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https://en.wikipedia.org/wiki/Andr%C3%A1s%20Jancs%C3%B3 | András Jancsó (born 22 April 1996) is a Hungarian football player who plays for Szombathelyi Haladás.
Club statistics
Updated to games played as of 8 December 2018.
References
HLSZ
1996 births
Living people
Footballers from Szombathely
Hungarian men's footballers
Hungary men's youth international footballers
Hungary men's under-21 international footballers
Men's association football midfielders
Szombathelyi Haladás footballers
Soproni VSE players
Gyirmót FC Győr players
Szentlőrinci SE footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
21st-century Hungarian people |
https://en.wikipedia.org/wiki/Chang%27s%20model | In mathematical set theory, Chang's model is the smallest inner model of set theory closed under countable sequences. It was introduced by . More generally Chang introduced the smallest inner model closed under taking sequences of length less than κ for any infinite cardinal κ. For κ countable this is the constructible universe, and for κ the first uncountable cardinal it is Chang's model.
Chang's model is a model of ZF. Kenneth Kunen proved in that the axiom of choice fails in Chang's model provided there are sufficient large cardinals, such as uncountable many measurable cardinals.
References
Inner model theory |
https://en.wikipedia.org/wiki/V%C3%ADctor%20Aguirre-Torres | Victor M. A. Aguirre-Torres is an internationally recognized econometrician, professor and researcher of the Academic Department of Statistics at the Instituto Tecnológico Autónomo de México (ITAM). He is a member of the Mexican Academy of Sciences (Academia Mexicana de Ciencias). Since 1991, he has formed a significant number of leaders in México, with nearly 46 generations to his credit.
Besides his family, he has a passion for teaching and research in statistics and econometrics. He has over 33 publications in research journals and 23 distinctions, among which stand out, those obtained as the Best Paper Award of The 2009 International Conference of Computational Statistics and Data Engineering, in London, England;. He has been a member of the National Accreditation Board of Research (SNI), area of Physics and Mathematics, since 1988.
In 1982, he received the Ph.D. degree in Statistics from North Carolina State University (NCSU). Before that he obtained a Master of Statistics from NCSU and a Master of Science in mathematics from the National Polytechnic Institute, Mexico City. His alma mater is the National Polytechnic Institute, Mexico City, where he earned a Physics and Mathematics degree.
He has given more than 33 international seminars and has been invited to over 32 talks and 47 contributed talks.
Among his achievements, he was leader in the creation of the Statistics Group at the Center for Research in Mathematics in Guanajuato (CIMAT).
Awards
Elected member of the National Accreditation Board of Research (SNI), level 2. Area of Physics and Mathematics for the periods: 2014-2018 and 2010–2013.
Best Paper Award of The 2009 International Conference of Computational Statistics and Data Engineering. London, England. 2009
Elected member of the National Accreditation Board of Research (SNI), level 1. Area of Physics and Mathematics for the periods: 2006–2009, 2002–2005, 1999–2001, 1996–1999, 1988–1991.
Outstanding Academic Performance Award, ITAM in the years: 1997, 1996, 1994, 1993, 1992, 1991.
Outstanding Academic Performance, Continuing Education, ITAM 2000.
Mexico's National University Recognition for Coordinating the Masters Program in Statistics and OR. 1997.
Elected member of the National Accreditation Board of Research (SNI), level Candidate. Area of Physics and Mathematics, 1985–1988.
Elected member of Phi-Kappa-Phi Honor Society Mathematics, NCSU Chapter, USA.
Elected Gertrude M. Cox Fellow, Statistics Department, NCSU, USA.
Mexico's National Science Foundation Scholarship for Doctoral Studies, 1979–1982.
Elected Best Math Student of the National Polytechnic Institute, Mexican Institute of Culture, 1977.
External links
Faculty's website at Instituto Tecnológico Autónomo de México.
References
1954 births
Living people
20th-century Mexican economists
Academic staff of the Instituto Tecnológico Autónomo de México
North Carolina State University alumni
Econometricians
21st-century Mexican economists |
https://en.wikipedia.org/wiki/Glossary%20of%20set%20theory | This is a glossary of set theory.
Greek
!$@
A
B
C
D
E
F
G
H
I
See proper, below.
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
XYZ
See also
Glossary of Principia Mathematica
List of topics in set theory
Set-builder notation
References
Set theory
Set theory
Wikipedia glossaries using description lists |
https://en.wikipedia.org/wiki/Ivan%20Brki%C4%87%20%28footballer%29 | Ivan Brkić (born 29 June 1995) is a Croatian professional footballer who plays as a goalkeeper for Azerbaijan Premier League club Neftçi.
Career statistics
Club
1 One appearance in 2015–16 relegation play-offs.
References
External links
Ivan Brkić at Sofascore
1995 births
Living people
Sportspeople from Koprivnica
Men's association football goalkeepers
Croatian men's footballers
Croatia men's under-21 international footballers
NK Istra 1961 players
NK Lokomotiva Zagreb players
NK Imotski players
HNK Cibalia players
HŠK Zrinjski Mostar players
Riga FC players
Neftçi PFK players
Croatian Football League players
First Football League (Croatia) players
Premier League of Bosnia and Herzegovina players
Latvian Higher League players
Azerbaijan Premier League players
Croatian expatriate men's footballers
Expatriate men's footballers in Bosnia and Herzegovina
Croatian expatriate sportspeople in Bosnia and Herzegovina
Expatriate men's footballers in Latvia
Croatian expatriate sportspeople in Latvia
Expatriate men's footballers in Azerbaijan
Croatian expatriate sportspeople in Azerbaijan |
https://en.wikipedia.org/wiki/Place-permutation%20action | In mathematics, there are two natural interpretations of the place-permutation action of symmetric groups, in which the group elements act on positions or places. Each may be regarded as either a left or a right action, depending on the order in which one chooses to compose permutations. There are just two interpretations of the meaning of "acting by a permutation " but these lead to four variations, depending whether maps are written on the left or right of their arguments. The presence of so many variations often leads to confusion. When regarding the group algebra of a symmetric group as a diagram algebra it is natural to write maps on the right so as to compute compositions of diagrams from left to right.
Maps written on the left
First we assume that maps are written on the left of their arguments, so that compositions take place from right to left. Let be the symmetric group on letters, with compositions computed from right to left.
Imagine a situation in which elements of act on the “places” (i.e., positions) of something. The places could be vertices of a regular polygon of sides, the tensor positions of a simple tensor, or even the inputs of a polynomial of variables. So we have places, numbered in order from 1 to , occupied by objects that we can number . In short, we can regard our items as a word of length in which the position of each element is significant. Now what does it mean to act by “place-permutation” on ? There are two possible answers:
an element can move the item in the th place to the th place, or
it can do the opposite, moving an item from the th place to the th place.
Each of these interpretations of the meaning of an “action” by (on the places) is equally natural, and both are widely used by mathematicians. Thus, when encountering an instance of a "place-permutation" action one must take care to determine from the context which interpretation is intended, if the author does not give specific formulas.
Consider the first interpretation. The following descriptions are all equivalent ways to describe the rule for the first interpretation of the action:
For each , move the item in the th place to the th place.
For each , move the item in the th place to the th place.
For each , replace the item in the th position by the one that was in the th place.
This action may be written as the rule .
Now if we act on this by another permutation then we need to first relabel the items by writing . Then takes this to This proves that the action is a left action: .
Now we consider the second interpretation of the action of , which is the opposite of the first. The following descriptions of the second interpretation are all equivalent:
For each , move the item in the th place to the th place.
For each , move the item in the th place to the th place.
For each , replace the item in the th position by the one that was in the th place.
This action may be written as the rule .
In order to act on this by ano |
https://en.wikipedia.org/wiki/%CE%97%20set | In mathematics, an η set (eta set) is a type of totally ordered set introduced by that generalizes the order type η of the rational numbers.
Definition
If is an ordinal then an set is a totally ordered set in which for any two subsets and of cardinality less than , if every element of is less than every element of then there is some element greater than all elements of and less than all elements of .
Examples
The only non-empty countable η0 set (up to isomorphism) is the ordered set of rational numbers.
Suppose that κ = ℵα is a regular cardinal and let X be the set of all functions f from κ to {−1,0,1} such that if f(α) = 0 then f(β) = 0 for all β > α, ordered lexicographically. Then X is a ηα set. The union of all these sets is the class of surreal numbers.
A dense totally ordered set without endpoints is an ηα set if and only if it is ℵα saturated.
Properties
Any ηα set X is universal for totally ordered sets of cardinality at most ℵα, meaning that any such set can be embedded into X.
For any given ordinal α, any two ηα sets of cardinality ℵα are isomorphic (as ordered sets). An ηα set of cardinality ℵα exists if ℵα is regular and Σβ<α 2ℵβ ≤ ℵα.
References
English translation in
Order theory |
https://en.wikipedia.org/wiki/Kingman%27s%20subadditive%20ergodic%20theorem | In mathematics, Kingman's subadditive ergodic theorem is one of several ergodic theorems. It can be seen as a generalization of Birkhoff's ergodic theorem.
Intuitively, the subadditive ergodic theorem is a kind of random variable version of Fekete's lemma (hence the name ergodic). As a result, it can be rephrased in the language of probability, e.g. using a sequence of random variables and expected values. The theorem is named after John Kingman.
Statement of theorem
Let be a measure-preserving transformation on the probability space , and let be a sequence of functions such that (subadditivity relation). Then
for -a.e. x, where g(x) is T-invariant. If T is ergodic, then g(x) is a constant.
Applications
Taking recovers Birkhoff's pointwise ergodic theorem.
Kingman's subadditive ergodic theorem can be used to prove statements about Lyapunov exponents. It also has applications to percolations and probability/random variables.
References
External links
Theorem proof (Steele)
Ergodic theory |
https://en.wikipedia.org/wiki/B%C3%A9zier%20spline | Depending on the author, Bézier spline may refer to:
a Bézier curve or
a composite Bézier curve
Mathematics disambiguation pages |
https://en.wikipedia.org/wiki/Don%C3%A1t%20Szivacski | Donát Szivacski (born 18 January 1997 in Kecskemét) is a Hungarian football player who currently plays for Vasas SC.
Club statistics
Updated to games played as of 17 February 2019.
References
MLSZ
1997 births
Living people
Footballers from Szeged
Hungarian men's footballers
Men's association football midfielders
Kecskeméti TE players
Vasas SC players
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/Kawkab%2C%20Hama | Kawkab () also known as Kokab is a Syrian village located in the Suran Subdistrict in Hama District. According to the Syria Central Bureau of Statistics (CBS), Kawkab had a population of 1,639 in the 2004 census.
References
Populated places in Hama District |
https://en.wikipedia.org/wiki/Shiraaya | Shiraaya () is a Syrian village located in the Subdistrict of the Hama District in the Hama Governorate. According to the Syria Central Bureau of Statistics (CBS), Shiraaya had a population of 100 in the 2004 census.
References
Populated places in Hama District |
https://en.wikipedia.org/wiki/Conductor%20of%20an%20elliptic%20curve | In mathematics, the conductor of an elliptic curve over the field of rational numbers (or more generally a local or global field) is an integral ideal, which is analogous to the Artin conductor of a Galois representation. It is given as a product of prime ideals, together with associated exponents, which encode the ramification in the field extensions generated by the points of finite order in the group law of the elliptic curve. The primes involved in the conductor are precisely the primes of bad reduction of the curve: this is the Néron–Ogg–Shafarevich criterion.
Ogg's formula expresses the conductor in terms of the discriminant and the number of components of the special fiber over a local field, which can be computed using Tate's algorithm.
History
The conductor of an elliptic curve over a local field was implicitly studied (but not named) by in the form of an integer invariant ε+δ which later turned out to be the exponent of the conductor.
The conductor of an elliptic curve over the rationals was introduced and named by as a constant appearing in the functional equation of its L-series, analogous to the way the conductor of a global field appears in the functional equation of its zeta function. He showed that it could be written as a product over primes with exponents given by order(Δ) − μ + 1, which by Ogg's formula is equal to ε+δ. A similar definition works for any global field. Weil also suggested that the conductor was equal to the level of a modular form corresponding to the elliptic curve.
extended the theory to conductors of abelian varieties.
Definition
Let E be an elliptic curve defined over a local field K and p a prime ideal of the ring of integers of K. We consider a minimal equation for E: a generalised Weierstrass equation whose coefficients are p-integral and with the valuation of the discriminant νp(Δ) as small as possible. If the discriminant is a p-unit then E has good reduction at p and the exponent of the conductor is zero.
We can write the exponent f of the conductor as a sum ε + δ of two terms, corresponding to the tame and wild ramification. The tame ramification part ε is defined in terms of the reduction type: ε=0 for good reduction, ε=1 for multiplicative reduction and ε=2 for additive reduction. The wild ramification term δ is zero unless p divides 2 or 3, and in the latter cases it is defined in terms of the wild ramification of the extensions of K by the division points of E by Serre's formula
Here M is the group of points on the elliptic curve of order l for a prime l, P is the Swan representation, and G the Galois group of a finite extension of K such that the points of M are defined over it (so that G acts on M)
Ogg's formula
The exponent of the conductor is related to other invariants of the elliptic curve by Ogg's formula:
where n is the number of components (without counting multiplicities) of the singular fibre of the Néron minimal model for E. (This is sometimes used as a definition of the |
https://en.wikipedia.org/wiki/Amaral%20%28footballer%2C%20born%201988%29 | Mauricio Azevedo Alves (born May 1, 1988), better known as Amaral, is a Brazilian football defensive midfielder who currently plays for Moto Club.
Career
Career statistics
(Correct )
according to combined sources on the Flamengo official website and Flaestatística.
Honours
Flamengo
Copa do Brasil: 2013
Campeonato Carioca: 2014
Vitória
Campeonato Baiano: 2016
References
External links
1988 births
Living people
Brazilian men's footballers
Men's association football midfielders
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
CR Flamengo footballers
Nova Iguaçu FC players
Quissamã Futebol Clube players
Esporte Clube Vitória players
Boa Esporte Clube players
Centro Sportivo Alagoano players
Moto Club de São Luís players |
https://en.wikipedia.org/wiki/Corank | In mathematics, corank is complementary to the concept of the rank of a mathematical object, and may refer to the dimension of the left nullspace of a matrix, the dimension of the cokernel of a linear transformation of a vector space, or the number of elements of a matroid minus its rank.
Left nullspace of a matrix
The corank of an matrix is where is the rank of the matrix. It is the dimension of the left nullspace and of the cokernel of the matrix.
Cokernel of a linear transformation
Generalizing matrices to linear transformations of vector spaces, the corank of a linear transformation is the dimension of the cokernel of the transformation, which is the quotient of the codomain by the image of the transformation.
Matroid
For a matroid with elements and matroid rank , the corank or nullity of the matroid is . In the case of linear matroids this coincides with the matrix corank. In the case of graphic matroids the corank is also known as the circuit rank or cyclomatic number.
Linear algebra
Matroid theory |
https://en.wikipedia.org/wiki/2014%E2%80%9315%20Associa%C3%A7%C3%A3o%20Acad%C3%A9mica%20de%20Coimbra%20%E2%80%93%20O.A.F.%20season | This article shows Associação Académica de Coimbra – O.A.F.'s player statistics and all matches that the club plays during the 2014–15 season. This season will be their 13th consecutive season in the top-flight of Portuguese football.
Competitions
Pre-season
Primeira Liga
League table
Results by round
Matches
Taça de Portugal
Third round
Taça da Liga
Third round
Players
Current squad
As of 1 June 2015.
Transfers
In
Out
References
External links
Official club website
2014-15
Portuguese football clubs 2014–15 season |
https://en.wikipedia.org/wiki/%C5%81ukasiewicz%E2%80%93Moisil%20algebra | Łukasiewicz–Moisil algebras (LMn algebras) were introduced in the 1940s by Grigore Moisil (initially under the name of Łukasiewicz algebras) in the hope of giving algebraic semantics for the n-valued Łukasiewicz logic. However, in 1956 Alan Rose discovered that for n ≥ 5, the Łukasiewicz–Moisil algebra does not model the Łukasiewicz logic. A faithful model for the ℵ0-valued (infinitely-many-valued) Łukasiewicz–Tarski logic was provided by C. C. Chang's MV-algebra, introduced in 1958. For the axiomatically more complicated (finite) n-valued Łukasiewicz logics, suitable algebras were published in 1977 by Revaz Grigolia and called MVn-algebras. MVn-algebras are a subclass of LMn-algebras, and the inclusion is strict for n ≥ 5. In 1982 Roberto Cignoli published some additional constraints that added to LMn-algebras produce proper models for n-valued Łukasiewicz logic; Cignoli called his discovery proper Łukasiewicz algebras.
Moisil however, published in 1964 a logic to match his algebra (in the general n ≥ 5 case), now called Moisil logic. After coming in contact with Zadeh's fuzzy logic, in 1968 Moisil also introduced an infinitely-many-valued logic variant and its corresponding LMθ algebras. Although the Łukasiewicz implication cannot be defined in a LMn algebra for n ≥ 5, the Heyting implication can be, i.e. LMn algebras are Heyting algebras; as a result, Moisil logics can also be developed (from a purely logical standpoint) in the framework of Brower’s intuitionistic logic.
Definition
A LMn algebra is a De Morgan algebra (a notion also introduced by Moisil) with n-1 additional unary, "modal" operations: , i.e. an algebra of signature where J = { 1, 2, ... n-1 }. (Some sources denote the additional operators as to emphasize that they depend on the order n of the algebra.) The additional unary operators ∇j must satisfy the following axioms for all x, y ∈ A and j, k ∈ J:
if for all j ∈ J, then x = y.
(The adjective "modal" is related to the [ultimately failed] program of Tarksi and Łukasiewicz to axiomatize modal logic using many-valued logic.)
Elementary properties
The duals of some of the above axioms follow as properties:
Additionally: and . In other words, the unary "modal" operations are lattice endomorphisms.
Examples
LM2 algebras are the Boolean algebras. The canonical Łukasiewicz algebra that Moisil had in mind were over the set L_n = } with negation conjunction and disjunction and the unary "modal" operators:
If B is a Boolean algebra, then the algebra over the set B[2] ≝ {(x, y) ∈ B×B | x ≤ y} with the lattice operations defined pointwise and with ¬(x, y) ≝ (¬y, ¬x), and with the unary "modal" operators ∇2(x, y) ≝ (y, y) and ∇1(x, y) = ¬∇2¬(x, y) = (x, x) [derived by axiom 4] is a three-valued Łukasiewicz algebra.
Representation
Moisil proved that every LMn algebra can be embedded in a direct product (of copies) of the canonical algebra. As a corollary, every LMn algebra is a subdirect product of subal |
https://en.wikipedia.org/wiki/Timeline%20of%20computational%20mathematics | This is a timeline of key developments in computational mathematics.
1940s
Monte Carlo simulation (voted one of the top 10 algorithms of the 20th century) invented at Los Alamos by von Neumann, Ulam and Metropolis.
Dantzig introduces the simplex algorithm (voted one of the top 10 algorithms of the 20th century).
First hydro simulations at Los Alamos occurred.
Ulam and von Neumann introduce the notion of cellular automata.
A routine for the Manchester Baby written to factor a large number (2^18), one of the first in computational number theory. The Manchester group would make several other breakthroughs in this area.
LU decomposition technique first discovered.
1950s
Hestenes, Stiefel, and Lanczos, all from the Institute for Numerical Analysis at the National Bureau of Standards, initiate the development of Krylov subspace iteration methods. Voted one of the top 10 algorithms of the 20th century.
Equations of State Calculations by Fast Computing Machines introduces the Metropolis–Hastings algorithm. Also, important earlier independent work by Alder and S. Frankel.
Enrico Fermi, Stanislaw Ulam, John Pasta, and Mary Tsingou, discover the Fermi–Pasta–Ulam–Tsingou problem.
In network theory, Ford & Fulkerson compute a solution to the maximum flow problem.
Householder invents his eponymous matrices and transformation method (voted one of the top 10 algorithms of the 20th century).
Molecular dynamics invented by Alder and Wainwright
John G.F. Francis and Vera Kublanovskaya invent QR factorization (voted one of the top 10 algorithms of the 20th century).
1960s
First recorded use of the term "finite element method" by Ray Clough, to describe the methods of Courant, Hrenikoff and Zienkiewicz, among others. See also here.
Using computational investigations of the 3-body problem, Minovitch formulates the gravity assist method.
Molecular dynamics was invented independently by Aneesur Rahman.
Cooley and Tukey re-invent the Fast Fourier transform (voted one of the top 10 algorithms of the 20th century), an algorithm first discovered by Gauss.
Edward Lorenz discovers the butterfly effect on a computer, attracting interest in chaos theory.
Kruskal and Zabusky follow up the Fermi–Pasta–Ulam–Tsingou problem with further numerical experiments, and coin the term "soliton".
Birch and Swinnerton-Dyer conjecture formulated through investigations on a computer.
Grobner bases and Buchberger's algorithm invented for algebra
Frenchman Verlet (re)discovers a numerical integration algorithm, (first used in 1791 by Delambre, by Cowell and Crommelin in 1909, and by Carl Fredrik Störmer in 1907, hence the alternative names Störmer's method or the Verlet-Störmer method) for dynamics.
Risch invents algorithm for symbolic integration.
1970s
Computer algebra replicates and extends the work of Delaunay in lunar theory.
Mandelbrot, from studies of the Fatou, Julia and Mandelbrot sets, coined and popularized the term 'fractal' to describe these str |
https://en.wikipedia.org/wiki/2014%E2%80%9315%20Botola | The 2014–15 Botola was the 58th season of the Moroccan Top League and the 4th under its new format of Moroccan Pro League.
Teams locations
League table
Season statistics
Top goalscorers
.
Annual awards
The Royal Moroccan Football Federation, in coordination with the LNFP ( Ligue Nationale du Football Professionnel) and the UMFP (Union Marocaine des Footballeurs Professionnels), organized the 1st edition of the "Stars' Night" in honor of the players and coaches who were distinguished during the 2014/2015 season.
See also
2014–15 GNF 2
References
External links
Fédération Royale Marocaine de Football
Botola on fifa.com
Botola seasons
Morocco
1 |
https://en.wikipedia.org/wiki/Statistics%20Korea | Statistics Korea (KOSTAT; ) is a government organization responsible for managing national statistics in South Korea. KOSTAT is headquartered in Daejeon, South Korea and operates under the Ministry of Economy and Finance.
Statistics Korea generates population and household census yearly (every 5 years until 2015). It also gathers analytic and administrative statistics.
See also
List of national and international statistical services
Official statistics
References
External links
Official site, in Korean and English
Government agencies of South Korea
South Korea |
https://en.wikipedia.org/wiki/Barrier%20resilience | Barrier resilience is an algorithmic optimization problem in computational geometry motivated by the design of wireless sensor networks, in which one seeks a path through a collection of barriers (often modeled as unit disks) that passes through as few barriers as possible.
Definitions
The barrier resilience problem was introduced by (using different terminology) to model the ability of wireless sensor networks to detect intruders robustly when some sensors may become faulty.
In this problem, the region under surveillance from each sensor is modeled as a unit disk in the Euclidean plane. An intruder can reach a target region of the plane without detection, if there exists a path in the plane connecting a given start region to the target region without crossing any of the sensor disks. The barrier resilience of a sensor network is defined to be the minimum, over all paths from the start region to the target region, of the number of sensor disks intersected by the path. The barrier resilience problem is the problem of computing this number by finding an optimal path through the barriers.
A simplification of the problem, which encapsulates most of its essential features, makes the target region be the origin of the plane, and the start region be the set of points outside the convex hull of the sensor disks. In this version of the problem, the goal is to connect the origin to points arbitrarily far from the origin by a path through as few sensor disks as possible.
Another variation of the problem counts the number of times a path crosses the boundary of a sensor disk. If a path crosses the same disk multiple times, each crossing counts towards the total. The barrier thickness of a sensor network is the minimum number of crossings of a path from the start region to the target region.
Computational complexity
Barrier thickness may be computed in polynomial time by constructing the arrangement of the barriers (the subdivision of the plane formed by overlaying all barrier boundaries) and computing a shortest path in the dual graph of this subdivision.
The complexity of barrier resilience for unit disk barriers is an open problem. It may be solved by a fixed-parameter tractable algorithm whose time is cubic in the total number of barriers and exponential in the square of the resilience, but it is not known whether it has a fully polynomial time solution.
The corresponding problem for barriers of some other shapes, including unit-length line segments or axis-aligned rectangles of aspect ratio close to 1, is known to be NP-hard.
A variation of the barrier resilience problem, studied by , restricts both the sensors and the escape path to a rectangle in the plane. In this variation, the goal is to find a path from the top side of the rectangle to the bottom side that passes through as few of the sensor disks as possible. By applying Menger's theorem to the unit disk graph defined from the barriers, this minimal number of disks can be shown to equal the |
https://en.wikipedia.org/wiki/Satkhira%20Government%20College | {
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22.7103949,
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}Satkhira Government College is a government college in Satkhira, Bangladesh. This college has 16 department, 17 stuff and 2 student hostel.
Available courses
Graduation courses-
Bangla
English
Economics
Political science
Philosophy
History
Islamic studies
Mathematics
Physics
Chemistry
Botany
Zoology
Geography
Environmental science
Management
Accounting
Post-Graduation courses-
Economics
Bangla
History
Islamic studies
Management
Accounting
Other facilities
Number of Boys Hostel : 02
Number of Girlss Hostel : 01 (Under Construction)
Computer Lab: 02
Digital Multimedia Class room: 16
Number of Books in Central Library: 30000+
Number of Books in seminar library: 16000+
Notable alumni
Pori Moni, actress
Hasan Foez Siddique, Chief Justice of Bangladesh
References
http://www.nubd.info/college/college.php?code=0201
Colleges affiliated to National University, Bangladesh
Universities and colleges in Bangladesh
Educational institutions of Khulna Division
Educational institutions established in 1946
1940s establishments in East Pakistan |
https://en.wikipedia.org/wiki/Ronald%20Does | Ronaldus Joannes Michael Maria "Ronald" Does (born 13 January 1955 in Haarlem) is a Dutch mathematician, known for several contributions to statistics and Lean Six Sigma. His research interests include control charts, Lean Six Sigma, and the integration of industrial statistics in services and healthcare.
Since 1991 he has been holding a full-professorship in Industrial Statistics at the University of Amsterdam, first at its Korteweg-de Vries Institute for Mathematics, and since April 2009 at the department of Operations Management. In 2007 he has been appointed as fellow of the American Society for Quality and in 2014 as fellow of the American Statistical Association. He is the managing director and founder of the Institute for Business and Industrial Statistics of the University of Amsterdam. Since 2011 he has also been director of the Executive Programmes of the University of Amsterdam.
Books
"Lean Six Sigma Stap voor Stap" (2008, in Dutch)
"Lean Six Sigma for Services and Healthcare" (2012)
References
External links
Homepage (Dutch)
1955 births
Living people
Dutch mathematicians
Leiden University alumni
Academic staff of the University of Amsterdam
Scientists from Haarlem
Fellows of the American Statistical Association |
https://en.wikipedia.org/wiki/Parkland%20Village | Parkland Village is an unincorporated community in Alberta, Canada within Parkland County. It was previously recognized as a designated place by Statistics Canada in the 2001 Census of Canada. It is located on Range Road 272, north of Highway 16 (Yellowhead Highway) and the City of Spruce Grove.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Parkland Village had a population of 1,479 living in 674 of its 704 total private dwellings, a change of from its 2016 population of 1,934. With a land area of , it had a population density of in 2021.
Education
Parkland Village is home to Parkland Village School. Administered by Parkland School Division No. 70, the school offers instruction to students in kindergarten through grade four. Its catchment area includes Parkland Village, nearby Acheson and surrounding rural areas of Parkland County. The school has a student population of 182.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Parkland County |
https://en.wikipedia.org/wiki/Donald%20Solitar | Donald Solitar (September 5, 1932 in Brooklyn, New York, United States – April 28, 2008 in Toronto, Canada) was an American and Canadian mathematician, known for his work in combinatorial group theory. The Baumslag–Solitar groups are named after him and Gilbert Baumslag, after their joint 1962 paper on these groups.
Life
Solitar competed on the mathematics team of Brooklyn Technical High School with his future co-author Abe Karrass, one year ahead of him in school. He graduated from Brooklyn College in 1953 (with the assistance of tutoring from Karrass, who went to New York University) and went to Princeton University for graduate study in mathematics. However, his intended mentor there, Emil Artin, was no longer interested in group theory, so he left with a master's degree and earned his doctorate from New York University instead, in 1958, under the supervision of Wilhelm Magnus.
After finishing his studies, he joined the faculty of Adelphi University in 1959, and Karrass soon joined him there as a doctoral student, earning a Ph.D. under Solitar's supervision in 1961; this was the first Ph.D. awarded at Adelphi. Karrass remained on the faculty with Solitar, where they founded a summer institute for high school mathematics teachers. Solitar moved to Polytechnic University in 1967, and then (as department chair) to York University in 1968, along with Karrass.
Solitar married J. Francien Hageman, a Dutch woman, in 1976. He died of a heart attack on April 28, 2008.
Selected publications
Books
.
Research articles
.
.
.
Awards and honors
Solitar became a Fellow of the Royal Society of Canada in 1982.
References
1932 births
2008 deaths
20th-century American mathematicians
Canadian mathematicians
Fellows of the Royal Society of Canada
Brooklyn College alumni
Princeton University alumni
New York University alumni
Adelphi University faculty
New York University faculty
Academic staff of York University
Mathematicians from New York (state) |
https://en.wikipedia.org/wiki/Rational%20monoid | In mathematics, a rational monoid is a monoid, an algebraic structure, for which each element can be represented in a "normal form" that can be computed by a finite transducer: multiplication in such a monoid is "easy", in the sense that it can be described by a rational function.
Definition
Consider a monoid M. Consider a pair (A,L) where A is a finite subset of M that generates M as a monoid, and L is a language on A (that is, a subset of the set of all strings A∗). Let φ be the map from the free monoid A∗ to M given by evaluating a string as a product in M. We say that L is a rational cross-section if φ induces a bijection between L and M. We say that (A,L) is a rational structure for M if in addition the kernel of φ, viewed as a subset of the product monoid A∗×A∗ is a rational set.
A quasi-rational monoid is one for which L is a rational relation: a rational monoid is one for which there is also a rational function cross-section of L. Since L is a subset of a free monoid, Kleene's theorem holds and a rational function is just one that can be instantiated by a finite state transducer.
Examples
A finite monoid is rational.
A group is a rational monoid if and only if it is finite.
A finitely generated free monoid is rational.
The monoid M4 generated by the set {0,e, a,b, x,y} subject to relations in which e is the identity, 0 is an absorbing element, each of a and b commutes with each of x and y and ax = bx, ay = by = bby, xx = xy = yx = yy = 0 is rational but not automatic.
The Fibonacci monoid, the quotient of the free monoid on two generators {a,b}∗ by the congruence aab = bba.
Green's relations
The Green's relations for a rational monoid satisfy D = J.
Properties
Kleene's theorem holds for rational monoids: that is, a subset is a recognisable set if and only if it is a rational set.
A rational monoid is not necessarily automatic, and vice versa. However, a rational monoid is asynchronously automatic and hyperbolic.
A rational monoid is a regulator monoid and a quasi-rational monoid: each of these implies that it is a Kleene monoid, that is, a monoid in which Kleene's theorem holds.
References
Algebraic structures
Semigroup theory |
https://en.wikipedia.org/wiki/Rosenbrock%20system%20matrix | In applied mathematics, the Rosenbrock system matrix or Rosenbrock's system matrix of a linear time-invariant system is a useful representation bridging state-space representation and transfer function matrix form. It was proposed in 1967 by Howard H. Rosenbrock.
Definition
Consider the dynamic system
The Rosenbrock system matrix is given by
In the original work by Rosenbrock, the constant matrix is allowed to be a polynomial in .
The transfer function between the input and output is given by
where is the column of and is the row of .
Based in this representation, Rosenbrock developed his version of the PBH test.
Short form
For computational purposes, a short form of the Rosenbrock system matrix is more appropriate and given by
The short form of the Rosenbrock system matrix has been widely used in H-infinity methods in control theory, where it is also referred to as packed form; see command pck in MATLAB. An interpretation of the Rosenbrock System Matrix as a Linear Fractional Transformation can be found in.
One of the first applications of the Rosenbrock form was the development of an efficient computational method for Kalman decomposition, which is based on the pivot element method. A variant of Rosenbrock’s method is implemented in the minreal command of Matlab and
GNU Octave.
References
1967 introductions
Control theory
Matrices |
https://en.wikipedia.org/wiki/Hodge%E2%80%93de%20Rham%20spectral%20sequence | In mathematics, the Hodge–de Rham spectral sequence (named in honor of W. V. D. Hodge and Georges de Rham) is an alternative term sometimes used to describe the Frölicher spectral sequence (named after Alfred Frölicher, who actually discovered it). This spectral sequence describes the precise relationship between the Dolbeault cohomology and the de Rham cohomology of a general complex manifold. On a compact Kähler manifold, the sequence degenerates, thereby leading to the Hodge decomposition of the de Rham cohomology.
Description of the spectral sequence
The spectral sequence is as follows:
where X is a complex manifold, is its cohomology with complex coefficients and the left hand term, which is the -page of the spectral sequence, is the cohomology with values in the sheaf of holomorphic differential forms.
The existence of the spectral sequence as stated above follows from the Poincaré lemma, which gives a quasi-isomorphism of complexes of sheaves
together with the usual spectral sequence resulting from a filtered object, in this case the Hodge filtration
of .
Degeneration
The central theorem related to this spectral sequence is that for a compact Kähler manifold X, for example a projective variety, the above spectral sequence degenerates at the -page. In particular, it gives an isomorphism referred to as the Hodge decomposition
The degeneration of the spectral sequence can be shown using Hodge theory. An extension of this degeneration in a relative situation, for a proper smooth map , was also shown by Deligne.
Purely algebraic proof
For smooth proper varieties over a field of characteristic 0, the spectral sequence can also be written as
where denotes the sheaf of algebraic differential forms (also known as Kähler differentials) on X, is the (algebraic) de Rham complex, consisting of the with the differential being the exterior derivative. In this guise, all terms in the spectral sequence are of purely algebraic (as opposed to analytic) nature. In particular, the question of the degeneration of this spectral sequence makes sense for varieties over a field of characteristic p>0.
showed that for a smooth proper scheme X over a perfect field k of positive characteristic p, the spectral sequence degenerates, provided that dim(X)<p and X admits a smooth proper lift over the ring of Witt vectors W2(k) of length two (for example, for k=Fp, this ring would be Z/p2). Their proof uses the Cartier isomorphism, which only exists in positive characteristic. This degeneration result in characteristic p>0 can then be used to also prove the degeneration for the spectral sequence for X over a field of characteristic 0.
Non-commutative version
The de Rham complex and also the de Rham cohomology of a variety admit generalizations to non-commutative geometry. This more general setup studies dg categories. To a dg category, one can associate its Hochschild homology, and also its periodic cyclic homology. When applied to the category of perf |
https://en.wikipedia.org/wiki/Partial%20groupoid | In abstract algebra, a partial groupoid (also called halfgroupoid, pargoid, or partial magma) is a set endowed with a partial binary operation.
A partial groupoid is a partial algebra.
Partial semigroup
A partial groupoid is called a partial semigroup (also called semigroupoid, semicategory, naked category, or precategory) if the following associative law holds:
For all such that and , the following two statements hold:
if and only if , and
if (and, because of 1., also ).
References
Further reading
Algebraic structures |
https://en.wikipedia.org/wiki/Partial%20algebra | In abstract algebra, a partial algebra is a generalization of universal algebra to partial operations.
Example(s)
partial groupoid
field — the multiplicative inversion is the only proper partial operation
effect algebras
Structure
There is a "Meta Birkhoff Theorem" by Andreka, Nemeti and Sain (1982).
References
Further reading
Algebraic structures |
https://en.wikipedia.org/wiki/B%C3%BCy%C3%BCkdere%20Avenue | {
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Büyükdere Avenue () is a major avenue which runs through the districts of Şişli (Esentepe quarter), Beşiktaş (Levent quarter) and Sarıyer (Maslak quarter) on the European side of Istanbul, Turkey. It begins at Şişli Mosque and runs in an eastward direction partly under the viaduct of the inner-city motorway O-1 through Mecidiyeköy, Esentepe, until reaching Zincirlikuyu; where it joins with Barbaros Boulevard and turns northward passing through Levent, Sanayi Mahallesi, Maslak and by the Fatih Forest, ending at the Hacıosman Slope on the Sarıyer district border. Its total length is . From Zincirlikuyu to Maslak, it forms a border line between the districts of Kağıthane in the east and Beşiktaş in the west. It is named after the Büyükdere neighborhood of Sarıyer district, where it connects to. It is a major artery of the Istanbul Central Business District, which is not located in the historic center of the city.
The metro line M2 (Yenikapı–Hacıosman) follows the avenue between Şişli and Hacıosman, featuring nine metro stations. Headquarters of many banks, business centers, shopping centers, luxury hotels and numerous skyscrapers built in recent years are located around Büyükdere Avenue, making it an important route of financial, business and social life.
Residential or office skyscrapers found on Büyükdere Avenue include the Diamond of Istanbul, Istanbul Sapphire, Isbank Tower 1, Sabancı Center, Kanyon Towers, Finansbank Tower, among others. Notable shopping malls on the avenue include Zorlu Center, Kanyon Shopping Mall, MetroCity AVM and Özdilek Park.
Educational institutions on the avenue include Haliç University, ISOV Vocational High School for Construction, Istanbul Technical University's Maslak Campus, Işık University, and Yıldız Technical University Vocational College.
Two major cemeteries are situated on the avenue: the Mecidiyeköy Italo-Jewish Cemetery and Zincirlikuyu Cemetery.
On November 20, 2003, the headquarters of the HSBC Bank Turkey on Büyükdere Avenue in Levent was car bombed by a terrorist (suicide bomber) linked to Al Qaeda, killing and wounding a number of people. The street was closed to traffic for ten hours.
References
External links
Şişli
Streets in Istanbul
Istanbul Central Business District |
https://en.wikipedia.org/wiki/Alexander%20Varchenko | Alexander Nikolaevich Varchenko (, born February 6, 1949) is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics.
Education and career
From 1964 to 1966 Varchenko studied at the Moscow Kolmogorov boarding school No. 18 for gifted high school students, where Andrey Kolmogorov and Ya. A. Smorodinsky were lecturing mathematics and physics. Varchenko graduated from Moscow State University in 1971. He was a student of Vladimir Arnold. Varchenko defended his Ph.D. thesis Theorems on Topological Equisingularity of Families of Algebraic Sets and Maps in 1974 and Doctor of Science thesis Asymptotics of Integrals and Algebro-Geometric Invariants of Critical Points of Functions in 1982. From 1974 to 1984 he was a research scientist at the Moscow State University, in 1985–1990 a professor at the Gubkin Institute of Gas and Oil, and since 1991 he has been the Ernest Eliel Professor at the University of North Carolina at Chapel Hill.
Research
In 1969 Varchenko identified the monodromy group of a critical point of type of a function of an odd number of variables with the symmetric group which is the Weyl group of the simple Lie algebra of type .
In 1971, Varchenko proved that a family of complex quasi-projective algebraic sets with an irreducible base forms a topologically locally trivial bundle over a Zariski open subset of the base. This statement, conjectured by Oscar Zariski, had filled up a gap in the proof of Zariski's theorem on the fundamental group of the complement to a complex algebraic hypersurface published in 1937. In 1973, Varchenko proved René Thom's conjecture that a germ of a generic smooth map is topologically equivalent to a germ of a polynomial map and has a finite dimensional polynomial topological versal deformation, while the non-generic maps form a subset of infinite codimension in the space of all germs.
Varchenko was among creators of the theory of Newton polygons in singularity theory, in particular, he gave a formula, relating Newton polygons and asymptotics of the oscillatory integrals associated with a critical point of a function. Using the formula, Varchenko constructed a counterexample to V. I. Arnold's semicontinuity conjecture that the brightness of light at a point on a caustic is not less than the brightness at the neighboring points.
Varchenko formulated a conjecture on the semicontinuity of the spectrum of a critical point under deformations of the critical point and proved it for deformations of low weight of quasi-homogeneous singularities. Using the semicontinuity, Varchenko gave an estimate from above for the number of singular points of a projective hypersurface of given degree and dimension.
Varchenko introduced the asymptotic mixed Hodge structure on the cohomology, vanishing at a critical point of a function, by studying asymptotics of integrals of holomorphic differential forms over families of vanishing cycles. Such an integral depends on the paramet |
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20Joseph%20Fourier | This is a list of things named after Joseph Fourier:
Mathematics
Budan–Fourier theorem, see Budan's theorem
Fourier's theorem
Fourier–Motzkin elimination
Fourier algebra
Fourier division
Fourier method
Analysis
Fourier analysis
Fourier series
Fourier–Bessel series
Fourier sine and cosine series
Generalized Fourier series
Laplace–Fourier series, see Laplace series
Fourier–Legendre series
Fourier transform (List of Fourier-related transforms):
Discrete-time Fourier transform (DTFT), the reverse of the Fourier series, a special case of the Z-transform around the unit circle in the complex plane
Discrete Fourier transform (DFT), occasionally called the finite Fourier transform, the Fourier transform of a discrete periodic sequence (yielding discrete periodic frequencies), which can also be thought of as the DTFT of a finite-length sequence evaluated at discrete frequencies
Fast Fourier transform (FFT), a fast algorithm for computing a Discrete Fourier transform
Finite Fourier transform
Fractional Fourier transform (FRFT), a linear transformation generalizing the Fourier transform, used in the area of harmonic analysis
Fourier–Deligne transform
Fourier–Mukai transform
Fourier inversion theorem
Fourier integral theorem
In physics and engineering
Fourier's law of heat conduction
Fourier number () (also known as the Fourier modulus), a ratio of the rate of heat conduction to the rate of thermal energy storage
Fourier optics
Fourier-transform spectroscopy, a measurement technique whereby spectra are collected based on measurements of the temporal coherence of a radiative source
Other
Joseph Fourier University
10101 Fourier
See also
Fourier (disambiguation)
List of Fourier-related transforms
List of Fourier analysis topics
Fourier
Joseph Fourier |
https://en.wikipedia.org/wiki/Tyra%20White | Tyra Marie White (born Match 23, 1989) is a basketball player who was drafted by the Los Angeles Sparks. She played college basketball for Texas A&M University.
Texas A&M statistics
Source
References
External links
Texas A&M Aggies bio
Tyra White Honors and Awards at macklinlovett.com
1989 births
Living people
American women's basketball players
Basketball players from Kansas City, Missouri
Guards (basketball)
Los Angeles Sparks draft picks
McDonald's High School All-Americans
Texas A&M Aggies women's basketball players |
https://en.wikipedia.org/wiki/1994%E2%80%9395%20Second%20League%20of%20FR%20Yugoslavia | Statistics of Second League of FR Yugoslavia () for the 1994–95 season.
Overview
The league was divided into 2 groups, A and B, consisting each of 10 clubs. Both groups were played in league system. By winter break all clubs in each group meet each other twice, home and away, with the bottom four classified from A group moving to the group B, and being replaced by the top four from the B group. At the end of the season the same situation happened with four teams being replaced from A and B groups, adding the fact that the bottom three clubs from the B group were relegated into the third national tier. The champion and the second following team were promoted into the 1995–96 First League of FR Yugoslavia.
At the end of the season FK Mladost Lučani became champions, and together with FK Čukarički and FK Mladost Bački Jarak got promoted.
Club names
Some club names were written in a different way in other sources, and that is because some clubs had in their names the sponsorship company included. These cases were:
Čukarički / Čukarički Stankom
Novi Sad / Novi Sad Gumins
Budućnost Valjevo / Budućnost Vujić
Final table
References
External sources
Season tables at FSGZ
Yugoslav Second League seasons
Yugo
2 |
https://en.wikipedia.org/wiki/1995%E2%80%9396%20Second%20League%20of%20FR%20Yugoslavia | Statistics of Second League of FR Yugoslavia () for the 1995–96 season.
Overview
The league was divided into 2 groups, A and B, consisting each of 10 clubs. Both groups were played in league system. By winter break all clubs in each group meet each other twice, home and away, with the bottom four classified from A group moving to the group B, and being replaced by the top four from the B group. At the end of the season the same situation happened with four teams being replaced from A and B groups, adding the fact that the bottom three clubs from the B group were relegated into the third national tier. The champion and the second following team were promoted into the 1996–97 First League of FR Yugoslavia.
At the end of the season FK Budućnost Valjevo became champions, and together with OFK Kikinda, FK Železnik, FK Spartak Subotica, FK Rudar Pljevlja and FK Sutjeska Nikšić got promoted.
Club names
Some club names were written in a different way in other sources, and that is because some clubs had in their names the sponsorship company included. These cases were:
Budućnost Valjevo / Budućnost Vujić
RFK Novi Sad / Novi Sad Gumins
Jedinstvo Paraćin / Jedinstvo Cement
Final table
References
External sources
Season tables at FSGZ
Yugoslav Second League seasons
Yugo
2 |
https://en.wikipedia.org/wiki/Normal%20form%20%28dynamical%20systems%29 | In mathematics, the normal form of a dynamical system is a simplified form that can be useful in determining the system's behavior.
Normal forms are often used for determining local bifurcations in a system. All systems exhibiting a certain type of bifurcation are locally (around the equilibrium) topologically equivalent to the normal form of the bifurcation. For example, the normal form of a saddle-node bifurcation is
where is the bifurcation parameter. The transcritical bifurcation
near can be converted to the normal form
with the transformation .
See also canonical form for use of the terms canonical form, normal form, or standard form more generally in mathematics.
References
Further reading
Bifurcation theory
Dynamical systems |
https://en.wikipedia.org/wiki/List%20of%20FC%20Krasnodar%20records%20and%20statistics | FC Krasnodar is a Russian professional football club based in Krasnodar.
This list encompasses the major records set by the club and their players in the Russian Premier League. The player records section includes details of the club's goalscorers and those who have made more than 50 appearances in first-team competitions.
Player
Most appearances
Players who've played over 50 competitive, professional matches only. Appearances include substitute appearances, (goals in parentheses).
Bold, players still at Krasnodar, Bold Italicised players currently away from Krasnodar on loan.
Goal scorers
Competitive, professional matches only, appearances including substitutes appear in brackets.
Bold, players still at Krasnodar, Bold Italicised players currently away from Krasnodar on loan.
International representatives
Current players
Players out on loan
Former players
References
2011–12 season
2012–13 season
2013–14 season
2014–15 season
External links
FC Krasnodar
FC Krasnodar |
https://en.wikipedia.org/wiki/Amir%20Hossein%20Tahuni | Amir Hossein Tahuni (, born 22 October 1992 in Iran) is an Iranian football midfielder, who currently plays for Shahrdari Mahshahr in League 2.
Club career
Club Career Statistics
Last Update: 23 April 2015
References
Living people
1992 births
Iranian men's footballers
Esteghlal F.C. players
F.C. Nassaji Mazandaran players
Men's association football midfielders
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/Cartesian%20monoidal%20category | In mathematics, specifically in the field known as category theory, a monoidal category where the monoidal ("tensor") product is the categorical product is called a cartesian monoidal category. Any category with finite products (a "finite product category") can be thought of as a cartesian monoidal category. In any cartesian monoidal category, the terminal object is the monoidal unit. Dually, a monoidal finite coproduct category with the monoidal structure given by the coproduct and unit the initial object is called a cocartesian monoidal category, and any finite coproduct category can be thought of as a cocartesian monoidal category.
Cartesian categories with an internal Hom functor that is an adjoint functor to the product are called Cartesian closed categories.
Properties
Cartesian monoidal categories have a number of special and important properties, such as the existence of diagonal maps Δx : x → x ⊗ x and augmentations ex : x → I for any object x. In applications to computer science we can think of Δ as "duplicating data" and e as "deleting data". These maps make any object into a comonoid. In fact, any object in a cartesian monoidal category becomes a comonoid in a unique way.
Examples
Cartesian monoidal categories:
Set, the category of sets with the singleton set serving as the unit.
Cat, the bicategory of small categories with the product category, where the category with one object and only its identity map is the unit.
Cocartesian monoidal categories:
Vect, the category of vector spaces over a given field, can be made cocartesian monoidal with the monoidal product given by the direct sum of vector spaces and the trivial vector space as unit.
Ab, the category of abelian groups, with the direct sum of abelian groups as monoidal product and the trivial group as unit.
More generally, the category R-Mod of (left) modules over a ring R (commutative or not) becomes a cocartesian monoidal category with the direct sum of modules as tensor product and the trivial module as unit.
In each of these categories of modules equipped with a cocartesian monoidal structure, finite products and coproducts coincide (in the sense that the product and coproduct of finitely many objects are isomorphic). Or more formally, if f : X1 ∐ ... ∐ Xn → X1 × ... × Xn is the "canonical" map from the n-ary coproduct of objects Xj to their product, for a natural number n, in the event that the map f is an isomorphism, we say that a biproduct for the objects Xj is an object isomorphic to and together with maps ij : Xj → X and pj : X → Xj such that the pair (X, {ij}) is a coproduct diagram for the objects Xj and the pair (X, {pj}) is a product diagram for the objects Xj , and where pj ∘ ij = idXj. If, in addition, the category in question has a zero object, so that for any objects A and B there is a unique map 0A,B : A → 0 → B, it often follows that pk ∘ ij = : δij, the Kronecker delta, where we interpret 0 and 1 as the 0 maps and identity maps of the object |
https://en.wikipedia.org/wiki/Mean-field%20particle%20methods | Mean-field particle methods are a broad class of interacting type Monte Carlo algorithms for simulating from a sequence of probability distributions satisfying a nonlinear evolution equation. These flows of probability measures can always be interpreted as the distributions of the random states of a Markov process whose transition probabilities depends on the distributions of the current random states. A natural way to simulate these sophisticated nonlinear Markov processes is to sample a large number of copies of the process, replacing in the evolution equation the unknown distributions of the random states by the sampled empirical measures. In contrast with traditional Monte Carlo and Markov chain Monte Carlo methods these mean-field particle techniques rely on sequential interacting samples. The terminology mean-field reflects the fact that each of the samples (a.k.a. particles, individuals, walkers, agents, creatures, or phenotypes) interacts with the empirical measures of the process. When the size of the system tends to infinity, these random empirical measures converge to the deterministic distribution of the random states of the nonlinear Markov chain, so that the statistical interaction between particles vanishes. In other words, starting with a chaotic configuration based on independent copies of initial state of the nonlinear Markov chain model, the chaos propagates at any time horizon as the size the system tends to infinity; that is, finite blocks of particles reduces to independent copies of the nonlinear Markov process. This result is called the propagation of chaos property. The terminology "propagation of chaos" originated with the work of Mark Kac in 1976 on a colliding mean-field kinetic gas model.
History
The theory of mean-field interacting particle models had certainly started by the mid-1960s, with the work of Henry P. McKean Jr. on Markov interpretations of a class of nonlinear parabolic partial differential equations arising in fluid mechanics. The mathematical foundations of these classes of models were developed from the mid-1980s to the mid-1990s by several mathematicians, including Werner Braun, Klaus Hepp, Karl Oelschläger, Gérard Ben Arous and Marc Brunaud, Donald Dawson, Jean Vaillancourt and Jürgen Gärtner, Christian Léonard, Sylvie Méléard, Sylvie Roelly, Alain-Sol Sznitman and Hiroshi Tanaka for diffusion type models; F. Alberto Grünbaum, Tokuzo Shiga, Hiroshi Tanaka,
Sylvie Méléard and Carl Graham for general classes of interacting jump-diffusion processes.
We also quote an earlier pioneering article by Theodore E. Harris and Herman Kahn, published in 1951, using mean-field but heuristic-like genetic methods for estimating particle transmission energies. Mean-field genetic type particle methods are also used as heuristic natural search algorithms (a.k.a. metaheuristic) in evolutionary computing. The origins of these mean-field computational techniques can be traced to 1950 and 1954 with the work of Alan |
https://en.wikipedia.org/wiki/Mikhail%20Fedoruk | Mikhail Petrovich Fedoruk () (born February 18, 1956) — is a rector of Novosibirsk State University, Doctor of Physics and Mathematics.
Biography
Mikhail P. Fedoruk born February 18, 1956, in the Kochenyovsky District of Novosibirsk District, Russia.
In 1982 he graduated from the Faculty of Physics, Novosibirsk State University and began his scientific career with postgraduate study in the Institute of Theoretical and Applied Mechanics SB RAS.
His teaching activities are connected with Novosibirsk State University. Since 1995 he worked as a lecturer at the Faculty of Mathematics and Mechanics, in 2003 became the first deputy dean of the faculty.
June 22, 2012 he was elected rector of NSU.
In 2022, he signed the Address of the Russian Union of Rectors, which called to support Putin in his invasion of Ukraine.
He is married and has a son.
References
1956 births
Living people
Soviet physicists
20th-century Russian physicists
21st-century Russian physicists |
https://en.wikipedia.org/wiki/Norbert%20S%C3%A1rk%C3%B6zi | Norbert Sárközi (born 5 March 1993 in Budapest) is a Hungarian football player.
Club statistics
Updated to games played as of 30 November 2014.
References
MLSZ
External links
1993 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football midfielders
Nemzeti Bajnokság I players
Dunaújváros PASE players
FK Csíkszereda Miercurea Ciuc players
Hungarian expatriate men's footballers
Expatriate men's footballers in Romania
Hungarian expatriate sportspeople in Romania |
https://en.wikipedia.org/wiki/Scientology%20in%20Egypt | The Church of Scientology has no official presence in Egypt and there are no known membership statistics available. In 2002, two members were detained by Egyptian authorities under the charges of "contempt of religion". However, some books by the founder, L. Ron Hubbard, have started to appear in several Egyptian bookstores in the late 2000s, and were even approved by Al-Azhar, the highest Sunni learning institution in the Muslim world. Egypt is listed on an official Scientology website as being a country "in which Dianetics and Scientology services are ministered". Narconon, an organization which promotes Hubbard's drug abuse treatment, has a branch in Fayoum.
Detention of two members
On December 24, 2001, Egyptian authorities arrested two members of the Church of Scientology: Mahmoud Massarwa, a 28-year-old Israeli citizen of Palestinian origin, and his Palestinian wife Wafaa Ahmad. They were charged with "contempt of religion" and were accused of trying to establish a branch in Egypt and harm the country's two main religions "with the aim of sparking riots". Two months later, a court extended their custody for 30 days to allow further police questioning, adding that they have confessed to have come to Egypt in order to spread their doctrine. Human rights director of the Church of Scientology, Leisa Goodman, denied these claims on behalf of the church and said that the couple was in the country representing the Italian branch of New Era Publications, a firm that publishes the works of L. Ron Hubbard, to promote Hubbard's book Dianetics: The Modern Science of Mental Health, stressing that the authorities had allowed the book's entry to Egypt. "We are greatly concerned at their prolonged detention, which appears to be a violation of their right to freedom of expression," Goodman said. The two were finally released the next month and the court ruled that condemning people for adopting new ideas is a violation of human rights.
Scientology books in Egypt
Arabic-language translations of books by L. Ron Hubbard, such as Dianetics and The Way to Happiness, have been sold in several book stores in Egypt and were made available at the annual Cairo International Book Fair. The books bore the approval stamp of Al-Azhar, the Muslim world's highest Sunni learning institution. They were printed in Denmark, both in English and Arabic, and shipped to Egypt by New Era Publications. Ahmed Abdel Khalek, a professor at Al-Azhar University who has served as chief-of-staff and translator to the Grand Imam of al-Azhar, said that he had no objections to the approval of the books unless they violated "morality and traditions". "We should be open-minded and listen to the other. After all, if I disagree with something in a book, I should write a rebuttal," he said. New Era Publications' public relations office said that Al-Azhar's move was essential and insisted that there was nothing religious about the books' nature.
Narconon
Narconon Egypt, a drug abuse treatment c |
https://en.wikipedia.org/wiki/Results%20in%20Mathematics | Results in Mathematics/Resultate der Mathematik is a peer-reviewed scientific journal that covers all aspects of pure and applied mathematics and is published by Birkhäuser. It was established in 1978 and the editor-in-chief is Catalin Badea (University of Lille).
Abstracting and indexing
This journal is abstracted and indexed by:
Science Citation Index Expanded
Mathematical Reviews
Scopus
Zentralblatt Math
Academic OneFile
Current Contents/Physical, Chemical and Earth Sciences
Mathematical Reviews
According to the Journal Citation Reports, the journal has a 2013 impact factor of 0.642.
References
External links
Springer Science+Business Media academic journals
Mathematics journals
Academic journals established in 1978
English-language journals
8 times per year journals |
https://en.wikipedia.org/wiki/T.%20Proctor%20Hall | Thomas Proctor Hall (1858–1931) was a Canadian physician who wrote mathematics, chemistry, physics, theology, and science fiction.
T. Proctor Hall was born October 7, 1858, at Hornby, Canada West. He attended Woodstock College and University of Toronto where in 1882 he obtained a bachelor's degree in chemistry. For two years he was a fellow at University of Toronto, then he served as science master in Woodstock, Ontario, for five years.
He proceeded to Illinois Wesleyan University for his doctorate. He then studied at Clark University where W. E. Story lectured on higher-dimensional space. Hall contributed to the topic with his article "The projection of fourfold figures upon a three-flat". He wrote, "Rotation is essentially motion in a plane, and when another dimension is added to the rotating body, another dimension is also added to the axis of rotation." From 1893 to 96 he was professor of natural science at Tabor Academy, Massachusetts.
Albert A. Michelson was teaching physics at Clark University. Examining methods of determining surface tension, in 1893 Hall published the article "New methods of measuring surface tension of liquids". The following year he contributed an article on stereochemistry to Science. And the next year he wrote on gravitation including the speculative kinetic gravity. From 1897 to 1901 he taught physics in Kansas City.
T. Proctor Hall became a medical doctor in 1902 after study in Chicago at the National Medical College. At the Louisiana Purchase Exposition in St. Louis in 1904 he spoke on "Principles of Electro-therapeutics" at the International Electrical Congress held in connection with the Exposition. From 1902 to 5 he was editor of American X-ray Journal. In 1905 Hall relocated to Vancouver, British Columbia, where he practiced medicine as Dr. Thomas P. Hall. He was a proponent of heliotherapy and wrote, "Sunshine has been used for ages in the cure of disease; and sunshine is only a very narrow range of ether waves. Now that the fuller range of ether waves is coming under control, we may surely expect to obtain a large increase of power over misfortune and disease," in a science fiction story.
T. Proctor Hall died in 1931.
Academy of science
T. P. Hall joined the British Columbia Academy of Science (BCAS) at its second meeting. He presented his paper "Scientific Theology" at a meeting December 3, 1910. The following March 4th the BCAS met at his home-office at 1301 Davie Street in Vancouver’s West End. Hall was elected Vice President for 1911-12. He spoke on "A Theory of Electromagnetism" on November 18 at the McGill University College. Hall was elected President of BCAS on April 13, 1912. In 1913 he was also President, with Charles Hill-Tout of Abbotsford Vice President. The following year Hall served as Secretary-Treasurer while Hill-Tout was President. That year BCAS published seven papers assembled in a book, two by Hall, including "Scientific Theology". The other was "A Geometric Vector Algebra", which |
https://en.wikipedia.org/wiki/Pseudocomplement | In mathematics, particularly in order theory, a pseudocomplement is one generalization of the notion of complement. In a lattice L with bottom element 0, an element x ∈ L is said to have a pseudocomplement if there exists a greatest element x* ∈ L with the property that x ∧ x* = 0. More formally, x* = max{ y ∈ L | x ∧ y = 0 }. The lattice L itself is called a pseudocomplemented lattice if every element of L is pseudocomplemented. Every pseudocomplemented lattice is necessarily bounded, i.e. it has a 1 as well. Since the pseudocomplement is unique by definition (if it exists), a pseudocomplemented lattice can be endowed with a unary operation * mapping every element to its pseudocomplement; this structure is sometimes called a p-algebra. However this latter term may have other meanings in other areas of mathematics.
Properties
In a p-algebra L, for all
The map x ↦ x* is antitone. In particular, 0* = 1 and 1* = 0.
The map x ↦ x** is a closure.
x* = x***.
(x∨y)* = x* ∧ y*.
(x∧y)** = x** ∧ y**.
The set S(L) ≝ { x** | x ∈ L } is called the skeleton of L. S(L) is a ∧-subsemilattice of L and together with x ∪ y = (x∨y)** = (x* ∧ y*)* forms a Boolean algebra (the complement in this algebra is *). In general, S(L) is not a sublattice of L. In a distributive p-algebra, S(L) is the set of complemented elements of L.
Every element x with the property x* = 0 (or equivalently, x** = 1) is called dense. Every element of the form x ∨ x* is dense. D(L), the set of all the dense elements in L is a filter of L. A distributive p-algebra is Boolean if and only if D(L) = {1}.
Pseudocomplemented lattices form a variety; indeed, so do pseudocomplemented semilattices.
Examples
Every finite distributive lattice is pseudocomplemented.
Every Stone algebra is pseudocomplemented. In fact, a Stone algebra can be defined as a pseudocomplemented distributive lattice L in which any of the following equivalent statements hold for all
S(L) is a sublattice of L;
(x∧y)* = x* ∨ y*;
(x∨y)** = x** ∨ y**;
x* ∨ x** = 1.
Every Heyting algebra is pseudocomplemented.
If X is a topological space, the (open set) topology on X is a pseudocomplemented (and distributive) lattice with the meet and join being the usual union and intersection of open sets. The pseudocomplement of an open set A is the interior of the set complement of A. Furthermore, the dense elements of this lattice are exactly the dense open subsets in the topological sense.
Relative pseudocomplement
A relative pseudocomplement of a with respect to b is a maximal element c such that a∧c≤b. This binary operation is denoted a→b. A lattice with the pseudocomplement for each two elements is called implicative lattice, or Brouwerian lattice. In general, an implicative lattice may not have a minimal element. If such a minimal element exists, then each pseudocomplement a* could be defined using relative pseudocomplement as a → 0.
See also
References
Lattice theory |
https://en.wikipedia.org/wiki/Arakawa%E2%80%93Kaneko%20zeta%20function | In mathematics, the Arakawa–Kaneko zeta function is a generalisation of the Riemann zeta function which generates special values of the polylogarithm function.
Definition
The zeta function is defined by
where Lik is the k-th polylogarithm
Properties
The integral converges for and has analytic continuation to the whole complex plane as an entire function.
The special case k = 1 gives where is the Riemann zeta-function.
The special case s = 1 remarkably also gives where is the Riemann zeta-function.
The values at integers are related to multiple zeta function values by
where
References
Zeta and L-functions |
https://en.wikipedia.org/wiki/Pentti%20Saikkonen | Pentti Juhani Saikkonen (born 12 February 1952) is a Finnish statistician specializing in time series analysis.
Since 2004 he is a professor of statistics at the University of Helsinki.
A native of Lahti, Saikkonen attended the University of Helsinki, where he earned his licentiate in 1981, and his doctorate in 1986.
Selected publications
References
External links
Website at the University of Helsinki
1952 births
Living people
Finnish statisticians
Time series econometricians
University of Helsinki alumni |
https://en.wikipedia.org/wiki/Circuit%20topology | The circuit topology of a folded linear polymer refers to the arrangement of its intra-molecular contacts. Examples of linear polymers with intra-molecular contacts are nucleic acids and proteins. Proteins fold via formation of contacts of various nature, including hydrogen bonds, disulfide bonds, and beta-beta interactions. RNA molecules fold by forming hydrogen bonds between nucleotides, forming nested or non-nested structures. Contacts in the genome are established via protein bridges including CTCF and cohesins and are measured by technologies including Hi-C. Circuit topology categorises the topological arrangement of these physical contacts, that are referred to as hard contacts (or h-contacts). Furthermore, chains can fold via knotting (or formation of "soft" contacts (s-contacts)). Circuit topology uses a similar language to categorise both "soft" and "hard" contacts, and provides a full description of a folded linear chain. In this framework, a "circuit" refers to a segment of the chain where each contact site within the segment forms connections with other contact sites within the same segment, and thus is not left unpaired. A folded chain can thus be studied based on its constituting circuits.
A simple example of a folded chain is a chain with two hard contacts. For a chain with two binary contacts, three arrangements are available: parallel (P), series (S) and crossed (X). For a chain with n contacts, the topology can be described by an n by n matrix in which each element illustrates the relation between a pair of contacts and may take one of the three states, P, S and X. Multivalent contacts can also be categorised in full or via decomposition into several binary contacts. Similarly, circuit topology allows for classification of the pairwise arrangements of chain crossings and tangles, thus providing a complete 3D description of folded chains. Furthermore, one can apply circuit topology operations to soft and hard contacts to generate complex folds, using a bottom-up engineering approach.
Both knot theory and circuit topology aim to describe chain entanglement, making it important to understand their relationship. Knot theory considers any entangled chain as a connected sum of prime knots, which are themselves undecomposable. Circuit topology splits any entangled chains (including prime knots) into basic structural units called soft contacts, and lists simple rules how soft contacts can be put together. An advantage of circuit topology is that it can be applied to open linear chains with intra-chain interactions, so called hard contacts. This enabled topological analysis of proteins and genomes, which are often described as "unknot" in knot theory. Finally, circuit topology enables studying interactions between hard contacts and entanglements and is able to identify slip-knots, while knot theory typically overlooks hard contacts and split knots. Thus, circuit topology serves as a complementary approach to knot theory.
Circuit top |
https://en.wikipedia.org/wiki/E-dense%20semigroup |
In abstract algebra, an E-dense semigroup (also called an E-inversive semigroup) is a semigroup in which every element a has at least one weak inverse x, meaning that xax = x. The notion of weak inverse is (as the name suggests) weaker than the notion of inverse used in a regular semigroup (which requires that axa=a).
The above definition of an E-inversive semigroup S is equivalent with any of the following:
for every element a ∈ S there exists another element b ∈ S such that ab is an idempotent.
for every element a ∈ S there exists another element c ∈ S such that ca is an idempotent.
This explains the name of the notion as the set of idempotents of a semigroup S is typically denoted by E(S).
The concept of E-inversive semigroup was introduced by Gabriel Thierrin in 1955. Some authors use E-dense to refer only to E-inversive semigroups in which the idempotents commute.
More generally, a subsemigroup T of S is said dense in S if, for all x ∈ S, there exists y ∈ S such that both xy ∈ T and yx ∈ T.
A semigroup with zero is said to be an E*-dense semigroup if every element other than the zero has at least one non-zero weak inverse. Semigroups in this class have also been called 0-inversive semigroups.
Examples
Any regular semigroup is E-dense (but not vice versa).
Any eventually regular semigroup is E-dense.
Any periodic semigroup (and in particular, any finite semigroup) is E-dense.
See also
Dense set
E-semigroup
References
Further reading
Mitsch, H. "Introduction to E-inversive semigroups." Semigroups : proceedings of the international conference ; Braga, Portugal, June 18–23, 1999. World Scientific, Singapore. 2000.
Semigroup theory
Algebraic structures |
https://en.wikipedia.org/wiki/Matti%20Nuutinen | Matti Nuutinen (born 6 May 1990) is a Finnish former basketball player. Since 2012, he played for the Finnish national team.
Honours
Korisliiga: 2012, 2013
Career statistics
EuroCup
|-
| style="text-align:left;"| 2013–14
| style="text-align:left;"| Bisons Loimaa
| 9 || 4 || 18.9 || .441|| .353 || 1.000 || 1.4 || .3 || .3 || .0 || 4.1 || 1.8
External links
Profile – Eurobasket.com
1990 births
Living people
Arkadikos B.C. players
Chorale Roanne Basket players
CSU Pitești players
Finnish expatriate basketball people in France
Finnish expatriate basketball people in Greece
Finnish expatriate basketball people in Spain
Finnish expatriate basketball people in Romania
Finnish men's basketball players
Kouvot players
Oviedo CB players
Power forwards (basketball)
Small forwards
Sportspeople from Turku
2014 FIBA Basketball World Cup players
Bisons Loimaa players
Vilpas Vikings players |
https://en.wikipedia.org/wiki/E-semigroup | In the area of mathematics known as semigroup theory, an E-semigroup is a semigroup in which the idempotents form a subsemigroup.
Certain classes of E-semigroups have been studied long before the more general class, in particular, a regular semigroup that is also an E-semigroup is known as an orthodox semigroup.
Weipoltshammer proved that the notion of weak inverse (the existence of which is one way to define E-inversive semigroups) can also be used to define/characterize E-semigroups as follows: a semigroup S is an E-semigroup if and only if, for all a and b ∈ S, W(ab) = W(b)W(a), where W(a) ≝ {x ∈ S | xax = x} is the set of weak inverses of a.
References
Semigroup theory
Algebraic structures |
https://en.wikipedia.org/wiki/Yusuke%20Minagawa | (born 9 October 1991) is a Japanese international football player who plays for Renofa Yamaguchi FC as a striker.
Club statistics
Updated to 17 December 2022.
1Includes Japanese Super Cup, J. League Championship and FIFA Club World Cup.
National team statistics
References
External links
Japan National Football Team Database
Profile at Vegalta Sendai
Profile at Yokohama FC
Profile at Roasso Kumamoto
Profile at Sanfrecce Hiroshima
1991 births
Living people
Chuo University alumni
Association football people from Saitama Prefecture
Japanese men's footballers
Japan men's international footballers
J1 League players
J2 League players
Sanfrecce Hiroshima players
Roasso Kumamoto players
Yokohama FC players
Vegalta Sendai players
Men's association football forwards
Universiade bronze medalists for Japan
Universiade medalists in football
Medalists at the 2013 Summer Universiade
People from Tokorozawa, Saitama
21st-century Japanese people |
https://en.wikipedia.org/wiki/Rhombic%20hexecontahedron | In geometry, a rhombic hexecontahedron is a stellation of the rhombic triacontahedron. It is nonconvex with 60 golden rhombic faces with icosahedral symmetry. It was described mathematically in 1940 by Helmut Unkelbach.
It is topologically identical to the convex deltoidal hexecontahedron which has kite faces.
Dissection
The rhombic hexecontahedron can be dissected into 20 acute golden rhombohedra meeting at a central point. This gives the volume of a hexecontahedron of side length a to be and the area to be .
Construction
A rhombic hexecontahedron can be constructed from a regular dodecahedron, by taking its vertices, its face centers and its edge centers and scaling them in or out from the body center to different extents. Thus, if the 20 vertices of a dodecahedron are pulled out to increase the circumradius by a factor of (ϕ+1)/2 ≈ 1.309, the 12 face centers are pushed in to decrease the inradius to (3-ϕ)/2 ≈ 0.691 of its original value, and the 30 edge centers are left unchanged, then a rhombic hexecontahedron is formed. (The circumradius is increased by 30.9% and the inradius is decreased by the same 30.9%.) Scaling the points by different amounts results in hexecontahedra with kite-shaped faces or other polyhedra.
Every golden rhombic face has a face center, a vertex, and two edge centers of the original dodecahedron, with the edge centers forming the short diagonal. Each edge center is connected to two vertices and two face centers. Each face center is connected to five edge centers, and each vertex is connected to three edge centers.
Stellation
The rhombic hexecontahedron is one of 227 self-supporting stellations of the rhombic triacontahedron. Its stellation diagram looks like this, with the original rhombic triacontahedron faces as the central rhombus.
Related polyhedra
The great rhombic triacontahedron contains the 30 larger intersecting rhombic faces:
In popular culture
In Brazilian culture, handcrafted rhombic hexecontahedra used to be made from colored fabric and cardboard, called ("world turners" in Portuguese) or happiness stars, sewn by mothers and given as wedding gifts to their daughters. The custom got lost with the urbanization of Brazil, though the technique for producing the handicrafts was still taught in Brazilian rural schools up until the first half of the twentieth century.
The logo of the WolframAlpha website is a red rhombic hexecontahedron and was inspired by the logo of the related Mathematica software.
References
Bibliography
Unkelbach, H. "Die kantensymmetrischen, gleichkantigen Polyeder. Deutsche Math. 5, 306-316, 1940.
Grünbaum, B. Parallelogram-Faced Isohedra with Edges in Mirror-Planes.'' Discrete Math. 221, 93–100, 2000.
External links
http://www.georgehart.com/virtual-polyhedra/zonohedra-info.html
The Bilinski dodecahedron, and assorted parallelohedra, zonohedra, monohedra, isozonohedra and otherhedra. Branko Grünbaum
Zonohedra
Polyhedral stellation |
https://en.wikipedia.org/wiki/Octagrammic%20cupola | In geometry, the octagrammic cupola is a star-cupola made from an octagram, {8/3} and parallel hexadecagram, {16/3}, connected by 8 equilateral triangles and squares.
Related polyhedra
Crossed octagrammic cupola
The crossed octagrammic cupola is a star-cupola made from an octagram, {8/5} and parallel hexadecagram, {16/5}, connected by 8 equilateral triangles and squares.
References
Jim McNeill, Cupola OR Semicupola
Richard Klitzing, Axial-Symmetrical Edge Facetings of Uniform Polyhedra
External links
VRML models 8-3 8-5
Prismatoid polyhedra |
https://en.wikipedia.org/wiki/Displaced%20Poisson%20distribution | In statistics, the displaced Poisson, also known as the hyper-Poisson distribution, is a generalization of the Poisson distribution.
The probability mass function is
where and r is a new parameter; the Poisson distribution is recovered at r = 0. Here is the Pearson's incomplete gamma function:
where s is the integral part of r.
The motivation given by Staff is that the ratio of successive probabilities in the Poisson distribution (that is ) is given by for and the displaced Poisson generalizes this ratio to .
References
Discrete distributions |
https://en.wikipedia.org/wiki/Heptagrammic%20cupola | In geometry, the heptagrammic cupola is a star-cupola made from a heptagram, {7/3} and parallel tetradecagram, {14/3}, connected by 7 mutually intersecting equilateral triangles and squares.
Related polyhedra
Crossed heptagrammic cupola
The crossed heptagrammic cupola is a star-cupola made from a heptagram, {7/5} and parallel tetradecagram, {14/5}, connected by 7 mutually intersecting equilateral triangles and squares.
References
Jim McNeill, Cupola OR Semicupola
External links
VRML models 7-3 7-5
Prismatoid polyhedra |
https://en.wikipedia.org/wiki/Baumgartner%27s%20axiom | In mathematical set theory, Baumgartner's axiom (BA) can be one of three different axioms introduced by James Earl Baumgartner.
A subset of the real line is said to be -dense if every two points are separated by exactly other points, where is the smallest uncountable cardinality. This would be true for the real line itself under the continuum hypothesis. An axiom introduced by states that all -dense subsets of the real line are order-isomorphic, providing a higher-cardinality analogue of Cantor's isomorphism theorem that countable dense subsets are isomorphic. Baumgartner's axiom is a consequence of the proper forcing axiom. It is consistent with a combination of ZFC, Martin's axiom, and the negation of the continuum hypothesis, but not implied by those hypotheses.
Another axiom introduced by states that Martin's axiom for partially ordered sets MAP(κ) is true for all partially ordered sets P that are countable closed, well met and ℵ1-linked and all cardinals κ less than 2ℵ1.
Baumgartner's axiom A is an axiom for partially ordered sets introduced in . A partial order (P, ≤) is said to satisfy axiom A if there is a family ≤n of partial orderings on P for n = 0, 1, 2, ... such that
≤0 is the same as ≤
If p ≤n+1q then p ≤nq
If there is a sequence pn with pn+1 ≤n pn then there is a q with q ≤n pn for all n.
If I is a pairwise incompatible subset of P then for all p and for all natural numbers n there is a q such that q ≤n p and the number of elements of I compatible with q is countable.
References
Axioms of set theory |
https://en.wikipedia.org/wiki/Pseudo-intersection | In mathematical set theory, a pseudo-intersection of a family of sets is an infinite set S such that each element of the family contains all but a finite number of elements of S. The pseudo-intersection number, sometimes denoted by the fraktur letter 𝔭, is the smallest size of a family of infinite subsets of the natural numbers that has the strong finite intersection property but has no pseudo-intersection.
References
Set theory |
https://en.wikipedia.org/wiki/Verkin%20Institute%20for%20Low%20Temperature%20Physics%20and%20Engineering | The B. Verkin Institute for Low Temperature Physics and Engineering () is a research institute that conducts basic research in experimental and theoretical physics, mathematics, as well as in the field of applied physics. It was founded in 1960 by Borys Verkin, Oleksandr Galkin, Borys. Eselson and Ihor Dmytrenko. The first director was Borys Verkin.
Main areas of research are high-temperature superconductivity, weak superconductivity, magneto antiferromagnets, physics of low-dimensional systems, point-contact spectroscopy, quantum crystals, nonlinear phenomena in metals, physics of disordered systems, quantum phenomena in plasticity and others. The institute has published about 250 monographs, textbooks, reference books, more than 12,000 articles and reviews in ranking scientific journals, and has trained more than 850 highly qualified experts — PhDs.
History
On May 13, 1960 the presidium of the National Academy of Sciences of Ukraine issued a decision to establish the Kharkiv Physics and Technical Institute for Low Temperatures on the initiative of several scientists from the Ukrainian Institute of Physics and Technology.
The institute was created by nine laboratories involved in low temperature physics. Four math departments were also established. In 1987 they were organized into the ILTPE Mathematics Department.
In 1991 ILTPE was named after its founder — B. Verkin.
Directors
1960 — 1988 Borys Verkin
1988 — 1991 Anatolii Zvyagin
1991 — 2006 Viktor Yeremenko
2006 — 2020 Serhiy Hnatchenko
2021 - Yurii Naidyuk
Structure
Physics departments
Department of Magnetism
Department of Optical and Magnetic Properties of Solids
Department of Magnetic and Elastic Properties of Solids
Department of Transport Properties of Conducting and Superconducting Systems
Department of Physics of Real Crystals
Department of Thermal Properties and Structure of Solids and Nanosystems
Department of Physics of Quantum Fluids and Crystals
Department of Spectroscopy of Molecular Systems and Nanostructured Materials
Department of Superconducting and Mesoscopic Structures
Department of Molecular Biophysics
Department of Point-Contact Spectroscopy
Department of Theoretical Physics
Mathematics departments
Department of Mathematical Physics
Department of Differential Equations and Geometry
Department of Statistical Methods in Mathematical Physics
Department of Function Theory
Scientific & Technical departments
Department of Information Systems
Department of low-temperatures and space materials
Publications
ILTPE publishes two scientific journals included on a list of leading peer-reviewed scientific journals and publications:
Low Temperature Physics, published since January 1975 in Russian, as well as the American Institute of Physics in English under the title Low Temperature Physics 1997. Published monthly. The magazine has Ukraine's highest impact factor of scientific journals.
Journal of Mathematical Physics, Analysis, Geometry, published s |
https://en.wikipedia.org/wiki/Erfan%20Maftoolkar | Erfan Maftoolkar is an Iranian footballer who plays as a forward for Foolad Yazd in the Azadegan League.
Club career statistics
Last Update: 5 September 2014
Honours
Club
Sepahan
Iran Pro League (1): 2014–15
References
Sepahan S.C. footballers
1994 births
Living people
Footballers from Isfahan
Sanaye Giti Pasand F.C. players
Iran men's under-20 international footballers
Iranian men's footballers
Men's association football forwards |
https://en.wikipedia.org/wiki/Hexecontahedron | In geometry, a hexecontahedron (or hexacontahedron) is a polyhedron with 60 faces. There are many symmetric forms, and the ones with highest symmetry have icosahedral symmetry:
Four Catalan solids, convex:
Pentakis dodecahedron - isosceles triangles
Deltoidal hexecontahedron - kites
Pentagonal hexecontahedron - pentagons
Triakis icosahedron - isosceles triangles
Concave
Rhombic hexecontahedron - rhombi
27 uniform star-polyhedral duals: (self-intersecting)
Small dodecicosacron, Great dodecicosacron
Small rhombidodecacron, Great rhombidodecacron
Small dodecacronic hexecontahedron, Great dodecacronic hexecontahedron
Rhombicosacron
Small icosacronic hexecontahedron, Medial icosacronic hexecontahedron, Great icosacronic hexecontahedron
Small stellapentakis dodecahedron, Great stellapentakis dodecahedron
Great pentakis dodecahedron
Great triakis icosahedron
Small ditrigonal dodecacronic hexecontahedron, Great ditrigonal dodecacronic hexecontahedron
Medial deltoidal hexecontahedron, Great deltoidal hexecontahedron
Medial pentagonal hexecontahedron, Great pentagonal hexecontahedron
Medial inverted pentagonal hexecontahedron, Great inverted pentagonal hexecontahedron
Great pentagrammic hexecontahedron
Small hexagonal hexecontahedron, Medial hexagonal hexecontahedron, Great hexagonal hexecontahedron
Small hexagrammic hexecontahedron
References
Polyhedra |
https://en.wikipedia.org/wiki/List%20of%20Djurg%C3%A5rdens%20IF%20Fotboll%20records%20and%20statistics | Djurgårdens IF Fotboll is a Swedish professional football club based in Stockholm.
The list encompasses the major honours won by Djurgården, records set by the club, their managers and their players.
Honours
Domestic
Swedish Champions
Winners (12): 1912, 1915, 1917, 1920, 1954–1955, 1959, 1964, 1966, 2002, 2003, 2005, 2019
League
Allsvenskan:
Winners (8): 1954–1955, 1959, 1964, 1966, 2002, 2003, 2005, 2019
Runners-up (4): 1962, 1967, 2001, 2022
Superettan:
Winners (1): 2000
Division 1 Norra:
Winners (3): 1987, 1994, 1998
Runners-up (1): 1997
Svenska Serien:
Runners-up (1): 1911–1912
Cups
Svenska Cupen:
Winners (5): 1989–1990, 2002, 2004, 2005, 2017-2018
Runners-up (4): 1951, 1974–1975, 1988–1989, 2013
Svenska Mästerskapet:
Winners (4): 1912, 1915, 1917, 1920
Runners-up (7): 1904, 1906, 1909, 1910, 1913, 1916, 1919
Allsvenskan play-offs:
Runners-up (1): 1988
Corinthian Bowl:
Winners (1): 1910
Runners-up (2): 1908, 1911
Rosenska Pokalen:
Runners-up (2): 1902
Wicanderska Välgörenhetsskölden:
Winners (4): 1907, 1910, 1913, 1915
Runners-up (3): 1908, 1914, 1916
Doubles
2002: League and Svenska Cupen
2005: League and Svenska Cupen
Player records
Appearances
Most appearances in all competitions: Gösta Sandberg, 328
Most league appearances: Gösta Sandberg, 322
Most Allsvenskan appearances: Sven Lindman, 312
Most cup appearances: Haris Radetinac, 34
Most continental appearances: Haris Radetinac, 21
Youngest first-team player: Isak Alemayehu Mulugeta – (against Mjällby AIF, Allsvenskan, 6 November 2022)
Oldest first-team player: Björn Alkeby – (against Ope IF, Division 1 Norra, 29 August 1993)
Most consecutive appearances: Sven Lindman, 175 (1970–1977)
Most appearances
Competitive matches only, includes appearances as substitute. Numbers in brackets indicate goals scored.
Goalscorers
Most goals in all competitions: Gösta Sandberg, 79
Most league goals: Gösta Sandberg, 77
Most Allsvenskan goals: Gösta Sandberg, 70
Most cup goals: Andreas Johansson, 16
Most continental goals: Fredrik Dahlström and Kaj Eskelinen, both 5
Most goals in a season: Leif Skiöld, 30 goals (in the 1961 season)
Most league goals in a season: Leif Skiöld, 27 goals (in the 1961 season)
Most goals in a single match: Leif Skiöld, 6 goals (against IFK Eskilstuna, Division 2 Svealand, 23 September 1961)
Youngest goalscorer: Roger Lindevall – (against AIK, Allsvenskan, 2 June 1977)
Oldest goalscorer: Sven Lindman – (against IFK Norrköping, Allsvenskan, 11 June 1980)
Top goalscorers
Competitive matches only. Numbers in brackets indicate appearances made.
International
First capped players: Ivar Friberg, Erik Lavass, Samuel Lindqvist, and Bertil Nordenskjöld for Sweden v. Norway (11 September 1910)
Most capped Djurgården player for Sweden while playing for the club: Gösta Sandberg, 52 caps whilst an Djurgården player
First player to play in a World Cup: Hasse Jeppson for Sweden v. Italy (25 June 1950)
First player to play in a |
https://en.wikipedia.org/wiki/Wiktor%20Eckhaus | Wiktor Eckhaus (28 June 1930 – 1 October 2000) was a Polish–Dutch mathematician, known for his work on the field of differential equations. He was Professor Emeritus of Applied Mathematics at the Utrecht University.
Biography
Eckhaus was born into a wealthy family, and raised in Warsaw where his father was managing a fur company. During the German occupation of Poland, he, his mother and sister had to hide because of their Jewish descent. His father, after being a prisoner of war, joined the Russian Army. After the war, in 1947, the re-united family came to Amsterdam – via a refugee camp in Austria.
Wiktor passed the state exam of the Hogere Burgerschool in 1948, and started to study aeronautics at the Delft University of Technology. Following his graduation he worked with the National Aerospace Laboratory in Amsterdam, from 1953 till 1957. In the period 1957–1960 he worked at the Massachusetts Institute of Technology, where Eckhaus earned a PhD in 1959 under Leon Trilling on a dissertation entitled "Some problems of unsteady flow with discontinuities".
In 1960, he became a "maître de recherches" (senior research fellow) at the Department of Mechanics of the Sorbonne. In 1964 he was a visiting professor at the University of Amsterdam and the Mathematical Centre. Thereafter, in 1965, he became professor at the Delft University of Technology, in pure and applied mathematics and mechanics. From 1972 until his retirement in 1994, Eckhaus was professor of applied mathematics at the Utrecht University.
Initially he studied the flow around airfoils, leading to his research on the stability of solutions to (weakly nonlinear) differential equations. This resulted in what is now known as the Eckhaus instability criterion and Eckhaus instability, appearing for instance as a secondary instability in models of Rayleigh–Bénard convection. Later, Eckhaus worked on singular perturbation theory and soliton equations.
In 1983 he treated strongly singular relaxation oscillations – called "canards" (French for "ducks") – resulting in his most-read paper "Relaxation oscillations including a standard chase on French ducks". Eckhaus used standard methods of analysis, on a problem qualified before, by Marc Diener, as an example of a problem only treatable through the use of non-standard analysis.
He became a member of the Royal Netherlands Academy of Arts and Sciences in 1987.
Publications
Notes
References
Also appeared as:
External links
1930 births
2000 deaths
People from Ivano-Frankivsk
People from Stanisławów Voivodeship
Ukrainian Jews
Polish emigrants to the Netherlands
Dutch people of Ukrainian-Jewish descent
Aerodynamicists
20th-century Dutch mathematicians
MIT School of Engineering alumni
Academic staff of Utrecht University
Academic staff of the Delft University of Technology
Members of the Royal Netherlands Academy of Arts and Sciences |
https://en.wikipedia.org/wiki/Sierpi%C5%84ski%20set | In mathematics, a Sierpiński set is an uncountable subset of a real vector space whose intersection with every measure-zero set is countable. The existence of Sierpiński sets is independent of the axioms of ZFC. showed that they exist if the continuum hypothesis is true. On the other hand, they do not exist if Martin's axiom for ℵ1 is true. Sierpiński sets are weakly Luzin sets but are not Luzin sets .
Example of a Sierpiński set
Choose a collection of 2ℵ0 measure-0 subsets of R such that every measure-0 subset is contained in one of them. By the continuum hypothesis, it is possible to enumerate them as Sα for countable ordinals α. For each countable ordinal β choose a real number xβ that is not in any of the sets Sα for α < β, which is possible as the union of these sets has measure 0 so is not the whole of R. Then the uncountable set X of all these real numbers xβ has only a countable number of elements in each set Sα, so is a Sierpiński set.
It is possible for a Sierpiński set to be a subgroup under addition. For this one modifies the construction above by choosing a real number xβ that is not in any of the countable number of sets of the form (Sα + X)/n for α < β, where n is a positive integer and X is an integral linear combination of the numbers xα for α < β. Then the group generated by these numbers is a Sierpiński set and a group under addition. More complicated variations of this construction produce examples of Sierpiński sets that are subfields or real-closed subfields of the real numbers.
References
Measure theory
Set theory |
https://en.wikipedia.org/wiki/Caroline%20Series | Caroline Mary Series (born 24 March 1951) is an English mathematician known for her work in hyperbolic geometry, Kleinian groups and dynamical systems.
Early life and education
Series was born on March 24, 1951, in Oxford to Annette and George Series. She attended Oxford High School for Girls and from 1969 studied at Somerville College, Oxford, where she was interviewed for admission by Anne Cobbe. She obtained a B.A. in Mathematics in 1972 and was awarded the university Mathematical Prize. She was awarded a Kennedy Scholarship and studied at Harvard University from 1972, obtaining her Ph.D. in 1976 supervised by George Mackey on the Ergodicity of product groups.
Career and research
In 1976–77 she was a lecturer at University of California, Berkeley, and in 1977–78 she was a research fellow at Newnham College, Cambridge. From 1978 she was at the University of Warwick, first as a lecturer, then, from 1987, as a reader, and from 1992 as a professor. From 1999 to 2004 she was Engineering and Physical Sciences Research Council (EPSRC) Senior Research Fellow at the University of Warwick.
In the 1970s, Series found illustrations of Rufus Bowen's Theory of Dynamic Systems in the geometry of continued fractions and two-dimensional hyperbolic geometry, effect of Fuchsian groups. After that she investigated similar, including fractal, geometric patterns in three-dimensional hyperbolic spaces, with Kleinian groups as symmetry groups. The computer images led to a book project with David Mumford and David Wright, which took over ten years. Other coauthors with whom she published in this area include Linda Keen and Joan Birman.
Series became the third woman to be president of the London Mathematical Society when she held the post in 2017–2019.
She is emeritus professor in mathematics at the University of Warwick.
Selected publications
with David Mumford and David Wright: Indra's Pearls. Cambridge University Press 2002.
Series, Wright Non euclidean geometry and Indra´s Pearls, Plus Magazine
Honours and awards
In 1987 she was awarded the Junior Whitehead Prize by the London Mathematical Society. In 1992 she held the Rouse Ball Lecture in Cambridge, and in 1986 she was the invited speaker at the International Congress of Mathematicians in Berkeley (Symbolic Dynamics for Geodesic Flows). From 1990 to 2001 she was the editor of the Student Texts of the London Mathematical Society. In 1986 she was a founding member of European Women in Mathematics (EWM). In 2009 she was the Emmy Noether visiting professor at the University of Göttingen. She was elected a Fellow of the American Mathematical Society in its inaugural class of 2013. She is an Honorary Fellow of Somerville College.
1972 –74 Kennedy Scholarship, Harvard University
1987 Junior Whitehead Prize, London Mathematical Society
2014 Senior Anne Bennett Prize, London Mathematical Society
2016 Fellow of the Royal Society
2017 Elected to the Academia Europaea
2021 David Crighton Medal, London M |
https://en.wikipedia.org/wiki/Roy%20Thomas%20Severn | Professor Roy Thomas Severn CBE DSc PhD FREng FICE (6 September 1929 – 25 November 2012) was a British civil engineer and earthquake engineering expert. Severn studied mathematics at Imperial College London and achieved a doctorate in civil engineering based upon his work on the design of Dukan Dam. After completing his National Service he accepted a position as lecturer in civil engineering at the University of Bristol, where he would spend the rest of his career. Severn specialised in earthquake engineering and established the Earthquake Engineering Research Centre at the university which became one of the foremost institutions in the world within the field. He served as pro-vice chancellor of the university and as president of the Institution of Civil Engineers.
Early life and army service
Severn was born in Hucknall in Nottinghamshire on 6 September 1929. His father was originally a coal miner before he found work at the Hucknall co-operative shop and later became manager of the Great Yarmouth branch. Severn was educated at Deacon's School, Peterborough and Great Yarmouth Grammar School before gaining a place at the Royal College of Science (RCS), part of the Imperial College London, to study mathematics.
Severn was a keen sportsman whilst a student and played cricket, rugby and football. Whilst playing for Wasps (Rugby) Football Club he met Professor Sammy Sparkes, also of Imperial College, who persuaded him to study civil engineering as a post-graduate, and also Deryck Norman de Garrs Allen, who became his PhD supervisor. Allen, who had studied under Sir Richard V. Southwell, was asked by Geoffrey Binnie's engineering consultancy to apply Southwell's equation-solving techniques to the design of the Dukan Dam in Iraq. Allen involved Severn in the project, as part of which the pair visited several arch dams and spent a significant amount of time solving complex design equations on mechanical calculators via relaxation methods. The project formed the basis of Severn's doctoral thesis.
Severn was required to serve in the British Army under the National Service programme and carried this out as an officer in the Royal Engineers. Entering as an officer cadet in 1954 he was commissioned as a second lieutenant on 4 June 1955. Severn studied at the Royal School of Military Survey in Curridge, Berkshire and served in Egypt, Cyprus and Aden before his service ended and he was placed in the Army Emergency Reserve of Officers on 29 September 1956. He was promoted to lieutenant in the reserve on 25 January 1957, and remained eligible for recall until he retired (with permission to retain use of his rank) on 1 April 1967.
University of Bristol
After he was demobilised from the army Severn, who decided he did not wish to work as a mathematician, entered upon a career in civil engineering academia and was appointed to lecture at the University of Bristol by Sir Alfred Pugsley, who was then professor of Civil Engineering. Within a year |
https://en.wikipedia.org/wiki/Mostowski%20model | In mathematical set theory, the Mostowski model is a model of set theory with atoms where the full axiom of choice fails, but every set can be linearly ordered. It was introduced by . The Mostowski model can be constructed as the permutation model corresponding to the group of all automorphisms of the ordered set of rational numbers and the ideal of finite subsets of the rational numbers.
References
Set theory |
https://en.wikipedia.org/wiki/Permutation%20model | In mathematical set theory, a permutation model is a model of set theory with atoms (ZFA) constructed using a group of permutations of the atoms. A symmetric model is similar except that it is a model of ZF (without atoms) and is constructed using a group of permutations of a forcing poset. One application is to show the independence of the axiom of choice from the other axioms of ZFA or ZF.
Permutation models were introduced by and developed further by .
Symmetric models were introduced by Paul Cohen.
Construction of permutation models
Suppose that A is a set of atoms, and G is a group of permutations of A. A normal filter of G is a collection F of subgroups of G such that
G is in F
The intersection of two elements of F is in F
Any subgroup containing an element of F is in F
Any conjugate of an element of F is in F
The subgroup fixing any element of A is in F.
If V is a model of ZFA with A the set of atoms, then an element of V is called symmetric if the subgroup fixing it is in F, and is called hereditarily symmetric if it and all elements of its transitive closure are symmetric. The permutation model consists of all hereditarily symmetric elements, and is a model of ZFA.
Construction of filters on a group
A filter on a group can be constructed from an invariant ideal on of the Boolean algebra of subsets of A containing all elements of A. Here an ideal is a collection I of subsets of A closed under taking finite unions and subsets, and is called invariant if it is invariant under the action of the group G. For each element S of the ideal one can take the subgroup of G consisting of all elements fixing every element S. These subgroups generate a normal filter of G.
References
Set theory |
https://en.wikipedia.org/wiki/Mathematical%20theory | A mathematical theory is a mathematical model of a branch of mathematics that is based on a set of axioms. It can also simultaneously be a body of knowledge (e.g., based on known axioms and definitions), and so in this sense can refer to an area of mathematical research within the established framework.
Explanatory depth is one of the most significant theoretical virtues in mathematics. For example, set theory has the ability to systematize and explain number theory and geometry/analysis. Despite the widely logical necessity (and self-evidence) of arithmetic truths such as 1<3, 2+2=4, 6-1=5, and so on, a theory that just postulates an infinite blizzard of such truths would be inadequate. Rather an adequate theory is one in which such truths are derived from explanatorily prior axioms, such as the Peano Axioms or set theoretic axioms, which lie at the foundation of ZFC axiomatic set theory.
The singular accomplishment of axiomatic set theory is its ability to give a foundation for the derivation of the entirety of classical mathematics from a handful of axioms. The reason set theory is so prized is because of its explanatory depth. So a mathematical theory which just postulates an infinity of arithmetic truths without explanatory depth would not be a serious competitor to Peano arithmetic or Zermelo-Fraenkel set theory.
See also
List of mathematical theories
Theorem, a statement with a mathematical proof
Theory (mathematical logic)
Unifying theories in mathematics
References
External links
Formal theories
Mathematical terminology |
https://en.wikipedia.org/wiki/Madiyar%20Ibraibekov | Madiyar Sandybaiuly Ibraibekov (; born September 4, 1995) a Kazakh professional ice hockey defenceman who played for Barys Astana of the Kontinental Hockey League (KHL).
Career statistics
Regular season and playoffs
International
References
External links
1995 births
Living people
Asian Games gold medalists for Kazakhstan
Asian Games medalists in ice hockey
Barys Astana draft picks
Barys Nur-Sultan players
Competitors at the 2017 Winter Universiade
Ice hockey people from Moscow
Ice hockey players at the 2017 Asian Winter Games
Kazakhstani ice hockey defencemen
Medalists at the 2017 Asian Winter Games
Nomad Astana players
Snezhnye Barsy players
Universiade medalists in ice hockey
Universiade silver medalists for Kazakhstan |
https://en.wikipedia.org/wiki/Ricci%20soliton | In differential geometry, a complete Riemannian manifold is called a Ricci soliton if, and only if, there exists a smooth vector field such that
for some constant . Here is the Ricci curvature tensor and represents the Lie derivative. If there exists a function such that we call a gradient Ricci soliton and the soliton equation becomes
Note that when or the above equations reduce to the Einstein equation. For this reason Ricci solitons are a generalization of Einstein manifolds.
Self-similar solutions to Ricci flow
A Ricci soliton yields a self-similar solution to the Ricci flow equation
In particular, letting
and integrating the time-dependent vector field to give a family of diffeomorphisms , with the identity, yields a Ricci flow solution by taking
In this expression refers to the pullback of the metric by the diffeomorphism . Therefore, up to diffeomorphism and depending on the sign of , a Ricci soliton homothetically shrinks, remains steady or expands under Ricci flow.
Examples of Ricci solitons
Shrinking ()
Gaussian shrinking soliton
Shrinking round sphere
Shrinking round cylinder
The four dimensional FIK shrinker
The four dimensional BCCD shrinker
Compact gradient Kahler-Ricci shrinkers
Einstein manifolds of positive scalar curvature
Steady ()
The 2d cigar soliton (a.k.a. Witten's black hole)
The 3d rotationally symmetric Bryant soliton and its generalization to higher dimensions
Ricci flat manifolds
Expanding ()
Expanding Kahler-Ricci solitons on the complex line bundles over .
Einstein manifolds of negative scalar curvature
Singularity models in Ricci flow
Shrinking and steady Ricci solitons are fundamental objects in the study of Ricci flow as they appear as blow-up limits of singularities. In particular, it is known that all Type I singularities are modeled on non-collapsed gradient shrinking Ricci solitons. Type II singularities are expected to be modeled on steady Ricci solitons in general, however to date this has not been proven, even though all known examples are.
Notes
References
Riemannian geometry |
https://en.wikipedia.org/wiki/Esenin-Volpin%27s%20theorem | In mathematics, Esenin-Volpin's theorem states that weight of an infinite compact dyadic space is the supremum of the weights of its points.
It was introduced by . It was generalized by and .
References
General topology
Theorems in topology |
https://en.wikipedia.org/wiki/Dyadic%20space | In mathematics, a dyadic compactum is a Hausdorff topological space that is the continuous image of a product of discrete two-point spaces, and a dyadic space is a topological space with a compactification which is a dyadic compactum. However, many authors use the term dyadic space with the same meaning as dyadic compactum above.
Dyadic compacta and spaces satisfy the Suslin condition, and were introduced by Russian mathematician Pavel Alexandrov. Polyadic spaces are generalisation of dyadic spaces.
References
Properties of topological spaces |
https://en.wikipedia.org/wiki/Marian%20Small | Marian Small (born 1948) is a Canadian educational researcher, academic, author, and public speaker. She has co-authored mathematics textbooks used in Canada, Austria, and the United States, and is a proponent of a constructivist approach to mathematical instruction within K–12 classrooms.
Career
Small began teaching at the University of New Brunswick's Faculty of Education in 1973. Within that faculty she served as department chair, acting associate dean, acting dean, dean, and acting vice-president.
Small served two terms on New Brunswick's School District 18.
Approach to mathematics instruction
Small advocates a "constructivism" approach to mathematics instruction, which encourages students to construct explanations to math problems. "There is a strongly held belief in the mathematics education community", wrote Small, "that mathematics is best learned when students are actively engaged in constructing their own understandings. This is only likely to happen in classrooms that emphasize rich problem solving and the exchange of many approaches to mathematical situations, and that give attention to and value students’ mathematical reasoning".
To demonstrate this approach, Small provides an example of students learning to add 47 and 38. A traditional approach to math instruction would show students how to add these two numbers by "grouping the ones, trading, and then grouping the tens". Small explains that in a constructivist classroom, "the teacher might provide students with a variety of counting materials and pose a problem such as, "one bus has 47 students in it; another has 38. How many students are on both buses?" and allow students to use their own strategies to solve the problem". This would be followed by a classroom discussion where the various approaches used by students were shared and additional ideas were added.
Small's approach is enhanced by skillful questioning by the classroom teacher.
Controversy
Small's style of math instruction has been described as a "random abstract approach" by those favouring more traditional skills-based pedagogy. Toronto's Globe and Mail stated: "in the latest—arguably fiercest—of the "math wars" to break out in Canada, she would be Public Enemy No. 1 for those who think kids are fast losing their number sense because of the "fuzzy-math, basic-skills-lite" teaching Dr. Small and many of her contemporaries promote".
Regarding her role in the math wars, Small has acknowledged the "concern about less emphasis on memorizing the facts and allowing calculator use" as well as the "very loud and impassioned debate on these matters". Regarding the different approaches along the continuum of math instruction, Small stated "neither is better—they are different. In fact, the more tools and approaches that we have, the more likely we are to be successful at a task".
Publications
Making Math Meaningful to Canadian Students K–8
Big Ideas from Dr. Small K–3
Big Ideas from Dr. Small 4–8
Big Ideas fro |
https://en.wikipedia.org/wiki/Vinogradov%27s%20mean-value%20theorem | In mathematics, Vinogradov's mean value theorem is an estimate for the number of equal sums of powers.
It is an important inequality in analytic number theory, named for I. M. Vinogradov.
More specifically, let count the number of solutions to the system of simultaneous Diophantine equations in variables given by
with
.
That is, it counts the number of equal sums of powers with equal numbers of terms () and equal exponents (),
up to th powers and up to powers of . An alternative analytic expression for is
where
Vinogradov's mean-value theorem gives an upper bound on the value of .
A strong estimate for is an important part of the Hardy-Littlewood method for attacking Waring's problem and also for demonstrating a zero free region for the Riemann zeta-function in the critical strip. Various bounds have been produced for , valid for different relative ranges of and . The classical form of the theorem applies when is very large in terms of .
An analysis of the proofs of the Vinogradov mean-value conjecture can be found in the Bourbaki Séminaire talk by Lillian Pierce.
Lower bounds
By considering the solutions where
one can see that .
A more careful analysis (see Vaughan equation 7.4) provides the lower bound
Proof of the Main conjecture
The main conjecture of Vinogradov's mean value theorem was that the upper bound is close to this lower bound. More specifically that for any we have
This was proved by Jean Bourgain, Ciprian Demeter, and Larry Guth and by a different method by Trevor Wooley.
If
this is equivalent to the bound
Similarly if the conjectural form is equivalent to the bound
Stronger forms of the theorem lead to an asymptotic expression for , in particular for large relative to the expression
where is a fixed positive number depending on at most and , holds, see Theorem 1.2 in.
History
Vinogradov's original theorem of 1935 showed that for fixed with
there exists a positive constant such that
Although this was a ground-breaking result, it falls short of the full conjectured form. Instead it demonstrates the conjectured form when
.
Vinogradov's approach was improved upon by Karatsuba and Stechkin who showed that for there exists a positive constant such that
where
Noting that for
we have
,
this proves that the conjectural form holds for of this size.
The method can be sharpened further to prove the asymptotic estimate
for large in terms of .
In 2012 Wooley improved the range of for which the conjectural form holds. He proved that for
and
and for any we have
Ford and Wooley have shown that the conjectural form is established for small in terms of . Specifically they show that for
and
for any
we have
References
Theorems in analytic number theory |
https://en.wikipedia.org/wiki/Gelfand%20ring | In mathematics, a Gelfand ring is an associative ring R with identity such that if I and J are distinct right ideals then there are elements i and j such that iRj=0, i is not in I, and j is not in J. introduced them as rings for which one could prove a generalization of Gelfand duality, and named them after Israel Gelfand.
In the commutative case, Gelfand rings can also be characterized as the rings such that, for every and summing to , there exists and such that
.
Moreover, their prime spectrum deformation retracts onto the maximal spectrum.
References
Ring theory |
https://en.wikipedia.org/wiki/Ahmed%20Al-Siyabi | Ahmed Khalfan Muhail Al-Siyabi (; born 16 July 1993), commonly known as Ahmed Al-Siyabi, is an Omani footballer who plays for Sur SC in Oman Professional League.
Club career statistics
International career
Ahmed He was selected for the national team for the first time in 2012. He made his first appearance for Oman on 25 December 2013 against Kuwait in the 2012 WAFF Championship. He has made an appearances in the 2012 WAFF Championship.
Honours
Club
With Sur
Oman Professional League Cup (1): 2007
References
External links
1993 births
Living people
People from Sur, Oman
Omani men's footballers
Oman men's international footballers
Men's association football forwards
Sur SC players
Oman Professional League players
Footballers at the 2014 Asian Games
Asian Games competitors for Oman |
https://en.wikipedia.org/wiki/Kristian%20Benk%C5%91 | Kristian Benkő (born 3 June 1994) is a Swedish professional footballer who plays for Lombard-Pápa TFC.
Club statistics
Updated to games played as of 6 December 2014.
References
Profile at MLSZ
Profile at HLSZ
1994 births
Living people
Footballers from Malmö
Swedish people of Hungarian descent
Swedish men's footballers
Men's association football midfielders
Rákospalotai EAC footballers
Pápai FC footballers
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/Learning%20with%20FuzzyWOMP | Learning with FuzzyWOMP is an educational maths game aimed at preschoolers, released by Sierra On-Line in 1984 for the Apple II. The game is similar to Learning with Leeper (1983).
History
In 1984, Sierra On-Line added three programs to their line of educational software with Wizard of Id's Touch Type, Story Maker, and Learning with Fuzzywomp".
Gameplay
Mobygames describes the gameplay: "There are four kinds of education as different games for kids. They include knowledge and order of the digits (the digits as smoke fly out from a pipe, and you must help FuzzyWOMP to blow them out in proper order); digit definition (clown shows the digit and FuzzyWOMP have to roll so many balls down - if number is proper then clown juggles with them else he is upset); calculating, comparing, or memorizing (the domino shows and then hides, and FuzzyWOMP have to choose the same from the six possible variants); shooting (after creating your assistant you have to shoot FuzzyWOMP)."
Creative Computing (Volume 10, Number 4) explained: "Learning with Fuzzywomp includes four games for pre-readers which teach such basic skills as pattern matching, counting, number sequencing, and creative play. No adult supervision is required to play this game, which is available for the Apple and sells for $29.95."
RedKingsDreams argues the game teaches the following skills: goal seeking, contextual understanding, symbolic logic, and numerical literacy.
Reception
Vintage Sierra wrote "This collection of four animated learning games is tailored to meet the needs of the child who cannot read; no words are used. Just show your child how to use the joystick and Fuzzywomp will demonstrate each game." Commenting on how her 3-year old daughter reacted to Learning with Fuzzywomp, Evan Stubbs of RedKingsDream concluded: "An interesting game from the early days of Sierra – there’s no text in the entire game, encouraging her to learn goals through symbolic representation. She makes the intuitive leap to what she needs to do by watching what the game shows her (without any explanation that that’s what she’s supposed to be looking for). Apart from that, it focuses on basic image recognition and counting."
Learning with FuzzyWOMP received a Parent's Choice Award for ages 3–6.
References
Sierra Entertainment games
1984 video games
Apple II games
Apple II-only games
Children's educational video games
Video games developed in the United States |
https://en.wikipedia.org/wiki/K-space%20%28functional%20analysis%29 | In mathematics, more specifically in functional analysis, a K-space is an F-space such that every extension of F-spaces (or twisted sum) of the form
is equivalent to the trivial one
where is the real line.
Examples
The spaces for are K-spaces, as are all finite dimensional Banach spaces.
N. J. Kalton and N. P. Roberts proved that the Banach space is not a K-space.
See also
References
Functional analysis
F-spaces
Topological vector spaces |
https://en.wikipedia.org/wiki/Extension%20of%20a%20topological%20group | In mathematics, more specifically in topological groups, an extension of topological groups, or a topological extension, is a short exact sequence where and are topological groups and and are continuous homomorphisms which are also open onto their images. Every extension of topological groups is therefore a group extension.
Classification of extensions of topological groups
We say that the topological extensions
and
are equivalent (or congruent) if there exists a topological isomorphism making commutative the diagram of Figure 1.
We say that the topological extension
is a split extension (or splits) if it is equivalent to the trivial extension
where is the natural inclusion over the first factor and is the natural projection over the second factor.
It is easy to prove that the topological extension splits if and only if there is a continuous homomorphism such that is the identity map on
Note that the topological extension splits if and only if the subgroup is a topological direct summand of
Examples
Take the real numbers and the integer numbers. Take the natural inclusion and the natural projection. Then
is an extension of topological abelian groups. Indeed it is an example of a non-splitting extension.
Extensions of locally compact abelian groups (LCA)
An extension of topological abelian groups will be a short exact sequence where and are locally compact abelian groups and and are relatively open continuous homomorphisms.
Let be an extension of locally compact abelian groups
Take and the Pontryagin duals of and and take and the dual maps of and . Then the sequence
is an extension of locally compact abelian groups.
Extensions of topological abelian groups by the unit circle
A very special kind of topological extensions are the ones of the form where is the unit circle and and are topological abelian groups.
The class S(T)
A topological abelian group belongs to the class if and only if every topological extension of the form splits
Every locally compact abelian group belongs to . In other words every topological extension where is a locally compact abelian group, splits.
Every locally precompact abelian group belongs to .
The Banach space (and in particular topological abelian group) does not belong to .
References
Topological groups
Topology |
https://en.wikipedia.org/wiki/The%20Mathematics%20of%20Life | The Mathematics of Life is a 2011 popular science book by mathematician Ian Stewart, on the increasing role of mathematics in biology.
Overview
Stewart discusses the mathematics behind such topics as population growth, speciation, brain function, chaos theory, game theory, networking, symmetry, and animal coloration, with little recourse to equations. He identifies six revolutions which modernized biology:
The invention of the microscope
A systematic means of classifying species
Evidence of evolution
The expansion of the field of genetics
The discovery of the structure of DNA
The application of new mathematics to biology
Reception
Writer Alex Bellos described The Mathematics of Life as "a testament to the versatility of maths and how it is shaping our understanding of the world." Kirkus Reviews called the book "an ingenious overview of biology with emphasis on mathematical ideas—stimulating but requiring careful reading despite the lack of equations." A review in Notices of the American Mathematical Society noted that the book "does an admirable job of unfolding the mathematics undergirding so much of the research being carried out today in the many fields that comprise the subject of biology."
Mathematician and science writer Keith Devlin criticized the book, writing that "readers of the author's many general-audience books on mathematics may be surprised to find themselves at times frustrated by his latest outing, which is marred by overlapping and often repetitious passages."
References
Books by Ian Stewart (mathematician)
Popular mathematics books
Biology books
Basic Books books
2011 non-fiction books |
https://en.wikipedia.org/wiki/Caregiving%20by%20country | Caregiving by country is the regional variation of caregiving practices as distinguished among countries.
Caregivers Internationally
Australia
According to the Australian Bureau of Statistics 2001 paper on the health and well-being of Carers, Carers save the Australian Federal Government over $30 billion a year, according to the same statistics there are over 300 000 Young Carers (Carers Australia states that a Young carer is any carer under the age of 25) with 1.5 million potential young carers, where potential is defined as a young person who lives in a household where there is at least one person who requires full-time care (Is disabled etc.). In 2015, carers provided around 1.9 billion hours of unpaid care. According to a new study by the University of Queensland, Australian carers are providing $13.2 billion worth of free mental health support to their friends and family members. This "hidden workforce" is an equivalent of 173,000 full-time mental health support workers.
In Australia they also have The Australian National Young Carers Action Team (ANYCAT) whose goal is to advocate on behalf of young carers (Being young carers themselves) each board member is the sole representative of their state or territory and represent as few as 75 000 Young Carers.
In Most states and Territories they have an ANYCAT equivalent team or Board. In Queensland this is called Young Carers Action Board Queensland (YCABQ).
China
According to the National Bureau of Statistics of China 2011 report regarding China's total population and structural changes, people belong to the age group of 60 years and above accounted for 184.99 million, which occupied 13.7 percent of the total national population at the end of 2011. The number has risen 0.47 percentage point comparing to the year of 2010. Of these, people age 65 years and above figured up 122.88 million that occupied 9.1 percent of the total and has increased 0.25 percentage points.
As a steadily increasing older population with a growing demand for long-term care, an issue of lacking of elderly care facilities as well as inadequate training for skilled caregivers has generated a social concern pertaining to elder care. According to the official Chinese media Xinhua, professionally qualified caregivers are in great request with approximately 10 million people needed to provide care for the Chinese aging population. However, the report also stated that only 300,000 people currently working as caregivers with less than 1/3 of them are trained properly.
There is no organized caregiver association in China. As a result, family members still construct the major source of caregiving in China especially in rural area where the quality of health services is a problem. A recent study aims to examine the effect of depression on family members of whom sons and daughters-in-law carry out main responsibilities in caring for elderly parents have indicated several findings, including:
The majority of caregivers choose to |
https://en.wikipedia.org/wiki/Princeton%20Lectures%20in%20Analysis | The Princeton Lectures in Analysis is a series of four mathematics textbooks, each covering a different area of mathematical analysis. They were written by Elias M. Stein and Rami Shakarchi and published by Princeton University Press between 2003 and 2011. They are, in order, Fourier Analysis: An Introduction; Complex Analysis; Real Analysis: Measure Theory, Integration, and Hilbert Spaces; and Functional Analysis: Introduction to Further Topics in Analysis.
Stein and Shakarchi wrote the books based on a sequence of intensive undergraduate courses Stein began teaching in the spring of 2000 at Princeton University. At the time Stein was a mathematics professor at Princeton and Shakarchi was a graduate student in mathematics. Though Shakarchi graduated in 2002, the collaboration continued until the final volume was published in 2011. The series emphasizes the unity among the branches of analysis and the applicability of analysis to other areas of mathematics.
The Princeton Lectures in Analysis has been identified as a well written and influential series of textbooks, suitable for advanced undergraduates and beginning graduate students in mathematics.
History
The first author, Elias M. Stein, was a mathematician who made significant research contributions to the field of mathematical analysis. Before 2000 he had authored or co-authored several influential advanced textbooks on analysis.
Beginning in the spring of 2000, Stein taught a sequence of four intensive undergraduate courses in analysis at Princeton University, where he was a mathematics professor. At the same time he collaborated with Rami Shakarchi, then a graduate student in Princeton's math department studying under Charles Fefferman, to turn each of the courses into a textbook. Stein taught Fourier analysis in that first semester, and by the fall of 2000 the first manuscript was nearly finished. That fall Stein taught the course in complex analysis while he and Shakarchi worked on the corresponding manuscript. Paul Hagelstein, then a postdoctoral scholar in the Princeton math department, was a teaching assistant for this course. In spring 2001, when Stein moved on to the real analysis course, Hagelstein started the sequence anew, beginning with the Fourier analysis course. Hagelstein and his students used Stein and Shakarchi's drafts as texts, and they made suggestions to the authors as they prepared the manuscripts for publication. The project received financial support from Princeton University and from the National Science Foundation.
Shakarchi earned his Ph.D. from Princeton in 2002 and moved to London to work in finance. Nonetheless he continued working on the books, even as his employer, Lehman Brothers, collapsed in 2008. The first two volumes were published in 2003. The third followed in 2005, and the fourth in 2011. Princeton University Press published all four.
Contents
The volumes are split into seven to ten chapters each. Each chapter begins with an epigraph providi |
https://en.wikipedia.org/wiki/Askold%20Khovanskii | Askold Georgievich Khovanskii (; born 3 June 1947, Moscow) is a Russian and Canadian mathematician currently a professor of mathematics at the University of Toronto, Canada. His areas of research are algebraic geometry, commutative algebra, singularity theory, differential geometry and differential equations. His research is in the development of the theory of toric varieties and Newton polyhedra in algebraic geometry. He is also the inventor of the theory of fewnomials, and the Bernstein–Khovanskii–Kushnirenko theorem is named after him.
He obtained his Ph.D. from Steklov Mathematical Institute in Moscow under the supervision of Vladimir Arnold. In his Ph.D. thesis, he developed a topological version of Galois theory. He studies the theory of Newton–Okounkov bodies, or Okounkov bodies for short.
Among his graduate students are Olga Gel'fond, Feodor Borodich, H. Petrov-Tan'kin, Kiumars Kaveh, Farzali Izadi, Ivan Soprunov, Jenya Soprunova, Vladlen Timorin, Valentina Kirichenko, Sergey Chulkov, V. Kisunko, Mikhail Mazin, O. Ivrii, K. Matveev, Yuri Burda, and J. Yang.
In 2014, he received the Jeffery–Williams Prize of the Canadian Mathematical Society for outstanding contributions to mathematical research in Canada.
References
External links
Homepage of Askold Khovanskii at the University of Toronto
Moscow Mathematical Journal volume in honor of Askold Khovanskii (Mosc. Math. J., 7:2 (2007), 169–171)
Askoldfest
1947 births
Living people
Russian mathematicians
Canadian mathematicians
Moscow State University alumni
Steklov Institute of Mathematics alumni
Academic staff of the Independent University of Moscow
Academic staff of the University of Toronto
Geometers
Russian people of Lithuanian descent
Algebraic geometers
Soviet mathematicians |
https://en.wikipedia.org/wiki/Direct%20sum%20of%20topological%20groups | In mathematics, a topological group is called the topological direct sum of two subgroups and if the map
is a topological isomorphism, meaning that it is a homeomorphism and a group isomorphism.
Definition
More generally, is called the direct sum of a finite set of subgroups of the map
is a topological isomorphism.
If a topological group is the topological direct sum of the family of subgroups then in particular, as an abstract group (without topology) it is also the direct sum (in the usual way) of the family
Topological direct summands
Given a topological group we say that a subgroup is a topological direct summand of (or that splits topologically from ) if and only if there exist another subgroup such that is the direct sum of the subgroups and
A the subgroup is a topological direct summand if and only if the extension of topological groups
splits, where is the natural inclusion and is the natural projection.
Examples
Suppose that is a locally compact abelian group that contains the unit circle as a subgroup. Then is a topological direct summand of The same assertion is true for the real numbers
See also
References
Topological groups
Topology |
https://en.wikipedia.org/wiki/Icosahedron | In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes . The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non-similar shapes of icosahedra, some of them being more symmetrical than others. The best known is the (convex, non-stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles.
Regular icosahedra
There are two objects, one convex and one nonconvex, that can both be called regular icosahedra. Each has 30 edges and 20 equilateral triangle faces with five meeting at each of its twelve vertices. Both have icosahedral symmetry. The term "regular icosahedron" generally refers to the convex variety, while the nonconvex form is called a great icosahedron.
Convex regular icosahedron
The convex regular icosahedron is usually referred to simply as the regular icosahedron, one of the five regular Platonic solids, and is represented by its Schläfli symbol {3, 5}, containing 20 triangular faces, with 5 faces meeting around each vertex.
Its dual polyhedron is the regular dodecahedron {5, 3} having three regular pentagonal faces around each vertex.
Great icosahedron
The great icosahedron is one of the four regular star Kepler-Poinsot polyhedra. Its Schläfli symbol is {3, }. Like the convex form, it also has 20 equilateral triangle faces, but its vertex figure is a pentagram rather than a pentagon, leading to geometrically intersecting faces. The intersections of the triangles do not represent new edges.
Its dual polyhedron is the great stellated dodecahedron {, 3}, having three regular star pentagonal faces around each vertex.
Stellated icosahedra
Stellation is the process of extending the faces or edges of a polyhedron until they meet to form a new polyhedron. It is done symmetrically so that the resulting figure retains the overall symmetry of the parent figure.
In their book The Fifty-Nine Icosahedra, Coxeter et al. enumerated 58 such stellations of the regular icosahedron.
Of these, many have a single face in each of the 20 face planes and so are also icosahedra. The great icosahedron is among them.
Other stellations have more than one face in each plane or form compounds of simpler polyhedra. These are not strictly icosahedra, although they are often referred to as such.
Pyritohedral symmetry
A regular icosahedron can be distorted or marked up as a lower pyritohedral symmetry, and is called a snub octahedron, snub tetratetrahedron, snub tetrahedron, and pseudo-icosahedron. This can be seen as an alternated truncated octahedron. If all the triangles are equilateral, the symmetry can also be distinguished by colouring the 8 and 12 triangle sets differently.
Pyritohedral symmetry has the symbol (3*2), [3+,4], with order 24. Tetrahedral symmetry has the symbol (332), [3,3]+, with order 12. These lower symmetries allow geometric distortions from 20 equilateral triangular faces, instead having 8 equilateral triangles and 12 congruent isoscel |
https://en.wikipedia.org/wiki/Phil%20Taylor%20career%20statistics | This is a list of the main career statistics of English professional darts player, Phil Taylor, whose professional career lasted from 1987 to 2018. Taylor won 214 professional titles and was runner-up in 48 finals. He won a record 85 major titles and a record 16 World Championships. In team events, he won 10 titles including being a four-time winner of the PDC World Cup of Darts and has had 2 runners-up finishes in team events. In 1999 and 2004 he defeated the reigning BDO champion in a special challenge match.
Career finals
BDO major finals: 7 (4 titles, 3 runners-up)
PDC major finals: 92 (79 titles, 13 runners-up)
Independent major finals: 2 (2 titles)
PDC world series finals: 10 (8 titles, 2 runners-up)
PDC team finals: 8 (6 titles, 2 runners-up)
Other WDF/BDO finals
WDF major finals: 2 (2 titles)
WDF team finals: 4 (4 titles)
Champion vs Champion: 2 (2 titles)
* The match was best of 13 sets, but Fordham retired after the seventh set due to ill-health
Seniors major finals: 2 (2 runners-up)
Performance timelines
(W) Won; (F) finalist; (SF) semifinalist; (QF) quarterfinalist; (#R) rounds 6, 5, 4, 3, 2, 1; (RR) round-robin stage; (Prel.) Preliminary round; (DNQ) Did not qualify; (DNP) Did not participate; (NH) Not held
Majors
World Series of Darts
Head-to-head record
Only players who have featured in a major PDC or BDO final are listed.
Players who have been world champions are in boldface.
Won–Lost–Draw, in that order.
Raymond van Barneveld 61–18–4 (73.49%)
Adrian Lewis 55–17–2 (74.32%)
James Wade 51–14–6 (71.83%)
Simon Whitlock 41–7 (85.42%)
Ronnie Baxter 41–5 (89.13%)
Gary Anderson 40–17–3 (66.67%)
Terry Jenkins 39–4–3 (84.78%)
Andy Hamilton 38–5 (88.37%)
Dennis Priestley 37–6–1 (84.09%)
Colin Lloyd 35–4–1 (87.50%)
Michael van Gerwen 34–26–2 (54.84%)
Wes Newton 32–2 (94.12%)
Kevin Painter 32–1 (96.97%)
Mervyn King 31–8–2 (75.61%)
John Part 31–6 (83.78%)
Wayne Mardle 29–3 (90.63%)
Mark Walsh 26–5 (83.87%)
Steve Beaton 26–2 (92.86%)
Roland Scholten 25–0–2 (92.59%)
Paul Nicholson 24–2 (92.31%)
Dave Chisnall 23–9 (71.88%)
Vincent van der Voort 23–4 (85.19%)
Peter Wright 22–11–3 (62.86%)
Robert Thornton 22–6 (78.57%)
Peter Manley 22–3 (88%)
Mark Webster 20–2 (90.91%)
Alan Warriner-Little 19–3 (86.36%)
Colin Osborne 19–2 (90.48%)
Bob Anderson 18–3 (85.71%)
Brendan Dolan 18–1 (94.74%)
Jelle Klaasen 14–3 (82.35%)
Wayne Jones 15–1 (93.75%)
Mark Dudbridge 14–1–1 (87.50%)
John Lowe 12–1 (92.31%)
Kim Huybrechts 11–1–1 (84.62%)
Shayne Burgess 11–0 (100%)
Richie Burnett 10–1 (90.91%)
Co Stompé 10–1 (90.91%)
Stephen Bunting 9–1–1 (81.82%)
Rod Harrington 9–7 (60%)
Andy Fordham 7–0 (100%)
Gary Mawson 6–1 (85.71%)
Darren Webster 6–2 (75%)
Dave Askew 5–1 (83.33%)
Darryl Fitton 5–1 (83.33%)
Mensur Suljović 5–1 (83.33%)
Barrie Bates 4–1 (80%)
Peter Evison 4–4 (50%)
Dave Whitcombe 4–1 (80%)
Robbie Green 4–0 (100%)
Keith Deller 4–0 (100%)
Colin Monk 4–0 (100%)
Martin Phillips 4–0 (100%)
Mart |
https://en.wikipedia.org/wiki/Determinant%20method | In mathematics, the determinant method is any of a family of techniques in analytic number theory.
The name was coined by Roger Heath-Brown and comes from the fact that the center piece of the method is estimating a certain determinant. Its main application is to give an upper bound for the number of rational points of bounded height on or near algebraic varieties defined over the rational numbers. The main novelty of the determinant method is that in all incarnations, the estimates obtained are uniform with respect to the coefficients of the polynomials defining the variety and only depend on the degree and dimension of the variety.
Development
The original version of the determinant method was developed by Enrico Bombieri and Jonathan Pila in 1989. In its original context, Bombieri and Pila's results applied only to as their arguments depended heavily on the geometry of the plane. The Bombieri-Pila version of the determinant method would later be dubbed the real-analytic determinant method. Oscar Marmon generalized Bombieri and Pila's results in 2010.
Bombieri and Pila's result was novel because of its uniformity with respect to the polynomials defining the curves. Roger Heath-Brown obtained the analogous result of Bombieri and Pila in higher dimensions in 2002, using a different argument. Heath-Brown's approach would later be dubbed the local p-adic determinant method. The main use of Heath-Brown's determinant method has been to try to solve the so-called dimension growth conjecture.
Aside from the real-analytic approach of Bombieri and Pila and Heath-Brown's local -adic approach, other approaches include the approximate determinant method also due to Heath-Brown, the global determinant method of Salberger, and a new variant of the approximate determinant method due to Dietmann and Marmon which applies to polynomials which are close to being bihomogeneous.
In 2012, this method is reformulated by the language of Arakelov theory by Huayi Chen.
In 2016, Stanley Yao Xiao obtained a generalization of Salberger's global determinant method to the setting of weighted projective space.
References
Analytic number theory |
https://en.wikipedia.org/wiki/Denis%20Pidev | Denis Pidev (; born 1 December 1992) is a Bulgarian footballer who plays as a defender.
Career
On 8 July 2017, Pidev joined Third League club CSKA 1948.
Career statistics
Club
References
External links
1992 births
Living people
Bulgarian men's footballers
Men's association football defenders
First Professional Football League (Bulgaria) players
Second Professional Football League (Bulgaria) players
FC Chavdar Etropole players
FC Marek Dupnitsa players
FC Vereya players
FC Montana players
FC Lokomotiv 1929 Sofia players |
https://en.wikipedia.org/wiki/WUSA%20records%20and%20statistics | The following is a compilation of notable records and statistics for teams and players in and seasons of the Women's United Soccer Association.
Champions and regular season winners
Scoring
Players
Games
All-time successes and records
Tiebreak for otherwise identical records is most recent success, followed by highest average regular season rank
Regular-season records
Playoff records
1Ties after 90min decided by two 7.5min golden goal overtime periods, followed by shootout if still tiedSort order is Pts, appearance%, finishing position
Attendance
See also
Women's soccer in the United States
WPS records and statistics
NWSL records and statistics
References
Records and statistics
All-time football league tables
Association football league records and statistics
Women's association football records and statistics |
https://en.wikipedia.org/wiki/J%C3%A1nos%20Pat%C3%A1ly | János Patály (born 29 February 1988) is a Hungarian football player who currently plays for Nyíregyháza Spartacus FC.
Club statistics
Updated to games played as of 18 November 2014.
External links
Profile at MLSZ
Profile at HLSZ
1988 births
Living people
People from Mátészalka
Hungarian men's footballers
Men's association football defenders
Nyíregyháza Spartacus FC players
Nemzeti Bajnokság I players
Footballers from Szabolcs-Szatmár-Bereg County |
https://en.wikipedia.org/wiki/Gerg%C5%91%20Gengeliczki | Gergő Gengeliczki (born 8 June 1993) is a Hungarian football player who plays for Nyíregyháza.
Club statistics
Updated to games played as of 19 May 2019.
External links
Profile at MLSZ
1993 births
Footballers from Budapest
Living people
Hungarian men's footballers
Men's association football defenders
Budapest Honvéd FC II players
Budapest Honvéd FC players
Nyíregyháza Spartacus FC players
Mezőkövesdi SE footballers
Dunaújváros PASE players
Soroksár SC players
MTK Budapest FC players
Győri ETO FC players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/Three-part%20lesson | A three-part lesson is an inquiry-based learning method used to teach mathematics in K–12 schools.
The three-part lesson has been attributed to John A. Van de Walle, a mathematician at Virginia Commonwealth University.
Components
Getting started phase (10 to 15 minutes)
The purpose is to cognitively prepare students for the math lesson by having them think about a procedure, strategy or concept used in a prior lesson. Teachers determine what specific previous learning they wish students to recall, based on outcomes desired for that particular lesson. The role of the teacher is to "get students mentally prepared to work on the problem".
Marian Small, a proponent of a constructivist approach to mathematical instruction, provides an example of an inquiry-based question from which a three-part lesson could be created: "one bus has 47 students in it; another has 38. How many students are on both buses?"
Work phase (30 to 40 minutes)
Students engage in solving math problems individually, in pairs, or in small groups, and "record the mathematical thinking they used to develop solutions". Students then plan the strategies, methods, and concrete materials they will use to solve the problem. The teacher will circulate and make observations about the ways students are interacting, and will note the mathematical language they are using as well as the mathematical models they are employing to solve the problem. If a student is having difficulty, "the teacher might pose questions to provoke further thinking or have other students explain their plan for solving the problem". Teachers are advised to be active listeners in this phase, and to take notes. This is also a phase in which teachers can assess students.
Consolidation and practice phase (10 to 15 minutes)
In this final phase, the teacher oversees the sharing of solutions by students, and may employ other teaching techniques such as "math congress", "gallery walk", or "bansho". If new methods and strategies were discovered by students during the work phase, the teacher will post these on the class's "strategy wall", or use them to develop an "anchor chart". Teachers are not to evaluate students in this phase, but should be actively listening "to both good and not so good ideas".
Effectiveness
Advocates of the three-part lesson state that students develop "independence and confidence by choosing the methods, strategies and concrete materials they will use, as well as ways to record their solutions". They claim students learn to discern similarities and differences in the mathematics, and also that "through such rich mathematics classroom discourse, students develop and consolidate their understanding of the learning goal of the lesson in terms of making connections to prior knowledge and experiences and making generalizations". Advocates also claim "students are more enthusiastic about the subject" when inquiry-based math instruction is used.
Opponents of inquiry-based methods such as the |
https://en.wikipedia.org/wiki/Ebrahim%20Abednezhad | Ebrahim Abednezhad (, born 22 August 1992) is an Iranian footballer.
Career statistics
References
1992 births
Living people
Iranian men's footballers
Footballers from Tabriz
Tractor S.C. players
Machine Sazi F.C. players
Sumgayit FK players
Persian Gulf Pro League players
Azerbaijan Premier League players
Men's association football midfielders
Iranian expatriate men's footballers
Expatriate men's footballers in Turkey
Iranian expatriate sportspeople in Turkey |
https://en.wikipedia.org/wiki/Pantachy | In mathematics, a pantachy or pantachie (from the Greek word πανταχη meaning everywhere) is a maximal totally ordered subset of a partially ordered set, especially a set of equivalence classes of sequences of real numbers. The term was introduced by to mean a dense subset of an ordered set, and he also introduced "infinitary pantachies" to mean the ordered set of equivalence classes of real functions ordered by domination, but as Felix Hausdorff pointed out this is not a totally ordered set. redefined a pantachy to be a maximal totally ordered subset of this set.
Notes
References
English translation in
Order theory
Set theory |
https://en.wikipedia.org/wiki/David%20Acheson%20%28mathematician%29 | David John Acheson (born 1946) is a British applied mathematician at Jesus College, Oxford.
He was educated at Highgate School, King's College London (BSc Mathematics and Physics, 1967) and the University of East Anglia (PhD, 1971). He was appointed a Fellow in Mathematics at Jesus College, Oxford in 1977 and became an Emeritus Fellow in 2008. He served as president of the Mathematical Association from 2010 to 2011. He was awarded an Honorary Doctorate of Science from the University of East Anglia in 2013.
His early research was on geophysical and astrophysical fluid dynamics, beginning with the discovery in 1972 of a magnetic 'field gradient' instability in rotating fluids. In 1976, he discovered the first examples of wave over-reflection (i.e. reflection coefficient greater than unity) in a stable system. In 1978 his research focused on magnetic fields and differential rotation in stars, with new results on magnetic buoyancy, the Taylor instability, Goldreich-Schubert instability, and magnetorotational instability. In 1992 he discovered the 'upside-down pendulums theorem' (which is very loosely connected with the Indian Rope Trick).
Books
Elementary Fluid Dynamics (1990)
From Calculus to Chaos (1997)
1089 and All That (2002)
The Calculus Story: A Mathematical Adventure (2017)
The Wonder Book of Geometry: A Mathematical Story (2020)
The Spirit of Mathematics: Algebra and All That (2023)
References
1946 births
Living people
People educated at Highgate School
Alumni of King's College London
Alumni of the University of East Anglia
Fellows of Jesus College, Oxford
Place of birth missing (living people)
20th-century British mathematicians
21st-century British mathematicians
Mathematics writers
Fluid dynamicists
British non-fiction writers
20th-century British writers
21st-century British writers
20th-century British male writers
Male non-fiction writers |
https://en.wikipedia.org/wiki/International%20Association%20for%20Mathematical%20Geosciences | The International Association for Mathematical Geosciences (IAMG) is a nonprofit organization of geoscientists. It aims to promote international cooperation in the application and use of mathematics in geological research and technology. IAMG's activities are to organize meetings, issue of publications on the application of mathematics in the geological sciences, extend cooperation with other organizations professionally concerned with applications of mathematics and statistics to the biological sciences, earth sciences, engineering, environmental sciences, and planetary sciences. IAMG is a not for profit 501(c)(3) organization.
History
The IAMG was established in August 1968 at the International Geological Congress in Prague, Czechoslovakia.
Publications
IAMG publishes a semiannual Newsletter and the following scientific journals:
Applied Computing and Geosciences
Computers & Geosciences
Mathematical Geosciences
Natural Resources Research
It also publices a monograph series, Studies in Mathematical Geosciences.
Presidents
Presidents of the International Association for Mathematical Geosciences (IAMG) include:
Peter Dowd (academic) (Australia) (2020-2024)
Jennifer McKinley (N. Ireland) (2016-2020)
Qiuming Cheng (Canada and China) (2012-2016)
Vera Pawlowsky-Glahn (Spain) (2008-2012)
Frits P. Agterberg (Canada) (2004-2008)
Graeme Bonham-Carter (Canada) (2000-2004)
Ricardo A. Olea (USA) (1996-2000)
Michael Ed. Hohn (USA) (1992-1996)
Richard B. McCammon (USA) (1989-1992)
John C. Davis (USA) (1984-1989)
E. H. Timothy Whitten (USA) (1980-1984)
Daniel F. Merriam (USA) (1976-1980)
(Sweden) (1972-1976)
Andrei B. Vistelius (USSR) (1968-1972)
Recognition
The IAMG offers medals, lectureships, prizes, and awards.
Medal(s)
William Christian Krumbein Medal (established in 1976), is named after William Christian Krumbein. It is awarded to senior scientists for career achievement, which includes distinction in application of mathematics or informatics in the earth sciences, service to the IAMG, and support to professions involved in the earth sciences.
Special Lectureships
The Georges Matheron Lectureship (established 2006), named after Georges Matheron, a leader in the field of geostatistics. The Lectures Committee seeks nominations and selects each year a Georges Matheron Lecturer who is a scientist with proven research ability in the field of spatial statistics or mathematical morphology.
The IAMG Distinguished Lectureship is awarded once in every two years. The purpose of the IAMG Distinguished Lecture series is to demonstrate to the broader geological community the power of mathematical geology to address routine geological interpretation and to deliver this knowledge to audiences in selected parts the world.
Prize(s)
Felix Chayes Prize for Excellence in Research in Mathematical Petrology is a cash prize endowed in honor of Felix Chayes that is given to recipients of exceptional potential and proven research ability. The prize |
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