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https://en.wikipedia.org/wiki/Yuki%20Igari | is a former Japanese football player.
Club statistics
References
External links
1988 births
Living people
Association football people from Kanagawa Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Shonan Bellmare players
SP Kyoto FC players
Fukushima United FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Tsuyoshi%20Shimamura | is a former Japanese footballer.
Career
After a long career with Shonan Bellmare, he announced his retirement in December 2018.
Career statistics
Updated to 23 February 2019.
References
External links
Profile at Shonan Bellmare
1985 births
Living people
Waseda University alumni
Association football people from Saitama Prefecture
Japanese men's footballers
J1 League players
J2 League players
Shonan Bellmare players
Tokushima Vortis players
Men's association football defenders |
https://en.wikipedia.org/wiki/Moti%20Gitik | Moti Gitik () is a mathematician, working in set theory, who is professor at the Tel-Aviv University. He was an invited speaker at the 2002 International Congresses of Mathematicians, and became a fellow of the American Mathematical Society in 2012.
Research
Gitik proved the consistency of "all uncountable cardinals are singular" (a strong negation of the axiom of choice) from the consistency of "there is a proper class of strongly compact cardinals". He further proved the equiconsistency of the following statements:
There is a cardinal κ with Mitchell order κ++.
There is a measurable cardinal κ with 2κ > κ+.
There is a strong limit singular cardinal λ with 2λ > λ+.
The GCH holds below ℵω, and 2ℵω=ℵω+2.
Gitik discovered several methods for building models of ZFC with complicated Cardinal Arithmetic structure. His main results deal with consistency and equi-consistency of non-trivial patterns of the Power Function over singular cardinals.
Selected publications
See also
References
Living people
Academic staff of Tel Aviv University
Fellows of the American Mathematical Society
20th-century Israeli mathematicians
21st-century Israeli mathematicians
Set theorists
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Purity%20%28algebraic%20geometry%29 | In the mathematical field of algebraic geometry, purity is a theme covering a number of results and conjectures, which collectively address the question of proving that "when something happens, it happens in a particular codimension".
Purity of the branch locus
For example, ramification is a phenomenon of codimension 1 (in the geometry of complex manifolds, reflecting as for Riemann surfaces that ramify at single points that it happens in real codimension two). A classical result, Zariski–Nagata purity of Masayoshi Nagata and Oscar Zariski, called also purity of the branch locus, proves that on a non-singular algebraic variety a branch locus, namely the set of points at which a morphism ramifies, must be made up purely of codimension 1 subvarieties (a Weil divisor). There have been numerous extensions of this result into theorems of commutative algebra and scheme theory, establishing purity of the branch locus in the sense of description of the restrictions on the possible "open subsets of failure" to be an étale morphism.
Cohomological purity
There is also a homological notion of purity that is related, namely a collection of results stating that cohomology groups from a particular theory are trivial with the possible exception of one index i. Such results were established in étale cohomology by Michael Artin (included in SGA 4), and were foundational in setting up the theory to contain expected analogues of results from singular cohomology. A general statement of Alexander Grothendieck known as the absolute cohomological purity conjecture was proved by Ofer Gabber. It concerns a closed immersion of schemes (regular, noetherian) that is purely of codimension d, and the relative local cohomology in the étale theory. With coefficients mod n where n is invertible, the cohomology should occur only with index 2d (and take on a predicted value).
Notes
Algebraic geometry |
https://en.wikipedia.org/wiki/Clark%20Kimberling | Clark Kimberling (born November 7, 1942 in Hinsdale, Illinois) is a mathematician, musician, and composer. He has been a mathematics professor since 1970 at the University of Evansville. His research interests include triangle centers, integer sequences, and hymnology.
Kimberling received his PhD in mathematics in 1970 from the Illinois Institute of Technology, under the supervision of Abe Sklar. Since at least 1994, he has maintained a list of triangle centers and their properties. In its current on-line form, the Encyclopedia of Triangle Centers, this list comprises tens of thousands of entries.
He has contributed to The Hymn, the journal of the Hymn Society in the United States and Canada; and in the Canterbury Dictionary of Hymnology.
Kimberling's golden triangle
Robert C. Schoen has defined a "golden triangle" as a triangle with two of its sides in the golden ratio. Kimberling has proposed that Schoen's definition of golden triangle be extended to include triangles which have angles that are in the golden ratio. Kimberling has described a "doubly golden triangle" which has two sides that are in golden ratio and which also has two angles that are in golden ratio.
References
External links
Kimberling's home page at UE
Encyclopedia of Triangle Centers
Living people
1942 births
20th-century American mathematicians
21st-century American mathematicians
Geometers
Hymnologists
Illinois Institute of Technology alumni
Number theorists
Musicians from Evansville, Indiana
People from Hinsdale, Illinois
American recorder players
University of Evansville faculty
Mathematicians from Illinois |
https://en.wikipedia.org/wiki/Jacobian%20curve | In mathematics, the Jacobi curve is a representation of an elliptic curve different from the usual one defined by the Weierstrass equation. Sometimes it is used in cryptography instead of the Weierstrass form because it can provide a defence against simple and differential power analysis style (SPA) attacks; it is possible, indeed, to use the general addition formula also for doubling a point on an elliptic curve of this form: in this way the two operations become indistinguishable from some side-channel information. The Jacobi curve also offers faster arithmetic compared to the Weierstrass curve.
The Jacobi curve can be of two types: the Jacobi intersection, that is given by an intersection of two surfaces, and the Jacobi quartic.
Elliptic Curves: Basics
Given an elliptic curve, it is possible to do some "operations" between its points: for example one can add two points P and Q obtaining the point P + Q that belongs to the curve ; given a point P on the elliptic curve, it is possible to "double" P, that means find [2]P = P + P (the square brackets are used to indicate [n]P, the point P added n times), and also find the negation of P, that means find –P. In this way, the points of an elliptic curve forms a group. Note that the identity element of the group operation is not a point on the affine plane, it only appears in the projective coordinates: then O = (0: 1: 0) is the "point at infinity", that is the neutral element in the group law. Adding and doubling formulas are useful also to compute [n]P, the n-th multiple of a point P on an elliptic curve: this operation is considered the most in elliptic curve cryptography.
An elliptic curve E, over a field K can be put in the Weierstrass form y2 = x3 + ax + b, with a, b in K. What will be of importance later are point of order 2, that is P on E such that [2]P = O and P ≠ O. If P = (p, 0) is a point on E, then it has order 2; more generally the points of order 2 correspond to the roots of the polynomial f(x) = x3 + ax + b.
From now on, we will use Ea,b to denote the elliptic curve with Weierstrass form y2 = x3 + ax + b.
If Ea,b is such that the cubic polynomial x3 + ax + b has three distinct roots in K and b = 0 we can write Ea,b in the Legendre normal form:
Ea,b: y2 = x(x + 1)(x + j)
In this case we have three points of order two: (0, 0), (–1, 0), (–j, 0). In this case we use the notation E[j]. Note that j can be expressed in terms of a, b.
Definition: Jacobi intersection
An elliptic curve in P3(K) can be represented as the intersection of two quadric surfaces:
It is possible to define the Jacobi form of an elliptic curve as the intersection of two quadrics. Let Ea,b be an elliptic curve in the Weierstrass form, we apply the following map to it:
We see that the following system of equations holds:
The curve E[j] corresponds to the following intersection of surfaces in P3(K):
.
The "special case", E[0], the elliptic curve has a double point and thus it is singular.
S1 is obtained b |
https://en.wikipedia.org/wiki/List%20of%20Thor%20and%20Delta%20launches%20%281980%E2%80%931989%29 | Between 1980 and 1989, there were 58 Thor missiles launched, of which 56 were successful, giving a 96.6% success rate.
Launch statistics
Rocket configurations
Launch sites
Launch outcomes
1980
There were 5 Thor missiles launched in 1980. 4 of the 5 launches were successful, giving an 80% success rate.
1981
There were 7 Thor missiles launched in 1981. All 7 launches were successful.
1982
There were 8 Thor missiles launched in 1982. All 8 launches were successful.
1983
There were 10 Thor missiles launched in 1983. All 10 launches were successful.
1984
There were 6 Thor missiles launched in 1984. All 6 launches were successful.
1986
There were 4 Thor missiles launched in 1986. 3 of the 4 launches were successful, giving a 75% success rate.
1987
There were 4 Thor missiles launched in 1987. All 4 launches were successful.
1988
There were 3 Thor missiles launched in 1988. All 3 launches were successful.
1989
There were 9 Thor missiles launched in 1989. All 9 launches were successful.
References
Lists of Thor and Delta launches
Lists of Thor launches
Lists of Delta launches |
https://en.wikipedia.org/wiki/Seven-dimensional%20space | In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space. When n = 7, the set of all such locations is called 7-dimensional space. Often such a space is studied as a vector space, without any notion of distance. Seven-dimensional Euclidean space is seven-dimensional space equipped with a Euclidean metric, which is defined by the dot product.
More generally, the term may refer to a seven-dimensional vector space over any field, such as a seven-dimensional complex vector space, which has 14 real dimensions. It may also refer to a seven-dimensional manifold such as a 7-sphere, or a variety of other geometric constructions.
Seven-dimensional spaces have a number of special properties, many of them related to the octonions. An especially distinctive property is that a cross product can be defined only in three or seven dimensions. This is related to Hurwitz's theorem, which prohibits the existence of algebraic structures like the quaternions and octonions in dimensions other than 2, 4, and 8. The first exotic spheres ever discovered were seven-dimensional.
Geometry
7-polytope
A polytope in seven dimensions is called a 7-polytope. The most studied are the regular polytopes, of which there are only three in seven dimensions: the 7-simplex, 7-cube, and 7-orthoplex. A wider family are the uniform 7-polytopes, constructed from fundamental symmetry domains of reflection, each domain defined by a Coxeter group. Each uniform polytope is defined by a ringed Coxeter-Dynkin diagram. The 7-demicube is a unique polytope from the D7 family, and 321, 231, and 132 polytopes from the E7 family.
6-sphere
The 6-sphere or hypersphere in seven-dimensional Euclidean space is the six-dimensional surface equidistant from a point, e.g. the origin. It has symbol , with formal definition for the 6-sphere with radius r of
The volume of the space bounded by this 6-sphere is
which is 4.72477 × r7, or 0.0369 of the 7-cube that contains the 6-sphere
Applications
Cross product
A cross product, that is a vector-valued, bilinear, anticommutative and orthogonal product of two vectors, is defined in seven dimensions. Along with the more usual cross product in three dimensions it is the only such product, except for trivial products.
Exotic spheres
In 1956, John Milnor constructed an exotic sphere in 7 dimensions and showed that there are at least 7 differentiable structures on the 7-sphere. In 1963 he showed that the exact number of such structures is 28.
See also
Euclidean geometry
List of geometry topics
List of regular polytopes
References
H.S.M. Coxeter: Regular Polytopes. Dover, 1973
J.W. Milnor: On manifolds homeomorphic to the 7-sphere. Annals of Mathematics 64, 1956
External links
Dimension
Multi-dimensional geometry
7 (number) |
https://en.wikipedia.org/wiki/Nash%20blowing-up | In algebraic geometry, Nash blowing-up is a process in which, roughly speaking, each singular point is replaced by all limiting positions of the tangent spaces at the non-singular points. More formally, let be an algebraic variety of pure dimension r embedded in a smooth variety of dimension n, and let be the complement of the singular locus of . Define a map , where is the Grassmannian of r-planes in the tangent bundle of , by , where is the tangent space of at . The closure of the image of this map together with the projection to is called the Nash blow-up of .
Although the above construction uses an embedding, the Nash blow-up itself is unique up to unique isomorphism.
Properties
Nash blowing-up is locally a monoidal transformation.
If X is a complete intersection defined by the vanishing of then the Nash blow-up is the blow-up with center given by the ideal generated by the (n − r)-minors of the matrix with entries .
For a variety over a field of characteristic zero, the Nash blow-up is an isomorphism if and only if X is non-singular.
For an algebraic curve over an algebraically closed field of characteristic zero, repeated Nash blowing-up leads to desingularization after a finite number of steps.
Both of the prior properties may fail in positive characteristic. For example, in characteristic q > 0, the curve has a Nash blow-up which is the monoidal transformation with center given by the ideal , for q = 2, or , for . Since the center is a hypersurface the blow-up is an isomorphism.
See also
Blowing up
Resolution of singularities
References
Algebraic geometry |
https://en.wikipedia.org/wiki/History%20of%20probability | Probability has a dual aspect: on the one hand the likelihood of hypotheses given the evidence for them, and on the other hand the behavior of stochastic processes such as the throwing of dice or coins. The study of the former is historically older in, for example, the law of evidence, while the mathematical treatment of dice began with the work of Cardano, Pascal, Fermat and Christiaan Huygens between the 16th and 17th century.
Probability deals with random experiments with a known distribution, Statistics deals wirh inference from the data about the unknown distribution.
Etymology
Probable and probability and their cognates in other modern languages derive from medieval learned Latin probabilis, deriving from Cicero and generally applied to an opinion to mean plausible or generally approved. The form probability is from Old French (14 c.) and directly from Latin (nominative ) "credibility, probability," from (see probable).
The mathematical sense of the term is from 1718. In the 18th century, the term chance was also used in the mathematical sense of "probability" (and probability theory was called Doctrine of Chances). This word is ultimately from Latin cadentia, i.e. "a fall, case".
The English adjective likely is of Germanic origin, most likely from Old Norse (Old English had with the same sense), originally meaning "having the appearance of being strong or able" "having the similar appearance or qualities", with a meaning of "probably" recorded mid-15c. The derived noun likelihood had a meaning of "similarity, resemblance" but took on a meaning of "probability" from the mid 15th century. The meaning "something likely to be true" is from 1570s.
Origins
Ancient and medieval law of evidence developed a grading of degrees of proof, credibility, presumptions and half-proof to deal with the uncertainties of evidence in court.
In Renaissance times, betting was discussed in terms of odds such as "ten to one" and maritime insurance premiums were estimated based on intuitive risks, but there was no theory on how to calculate such odds or premiums.
The mathematical methods of probability arose in the investigations first of Gerolamo Cardano in the 1560s (not published until 100 years later), and then in the correspondence Pierre de Fermat and Blaise Pascal (1654) on such questions as the fair division of the stake in an interrupted game of chance. Christiaan Huygens (1657) gave a comprehensive treatment of the subject.
From Games, Gods and Gambling by F. N. David:
In ancient times there were games played using astragali, or Talus bone. The Pottery of ancient Greece was evidence to show that there was a circle drawn on the floor and the astragali were tossed into this circle, much like playing marbles. In Egypt, excavators of tombs found a game they called "Hounds and Jackals", which closely resembles the modern game "Snakes and Ladders". It seems that this is the early stages of the creation of dice.
The first dice game mentioned in |
https://en.wikipedia.org/wiki/Eight-dimensional%20space | In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space. When n = 8, the set of all such locations is called 8-dimensional space. Often such spaces are studied as vector spaces, without any notion of distance. Eight-dimensional Euclidean space is eight-dimensional space equipped with the Euclidean metric.
More generally the term may refer to an eight-dimensional vector space over any field, such as an eight-dimensional complex vector space, which has 16 real dimensions. It may also refer to an eight-dimensional manifold such as an 8-sphere, or a variety of other geometric constructions.
Geometry
8-polytope
A polytope in eight dimensions is called an 8-polytope. The most studied are the regular polytopes, of which there are only three in eight dimensions: the 8-simplex, 8-cube, and 8-orthoplex. A broader family are the uniform 8-polytopes, constructed from fundamental symmetry domains of reflection, each domain defined by a Coxeter group. Each uniform polytope is defined by a ringed Coxeter-Dynkin diagram. The 8-demicube is a unique polytope from the D8 family, and 421, 241, and 142 polytopes from the E8 family.
7-sphere
The 7-sphere or hypersphere in eight dimensions is the seven-dimensional surface equidistant from a point, e.g. the origin. It has symbol , with formal definition for the 7-sphere with radius r of
The volume of the space bounded by this 7-sphere is
which is 4.05871 × r8, or 0.01585 of the 8-cube that contains the 7-sphere.
Kissing number problem
The kissing number problem has been solved in eight dimensions, thanks to the existence of the 421 polytope and its associated lattice. The kissing number in eight dimensions is 240.
Octonions
The octonions are a normed division algebra over the real numbers, the largest such algebra. Mathematically they can be specified by 8-tuplets of real numbers, so form an 8-dimensional vector space over the reals, with addition of vectors being the addition in the algebra. A normed algebra is one with a product that satisfies
for all x and y in the algebra. A normed division algebra additionally must be finite-dimensional, and have the property that every non-zero vector has a unique multiplicative inverse. Hurwitz's theorem prohibits such a structure from existing in dimensions other than 1, 2, 4, or 8.
Biquaternions
The complexified quaternions , or "biquaternions," are an eight-dimensional algebra dating to William Rowan Hamilton's work in the 1850s. This algebra is equivalent (that is, isomorphic) to the Clifford algebra and the Pauli algebra. It has also been proposed as a practical or pedagogical tool for doing calculations in special relativity, and in that context goes by the name Algebra of physical space (not to be confused with the Spacetime algebra, which is 16-dimensional.)
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edit |
https://en.wikipedia.org/wiki/Joseph%20Pereira | Joseph Pereira (born 27 June) is an Indian football player who plays for Sporting Clube de Goa as a forward.
Career statistics
Club
Statistics accurate as of 11 May 2013
External links
http://goal.com/en-india/people/india/25976/joseph-pereira
1982 births
Living people
Indian men's footballers
I-League players
Footballers from Goa
Sporting Clube de Goa players
Men's association football forwards |
https://en.wikipedia.org/wiki/Chopinzinho | Chopinzinho is a municipality in the state of Paraná in the Southern Region of Brazil. According to the 2020 population estimate taken by the Brazilian Institute of Geography and Statistics the municipality has a population of 19,167 inhabitants and an area of .
Notable people
Elize Matsunaga—murderer. Subject of the Netflix documentary Elize Matsunaga: Once Upon a Crime.
See also
List of municipalities in Paraná
References
Municipalities in Paraná |
https://en.wikipedia.org/wiki/Oliver%20Fink | Oliver Fink (; born 6 June 1982) is German former footballer.
Personal life
He is the older brother of fellow footballer Tobias Fink.
Career statistics
1.Includes Promotion playoff.
References
External links
Living people
1982 births
German men's footballers
Men's association football midfielders
Fortuna Düsseldorf players
SSV Jahn Regensburg players
SSV Jahn Regensburg II players
SV Wacker Burghausen players
SpVgg Unterhaching players
Fortuna Düsseldorf II players
Bundesliga players
2. Bundesliga players
3. Liga players
Regionalliga players
Footballers from the Upper Palatinate
People from Amberg-Sulzbach |
https://en.wikipedia.org/wiki/Poincar%C3%A9%E2%80%93Steklov%20operator | In mathematics, a Poincaré–Steklov operator (after Henri Poincaré and Vladimir Steklov) maps the values of one boundary condition of the solution of an elliptic partial differential equation in a domain to the values of another boundary condition. Usually, either of the boundary conditions determines the solution. Thus, a Poincaré–Steklov operator encapsulates the boundary response of the system modelled by the partial differential equation. When the partial differential equation is discretized, for example by finite elements or finite differences, the discretization of the Poincaré–Steklov operator is the Schur complement obtained by eliminating all degrees of freedom inside the domain.
Note that there may be many suitable different boundary conditions for a given partial differential equation and the direction in which a Poincaré–Steklov operator maps the values of one into another is given only by a convention.
Dirichlet-to-Neumann operator on a bounded domain
Consider a steady-state distribution of temperature in a body for given temperature values on the body surface. Then the resulting heat flux through the boundary (that is, the heat flux that would be required to maintain the
given surface temperature) is determined uniquely. The mapping of the surface temperature to the surface heat flux is a Poincaré–Steklov operator. This particular Poincaré–Steklov operator is called the Dirichlet to Neumann (DtN) operator. The values of the temperature on the surface is the Dirichlet boundary condition of the Laplace equation, which describes the distribution of the temperature inside the body. The heat flux through the surface is the Neumann boundary condition (proportional to the normal derivative of the temperature).
Mathematically, for a function harmonic in a domain , the Dirichlet-to-Neumann operator maps the values of on the boundary of to the normal derivative on the boundary of . This Poincaré–Steklov operator is at the foundation of iterative substructuring.
Calderón's inverse boundary problem is the problem of finding the coefficient of a divergence form elliptic partial differential equation from its Dirichlet-to-Neumann operator. This is the mathematical formulation of electrical impedance tomography.
Dirichlet-to-Neumann operator for a boundary condition at infinity
The solution of partial differential equation in an external domain gives rise to a Poincaré–Steklov operator that brings the boundary condition from infinity to the boundary. One example is the Dirichlet-to-Neumann operator that maps the given temperature on the boundary of a cavity in infinite medium with zero temperature at infinity to the heat flux on the cavity boundary. Similarly, one can define the Dirichlet-to-Neumann operator on the boundary of a sphere for the solution for the Helmholtz equation in the exterior of the sphere. Approximations of this operator are at the foundation of a class of method for the modeling of acoustic scattering in infinite m |
https://en.wikipedia.org/wiki/Masato%20Fujita | is a Japanese football player who has played for the J2 League team Ventforet Kofu.
Career statistics
Updated to 24 February 2019.
References
External links
Profile at Sagan Tosu
1986 births
Living people
Meiji University alumni
Association football people from Ōita Prefecture
Japanese men's footballers
J1 League players
J2 League players
Tokyo Verdy players
Yokohama F. Marinos players
Yokohama FC players
Kashiwa Reysol players
Sagan Tosu players
Ventforet Kofu players
Men's association football defenders
Sportspeople from Ōita (city) |
https://en.wikipedia.org/wiki/List%20of%20South%20African%20airports%20by%20passenger%20movements | The following is a list of South African airports by passenger movements.
Statistics
All information below is sourced from the annual statistics published by the Airports Company South Africa. Figures are between 1 April and 31 March the following year. Airports not controlled by the Airports Company South Africa do not generally publish or are delayed when updating their passenger statistics. Airports without official statistics have been displayed as current seat capacity on regularly scheduled flights. These seats, although not always full, give an accurate number of passengers expected.
2022/2023 statistics
Historical
At a glance
2020–2022 COVID-19
During the lockdowns for the COVID-19 pandemic, most commercial flights were halted at first.
2012–13
2011–12
2010–11
2009–10
2007–08
2006–07
2005–06
2004–05
See also
List of airports in South Africa
References
External links
Airports Company of South Africa
airports by passenger movements
List, passenger movements
So |
https://en.wikipedia.org/wiki/Lisp%20Algebraic%20Manipulator | The Lisp Algebraic Manipulator (also known as LAM) was created by Ray d'Inverno, who had written Atlas LISP Algebraic Manipulation (ALAM was designed in 1970). LAM later became the basis for the interactive computer package SHEEP.
Notes
Computer algebra systems
Tensors |
https://en.wikipedia.org/wiki/MacMahon%27s%20master%20theorem | In mathematics, MacMahon's master theorem (MMT) is a result in enumerative combinatorics and linear algebra. It was discovered by Percy MacMahon and proved in his monograph Combinatory analysis (1916). It is often used to derive binomial identities, most notably Dixon's identity.
Background
In the monograph, MacMahon found so many applications of his result, he called it "a master theorem in the Theory of Permutations." He explained the title as follows: "a Master Theorem from the masterly and rapid fashion in which it deals with various questions otherwise troublesome to solve."
The result was re-derived (with attribution) a number of times, most notably by I. J. Good who derived it from his multilinear generalization of the Lagrange inversion theorem. MMT was also popularized by Carlitz who found an exponential power series version. In 1962, Good found a short proof of Dixon's identity from MMT. In 1969, Cartier and Foata found a new proof of MMT by combining algebraic and bijective ideas (built on Foata's thesis) and further applications to combinatorics on words, introducing the concept of traces. Since then, MMT has become a standard tool in enumerative combinatorics.
Although various q-Dixon identities have been known for decades, except for a Krattenthaler–Schlosser extension (1999), the proper q-analog of MMT remained elusive. After Garoufalidis–Lê–Zeilberger's quantum extension (2006), a number of noncommutative extensions were developed by Foata–Han, Konvalinka–Pak, and Etingof–Pak. Further connections to Koszul algebra and quasideterminants were also found by Hai–Lorentz, Hai–Kriegk–Lorenz, Konvalinka–Pak, and others.
Finally, according to J. D. Louck, the theoretical physicist Julian Schwinger re-discovered the MMT in the context of his generating function approach to the angular momentum theory of many-particle systems. Louck writes:
Precise statement
Let be a complex matrix, and let be formal variables. Consider a coefficient
(Here the notation means "the coefficient of monomial in ".) Let be another set of formal variables, and let be a diagonal matrix. Then
where the sum runs over all nonnegative integer vectors ,
and denotes the identity matrix of size .
Derivation of Dixon's identity
Consider a matrix
Compute the coefficients G(2n, 2n, 2n) directly from the definition:
where the last equality follows from the fact that on the right-hand side we have the product of the following coefficients:
which are computed from the binomial theorem. On the other hand, we can compute the determinant explicitly:
Therefore, by the MMT, we have a new formula for the same coefficients:
where the last equality follows from the fact that we need to use an equal number of times all three terms in the power. Now equating the two formulas for coefficients G(2n, 2n, 2n) we obtain an equivalent version of Dixon's identity:
See also
Permanent
References
P.A. MacMahon, Combinatory analysis, vols 1 and 2, Camb |
https://en.wikipedia.org/wiki/Simons%20Center%20for%20Geometry%20and%20Physics | The Simons Center for Geometry and Physics is a center for theoretical physics and mathematics at Stony Brook University in New York. The focus of the center is mathematical physics and the interface of geometry and physics. It was founded in 2007 by a gift from the James and Marilyn Simons Foundation. The center's current director is physicist Luis Álvarez-Gaumé.
History
Background
James H. Simons was the chair of the mathematics department at Stony Brook from 1968 to 1976. After deciding to leave academia, he then went on to make billions with his investment firm Renaissance Technologies. On February 27, 2008 he announced a donation totaling $60 million (including a $25 million gift two years prior) to the mathematics and physics departments. This was the largest single gift ever given to any of the SUNY schools. The gift came during Stony Brook's 50th anniversary and shortly after Gov. Spitzer announced his commitment to make Stony Brook a “flagship” of the SUNY system that would rival the nation’s most prestigious state research universities. During his announcement speech, Jim Simons said, "From Archimedes to Newton to Einstein, much of the most profound work in physics has been deeply intertwined with the geometric side of mathematics. Since then, in particular with the advent of such areas as quantum field theory and string theory, developments in geometry and physics have become if anything more interrelated. The new Center will give many of the world's best mathematicians and physicists the opportunity to work and interact in an environment and an architecture carefully designed to enhance progress. We believe there is a chance that work accomplished at the Center will significantly change and deepen our understanding of the physical universe and of its basic mathematical structure." The Center results from extensive thought and planning between faculty, department chairs, and others, including Cumrun Vafa of Harvard, who directs the Simons Foundation-supported summer institutes on string theory at Stony Brook, and Isadore Singer of MIT.
Establishment
John Morgan served as the founding director from 2009 to 2016. Luis Álvarez-Gaumé has been the director since 2016.
Building
The Simons Center's building was completed in September 2010. The building is adjacent to the physics and mathematics departments to allow for close collaboration with the mathematics department and the C. N. Yang Institute for Theoretical Physics. The building offers of floor space, spread over six stories, and includes a 236-seat auditorium, a 90-seat lecture hall, offices, seminar rooms, and a cafe. The building is LEED Gold certified and is connected to the Math Tower via an elevated walkway.
Faculty
The Center's permanent faculty currently consists of mathematicians Simon Donaldson, Kenji Fukaya, and John Pardon, and physicists Nikita Nekrasov and Zohar Komargodski. The Center's academic staff also includes roughly 10 research assistant professors and 20 |
https://en.wikipedia.org/wiki/Campo%20Redondo | Campo Redondo is a municipality in the state of Rio Grande do Norte in the Northeast region of Brazil. According to the census conducted by the IBGE (Brazilian Institute of Geography and Statistics) in the year 2010, its population is 10 427 inhabitants. In 2022, the same body carried out the demographic census of 2022 and released the previous results of the Census. According to IBGE, Campo Redondo had a population deficit, with 210 fewer inhabitants compared to the 2010 Census. The territorial extension of the municipality is 213 km².
Campo Redondo is bordered by the municipalities of São Tomé and Lajes Pintadas (north), Currais Novos (west), Santa Cruz (east) and Coronel Ezequiel (south). It is also bordered by the state of Paraíba (southwest).
See also
List of municipalities in Rio Grande do Norte
References
Municipalities in Rio Grande do Norte |
https://en.wikipedia.org/wiki/Twists%20of%20elliptic%20curves | In the mathematical field of algebraic geometry, an elliptic curve E over a field K has an associated quadratic twist, that is another elliptic curve which is isomorphic to E over an algebraic closure of K. In particular, an isomorphism between elliptic curves is an isogeny of degree 1, that is an invertible isogeny. Some curves have higher order twists such as cubic and quartic twists. The curve and its twists have the same j-invariant.
Applications of twists include cryptography, the solution of Diophantine equations, and when generalized to hyperelliptic curves, the study of the Sato–Tate conjecture.
Quadratic twist
First assume is a field of characteristic different from 2. Let be an elliptic curve over of the form:
Given not a square in , the quadratic twist of is the curve , defined by the equation:
or equivalently
The two elliptic curves and are not isomorphic over , but rather over the field extension . Qualitatively speaking, the arithmetic of a curve and its quadratic twist can look very different in the field , while the complex analysis of the curves is the same; and so a family of curves related by twisting becomes a useful setting in which to study the arithmetic properties of elliptic curves.
Twists can also be defined when the base field is of characteristic 2. Let be an elliptic curve over of the form:
Given such that is an irreducible polynomial over , the quadratic twist of is the curve , defined by the equation:
The two elliptic curves and are not isomorphic over , but over the field extension .
Quadratic twist over finite fields
If is a finite field with elements, then for all there exist a such that the point belongs to either or . In fact, if is on just one of the curves, there is exactly one other on that same curve (which can happen if the characteristic is not ).
As a consequence, or equivalently , where is the trace of the Frobenius endomorphism of the curve.
Quartic twist
It is possible to "twist" elliptic curves with j-invariant equal to 1728 by quartic characters; twisting a curve by a quartic twist, one obtains precisely four curves: one is isomorphic to , one is its quadratic twist, and only the other two are really new. Also in this case, twisted curves are isomorphic over the field extension given by the twist degree.
Cubic twist
Analogously to the quartic twist case, an elliptic curve over with j-invariant equal to zero can be twisted by cubic characters. The curves obtained are isomorphic to the starting curve over the field extension given by the twist degree.
Generalization
Twists can be defined for other smooth projective curves as well. Let be a field and be curve over that field, i.e., a projective variety of dimension 1 over that is irreducible and geometrically connected. Then a twist of is another smooth projective curve for which there exists a -isomorphism between and , where the field is the algebraic closure of .
Examples
Twisted |
https://en.wikipedia.org/wiki/Focaloid | In geometry, a focaloid is a shell bounded by two concentric, confocal ellipses (in 2D) or ellipsoids (in 3D). When the thickness of the shell becomes negligible, it is called a thin focaloid.
Mathematical definition (3D)
If one boundary surface is given by
with semiaxes a, b, c the second surface is given by
The thin focaloid is then given by the limit .
In general, a focaloid could be understood as a shell consisting out of two closed coordinate surfaces of a confocal ellipsoidal coordinate system.
Confocal
Confocal ellipsoids share the same foci, which are given for the example above by
Physical significance
A focaloid can be used as a construction element of a matter or charge distribution. The particular importance of focaloids lies in the fact that two different but confocal focaloids of the same mass or charge produce the same action on a test mass or charge in the exterior region.
See also
Homoeoid
Confocal conic sections
References
Subrahmanyan Chandrasekhar (1969): Ellipsoidal Figures of Equilibrium. Yale University Press, London, Connecticut
Routh, E. J.: A Treatise on Analytical Statics, Vol II, Cambridge University Press, Cambridge (1882).
External links
Surfaces
Potential theory |
https://en.wikipedia.org/wiki/J%C3%A1n%20Taba%C4%8Dek | Ján Tabaček (born 7 April 1980 in Martin) is a Slovak ice hockey player who is currently playing for HK Martin in the Slovak 1. Liga.
Career statistics
External links
1980 births
Living people
Slovak ice hockey defencemen
Cincinnati Mighty Ducks players
Dayton Bombers players
GCK Lions players
HC Slovan Bratislava players
HC Sparta Praha players
HC Košice players
Lempäälän Kisa players
MHC Martin players
MHk 32 Liptovský Mikuláš players
Anaheim Ducks draft picks
Ice hockey people from Martin, Slovakia
Tappara players
ZSC Lions players
Slovak expatriate ice hockey players in the United States
Slovak expatriate ice hockey players in the Czech Republic
Slovak expatriate ice hockey players in Finland
Slovak expatriate ice hockey players in Switzerland |
https://en.wikipedia.org/wiki/Tengenjutsu | Tengenjutsu may refer to:
Tian yuan shu, in Japanese tengenjutsu (), a method of algebra in Chinese and Japanese mathematics
Tengenjutsu (fortune telling) (), a Japanese fortune telling method |
https://en.wikipedia.org/wiki/One-dimensional%20space | In physics and mathematics, a sequence of n numbers can specify a location in n-dimensional space. When , the set of all such locations is called a one-dimensional space. An example of a one-dimensional space is the number line, where the position of each point on it can be described by a single number.
In algebraic geometry there are several structures that are technically one-dimensional spaces but referred to in other terms. A field k is a one-dimensional vector space over itself. Similarly, the projective line over k is a one-dimensional space. In particular, if , the complex numbers, then the complex projective line is one-dimensional with respect to , even though it is also known as the Riemann sphere.
More generally, a ring is a length-one module over itself. Similarly, the projective line over a ring is a one-dimensional space over the ring. In case the ring is an algebra over a field, these spaces are one-dimensional with respect to the algebra, even if the algebra is of higher dimensionality.
Hypersphere
The hypersphere in 1 dimension is a pair of points, sometimes called a 0-sphere as its surface is zero-dimensional. Its length is
where is the radius.
Coordinate systems in one-dimensional space
One dimensional coordinate systems include the number line.
See also
Univariate
References
Dimension
1 (number) |
https://en.wikipedia.org/wiki/Suresh%20Venapally | Suresh Venepally (; born 1966) is an Indian mathematician known for his research work in algebra. He is a professor at Emory University.
Background
Suresh was born in Vangoor, Telangana, India and studied in ZPHS at Vangoor up to 9th standard. He did his M.Sc at University of Hyderabad.
He joined Tata Institute of Fundamental Research (TIFR) in 1989 and got his PhD in under the guidance of Raman Parimala (1994). He later joined the faculty at University of Hyderabad.
Honors
Shanti Swarup Bhatnagar Award for Mathematical Sciences in 2009
Invited speaker at the International Congress of Mathematicians held at Hyderabad, India in 2010
Fellow of the Indian Academy of Sciences
Andhra Pradesh Scientist Award, 2008
B. M. Birla Science prize, 2004
INSA Medal for Young Scientists, 1997
Selected publications
1995: "Zero-cycles on quadric fibrations: finiteness theorems and the cycle map", Invent. Math. 122, 83–117 (with Raman Parimala)
1998: "Isotropy of quadratic forms over function fields in one variable over p-adic fields", Publ. de I.H.E.S. 88, 129–150 (with Raman Parimala)
2001: Hermitian analogue of a theorem of Springer", J.Alg. 243(2), 780-789 (with Raman Parimala and Ramaiyengar Sridharan)
2010: "Bounding the symbol length in the Galois cohomology of function field of p-adic curves", Comment. Math. Helv. 85(2), 337–346 , "The u-invariant of the function fields of p-adic curves" Ann. Math. 172(2), 1391-1405 (with Raman Parimala)
References
External links
Emory University faculty web page
University of Hyderabad faculty web page
20th-century Indian mathematicians
Algebraists
Living people
Emory University faculty
1966 births
Tata Institute of Fundamental Research alumni
Scientists from Telangana
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/Tian%20yuan%20shu | Tian yuan shu () is a Chinese system of algebra for polynomial equations. Some of the earliest existing writings were created in the 13th century during the Yuan dynasty. However, the tianyuanshu method was known much earlier, in the Song dynasty and possibly before.
History
The Tianyuanshu was explained in the writings of Zhu Shijie (Jade Mirror of the Four Unknowns) and Li Zhi (Ceyuan haijing), two Chinese mathematicians during the Mongol Yuan dynasty.
However, after the Ming overthrew the Mongol Yuan, Zhu and Li's mathematical works went into disuse as the Ming literati became suspicious of knowledge imported from Mongol Yuan times.
Only recently, with the advent of modern mathematics in China, has the tianyuanshu been re-deciphered.
Meanwhile, tian yuan shu arrived in Japan, where it is called tengen-jutsu. Zhu's text Suanxue qimeng was deciphered and was important in the development of Japanese mathematics (wasan) in the 17th and 18th centuries.
Description
Tian yuan shu means "method of the heavenly element" or "technique of the celestial unknown". The "heavenly element" is the unknown variable, usually written in modern notation.
It is a positional system of rod numerals to represent polynomial equations. For example, is represented as
, which in Arabic numerals is
The (yuan) denotes the unknown , so the numerals on that line mean . The line below is the constant term () and the line above is the coefficient of the quadratic () term. The system accommodates arbitrarily high exponents of the unknown by adding more lines on top and negative exponents by adding lines below the constant term. Decimals can also be represented.
In later writings of Li Zhi and Zhu Shijie, the line order was reversed so that the first line is the lowest exponent.
See also
Yigu yanduan
Ceyuan haijing
References
Bibliography
Chinese mathematics
Japanese mathematics
Polynomials
13th-century Chinese books |
https://en.wikipedia.org/wiki/Rural%20Canada | Rural areas in Canada, often called rural Canada, generally refers to areas in Canada outside of census metropolitan areas and census agglomerations, according to Statistics Canada. Rural areas cover approximately of Canada's land area .
Rural Canada is usually defined by low population density, small population size, and distance from major agglomerations.
, nearly 6 million people (16% of the total Canadian population) lived in rural areas of Canada. In the 2006 census, the Canadian population living in a rural area was between 19% and 30% of the total population, depending on the definition of "rural" used.
Census
In Statistics Canada’s definition, "rural area" refers to areas in Canada outside of census metropolitan areas and census agglomerations.
This definition has changed over time.
See also
List of rural municipalities in Alberta
List of rural municipalities in Manitoba
List of rural municipalities in Prince Edward Island
List of rural municipalities in Saskatchewan
References
Further reading
"Canada's 2021 Census of Agriculture: A story about the transformation of the agriculture industry and adaptiveness of Canadian farmers." Statistics Canada. 2022 May 11.
Geography of Canada
Canada
Regions of Canada |
https://en.wikipedia.org/wiki/Kulilits | Kulilits is a Philippine children's television show on ABS-CBN. It features teaching children moral and values to singing new songs to dances and to mathematics. The show is hosted by Cha-Cha Cañete, Bugoy Cariño and Izzy Canillo. It aired from October 31, 2009, to September 18, 2010, replacing Wonder Mom.
References
See also
List of programs aired by ABS-CBN
ABS-CBN News and Current Affairs
ABS-CBN original programming
Philippine children's television series
2009 Philippine television series debuts
2010 Philippine television series endings
Filipino-language television shows |
https://en.wikipedia.org/wiki/ALICEWEB | ALICEWEB is an acronym for Análise de Informações de Comércio Exterior-Web, was the official website of the Brazilian government about their foreign trade statistics. It was made available from 2001 onwards, aiming at easy and clear publication of foreign trade statistics.
Access to Aliceweb is free. Users can check the data and choose to generate files containing the results of the queries and have these results emailed to them. The system has Brazilian foreign trade data from 1989 until the most recent month.
It is developed and maintained by the Secretariat of Foreign Trade (SECEX), of the Ministry of Development, Industry and Foreign Trade (MDIC).
References
External links
ALICEWEB
Government services portals
Government of Brazil
Economic data
Brazilian websites |
https://en.wikipedia.org/wiki/International%20Journal%20of%20Biomathematics | The International Journal of Biomathematics is a quarterly mathematics journal covering research in the area of biomathematics, including mathematical ecology, infectious disease dynamical system, biostatistics and bioinformatics. It was established in 2008 and is published by World Scientific. The current editor-in-chief is Lansun Chen (Anshan Normal University).
References
External links
Mathematics journals
World Scientific academic journals
Quarterly journals
English-language journals
Academic journals established in 2008
Biology journals |
https://en.wikipedia.org/wiki/International%20Journal%20of%20Computational%20Geometry%20and%20Applications | The International Journal of Computational Geometry and Applications (IJCGA) is a bimonthly journal published since 1991, by World Scientific. It covers the application of computational geometry in design and analysis of algorithms, focusing on problems arising in various fields of science and engineering such as computer-aided geometry design (CAGD), operations research, and others.
The current editors-in-chief are D.-T. Lee of the Institute of Information Science in Taiwan, and Joseph S. B. Mitchell from the Department of Applied Mathematics and Statistics
in the State University of New York at Stony Brook.
Abstracting and indexing
Current Contents/Engineering, Computing & Technology
ISI Alerting Services
Science Citation Index Expanded (also known as SciSearch)
CompuMath Citation Index
Mathematical Reviews
INSPEC
DBLP Bibliography Server
Zentralblatt MATH
Computer Abstracts
References
External links
IJCGA Journal Website
Computer science journals
World Scientific academic journals
Bimonthly journals
Mathematics journals
English-language journals
Computational geometry |
https://en.wikipedia.org/wiki/Robbie%20Neale | Robbie Neale (born April 17, 1953) is a Canadian retired ice hockey forward who played 59 games in the World Hockey Association.
Career statistics
External links
1953 births
Living people
Brandon Wheat Kings players
Canadian ice hockey forwards
Cleveland Crusaders draft picks
Cleveland Crusaders players
Detroit Red Wings draft picks
Ice hockey people from Winnipeg
Winnipeg Jets (WHA) players |
https://en.wikipedia.org/wiki/Roy%20Mitchell%20%28ice%20hockey%29 | Roy Mitchell (born March 14, 1969) is a Canadian former professional ice hockey player who played three games in the National Hockey League for the Minnesota North Stars.
Career statistics
External links
1969 births
Living people
Canadian ice hockey defencemen
Ice hockey people from Edmonton
Minnesota North Stars players
Montreal Canadiens draft picks
Edmonton Sled Dogs players
Portland Winterhawks players
Sherbrooke Canadiens players
Central Texas Stampede players |
https://en.wikipedia.org/wiki/Vinzenz%20Bronzin | Vinzenz Bronzin (born 1872 in Rovigno – died 1970 in Trieste) was an Italian mathematics professor, known today for an early ("rediscovered") option pricing formula, similar to, and predating, the Black–Scholes 1973 formula;
he also provided a formulation of put–call parity,
written up formally only in 1969 by Stoll.
Bronzin was born in Rovigno (now Rovinj), Istria.
He studied engineering at the Vienna Polytechnic Institute, and then mathematics and pedagogics at the University of Vienna.
He was made a professor at the Accademia di Commercio e Nautica, Trieste, Italy, in 1900;
his focus was "Political and Commercial Arithmetic", which included actuarial science and probability theory.
In 1910 he accepted the position of director.
In 1937 he resigned from all of his positions at the Academia at the age of 65.
In 1908 Bronzin published his Theorie der Prämiengeschäfte (German: "Theory of Premium Contracts") discussing a then current type of option contract.
Almost every element of modern option pricing can be found in Bronzin’s book;
however, like Louis Bachelier's now famous dissertation (1900), the work seems to have been forgotten shortly after it was published.
Bronzin’s "methodological setup is completely different from Bachelier’s," at least in terms of the underlying stochastic framework;
he takes a much more "pragmatic" approach, directly making assumptions on the share price distribution at maturity, and deriving a "rich set of closed form solutions for the value of options."
See also
Louis Bachelier
Jules Regnault
References
19th-century Italian mathematicians
20th-century Italian mathematicians
1872 births
1970 deaths
Financial economists
Mathematicians from Austria-Hungary |
https://en.wikipedia.org/wiki/International%20Journal%20of%20Mathematics | The International Journal of Mathematics was founded in 1990 and is published monthly (with the exception of June and December) by World Scientific. The journal covers mathematics in general.
According to the Journal Citation Reports, the journal has a 2020 impact factor of 0.688.
Abstracting and indexing
The journal is abstracted and indexed in:
Science Citation Index
ISI Alerting Services
CompuMath Citation Index
Current Contents/Physical, Chemical & Earth Sciences
Zentralblatt MATH
Mathematical Reviews
CSA Aerospace Sciences Abstracts
Mathematics journals
Academic journals established in 1990
World Scientific academic journals
English-language journals |
https://en.wikipedia.org/wiki/Leroy%20Milton%20Kelly | Leroy Milton Kelly (May 8, 1914 – February 21, 2002) was an American mathematician whose research primarily concerned combinatorial geometry. In 1986 he settled a conjecture of Jean-Pierre Serre by proving that n points in complex 3-space, not all lying on a plane, determine an ordinary line—that is, a line containing only two of the n points. He taught at Michigan State University.
Kelly received his Ph.D. at the University of Missouri in 1948, advised by Leonard Mascot Blumenthal.
Selected publications
.
.
References
1914 births
2002 deaths
20th-century American mathematicians
21st-century American mathematicians
Geometers
University of Missouri alumni
Michigan State University faculty |
https://en.wikipedia.org/wiki/Carolyn%20S.%20Gordon | Carolyn S. Gordon (born 1950) is a mathematician and Benjamin Cheney Professor of Mathematics at Dartmouth College. She is most well known for giving a negative answer to the question "Can you hear the shape of a drum?" in her work with David Webb and Scott A. Wolpert. She is a Chauvenet Prize winner and a 2010 Noether Lecturer.
Early life and education
Gordon received her Bachelor of Science degree from the Purdue University. She entered graduate studies at the Washington University in St. Louis, earning her Doctor of Philosophy in mathematics in 1979. Her doctoral advisor was Edward Nathan Wilson and her thesis was on isometry groups of homogeneous manifolds. She completed a postdoc at Technion Israel Institute of Technology and held positions at Lehigh University and Washington University in St. Louis.
Career
Gordon is most well known for her work in isospectral geometry, for which hearing the shape of a drum is the prototypical example. In 1966 Mark Kac asked whether the shape of a drum could be determined by the sound it makes (whether a Riemannian manifold is determined by the spectrum of its Laplace–Beltrami operator). John Milnor observed that a theorem due to Witt implied the existence of a pair of 16-dimensional tori that have the same spectrum but different shapes. However, the problem in two dimensions remained open until 1992, when Gordon, with coauthors Webb and Wolpert, constructed a pair of regions in the Euclidean plane that have different shapes but identical eigenvalues (see figure on right). In further work, Gordon and Webb produced convex isospectral domains in the hyperbolic plane and in Euclidean space.
Gordon has written or coauthored over 30 articles on isospectral geometry including work on isospectral closed Riemannian manifolds with a common Riemannian covering. These isospectral Riemannian manifolds have the same local geometry but different topology. They can be found using the "Sunada method," due to Toshikazu Sunada. In 1993 she found isospectral Riemannian manifolds which are not locally isometric and, since that time, has worked with coauthors to produce a number of other such examples.
Gordon has also worked on projects concerning the homology class, length spectrum (the collection of lengths of all closed geodesics, together with multiplicities) and geodesic flow on isospectral Riemannian manifolds.
Selected awards and honors
In 2001 Gordon and Webb were awarded the Mathematical Association of America Chauvenet Prize for their 1996 American Scientist paper, "You can't hear the shape of a drum". In 1990 she was awarded an AMS Centennial Fellowship by the American Mathematical Society for outstanding early career research. In 1999 Gordon presented an AMS-MAA joint invited address. In 2010 she was selected as a Noether Lecturer. In 2012 she became a fellow of the American Mathematical Society and of the American Association for the Advancement of Science. She was also an AMS Council member at large fr |
https://en.wikipedia.org/wiki/Measure%20algebra | In mathematics, a measure algebra is a Boolean algebra with a countably additive positive measure. A probability measure on a measure space gives a measure algebra on the Boolean algebra of measurable sets modulo null sets.
Definition
A measure algebra is a Boolean algebra B with a measure m, which is a real-valued function on B such that:
m(0)=0, m(1)=1
m(x) >0 if x≠0
m is countably additive: m(Σxi) = Σm(xi) if the xi are a countable set of elements that are disjoint (xi ∧ xj=0 whenever i≠j).
References
Measure theory |
https://en.wikipedia.org/wiki/Peter%20Grindrod | Peter Grindrod is a British mathematician.
Career
Grindrod was appointed a CBE in 2005 for services to mathematics R&D. He is a former member of the EPSRC Council (2000–04) and chair of the EPSRC's User Panel. He is a former president of the Institute of Mathematics and its Applications, the UK's professional and learned society for mathematicians (2006–08). He is also former member of BBSRC Council (2009–13). He is a former independent member of the MOD DSAC (2008–13). He was one of the founding directors (trustees) of the Alan Turing Institute, the UK's national centre for Data Science and AI.
He is active in considering novel ways to achieve higher impact from the UK's research and development programmes and he has written recently on the intrinsic lack of risk-taking within public R&D funding, due to wrong-framing of proposed projects (as individual bets, all judged absolutely and seeking success, rather than as a portfolio of investments of very distinct types and distinct levels of risks and possible returns); and the dead hand of consensual peer-review processes, which results in only rather safe-science (de-risked) being funded and avoids any investments where there is controversy or a lack of a reviewer consensus (which could indicate disruptive opportunities outside of the present paradigm). He has recently applied such thinking to the MOD's AI programme, the UK's national AI strategy and portfolio, and the forthcoming UK ARIA.
Grindrod began working in the theory and application of reaction diffusion equations. He obtained a degree in maths from the University of Bristol (1981) and a PhD from the University of Dundee (1983), after which followed a short period of post doctoral research in dynamical systems and nonlinear PDEs at Dundee. Between 1984 and 1989 he worked at the Mathematical Institute at the University of Oxford, largely on both applications and modelling within physiology and biology.
In 1989 he joined a commercial consulting company working in the environmental sciences, building up a mathematical modelling group on multidisciplinary projects in the UK, Europe, US and Japan. His research ranged from the application of fractals to simulating subsurface environments (micro medium structure controlling channelling flow and dispersion phenomena at the macroscopic scale), and non-linear multiphase (solutes, gases, and especially colloidal) dispersion processes, fully coupled chemical-temperature–hydration systems, through to the development of frameworks for estimating uncertainties within risk assessments, and the analysis of public risk perception.
He has developed models and methods for analyzing large networks (range dependent random graphs) occurring within the biosciences, such as in genome, proteome and metabolome interactions. He is interested in applications of mathematics to phenomena in the Digital Economy, and within neurodynamics. He is working on methods for analysing very large and evolving graphs/networks |
https://en.wikipedia.org/wiki/Wrapped%20Cauchy%20distribution | In probability theory and directional statistics, a wrapped Cauchy distribution is a wrapped probability distribution that results from the "wrapping" of the Cauchy distribution around the unit circle. The Cauchy distribution is sometimes known as a Lorentzian distribution, and the wrapped Cauchy distribution may sometimes be referred to as a wrapped Lorentzian distribution.
The wrapped Cauchy distribution is often found in the field of spectroscopy where it is used to analyze diffraction patterns (e.g. see Fabry–Pérot interferometer).
Description
The probability density function of the wrapped Cauchy distribution is:
where is the scale factor and is the peak position of the "unwrapped" distribution. Expressing the above pdf in terms of the characteristic function of the Cauchy distribution yields:
The PDF may also be expressed in terms of the circular variable z = eiθ and the complex parameter ζ = ei(μ+iγ)
where, as shown below, ζ = ⟨z⟩.
In terms of the circular variable the circular moments of the wrapped Cauchy distribution are the characteristic function of the Cauchy distribution evaluated at integer arguments:
where is some interval of length . The first moment is then the average value of z, also known as the mean resultant, or mean resultant vector:
The mean angle is
and the length of the mean resultant is
yielding a circular variance of 1 − R.
Estimation of parameters
A series of N measurements drawn from a wrapped Cauchy distribution may be used to estimate certain parameters of the distribution. The average of the series is defined as
and its expectation value will be just the first moment:
In other words, is an unbiased estimator of the first moment. If we assume that the peak position lies in the interval , then Arg will be a (biased) estimator of the peak position .
Viewing the as a set of vectors in the complex plane, the statistic is the length of the averaged vector:
and its expectation value is
In other words, the statistic
will be an unbiased estimator of , and will be a (biased) estimator of .
Entropy
The information entropy of the wrapped Cauchy distribution is defined as:
where is any interval of length . The logarithm of the density of the wrapped Cauchy distribution may be written as a Fourier series in :
where
which yields:
(c.f. Gradshteyn and Ryzhik 4.224.15) and
(c.f. Gradshteyn and Ryzhik 4.397.6). The characteristic function representation for the wrapped Cauchy distribution in the left side of the integral is:
where . Substituting these expressions into the entropy integral, exchanging the order of integration and summation, and using the orthogonality of the cosines, the entropy may be written:
The series is just the Taylor expansion for the logarithm of so the entropy may be written in closed form as:
Circular Cauchy distribution
If X is Cauchy distributed with median μ and scale parameter γ, then the complex variable
has unit modulus and is distributed on the unit |
https://en.wikipedia.org/wiki/Askold%20Vinogradov | Askold Ivanovich Vinogradov () (1929 – 31 December 2005) was a Russian mathematician who worked in analytic number theory. The Bombieri–Vinogradov theorem is partially named after him.
References
External links
Publications of A.I. Vinogradov
Russian mathematicians
1929 births
2005 deaths |
https://en.wikipedia.org/wiki/Alexei%20Skorobogatov | Alexei Nikolaievich Skorobogatov () is a British-Russian mathematician and Professor in Pure Mathematics at Imperial College London specialising in algebraic geometry. His work has focused on rational points, the Hasse principle, the Manin obstruction, exponential sums, and error-correcting codes.
Education
He completed his dissertation under the supervision of Yuri Manin, for which he was awarded a Ph.D. degree.
Awards
In 2001 he was awarded a Whitehead Prize by the London Mathematical Society.
He was elected as a Fellow of the American Mathematical Society in the 2020 Class, for "contributions to the Diophantine geometry of surfaces and higher dimensional varieties".
Books
References
External links
Alexei Skorobogatov's professional webpage
Alexei Skorobogatov's personal webpage
1961 births
Living people
20th-century Russian mathematicians
21st-century Russian mathematicians
Academics of Imperial College London
Whitehead Prize winners
Fellows of the American Mathematical Society
Moscow State University alumni |
https://en.wikipedia.org/wiki/Viacheslav%20V.%20Nikulin | Viacheslav Valentinovich Nikulin (Slava) is a Russian mathematician working in the algebraic geometry of K3 surfaces and Calabi–Yau threefolds, mirror symmetry, the arithmetic of quadratic forms, and hyperbolic Kac–Moody algebras. He is a professor of mathematics at the University of Liverpool. A third chair of mathematics was established for Nikulin in 1999, the second chair having been established in 1964 for C. T. C. Wall and the first having been established in 1882. Nikulin has made contributions towards the solution of Hilbert's 16th problem.
Publications
References
Academics of the University of Liverpool
Living people
Russian mathematicians
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Sheen%20T.%20Kassouf | Sheen T. Kassouf (11 August 1928 – 10 August 2005) was an American economist from New York known for research in financial mathematics. In 1957 he married Gloria Daher in Brooklyn, New York. Kassouf received a PhD in economics from Columbia University (1965) and was later professor of economics at University of California Irvine. Together with Edward O. Thorp he co-authored the book Beat the Market in 1967.
Publications
Kassouf, S. T. ; Thorp, E. O., Beat the Market: A Scientific Stock Market System, ()
Access to all published works - UCI Department of Economics
References
External links
Sheen Kassouf Page - UCI Department of Economics
1928 births
2005 deaths
Economists from California
Financial economists
Columbia Graduate School of Arts and Sciences alumni
University of California, Irvine faculty
American economics writers
American male non-fiction writers
20th-century American economists
20th-century American male writers |
https://en.wikipedia.org/wiki/Jensen%27s%20covering%20theorem | In set theory, Jensen's covering theorem states that if 0# does not exist then every uncountable set of ordinals is contained in a constructible set of the same cardinality. Informally this conclusion says that the constructible universe is close to the universe of all sets. The first proof appeared in . Silver later gave a fine-structure-free proof using his machines and finally gave an even simpler proof.
The converse of Jensen's covering theorem is also true: if 0# exists then the countable set of all cardinals less than cannot be covered by a constructible set of cardinality less than .
In his book Proper Forcing, Shelah proved a strong form of Jensen's covering lemma.
Hugh Woodin states it as:
Theorem 3.33 (Jensen). One of the following holds.
(1) Suppose λ is a singular cardinal. Then λ is singular in L and its successor cardinal is its successor cardinal in L.
(2) Every uncountable cardinal is inaccessible in L.
References
Notes
Set theory |
https://en.wikipedia.org/wiki/Anton%20Kotzig | Anton Kotzig (22 October 1919 – 20 April 1991) was a Slovak–Canadian mathematician, expert in statistics, combinatorics and graph theory.
The Ringel–Kotzig conjecture on graceful labeling of trees is named after him and Gerhard Ringel.
Kotzig's theorem on the degrees of vertices in convex polyhedra is also named after him.
Biography
Kotzig was born in Kočovce, a village in Western Slovakia, in 1919. He studied at the secondary grammar school in Nové Mesto nad Váhom, and began his undergraduate studies at Charles University in Prague. After the closure of Czech universities in 1939, he moved to Bratislava, where in 1943 he earned a doctoral degree (RNDr.) in mathematical statistics from Comenius University in Bratislava. He remained in Bratislava working at the Central Bureau of Social Insurance for Slovakia, as the head of department of mathematical statistics.
Later he published a book on economy planning. From 1951 to 1959, he lectured at Vysoká škola Ekonomická (today University of Economics in Bratislava), where he served as rector from 1952 to 1958. Thus he spent 20 years in close contact with applications of mathematics.
In 1959, he left the University of Economics to become the head of the newly created Mathematical Institute of the Slovak Academy of Sciences, where he remained until 1964. From 1965 to 1969, he was head of the department of Applied Mathematics on Faculty of Natural Sciences of Comenius University, where he was also dean for one year. He also earned a habilitation degree (DrSc.) from Charles University in 1961 for a thesis in graph theory (relation and regular relation of finite graphs).
Kotzig established the now well-known Slovak School of Graph Theory. One of his first students was Juraj Bosák, who was awarded the Czechoslovak State Prize in 1969.
In 1969, Kotzig moved to Canada, and spent a year at the University of Calgary. He became a researcher at the Centre de recherches mathematiques (CRM) and the University of Montreal in 1970, where he remained until his death. Because of the political situation, he could not travel back to Czechoslovakia, and remained in his adopted country without his books and notes. Although he was separated from his Slovak students, he continued doing mathematics.
He died on April 20. 1991 in Montreal, leaving his wife Edita, and a son Ľuboš.
Contributions
By 1969, the list of his publications already included over 60 articles and 4 books. Many of his results have become classical, including results about graph relations, 1-factors and cubic graphs. As they were published only in Slovak, many of them remained unknown and some of the results were independently rediscovered much later by other mathematicians. In Canada he wrote more than 75 additional articles. His publications covers a wide range of topics in graph theory and combinatorics: convex polyhedra, quasigroups, special decompositions into Hamiltonian paths, Latin squares, decompositions of complete graphs, perfect systems o |
https://en.wikipedia.org/wiki/Slow%20manifold | In mathematics, the slow manifold of an equilibrium point of a dynamical system occurs as the most common example of a center manifold. One of the main methods of simplifying dynamical systems, is to reduce the dimension of the system to that of the slow manifold—center manifold theory rigorously justifies the modelling. For example, some global and regional models of the atmosphere or oceans resolve the so-called quasi-geostrophic flow dynamics on the slow manifold of the atmosphere/oceanic dynamics,
and is thus crucial to forecasting with a climate model.
In some cases, a slow manifold is defined to be the invariant manifold on which the dynamics are slow compared to the dynamics off the manifold. The slow manifold in a particular problem would be a sub-manifold of either the stable, unstable, or center manifold, exclusively, that has the same dimension of, and is tangent to, the eigenspace with an associated eigenvalue (or eigenvalue pair) that has the smallest real part in magnitude. This generalizes the definition described in the first paragraph. Furthermore, one might define the slow manifold to be tangent to more than one eigenspace by choosing a cut-off point in an ordering of the real part eigenvalues in magnitude from least to greatest. In practice, one should be careful to see what definition the literature is suggesting.
Definition
Consider the dynamical system
for an evolving state vector and with equilibrium point . Then the linearization of the system at the equilibrium point is
The matrix defines four invariant subspaces characterized by the eigenvalues of the matrix: as described in the entry for the center manifold three of the subspaces are the stable, unstable and center subspaces corresponding to the span of the eigenvectors with eigenvalues that have real part negative, positive, and zero, respectively; the fourth subspace is the slow subspace given by the span of the eigenvectors, and generalized eigenvectors, corresponding to the eigenvalue precisely (more generally, corresponding to all eigenvalues with separated by a gap from all other eigenvalues, those with ). The slow subspace is a subspace of the center subspace, or identical to it, or possibly empty.
Correspondingly, the nonlinear system has invariant manifolds, made of trajectories of the nonlinear system, corresponding to each of these invariant subspaces. There is an invariant manifold tangent to the slow subspace and with the same dimension; this manifold is the slow manifold.
Stochastic slow manifolds also exist for noisy dynamical systems (stochastic differential equation), as do also stochastic center, stable and unstable manifolds. Such stochastic slow manifolds are similarly useful in modeling emergent stochastic dynamics, but there are many fascinating issues to resolve such as history and future dependent integrals of the noise.
Examples
Simple case with two variables
The coupled system in two variables and
has the exact slow manifo |
https://en.wikipedia.org/wiki/Li%20Xiaoxu | Li Xiaoxu () is a Chinese basketball player who currently plays for Liaoning Flying Leopards in the Chinese Basketball Association.
Career statistics
CBA statistics
References
1990 births
Living people
Power forwards (basketball)
Liaoning Flying Leopards players
Chinese men's basketball players
Olympic basketball players for China
Sportspeople from Anshan
Basketball players from Liaoning
Asian Games medalists in basketball
Basketball players at the 2010 Asian Games
Basketball players at the 2014 Asian Games
Asian Games gold medalists for China
Medalists at the 2010 Asian Games
21st-century Chinese people |
https://en.wikipedia.org/wiki/Covering%20theorem | In mathematics, covering theorem can refer to
Besicovitch covering theorem
Jensen's covering theorem
Vitali covering lemma |
https://en.wikipedia.org/wiki/Scale%20%28descriptive%20set%20theory%29 | In the mathematical discipline of descriptive set theory, a scale is a certain kind of object defined on a set of points in some Polish space (for example, a scale might be defined on a set of real numbers). Scales were originally isolated as a concept in the theory of uniformization, but have found wide applicability in descriptive set theory, with applications such as establishing bounds on the possible lengths of wellorderings of a given complexity, and showing (under certain assumptions) that there are largest countable sets of certain complexities.
Formal definition
Given a pointset A contained in some product space
where each Xk is either the Baire space or a countably infinite discrete set, we say that a norm on A is a map from A into the ordinal numbers. Each norm has an associated prewellordering, where one element of A precedes another element if the norm of the first is less than the norm of the second.
A scale on A is a countably infinite collection of norms
with the following properties:
If the sequence xi is such that
xi is an element of A for each natural number i, and
xi converges to an element x in the product space X, and
for each natural number n there is an ordinal λn such that φn(xi)=λn for all sufficiently large i, then
x is an element of A, and
for each n, φn(x)≤λn.
By itself, at least granted the axiom of choice, the existence of a scale on a pointset is trivial, as A can be wellordered and each φn can simply enumerate A. To make the concept useful, a definability criterion must be imposed on the norms (individually and together). Here "definability" is understood in the usual sense of descriptive set theory; it need not be definability in an absolute sense, but rather indicates membership in some pointclass of sets of reals. The norms φn themselves are not sets of reals, but the corresponding prewellorderings are (at least in essence).
The idea is that, for a given pointclass Γ, we want the prewellorderings below a given point in A to be uniformly represented both as a set in Γ and as one in the dual pointclass of Γ, relative to the "larger" point being an element of A. Formally, we say that the φn form a Γ-scale on A if they form a scale on A and there are ternary relations S and T such that, if y is an element of A, then
where S is in Γ and T is in the dual pointclass of Γ (that is, the complement of T is in Γ). Note here that we think of φn(x) as being ∞ whenever x∉A; thus the condition φn(x)≤φn(y), for y∈A, also implies x∈A.
The definition does not imply that the collection of norms is in the intersection of Γ with the dual pointclass of Γ. This is because the three-way equivalence is conditional on y being an element of A. For y not in A, it might be the case that one or both of S(n,x,y) or T(n,x,y) fail to hold, even if x is in A (and therefore automatically φn(x)≤φn(y)=∞).
Applications
Scale property
The scale property is a strengthening of the prewellordering property. For pointclasses of a |
https://en.wikipedia.org/wiki/Ernst%20Sejersted%20Selmer | Ernst Sejersted Selmer (11 February 1920 – 8 November 2006) was a Norwegian mathematician, who worked in number theory, as well as a cryptologist. The Selmer group of an Abelian variety is named after him. His primary contributions to mathematics reside within the field of diophantine equations. He started working as a cryptologist during the Second World War; due to his work, Norway became a NATO superpower in the field of encryption.
Biography
Early life
Ernest S. Selmer was born in Oslo in the family of Professor Ernst W. Selmer and Ella Selmer (born Sejersted). He was the brother of Knut S. Selmer who married with Elisabeth Schweigaard, as well as first cousin of Francis Sejersted.
Already early in school, Selmer demonstrated mathematical talent. When attending Stabekk high school he was an editor of the school's magazine Tall og tanker (numbers and thoughts). In 1938, he won Crown Prince Olav's Mathematics Prize for high school graduates. From 1942–1943, he studied at the University of Oslo. As a student at the university during World War II, Selmer was involved in encrypting secret messages for the Norwegian resistance movement. During the autumn of 1943 when the Germans forced the University to close he escaped to Sweden, just in time before the Nazi Germany secret police Gestapo closed the university and arrested the male students.
In 1944 Selmer was sent to London, where he took technical responsibility for all Norwegian military and civilian cipher machines. The communication was mainly carried out using the Hagelin cipher machine. When the war ended, Selmer returned to Norway, and in 1946, was hired as a lecturer in the University of Oslo. In the same year, he started working for the Cipher Department of the Armed Forces Security Service as a consultant. With colleagues, he built a communication system for Norway's equivalent of the MI5, which was used from 1949 till 1960. Selmer spent the spring of 1949 at the Cambridge University working with the famous mathematician JWS Cassels. As a result of their collaboration, a group related to an Abelian variety—namely, the Selmer group—was discovered and named after Selmer. In 1993, Andrew Wiles used Selmer's group in his proof of the Fermat's last theorem.
Middle years
Selmer received his dr.philos in 1952 from the University of Oslo and was at the same time hired as a lecturer for the university. Among Selmer's lectures, his lectures on data processing is of particular note, as it helped lay the foundation for the Department of Informatics at the university. In the same year, he received a Rockefeller Foundation Fellowship to study in the United States during the years 1951–1952. Selmer arrived in January 1951 as a visiting scholar at the Institute for Advanced Study in Princeton, N.J. where the IAS machine was being constructed for John von Neumann. During his stay in Princeton he also met with people such as Albert Einstein, J. Robert Oppenheimer and his countryman Atle Selberg. E |
https://en.wikipedia.org/wiki/Poisson%20number | Poisson number can refer to:
In mechanics, the reciprocal of Poisson's ratio. 1 / v.
In statistics, a number drawn from a Poisson distribution |
https://en.wikipedia.org/wiki/Quantum%20affine%20algebra | In mathematics, a quantum affine algebra (or affine quantum group) is a Hopf algebra that is a q-deformation of the universal enveloping algebra of an affine Lie algebra. They were introduced independently by and as a special case of their general construction of a quantum group from a Cartan matrix. One of their principal applications has been to the theory of solvable lattice models in quantum statistical mechanics, where the Yang–Baxter equation occurs with a spectral parameter. Combinatorial aspects of the representation theory of quantum affine algebras can be described simply using crystal bases, which correspond to the degenerate case when the deformation parameter q vanishes and the Hamiltonian of the associated lattice model can be explicitly diagonalized.
See also
Quantum enveloping algebra
Quantum KZ equations
Littelmann path model
Yangian
References
Quantum groups
Representation theory
Exactly solvable models
Mathematical quantization |
https://en.wikipedia.org/wiki/Volcano%20plot%20%28statistics%29 | In statistics, a volcano plot is a type of scatter-plot that is used to quickly identify changes in large data sets composed of replicate data. It plots significance versus fold-change on the y and x axes, respectively. These plots are increasingly common in omic experiments such as genomics, proteomics, and metabolomics where one often has a list of many thousands of replicate data points between two conditions and one wishes to quickly identify the most meaningful changes. A volcano plot combines a measure of statistical significance from a statistical test (e.g., a p value from an ANOVA model) with the magnitude of the change, enabling quick visual identification of those data-points (genes, etc.) that display large magnitude changes that are also statistically significant.
A volcano plot is constructed by plotting the negative logarithm of the p value on the y axis (usually base 10). This results in data points with low p values (highly significant) appearing toward the top of the plot. The x axis is the logarithm of the fold change between the two conditions. The logarithm of the fold change is used so that changes in both directions appear equidistant from the center. Plotting points in this way results in two regions of interest in the plot: those points that are found toward the top of the plot that are far to either the left- or right-hand sides. These represent values that display large magnitude fold changes (hence being left or right of center) as well as high statistical significance (hence being toward the top).
Additional information can be added by coloring the points according to a third dimension of data (such as signal intensity), but this is not uniformly employed. Volcano plots are also used to graphically display a significance analysis of microarrays (SAM) gene selection criterion, an example of regularization.
The concept of volcano plot can be generalized to other applications, where the x axis is related to a measure of
the strength of a statistical signal, and y axis is related to a measure of the statistical significance of the signal.
For example, in a genetic association case-control study, such as Genome-wide association study,
a point in a volcano plot represents a single-nucleotide polymorphism.
Its x value can be the logarithm of the odds ratio and its y value can be -log10 of the p value from a Chi-square test
or a Chi-square test statistic.
Volcano plots show a characteristic upwards two arm shape because the x axis, i.e. the underlying log2-fold changes, are generally normal distribution whereas the y axis, the log10-p values, tend toward greater significance for fold-changes that deviate more strongly from zero.
The density of the normal distribution takes the form
.
So the
of that is
and the negative
is
which is a parabola whose arms reach upwards
on the left and right sides.
The upper bound of the data is one parabola
and the lower bound is another parabola.
References
External links
NCI |
https://en.wikipedia.org/wiki/Quantum%20inverse%20scattering%20method | In quantum physics, the quantum inverse scattering method (QISM) or the algebraic Bethe ansatz is a method for solving integrable models in 1+1 dimensions, introduced by Leon Takhtajan and L. D. Faddeev in 1979.
It can be viewed as a quantized version of the classical inverse scattering method pioneered by Norman Zabusky and Martin Kruskal used to investigate the Korteweg–de Vries equation and later other integrable partial differential equations. In both, a Lax matrix features heavily and scattering data is used to construct solutions to the original system.
While the classical inverse scattering method is used to solve integrable partial differential equations which model continuous media (for example, the KdV equation models shallow water waves), the QISM is used to solve many-body quantum systems, sometimes known as spin chains, of which the Heisenberg spin chain is the best-studied and most famous example. These are typically discrete systems, with particles fixed at different points of a lattice, but limits of results obtained by the QISM can give predictions even for field theories defined on a continuum, such as the quantum sine-Gordon model.
Discussion
The quantum inverse scattering method relates two different approaches:
the Bethe ansatz, a method of solving integrable quantum models in one space and one time dimension.
the inverse scattering transform, a method of solving classical integrable differential equations of the evolutionary type.
This method led to the formulation of quantum groups, in particular the Yangian. The center of the Yangian, given by the quantum determinant plays a prominent role in the method.
An important concept in the inverse scattering transform is the Lax representation. The quantum inverse scattering method starts by the quantization of the Lax representation and reproduces the results of the Bethe ansatz. In fact, it allows the Bethe ansatz to be written in a new form: the algebraic Bethe ansatz. This led to further progress in the understanding of quantum integrable systems, such as the quantum Heisenberg model, the quantum nonlinear Schrödinger equation (also known as the Lieb–Liniger model or the Tonks–Girardeau gas) and the Hubbard model.
The theory of correlation functions was developed, relating determinant representations, descriptions by differential equations and the Riemann–Hilbert problem. Asymptotics of correlation functions which include space, time and temperature dependence were evaluated in 1991.
Explicit expressions for the higher conservation laws of the integrable models were obtained in 1989.
Essential progress was achieved in study of ice-type models: the bulk free energy of the
six vertex model depends on boundary conditions even in the thermodynamic limit.
Procedure
The steps can be summarized as follows :
Take an R-matrix which solves the Yang–Baxter equation.
Take a representation of an algebra satisfying the RTT relations.
Find the spectrum of the generating fun |
https://en.wikipedia.org/wiki/Simplification | Simplification, Simplify, or Simplified may refer to:
Mathematics
Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler (usually shorter), for example
Simplification of algebraic expressions, in computer algebra
Simplification of boolean expressions i.e. logic optimization
Simplification by conjunction elimination in inference in logic yields a simpler, but generally non-equivalent formula
Simplification of fractions
Science
Approximations simplify a more detailed or difficult to use process or model
Linguistics
Simplification of Chinese characters
Simplified English (disambiguation)
Text simplification
Music
Simplify, a 1999 album by Ryan Shupe & the RubberBand
Simplified (band), a 2002 rock band from Charlotte, North Carolina
Simplified (album), a 2005 album by Simply Red
"Simplify", a 2008 song by Sanguine
"Simplify", a 2018 song by Young the Giant from Mirror Master
See also
Muntzing (simplification of electric circuits)
Reduction (mathematics)
Simplicity
Oversimplification
Dumbing down |
https://en.wikipedia.org/wiki/2009%20Dhivehi%20League | Statistics of the Maldives 2009 Wataniya Dhivehi League
Dhivehi League
2010 Dhivehi League promotion/relegation play-off
External links
Maldives 2009, RSSSF.com
Dhivehi League seasons
Maldives
Maldives
1 |
https://en.wikipedia.org/wiki/Lafragua | Lafragua Municipality is a municipality in the Mexican state of Puebla. According to the National Statistics Institute (INEGI), it had a population of 10,551 inhabitants in the 2005 census. By the 2010 census it had dropped to 7,767 inhabitants, 761 of whom lived in Saltillo, the municipal seat. Its total area is 128.85 km². The Saltillo name comes from the Nahuatl words Atlcholoa in atl, which means water, and Choloa, meaning drip. Therefore, means water that drips. The name Lafragua is in honor of José María Lafragua.
Its geographical coordinates are 19° 17′ 52” North, and 97° 17′ 54” West at Saltillo. Its average altitude is 2,860 m above sea level. The elevation at Saltillo is officially 2,829 meters (9,281.5 ft.), making it the third-highest municipal seat in Mexico (after Emiliano Zapata, Tlaxcala and El Porvenir, Chiapas).
Source: Statistics from INEGI
External links
https://web.archive.org/web/20110724165337/http://www.e-local.gob.mx/work/templates/enciclo/puebla/Mpios/21093a.htm
References
Municipalities of Puebla |
https://en.wikipedia.org/wiki/Atlantic%20Coastal%20Cooperative%20Statistics%20Program | The Atlantic Coastal Cooperative Statistics Program (ACCSP) is a cooperative state-federal program of U.S. states and the District of Columbia. ACCSP was established to be the principal source of fisheries-dependent information on the Atlantic Coast of the United States.
Initial planning for an Atlantic coast fisheries-dependent program began in 1994 to address deficiencies in the data available for fisheries management along the Atlantic coast. The ACCSP was established in 1995 through a Memorandum of Understanding signed by the 23 state and federal agencies responsible for marine fisheries management on the Atlantic coast.
The federal partners are the United States Fish and Wildlife Service (FWS), National Marine Fisheries Service of the National Oceanic and Atmospheric Administration (NOAA). The state partners are the Maine Department of Marine Resources, New Hampshire Fish and Game Department, Massachusetts Division of Marine Fisheries, Rhode Island Division of Fish and Wildlife, Connecticut Department of Environmental Protection, New York State Department of Environmental Conservation, New Jersey Division of Fish and Wildlife, Delaware Department of Natural Resources, Pennsylvania Fish and Boat Commission, District of Columbia Fisheries and Wildlife, Maryland Department of Natural Resources, Virginia Marine Resources Commission, North Carolina Department of Environment and Natural Resources, South Carolina Department of Natural Resources, Florida Fish and Wildlife Conservation Commission, and Georgia Department of Natural Resources. Other partners include the New England Fishery Management Council, Potomac River Fisheries Commission, Atlantic States Marine Fisheries Commission, South Atlantic Fishery Management Council, and Mid-Atlantic Fishery Management Council.
The Program is separated into three divisions: a staff dedicated to handling the ACCSP standards, administrative aspects and outreach requirements of the program; a data team that seeks to identify, transform and audit datasets and answer data queries regarding fisheries' activities; and a software team that designs and builds the data collection systems for the program manages on behalf of its partners, and internal systems that support Program activities.
External links
Official website
Fisheries agencies
Natural resources agencies in the United States
United States Fish and Wildlife Service |
https://en.wikipedia.org/wiki/Mills%20ratio | In probability theory, the Mills ratio (or Mills's ratio) of a continuous random variable is the function
where is the probability density function, and
is the complementary cumulative distribution function (also called survival function). The concept is named after John P. Mills. The Mills ratio is related to the hazard rate h(x) which is defined as
by
Example
If has standard normal distribution then
where the sign means that the quotient of the two functions converges to 1 as , see Q-function for details. More precise asymptotics can be given.
Inverse Mills ratio
The inverse Mills ratio is the ratio of the probability density function to the complementary cumulative distribution function of a distribution. Its use is often motivated by the following property of the truncated normal distribution. If X is a random variable having a normal distribution with mean μ and variance σ2, then
where is a constant, denotes the standard normal density function, and is the standard normal cumulative distribution function. The two fractions are the inverse Mills ratios.
Use in regression
A common application of the inverse Mills ratio (sometimes also called “non-selection hazard”) arises in regression analysis to take account of a possible selection bias. If a dependent variable is censored (i.e., not for all observations a positive outcome is observed) it causes a concentration of observations at zero values. This problem was first acknowledged by Tobin (1958), who showed that if this is not taken into consideration in the estimation procedure, an ordinary least squares estimation will produce biased parameter estimates. With censored dependent variables there is a violation of the Gauss–Markov assumption of zero correlation between independent variables and the error term.
James Heckman proposed a two-stage estimation procedure using the inverse Mills ratio to correct for the selection bias. In a first step, a regression for observing a positive outcome of the dependent variable is modeled with a probit model. The inverse Mills ratio must be generated from the estimation of a probit model, a logit cannot be used. The probit model assumes that the error term follows a standard normal distribution. The estimated parameters are used to calculate the inverse Mills ratio, which is then included as an additional explanatory variable in the OLS estimation.
See also
Heckman correction
References
External links
Theory of probability distributions
Statistical ratios |
https://en.wikipedia.org/wiki/International%20Journal%20of%20Number%20Theory | The International Journal of Number Theory was established in 2005 and is published by World Scientific. It covers number theory, encompassing areas such as analytic number theory, diophantine equations, and modular forms.
According to the Journal Citation Reports, the journal has a 2020 impact factor of 0.674.
Abstracting and indexing
The journal is abstracted and indexed in Zentralblatt MATH, Mathematical Reviews, Science Citation Index Expanded, and Current Contents/Physical, Chemical and Earth Sciences.
External links
Academic journals established in 2005
Mathematics journals
World Scientific academic journals
English-language journals |
https://en.wikipedia.org/wiki/Journal%20of%20Algebra%20and%20Its%20Applications | The Journal of Algebra and Its Applications covers both theoretical and applied algebra, with a focus on practical applications. It is published by World Scientific.
According to the Journal Citation Reports, the journal has a 2020 impact factor of 0.736.
Abstracting and indexing
The journal is abstracted and indexed in:
Mathematical Reviews
Zentralblatt MATH
Science Citation Index Expanded
Current Contents/Physical Chemical and Earth Sciences
Journal Citation Reports/Science Edition
INSPEC
References
Academic journals established in 2008
Mathematics journals
World Scientific academic journals
English-language journals |
https://en.wikipedia.org/wiki/University%20of%20Toronto%20Department%20of%20Mathematics | The University of Toronto Department of Mathematics is an academic department within the Faculty of Arts and Science at the University of Toronto. It is located at the university's main campus at the Bahen Centre for Information Technology.
The University of Toronto was ranked first in Canada for Mathematics in 2018 by the QS World University Rankings, the Times Higher Education World University Rankings, and the Maclean's University Rankings.
History
For most of the second half of the 19th century, the University of Toronto was the only English-language university in Canada to offer programs with specializations, one being in mathematics and natural philosophy. The university launched its mathematics program in 1877, which became a model for the rest of Canada during the first half of the 20th century. The Mathematical and Physical Society was founded in 1882 as a mathematics student society.
In the early 20th century, the department became the first in North American to explore the field of actuarial science. At the same time, the University of Toronto's mathematics department increasingly took the lead on mathematical research in Canada. Faculty member John Charles Fields, appointed professor in 1902, was perhaps the most important in developing research at Toronto. Fields organized the 1924 International Congress of Mathematicians held in Toronto, and would later found the Fields Medal.
Fields's student, Samuel Beatty, was the first mathematics Ph.D. in Canada, obtaining his degree in 1915 (Beatty would later serve as head of the mathematics department and first president of the Canadian Mathematical Society in 1945). In the next twenty years, Toronto was to produce eight doctorates in mathematics, two of them women.
The Department's competitive mathematics team, consisting of Irving Kaplansky, Nathan Mendelsohn and John Coleman, won first place in the first year of the William Lowell Putnam Mathematical Competition in 1938. While competition rules prevented the University of Toronto from entering a team the following year, the team in won again in 1940, 1942 and 1946.
Meanwhile, the first Canadian mathematics journal, Canadian Journal of Mathematics, began publication by the University of Toronto Press in 1949, with faculty members Harold Coxeter and Gilbert de Beauregard Robinson as Editor-in-Chief and Managing Editor, respectively.
The department moved from University College to Baldwin House in 1958, and then to Sidney Smith Hall upon its completion in 1961. The statistics sub-department, first established in 1947, became a separate department in 1978.
The department was one of the founders of the Fields Institute for Research in Mathematical Sciences in 1991. Initially based at the University of Waterloo, the institute is now located at the University of Toronto. In 2006, the Department of Mathematics moved to the sixth floor of the Bahen Centre for Information Technology, located directly behind the Fields Institute.
Academics
|
https://en.wikipedia.org/wiki/Boye%20Str%C3%B8m | Boye Christian Riis Strøm (18 June 1847 – 1930) was a Norwegian statistician and civil servant.
He was born in Grue, and graduated with the cand.jur. degree in 1870. He was the director of Statistics Norway from 1882 to 1886, and published the yearbook Statistisk aarbog for Kongeriget Norge. From 1889 to 1915 he served as the Diocesan Governor of Tromsø stiftamt and the County Governor of Tromsø amt.
References
1847 births
1930 deaths
People from Grue, Norway
Norwegian statisticians
Directors of government agencies of Norway
County governors of Norway |
https://en.wikipedia.org/wiki/Koji%20Hashimoto%20%28footballer%29 | is a Japanese football player currently playing for Suzuka Point Getters in the Japan Football League. He is currently the club's captain.
Career statistics
Updated to 1 October 2022.
References
External links
Profile at Mito HollyHock
1986 births
Living people
Sportspeople from Kanazawa, Ishikawa
Meiji University alumni
Association football people from Ishikawa Prefecture
Japanese men's footballers
Japanese expatriate men's footballers
Men's association football midfielders
J1 League players
J2 League players
J3 League players
Japan Football League players
Nagoya Grampus players
Mito HollyHock players
Omiya Ardija players
Kawasaki Frontale players
Iwate Grulla Morioka players
Suzuka Point Getters players
Orange County SC players
USL Championship players
Japanese expatriate sportspeople in the United States
Expatriate men's soccer players in the United States |
https://en.wikipedia.org/wiki/Taishi%20Taguchi | is a Japanese football player currently playing for JEF United Chiba.
Club statistics
Updated to 15 January 2021.
1Includes Emperor's Cup.
2Includes J. League Cup.
3Includes AFC Champions League.
National team statistics
References
External links
Profile at Júbilo Iwata
Profile at Nagoya Grampus
Japan National Football Team Database
1991 births
Living people
Association football people from Okinawa Prefecture
Japanese men's footballers
Japan men's international footballers
J1 League players
J2 League players
Nagoya Grampus players
Júbilo Iwata players
JEF United Chiba players
Men's association football midfielders
People from Naha |
https://en.wikipedia.org/wiki/James%20McKernan | James McKernan (born 1964) is a mathematician, and a professor of mathematics at the University of California, San Diego. He was a professor at MIT from 2007 until 2013.
Education
McKernan was educated at the Campion School, Hornchurch, and Trinity College, Cambridge, before going on to earn his Ph.D. from Harvard University in 1991. His dissertation, On the Hyperplane Sections of a Variety in Projective Space, was supervised by Joe Harris.
Recognition
McKernan was the joint winner of the Cole Prize in 2009, and joint recipient of the Clay Research Award in 2007. Both honors were received jointly with his colleague Christopher Hacon. He gave an invited talk at the International Congress of Mathematicians in 2010, on the topic of "Algebraic Geometry". He was the joint winner (with Christopher Hacon) of the 2018 Breakthrough Prize in Mathematics.
He was elected as a Fellow of the American Mathematical Society in the 2020 Class, for "contributions to algebraic geometry, in particular his proof of the finite generation of the canonical ring, the existence of flips and the boundedness of varieties of log general type".
References
External links
Citation for 2009 Cole Prize in Algebra
The work of Hacon and McKernan
1964 births
Living people
Algebraic geometers
20th-century British mathematicians
21st-century British mathematicians
Alumni of Trinity College, Cambridge
Harvard University alumni
University of California, Santa Barbara faculty
Clay Research Award recipients
Fellows of the Royal Society
Fellows of the American Mathematical Society
Simons Investigator |
https://en.wikipedia.org/wiki/Classification%20of%20the%20Functions%20of%20Government | Classification of the Functions of Government (COFOG) is a classification defined by the United Nations Statistics Division. These functions are designed to be general enough to apply to the government of different countries. The accounts of each country in the United Nations are presented under these categories. The value of this is that the accounts of different countries can be compared.
References
External links
CKAN COFOG Package
Government
Classification systems |
https://en.wikipedia.org/wiki/Bit-reversal%20permutation | In applied mathematics, a bit-reversal permutation is a permutation of a sequence of items, where is a power of two. It is defined by indexing the elements of the sequence by the numbers from to , representing each of these numbers by its binary representation (padded to have length exactly ), and mapping each item to the item whose representation has the same bits in the reversed order.
Repeating the same permutation twice returns to the original ordering on the items, so the bit reversal permutation is an involution.
This permutation can be applied to any sequence in linear time while performing only simple index calculations. It has applications in the generation of low-discrepancy sequences and in the evaluation of fast Fourier transforms.
Example
Consider the sequence of eight letters . Their indexes are the binary numbers 000, 001, 010, 011, 100, 101, 110, and 111, which when reversed become 000, 100, 010, 110, 001, 101, 011, and 111.
Thus, the letter a in position 000 is mapped to the same position (000), the letter b in position 001 is mapped to the fifth position (the one numbered 100), etc., giving the new sequence . Repeating the same permutation on this new sequence returns to the starting sequence.
Writing the index numbers in decimal (but, as above, starting with position 0 rather than the more conventional start of 1 for a permutation), the bit-reversal permutations on items, for , are:
Each permutation in this sequence can be generated by concatenating two sequences of numbers: the previous permutation, with its values doubled, and the same sequence with each value increased by one.
Thus, for example doubling the length-4 permutation gives , adding one gives , and concatenating these two sequences gives the length-8 permutation .
Generalizations
The generalization to radix representations, for , and to , is a digit-reversal permutation, in which the base- digits of the index of each element are reversed to obtain the permuted index. The same idea can also been generalized to mixed radix number systems. In such cases, the digit-reversal permutation should simultaneously reverses the digits of each item and the bases of the number system, so that each reversed digit remains within the range defined by its base.
Permutations that generalize the bit-reversal permutation by reversing contiguous blocks of bits within the binary representations of their indices can be used to interleave two equal-length sequences of data in-place.
There are two extensions of the bit-reversal permutation to sequences of arbitrary length. These extensions coincide with bit-reversal for sequences whose length is a power of 2, and their purpose is to separate adjacent items in a sequence for the efficient operation of the Kaczmarz algorithm. The first of these extensions, called efficient ordering, operates on composite numbers, and it is based on decomposing the number into its prime components.
The second extension, called EBR (extended b |
https://en.wikipedia.org/wiki/Metastate | In statistical mechanics, the metastate is a probability measure on the
space of all thermodynamic states for a system with quenched randomness. The term metastate, in this context, was first used in by Charles M. Newman and Daniel L. Stein in 1996..
Two different versions have been proposed:
1) The Aizenman-Wehr construction, a canonical ensemble approach,
constructs the metastate through an ensemble of states obtained by varying
the random parameters in the Hamiltonian outside of the volume being
considered.
2) The Newman-Stein metastate, a microcanonical ensemble approach,
constructs an empirical average from a deterministic (i.e., chosen
independently of the randomness) subsequence of finite-volume Gibbs distributions.
It was proved for Euclidean lattices that there always
exists a deterministic subsequence along which the Newman-Stein and
Aizenman-Wehr constructions result in the same metastate. The metastate is
especially useful in systems where deterministic sequences of volumes fail
to converge to a thermodynamic state, and/or there are many competing
observable thermodynamic states.
As an alternative usage, "metastate" can refer to thermodynamic states, where the system is in a metastable state (for example superheated or undercooled liquids, when the actual temperature of the liquid is above or below the boiling or freezing temperature, but the material is still in a liquid state).
References
Statistical mechanics
Condensed matter physics |
https://en.wikipedia.org/wiki/Biconjugate%20gradient%20stabilized%20method | In numerical linear algebra, the biconjugate gradient stabilized method, often abbreviated as BiCGSTAB, is an iterative method developed by H. A. van der Vorst for the numerical solution of nonsymmetric linear systems. It is a variant of the biconjugate gradient method (BiCG) and has faster and smoother convergence than the original BiCG as well as other variants such as the conjugate gradient squared method (CGS). It is a Krylov subspace method. Unlike the original BiCG method, it doesn't require multiplication by the transpose of the system matrix.
Algorithmic steps
Unpreconditioned BiCGSTAB
In the following sections, denotes the dot product of vectors. To solve a linear system , BiCGSTAB starts with an initial guess and proceeds as follows:
Choose an arbitrary vector such that , e.g.,
For
If is accurate enough, i.e., if s is small enough, then set and quit
If is accurate enough, i.e., if is small enough, then quit
Preconditioned BiCGSTAB
Preconditioners are usually used to accelerate convergence of iterative methods. To solve a linear system with a preconditioner , preconditioned BiCGSTAB starts with an initial guess and proceeds as follows:
Choose an arbitrary vector such that , e.g.,
For
If is accurate enough then and quit
If is accurate enough then quit
This formulation is equivalent to applying unpreconditioned BiCGSTAB to the explicitly preconditioned system
with , and . In other words, both left- and right-preconditioning are possible with this formulation.
Derivation
BiCG in polynomial form
In BiCG, the search directions and and the residuals and are updated using the following recurrence relations:
,
,
,
.
The constants and are chosen to be
,
where so that the residuals and the search directions satisfy biorthogonality and biconjugacy, respectively, i.e., for ,
,
.
It is straightforward to show that
,
,
,
where and are th-degree polynomials in . These polynomials satisfy the following recurrence relations:
,
.
Derivation of BiCGSTAB from BiCG
It is unnecessary to explicitly keep track of the residuals and search directions of BiCG. In other words, the BiCG iterations can be performed implicitly. In BiCGSTAB, one wishes to have recurrence relations for
where with suitable constants instead of in the hope that will enable faster and smoother convergence in than .
It follows from the recurrence relations for and and the definition of that
,
which entails the necessity of a recurrence relation for . This can also be derived from the BiCG relations:
.
Similarly to defining , BiCGSTAB defines
.
Written in vector form, the recurrence relations for and are
,
.
To derive a recurrence relation for , define
.
The recurrence relation for can then be written as
,
which corresponds to
.
Determination of BiCGSTAB constants
Now it remains to determine the BiCG constants and and choose a suitable .
In BiCG, with
. |
https://en.wikipedia.org/wiki/Journal%20of%20Nonlinear%20Mathematical%20Physics | The Journal of Nonlinear Mathematical Physics (JNMP) is a mathematical journal published by Atlantis Press. It covers nonlinear problems in physics and mathematics, include applications, with topics such as quantum algebras and integrability; non-commutative geometry; spectral theory; and instanton, monopoles and gauge theory.
Abstracting and indexing
The journal is abstracted and indexed by:
Mathematical Reviews
Zentralblatt MATH
Science Citation Index Expanded
ISI Alerting Services
CompuMath Citation Index
Current Contents/Physical, Chemical and Earth Sciences
Inspec
References
External links
JNMP Journal Website
Mathematics journals
Academic journals established in 1994
English-language journals |
https://en.wikipedia.org/wiki/Make%20Up%20Your%20Mind%20%28song%29 | "Make Up Your Mind" is a song by Canadian rock group Theory of a Deadman and is the second single from their eponymous debut album (2002). Released on January 13, 2003, the song's lyrics were written by the band's lead guitarist and singer Tyler Connolly and Nickelback frontman Chad Kroeger. Kroeger also produced the track along with Joey Moi. It peaked at number 13 on the Canadian Singles chart as well as the Billboard Mainstream Rock chart.
Background and development
"Make Up Your Mind" is a ballad written by lead guitarist and singer Tyler Connolly and Chad Kroeger. Kroeger also produced the track along with Joey Moi.
Release and commercial performance
The song was released in February 2003, as the second single off the band's debut studio album, Theory of a Deadman (2002). It peaked at number 13 on the Canadian Singles chart. In the United States, it reached numbers 36, 38, and 13 on Billboard's Adult Top 40, Alternative Songs (formerly Modern Rock Tracks), and Mainstream Rock charts, respectively. The single also made an appearance on Belgium's Ultratop 50 Singles chart.
Music video
The music video for "Make Up Your Mind" was directed by Gregory Dark and revolves around the dream a woman has of her wedding day, which involves her walking down the aisle as she kisses and touches random guests at an outdoor ceremony. The dream ends when she leaps off a cliff. The band is seen performing on rocky terrain throughout the video.
Track listings
US promo CD
"Make Up Your Mind" (radio mix) – 3:48
"Make Up Your Mind" (reduced guitar mix) – 3:48
"Make Up Your Mind" (acoustic guitar version) – 3:48
European CD single
"Make Up Your Mind" (radio mix)
"Midnight Rider"
Personnel
Credits are lifted from the US promo CD liner notes.
Theory of a Deadman
Tyler Connolly – lead vocals, guitar, writing
Tim Hart – drums, background vocals
Dean Back – bass
David Brenner – guitar
Others
Chad Kroeger – writing, production
Joey Moi – production
Randy Staub – mixing
Charts
Release history
References
Theory of a Deadman songs
2002 songs
2003 singles
604 Records singles
Songs written by Chad Kroeger
Songs written by Tyler Connolly
Music videos directed by Gregory Dark |
https://en.wikipedia.org/wiki/H.%20Scott%20Bierman | Harold Scott Bierman (born c. 1955) is an economist, author, and President of Beloit College in Beloit, Wisconsin.
Bierman graduated from Bates College in Maine in 1977 with a B.A. in mathematics and economics and then received a Ph.D. in economics from the University of Virginia. While serving as a professor at Carleton College in Minnesota for 27 years, he also served as academic dean, chair of the economics department, and faculty president. Bierman has authored several books and written extensively on a wide range of topics, particularly Game Theory, public sector, experimental economics and industrial organization. In 2009 Bierman became the 11th President of Beloit College in Wisconsin. He also serves on the board of trustees at Bates College.
He joined the Carleton faculty in 1982 and was named chair of the economics department in 1991. From 1997 to 2000 he was faculty president, serving as liaison between faculty and the dean and president on curricular and personnel issues. He also founded and chaired the Carleton Faculty Council.
References
21st-century American economists
Living people
1950s births
Bates College alumni
University of Virginia alumni
Presidents of Beloit College |
https://en.wikipedia.org/wiki/Noncommutative%20residue | In mathematics, noncommutative residue, defined independently by M. and , is a certain trace on the algebra of pseudodifferential operators on a compact differentiable manifold that is expressed via a local density. In the case of the circle, the noncommutative residue had been studied earlier by M. and Y. in the context of one-dimensional integrable systems.
See also
Dixmier trace
References
Noncommutative geometry |
https://en.wikipedia.org/wiki/New%20Mathematics%20and%20Natural%20Computation | New Mathematics and Natural Computation is an interdisciplinary journal founded in 2005 and is now published by World Scientific. It covers mathematical uncertainty and its applications to computational, biological and social sciences, with a specific focus on relatively unexplored areas in mathematical uncertainty, such as fuzzy sets and fuzzy logic.
Abstracting and indexing
The journal is abstracted and indexed in:
Mathematical Reviews
Zentralblatt MATH
As of 2013, it had a SCImago Journal Rank in the bottom quartile of journals in applied and computational mathematics, computer science applications, and human-computer interaction.
References
External links
Journal Website
World Scientific academic journals
Mathematics journals
Academic journals established in 2005
English-language journals |
https://en.wikipedia.org/wiki/Open%20Systems%20%26%20Information%20Dynamics | Open Systems & Information Dynamics (OSID) is a journal published by World Scientific. It covers interdisciplinary research in mathematics, physics, engineering and life sciences based upon the fields of information processing, storage and transmission, in both quantum and classical settings, with a theoretical focus. Topics include quantum information theory, open systems, decoherence, complexity theory of classical and quantum systems and other models of information processing.
Abstracting and indexing
The journal is abstracted and indexed in:
COMPUMATH Citation Index
Current Contents/Engineering, Computing and Technology
Current Contents/Physical, Chemical and Earth Sciences
Inspec
ISI Alerting Services
MATH
Science Citation Index Expanded (also known as SciSearch)
Statistical Theory and Method Abstracts
Zentralblatt MATH
References
External links
Journal Website
Mathematics journals
World Scientific academic journals |
https://en.wikipedia.org/wiki/Tate%E2%80%93Shafarevich%20group | In arithmetic geometry, the Tate–Shafarevich group of an abelian variety (or more generally a group scheme) defined over a number field consists of the elements of the Weil–Châtelet group , where is the absolute Galois group of , that become trivial in all of the completions of (i.e., the real and complex completions as well as the -adic fields obtained from by completing with respect to all its Archimedean and non Archimedean valuations ). Thus, in terms of Galois cohomology, can be defined as
This group was introduced by Serge Lang and John Tate and Igor Shafarevich. Cassels introduced the notation , where is the Cyrillic letter "Sha", for Shafarevich, replacing the older notation or .
Elements of the Tate–Shafarevich group
Geometrically, the non-trivial elements of the Tate–Shafarevich group can be thought of as the homogeneous spaces of that have -rational points for every place of , but no -rational point. Thus, the group measures the extent to which the Hasse principle fails to hold for rational equations with coefficients in the field . Carl-Erik Lind gave an example of such a homogeneous space, by showing that the genus 1 curve has solutions over the reals and over all -adic fields, but has no rational points.
Ernst S. Selmer gave many more examples, such as .
The special case of the Tate–Shafarevich group for the finite group scheme consisting of points of some given finite order of an abelian variety is closely related to the Selmer group.
Tate-Shafarevich conjecture
The Tate–Shafarevich conjecture states that the Tate–Shafarevich group is finite. Karl Rubin proved this for some elliptic curves of rank at most 1 with complex multiplication. Victor A. Kolyvagin extended this to modular elliptic curves over the rationals of analytic rank at most 1 (The modularity theorem later showed that the modularity assumption always holds).
Cassels–Tate pairing
The Cassels–Tate pairing is a bilinear pairing , where is an abelian variety and is its dual. Cassels introduced this for elliptic curves, when can be identified with and the pairing is an alternating form. The kernel of this form is the subgroup of divisible elements, which is trivial if the Tate–Shafarevich conjecture is true. Tate extended the pairing to general abelian varieties, as a variation of Tate duality. A choice of polarization on A gives a map from to , which induces a bilinear pairing on with values in , but unlike the case of elliptic curves this need not be alternating or even skew symmetric.
For an elliptic curve, Cassels showed that the pairing is alternating, and a consequence is that if the order of is finite then it is a square. For more general abelian varieties it was sometimes incorrectly believed for many years that the order of is a square whenever it is finite; this mistake originated in a paper by Swinnerton-Dyer, who misquoted one of the results of Tate. Poonen and Stoll gave some examples where the order is twice a square, such as t |
https://en.wikipedia.org/wiki/Matthews%20Batswadi | Maths Batswadi (born 1949), a South African athlete, was the first black athlete to be awarded Springbok Colours, the name then given to South African national sporting colours, after the implementation of the policy of apartheid by the National Party in 1948.
Batswadi received Springbok Colours in 1977 after the national athletics federation, the South African Amateur Athletics Association, deracialised its constitution to allow blacks and whites to compete against each other.
Batswadi won nine national titles from 1975 to 1980 and was renowned for his frontrunning tactics. He was born at Dithakong, near Vryburg in the Northern Cape Province, and retired from athletics competition in 1986.
His stadium record for the 10 000 metres of 28:46.8 at the Germiston Stadium in Ekurhuleni, set at the South African Athletics Championships in 1978, still stands. The Germiston Stadium is located at an altitude of 1600 metres above sea-level and the performance is thus noteworthy. The 1978 National Championships was also significant because it signalled the emergence of Batswadi's namesake, Matthews Motshwarateu, who won the 5000 metres in 14:07.
He won his first national title, the South African men's Cross Country Championships, in Roodepoort in 1975, while he was still working underground in the Western Deep Levels Gold Mine, then the deepest mine in the world. He went on to win a further eight national titles on the track, road and over cross country, with the 1980 SA Half Marathon Championships, being his final national title.
His attempt to run a marathon at the 1981 Sun City marathon was unsuccessful and he withdrew at 15 km.
His personal best time for the 5000m was 13:35 in 1978 and his 10 000m best was 28:00.72 set in Port Elizabeth in April 1980.
After many years in seclusion in Dithakong, Batswadi was located there in good health by another South African athletics great, also bearing the Christian name, Matthews, Matthews Temane in December 2009.
Notes
References
1949 births
Living people |
https://en.wikipedia.org/wiki/Telescoping%20Markov%20chain | In probability theory, a telescoping Markov chain (TMC) is a vector-valued stochastic process that satisfies a Markov property and admits a hierarchical format through a network of transition matrices with cascading dependence.
For any consider the set of spaces . The hierarchical process defined in the product-space
is said to be a TMC if there is a set of transition probability kernels such that
is a Markov chain with transition probability matrix
there is a cascading dependence in every level of the hierarchy,
for all
satisfies a Markov property with a transition kernel that can be written in terms of the 's,
where and
Markov processes |
https://en.wikipedia.org/wiki/Lesley%20Sibner | Lesley Millman Sibner (August 13, 1934 – September 11, 2013) was an American mathematician and professor of mathematics at Polytechnic Institute of New York University. She earned her Bachelors at City College CUNY in Mathematics. She completed her doctorate at Courant Institute NYU in 1964 under the joint supervision of Lipman Bers and Cathleen Morawetz. Her thesis concerned partial differential equations of mixed-type.
Research career
In 1964, Lesley Sibner became an instructor at Stanford University for two years. She was a Fulbright Scholar at the Institut Henri Poincaré in Paris the following year. At this time, in addition to solo work on the Tricomi equation and compressible flows, she began working with her husband Robert Sibner on a problem suggested by Lipman Bers: do there exists compressible flows on a Riemann surface? As part of her work in this direction, she studied differential geometry and Hodge theory eventually proving a nonlinear Hodge–DeRham theorem with Robert Sibner based on a physical interpretation of one-dimensional harmonic forms on closed manifolds. The techniques are related to her prior work on compressible flows. They kept working together on related problems and applications of this important work for many years.
In 1967 she joined the faculty at Polytechnic University in Brooklyn, New York. In 1969 she proved the Morse index theorem for degenerate elliptic operators by extending classical Sturm–Liouville theory.
In 1971-1972 she spent a year at the Institute for Advanced Study where she met Michael Atiyah and Raoul Bott. She realized she could use her knowledge of analysis to solve geometric problems related to the Atiyah–Bott fixed-point theorem. In 1974,
Lesley and Robert Sibner produced a constructive proof of the Riemann–Roch theorem.
Karen Uhlenbeck suggested that Lesley Sibner work on Yang-Mills equation. In 1979-1980 she visited Harvard University where she learned gauge field theory from Clifford Taubes. This lead results about point singularities in the Yang-Mills equation and the Yang–Mills–Higgs equations. Her interest in singularities soon brought her deeper into geometry, leading to a classification of singular connections and to a condition for removing two-dimensional singularities in work with Robert Sibner.
Realizing that instantons could under certain circumstances be viewed as monopoles, the Sibners and Uhlenbeck constructed non-minimal unstable critical points of the Yang-Mills functional over the four-sphere in 1989. She was invited to present this work at the Geometry Festival. She was a Bunting Scholar at the Radcliffe Institute for Advanced Study in 1991. For the subsequent decades, Lesley Sibner focussed on gauge theory and gravitational instantons. Although the research sounds very physical, in fact throughout her career, Lesley Sibner applied physical intuition to prove important geometric and topological theorems.
In 2012 she became a fellow of the American Mathematic |
https://en.wikipedia.org/wiki/Thomas%20Frei%20%28biathlete%29 | Thomas Frei (born 17 April 1980) is a retired Swiss biathlete.
References
External links
Profile on biathlonworld.com
Statistics
1980 births
Living people
Swiss male biathletes
Biathletes at the 2010 Winter Olympics
Olympic biathletes for Switzerland
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/1945%20Campe%C3%B3n%20de%20Campeones | The 1945 Campeon de Campeones was the 4th Mexican Super Cup football one-leg match played on 1 June 1945.
League winners: Club España
Cup winners: Puebla
Match details
References
- Statistics of Mexican Super Cup. (RSSSF)
Campeón de Campeones
Campeón
June 1945 sports events in North America |
https://en.wikipedia.org/wiki/Yang%E2%80%93Mills%E2%80%93Higgs%20equations | In mathematics, the Yang–Mills–Higgs equations are a set of non-linear partial differential equations for a Yang–Mills field, given by a connection, and a Higgs field, given by a section of a vector bundle (specifically, the adjoint bundle). These equations are
with a boundary condition
where
A is a connection on a vector bundle,
D is the exterior covariant derivative,
F is the curvature of that connection,
Φ is a section of that vector bundle,
∗ is the Hodge star, and
[·,·] is the natural, graded bracket.
These equations are named after Chen Ning Yang, Robert Mills, and Peter Higgs. They are very closely related to the Ginzburg–Landau equations, when these are expressed in a general geometric setting.
M.V. Goganov and L.V. Kapitanskii have shown that the Cauchy problem for hyperbolic Yang–Mills–Higgs equations in Hamiltonian gauge on 4-dimensional Minkowski space have a unique global solution with no restrictions at the spatial infinity. Furthermore, the solution has the finite propagation speed property.
Lagrangian
The equations arise as the equations of motion of the Lagrangian density
where is an invariant symmetric bilinear form on the adjoint bundle. This is sometimes written as due to the fact that such a form can arise from the trace on under some representation; in particular here we are concerned with the adjoint representation, and the trace on this representation is the Killing form.
For the particular form of the Yang–Mills–Higgs equations given above, the potential is vanishing. Another common choice is , corresponding to a massive Higgs field.
This theory is a particular case of scalar chromodynamics where the Higgs field is valued in the adjoint representation as opposed to a general representation.
See also
Yang–Mills equations
Scalar chromodynamics
References
M.V. Goganov and L.V. Kapitansii, "Global solvability of the initial problem for Yang-Mills-Higgs equations", Zapiski LOMI 147,18–48, (1985); J. Sov. Math, 37, 802–822 (1987).
Partial differential equations |
https://en.wikipedia.org/wiki/Twisted%20Hessian%20curves | In mathematics, the Twisted Hessian curve represents a generalization of Hessian curves; it was introduced in elliptic curve cryptography to speed up the addition and doubling formulas and to have strongly unified arithmetic. In some operations (see the last sections), it is close in speed to Edwards curves.
Definition
Let K be a field. According to twisted Hessian curves were introduced by Bernstein, Lange,
and Kohel.
The twisted Hessian form in affine coordinates is given by:
and in projective coordinates:
where and and a, d in K
Note that these curves are birationally equivalent to Hessian curves.
The Hessian curve is just a special case of Twisted Hessian curve, with a=1.
Considering the equation a · x3 + y3 + 1 = d · x · y, note that:
if a has a cube root in K, there exists a unique b such that a = b3.Otherwise, it is necessary to consider an extension field of K (e.g., K(a1/3)). Then, since b3 · x3 = bx3, defining t = b · x, the following equation is needed (in Hessian form) to do the transformation:
.
This means that Twisted Hessian curves are birationally equivalent to elliptic curve in Weierstrass form.
Group law
It is interesting to analyze the group law of the elliptic curve, defining the addition and doubling formulas (because the simple power analysis and differential power analysis attacks are based on the running time of these operations). In general, the group law is defined in the following way: if three points lies in the same line then they sum up to zero. So, by this property, the explicit formulas for the group law depend on the curve shape.
Let P = (x1, y1) be a point, then its inverse is −P = (x1/y1, 1/y1) in the plane.
In projective coordinates, let P = (X : Y : Z) be one point, then −P = (X1/Y1 : 1/Y1 : Z) is the inverse of P.
Furthermore, the neutral element (in affine plane) is: θ = (0, −1) and in projective coordinates: θ = (0 : −1 : 1).
In some applications of elliptic curve cryptography and the elliptic curve method of integer factorization (ECM) it is necessary to compute the scalar multiplications of P, say [n]P for some integer n, and they are based on the double-and-add method; so the addition and doubling formulas are needed.
The addition and doubling formulas for this elliptic curve can be defined, using the affine coordinates to simplify the notation:
Addition formulas
Let p = (x1, y1) and Q = (x2, y2); then, R = P + Q = (x3, y3) is given by the following equations:
Doubling formulas
Let P = (x, y); then [2]P = (x1, y1) is given by the following equations:
Algorithms and examples
Here some efficient algorithms of the addition and doubling law are given; they can be important in cryptographic computations, and the projective coordinates are used to this purpose.
Addition
The cost of this algorithm is 12 multiplications, one multiplication by a (constant) and 3 additions.
Example:
let P1 = (1 : −1 : 1) and P2 = (−2 : 1 : 1) be points over a twisted Hessian curve with a=2 and d=- |
https://en.wikipedia.org/wiki/Matchstick%20graph | In geometric graph theory, a branch of mathematics, a matchstick graph is a graph that can be drawn in the plane in such a way that its edges are line segments with length one that do not cross each other. That is, it is a graph that has an embedding which is simultaneously a unit distance graph and a plane graph. For this reason, matchstick graphs have also been called planar unit-distance graphs. Informally, matchstick graphs can be made by placing noncrossing matchsticks on a flat surface, hence the name.
Regular matchstick graphs
Much of the research on matchstick graphs has concerned regular graphs, in which each vertex has the same number of neighbors. This number is called the degree of the graph.
Regular matchstick graphs can have degree 0, 1, 2, 3, or 4. The complete graphs with one, two, and three vertices (a single vertex, a single edge, and a triangle) are all matchstick graphs and are 0-, 1-, and 2-regular respectively. The smallest 3-regular matchstick graph is formed from two copies of the diamond graph placed in such a way that corresponding vertices are at unit distance from each other; its bipartite double cover is the 8-crossed prism graph.
In 1986, Heiko Harborth presented the graph that became known as the Harborth Graph. It has 104 edges and 52 vertices, and is the smallest known example of a 4-regular matchstick graph. It is a rigid graph.
Every 4-regular matchstick graph contains at least 20 vertices. Examples of 4-regular matchstick graphs are currently known for all number of vertices ≥ 52 except for 53, 55, 56, 58, 59, 61 and 62. The graphs with 54, 57, 65, 67, 73, 74, 77 and 85 vertices were first published in 2016. For 52, 54, 57, 60 and 64 vertices only one example is known. Of these five graphs only the one with 60 vertices is flexible, the other four are rigid.
It is not possible for a regular matchstick graph to have degree greater than four. More strongly, every -vertex matchstick graph has vertices of degree four or less. The smallest 3-regular matchstick graph without triangles (girth ≥ 4) has 20 vertices, as proved by Kurz and Mazzuoccolo.
The smallest known example of a 3-regular matchstick graph of girth 5 has 54 vertices and was first presented by Mike Winkler in 2019.
The maximum number of edges a matchstick graph on vertices can have is .
Computational complexity
It is NP-hard to test whether a given undirected planar graph can be realized as a matchstick graph. More precisely, this problem is complete for the existential theory of the reals. provides some easily tested necessary criteria for a graph to be a matchstick graph, but these are not also sufficient criteria: a graph may pass Kurz's tests and still not be a matchstick graph.
It is also NP-complete to determine whether a matchstick graph has a Hamiltonian cycle, even when the vertices of the graph all have integer coordinates that are given as part of the input to the problem.
Combinatorial enumeration
The numbers of distinct (nonis |
https://en.wikipedia.org/wiki/Drummond%20geometry | Drummond Geometry is a trading method consisting of a series of technical analysis tools invented by the Canadian trader Charles Drummond starting in the 1970s and continuing to the present (2021). The method establishes support and resistance areas in multiple time periods and uses these to determine high probability trading areas.
Drummond Geometry consists of the following:
Short term trend lines based on two bars in various configurations.
Short term 3-period displaced moving averages.
An envelope consisting of two trading bands.
Co-ordination of these elements in three or more time frames.
Typical time-frames vary according to the trader's goal:
Daily, weekly, monthly for swing traders. Daily, Monthly, quarterly and yearly for long-term position traders.
15-minute, hourly, and daily for intraday traders Some short-term traders also use 1 to 5 minute charts, tick charts, renko charts,
and other rapidly changing market charting tools.
The usual moving average length for the envelopes and midline is 3-periods.
The method also relies on a moving average based on the "PL Dot". The formula for the PL Dot is the average of the high, low, and close of the last three bars, displaced forward one bar:
Each completed bar generates a new PL dot and this series of dots form a moving average, which is plotted either as a continuous line or as an individual dot on each bar. Both the dot itself and the moving average formed by the dots are by convention called the "PL Dot."
Indicators derived from Drummond Geometry
Indicators developed for the efficient application of P&L charting or Drummond geometry include the assemblage of several P&L lines and levels into groups that represent future support and resistance "zones," which are further classified into "nearby" and "further-out" support and resistance areas.
Other indicators include multiple time period overlays of support and resistance from one time period onto a lower time period, for example from a daily time period onto an hourly or a tick chart, or of monthly and weekly overlays onto a daily chart.
Recent Enhancements
Recent enhancements include the "EOTEM" or "Pipes" indicators which combine momentum indicators, and predicted resistance and support areas. The "Pipes" indicator includes elements from traditional Drummond Geometry as well (the trading bands and the "PL dot" moving average).
Effectiveness
Statistical studies show positive effectiveness of the predicted support and resistance levels established by Drummond Geometry. Individual traders have reported both better and worse results as the trading approach requires traders to recognize signals and take action on them, and that skill varies by individuals.
A raw statistical analysis of the tools has been published; see this research report chart created by a Drummond analyst:
Efficiency of Drummond P&L Lines Holding or Breaking This statistical analysis can be misleading, if not carefully interpreted, caveat emptor. If, |
https://en.wikipedia.org/wiki/Dori%20%28footballer%29 | Dorielton Gomes Nascimento (March 7, 1990), known as Dori, is a Brazilian professional footballer who plays as a forward for Bangladesh Premier League club Bashundhara Kings.
Career statistics
.
Honours
Fluminense
Copa Libertadores runner-up: 2008
Dhaka Abahani
Bangladesh Premier League runner-up: 2021–22
Federation Cup: 2021–22
Independence Cup: 2021–22
Bashundhara Kings
Bangladesh Premier League: 2022–23
Independence Cup: 2022–23
Federation Cup third place: 2022–23
References
External links
1990 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Fluminense FC players
Brasiliense FC players
Changchun Yatai F.C. players
Clube Náutico Capibaribe players
Shaanxi Wuzhou F.C. players
Shaoxing Keqiao Yuejia F.C. players
Inner Mongolia Zhongyou F.C. players
Meizhou Hakka F.C. players
Expatriate men's footballers in China
Brazilian expatriate sportspeople in China
Chinese Super League players
China League One players
Men's association football forwards
Expatriate men's footballers in Bangladesh
Brazilian expatriate sportspeople in Bangladesh |
https://en.wikipedia.org/wiki/Doubling-oriented%20Doche%E2%80%93Icart%E2%80%93Kohel%20curve | In mathematics, the doubling-oriented Doche–Icart–Kohel curve is a form in which an elliptic curve can be written. It is a special case of Weierstrass form and it is also important in elliptic-curve cryptography because the doubling speeds up considerably (computing as composition of 2-isogeny and its dual).
It has been introduced by Christophe Doche, Thomas Icart, and David R. Kohel in Efficient Scalar Multiplication by Isogeny Decompositions.
Definition
Let be a field and let . Then, the Doubling-oriented Doche–Icart–Kohel curve with parameter a in affine coordinates is represented by:
Equivalently, in projective coordinates:
with and .
Notice that, since this curve is a special case of Weierstrass form, transformations to the most common form of elliptic curve (Weierstrass form) are not needed.
Group law
It is interesting to analyze the group law in elliptic curve cryptography, defining the addition and doubling formulas, because these formulas are necessary to compute multiples of points [n]P (see Exponentiation by squaring). In general, the group law is defined in the following way: if three points lies in the same line then they sum up to zero. So, by this property, the group laws are different for every curve shape.
In this case, since these curves are special cases of Weierstrass curves, the addition is just the standard addition on Weierstrass curves. On the other hand, to double a point, the standard doubling formula can be used, but it would not be so fast.
In this case, the neutral element is (in projective coordinates), for which . Then, if is a non-trivial element (), then the inverse of this point (by addition) is –P=(x,-y).
Addition
In this case, affine coordinates will be used to define the addition formula:
(x1,y1)+(x2,y2)=(x3,y3) where
x3 = (-x13+(x2-a)x12+(x22+2ax2)x1+(y12-2y2y1+(-x23-ax22+y22)))/(x12-2x2x1+x22)
y3 = ((-y1+2y2)x13+(-ay1+(-3y2x2+ay2))x12+((3x22+2ax2)y1-2ay2x2)x1+(y13-3y2y12+(-2x23-ax22+3y22)y1+(y2x23+ay2x22-y23)))/(-x13+3x2x12-3x22x1+x23)
Doubling
2(x1,y1)=(x3,y3)
x3 = 1/(4y12)x14-8a/y12x12+64a2/y12
y3 = 1/(8y13)x16+((-a2+40a)/(4y13))x14+((ay12+(16a3-640a2))/(4y13))x12+((-4a2y12-512a3)/y13)
Algorithms and examples
Addition
The fastest addition is the following one (comparing with the results given in: http://hyperelliptic.org/EFD/g1p/index.html), and the cost that it takes is 4 multiplications, 4 squaring and 10 addition.
A = Y2-Y1
AA = A2
B = X2-X1
CC = B2
F = X1CC
Z3 = 2CC
D = X2Z3
ZZ3 = Z32
X3 = 2(AA-F)-aZ3-D
Y3 = ((A+B)2-AA-CC)(D-X3)-Y2ZZ3
Example
Let . Let P=(X1,Y1)=(2,1), Q=(X2,Y2)=(1,-1) and a=1, then
A=2
AA=4
B=1
CC=1
F=2
Z3=4
D=4
ZZ3=16
X3=-4
Y3=336
Thus, P+Q=(-4:336:4)
Doubling
The following algorithm is the fastest one (see the following link to compare: http://hyperelliptic.org/EFD/g1p/index.html), and the cost that it takes is 1 multiplication, 5 squaring and 7 additions.
A = X12
B = A-a16
C = a2A
YY = Y12
YY2 = 2YY
Z3 = 2YY2
X3 = B2 |
https://en.wikipedia.org/wiki/List%20of%20gardens%20in%20Italy | This is a list of gardens in Italy. The Italian garden is stylistically based on symmetry, axial geometry and on the principle of imposing order over nature. It influenced the history of gardening, especially French gardens and English gardens. The Italian garden was influenced by Roman gardens and Italian Renaissance gardens.
A
Arboreto di Arco
Arboreto Pascul
Arboretum Apenninicum
B
Bardini Gardens
Biennale Gardens
Boboli Gardens
C
Cortile del Belvedere
D
Ducal Palace of Colorno
Ducal Palace of Sassuolo
F
Farnese Gardens
La Foce
G
Garden of Eden
Garden of Ninfa
Gardens of Augustus
Gardens of Bomarzo
Gardens of Lucullus
Gardens of Maecenas
Giardini della Biennale
Giardini della rotonda di Padova
Giardini Papadopoli
Giardini Ravino
Giardino Alpino "Antonio Segni"
Giardino dei Semplici
Giardino dell'Iris
Giardino delle Rose
Giardino Montano dell' Orecchiella
Giardino Montano Linasia
I
Isola Bella (Lago Maggiore)
Isola del Garda
Isola Madre
L
Lowe Gardens
M
Minerva's Garden
Moreno Gardens
La Mortella
O
Orange Garden
P
Palace of Portici
Palazzo Giusti
Palazzo Pfanner
Pallanca exotic gardens
Parco Giardino Sigurtà
Park of the Monsters
The Parks of Genoa
R
Royal Palace of Caserta
T
Tarot Garden
Torrecchia Vecchia
Trauttmansdorff Castle Gardens
V
Varramista Gardens
Villa Aldobrandini
Villa Arrighetti
Villa Barbarigo (Valsanzibio)
Villa Borghese gardens
Villa Carlotta
Villa Cetinale
Villa Cicogna Mozzoni
Villa Cimbrone
Villa d'Este
Villa del Balbianello
Villa Della Porta Bozzolo
Villa di Castello
Villa di Corliano
Villa di Pratolino
Villa di Quarto
Villa Durazzo-Pallavicini
Villa Gamberaia
Villa Lancellotti
Villa Lante
Villa Ludovisi
Villa Marlia
Villa Massei
Villa Medici at Cafaggiolo
Villa Medici at Careggi
Villa Medici in Fiesole
Villa Palmieri
Villa San Michele
W
Winter Gardens
See also
List of botanical gardens in Italy
List of Grandi Giardini Italiani
List of garden types
Giardino all'italiana
Italian Renaissance garden
01
Italy
Gardens |
https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Zassenhaus%20algorithm | In mathematics, in particular in computational algebra, the Berlekamp–Zassenhaus algorithm is an algorithm for factoring polynomials over the integers, named after Elwyn Berlekamp and Hans Zassenhaus. As a consequence of Gauss's lemma, this amounts to solving the problem also over the rationals.
The algorithm starts by finding factorizations over suitable finite fields using Hensel's lemma to lift the solution from modulo a prime p to a convenient power of p. After this the right factors are found as a subset of these.
The worst case of this algorithm is exponential in the number of factors.
improved this algorithm by using the LLL algorithm, substantially reducing the time needed to choose the right subsets of mod p factors.
References
.
.
.
.
.
.
External links
See also
Berlekamp's algorithm
Computer algebra |
https://en.wikipedia.org/wiki/Andrew%20Gelman | Andrew Eric Gelman (born February 11, 1965) is an American statistician and professor of statistics and political science at Columbia University.
Gelman received bachelor of science degrees in mathematics and in physics from MIT, where he was a National Merit Scholar, in 1986. He then received a master of science in 1987 and a doctor of philosophy in 1990, both in statistics from Harvard University, under the supervision of Donald Rubin.
Career
Gelman is the Higgins Professor of Statistics and Professor of Political Science and the Director of the Applied Statistics Center at Columbia University. He is a major contributor to statistical philosophy and methods especially in Bayesian statistics and hierarchical models.
He is one of the leaders of the development of the statistical programming framework Stan.
Perspective on Statistical Inference and Hypothesis Testing
Gelman's approach to statistical inference emphasizes studying variation and the associations between data, rather than searching for statistical significance.
Gelman says his approach to hypothesis testing is "(nearly) the opposite of the conventional view" of what is typical for statistical inference. While the standard approach may be seen as having the goal of rejecting a null hypothesis, Gelman argues that you can't learn much from a rejection. On the other hand, a non-rejection tells you something: "[it] tells you that your study is noisy, that you don't have enough information in your study to identify what you care about—even if the study is done perfectly, even if measurements are unbiased and your sample is representative of your population, etc. That can be some useful knowledge, it means you're off the hook trying to explain some pattern that might just be noise." Gelman also works within the context of larger confirmationist and falsificationist paradigms of science.
Gelman's unique approach to statistical inference is a major recurring theme of his work.
Popular press
Gelman is notable for his efforts to make political science and statistics more accessible to journalists and to the public. He was one of the primary authors of "The Monkey Cage", blog published by The Washington Post. The blog is dedicated to providing informed commentary on politics and making political science more accessible.
Gelman also keeps his own blog which deals with statistical practices in social science. He frequently writes about Bayesian statistics, displaying data, and interesting trends in social science. According to The New York Times, on the blog "he posts his thoughts on best statistical practices in the sciences, with a frequent emphasis on what he sees as the absurd and unscientific... He is respected enough that his posts are well read; he is cutting enough that many of his critiques are enjoyed with a strong sense of schadenfreude."
Gelman is a prominent critic of poor methodological work and he identifies such work as contributing to the replication crisis.
Honors
He |
https://en.wikipedia.org/wiki/Mathematical%20sciences | The mathematical sciences are a group of areas of study that includes, in addition to mathematics, those academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper.
Statistics, for example, is mathematical in its methods but grew out of bureaucratic and scientific observations, which merged with inverse probability and then grew through applications in some areas of physics, biometrics, and the social sciences to become its own separate, though closely allied, field. Theoretical astronomy, theoretical physics, theoretical and applied mechanics, continuum mechanics, mathematical chemistry, actuarial science, computer science, computational science, data science, operations research, quantitative biology, control theory, econometrics, geophysics and mathematical geosciences are likewise other fields often considered part of the mathematical sciences.
Some institutions offer degrees in mathematical sciences (e.g. the United States Military Academy, Stanford University, and University of Khartoum) or applied mathematical sciences (for example, the University of Rhode Island).
See also
References
External links
Division of Mathematical Sciences at the National Science Foundation, including a list of disciplinary areas supported
Faculty of Mathematical Sciences at University of Khartoum, offers academic degrees in Mathematics, Computer Sciences and Statistics
Programs of the Mathematical Sciences Research Institute
Research topics studied at the Isaac Newton Institute for Mathematical Sciences
Mathematical Sciences in the U.S. FY 2016 Budget; a report from the AAAS
Applied mathematics |
https://en.wikipedia.org/wiki/Adolph%20P.%20Yushkevich | Adolph-Andrei Pavlovich Yushkevich (; 15 July 1906 – 17 July 1993) was a Soviet historian of mathematics, leading expert in medieval mathematics of the East and the work of Leonhard Euler. He is a winner of George Sarton Medal by the History of Science Society for a lifetime of scholarly achievement.
Biography
Yushkevich was born in Odessa, Russian Empire to a Jewish family. His father was Pavel Yushkevich a Sorbonne-educated philosopher and a mathematician, active in politics as a Menshevik who was in "ssylka" (deportation) in Siberia, and later in France. His uncle, Semen Solomonovich Yushkevich was a well-known Jewish writer. Yushkevich grew up in St. Petersburg and later in Paris where he lived until Russian Revolution of 1917, when Yushkevich family returned to Odessa. For a time, Sofya Yanovskaya was one of Adolf's teachers in a gymnasium.
In 1923, Yushkevich started his studies at the Department of Mathematics of Moscow State University. His doctoral advisor was Dmitri Egorov, but he was awarded a Ph.D. degree without a defense. From 1930 to 1952 he worked at Bauman Technical University where he rose to professorship in 1940 and head of the department of mathematics in 1941. In the years 1941–1943 he was evacuated to Izhevsk, together with the whole Bauman Technical University. Starting 1952, he became a full-time researcher at Vavilov Institute of Natural History, where he worked until retirement.
Yushkevich published over 300 works in history of mathematics. For his work, he received numerous honors, including George Sarton Medal (1978), Koyré Medal by the International Academy of the History of Science (1971), May Prize (1989) by the International Commission on the History of Mathematics, Prize of the German Academy of Sciences Berlin (twice, in 1978 and 1983), and Prize of the French Academy of Sciences (1982). He was a member of several foreign academies, including German Academy of Sciences Leopoldina, and president of the International Academy of the History of Science (1965–1968).
Yushkevich died in Moscow in 1993. He bequeathed his personal library to the Vavilov Institute.
References
I.G. Bashmakova, A.O. Gelfond, B.A. Rosenfeld, K.A. Rybnikov, S.A. Yanovskaya, Adolf Pavlovich Yushkevich is 60 (in Russian), Russian Mathematical Surveys 22 (1967), 187–194.
I.G. Bashmakova et al. Adolf-Andrei Pavlovich Yushkevich (in memoriam), Russian Mathematical Surveys, 49:4 (1994), 75–77.
Adolf-Andrei Pavlovich Yushkevich (in Russian).
Boris Rosenfeld, Memoirs (in Russian).
K. Shelma, "An interview with Adolf-Andrei Pavlovich Iushkevich", in Voprosy Istorii Estestvoznaniya i Techniki (ed. by B.G. Yudin), Vol. 94, No. 1-2 (1994), 26–42.
S.S. Demidov, T.A. Tokareva, Adolf P. Yushkevich (1906–1993) and formation of the society of mathematical historians (in Russian), in Proc. 6-th Tambov All-Russian Conference in History of Mathematics, Pershin Publ., 2006, 9–28.
External links
A.P. Yushkevich, The Lusin Affair.
A |
https://en.wikipedia.org/wiki/Tatsuki%20Kobayashi | is a Japanese football player currently playing for Thespakusatsu Gunma.
Career statistics
Updated to 23 February 2019.
References
External links
Profile at Thespakusatsu Gunma
1985 births
Living people
Komazawa University alumni
Association football people from Tochigi Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Shonan Bellmare players
Thespakusatsu Gunma players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Crime%20in%20London | Figures on crime in London are based primarily on two sets of statistics: the Crime Survey for England and Wales (CSEW) and police recorded crime data. Greater London is generally served by three police forces; the Metropolitan Police which is responsible for policing the vast majority of the capital, the City of London Police which is responsible for The Square Mile of the City of London and the British Transport Police, which polices the national rail network and the London Underground. A fourth police force in London, the Ministry of Defence Police, do not generally become involved with policing the general public. London also has a number of small constabularies for policing parks. Within the Home Office crime statistic publications, Greater London is referred to as the London Region.
Current trends
The Mayor's Office for Policing & Crime (MOPAC) prepares quarterly performance reports for policing and crime in the Greater London area. Q1 2021 showed a reduction in all crime in London with the exception of hate crimes and domestic violence. Total notifiable offences (TNO) had decreased by 17.2% when compared to the same quarter in 2019/20 (-20,465) and had decreased by 8.1% (17,148) compared to Q2 2020. These figures include COVID-19 lockdown periods.
The Office for National Statistics data between June 2016 and March 2020 showed per person crime had increased by 31% in England and by a lower margin of 18% in London since 2016. These statistics only count crime recorded by police, and it's estimated by that overall crime continues to decrease.
The increase in crime recorded in London is not uniform across different types of offence. For example, while homicides increased over the period by 23% in London compared to 8% across England, violence against the person in general increased by 2% in London compared to 7% across England. Over the same period, sexual offences recorded by police in London fell by 2% while in England they remained flat; robbery increased by 16% in London, compared to 6% across England. Otherwise, the increase in London over 2019/20 was largely driven by an increase in theft offences, including burglary. Theft is stealing from a person without the use or threat of force, robbery is stealing by using force or the threat of force on someone and burglary is entering a property illegally in order to steal. Theft offences account for 50% of the Metropolitan Police's recorded crimes and increased by 4% last year. Across England, they fell 5%.
Over the longer period, the trend is similar. Since 2016, the number of police recorded theft offences (without force or threat) per person has increased by 23% in London, compared to a rise of 7% in England more widely, accounting for much of the recorded increase in crime in the capital.
His Majesty's Inspectorate of Constabulary and Fire & Rescue Services (HMICFRS) independently assess the effectiveness and efficiency of police forces. In 2018, they reported the Met recorded just 89. |
https://en.wikipedia.org/wiki/Kenneth%20O.%20May%20Prize | Kenneth O. May Prize and Medal in history of mathematics is an award of the International Commission on the History of Mathematics (ICHM) "for the encouragement and promotion of the history of mathematics internationally". It was established in 1989 and is named in honor of Kenneth O. May, the founder of ICHM. Since then, the award is given every four years, at the ICHM congress.
Kenneth O. May Prize winners
Source: (1989-2005) A Brief History of the Kenneth O. May Prize
2017: Eberhard Knobloch and Roshdi Rashed
2013: Menso Folkerts and Jens Høyrup
2009: Ivor Grattan-Guinness and Radha Charan Gupta
2005: Henk J. M. Bos
2001: Ubiratàn D'Ambrosio and Lam Lay Yong
1997: René Taton
1993: Christoph Scriba and Hans Wussing
1989: Dirk Struik and Adolph P. Yushkevich
See also
List of history awards
List of mathematics awards
References
A Brief History of the Kenneth O. May Prize in the History of Mathematics
BLC Newsletter August 2009
Mathematics awards
History of science awards
Awards established in 1989 |
https://en.wikipedia.org/wiki/Cipolla%27s%20algorithm | In computational number theory, Cipolla's algorithm is a technique for solving a congruence of the form
where , so n is the square of x, and where is an odd prime. Here denotes the finite field with elements; . The algorithm is named after Michele Cipolla, an Italian mathematician who discovered it in 1907.
Apart from prime moduli, Cipolla's algorithm is also able to take square roots modulo prime powers.
Algorithm
Inputs:
, an odd prime,
, which is a square.
Outputs:
, satisfying
Step 1 is to find an such that is not a square. There is no known deterministic algorithm for finding such an , but the following trial and error method can be used. Simply pick an and by computing the Legendre symbol one can see whether satisfies the condition. The chance that a random will satisfy is . With large enough this is about . Therefore, the expected number of trials before finding a suitable is about 2.
Step 2 is to compute x by computing within the field extension . This x will be the one satisfying
If , then also holds. And since p is odd, . So whenever a solution x is found, there's always a second solution, -x.
Example
(Note: All elements before step two are considered as an element of and all elements in step two are considered as elements of .)
Find all x such that
Before applying the algorithm, it must be checked that is indeed a square in . Therefore, the Legendre symbol has to be equal to 1. This can be computed using Euler's criterion: This confirms 10 being a square and hence the algorithm can be applied.
Step 1: Find an a such that is not a square. As stated, this has to be done by trial and error. Choose . Then becomes 7. The Legendre symbol has to be −1. Again this can be computed using Euler's criterion: So is a suitable choice for a.
Step 2: Compute in :
So is a solution, as well as . Indeed,
Proof
The first part of the proof is to verify that is indeed a field. For the sake of notation simplicity, is defined as . Of course, is a quadratic non-residue, so there is no square root in . This can roughly be seen as analogous to the complex number i.
The field arithmetic is quite obvious. Addition is defined as
.
Multiplication is also defined as usual. With keeping in mind that , it becomes
.
Now the field properties have to be checked.
The properties of closure under addition and multiplication, associativity, commutativity and distributivity are easily seen. This is because in this case the field is somewhat resembles the field of complex numbers (with being the analogon of i).
The additive identity is , or more formally : Let , then
.
The multiplicative identity is , or more formally :
.
The only thing left for being a field is the existence of additive and multiplicative inverses. It is easily seen that the additive inverse of is , which is an element of , because . In fact, those are the additive inverse elements of x and y. For showing that every non-zero element has a multiplicative in |
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