004), pp. no. 4, 57–97 .
G. Miermont, Tessellations of random maps of arbitrary genus, Ann. Scient. Ec. Norm. Supér. 42, fascicule 5, 725–781 (2009). URL
G. Miermont, "The Brownian map is the scaling limit of uniform random plane quadrangulations". Acta Math. 210, 319–401 (2013) .
References
External links
Grégory Miermont's website
1979 births
Living people
Academic staff of the École Normale Supérieure
Probability theorists
21st-century French mathematicians
École Normale Supérieure alumni
Pierre and Marie Curie University alumni
Scientists from Paris |
https://en.wikipedia.org/wiki/Marayan | Marayan (, also spelled Mir'ian) is a village in northwestern Syria, administratively part of the Ariha District of the Idlib Governorate. According to the Syria Central Bureau of Statistics, Marayan had a population of 2,274 in the 2004 census. Its inhabitants are predominantly Sunni Muslims. Nearby localities include Ihsim and Iblin to the south, Sarjah to the east, and al-Rami and Ariha to the north.
In the 1960s, Marayan was a small village containing a mosque and a spring. In the village's immediate vicinity are the ruins of Byzantine-era grottoes, which were being used as underground residences in the 1960s.
References
Bibliography
Populated places in Ariha District |
https://en.wikipedia.org/wiki/Ihsim | Ihsim (, also spelled Ehsem) is a town in northwestern Syria, administratively part of the Ariha District of the Idlib Governorate. According to the Syria Central Bureau of Statistics, Marayan had a population of 5,870 in the 2004 census. It is the administrative center of the Ihsim Subdistrict, which contained a total of 19 localities with a collective population of 65,409 in 2004. Nearby localities include Iblin to the west, al-Barah to the south, al-Dana, Syria to the east, and Marayan to the north.
References
Populated places in Ariha District |
https://en.wikipedia.org/wiki/Muhambal | Muhambal (, also spelled Mhambal or Mahambel) is a town in northwestern Syria, administratively part of the Ariha District of the Idlib Governorate. According to the Syria Central Bureau of Statistics, Muhambal had a population of 4,970 in the 2004 census. It is the administrative center of the Muhambal Subdistrict, which contained 21 localities with a collective population of 27,089 in 2004. Nearby localities include Jisr al-Shughur, Bishlamun and Bizit to the west, Juzif to the south, al-Rami to the east, and Ayn Shib to the north.
References
Populated places in Ariha District |
https://en.wikipedia.org/wiki/Global%20mode | In mathematics and physics, a global mode of a system is one in which the system executes coherent oscillations in time. Suppose a quantity which depends on space and time is governed by some partial differential equation which does not have an explicit dependence on . Then a global mode is a solution of this PDE of the form , for some frequency . If is complex, then the imaginary part corresponds to the mode exhibiting exponential growth or exponential decay.
The concept of a global mode can be compared to that of a normal mode; the PDE may be thought of as a dynamical system of infinitely many equations coupled together. Global modes are used in the stability analysis of hydrodynamical systems. Philip Drazin introduced the concept of a global mode in his 1974 paper, and gave a technique for finding the normal modes of a linear PDE problem in which the coefficients or geometry vary slowly in . This technique is based on the WKBJ approximation, which is a special case of multiple-scale analysis. His method extends the Briggs–Bers technique, which gives a stability analysis for linear PDEs with constant coefficients.
In practice
Since Drazin's 1974 paper, other authors have studied more realistic problems in fluid dynamics using a global mode analysis. Such problems are often highly nonlinear, and attempts to analyse them have often relied on laboratory or numerical experiment. Examples of global modes in practice include the oscillatory wakes produced when fluid flows past an object, such as a vortex street.
References
Partial differential equations |
https://en.wikipedia.org/wiki/Stuck%20in%20This%20Ocean | Stuck in This Ocean is the debut album by the Manchester band Airship, released 5 September 2011 on PIAS Records.
Track listing
Algebra
Invertebrate
Kids
Gold Watches
Spirit Party
The Trial Of Mr Riddle
Organ
Test
Vampires
This Is Hell
Stuck in This Ocean
References
2011 debut albums
PIAS Recordings albums |
https://en.wikipedia.org/wiki/How%20to%20Bake%20Pi | How to Bake Pi is a popular mathematics book by Eugenia Cheng published in 2015. Each chapter of the book begins with a recipe for a dessert, to illustrate the methods and principles of mathematics and how they relate to one another. The book is an explanation of the foundations and architecture of category theory, a branch of mathematics that formalizes mathematical structure and its concepts.
References
2015 non-fiction books
Popular mathematics books
Basic Books books |
https://en.wikipedia.org/wiki/Quotient%20%28disambiguation%29 | Quotient is the result of division in mathematics.
Quotient may also refer to:
Mathematics
Quotient set by an equivalence relation
Quotient group
Quotient ring
Quotient module
Quotient space (linear algebra)
Quotient space (topology), by an equivalence relation in the case of a topological space
Quotient (universal algebra)
Quotient object in a category
Quotient category
Quotient of a formal language
Quotient type
Other uses
Intelligence quotient, a psychological measurement of human intelligence
Quotient Technology, the parent company of Coupons.com
Quotients (EP), music by the band Hyland
Runs Per Wicket Ratio, a statistic used to rank teams in league tables in cricket, also known as Quotient |
https://en.wikipedia.org/wiki/Mosaab%20Al-Otaibi | Mosaab Bander Al-Otaibi (; born 3 March 1992) is a Saudi professional footballer who most recently played for Al-Adalh. He primarily plays as a winger or as an attacking midfielder.
Career statistics
Honours
Clubs
Al-Nassr
Saudi Professional League 2014–15
References
Living people
Saudi Arabian men's footballers
1992 births
Footballers from Riyadh
Al Nassr FC players
Al-Khaleej FC players
Al Taawoun FC players
Al Faisaly FC players
Al Batin FC players
Al-Adalah FC players
Saudi Pro League players
Saudi First Division League players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Filip%20Pajovi%C4%87 | Filip Pajović (; born 30 July 1993) is a Serbian football goalkeeper who plays for Radnički 1923.
Club statistics
Updated to games played as of 27 June 2020.
Honours
Videoton
Ligakupa: 2012
Nemzeti Bajnokság I: 2014–15
References
External links
Filip Pajović stats at utakmica.rs
1993 births
Living people
Footballers from Zrenjanin
Men's association football goalkeepers
Serbian men's footballers
Serbia men's youth international footballers
FK Vojvodina players
FK Čukarički players
Serbian SuperLiga players
Serbian expatriate men's footballers
Serbian expatriate sportspeople in Hungary
Expatriate men's footballers in Hungary
Fehérvár FC players
Puskás Akadémia FC players
Újpest FC players
FK Radnički 1923 players
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/Cyclic%20cover | In algebraic topology and algebraic geometry, a cyclic cover or cyclic covering is a covering space for which the set of covering transformations forms a cyclic group. As with cyclic groups, there may be both finite and infinite cyclic covers.
Cyclic covers have proven useful in the descriptions of knot topology and the algebraic geometry of Calabi–Yau manifolds.
In classical algebraic geometry, cyclic covers are a tool used to create new objects from existing ones through, for example, a field extension by a root element. The powers of the root element form a cyclic group and provide the basis for a cyclic cover. A line bundle over a complex projective variety with torsion index may induce a cyclic Galois covering with cyclic group of order .
References
Further reading
Algebraic geometry
Algebraic topology |
https://en.wikipedia.org/wiki/Azathoth%20%28disambiguation%29 | Azathoth may refer to:
Azathoth, the Lovecraftian Outer God ruler
Azathoth (short story), the short story in which he first appears
Azathoth (geometry), also known as the great retrosnub icosidodecahedron |
https://en.wikipedia.org/wiki/Ronald%20J.%20Stern | Ronald John Stern (born 20 January 1947) is a mathematician who works on topology, geometry, and gauge theory. He is emeritus professor at the University of California, Irvine.
Stern was the first in his family to receive a college education and earned his bachelor's degree in mathematics from Knox College in Galesburg, Illinois. He then earned his Ph.D. in 1973 from the University of California, Los Angeles under the joint supervision of Robert Duncan Edwards (de) and Robert F. Brown.
Before joining the faculty at the University of California, Irvine in 1989, Stern was a professor at the University of Utah and a visiting professor at UCLA and the University of Hawaii.
He was an Invited Speaker at the 1998 International Congress of Mathematicians, in Berlin.
He is a Fellow of the American Mathematical Society.
Selected papers
These are his most cited papers (according to Google Scholar), they are all joint work with Ron Fintushel:
"Knots, links, and 4-manifolds", Inventiones mathematicae 134 (2), pp. 363–400 (1998)
"Rational blowdowns of smooth 4-manifolds", Journal of Differential Geometry 46 (2), pp. 181–235 (1997)
"Instanton homology of Seifert fibred homology three spheres", Proceedings of the London Mathematical Society 61 (3), pp. 109–137 (1990)
"Immersed spheres in 4-manifolds and the immersed Thom conjecture", Turkish Journal of Mathematics 19 (2), pp. 145–157 (1995)
"Pseudofree orbifolds", Annals of Mathematics, pp. 335–364 (1985)
"Constructing lens spaces by surgery on knots", Mathematische Zeitschrift 175 (1), pp. 33–51 (1980)
"The blowup formula for Donaldson invariants", Annals of Mathematics 143 (3), pp. 529–546 (1996)
See also
Fintushel–Stern knot
References
External links
(publications with online links)
1947 births
Living people
American mathematicians
University of California, Los Angeles alumni
University of California, Irvine faculty
Topologists
Fellows of the American Mathematical Society
University of Utah faculty
Knox College (Illinois) alumni
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/Universal%20representation%20%28C%2A-algebra%29 | In the theory of C*-algebras, the universal representation of a C*-algebra is a faithful representation which is the direct sum of the GNS representations corresponding to the states of the C*-algebra. The various properties of the universal representation are used to obtain information about the ideals and quotients of the C*-algebra. The close relationship between an arbitrary representation of a C*-algebra and its universal representation can be exploited to obtain several criteria for determining whether a linear functional on the algebra is ultraweakly continuous. The method of using the properties of the universal representation as a tool to prove results about the C*-algebra and its representations is commonly referred to as universal representation techniques in the literature.
Formal definition and properties
Definition. Let A be a C*-algebra with state space S. The representation
on the Hilbert space is known as the universal representation of A.
As the universal representation is faithful, A is *-isomorphic to the C*-subalgebra Φ(A) of B(HΦ).
States of Φ(A)
With τ a state of A, let πτ denote the corresponding GNS representation on the Hilbert space Hτ. Using the notation defined here, τ is ωx ∘ πτ for a suitable unit vector x(=xτ) in Hτ. Thus τ is ωy ∘ Φ, where y is the unit vector Σρ∈S ⊕yρ in HΦ, defined by yτ=x, yρ=0(ρ≠τ). Since the mapping τ → τ ∘ Φ−1 takes the state space of A onto the state space of Φ(A), it follows that each state of Φ(A) is a vector state.
Bounded functionals of Φ(A)
Let Φ(A)− denote the weak-operator closure of Φ(A) in B(HΦ). Each bounded linear functional ρ on Φ(A) is weak-operator continuous and extends uniquely preserving norm, to a weak-operator continuous linear functional on the von Neumann algebra Φ(A)−. If ρ is hermitian, or positive, the same is true of . The mapping ρ → is an isometric isomorphism from the dual space Φ(A)* onto the predual of Φ(A)−. As the set of linear functionals determining the weak topologies coincide, the weak-operator topology on Φ(A)− coincides with the ultraweak topology. Thus the weak-operator and ultraweak topologies on Φ(A) both coincide with the weak topology of Φ(A) obtained from its norm-dual as a Banach space.
Ideals of Φ(A)
If K is a convex subset of Φ(A), the ultraweak closure of K (denoted by K−)coincides with the strong-operator, weak-operator closures of K in B(HΦ). The norm closure of K is Φ(A) ∩ K−. One can give a description of norm-closed left ideals in Φ(A) from the structure theory of ideals for von Neumann algebras, which is relatively much more simple. If K is a norm-closed left ideal in Φ(A), there is a projection E in Φ(A)− such that
If K is a norm-closed two-sided ideal in Φ(A), E lies in the center of Φ(A)−.
Representations of A
If π is a representation of A, there is a projection P in the center of Φ(A)− and a *-isomorphism α from the von Neumann algebra Φ(A)−P onto π(A)− such that π(a) = α(Φ(a)P) for each a in A. This can be convenientl |
https://en.wikipedia.org/wiki/Ricardo%20Sagardia | Ricardo Hugo Sagardia Medrano (born March 4, 1993, in Bolivia) is a Bolivian footballer who since 2011 has played defender for Bolívar.
Club career statistics
References
External links
1993 births
Living people
Bolivian men's footballers
Club Bolívar players
Men's association football defenders |
https://en.wikipedia.org/wiki/Sverdrup%20Prize | The Sverdrup Prize (Sverdrupprisen) is a Norwegian honorary award concerning the fields of theoretical and applied statistics.
History
It was established in the memory of Erling Sverdrup (1917–1994) who was professor of mathematical statistics and insurance mathematics with the Department of Mathematics at the University of Oslo from 1953 until his retirement in 1984. Sverdrup was instrumental in building up and modernising the fields of statistics and actuarial science in Norway.
In 2007, the Norwegian Statistical Association (Norsk statistisk forening) announced the creation of the Sverdrup Prize, with the first prizes to be awarded in 2009. There is one Sverdup Prize to a prominent statistician ("an eminent representative of the statistics profession") and a second award to a younger statistician who has authored or coauthored a high quality journal article. The prizes entail a diploma and a stipend and are awarded every second year, typically in connection with the biennial conferences of the Norwegian Statistical Association.
Winners
References
Other sources
Norwegian Statistical Association's Sverdrup Prize
Sverdrup Prize awarded Nils Lid Hjort, 2013
Sverdrup Prize awarded Tore Schweder, 2011
Sverdrup Prize awarded Dag Tjøstheim, 2009
Academic awards
Norwegian awards |
https://en.wikipedia.org/wiki/Level%20structure%20%28algebraic%20geometry%29 | In algebraic geometry, a level structure on a space X is an extra structure attached to X that shrinks or eliminates the automorphism group of X, by demanding automorphisms to preserve the level structure; attaching a level structure is often phrased as rigidifying the geometry of X.
In applications, a level structure is used in the construction of moduli spaces; a moduli space is often constructed as a quotient. The presence of automorphisms poses a difficulty to forming a quotient; thus introducing level structures helps overcome this difficulty.
There is no single definition of a level structure; rather, depending on the space X, one introduces the notion of a level structure. The classic one is that on an elliptic curve (see #Example: an abelian scheme). There is a level structure attached to a formal group called a Drinfeld level structure, introduced in .
Level structures on elliptic curves
Classically, level structures on elliptic curves are given by a lattice containing the defining lattice of the variety. From the moduli theory of elliptic curves, all such lattices can be described as the lattice for in the upper-half plane. Then, the lattice generated by gives a lattice which contains all -torsion points on the elliptic curve denoted . In fact, given such a lattice is invariant under the action on , wherehence it gives a point in called the moduli space of level N structures of elliptic curves , which is a modular curve. In fact, this moduli space contains slightly more information: the Weil pairinggives a point in the -th roots of unity, hence in .
Example: an abelian scheme
Let be an abelian scheme whose geometric fibers have dimension g.
Let n be a positive integer that is prime to the residue field of each s in S. For n ≥ 2, a level n-structure is a set of sections such that
for each geometric point , form a basis for the group of points of order n in ,
is the identity section, where is the multiplication by n.
See also: modular curve#Examples, moduli stack of elliptic curves.
See also
Siegel modular form
Rigidity (mathematics)
Local rigidity
Notes
References
Further reading
Notes on principal bundles
J. Lurie, Level Structures on Elliptic Curves.
Algebraic geometry |
https://en.wikipedia.org/wiki/1749%20in%20Sweden | Events from the year 1749 in Sweden
Incumbents
Monarch – Frederick I
Events
- Treaty between Sweden and Denmark.
- Statistics Sweden
- Carl Linnaeus conduct his trip to Scania.
- Street lights are introduced in the capital when every house owner are obliged to place a light of some kind upon their house to light up the street. In practice, however, this instruction is insufficient.
- The Agricultural revolution, the Great Partition, in which farmers are given united land in individual farms rather than having their land spread in several fields around a village, is initiated in Sweden by Jacob Faggot.
- A new regulation is issued were the permits of street trade (Månglare), at the time already one of the most common for destitute city women, is henceforth to be given foremost in favor of women in need of supporting themselves.
Births
2 January - Carl Gustaf Nordin, historian and ecclesiastic (died 1812)
28 April - Adolf Fredrik Munck, royal favorite (died 1831)
- Sofia Lovisa Gråå, educator (died 1835)
- Ulla von Höpken, courtier (died 1810)
Deaths
- Johan August Meijerfeldt, general (born 1665)
23 July - Ingeborg i Mjärhult, natural healer, medicine woman, herbalist, natural philosopher, soothsayer and spiritual visionary (born 1665)
References
Years of the 18th century in Sweden
Sweden |
https://en.wikipedia.org/wiki/Dualizing%20sheaf | In algebraic geometry, the dualizing sheaf on a proper scheme X of dimension n over a field k is a coherent sheaf together with a linear functional
that induces a natural isomorphism of vector spaces
for each coherent sheaf F on X (the superscript * refers to a dual vector space). The linear functional is called a trace morphism.
A pair , if it is exists, is unique up to a natural isomorphism. In fact, in the language of category theory, is an object representing the contravariant functor from the category of coherent sheaves on X to the category of k-vector spaces.
For a normal projective variety X, the dualizing sheaf exists and it is in fact the canonical sheaf: where is a canonical divisor. More generally, the dualizing sheaf exists for any projective scheme.
There is the following variant of Serre's duality theorem: for a projective scheme X of pure dimension n and a Cohen–Macaulay sheaf F on X such that is of pure dimension n, there is a natural isomorphism
.
In particular, if X itself is a Cohen–Macaulay scheme, then the above duality holds for any locally free sheaf.
Relative dualizing sheaf
Given a proper finitely presented morphism of schemes , defines the relative dualizing sheaf or as the sheaf such that for each open subset and a quasi-coherent sheaf on , there is a canonical isomorphism
,
which is functorial in and commutes with open restrictions.
Example:
If is a local complete intersection morphism between schemes of finite type over a field, then (by definition) each point of has an open neighborhood and a factorization , a regular embedding of codimension followed by a smooth morphism of relative dimension . Then
where is the sheaf of relative Kähler differentials and is the normal bundle to .
Examples
Dualizing sheaf of a nodal curve
For a smooth curve C, its dualizing sheaf can be given by the canonical sheaf .
For a nodal curve C with a node p, we may consider the normalization with two points x, y identified. Let be the sheaf of rational 1-forms on with possible simple poles at x and y, and let be the subsheaf consisting of rational 1-forms with the sum of residues at x and y equal to zero. Then the direct image defines a dualizing sheaf for the nodal curve C. The construction can be easily generalized to nodal curves with multiple nodes.
This is used in the construction of the Hodge bundle on the compactified moduli space of curves: it allows us to extend the relative canonical sheaf over the boundary which parametrizes nodal curves. The Hodge bundle is then defined as the direct image of a relative dualizing sheaf.
Dualizing sheaf of projective schemes
As mentioned above, the dualizing sheaf exists for all projective schemes. For X a closed subscheme of Pn of codimension r, its dualizing sheaf can be given as . In other words, one uses the dualizing sheaf on the ambient Pn to construct the dualizing sheaf on X.
See also
coherent duality
reflexive sheaf
Gorenstein ring
Dualizing mod |
https://en.wikipedia.org/wiki/Predictive%20probability%20of%20success | Predictive probability of success (PPOS) is a statistics concept commonly used in the pharmaceutical industry including by health authorities to support decision making. In clinical trials, PPOS is the probability of observing a success in the future based on existing data. It is one type of probability of success. A Bayesian means by which the PPOS can be determined is through integrating the data's likelihood over possible future responses (posterior distribution).
Types of PPOS
Classification based on type of end point: Normal, binary, time to event.
Classification based on the relationship between the trial providing data and the trial to be predicted
Cross trial PPOS: using data from one trial to predict the other trial
Within trial PPOS: using data at interim analysis to predict the same trial at final analysis
Classification based on the relationship between the end point(s) with data and the end point to be predicted
1 to 1 PPOS: using one end point to predict the same end point
1 to 1* PPOS: using one end point to predict another different but correlated end point
Relationship with conditional power and predictive power
Conditional power is the probability of observing a statistically significance assuming the parameter equals to a specific value. More specifically, these parameters could be treatment and placebo event rates that could be fixed in future observations. This is a frequentist statistical power. Conditional power is often criticized for assuming the parameter equals to a specific value which is not known to be true. If the true value of the parameter is known, there is no need to do an experiment.
Predictive power addresses this issue assuming the parameter has a specific distribution. Predictive power is a Bayesian power. A parameter in Bayesian setting is a random variable. Predictive power is a function of a parameter(s), therefore predictive power is also a variable.
Both conditional power and predictive power use statistical significance as success criteria. However statistical significance is often not enough to define success. For example, health authorities often require the magnitude of treatment effect to be bigger than statistical significance to support a registration decision.
To address this issue, predictive power can be extended to the concept of PPOS. The success criteria for PPOS is not restricted to statistical significance. It can be something else such as clinical meaningful results. PPOS is conditional probability conditioned on a random variable, therefore it is also a random variable. The observed value is just a realization of the random variable.
Relationship with posterior probability of success
Posterior probability of success is calculated from posterior distribution. PPOS is calculated from predictive distribution. Posterior distribution is the summary of uncertainties about the parameter. Predictive distribution has not only the uncertainty about parameter but also the uncertain |
https://en.wikipedia.org/wiki/Chia-Kun%20Chu | Chia-Kun (John) Chu (; August 14, 1927 – January 2, 2023) was a Chinese-American applied mathematician who was the Fu Foundation Professor Emeritus of Applied Mathematics at Columbia University. He had been on Columbia faculty since 1965 and served as the department chairman of applied physics and nuclear engineering three times (1982–1983, 1985–1988, 1995–1997).
Biography
Chu received a bachelor's in mechanical engineering from Chiao-Tung University in 1948, a master's from Cornell University in 1950, and a Ph.D. from Courant Institute, New York University in 1959.
Chu was an internationally recognized applied mathematician and one of the pioneers of computational mathematics in fluid dynamics, magnetohydrodynamics, and shock waves. He developed approximations to the differential equations of fluid dynamics and coined the term "computational fluid dynamics".
Chu received numerous honors. He was a recipient of Guggenheim Fellowship and was elected fellow of American Physical Society and fellow of Japan Society for the Promotion of Science. He was awarded an honorary Doctor of Science degree from Columbia University in 2006.
Chia-Kun Chu was the son of bank chairman Ju Tang Chu. Chia-Kun Chu was also the brother-in-law of Z.Y. Fu, a Columbia donor who gave his name for the Fu Foundation School of Engineering and Applied Science.
Chia-Kun Chu died on January 2, 2023, at the age of 95.
References
Notes
1927 births
2023 deaths
21st-century American physicists
20th-century American mathematicians
National Chiao Tung University (Shanghai) alumni
Cornell University College of Engineering alumni
Courant Institute of Mathematical Sciences alumni
Fluid dynamicists
American academics of Chinese descent
Fellows of the American Physical Society
Columbia University faculty
Scientists from Shanghai |
https://en.wikipedia.org/wiki/Construction%20of%20an%20irreducible%20Markov%20chain%20in%20the%20Ising%20model | Construction of an irreducible Markov chain in the Ising model is a mathematical method to prove results.
In applied mathematics, the construction of an irreducible Markov Chain in the Ising model is the first step in overcoming a computational obstruction encountered when a Markov chain Monte Carlo method is used to get an exact goodness-of-fit test for the finite Ising model.
The Ising model is used to study magnetic phase transitions and is one of the models of interacting systems.
Markov bases
Every integer vector , can be uniquely written as , where and are nonnegative vectors. A Markov basis for the Ising model is a set of integer vectors such that:
(i) For all , there must be and .
(ii) For any and any , there always exist satisfy
and
for l = 1,...,k.
The element of is moved. Then, by using the Metropolis–Hastings algorithm, we can get an aperiodic, reversible, and irreducible Markov Chain.
The paper ‘Algebraic algorithms for sampling from conditional distributions,’ published by Persi Diaconis and Bernd Sturmfels in 1998, shows that a Markov basis can be defined algebraically as an Ising model. By the paper, any generating set for the ideal is a Markov basis for the Ising model.
Construction of an irreducible Markov chain
Without modifying the algorithm mentioned in the paper, it is impossible to get uniform samples from , otherwise leading to inaccurate p-values.
A simple swap is defined as of the form , where is the canonical basis vector of . Simple swaps change the states of two lattice points in y.
Z denotes the set of sample swaps. Then two configurations are -connected by Z, if there is a path between and in consisting of simple swaps , which means there exists such that
with
for l = 1,...,k
The algorithm can now be described as:
(i) Start with the Markov chain in a configuration
(ii) Select uniformly at random and let .
(iii) Accept if ; otherwise remain in y.
Although the resulting Markov Chain possibly cannot leave the initial state, the problem does not arise for a 1-dimensional Ising model. In higher dimensions, we can overcome this problem by using the Metropolis-Hastings algorithm in the smallest expanded sample space
Irreducibility in the 1-dimensional Ising model
The proof of irreducibility in the 1-dimensional Ising model requires two lemmas.
Lemma 1:The max-singleton configuration of for the 1-dimension Ising model is unique(up to location of its connected components) and consists of singletons and one connected components of size .
Lemma 2:For and , let denote the unique max-singleton configuration. There exists a sequence such that:
and
for l = 1,...,k
Since is the smallest expanded sample space which contains , any two configurations in can be connected by simple swaps Z without leaving . This is proved by Lemma 2, so we an get the irreducibility of the Markov Chain based on simple swaps for the 1-dimension Ising model.
It is also possible to get |
https://en.wikipedia.org/wiki/Optimistic%20knowledge%20gradient | In statistics The optimistic knowledge gradient is a approximation policy proposed by Xi Chen, Qihang Lin and Dengyong Zhou in 2013. This policy is created to solve the challenge of computationally intractable of large size of optimal computing budget allocation problem in binary/multi-class crowd labeling where each label from the crowd has a certain cost.
Motivation
The optimal computing budget allocation problem is formulated as a Bayesian Markov decision process(MDP) and is solved by using the dynamic programming (DP) algorithm where the Optimistic knowledge gradient policy is used to solve the computationally intractable of the dynamic programming (DP) algorithm.
Consider a budget allocation issue in crowdsourcing. The particular crowdsourcing problem we considering is crowd labeling. Crowd labeling is a large amount of labeling tasks which are hard to solve by machine, turn out to easy to solve by human beings, then we just outsourced to an unidentified group of random people in a distributed environment.
Methodology
We want to finish this labeling tasks rely on the power of the crowd hopefully. For example, suppose we want to identify a picture according to the people in a picture is adult or not, this is a Bernoulli labeling problem, and all of us can do in one or two seconds, this is an easy task for human being. However, if we have tens of thousands picture like this, then this is no longer the easy task any more. That's why we need to rely on crowdsourcing framework to make this fast. Crowdsourcing framework of this consists of two steps. Step one, we just dynamically acquire from the crowd for items. On the other sides, this is dynamic procedure. We don't just send out this picture to everyone and we focus every response, instead, we do this in quantity. We are going to decide which picture we send it in the next, and which worker we are going to hire in the crowd in the next. According to his or her historical labeling results. And each picture can be sent to multiple workers and every worker can also work on different pictures. Then after we collect enough number of labels for different picture, we go to the second steps where we want to infer true label of each picture based on the collected labels. So there are multiple ways we can do inference. For instance, the simplest we can do this is just majority vote. The problem is that no free lunch, we have to pays for worker for each label he or she provides and we only have a limited project budget. So the question is how to spend the limited budget in a smart way.
Challenges
Before showing the mathematic model, the paper mentions what kinds of challenges we are facing.
Challenge 1
First of all, the items have a different level of difficulty to compute the label, in a previous example, some picture are easy to classify. In this case, you will usually see very consistent labels from the crowd. However, if some pictures are ambiguous, people may disagree with each other resulting |
https://en.wikipedia.org/wiki/Guillermo%20Viscarra | Guillermo Viscarra Bruckner (born February 7, 1993) is a Bolivian professional footballer who plays as a goalkeeper for The Strongest and the Bolivia national team.
Club career statistics
References
External links
1993 births
Living people
Bolivian men's footballers
Esporte Clube Vitória players
Club Bolívar players
C.D. Jorge Wilstermann players
Oriente Petrolero players
Hapoel Ra'anana A.F.C. players
Israeli Premier League players
Bolivian Primera División players
Bolivian expatriate men's footballers
Expatriate men's footballers in Brazil
Expatriate men's footballers in Israel
Bolivian expatriate sportspeople in Brazil
Footballers from Santa Cruz de la Sierra
Men's association football goalkeepers
Bolivian people of German descent |
https://en.wikipedia.org/wiki/Cirquent%20calculus | Cirquent calculus is a proof calculus that manipulates graph-style constructs termed cirquents, as opposed to the traditional tree-style objects such as formulas or sequents. Cirquents come in a variety of forms, but they all share one main characteristic feature, making them different from the more traditional objects of syntactic manipulation. This feature is the ability to explicitly account for possible sharing of subcomponents between different components. For instance, it is possible to write an expression where two subexpressions F and E, while neither one is a subexpression of the other, still have a common occurrence of a subexpression G (as opposed to having two different occurrences of G, one in F and one in E).
Overview
The approach was introduced by G. Japaridze in as an alternative proof theory capable of "taming" various nontrivial fragments of his computability logic, which had otherwise resisted all axiomatization attempts within the traditional proof-theoretic frameworks. The origin of the term “cirquent” is CIRcuit+seQUENT, as the simplest form of cirquents, while resembling circuits rather than formulas, can be thought of as collections of one-sided sequents (for instance, sequents of a given level of a Gentzen-style proof tree) where some sequents may have shared elements.
The basic version of cirquent calculus was accompanied with an "abstract resource semantics" and the claim that the latter was an adequate formalization of the resource philosophy traditionally associated with linear logic. Based on that claim and the fact that the semantics induced a logic properly stronger than (affine) linear logic, Japaridze argued that linear logic was incomplete as a logic of resources. Furthermore, he argued that not only the deductive power but also the expressive power of linear logic was weak, for it, unlike cirquent calculus, failed to capture the ubiquitous phenomenon of resource sharing.
The resource philosophy of cirquent calculus sees the approaches of linear logic and classical logic as two extremes: the former does not allow any sharing at all, while in the latter “everything is shared that can be shared”. Unlike cirquent calculus, neither approach thus permits mixed cases where some identical subformulas are shared and some not.
Among the later-found applications of cirquent calculus was the use of it to define a semantics for purely propositional independence-friendly logic. The corresponding logic was axiomatized by W. Xu.
Syntactically, cirquent calculi are deep inference systems with the unique feature of subformula-sharing. This feature has been shown to provide speedup for certain proofs. For instance, polynomial size analytic proofs for the propositional pigeonhole have been constructed. Only quasipolynomial analytic proofs have been found for this principle in other deep inference systems. In resolution or analytic Gentzen-style systems, the pigeonhole principle is known to have only exponential size p |
https://en.wikipedia.org/wiki/Eigenoperator | In mathematics, an eigenoperator, A, of a matrix H is a linear operator such that
where is a corresponding scalar called an eigenvalue.
References
Linear algebra
Matrix theory |
https://en.wikipedia.org/wiki/SportVU | SportVU is a camera system that collects data 25 times per second. Its aim is to follow the ball and all players on court. SportVU provides statistics such as real-time player and ball positioning through software and statistical algorithms. Through this data, STATS presents performance metrics for players and teams to use.
STATS was first created for soccer, however it later expanded the core SportVU technology into basketball beginning with the 2010-2011 NBA season. Currently, STATS is the Official Tracking partner of the NBA. The NBA uses statistics collected by SportVU on NBA.com and NBATV as well as in arenas across the country to provide information for the audience. SportVU statistics are utilized by teams in the league for the purpose of analytics and player development. The cameras keep a digitized visual record of every game, collecting players' positions and speed.
History
2005-2010
SportVU was created in 2005 by scientists, Gal Oz and Miky Tamir, who had a background in missile tracking and advanced optical recognition. They had previously used the same science to track soccer matches in Israel.
SportVU was featured at national trade shows NAB 2007, in Las Vegas, and International Broadcasting Convention 2007, in Amsterdam. In 2008, SportVU was acquired by STATS LLC. STATS then centers SportVU efforts on basketball. During the 2009 NBA Finals in Orlando, STATS demoed their SportVU technology for NBA executives. At the start of the 2010-2011 NBA season, four teams were contracted to use SportVU, the Dallas Mavericks, Houston Rockets, Oklahoma City Thunder and San Antonio Spurs.
2011-2015
SportVU converted their tracking system from delayed processing to real-time data delivery during the 2011-2012 NBA season. At the start of the 2012-2013 season, 10 teams were using SportVU.
Since the 2013-2014 NBA season, the SportVU camera system was installed in all NBA arenas. In the same year, STATS added the ICE analytics platform to organize, display and analyze SportVU data. NBA team, Toronto Raptors, shared with sports blog, Grantland, their progress with the use of SportVU's new algorithms. The Raptors Analytics Team created a graphical user interface to play video footage of the play from the X-Y coordinates.
2016-2017
In 2016, STATS and the NBA met an agreement to extend SportVU tracking data to more media outlets including ESPN, NBA on TNT, and Bleacher Report.
Beginning in the 2016-2017 season, STATS was used as France's Ligue de Football Professionnel's official data and tracking provider. STATS used SportVU to provide football data and statistics.
After NBA's adoption of SportVU tracking technology in 2013, statisticians and data scientists used tools such as machine learning to provide more complex statistics from the tracking data. At the 10th annual MIT Sloan Sports Analytics Conference in 2016, STATS's own Director of Data Science and his team was awarded for their contributions to a research paper on the prediction |
https://en.wikipedia.org/wiki/Raymond%20E.%20Goldstein | Raymond Ethan Goldstein (born 1961) FRS FInstP is Schlumberger Professor of Complex Physical Systems in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge and a Fellow of Churchill College, Cambridge.
Education
Goldstein was educated at the West Orange Public Schools and Massachusetts Institute of Technology (MIT) where he graduated Phi Beta Kappa with double major Bachelor of Science degrees in Physics and Chemistry in 1983. He continued his education at Cornell University where he was awarded a Master of Science degree in Physics in 1986, followed by a PhD in 1988 for research on phase transitions and critical phenomena supervised by Neil Ashcroft.
Research
Goldstein's research focuses on understanding nonequilibrium phenomena in the natural world, with particular emphasis on biophysics and has been funded by the Engineering and Physical Sciences Research Council (EPSRC), the Biotechnology and Biological Sciences Research Council (BBSRC) and the European Union 7th Framework Programme on Research & Innovation (FP7). His research has been published in leading peer reviewed scientific journals including Proceedings of the National Academy of Sciences of the United States of America, Physical Review Letters, and the Journal of Fluid Mechanics.
Career
Goldstein has held academic appointments at the University of Chicago, Princeton University and the University of Arizona. He was appointed Schlumberger Professor at the University of Cambridge in 2006.
Awards and honours
Goldstein was awarded the Stefanos Pnevmatikos International Award in 2000. He was elected Fellow of the American Physical Society in 2002, Fellow of the Institute of Physics (FInstP) in 2009 and the Institute of Mathematics and its Applications (FIMA) in 2010. With Joseph Keller, Patrick B. Warren and Robin C. Ball, Goldstein was awarded an Ig Nobel Prize in 2012 for calculating the forces that shape and move ponytail hair.
Goldstein was elected a Fellow of the Royal Society (FRS) in 2013. His nomination reads:
He was awarded the 2016 Batchelor Prize of the International Union of Theoretical and Applied Mechanics for his research into active matter fluid mechanics., and the Institute of Physics Rosalind Franklin Medal and Prize for revealing the physical basis for fluid motion in and around active cells.
Personal life
Goldstein married Argentine mathematical physicist Adriana Pesci.
References
1961 births
Living people
People from West Orange, New Jersey
Cornell University alumni
Massachusetts Institute of Technology School of Science alumni
American biophysicists
Academics of the University of Cambridge
Fellows of the Royal Society
Fellows of the Institute of Physics
Fellows of the American Physical Society |
https://en.wikipedia.org/wiki/Desuspension | In topology, a field within mathematics, desuspension is an operation inverse to suspension.
Definition
In general, given an n-dimensional space , the suspension has dimension n + 1. Thus, the operation of suspension creates a way of moving up in dimension. In the 1950s, to define a way of moving down, mathematicians introduced an inverse operation , called desuspension. Therefore, given an n-dimensional space , the desuspension has dimension n – 1.
In general, .
Reasons
The reasons to introduce desuspension:
Desuspension makes the category of spaces a triangulated category.
If arbitrary coproducts were allowed, desuspension would result in all cohomology functors being representable.
See also
Cone (topology)
Equidimensionality
Join (topology)
References
External links
Desuspension at an Odd Prime
When can you desuspend a homotopy cogroup?
Topology
Homotopy theory |
https://en.wikipedia.org/wiki/Ebtisam%20Abdulaziz | Ebtisam Abdulaziz (born 1975) is a contemporary Emirati artist and writer born and raised in Sharjah, UAE. She works with geometry and mathematics to address issues of belonging and identity through installations, performance art and other media.
Selected exhibitions
2014 NYU Abu Dhabi Art Gallery, Abu Dhabi, UAE
2014 View From Inside - Fotofest
2014 32nd Emirates Fine Arts Society Annual Exhibition, UAE
2013 Autobiography, The Third Line, Dubai, UAE
2013 Biennale, Houston, USA
2013 Emirati Expressions, Manarat Al Saadiyat, Abu Dhabi, UAE.
2013 The Beginning of Thinking is Geometric, Maraya Arts Centre, Sharjah, UAE
2013 Three Generations, Sotheby's, London UK.
2012 Arab Express, The Mori Art Museum, Tokyo, Japan
2012 25 years of Arab Creativity, L’institut du Monde Arabe, Paris, France
2012 Inventing The World: The Artists as a Citizen, Benin Biennial, Kora Centre, Benin
2009 UAE Pavilions at 53rd Venice Biennale
2007 Ebtisam Abdulaziz, Sharjah Contemporary Art Museum, Sharjah, UAE
2005 Sharjah Biennial, UAE
Collection
Ebtisam's work is housed in several public and private collections including:
Farook Collection
Ministry of Culture, UAE
Youth and Community Development, UAE
Renault Collection, France
Deutsche Bank AG, Germany
See also
Emirates Fine Arts Society
References
Emirati women artists
Emirati contemporary artists
People from the Emirate of Sharjah
1975 births
Living people |
https://en.wikipedia.org/wiki/Gridiron%21 | Gridiron! is a football game by Bethesda Softworks.
Gameplay
Gridiron! is a game in which statistics for players are provided on an NFL DataDisc.
Reception
Wyatt Lee reviewed the game for Computer Gaming World, and stated that "Although this game is only available for the Amiga and Atari ST, the graphics are not as spectacular as one would expect for these machines."
Atari Explorer rated the game an 8 of 10.
John Harrington reviewed Gridiron! for Games International magazine, and gave it a rating of 8 out of 10, and stated that "I was dubious about the decision to combine strategy and arcade action but in Gridiron! it works."
The game sold well and was awarded Sports game of the year, as well as voted as one of the 40 Best Games of All Time by Amiga World. Bethesda founder Christopher Weaver said in 1994 that Gridiron "put us on the map"
References
1986 video games
American football video games
Amiga games
Atari ST games
Bethesda Softworks games
Video games developed in the United States
Video games set in the United States |
https://en.wikipedia.org/wiki/Cohen%27s%20h | In statistics, Cohen's h, popularized by Jacob Cohen, is a measure of distance between two proportions or probabilities. Cohen's h has several related uses:
It can be used to describe the difference between two proportions as "small", "medium", or "large".
It can be used to determine if the difference between two proportions is "meaningful".
It can be used in calculating the sample size for a future study.
When measuring differences between proportions, Cohen's h can be used in conjunction with hypothesis testing. A "statistically significant" difference between two proportions is understood to mean that, given the data, it is likely that there is a difference in the population proportions. However, this difference might be too small to be meaningful—the statistically significant result does not tell us the size of the difference. Cohen's h, on the other hand, quantifies the size of the difference, allowing us to decide if the difference is meaningful.
Uses
Researchers have used Cohen's h as follows.
Describe the differences in proportions using the rule of thumb criteria set out by Cohen. Namely, h = 0.2 is a "small" difference, h = 0.5 is a "medium" difference, and h = 0.8 is a "large" difference.
Only discuss differences that have h greater than some threshold value, such as 0.2.
When the sample size is so large that many differences are likely to be statistically significant, Cohen's h identifies "meaningful", "clinically meaningful", or "practically significant" differences.
Calculation
Given a probability or proportion p, between 0 and 1, its arcsine transformation is
Given two proportions, and , h is defined as the difference between their arcsine transformations. Namely,
This is also sometimes called "directional h" because, in addition to showing the magnitude of the difference, it shows which of the two proportions is greater.
Often, researchers mean "nondirectional h", which is just the absolute value of the directional h:
In R, Cohen's h can be calculated using the ES.h function in the pwr package or the cohenH function in the rcompanion package
Interpretation
Cohen provides the following descriptive interpretations of h as a rule of thumb:
h = 0.20: "small effect size".
h = 0.50: "medium effect size".
h = 0.80: "large effect size".
Cohen cautions that:
Nevertheless, many researchers do use these conventions as given.
See also
Estimation statistics
Clinical significance
Cohen's d
Odds ratio
Effect size
Sample size determination
References
Effect size
Statistical hypothesis testing
Medical statistics
Clinical research
Clinical trials
Biostatistics
Sampling (statistics) |
https://en.wikipedia.org/wiki/Lagos%20Bureau%20of%20Statistics | The Lagos Bureau of Statistics is a department in the Lagos State Ministry of Economic Planning and Budget concerned with the coordination of statistical activities in Lagos State, the most populous state of Nigeria. The department focusses on the collections of statistical data on topics including population, housing, finance, education, health, agriculture, and social welfare services. The department also collaborates with international bodies, federal, state and local governments, and other statistical agencies.
Publications
Digest of statistics is one of the annual publication of the department. It contains the statistical data on the Socioeconomic activities of the State. It features data on the State population, Traffic Management, Waste Management and Environment. It also provides information on Motor Vehicle Registration, Road Accidents, Traffic Management, Price Index Housing, among other sectors.
Other publications includes Abstract of Local Government Statistics, Basic Statistical Hotline, Price Statistics Bulletin, Statistical year book and Motor Vehicles Statistics.
Vision
To continue to serve as the state's one-stop shop for high-quality, dependable, and stable statistics.
Mission
Assuring a digitalized, effective, and timely statistics system for planning, policy formation, and decision-making.
References
Lagos State |
https://en.wikipedia.org/wiki/Roger%20E.%20Kirk | Roger E. Kirk (born February 23, 1930) is a professor of psychology and statistics at Baylor University. He earned his B.A., M.A., and Ph.D. from Ohio State University. Before joining the faculty of Psychology and Neuroscience at Baylor University he was the Senior Psychoacoustical Engineer at the Baldwin Piano and Organ Company in Cincinnati, Ohio. Professor Kirk is a fellow of the American Psychological Association, the American Psychological Society, and the American Educational Research Association.
Kirk has written five books. His first book, Experimental Design: Procedures for the Behavioral Sciences, now in a fourth edition, was designated a Citation Classic by the Institute for Scientific Information. His introductory statistics book is in a fifth edition. He and his wife are also avid ballroom dancers and he frequently uses the stairs to get to his 3rd story office.
References
1930 births
Living people
People from Ohio
21st-century American psychologists
Educational psychologists
Ohio State University alumni
Fellows of the American Psychological Association
20th-century American psychologists |
https://en.wikipedia.org/wiki/Raymond%20Keiller%20Butchart | Raymond Keiller Butchart FRSE (1888–1930) was a short-lived Scottish mathematician. He served for two years as Professor of Mathematics at the illustrious Raffles College in Singapore. He lost a leg in the First World War.
Life
He was born in Dundee in Scotland on 4 May 1888, the only son of Margaret and Robert K Butchart. His father was a manager in a local jute spinning mill.
He attended Morgan Academy and the High School of Dundee before receiving a place at the University of St Andrews where he received a bachelor's degree in mathematics in 1913. During this time he studied at University College, Dundee, now the University of Dundee, which was then a college of the university in St Andrews. After graduating he worked as a student assistant in the Mathematics department of University College, Dundee until December 1914. He then gave up a position in Wilson College in Bombay to instead serve his country. He received a commission as a lieutenant in the 14th battalion Royal Scots on 24 December 1915.
After training at Stobs in the Scottish borders he got a position as brigade signals officer. He left for France and Flanders in the summer of 1915. He rose to the rank of captain. He was seriously wounded and lost a leg. He was not discharged from the army until 1920.
He was elected a fellow of the Royal Society of Edinburgh in February 1915 (shortly before being sent to France). His proposers included D'Arcy Wentworth Thompson.
In July 1921 the University of St Andrews awarded him a PhD and gave him the new title of lecturer in mathematics.
From 1928 to 1930 he was professor of mathematics at Raffles College in Singapore and apparently very much enjoyed the climate there. He left Singapore with his wife on 24 March 1930, for their first return trip to Scotland.
He died of malaria, which materialised soon after boarding ship. He died in the Indian Ocean. He was buried at sea, 65 miles south-east of Colombo on the same day, 30 March 1930.
Family
He married Jean Ainslie Broome in 1921.
Publications
The Dissipation of Energy in Simple and Multiple Wires (1921)
References
1888 births
1930 deaths
People from Dundee
Scottish mathematicians
Scottish amputees
20th-century Scottish mathematicians
British Army personnel of World War I
Deaths from malaria
Burials at sea
People educated at Morgan Academy
People educated at the High School of Dundee
Alumni of the University of St Andrews
Alumni of the University of Dundee
Fellows of the Royal Society of Edinburgh
Academic staff of the National University of Singapore
Academics of the University of St Andrews
British scientists with disabilities |
https://en.wikipedia.org/wiki/Yves%20Le%20Jan | Yves Le Jan (born 15 April 1952 in Grenoble) is a French mathematician working in Probability theory and Stochastic processes.
Le Jan studied from 1971 to 1974 at the École normale supérieure, finishing with an Agrégation. 1975 he became a researcher (Attaché de Recherche) at the CNRS (from 1987 Directeur de Recherche) and in 1979 obtained his PhD (Doctorat d´Etat). Since 1993 he is Professor at the University of Paris-Sud. From 2001 to 2004 he was leading its group on probability theory and statistics.
In 2006 he was invited speaker at the International Congress of Mathematicians in Madrid (New developments in stochastic dynamics). In 2008 he became Senior Member of the Institut Universitaire de France. In 2011 he was Doob Lecturer at the 8th World Congress in Probability and Statistics in Istanbul.
In 2011 he was awarded the Sophie Germain Prize and in 1995 the Poncelet Prize of the French Academy of Sciences.
From 2000 to 2006 he was Editor of Annales Henri Poincaré.
Books
with Jacques Franchi Hyperbolic dynamics and Brownian motion : an introduction, Oxford University Press 2012
with K. David Elworthy, Xue-Mei Li The Geometry of Filtering, Birkhäuser 2010
with K. David Elworthy, Xue-Mei Li On the geometry of diffusion operators and stochastic flows, Springer Verlag 1999
Markov paths, loops and fields, École d’Été de Probabilités de Saint-Flour XXXVIII-2008, Springer Verlag 2011
References
External links
Homepage
http://www.idref.fr/076172937
http://www.math.u-psud.fr/~lejan/CVanglais.pdf
1952 births
Living people
French mathematicians
École Normale Supérieure alumni
Academic staff of Paris-Sud University |
https://en.wikipedia.org/wiki/IZOSTAT | IZOSTAT (ИЗОСТАТ) () was the "All-union Institute of Pictorial Statistics of Soviet Construction and Economy," an agency of the Soviet government that designed, created, published, and distributed graphic representations of Soviet industry that were easily understandable without written explanations. Founded as an educational unit, Izostat evolved into a producer of propaganda. It operated between 1931 and 1940.
Viennese Origins
In Red Vienna of the 1920s under the Social Democratic Party of Austria, philosopher and logician of the Vienna Circle, Otto Neurath, founded a new museum for housing and city planning called Siedlungsmuseum, renamed in 1925 the Gesellschafts- und Wirtschaftsmuseum in Wien (Museum of Society and Economy in Vienna). To make the museum's displays widely understandable for visitors from all around the polyglot Austro-Hungarian Empire, Neurath worked on graphic design and visual education, believing that "Words divide, pictures unite," a coinage of his own that he displayed on the wall of his office there. In the late 1920s, his assistant, graphic designer and communications theorist Rudolf Modley, contributed to a new means of communication: a visual "language." With the illustrator Gerd Arntz and with Marie Reidemeister, Neurath's team developed novel ways of representing quantitative information via easily interpretable icons. The forerunner of contemporary Infographics, he initially called this the Vienna Method of Pictorial Statistics. As his ambitions for the project expanded beyond social and economic data related to Vienna, he renamed the project "Isotype," an acronymic nickname for the project's full title: International System of Typographic Picture Education. At international conventions of city planners, Neurath presented and promoted his communication tools.
Neurath's methods made such an impact on a delegation from the Soviet Embassy, another government with a polyglot population, the Soviet government in Moscow invited Neurath and Reidemeister to assist with the creation of an educational institution based on the same principles.
Establishment
Neurath and Reidemeister accepted the invitation, and Neurath committed to spending sixty days each year in the Soviet Union to assist started in 1931. The institute was located in 9 Bol'shoi Komsomol'sky pereulok. Neurath's colleagues Gerd Arntz and Peter Alma also spent time working at IZOSTAT between 1931 and 1934. In 1932 Izostat published a monograph about its methods in Pictorial statistics and the Vienna Method (Изобразительная статистика и венский метод) by Ivan Petrovich Ivanitsky.
Output
With a staff that eventually grew to seventy, Izostat's main goal was to develop infographics that communicated both the successes of the First five-year plan (1928–1932), especially in the development of coal, iron, steel, and electricity, and predictions of the anticipated successes of the Second five-year plan in roads, railways, and waterways. Izostat’s output was no |
https://en.wikipedia.org/wiki/Regular%20embedding | In algebraic geometry, a closed immersion of schemes is a regular embedding of codimension r if each point x in X has an open affine neighborhood U in Y such that the ideal of is generated by a regular sequence of length r. A regular embedding of codimension one is precisely an effective Cartier divisor.
Examples and usage
For example, if X and Y are smooth over a scheme S and if i is an S-morphism, then i is a regular embedding. In particular, every section of a smooth morphism is a regular embedding. If is regularly embedded into a regular scheme, then B is a complete intersection ring.
The notion is used, for instance, in an essential way in Fulton's approach to intersection theory. The important fact is that when i is a regular embedding, if I is the ideal sheaf of X in Y, then the normal sheaf, the dual of , is locally free (thus a vector bundle) and the natural map is an isomorphism: the normal cone coincides with the normal bundle.
Non-examples
One non-example is a scheme which isn't equidimensional. For example, the scheme
is the union of and . Then, the embedding isn't regular since taking any non-origin point on the -axis is of dimension while any non-origin point on the -plane is of dimension .
Local complete intersection morphisms and virtual tangent bundles
A morphism of finite type is called a (local) complete intersection morphism if each point x in X has an open affine neighborhood U so that f |U factors as where j is a regular embedding and g is smooth.
For example, if f is a morphism between smooth varieties, then f factors as where the first map is the graph morphism and so is a complete intersection morphism. Notice that this definition is compatible with the one in EGA IV for the special case of flat morphisms.
Let be a local-complete-intersection morphism that admits a global factorization: it is a composition where is a regular embedding and a smooth morphism. Then the virtual tangent bundle is an element of the Grothendieck group of vector bundles on X given as:
,
where is the relative tangent sheaf of
(which is locally free since is smooth)
and is the normal sheaf
(where is the ideal sheaf of in ), which is locally free since
is a regular embedding.
More generally,
if is a any local complete intersection morphism of schemes, its
cotangent complex is perfect of Tor-amplitude [-1,0].
If moreover is locally of finite type and locally Noetherian, then the converse is also true.
These notions are used for instance in the Grothendieck–Riemann–Roch theorem.
Non-Noetherian case
SGA 6 Exposé VII uses the following slightly weaker form of the notion of a regular embedding, which agrees with the one presented above for Noetherian schemes:
First, given a projective module E over a commutative ring A, an A-linear map is called Koszul-regular if the Koszul complex determined by it is acyclic in dimension > 0 (consequently, it is a resolution of the cokernel of u).
Then a closed immersio |
https://en.wikipedia.org/wiki/List%20of%20Zamalek%20SC%20records%20and%20statistics | This article includes records and statistics related to Zamalek SC.
All stats are accurate as of 27 June 2015.
Honours
Worldwide / Intercontinental
Afro-Asian Cup
Winners (2): 1987, 1997
Runners-up (1): 1994
African
CAF Champions League
Winners (5): 1984, 1986, 1993, 1996, 2002
Runners-up (3): 1994, 2016, 2020
African Cup Winners' Cup
Winners (1): 2000
CAF Confederation Cup
Winners (1): 2019
CAF Super Cup
Winners (4): 1994, 1997, 2003, 2020 (February)
Runners-up (1): 2001
UAFA Competitions
Arab Champions Cup
Winners (1): 2003
League
Egyptian Premier League
Winners (14): 1959–60, 1963–64, 1964–65, 1977–78, 1983–84, 1987–88, 1991–92, 1992–93, 2000–01, 2002–03, 2003–04, 2014–15, 2020–21, 2021–22
Runners-up (34): 1950–51, 1952–53, 1953–54, 1955–56, 1956–57, 1957–58, 1958–59, 1960–61, 1961–62, 1962–63, 1965–66, 1972–73, 1976–77, 1978–79, 1979–80, 1980–81, 1981–82, 1982–83, 1984–85, 1985–86, 1986–87, 1988–89, 1994–95, 1995–96, 1996–97, 1997–98, 1998–99, 2005–06, 2006–07, 2009–10, 2010–11, 2015–16, 2018–19, 2019–20
Cairo League
Winners (15): 1922–23, 1923–24, 1928–29, 1929–30, 1931–32, 1939–40, 1940–41, 1943–44, 1944–45, 1945–46, 1946–47, 1948–49, 1950–51, 1951–52, 1952–53
Runners-up (6): 1936–37, 1937–38, 1941–42, 1942–43, 1945–46, 1957–58
Cup
Egypt Cup
Winners (28): 1922, 1932, 1935, 1938, 1941, 1943, 1944, 1952, 1955, 1957, 1958, 1959, 1960, 1962, 1975, 1977, 1979, 1988, 1999, 2002, 2008, 2013, 2014, 2015, 2015–16, 2017–18, 2018–19, 2020–21
Runners-up (13): 1927–28, 1930–31, 1932–33, 1933–34, 1941–42, 1947–48, 1948–49, 1952–53, 1962–63, 1977–78, 1991–92, 2005–06, 2006–07, 2010–11
Egyptian Super Cup
Winners (4): 2001–02, 2002–03, 2015–16, 2019–20
Runners-up (5): 2003–04, 2004–05, 2008–09, 2014–15, 2015–16
Sultan Hussein Cup
Winners (2): 1920–21, 1921–22
Runners-up (3): 1923–24, 1929–30, 1936–37
King Fouad Cup
Winners (3)
Saudi-Egyptian Super Cup (League Winners)
Winners (2): 2003, 2018
Jordan International Cup (Egyptian-Jordanian Cup)
Winners (2): 1986, 1987
Independence Cup (Friendship Cup)
Winners (2)
Domestic
Alexandria Summer League
Winners (3): 1982, 1984, 2004
Giza League
Winners (1)
October League Cup
Winners (1): 1973–74
Egypt's Love Cup
Winners (1): 1986
Union Cup "Egypt" (association football)
Winners (1): 1995
Egypt Confederation Cup Refresher
Winners (4)
All trophies are approved by Egyptian football Association website and Zamalek SC Official Facebook page.
Players
Appearances
Goalscorers
Most goals scored in all competitions: 138 – Abdel Halim Ali
Most goals scored in the League: 81 – Abdel Halim Ali
Most goals scored in October League Cup: 9 - Hassan Shehata
Most goals scored in the cup: 23 – Alaa El-Hamouly
Most goals scored in all African competitions: 23 – Abdel Halim Ali
Most goals scored in all Arabian competitions: 13 – Abdel Halim Ali
Awards Winners
African Footballer of The Year
The following players won African Footballer of the Year while playing for Zamalek:
Emmanuel Amuneke – 19 |
https://en.wikipedia.org/wiki/2015%20Graz%20car%20attack | {
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https://en.wikipedia.org/wiki/Geometry%20of%20Fear | The Geometry of Fear was an informal group or school of young British sculptors in the years after the Second World War. The term was coined by Herbert Read in 1952 in his description of the work of the eight British artists represented in the "New Aspects of British Sculpture" exhibition at the Biennale di Venezia of 1952.
Venice
The eight artists who exhibited "New Aspects of British Sculpture" in the British pavilion at the Biennale di Venezia of 1952 were Robert Adams, Kenneth Armitage, Reg Butler, Lynn Chadwick, Geoffrey Clarke, Bernard Meadows, Eduardo Paolozzi and William Turnbull. All were under 40, with years of birth ranging from 1913 to 1924, and of a younger generation than established British sculptors such as Barbara Hepworth and Henry Moore. A large bronze by Moore, Double Standing Figure, stood outside the British pavilion, and contrasted strongly with the works inside. Unlike the smoothly carved work of Hepworth and Moore, these were angular, jagged, rough-textured or spiky. They were more linear and open; Philip Hendy compared Butler's sculptures to three-dimensional drawings. Many of the sculptures in the pavilion were of human or animal figures, and several showed the influence of the continental sculptors Germaine Richier and Alberto Giacometti, works by whom had been shown at the Anglo-French Art Centre in London in 1947. The British sculptures were seen as reflecting the angst, the anxieties and the guilt of the immediate post-War period, with the recent memory of the War, the Holocaust and Hiroshima, and the fear of nuclear proliferation and the effects of the Cold War.
In his catalogue description, Herbert Read wrote:
Read's quotation "scuttling across the floors of silent seas" is from The Love Song of J. Alfred Prufrock by T.S. Eliot and is a reference to Crab, a sculpture by Bernard Meadows in the exhibition. Read's words were widely quoted, and despite the differences in style and technique between the eight artists, they came to be known as the Geometry of Fear group.
Reception
The Geometry of Fear exhibition was well received, both within and outside Britain. Alfred Barr, the former director of the New York Museum of Modern Art, spoke highly of the sculptors and bought work by three of them – Robert Adams, Reg Butler and Lynn Chadwick – for the museum; he described the exhibition as "the most distinguished national showing of the Biennale". All eight sculptors achieved rapid recognition and career success in the 1950s. In 1953 Butler won the international competition to design the monument to the Unknown Political Prisoner, chosen over more than two thousand entries including submissions by Naum Gabo and Barbara Hepworth; the prize was £4500, enough at the time to buy a large house. In 1956 Lynn Chadwick won the Grand Prize for Sculpture at the Biennale di Venezia of that year, selected over César, Giacometti and Richier.
Within a decade the Geometry of Fear group had fallen from view. In the 1960s British s |
https://en.wikipedia.org/wiki/Tamer%20Seyam | Tamer Mohammed Sobhi Seyam (; born 25 November 1992) is a Palestinian professional footballer who plays for as a forward for Thai club PT Prachuap and the Palestine national team.
Career statistics
International
Scores and results list Palestine's goal tally first.
Honours
Palestine
AFC Challenge Cup: 2014
References
External links
1992 births
Living people
Footballers from Jerusalem
Palestinian men's footballers
Men's association football forwards
Shabab Al-Khalil SC players
Hilal Al-Quds Club players
Hassania Agadir players
West Bank Premier League players
Botola players
Palestine men's international footballers
2019 AFC Asian Cup players
Palestinian expatriate men's footballers
Palestinian expatriate sportspeople in Morocco
Expatriate men's footballers in Morocco |
https://en.wikipedia.org/wiki/Bloch%27s%20higher%20Chow%20group | In algebraic geometry, Bloch's higher Chow groups, a generalization of Chow group, is a precursor and a basic example of motivic cohomology (for smooth varieties). It was introduced by Spencer Bloch and the basic theory has been developed by Bloch and Marc Levine.
In more precise terms, a theorem of Voevodsky implies: for a smooth scheme X over a field and integers p, q, there is a natural isomorphism
between motivic cohomology groups and higher Chow groups.
Motivation
One of the motivations for higher Chow groups comes from homotopy theory. In particular, if are algebraic cycles in which are rationally equivalent via a cycle , then can be thought of as a path between and , and the higher Chow groups are meant to encode the information of higher homotopy coherence. For example,can be thought of as the homotopy classes of cycles whilecan be thought of as the homotopy classes of homotopies of cycles.
Definition
Let X be a quasi-projective algebraic scheme over a field (“algebraic” means separated and of finite type).
For each integer , define
which is an algebraic analog of a standard q-simplex. For each sequence , the closed subscheme , which is isomorphic to , is called a face of .
For each i, there is the embedding
We write for the group of algebraic i-cycles on X and for the subgroup generated by closed subvarieties that intersect properly with for each face F of .
Since is an effective Cartier divisor, there is the Gysin homomorphism:
,
that (by definition) maps a subvariety V to the intersection
Define the boundary operator which yields the chain complex
Finally, the q-th higher Chow group of X is defined as the q-th homology of the above complex:
(More simply, since is naturally a simplicial abelian group, in view of the Dold–Kan correspondence, higher Chow groups can also be defined as homotopy groups .)
For example, if is a closed subvariety such that the intersections with the faces are proper, then
and this means, by Proposition 1.6. in Fulton’s intersection theory, that the image of is precisely the group of cycles rationally equivalent to zero; that is,
the r-th Chow group of X.
Properties
Functoriality
Proper maps are covariant between the higher chow groups while flat maps are contravariant. Also, whenever is smooth, any map to is contravariant.
Homotopy invariance
If is an algebraic vector bundle, then there is the homotopy equivalence
Localization
Given a closed equidimensional subscheme there is a localization long exact sequencewhere . In particular, this shows the higher chow groups naturally extend the exact sequence of chow groups.
Localization theorem
showed that, given an open subset , for ,
is a homotopy equivalence. In particular, if has pure codimension, then it yields the long exact sequence for higher Chow groups (called the localization sequence).
References
Peter Haine, An Overview of Motivic Cohomology
Vladmir Voevodsky, “Motivic cohomology groups are isomorphic t |
https://en.wikipedia.org/wiki/Evan%20Tom%20Davies | Evan Tom Davies (24 September 1904 – 8 October 1973) was a Welsh mathematician. He studied applications of the Lie derivative as it relates to Riemannian geometry as well as absolute differential calculus, and published a large number of papers relating to the subjects.
Early life
Davies was born in 1904 in Pencader, Carmarthenshire, a small village in Wales. He was the son of two farmers and attended a local primary school. After finishing primary school, Davies received a full ride scholarship to Llandysul County School in the neighbouring town of Llandysul. There he became friends with Evan James Williams, a future professor of physics at Aberystwyth University and member of the Royal Society. In 1921, he enrolled in Aberystwyth University. He would graduate with a Bachelor of Science with honours in the field of applied mathematics. After graduation he went to Swansea University where he studied pure mathematics and received his master's degree. Davies would move to Rome in August 1926 to study with the leading expert on absolute differential calculus, Tullio Levi-Civita. There he received his doctorate.
Career
In 1930, after a short academic break due to poor health, Davies accepted a position as an assistant lecturer at King's College London. There he was promoted twice, first to Lecturer in 1935, and later to Reader in 1946. Davies was affected by the evacuation of King's College due to the London Blitz and was forced to temporarily relocate to the University of Bristol. After the conclusion of the Second World War and his subsequent promotion to Lecturer; Davie would become the chair of mathematics at the University of Southampton. He stayed at Southampton until his retirement in 1969 at the age of 65. After retirement, he went on to be a professor of mathematics at the University of Calgary for a period two years until leaving to be a professor at the University of Waterloo. He died at the age of 69 while employed there.
Publications
On the infinitesimal deformations of a space (1933)
On the deformation of a subspace (1936)
On the infinitesimal deformations of tensor submanifolds (1937)
On the second and third fundamental forms of a subspace (1937)
Analogues of the Frenet formulae determined by deformation operators (1938)
Lie derivation in generalized metric spaces (1939)
Subspaces of a Finsler space (1945)
Motions in a metric space based on the notion of area (1945)
The theory of surfaces in a geometry based on the notion of area (1947)
On the invariant theory of contact transformations (1953)
Parallel distributions and contact transformations (1966)
Personal life
Davies' first marriage was to Margaret Helen Picton in 1941, but she died a few years later in 1944. In 1955 he remarried, to Hilda Gladys Boyens, and they had one son. He made a hobby of linguistics and was fluent in five languages.
References
External links
Welsh mathematicians
20th-century British mathematicians
20th-century linguists
Academic staff of the Univer |
https://en.wikipedia.org/wiki/Samuel%20Sanford%20Shapiro | Samuel Sanford Shapiro (born July 13, 1930) is an American statistician and engineer. He is a professor emeritus of statistics at Florida International University. He is known for his co-authorship of the Shapiro–Wilk test and the Shapiro–Francia test.
A native of New York City, Shapiro graduated from City College of New York with a degree in statistics in 1952, and took an MS in industrial engineering at Columbia University in 1954. He briefly served as a statistician in the US Army Chemical Corps, before earning a MS (1960) and PhD (1963) in statistics at Rutgers University. In 1972 he joined the faculty at Florida International University.
In 1987 he was elected a Fellow of the American Statistical Association.
References
External links
Website at Florida International University
1930 births
Living people
American statisticians
City College of New York alumni
Columbia School of Engineering and Applied Science alumni
Rutgers University alumni
Florida International University faculty
Fellows of the American Statistical Association |
https://en.wikipedia.org/wiki/Robert%20Brown%20Gardner | Robert Brown (Robby) Gardner (Tarrytown, New York, February 27, 1939 – May 5, 1998) was an American mathematician who worked on differential geometry.
Biography
Gardner graduated from Princeton University in 1959, earned a master's degree from Columbia University in 1960, and completed his PhD in 1965 from the University of California, Berkeley, under the supervision of Shiing-Shen Chern.
After this, he worked at many places, including the Institute for Advanced Study, and worked as assistant professor at Columbia University between 1967 and 1970. He joined the faculty of the University of North Carolina at Chapel Hill in 1971 and became a full professor there in 1977. He died on May 5, 1998.
Research
Gardner was the author and co-author of three influential books, produced more than fifty papers, eighteen masters students and thirteen Ph.D students. Robert Bryant, Duke University's Professor of Mathematics and the president of the American Mathematical Society (2015-2017) was a student of his.
His 1991 book, Exterior Differential Systems, coauthored with R. Bryant, S. S. Chern, H. Goldschmidt, and P. Griffiths, is the standard reference for the subject.
He is better known in the United States for his improvements and popularization of the methods of Élie Cartan (most notably, Cartan's equivalence method, an algorithmic procedure for determining if two geometric shapes are different). The works of Cartan were hard to grasp for most students, and Gardner worked to explain them in more accessible ways.
Legacy
In his memory, the UNC Mathematics Department created the Robert Brown Gardner Memorial Fund, devoted to supporting graduate student activities.
Selected publications
The Method of Equivalence and Its Applications
R. Bryant, S.-S. Chern, R. B. Gardner, H. Goldschmidt, P. Griffiths, Exterior Differential Systems, MSRI Publications, Springer, 1990
Lectures on Exterior Algebras Over Commutative Rings
Differential Geometric Methods in Partial Differential Equations
References
Further reading
Pat Eberlein, "Robby Gardner (February 27, 1939 - May 5, 1998)"
1939 births
1998 deaths
20th-century American mathematicians
Geometers
Princeton University alumni
Columbia University alumni
University of California, Berkeley alumni
Columbia University faculty
University of North Carolina at Chapel Hill faculty
Place of birth missing |
https://en.wikipedia.org/wiki/Max%20Simon%20%28mathematician%29 | Maximilian Simon (born 8 June 1844 in Kołobrzeg; died 15 January 1918 in Strasbourg) was a German historian of mathematics and mathematics teacher. He was concerned mostly with mathematics in the antiquity.
Born into a Jewish family, he studied from 1862 to 1866 at the Friedrich Wilhelm University of Berlin, obtaining his Ph.D. from Karl Weierstrass und Ernst Eduard Kummer
He was a mathematics teacher in Berlin from 1868 to 1871, and in Strasbourg from 1871 to 1912, where he became an honorary professor of the university.
Works
Euclid und die sechs planimetrischen Bücher, Teubner 1901
Über die Entwicklung der Elementargeometrie im 19 Jahrhundert, Bericht der Deutschen Mathematikervereinigung, Teubner 1906
Geschichte der Mathematik im Altertum in Verbindung mit antiker Kulturgeschichte, Berlin: B. Cassirer 1909
Nichteuklidische Geometrie in elementarer Behandlung ( ed.), Teubner 1925
Analytische Geometrie der Ebene, 3rd edition, 1900
Analytische Geometrie des Raumes, 2 volumes, Sammlung Göschen 1900, 1901
References
Joseph W. Dauben, Christoph J. Scriba (eds.): Writing the history of mathematics. Its historical development. Birkhäuser, Basel 2002, , (Science networks 27), p. 522.
19th-century German Jews
19th-century German mathematicians
1844 births
1918 deaths
University of Strasbourg alumni
20th-century German mathematicians |
https://en.wikipedia.org/wiki/Rabee%20Sufyani | Rabee Sufyani (Arabic: ربيع سفياني; born 26 January 1987) is a Saudi football player who plays as a winger.
Career statistics
International
Statistics accurate as of match played 10 August 2019.
International goals
Scores and results list Saudi Arabia's goal tally first.
Honours
Club
Al-Fateh
Pro League: 2012-13
Saudi Super Cup: 2013
Al-Nassr
Pro League: 2013–14
Saudi Crown Prince Cup: 2013–14
Al-Ittihad
Saudi Crown Prince Cup: 2016–17
King Cup: 2018
Al-Taawoun
King Cup: 2019
References
Saudi Arabian men's footballers
1987 births
Living people
Men's association football wingers
Al Hilal SFC players
Al Fateh SC players
Al Nassr FC players
Al Taawoun FC players
Al-Ittihad Club (Jeddah) players
Al-Ain FC (Saudi Arabia) players
Hajer FC players
Jeddah Club players
Footballers from Riyadh
Saudi First Division League players
Saudi Pro League players
Saudi Arabia men's international footballers |
https://en.wikipedia.org/wiki/Meyer%20Dwass | Meyer Dwass (April 9, 1923 – July 15, 1996) was an American mathematical statistician known for his contributions to applied probability. Dwass was a professor of statistics at Northwestern University.
Born in New Haven, Connecticut, Dwass attended George Washington University, earning a bachelor's degree in 1948. Under supervision of Wassilij Höffding, he earned a Ph.D. from University of North Carolina at Chapel Hill in 1952.
References
External links
1923 births
1996 deaths
American statisticians
George Washington University alumni
University of North Carolina at Chapel Hill alumni
Northwestern University faculty
Scientists from New Haven, Connecticut
Mathematical statisticians |
https://en.wikipedia.org/wiki/The%20Bridges%20Organization | The Bridges Organization is an organization that was founded in Kansas, United States, in 1998 with the goal of promoting interdisciplinary work in mathematics and art. The Bridges Conference is an annual conference on connections between art and mathematics. The conference features papers, educational workshops, an art exhibition, a mathematical poetry reading, and a short movie festival.
List of Bridges conferences
References
External links
1998 establishments in Kansas
Arts organizations established in 1998
Arts organizations based in Kansas
Mathematics organizations
Mathematics and art |
https://en.wikipedia.org/wiki/Karen%20Duncan | Karen A. Duncan is a biostatistician and health informatics specialist, who was named a Fellow of the Association for Computing Machinery in 2000.
Duncan earned a Ph.D. in biostatistics from the University of Oklahoma. She has worked as an associate professor at the Medical University of South Carolina, as a member of the technical staff at the Mitre Corporation, and as an independent consultant.
She is the author of the books Health Information and Health Reform: Understanding the Need for a National Health Information System (Jossey-Bass, 1994) and Community Health Information Systems: Lessons for the Future (Health Information Press, 1998).
References
Year of birth missing (living people)
Living people
Fellows of the Association for Computing Machinery
Biostatisticians
Women statisticians
Health informaticians
University of Oklahoma alumni
Medical University of South Carolina faculty
Mitre Corporation people |
https://en.wikipedia.org/wiki/Kim%20Min-tae | Kim Min-tae (; born 26 November 1993) is a South Korean professional footballer who plays as a centre back for club Shonan Bellmare, on loan from Kashima Antlers.
Club statistics
.
Honours
Nagoya Grampus
J.League Cup: 2021
References
External links
Profile at Kashima Antlers
1993 births
Living people
South Korean men's footballers
J1 League players
Vegalta Sendai players
Hokkaido Consadole Sapporo players
Kashima Antlers players
Shonan Bellmare players
South Korean expatriate sportspeople in Japan
Footballers at the 2016 Summer Olympics
Olympic footballers for South Korea
Footballers from Incheon
Men's association football defenders |
https://en.wikipedia.org/wiki/Kinleith | Kinleith is a rural settlement in the South Waikato District and Waikato region of New Zealand's North Island. It includes the Kinleith Mill.
Statistics New Zealand defines Kinleith as an area covering a land area of .
History
The estimated population of Kinleith reached 1,190 in 1996, 1,130 in 2001, 1,150 in 2006, 1,540 in 2013, and 2,440 in 2018.
Demography
Kinleith has an estimated population of .
There was a population density of 1.60 people per km2 in 2009.
As of the 2018 census, the median age was 30.0, the median income was $42,400, 9.3% of people earned over $100,00, 14.2% had a bachelor's degree or higher, and 3.5% of the workforce was unemployed.
Ethnically, the population was 83.6% New Zealand European, 19.5% Māori, 2.7% Pacific peoples, and 8.5% Asian; 17.0% were born overseas. Religiously, the population was 56.0% non-religious and 32.0% Christian.
Economy
In 2018, 52.6% of the workforce worked in primary industries, 9.6% worked in manufacturing, 4.0% worked in construction, 4.8% worked in education, 3.7% worked in transport, and 3.3% worked in healthcare.
Transportation
As of 2018, among those who commuted to work, 42.3% drove a car, 1.5% rode in a car, 0.8% walked, ran or cycled.
References
South Waikato District
Populated places in Waikato |
https://en.wikipedia.org/wiki/Helen%20Wills%20career%20statistics | This is a list of the main career statistics of American tennis player Helen Wills. During her career, which ran from 1919 through 1938, she won 19 singles titles at Grand Slam tournaments as well as 9 doubles and 3 mixed doubles titles. She won the Olympic gold medal in singles and doubles in 1924. Wills was unbeaten in 180 singles matches.
Grand Slam tournament finals
Singles: 22 (19 titles, 3 runner-ups)
Doubles: 10 finals (9 titles, 1 runner-up)
Mixed doubles: 7 finals (3 titles, 4 runner-ups)
Olympic finals
Singles: 1 final (1 gold medal)
Doubles: 1 final (1 gold medal)
Career finals
Singles: 67 (57 titles, 10 runner-ups)
Sources:Wright & Ditson's Lawn Tennis GuidesHelen Wills: Tennis, Art, Life
Team competitions
Wightman Cup
Wightman Cup reference
International matches
Double bagel match victories
During her career Wills defeated opponents 50 times without the loss of a game, i.e. via a double bagel (6–0, 6–0).
Source:Helen Wills: Tennis, Art, Life
Performance timelines
Singles
Note 1: Wills withdrew from both the French Championships and Wimbledon Championships in 1926 after having an appendectomy. The French walkover is not counted as a loss. One week prior to Wimbledon, the tournament was informed that she would not play. She was given a default from her opening round match, which Wimbledon does not consider to be a "loss".
Note 2: Prior to 1925, the French Championships was not open to international players.
Doubles
Mixed doubles
Longest winning streaks and records
180 match win streak from 1927–1933.
Did not lose a set from 1927–1933.
Wills was ranked world No. 1 for eight years.
See also
Suzanne Lenglen career statistics
References
Tennis career statistics |
https://en.wikipedia.org/wiki/FIFA%20U-17%20World%20Cup%20records%20and%20statistics | This is a list of records and statistics of the FIFA U-17 World Cup.
Debut of national teams
Overall team records
In this ranking 3 points are awarded for a win, 1 for a draw and 0 for a loss. As per statistical convention in football, matches decided in extra time are counted as wins and losses, while matches decided by penalty shoot-outs are counted as draws. Teams are ranked by total points, then by goal difference, then by goals scored.
Bold indicates team that qualified for 2023
Teams that have finished in the top four
1 = includes results representing Soviet Union
2 = includes results representing West Germany
Comprehensive team results by tournament
Legend
– Champions
– Runners-up
– Third place
– Fourth place
QF – Quarterfinals (1985-2005: first group stage, and since 2007: second group stage; final 8)
R2 – Round 2 (since 2007: knockout round of 16)
R1 – Round 1
– Did not qualify
– Did not enter / Withdrew
– Disqualified
– Country did not exist or national team was inactive
– Hosts
Q – Qualified for upcoming tournament
For each tournament, the flag of the host country and the number of teams in each finals tournament (in brackets) are shown.
Results of defending champions
Results of host nations
Results by confederation
AFC
CAF
CONCACAF
CONMEBOL
OFC
UEFA
Awards
Team: tournament position
Most championships 5; (1985, 1993, 2007, 2013, 2015)
Most finishes in the top two 8; (1985, 1987, 1993, 2001, 2007, 2009, 2013, 2015)
Most finishes in the top three 8; (1985, 1987, 1993, 2001, 2007, 2009, 2013, 2015), (1985, 1995, 1997, 1999, 2003, 2005, 2017, 2019)
Most World Cup appearances 17; (every tournament except 1993) and (every tournament except 2013)
Most second-place finishes 4; (1991, 2003, 2007, 2017)
Most third-place finishes 3; (1991, 1995, 2003)
Most fourth-place finishes 2; (2001, 2013) and (2003, 2009)
Most 3rd-4th-place finishes 5; (1991, 1995, 2001, 2003, 2013)
Consecutive
Most consecutive championships 2; (1997–1999), (2013–2015)
Most consecutive finishes in the top two 4; (1991–1997)
Most consecutive finishes in the top three 5; (1991–1999)
Most consecutive finishes in the top four 5; (1991–1999)
Most consecutive finals tournaments 14; (1985–2011)
Most consecutive second-place finishes no country has finished 2nd in two consecutive tournaments
Most consecutive third-place finishes no country has finished 3rd in two consecutive tournaments
Most consecutive fourth-place finishes no country has finished 4th in two consecutive tournaments
Most consecutive 3rd-4th-place finishes 2; (2001–2003)
Gaps
Longest gap between successive titles 16 years; (2003–2019)
Longest gap between successive appearances in the top two 14 years; (2005–2019)
Longest gap between successive appearances in the top three 22 years; (1985–2007)
Longest gap between successive appearances in the top four 18 years; (2001–2019)
Longest gap between successive appearances in the finals 26 years; , |
https://en.wikipedia.org/wiki/Bill%20Ferrar | Dr William Leonard Ferrar FRSE (21 October 1893 – 22 January 1990) was an English mathematician. He focused on interpolation theory and number theory.
Early life
Ferrar was born on 21 October 1893 in St Pauls, Bristol, the son of Maria Susannah Ferrar and her husband George William Persons Ferrar, a lamplighter.
He attended Bristol Grammar School. In 1912, he gained a place at The Queen's College in Oxford, winning the Junior Mathematical Scholarship in 1914. His studies were interrupted by the First World War during which he first spent as a telephonist in the artillery then as an Intelligence Officer in France.
He returned to Oxford in 1919 and graduated MA in 1920, and later received a doctorate (DSc).
Career
He spent his first 4 years working in Bangor then was invited to the University of Edinburgh by Edmund Whittaker as a lecturer in mathematics. There he worked with Edward Copson and Alec Aitken, and wrote papers on convergent series, interpolation theory, and number theory.
In 1925 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Edmund Whittaker, Edward Copson, Sir Charles Galton Darwin and David Gibb.
In the autumn of 1925 he took up a new role at the University of Oxford.
From its creation until 1933, he was the editor at the University of the Quarterly Journal of Mathematics in which he published many papers. In 1937, he became the bursar of Hertford College, Oxford which he was employed at for 22 years. After being the bursar in 1959 he became the Principal of the college. In 1947 he belated applied for a doctorate and received a DSc.
He died in Oxford on 22 January 1990. He is buried in Wolvercote Cemetery.
Publications
A Textbook of Convergence (1938)
Algebra: a Textbook of Determinants, Matrices and Quadratic Forms (1941, 2nd ed. 1957)Finite Matrices (1951)Mathematics for Science (1965)Integral Calculus (1966)Calculus for Beginners (1967)Advanced Mathematics for Science (1969)Differential CalculusHigher Algebra for Schools (1945)Higher Algebra''
Artistic recognition
His portrait was painted by Ruskin Spear in 1965.
Family
He was married to Edna Ferrar (1898-1986). Their son was Michael Ferrar.
References
1893 births
1990 deaths
Burials at Wolvercote Cemetery
20th-century English mathematicians
Alumni of The Queen's College, Oxford
Principals of Hertford College, Oxford |
https://en.wikipedia.org/wiki/2015%20FIFA%20Women%27s%20World%20Cup%20statistics | The following article outlines the statistics for the 2015 FIFA Women's World Cup, which took place in Canada from 6 June to 5 July.
Goals scored from penalty shoot-outs are not counted, and matches decided by penalty shoot-outs are counted as draws.
Goalscorers
Assists
Scoring
Overall
Overall
Timing
First goal of the tournament: Christine Sinclair (penalty) for Canada against China
First brace of the tournament: Isabell Herlovsen for Norway against Thailand
First hat-trick of the tournament: Célia Šašić for Germany against Ivory Coast
Latest goal in a match: 108 minutesFara Williams (penalty) for England against Germany
Teams
Most goals scored by a team: 20Germany
Fewest goals scored by a team: 1Ecuador
Best goal difference: +14Germany
Worst goal difference: -16Ecuador
Most goals scored in a match by both teams: 11Switzerland 10–1 Ecuador
Most goals scored in a match by one team: 10Germany against Ivory Coast, Switzerland against Ecuador
Most goals scored in a match by the losing team: 2Ivory Coast against Thailand, Japan against United States
Biggest margin of victory: 10 goalsGermany 10–0 Ivory Coast
Most clean sheets achieved by a team: 5United States
Fewest clean sheets achieved by a team: 0Costa Rica, Ivory Coast, Mexico, Nigeria, South Korea, Spain, Switzerland, Thailand
Most clean sheets given by an opposing team: 2China, Ecuador, Germany, New Zealand, Nigeria, South Korea, Switzerland, Thailand
Fewest clean sheets given by an opposing team: 0Japan, Norway
Most consecutive clean sheets achieved by a team: 5United States
Most consecutive clean sheets given by an opposing team: 2Germany, New Zealand, Nigeria
Individual
Most goals scored by one player in a match: 3Ramona Bachmann for Switzerland against Ecuador, Gaëlle Enganamouit for Cameroon against Ecuador, Fabienne Humm for Switzerland against Ecuador, Carli Lloyd for United States against Japan, Anja Mittag for Germany against Ivory Coast, Célia Šašić for Germany against Ivory Coast
Oldest goal scorer: 37 years, 3 months and 6 daysFormiga for Brazil against South Korea
Youngest goal scorer: 18 years, 8 months and 3 daysMelissa Herrera for Costa Rica against South Korea
Wins and losses
Match awards
Player of the Match
Clean sheets
Discipline
Total number of yellow cards: 110
Average number of yellow cards per match: 2.12
Total number of red cards: 3
Average number of red cards per match: 0.06
First yellow card of the tournament: Desiree Scott – Canada against China PR
First red card of the tournament: Ligia Moreira – Ecuador against Cameroon
Fastest dismissal from kick off: 47 minutes – Catalina Pérez – Colombia against United States
Latest dismissal in a match: 69 minutes – Sarah Nnodim – Nigeria against United States
Least time difference between two yellow cards given to the same player: 31 minutes – Sarah Nnodim – Nigeria against United States
Most yellow cards (team): 9 – Colombia
Most red cards (team): 1 – Colombia, Ecuador, Nigeria
Fe |
https://en.wikipedia.org/wiki/Brailovo | Brailovo () is a village in the municipality of Dolneni, North Macedonia.
Demographics
In statistics gathered by Vasil Kanchov in 1900, the village of Brailovo was inhabited by 250 Christian Bulgarians and 100 Muslim Albanians.
According to the 2021 census, the village had a total of 186 inhabitants. Ethnic groups in the village include:
Macedonians 183
Albanians 1
Serbs 1
Others 1
References
Villages in Dolneni Municipality |
https://en.wikipedia.org/wiki/David%20Dunson | David Brian Dunson (born 1972) is an American statistician who is Arts and Sciences Distinguished Professor of Statistical Science, Mathematics and Electrical & Computer Engineering at Duke University. His research focuses on developing statistical methods for complex and high-dimensional data. Particular themes of his work include the use of Bayesian hierarchical models, methods for learning latent structure in complex data, and the development of computationally efficient algorithms for uncertainty quantification. He is currently serving as joint Editor of the Journal of the Royal Statistical Society, Series B.
Dunson earned a bachelor's degree in mathematics from Pennsylvania State University in 1994, and completed his Ph.D. in biostatistics in 1997 from Emory University under the supervision of Betz Halloran. He was employed at the National Institute of Environmental Health Sciences from 1997 to 2008, joined the Duke faculty as an adjunct associate professor in 2000, and became a full-time Duke professor in 2008. He also held an adjunct faculty position at the University of North Carolina at Chapel Hill from 2001 to 2013.
Dunson became a Fellow of the American Statistical Association in 2007, the same year in which he won the Mortimer Spiegelman Award given annually to a young researcher in health statistics. He became a Fellow of the Institute of Mathematical Statistics in 2010, and in the same year won the COPSS Presidents' Award. He was named Arts & Sciences Distinguished Professor in 2013.
Selected works
References
External links
1972 births
Living people
American statisticians
Eberly College of Science alumni
Emory University alumni
Duke University faculty
Fellows of the American Statistical Association
Fellows of the Institute of Mathematical Statistics
Place of birth missing (living people)
Bayesian statisticians |
https://en.wikipedia.org/wiki/Zrze | Zrze () is a village in the municipality of Dolneni, North Macedonia.
Demographics
According to the statistics of Vasil Kanchov ("Macedonia. Ethnography and Statistics") from 1900, Zrze was inhabited by 485 Macedonian Christian inhabitants.The name of the village was "Ѕрѕе" in cyrillic alphabet later transcribed in latin as Zrze.
The first primary school was established in 1907.
According to the 2021 census, the village had a total of 39 inhabitants. Ethnic groups in the village include:
Macedonians 64
References
Villages in Dolneni Municipality |
https://en.wikipedia.org/wiki/Liouvillian%20function | In mathematics, the Liouvillian functions comprise a set of functions including the elementary functions and their repeated integrals. Liouvillian functions can be recursively defined as integrals of other Liouvillian functions.
More explicitly, a Liouvillian function is a function of one variable which is the composition of a finite number of arithmetic operations , exponentials, constants, solutions of algebraic equations (a generalization of nth roots), and antiderivatives. The logarithm function does not need to be explicitly included since it is the integral of .
It follows directly from the definition that the set of Liouvillian functions is closed under arithmetic operations, composition, and integration. It is also closed under differentiation. It is not closed under limits and infinite sums.
Liouvillian functions were introduced by Joseph Liouville in a series of papers from 1833 to 1841.
Examples
All elementary functions are Liouvillian.
Examples of well-known functions which are Liouvillian but not elementary are the nonelementary antiderivatives, for example:
The error function,
The exponential (Ei), logarithmic (Li or li) and Fresnel (S and C) integrals.
All Liouvillian functions are solutions of algebraic differential equations, but not conversely. Examples of functions which are solutions of algebraic differential equations but not Liouvillian include:
the Bessel functions (except special cases);
the hypergeometric functions (except special cases).
Examples of functions which are not solutions of algebraic differential equations and thus not Liouvillian include all transcendentally transcendental functions, such as:
the gamma function;
the zeta function.
See also
References
Further reading
Differential algebra
Computer algebra
Types of functions |
https://en.wikipedia.org/wiki/Siegmund%20G%C3%BCnther | Adam Wilhelm Siegmund Günther (6 February 1848 – 3 February 1923) was a German geographer, mathematician, historian of mathematics and natural scientist.
Early life
Born in 1848 to a German businessman, Günther would go on to attend several German universities including Erlangen, Heidelberg, Leipzig, Berlin, and Göttingen.
Career
In 1872 he began teaching at a school in Weissenburg, Bavaria. He completed his habilitation thesis on continued fractions entitled Darstellung der Näherungswerte der Kettenbrüche in independenter Form in 1873. The next year he began teaching at Munich Polytechnicum. In 1876, he began teaching at a university in Ansbach where he stayed for several years before moving to Munich and becoming a professor of geography until he retired; he served as the university's rector from 1911 to 1913.
For some years, Günther was a member of the federal parliament, the Reichstag, and later the Bavarian parliament, representing liberal parties.
His mathematical work included works on the determinant, hyperbolic functions, and parabolic logarithms and trigonometry.
Publications (selection)
Darstellung der Näherungswerthe der Kettenbrüche in independenter Form. Eduard Besold, Erlangen, 1873
Vermischte Untersuchungen zur Geschichte der mathematischen Wissenschaften. Teubner, Leipzig, 1876
Lehrbuch der Determinanten-Theorie für Studirende. Eduard Besold, Erlangen, 1877
Die Lehre von den gewöhnlichen und verallgemeinerten Hyperbelfunktionen. Louis Nebert, Halle, 1881
Parabolische Logarithmen und parabolische Trigonometrie. Teubner, Leipzig, 1882
Further reading
Andreas Daum, Wissenschaftspopularisierung im 19. Jahrhundert: Bürgerliche Kultur, naturwissenschaftliche Bildung und die deutsche Öffentlichkeit, 1848–1914. Munich: Oldenbourg, 1998.
Josef Reindl: Siegmund Günther. Nürnberg 1908 (online copy at the Univ. Heidelberg, German)
References
1848 births
1923 deaths
20th-century German mathematicians
19th-century German mathematicians
Academic staff of the Technical University of Munich
Presidents of the Technical University of Munich
Members of the Bavarian Chamber of Deputies
Mathematicians from the Kingdom of Bavaria
Mathematicians from the German Empire |
https://en.wikipedia.org/wiki/Radio%20coloring | In graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels to the graphs
such that the labels of adjacent vertices differ by at least two, and the labels of vertices at distance two from each other differ by at least one. Radio coloring was first studied by , under a different name, -labeling. It was called radio coloring by Frank Harary because it models the problem of channel assignment in radio broadcasting, while avoiding electromagnetic interference between radio stations that are near each other both in the graph and in their assigned channel frequencies.
The span of a radio coloring is its maximum label, and the radio coloring number of a graph is the smallest possible span of a radio coloring. For instance, the graph consisting of two vertices with a single edge has radio coloring number 3: it has a radio coloring with one vertex labeled 1 and the other labeled 3, but it is not possible for a radio coloring of this graph to use only the labels 1 and 2.
Computational complexity
Finding a radio coloring with a given (or minimum) span is NP-complete, even when restricted to planar graphs, split graphs, or the complements of bipartite graphs. However it is solvable in polynomial time for trees and cographs. For arbitrary graphs, it can be solved in singly-exponential time, significantly faster than a brute-force search through all possible colorings.
Other properties
Although the radio coloring number of an -vertex graph can range from 1 to , almost all -vertex graphs have radio coloring number exactly . This is because these graphs almost always have diameter at least two (forcing all vertices to have distinct colors, and forcing the radio coloring number to be at least ) but they also almost always have a Hamiltonian path in the complement graph. Consecutive vertices in this path can be assigned consecutive colors, allowing a radio coloring to avoid skipping any numbers.
References
Computational problems in graph theory
Extensions and generalizations of graphs
Graph coloring
NP-complete problems
NP-hard problems
Radio resource management |
https://en.wikipedia.org/wiki/Polynomial%20decomposition | In mathematics, a polynomial decomposition expresses a polynomial f as the functional composition of polynomials g and h, where g and h have degree greater than 1; it is an algebraic functional decomposition. Algorithms are known for decomposing univariate polynomials in polynomial time.
Polynomials which are decomposable in this way are composite polynomials; those which are not are indecomposable polynomials or sometimes prime polynomials (not to be confused with irreducible polynomials, which cannot be factored into products of polynomials). The degree of a composite polynomial is always a composite number, the product of the degrees of the composed polynomials.
The rest of this article discusses only univariate polynomials; algorithms also exist for multivariate polynomials of arbitrary degree.
Examples
In the simplest case, one of the polynomials is a monomial. For example,
decomposes into
since
using the ring operator symbol ∘ to denote function composition.
Less trivially,
Uniqueness
A polynomial may have distinct decompositions into indecomposable polynomials where where for some . The restriction in the definition to polynomials of degree greater than one excludes the infinitely many decompositions possible with linear polynomials.
Joseph Ritt proved that , and the degrees of the components are the same up to linear transformations, but possibly in different order; this is Ritt's polynomial decomposition theorem. For example, .
Applications
A polynomial decomposition may enable more efficient evaluation of a polynomial. For example,
can be calculated with 3 multiplications and 3 additions using the decomposition, while Horner's method would require 7 multiplications and 8 additions.
A polynomial decomposition enables calculation of symbolic roots using radicals, even for some irreducible polynomials. This technique is used in many computer algebra systems. For example, using the decomposition
the roots of this irreducible polynomial can be calculated as
Even in the case of quartic polynomials, where there is an explicit formula for the roots, solving using the decomposition often gives a simpler form. For example, the decomposition
gives the roots
but straightforward application of the quartic formula gives equivalent results but in a form that is difficult to simplify and difficult to understand; one of the four roots is:
Algorithms
The first algorithm for polynomial decomposition was published in 1985, though it had been discovered in 1976, and implemented in the Macsyma/Maxima computer algebra system. That algorithm takes exponential time in worst case, but works independently of the characteristic of the underlying field.
A 1989 algorithm runs in polynomial time but with restrictions on the characteristic.
A 2014 algorithm calculates a decomposition in polynomial time and without restrictions on the characteristic.
Notes
References
Polynomials
Computer algebra |
https://en.wikipedia.org/wiki/CONCACAF%20Gold%20Cup%20records%20and%20statistics | This is a list of records and statistics of the CONCACAF Gold Cup. The Gold Cup replaced the CONCACAF Championship, which was held ten times from 1963 to 1989. Before the merger and foundation of CONCACAF, the confederation was split into two entities with their own international tournament, NAFU's North American Nations Cup and the CCCF Championship.
Medal table
Comprehensive team results by tournament
Legend
For each tournament, the number of teams in each finals tournament are shown (in parentheses).
Notes
Invitees nations record
General statistics by tournament
Debut of teams
Each final tournament has had at least one team appearing for the first time. A total of 24 CONCACAF members have reached the finals.
Overall team records
In this ranking 3 points are awarded for a win, 1 for a draw and 0 for a loss. As per statistical convention in football, matches decided in extra time are counted as wins and losses, while matches decided by penalty shoot-outs are counted as draws. Teams are ranked by total points, then by goal difference, then by goals scored.
Notes
Teams yet to qualify for finals
The following seventeen teams which are current CONCACAF members have never qualified for the Gold Cup.
Legend
– Did not qualify
– Did not enter / withdrew / banned
For each tournament, the number of teams in each finals tournament (in brackets) are shown.
Host nations and venues
Co-hosted by the United States and Mexico in 1993 and 2003
Co-hosted by the United States and Canada in 2015 and 2023
Co-hosted by the United States, Costa Rica and Jamaica in 2019
Results of host nations and defending champions
Host nations
Defending champions
Notes
Active participation streaks
This is a list of active consecutive participations of national teams in the CONCACAF Gold Cup and CONCACAF Championship.
Active participation droughts
This is a list of droughts associated with the participation of national teams in the CONCACAF Gold Cup.
Does not include teams that have not yet made their first appearance, teams that no longer exist.
Player awards and records
Top 20 goal leaders
Only CONCACAF Gold Cup matches counted towards all-time records. Stats from qualification are not included.
Players in bold have not retired from international football and may still be called up to their national team.
Best goalkeeper award
2000: Craig Forrest
2002: Lars Hirschfeld
2003: Oswaldo Sánchez
2005: Jaime Penedo
2007: Franck Grandel
2009: Keylor Navas
2011: Noel Valladares
2013: Jaime Penedo
2015: Brad Guzan
2017: Andre Blake
2019: Guillermo Ochoa
2021: Matt Turner
2023: Guillermo Ochoa
References
External links
All-time football league tables |
https://en.wikipedia.org/wiki/Positive%20real%20numbers | In mathematics, the set of positive real numbers, is the subset of those real numbers that are greater than zero. The non-negative real numbers, also include zero. Although the symbols and are ambiguously used for either of these, the notation or for and or for has also been widely employed, is aligned with the practice in algebra of denoting the exclusion of the zero element with a star, and should be understandable to most practicing mathematicians.
In a complex plane, is identified with the positive real axis, and is usually drawn as a horizontal ray. This ray is used as reference in the polar form of a complex number. The real positive axis corresponds to complex numbers with argument
Properties
The set is closed under addition, multiplication, and division. It inherits a topology from the real line and, thus, has the structure of a multiplicative topological group or of an additive topological semigroup.
For a given positive real number the sequence of its integral powers has three different fates: When the limit is zero; when the sequence is constant; and when the sequence is unbounded.
and the multiplicative inverse function exchanges the intervals. The functions floor, and excess, have been used to describe an element as a continued fraction which is a sequence of integers obtained from the floor function after the excess has been reciprocated. For rational the sequence terminates with an exact fractional expression of and for quadratic irrational the sequence becomes a periodic continued fraction.
The ordered set forms a total order but is a well-ordered set. The doubly infinite geometric progression where is an integer, lies entirely in and serves to section it for access. forms a ratio scale, the highest level of measurement. Elements may be written in scientific notation as where and is the integer in the doubly infinite progression, and is called the decade. In the study of physical magnitudes, the order of decades provides positive and negative ordinals referring to an ordinal scale implicit in the ratio scale.
In the study of classical groups, for every the determinant gives a map from matrices over the reals to the real numbers: Restricting to invertible matrices gives a map from the general linear group to non-zero real numbers: Restricting to matrices with a positive determinant gives the map ; interpreting the image as a quotient group by the normal subgroup called the special linear group, expresses the positive reals as a Lie group.
Ratio scale
Among the levels of measurement the ratio scale provides the finest detail. The division function takes a value of one when numerator and denominator are equal. Other ratios are compared to one by logarithms, often common logarithm using base 10. The ratio scale then segments by orders of magnitude used in science and technology, expressed in various units of measurement.
An early expression of ratio scale was articulated geometrica |
https://en.wikipedia.org/wiki/Arthur%20Preston%20Mellish | Arthur Preston Mellish (10 June 1905 – 7 February 1930) was a Canadian mathematician, known for his generalization of Barbier's theorem.
Arthur Mellish received in 1928 an M.A. in mathematics from the University of British Columbia with thesis An illustrative example of the ellipsoid pendulum. He died at age 24 and had no mathematical publications during his lifetime. After his death, his colleagues at Brown University examined his notes on mathematics. Jacob Tamarkin prepared a paper based upon the notes and published it in the Annals of Mathematics in 1931.
In the statement of the following theorem, an oval means a closed convex curve.
Mellish's Theorem: The statements
(i) a curve is of constant width;
(ii) a curve is of constant diameter;
(iii) all the normals of a curve (an oval) are double;
(iv) the sum of radii of curvature at opposite points of a curve (an oval) is constant;
are equivalent, in the sense that whenever one of statements (i–iv) is true, all other statements also hold.
(v) All curves of the same (constant) width a have the same length L given by L = a.
References
1905 births
1930 deaths
University of British Columbia alumni
Canadian mathematicians
Differential geometers |
https://en.wikipedia.org/wiki/Lawrence%20Zalcman | Lawrence Allen Zalcman (June 9, 1943 – May 31, 2022) was a professor (and later a professor emeritus) of Mathematics at Bar-Ilan University in Israel. His research primarily concerned Complex analysis, potential theory, and the relations of these ideas to approximation theory, harmonic analysis, integral geometry and partial differential equations. On top of his scientific achievements, Zalcman received numerous awards for mathematical exposition, including the Chauvenet Prize in 1976, the Lester R. Ford Award in 1975 and 1981, and the Paul R. Halmos – Lester R. Ford Award in 2017. In addition to Bar-Ilan University, Zalcman taught at the University of Maryland and Stanford University in the United States.
Life and career
Zalcman was born in Kansas City, Missouri on June 9, 1943. In 1961, he graduated from Southwest High School in Kansas City, Missouri before continuing his education at Dartmouth College, where he would graduate in 1964. Zalcman went on to receive his Ph.D. from the Massachusetts Institute of Technology in 1968 under the supervision of Kenneth Myron Hoffman. In 2012, Zalcman became a fellow of the American Mathematical Society.
In the theory of normal families, Zalcman's Lemma, which he used as part of his treatment of Bloch's principle, is named after him. Other eponymous honors are Zalcman domains, which play a role in the classification of Riemann surfaces, and Zalcman functions in complex dynamics. In the theory of partial differential equations, the Pizzetti-Zalcman formula is partially named after him.
Lawrence Zalcman died in Jerusalem on May 31, 2022.
Selected publications
with Peter Lax: Complex proofs of real theorems, American Mathematical Society 2012
References
1943 births
2022 deaths
Israeli mathematicians
Fellows of the American Mathematical Society
Academic staff of Bar-Ilan University
Massachusetts Institute of Technology School of Science alumni
Complex analysts |
https://en.wikipedia.org/wiki/Mathiness | Mathiness is a term coined by Nobel prize winner economist Paul Romer to label a specific misuse of mathematics in economic analyses. An author committed to the norms of science should use mathematical reasoning to clarify their analyses. By contrast, "mathiness" is not intended to clarify, but instead to mislead. According to Romer, some researchers use unrealistic assumptions and strained interpretations of their results in order to push an ideological agenda, and use a smokescreen of fancy mathematics to disguise their intentions.
Introduction of the term
The first usage of the term was at the annual meeting of the American Economic Association in January 2015. Afterwards Paul Romer published his article Mathiness in the Theory of Economic Growth in the American Economic Review. The coinage mathiness follows the pattern of truthiness coined by comedian Stephen Colbert. Romer warns that mathiness is distorting economics:
He specifically points to some work by Edward C. Prescott, Robert Lucas, Jr., and Thomas Piketty, among others, and argues for a return to scientific rigor:
Long before Romer, Hayek had condemned scientism, specifically in the form of the misuse of mathematics in social science, in his 1974 Nobel Prize acceptance speech on "The Pretence of Knowledge", and in his 1942 essay "Scientism and the Study of Society", later published as The Counter-Revolution of Science.
Impact
Tim Harford draws a parallel to Politics and the English Language where George Orwell complained that politics prefers a rhetorical fog to the use of precise terms. Similarly the role of mathiness would be to hide unrealistic assumptions or pure hypothesis behind decorative math and therefore it is rather a case of politics than science.
Justin Fox notes that, in his book Misbehaving: The Making of Behavioral Economics, Richard Thaler documented how economists ignored real world phenomena because they did not fit into mainstream mathematical models.
J. Bradford DeLong argued that mathiness means "restricting your microfoundations in advance to guarantee a particular political result and hiding what you are doing in a blizzard of irrelevant and ungrounded algebra". He argues that this is what George Stigler did when he rejected the inclusion of monopolistic competition in his models because in his mind it was too intellectually dangerous. The notion of imperfect competition could give an opening to interventionist "planning" while being unaware of the magnitudes of potential government failure. Therefore, requiring that models assume perfect competition as a methodological principle was a "noble lie" to him. Paul Romer's problem is that he wants to analyze issues in which perfect competition is not leading forward but Prescott and Lucas are insisting on perfect competition as a methodological principle.
Paul Krugman thinks that the debate about drawing macroeconomic conclusions from the Great Recession is obstructed by the fact that there are economists, |
https://en.wikipedia.org/wiki/Garbi%C3%B1e%20Muguruza%20career%20statistics | This is a list of the main career statistics of Spanish professional tennis player, Garbiñe Muguruza. To date, she has won 15 WTA Tour-level tournaments, winning ten of them in singles and five in doubles. In her titles collection, she also has seven singles and one doubles titles on the ITF Circuit. Having good performances at the majors, she won the French Open title in 2016 and then the following year at Wimbledon. Along with that, she reached two more Grand Slam finals (2015 Wimbledon and 2020 Australian Open).
At the 2021 WTA Finals, she reached her first final there, and won the title defeating Anett Kontaveit. Muguruza reached her career-high ranking of world No. 1 on 11 September 2017. In 2015, when her breakthrough happened, she reached her first WTA 1000 final at the Wuhan Open. The following week, she won her first WTA 1000-level tournament at the China Open. Later, she won two more WTA 1000 titles; at the 2017 Cincinnati Open and the 2021 Dubai Championships.
Being more recognized for her singles results, she done well in doubles as well. Most significant results are the finals at the 2017 WTA Finals and three more from the WTA 1000 tier. She also reached semifinals at the 2014 French Open. All mentioned doubles achievements she made alongside compatriot Carla Suárez Navarro. On the 23 February 2015, she had her top 10 debut in the doubles rankings as No. 10, her highest up to date.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in Win–loss records.
Singles
Current through the 2023 Lyon Open.
Doubles
Current through the Tennis at the 2020 Summer Olympics.
Grand Slam tournament finals
Singles: 4 (2 titles, 2 runner-ups)
Other significant finals
Year-end championships finals
Singles: 1 (1 title)
Doubles: 1 (1 runner-up)
WTA 1000 finals
Singles: 5 (3 titles, 2 runner-ups)
Doubles: 3 (3 runner-ups)
WTA career finals
Singles: 17 (10 titles, 7 runner-ups)
Doubles: 10 (5 titles, 5 runner-ups)
ITF Circuit finals
Singles: 13 (7 titles, 6 runner-ups)
Doubles: 2 (1 title, 1 runner-up)
WTA Tour career earnings
Current as of 2022 US Open.
Career Grand Slam statistics
Seedings
The tournaments won by Muguruza are in boldface, and advanced into finals by Muguruza are in italics.
Best Grand Slam results details
Head to head
Record against top 10 players
Muguruza's record against players who have been ranked in the top 10. Active players are in boldface.
No. 1 wins
Top 10 wins
Longest winning streaks
9–match singles winning streak (2017)
Notes
References
Muguruza, Garbine
career |
https://en.wikipedia.org/wiki/Thierry%20Sardo | Thierry Sardo (born 14 June 1967 in Toulon, France) is a football coach. He was appointed head coach of the New Caledonia national football team on 3 February 2015.
Managerial Statistics
References
External links
1967 births
Living people
New Caledonia national football team managers
New Caledonian football managers
Footballers from Toulon |
https://en.wikipedia.org/wiki/Wilfrid%20Dixon | Wilfrid Joseph Dixon (December 13, 1915 – September 20, 2008) was an American mathematician and statistician. He made notable contributions to nonparametric statistics, statistical education and experimental design.
A native of Portland, Oregon, Dixon received a bachelor's degree in mathematics from Oregon State College in 1938. He continued his graduate studies at the University of Wisconsin–Madison, where he earned a master's degree in 1939. Under supervision of Samuel S. Wilks, he then earned a Ph.D. in mathematical statistics from Princeton in 1944. During World War II, he was an operations analyst on Guam.
Dixon was on the faculties at Oklahoma (1942–1943), Oregon (1946–1955), and UCLA (1955–1986, then emeritus). While at Oregon, Dixon (together with A.M. Mood) described and provided theory and estimation methods for the adaptive Up-and-Down experimental design, which was new and poorly documented at the time. This article became the cornerstone publication for up-and-down, a family of designs used in many scientific, engineering and medical fields, and to which Dixon continued to contribute in later years. In 1951 Dixon, together with Frank Massey, published a statistics textbook - the first such textbook intended to a non-mathematical audience. In 1955 he was elected as a Fellow of the American Statistical Association.
In the 1960s at UCLA, Dixon developed BMDP, a statistical software package for biomedical analyses.
His daughter, Janet D. Elashoff, is also a statistician who became a UCLA faculty member, and an ASA fellow in 1978. In December 2008 she funded the W. J. Dixon Award for Excellence in Statistical Consulting of the American Statistical Association in his honor.
References
External links
1915 births
2008 deaths
Scientists from Portland, Oregon
American statisticians
Oregon State University alumni
University of Wisconsin–Madison alumni
Princeton University alumni
University of California, Los Angeles faculty
Fellows of the American Statistical Association |
https://en.wikipedia.org/wiki/Betz%20Halloran | Mary Elizabeth (Betz) Halloran is an American biostatistician who works as a professor of biostatistics, professor of epidemiology, and adjunct professor of applied mathematics at the University of Washington.
Education and career
Halloran studied physics and philosophy of mathematics for two years as an undergraduate at Case Western Reserve University, from 1968 to 1970, before leaving school to join the counterculture movement in San Francisco. Deciding to study medicine, she returned to school, completing a bachelor's degree in general science at the University of Oregon in 1972.
She traveled to Berlin to continue her studies at the Max Planck Institute for Molecular Genetics and the Free University of Berlin from 1973 to 1975, studied medicine at the University of Southampton in England in 1981, and completed an M.D. at the Free University of Berlin in 1983. Her goal at that time was to practice medicine in the developing world, so she continued to study tropical diseases at the Bernhard Nocht Institute for Tropical Medicine in Hamburg in 1984, and then earned a master of public health degree from Harvard University in 1985. In that program, she rekindled her interest in mathematical modeling, and she stayed at Harvard as a graduate student, earning a D.Sc. in population sciences from Harvard in 1989.
After postdoctoral research at Princeton University and Imperial College London, she joined Emory University as an assistant professor of epidemiology and biostatistics in 1989, and was promoted to full professor in 1998. At Emory, she directed the Center for AIDS Research from 2002 to 2005, and the Center for Highthroughput Experimental Design and Analysis from 2004 to 2005. She moved to the University of Washington in 2005. In 2009, she founded the Summer Institute in Statistics and Modeling in Infectious
Diseases at the University of Washington, and continues to serve as its director.
Research
Halloran studies causal inference and the biostatistics of infectious diseases. She is a long-term collaborator with University of Florida researcher Ira Longini, with whom she studies the spread of influenza. She has also been quoted as an expert on the mortality rates of other diseases such as ebola and cholera, and the factors influencing those rates.
With Longini and Claudio J. Struchiner, she is a co-author of the book Design and Analysis of Vaccine Studies (Springer, 2009).
Awards and honors
In 1996, Halloran was elected as a fellow of the American Statistical Association, in 1997 she became a fellow of the Royal Statistical Society, and in 2009 she became a fellow of the American Association for the Advancement of Science.
In 2005 and 2006 she held the Dr. Ross Prentice Professorship of Biostatistics at the University of Washington.
References
American statisticians
20th-century American mathematicians
Biostatisticians
Emory University faculty
Fellows of the American Association for the Advancement of Science
Fellows of the American Sta |
https://en.wikipedia.org/wiki/Farthest-first%20traversal | In computational geometry, the farthest-first traversal of a compact metric space is a sequence of points in the space, where the first point is selected arbitrarily and each successive point is as far as possible from the set of previously-selected points. The same concept can also be applied to a finite set of geometric points, by restricting the selected points to belong to the set or equivalently by considering the finite metric space generated by these points. For a finite metric space or finite set of geometric points, the resulting sequence forms a permutation of the points, also known as the greedy permutation.
Every prefix of a farthest-first traversal provides a set of points that is widely spaced and close to all remaining points. More precisely, no other set of equally many points can be spaced more than twice as widely, and no other set of equally many points can be less than half as far to its farthest remaining point. In part because of these properties, farthest-point traversals have many applications, including the approximation of the traveling salesman problem and the metric -center problem. They may be constructed in polynomial time, or (for low-dimensional Euclidean spaces) approximated in near-linear time.
Definition and properties
A farthest-first traversal is a sequence of points in a compact metric space, with each point appearing at most once. If the space is finite, each point appears exactly once, and the traversal is a permutation of all of the points in the space. The first point of the sequence may be any point in the space. Each point after the first must have the maximum possible distance to the set of points earlier than in the sequence, where the distance from a point to a set is defined as the minimum of the pairwise distances to points in the set. A given space may have many different farthest-first traversals, depending both on the choice of the first point in the sequence (which may be any point in the space) and on ties for the maximum distance among later choices.
Farthest-point traversals may be characterized by the following properties. Fix a number , and consider the prefix formed by the first points of the farthest-first traversal of any metric space. Let be the distance between the final point of the prefix and the other points in the prefix. Then this subset has the following two properties:
All pairs of the selected points are at distance at least from each other, and
All points of the metric space are at distance at most from the subset.
Conversely any sequence having these properties, for all choices of , must be a farthest-first traversal. These are the two defining properties of a Delone set, so each prefix of the farthest-first traversal forms a Delone set.
Applications
used the farthest-first traversal to define the farthest-insertion heuristic for the travelling salesman problem. This heuristic finds approximate solutions to the travelling salesman problem by building up a tour on |
https://en.wikipedia.org/wiki/Foundations%20of%20Computational%20Mathematics | Foundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.
Aim
FoCM aims to explore the relationship between mathematics and computation, focusing both on the search for mathematical solutions to computational problems and computational solutions to mathematical problems. Topics of central interest in the Society include but are not restricted to:
Approximation Theory
Computational Algebraic Geometry
Computational Dynamics
Computational Harmonic Analysis, Image, and Signal Processing
Computational Number Theory
Computational Topology and Geometry
Continuous Optimization
Foundations of Numerical PDE's
Geometric Integration and Computational Mechanics
Graph Theory and Combinatorics
Information-based Complexity
Learning Theory
Multiresolution and Adaptivity in Numerical PDE's
Numerical Linear Algebra
Random Matrices
Real-Number Complexity
Special Functions and Orthogonal Polynomials
Stochastic Computing
Symbolic Analysis
History
The Society for the Foundations of Computational Mathematics was launched in the Northern summer of 1995, following a month-long AMS–SIAM Summer Seminar in Park City, Utah, which was organized principally by Stephen Smale. That meeting hosted a number of sub-conferences on the frontier of Mathematics and Computation, focusing on many topics from numerical analysis and on the importance of a foundational theory of real number computation. The main thrust was on creating a shared intellectual space for activity bringing together computation and mathematics. During the final week at Michael Shub's behest an informal lunch was arranged where Felipe Cucker, Arieh Iserles, Narendra Karmarkar, James Renegar, Michael Shub and Stephen Smale decided to go ahead and create a permanent entity that would organize periodic conferences covering subjects in the interplay between these two areas. After a discussion, the name Foundations of Computational Mathematics was settled, and Michael Shub was chosen to lead the initiative with a little team formed by himself, Arieh Iserles and James Renegar.
The first FoCM conference took place in Rio de Janeiro and was hosted by IMPA with the support of its then-director Jacob Palis. Several conferences were organized later (see below), bringing together some of the world leading mathematicians and computer scientists, although the society was not formally established as a legal entity until 1999 simultaneously with the creation of the journal Foundations of Computational Mathematics. Ever since, its main activities are its triennial meetings, special semesters and the support of the FoCM journal, as well as general advocacy of the mathematical areas underlying computation.
Meetings
The main FoCM conference is held every three years |
https://en.wikipedia.org/wiki/2015%E2%80%9316%20FK%20%C5%BDeljezni%C4%8Dar%20season | FK Željezničar is a football club in Bosnia and Herzegovina. This article summarizes statistics from the 2015–16 football season.
Squad statistics
Players
Total squad cost: €8.33M
From the youth system
Disciplinary record
Includes all competitive matches. The list is sorted by position, and then shirt number.
Transfers
In
Total expenditure:
Out
Total income: €1.115.000
Club
Coaching staff
{|
|valign="top"|
Other information
(Interim)
Competitions
Pre-season
Mid-season
Overall
Premijer Liga BiH
Results summary
Results by round
Matches
Kup Bosne i Hercegovine
Round of 32
Round of 16
Quarter-finals
Semi-finals
UEFA Europa League
First qualifying round
Second qualifying round
Third qualifying round
UEFA Youth League
Players
Total squad cost: €1.25M
First round
References
FK Željezničar Sarajevo seasons
Zeljeznicar |
https://en.wikipedia.org/wiki/Warwick%20Tucker | Warwick Tucker is an Australian mathematician at Monash University (previously deputy Chair and Chair at the Department of Mathematics at Uppsala University 2009–2020) who works on dynamical systems, chaos theory and computational mathematics. He is a recipient of the 2002 R. E. Moore Prize, and the 2004 EMS Prize.
Tucker obtained his Ph.D. in 1998 at Uppsala University (thesis: The Lorenz attractor exists) with Lennart Carleson as advisor.
In 2002, Tucker succeeded in solving an important open problem that had been posed by Stephen Smale (the fourteenth problem on Smale's list of problems).
He was an invited speaker at the conference Dynamics, Equations and Applications in Kraków in 2019.
References
External links
Year of birth missing (living people)
Living people
Swedish mathematicians
Dynamical systems theorists
Australian mathematicians
Academic staff of Uppsala University |
https://en.wikipedia.org/wiki/Mehdi%20Mohammadpour | Mehdi Mohammadpour () is an Iranian footballer who plays for Nassaji Mazandaran in the Azadegan League.
Club career statistics
References
External links
Mehdi Mohammadpour in varzesh11
Mehdi Mohammadpour at IRIFF
1985 births
Living people
Iranian men's footballers
Footballers from Tabriz
Shahrdari Ardabil F.C. players
Gostaresh Foulad F.C. players
Shahrdari Tabriz F.C. players
Machine Sazi F.C. players
Tractor S.C. players
Men's association football defenders |
https://en.wikipedia.org/wiki/The%20Art%20of%20Mathematics | The Art of Mathematics (), written by Hong Sung-Dae (), is a series of mathematics textbooks for high school students in South Korea. First published in 1966, it is the best-selling book series in South Korea, with about 46 million copies sold as of 2016. In Jeongeup, North Jeolla Province, the hometown of Hong Sung-Dae, a street is named Suhakjeongseok-gil () in honor of the author.'
Controversy
The similarities with the Japanese Textbook series Chart-Style Math () have caused the author to receive accusations of plagiarism. The chapter division, style of explanation, and formatting are visibly similar between the books. For instance, in the Japanese books, the order of questions are in "Example Questions, Practice Questions, Exercise Questions," while in The Art of Mathematics it is "Example Questions, Similar Questions, Practice Questions". The author Hong has denied all accusations, although he has admitted that the questions in the books were selected from 20 reference books around the world.
Major topics in the 11th edition
Changes in the 11th edition, published 2013-2015, reflect the 2009 revision of South Korea's National Curriculum. Each of the six volumes consist of two versions, one for average students () and one for higher-ability students ().
Mathematics I
Polynomials (다항식 da-hang-sik)
Equations and Inequalities (방정식과 부등식 bang-jeong-sik-gwa boo-deung-sik)
Graphs of Equations (방정식의 그래프 bang-jeong-sik-eui geu-re-pu)
Mathematics II
Sets and Propositions (집합과 명제 jib-hab-gwa myung-jeh)
Functions (함수 ham-soo)
Sequences (수열 soo-yeul)
Exponents and Logarithms (지수와 로그함수 ji-soo-wa lo-geu-ham-soo)
Probability and Statistics
Permutations and Combinations (순열과 조합 soon-yeul-gwa jo-hab)
Probability (확률 hwang-lyul)
Statistics (통계 tong-gye)
Calculus I
Limits of Sequences (수열의 극한 soo-yeul-eui geuk-han)
Limits and Continuity (극한과 연속성 geuk-han-gwa yeon-sok-sung)
Differentiation of Polynomial Functions (다항식의 미분 da-hang-sik-eui mi-boon)
Integration of Polynomial Functions (다항식의 적분 da-hang-sik-eui juck-boon)
Calculus II
Exponential and Logarithmic Functions (지수와 로그 함수 ji-soo-wa lo-geu-ham-soo)
Trigonometric Functions (삼각함수 sam-gak-ham-soo)
Differentiation (미분 mi-boon)
Integration (적분 juck-boon)
Geometry and Vectors
Plane Curves (평면곡선 pyung-myun-gog-seon)
Vectors in the Plane (평면 벡터 pyung-myun beg-teo)
Graphs and Vectors in Space (공간의 그래프와 벡터 gong-gan-eui geu-re-pu-wa beg-teo)
References
External links
publisher's website
Mathematics textbooks
1966 non-fiction books
Korean non-fiction books |
https://en.wikipedia.org/wiki/Sub-Gaussian%20distribution | In probability theory, a sub-Gaussian distribution is a probability distribution with strong tail decay. Informally, the tails of a sub-Gaussian distribution are dominated by (i.e. decay at least as fast as) the tails of a Gaussian. This property gives sub-Gaussian distributions their name.
Formally, the probability distribution of a random variable is called sub-Gaussian if there is a positive constant C such that for every ,
.
Sub-Gaussian properties
Let be a random variable. The following conditions are equivalent:
for all , where is a positive constant;
, where is a positive constant;
for all , where is a positive constant.
Proof. By the layer cake representation,After a change of variables , we find that
Using the Taylor series for : we obtain thatwhich is less than or equal to for . Take , then
By Markov's inequality,
Definitions
A random variable is called a sub-Gaussian random variable if either one of the equivalent conditions above holds.
The sub-Gaussian norm of , denoted as , is defined bywhich is the Orlicz norm of generated by the Orlicz function By condition above, sub-Gaussian random variables can be characterized as those random variables with finite sub-Gaussian norm.
More equivalent definitions
The following properties are equivalent:
The distribution of is sub-Gaussian.
Laplace transform condition: for some B, b > 0, holds for all .
Moment condition: for some K > 0, for all .
Moment generating function condition: for some , for all such that .
Union bound condition: for some c > 0, for all n > c, where are i.i.d copies of X.
Examples
A standard normal random variable is a sub-Gaussian random variable.
Let be a random variable with symmetric Bernoulli distribution. That is, takes values and with probabilities each. Since , it follows that and hence is a sub-Gaussian random variable.
See also
Platykurtic distribution
Notes
References
Vershynin, R. (2018). "High-dimensional probability: An introduction with applications in data science" (PDF). Volume 47 of Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge.
Zajkowskim, K. (2020). "On norms in some class of exponential type Orlicz spaces of random variables". Positivity. An International Mathematics Journal Devoted to Theory and Applications of Positivity. 24(5): 1231--1240. arXiv:1709.02970. doi.org/10.1007/s11117-019-00729-6.
Continuous distributions |
https://en.wikipedia.org/wiki/Arnold%27s%20spectral%20sequence | In mathematics, Arnold's spectral sequence (also spelled Arnol'd) is a spectral sequence used in singularity theory and normal form theory as an efficient computational tool for reducing a function to canonical form near critical points. It was introduced by Vladimir Arnold in 1975.
Definition
References
Spectral sequences
Singularity theory |
https://en.wikipedia.org/wiki/Nikolai%20Ivanov%20%28mathematician%29 | Nikolai V. Ivanov (, born 1954) is a Russian mathematician who works on topology, geometry and group theory (particularly, modular Teichmüller groups). He is a professor at Michigan State University.
He obtained his Ph.D. under the guidance of Vladimir Abramovich Rokhlin in 1980 at the Steklov Mathematical Institute.
According to Google Scholar, on 5 July 2020, Ivanov's works had received 2,376 citations and his h-index was 22.
He is a fellow of the American Mathematical Society since 2012.
He is the author of the 1992 book Subgroups of Teichmüller Modular Groups.
Among his contributions to mathematics are his classification of subgroups of surface mapping class groups, and the establishment that surface mapping class groups satisfy the Tits alternative.
Selected publications
"Automorphisms of complexes of curves and of Teichmuller spaces" (1997), International Mathematics Research Notices 14, pp. 651–666.
with John D. McCarthy: "On injective homomorphisms between Teichmüller modular groups I" (1999), Inventiones mathematicae 135 (2), pp. 425–486.
"On the homology stability for Teichmüller modular groups: closed surfaces and twisted coefficients" (1993), Contemporary Mathematics 150, pp. 149–149.
References
External links
N. V. Ivanov website
Ivanov's blog
1954 births
Topologists
Geometers
Living people
Fellows of the American Mathematical Society
Michigan State University faculty
Steklov Institute of Mathematics alumni
20th-century Russian mathematicians
21st-century Russian mathematicians
Soviet mathematicians |
https://en.wikipedia.org/wiki/SIEC | SIEC may refer to:
Symbiosis International Education Centre, now Symbiosis International University
SIEC (The Integrated National System for Criminal Statistics), see Domestic violence in Panama
Sydney International Equestrian Centre, known as SIEC
Sexuality Information and Education Council of the United States, known as SIECUS |
https://en.wikipedia.org/wiki/Shafarevich%27s%20theorem%20on%20solvable%20Galois%20groups | In mathematics, Shafarevich's theorem states that any finite solvable group is the Galois group of some finite extension of the rational numbers. It was first proved by , though Alexander Schmidt later pointed out a gap in the proof, which was fixed by .
References
Galois theory
Solvable groups |
https://en.wikipedia.org/wiki/2015%E2%80%9316%20F.C.%20Copenhagen%20season | This article shows statistics of individual players for the football club F.C. Copenhagen. It also lists all matches that F.C. Copenhagen played in the 2015–16 season.
Players
Squad information
This section show the squad as currently, considering all players who are confirmedly moved in and out (see section Players in / out).
Squad stats
Players in / out
In
Out
Club
Coaching staff
Other information
Competitions
Overall
Danish Superliga
League table
Results summary
Results by round
UEFA Europa League
Second qualifying round
Third qualifying round
Results summary
Matches
Competitive
References
External links
F.C. Copenhagen official website
2015–16
Danish football clubs 2015–16 season |
https://en.wikipedia.org/wiki/2002%E2%80%9303%20VfL%20Bochum%20season | The 2002–03 VfL Bochum season was the 65th season in club history.
Review and events
Matches
Legend
Bundesliga
DFB-Pokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Winter
In:
Out:
VfL Bochum II
Sources
External links
2002–03 VfL Bochum season at Weltfussball.de
2002–03 VfL Bochum season at kicker.de
2002–03 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/Esquerdinha%20%28footballer%2C%20born%201990%29 | Francisco Lisvaldo Daniel Duarte (born 16 November 1990 in Uiraúna), Brazil, commonly known as Esquerdinha, is a Brazilian footballer, who currently plays for Nacional-PB.
Career statistics
Club
References
External links
Esquerdinha at ZeroZero
1990 births
Living people
Brazilian men's footballers
Men's association football midfielders
Boa Esporte Clube players
Treze Futebol Clube players
Clube Atlético Bragantino players
KF Skënderbeu Korçë players
C.S. Marítimo players
Madureira Esporte Clube players
Ferroviário Atlético Clube (CE) players
Esporte Clube Juventude players
Alebrijes de Oaxaca players
Guarany Sporting Club players
Sousa Esporte Clube players
Associação Desportiva Recreativa e Cultural Icasa players
4 de Julho Esporte Clube players
América Futebol Clube (RN) players
Floresta Esporte Clube players
Nacional Atlético Clube (Patos) players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série C players
Campeonato Brasileiro Série D players
Kategoria Superiore players
Primeira Liga players
Ascenso MX players
Brazilian expatriate men's footballers
Brazilian expatriate sportspeople in Albania
Brazilian expatriate sportspeople in Portugal
Brazilian expatriate sportspeople in Mexico
Expatriate men's footballers in Albania
Expatriate men's footballers in Portugal
Expatriate men's footballers in Mexico |
https://en.wikipedia.org/wiki/Ternary%20equivalence%20relation | In mathematics, a ternary equivalence relation is a kind of ternary relation analogous to a binary equivalence relation. A ternary equivalence relation is symmetric, reflexive, and transitive. The classic example is the relation of collinearity among three points in Euclidean space. In an abstract set, a ternary equivalence relation determines a collection of equivalence classes or pencils that form a linear space in the sense of incidence geometry. In the same way, a binary equivalence relation on a set determines a partition.
Definition
A ternary equivalence relation on a set is a relation , written , that satisfies the following axioms:
Symmetry: If then and . (Therefore also , , and .)
Reflexivity: . Equivalently, if , , and are not all distinct, then .
Transitivity: If and and then . (Therefore also .)
References
Mathematical relations
Incidence geometry
Projective geometry |
https://en.wikipedia.org/wiki/Harald%20Niederreiter | Harald G. Niederreiter (born June 7, 1944) is an Austrian mathematician known for his work in discrepancy theory, algebraic geometry, quasi-Monte Carlo methods, and cryptography.
Education and career
Niederreiter was born on June 7, 1944, in Vienna, and grew up in Salzburg. He began studying mathematics at the University of Vienna in 1963, and finished his doctorate there in 1969, with a thesis on discrepancy in compact abelian groups supervised by Edmund Hlawka.
He began his academic career as an assistant professor at the University of Vienna, but soon moved to Southern Illinois University. During this period he also visited the University of Illinois at Urbana-Champaign, Institute for Advanced Study, and University of California, Los Angeles. In 1978 he moved again, becoming the head of a new mathematics department at the University of the West Indies in Jamaica. In 1981 he returned to Austria for a post at the Austrian Academy of Sciences, where from 1989 to 2000 he served as director of the Institutes of Information Processing and Discrete Mathematics. In 2001 he became a professor at the National University of Singapore. In 2009 he returned to Austria again, to the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences. He also worked from 2010 to 2011 as a professor at the King Fahd University of Petroleum and Minerals in Saudi Arabia.
Research
Niederreiter's initial research interests were in the abstract algebra of abelian groups and finite fields, subjects also represented by his later book Finite Fields (with Rudolf Lidl, 1983). From his doctoral thesis onwards, he also incorporated discrepancy theory and the theory of uniformly distributed sets in metric spaces into his study of these subjects.
In 1970, Niederreiter began to work on numerical analysis and random number generation, and in 1974 he published the book Uniform Distribution of Sequences. Combining his work on pseudorandom numbers with the Monte Carlo method, he did pioneering research in the quasi-Monte Carlo method in the late 1970s, and again later published a book on the topic, Random Number Generation and Quasi-Monte Carlo Methods (1995).
Niederreiter's interests in pseudorandom numbers also led him to study stream ciphers in the 1980s, and this interest branched out into other areas of cryptography such as public key cryptography. The Niederreiter cryptosystem, an encryption system based on error-correcting codes that can also be used for digital signatures, was developed by him in 1986. His work in cryptography is represented by his book Algebraic Geometry in Coding Theory and Cryptography (with C. P. Xing, 2009).
Returning to pure mathematics, Niederreiter has also made contributions to algebraic geometry with the discovery of many dense curves over finite fields, and published the book Rational Points on Curves over Finite Fields: Theory and Applications (with C. P. Xing, 2001).
Awards and honors
Niederreiter is a |
https://en.wikipedia.org/wiki/Ho%C3%A0ng%20Xu%C3%A2n%20S%C3%ADnh | Hoàng Xuân Sính (born September 8, 1933) is a Vietnamese mathematician, a student of Grothendieck, the first female mathematics professor in Vietnam, the founder of , and a recipient of the Ordre des Palmes Académiques.
Early life and career
Hoàng was born in Cót, in the Từ Liêm District of Vietnam, one of seven children of fabric merchant Hoàng Thuc Tan. Her mother died when she was eight years old, and she was raised by a stepmother. She has also frequently been said to be the granddaughter of Vietnamese mathematician Hoàng Xuân Hãn. She completed a bachelor's degree in 1951 in Hanoi, studying English and French, and then traveled to Paris for a second baccalaureate in mathematics. She stayed in France to study for an agrégation at the University of Toulouse, which she completed in 1959, before returning to Vietnam to become a mathematics teacher at the Hanoi National University of Education. Hoàng became the first female mathematics professor in Vietnam and at that time was one of a very small number of mathematicians there with a foreign education.
Work with Grothendieck
The French mathematician and pacifist Alexander Grothendieck visited North Vietnam in late 1967, during the Vietnam War, and spent a month teaching mathematics to the Hanoi University mathematics department staff, including Hoàng, who took the notes for the lectures. Because of the war, Grothendieck's lectures were held away from Hanoi, first in the nearby countryside and later in Đại Từ. After Grothendieck returned to France, he continued to teach Hoàng as a correspondence student. She earned her doctorate under Grothendieck's supervision from Paris Diderot University in 1975, with a handwritten thesis. Her thesis research, on algebraic structures based on categorical groups but with a group law that holds only up to isomorphism, prefigured much of the modern theory of 2-groups.
Later accomplishments
When she was promoted to full professor Hoàng became the first female full professor in Vietnam in any scientific or technical field. In 1988 she founded the first private university in Vietnam, in Hanoi, and became the president of its board of directors.
Recognition
In 2003 she was awarded France's Ordre des Palmes Académiques for her "contributions to boosting cooperation in culture and science between the two nations" of France and Vietnam.
References
1933 births
Living people
20th-century Vietnamese mathematicians
20th-century women mathematicians
Algebraic geometers
Academics from Hanoi
Paris Diderot University alumni
Academic staff of Hanoi National University of Education |
https://en.wikipedia.org/wiki/Diameter%20%28group%20theory%29 | In the area of abstract algebra known as group theory, the diameter of a finite group is a measure of its complexity.
Consider a finite group , and any set of generators . Define to be the graph diameter of the Cayley graph . Then the diameter of is the largest value of taken over all generating sets .
For instance, every finite cyclic group of order , the Cayley graph for a generating set with one generator is an -vertex cycle graph. The diameter of this graph, and of the group, is .
It is conjectured, for all non-abelian finite simple groups , that
Many partial results are known but the full conjecture remains open.
References
Finite groups
Measures of complexity |
https://en.wikipedia.org/wiki/1964%E2%80%9365%20Galatasaray%20S.K.%20season | The 1964–65 season was Galatasaray's 61st in existence and the 7th consecutive season in the 1. Lig. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
Players in / out
In
Out
1.Lig
Standings
Matches
Türkiye Kupası
Kick-off listed in local time (EET)
1/4 final
1/2 final
Final
European Cup
First round
Second round
Friendly Matches
TSYD Kupası
Ali Sami Yen - Şeref Bey Kupası
Atatürk Kupası
Attendances
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1964–65 season
1960s in Istanbul |
https://en.wikipedia.org/wiki/FIFA%20Beach%20Soccer%20World%20Cup%20records%20and%20statistics | This is a list of records and statistics of the FIFA Beach Soccer World Cup, including the Beach Soccer World Cup events held before FIFA sanctioning in 2005.
Debut of national teams
Overall team records (2005-present)
In this ranking 3 points are awarded for a win in normal time, 2 points for a win in extra time, 1 point is awarded for a win in penalty shoot-out and 0 for a loss. Teams are ranked by total points, then by goal difference, then by goals scored. Only the points from the 2005 tournament onward are counted.
Overall team records (total)
In this ranking 3 points are awarded for a win in normal time, 2 points for a win in extra time, 1 point is awarded for a win in penalty shoot-out and 0 for a loss. Teams are ranked by total points, then by goal difference, then by goals scored.
The following table shows the overall statistics of all 21 world cups, combining the results of both the Beach Soccer World Cup era and the FIFA Beach Soccer World Cup era.
Medal table
Comprehensive team results by tournament
Legend
— Champions
— Runners-up
— Third place
— Fourth place
QF — Quarterfinals (1999–2001, 2004–present)
R1 — Round 1
q — Qualified for upcoming tournament
— Qualified but withdrew (2005–)
— Did not participate (1995–2004), Did not qualify (2005–)
— Did not enter (2005–)
— Hosts
For each tournament, the number of teams in each finals tournament (in brackets) are shown.
Awards
The following documents the winners of the awards presented at the conclusion of the tournament. Eight awards are currently presented.
Golden Ball
The adidas Golden Ball award is awarded to the player who plays the most outstanding football during the tournament. It is selected by the media poll.
Golden Shoe
The adidas Golden Shoe is awarded to the top scorer of the tournament. If more than one player are equal by the same goals, the players will be selected based on the most assists during the tournament.
Golden Glove
The Golden Glove Award is awarded to the best goalkeeper of the tournament.
FIFA Fair Play Award
The FIFA Fair Play Award is given to the team who has the best fair play record during the tournament with the criteria set by FIFA Fair Play Committee.
Top goalscorers
From the data available the table below lists the all-time top 30 goalscorers, totalling goals scored by players across both world cup iterations.
See also
FIFA World Cup records and statistics
Notes
References
External links
at FIFA.com
FIFA Beach Soccer World Cup |
https://en.wikipedia.org/wiki/Princeton%20International%20School%20of%20Mathematics%20and%20Science | The Princeton International School of Mathematics and Science (PRISMS) is a coeducational, independent boarding and day school located in Princeton, New Jersey, United States that provides education to high school students in ninth through twelfth grades. It offers a rigorous academic program in mathematics, science, and engineering, as well as a range of humanities and language courses. The school aims to prepare students for careers in science, technology, engineering, and mathematics (STEM) fields. PRISMS places an emphasis on extracurricular activities, community service, and global citizenship.
The school also places a strong emphasis on developing students' critical thinking, problem-solving, and communication skills. The school's faculty comprises experienced educators and researchers who are committed to providing students with a challenging and supportive learning environment.
Admission to PRISMS is selective, and the school enrolls a diverse student body from around the world. The school has a strong record of preparing students for [colleges and universities in the US and internationally. As of the 2021–22 school year, the school had an enrollment of 118 students with 24 classroom teachers, which is a student–teacher ratio of 4.9:1.
It was founded in 2013 by Jiang Bairong. Plans were announced to expand the school to 300 students, with $20 million committed to startup costs.
The school has of land. The zoning from the American Boychoir School allowed for a maximum of 82 students, and nearby residents voiced opposition to the school's plans for expansion.
References
External links
Official website
Related information about the school
Boarding schools in New Jersey
Private high schools in Mercer County, New Jersey
Private middle schools in New Jersey
Schools in Princeton, New Jersey |
https://en.wikipedia.org/wiki/Jos%C3%A9%20Felipe%20Voloch | José Felipe Voloch (born 13 February 1963, in Rio de Janeiro) is a Brazilian mathematician who works on number theory and algebraic geometry and is a professor at Canterbury University.
Career
Voloch earned his Ph.D. from the University of Cambridge in 1985 under the supervision of John William Scott Cassels.
He was a professor at the University of Texas, Austin.
Awards
He is a member of the Brazilian Academy of Sciences.
Selected publications
References
External links
https://scholar.google.com/citations?user=r0Jun08AAAAJ
Brazilian mathematicians
1963 births
Living people
People from Rio de Janeiro (city)
Members of the Brazilian Academy of Sciences
Number theorists
Algebraic geometers
University of Texas at Austin faculty
Alumni of the University of Cambridge
Brazilian expatriate academics in the United States |
https://en.wikipedia.org/wiki/Integer%20complexity | In number theory, the integer complexity of an integer is the smallest number of ones that can be used to represent it using ones and any number of additions, multiplications, and parentheses. It is always within a constant factor of the logarithm of the given integer.
Example
For instance, the number 11 may be represented using eight ones:
11 = (1 + 1 + 1) × (1 + 1 + 1) + 1 + 1.
However, it has no representation using seven or fewer ones. Therefore, its complexity is eight.
The complexities of the numbers 1, 2, 3, ... are
1, 2, 3, 4, 5, 5, 6, 6, 6, 7, 8, 7, 8, 8, 8, 8, 9, 8, ...
The smallest numbers with complexity 1, 2, 3, ... are
1, 2, 3, 4, 5, 7, 10, 11, 17, 22, 23, 41, 47, ...
Upper and lower bounds
The question of expressing integers in this way was originally considered by . They asked for the largest number with a given complexity ; later, Selfridge showed that this number is
For example, when , and the largest integer that can be expressed using ten ones is . Its expression is
(1 + 1) × (1 + 1) × (1 + 1 + 1) × (1 + 1 + 1).
Thus, the complexity of an integer is at least . The complexity of is at most (approximately ): an expression of this length for can be found by applying Horner's method to the binary representation of . Almost all integers have a representation whose length is bounded by a logarithm with a smaller constant factor, .
Algorithms and counterexamples
The complexities of all integers up to some threshold can be calculated in total time .
Algorithms for computing the integer complexity have been used to disprove several conjectures about the complexity.
In particular, it is not necessarily the case that the optimal expression for a number is obtained either by subtracting one from or by expressing as the product of two smaller factors. The smallest example of a number whose optimal expression is not of this form is 353942783. It is a prime number, and therefore also disproves a conjecture of Richard K. Guy that the complexity of every prime number is one plus the complexity of . In fact, one can show that . Moreover, Venecia Wang gave some interesting examples, i.e. , , , but .
References
External links
Integer sequences |
https://en.wikipedia.org/wiki/N%20conjecture | In number theory the n conjecture is a conjecture stated by as a generalization of the abc conjecture to more than three integers.
Formulations
Given , let satisfy three conditions:
(i)
(ii)
(iii) no proper subsum of equals
First formulation
The n conjecture states that for every , there is a constant , depending on and , such that:
where denotes the radical of the integer , defined as the product of the distinct prime factors of .
Second formulation
Define the quality of as
The n conjecture states that .
Stronger form
proposed a stronger variant of the n conjecture, where setwise coprimeness of is replaced by pairwise coprimeness of .
There are two different formulations of this strong n conjecture.
Given , let satisfy three conditions:
(i) are pairwise coprime
(ii)
(iii) no proper subsum of equals
First formulation
The strong n conjecture states that for every , there is a constant , depending on and , such that:
Second formulation
Define the quality of as
The strong n conjecture states that .
References
Conjectures
Unsolved problems in number theory |
https://en.wikipedia.org/wiki/2003%E2%80%9304%20VfL%20Bochum%20season | The 2003–04 VfL Bochum season was the 66th season in club history.
Review and events
Matches
Legend
Bundesliga
DFB-Pokal
DFB-Ligapokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Winter
In:
Out:
VfL Bochum II
Sources
External links
2003–04 VfL Bochum season at Weltfussball.de
2003–04 VfL Bochum season at kicker.de
2003–04 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/Mathematical%20sculpture | A mathematical sculpture is a sculpture which uses mathematics as an essential conception. Helaman Ferguson, George W. Hart, Bathsheba Grossman, Peter Forakis and Jacobus Verhoeff are well-known mathematical sculptors.
References
Mathematics and art
Sculpture |
https://en.wikipedia.org/wiki/Anushka%20Ravishankar | Anushka Ravishankar is an author of children's books, and co-founder of Duckbill Books, a publishing house.
Early life
Ravishankar was born in Nashik, and graduated in mathematics from Fergusson College, Pune in 1981. While at college, she was influenced by the works of Lewis Carroll, Edward Lear and Edward Gorey. After completing her post-graduation in operations research, Ravishankar worked with an IT firm in Nashik for a while. She became a full-time writer after the birth of her daughter.
Children's literature
Ravishankar sent her first few stories to Tinkle, a comic book published by Amar Chitra Katha. When two of these stories won a contest organised by the magazine, the publisher of Tinkle offered her a job, but Ravishankar could only freelance for Tinkle as she was staying home to care for her young daughter. When her family moved to Chennai in 1996, she was hired to be an editor at Tara Books, a children's publishing house in the city. There she authored Tiger on a Tree, a book of nonsense verse that was translated to Japanese, Korean and French. While the book only sold about 2500 copies in India, it sold over 10000 copies in the United States and over 7000 copies in France. She also worked as Publishing Director at Scholastic India.
She founded the Duckbill Publishing House in 2012 with Sayoni Basu. In 2019 Penguin Random House India acquired all book publishing assets of the company.
She is sometimes called the Indian Dr. Seuss.
Writing style
While Ravishankar writes both picture books and chapter books, her specialty lies in writing nonsense verse for children. While her work does contain some nonsensical elements, it is not always pure nonsense. In her own words, "To Market! To Market! has a frame that is 'sensical', but the verse itself is quite nonsensical. I rely a lot on sound. Sometimes the sound takes you away from the meaning. Then, some of my books are really nonsense. Excuse Me, Is This India? is nonsense in the Carrollian sense."
A few of her books, like Catch that Crocodile!, Elephants Never Forget and Tiger on a Tree, were inspired by real-life events.
Ravishankar is also known to rewrite her verse on some occasions, after the illustrations are complete. She collaborates with artists from South Africa, Switzerland, Italy and India. While some of her books have an Indian flavour, most have a cross-cultural appeal.
References
Indian women children's writers
Year of birth missing (living people)
Living people
Indian children's writers
English-language writers from India
Women writers from Maharashtra |
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