source stringlengths 31 168 | text stringlengths 51 3k |
|---|---|
https://en.wikipedia.org/wiki/Blocking%20set | In geometry, specifically projective geometry, a blocking set is a set of points in a projective plane that every line intersects and that does not contain an entire line. The concept can be generalized in several ways. Instead of talking about points and lines, one could deal with n-dimensional subspaces and m-dimensional subspaces, or even more generally, objects of type 1 and objects of type 2 when some concept of intersection makes sense for these objects. A second way to generalize would be to move into more abstract settings than projective geometry. One can define a blocking set of a hypergraph as a set that meets all edges of the hypergraph.
Definition
In a finite projective plane π of order n, a blocking set is a set of points of π that every line intersects and that contains no line completely. Under this definition, if B is a blocking set, then complementary set of points, π\B is also a blocking set. A blocking set B is minimal if the removal of any point of B leaves a set which is not a blocking set. A blocking set of smallest size is called a committee. Every committee is a minimal blocking set, but not all minimal blocking sets are committees. Blocking sets exist in all projective planes except for the smallest projective plane of order 2, the Fano plane.
It is sometimes useful to drop the condition that a blocking set does not contain a line. Under this extended definition, and since, in a projective plane every pair of lines meet, every line would be a blocking set. Blocking sets which contained lines would be called trivial blocking sets, in this setting.
Examples
In any projective plane of order n (each line contains n + 1 points), the points on the lines forming a triangle without the vertices of the triangle (3(n - 1) points) form a minimal blocking set (if n = 2 this blocking set is trivial) which in general is not a committee.
Another general construction in an arbitrary projective plane of order n is to take all except one point, say P, on a given line and then one point on each of the other lines through P, making sure that these points are not all collinear (this last condition can not be satisfied if n = 2.) This produces a minimal blocking set of size 2n.
A projective triangle β of side m in PG(2,q) consists of 3(m - 1) points, m on each side of a triangle, such that the vertices A, B and C of the triangle are in β, and the following condition is satisfied: If point P on line AB and point Q on line BC are both in β, then the point of intersection of PQ and AC is in β.
A projective triad δ of side m is a set of 3m - 2 points, m of which lie on each of three concurrent lines such that the point of concurrency C is in δ and the following condition is satisfied: If a point P on one of the lines and a point Q on another line are in δ, then the point of intersection of PQ with the third line is in δ.
Theorem: In PG(2,q) with q odd, there exists a projective triangle of side (q + 3)/2 which is a blocking set of size 3( |
https://en.wikipedia.org/wiki/Cornish%20Canadians | Cornish Canadians are Canadians of Cornish descent, including those who were born in Cornwall. The number of Canadian citizens of Cornish descent cannot be determined through census statistics, though speculative estimates place the population as high as 20,000.
History
Early arrivals
It is recorded that the first Cornish to reach what is now Canadian soil did in the 16th century, reaching the coast of Newfoundland, part of the province of Newfoundland and Labrador.
Bruce Mines
Cornish emigrants settled the area around Bruce Mines starting in 1842. Located on the north shore of Lake Huron, the area had been associated with the native copper used by indigenous people, whose copper working in the upper Great Lakes dates back to the Old Copper complex. With the spread of knowledge of copper in the area among Europeans, a copper mine opened in 1846, with many local Cornish settlers being recruited to work there. This was the first copper mine in Canada.
Around this time, there was a depression in the Cornish mining industry, which contributed to the volume of people participating in the Cornish "Great Migration", the outflow of emigrants primarily to English-speaking colonies such as Canada and Australia. In 1848, a barque carrying fifty Cornish emigrants, mostly from the Hayle area, along with a stationary steam engine (built in a foundry at Copperhouse) and assortment of Cornish ore processing equipment, left the Port of Hayle bound for Montreal. The arrival of Cornish skilled workers and industrial equipment allowed the owners of the Bruce Mines to rapidly scale up mechanization of their operations.
Notable people
Frank Andrews (1854-after 1890), member of the Nova Scotia House of Assembly
Elizabeth Arden (1878-1966), businesswoman
Arthur James Bater (1889-1969), MP for The Battlefords
Truman Smith Baxter (1867-1931), mayor of Vancouver
Rick Blight (1955-2005), hockey player
Marie Bottrell (born 1961), country music singer
Frederick Buscombe (1862-1938), Mayor of Vancouver
Dick Cherry (born 1937), hockey player
Don Cherry (born 1934), hockey player and commentator
Dean Chynoweth (born 1968), hockey player
Ed Chynoweth (1941-2008), hockey owner
H. P. P. Crease (1823-1905), member of the British Columbia Supreme Court
William Dennis (1856-1920), member of the Senate of Canada
Claude Ernest Dolman (1906-1994), scientist
John Eyre (1824-1871), member of the Ontario Legislative Assembly
Thomas Greenway (1838-1908), Premier of Manitoba
Wilfred Grenfell (1865-1940), Episcopal missionary
W.O. Hamley (1818-1907), civil and naval officer
Derek Holman (born 1931), composer
Arthur Lobb (1871-1928), member of the Manitoba Legislative Assembly
Samuel A. Mitchell (1874-1960), astronomer
R. J. M. Parker (1881-1948), Lieutenant Governor of Saskatchewan
Robert Parkyn (1862-1939), member of the Alberta Legislative Assembly
James Pascoe (1863-1931), member of the Saskatchewan Legislative Assembly
J. Ernest Pascoe (1900-1972), Member of |
https://en.wikipedia.org/wiki/List%20of%20European%20Cup%20and%20EHF%20Champions%20League%20winning%20players |
See also
EHF Champions League
European Cup and EHF Champions League records and statistics
References
External links
EHF Champions League
EHF Champions League
European |
https://en.wikipedia.org/wiki/Exactness | In mathematics, exactness may refer to:
Exact category
Exact functor
Landweber exact functor theorem
Exact sequence
See also
Exactness of measurements
Accuracy and precision |
https://en.wikipedia.org/wiki/%28G%2CX%29-manifold | In geometry, if X is a manifold with an action of a topological group G by analytical diffeomorphisms, the notion of a (G, X)-structure on a topological space is a way to formalise it being locally isomorphic to X with its G-invariant structure; spaces with a (G, X)-structure are always manifolds and are called (G, X)-manifolds. This notion is often used with G being a Lie group and X a homogeneous space for G. Foundational examples are hyperbolic manifolds and affine manifolds.
Definition and examples
Formal definition
Let be a connected differential manifold and be a subgroup of the group of diffeomorphisms of which act analytically in the following sense:
if and there is a nonempty open subset such that are equal when restricted to then
(this definition is inspired by the analytic continuation property of analytic diffeomorphisms on an analytic manifold).
A -structure on a topological space is a manifold structure on whose atlas' charts has values in and transition maps belong to . This means that there exists:
a covering of by open sets (i.e. );
open embeddings called charts;
such that every transition map is the restriction of a diffeomorphism in .
Two such structures are equivalent when they are contained in a maximal one, equivalently when their union is also a structure (i.e. the maps and are restrictions of diffeomorphisms in ).
Riemannian examples
If is a Lie group and a Riemannian manifold with a faithful action of by isometries then the action is analytic. Usually one takes to be the full isometry group of . Then the category of manifolds is equivalent to the category of Riemannian manifolds which are locally isometric to (i.e. every point has a neighbourhood isometric to an open subset of ).
Often the examples of are homogeneous under , for example one can take with a left-invariant metric. A particularly simple example is and the group of euclidean isometries. Then a manifold is simply a flat manifold.
A particularly interesting example is when is a Riemannian symmetric space, for example hyperbolic space. The simplest such example is the hyperbolic plane, whose isometry group is isomorphic to .
Pseudo-Riemannian examples
When is Minkowski space and the Lorentz group the notion of a -structure is the same as that of a flat Lorentzian manifold.
Other examples
When is the affine space and the group of affine transformations then one gets the notion of an affine manifold.
When is the n-dimensional real projective space and one gets the notion of a projective structure.
Developing map and completeness
Developing map
Let be a -manifold which is connected (as a topological space). The developing map is a map from the universal cover to which is only well-defined up to composition by an element of .
A developing map is defined as follows: fix and let be any other point, a path from to , and (where is a small enough neighbourhood of ) a map obtained by composing a cha |
https://en.wikipedia.org/wiki/Ho%C3%A0ng%20Xu%C3%A2n%20H%C3%A3n | Hoàng Xuân Hãn (Đức Thọ, 1908 – Paris, 10 March 1996) was a Vietnamese professor of mathematics, linguist, historian and educationalist. He was Minister of Education in the short-lived 1945 cabinet of historian Trần Trọng Kim and drafted and issued the first Vietnamese education program.
Like many of the academics in the five-month Trần Trọng Kim government, afterwards Hãn returned to academic studies. He was the first Vietnamese historian to fully study the history of Nôm texts by the 17th Century Jesuits such as Girolamo Maiorica.
See also
Hoàng Xuân Sính, Vietnamese mathematician .
References
1908 births
1996 deaths
People educated at Lycee Albert Sarraut
20th-century Vietnamese mathematicians
People from Hà Tĩnh province
French-language literature of Vietnam |
https://en.wikipedia.org/wiki/Pioneers%20in%20Engineering | Pioneers in Engineering (PiE) is a student-run organization that promotes the study of science, technology, engineering, and mathematics, collectively known as STEM fields. The organization was established in 2008 as a non-profit corporation by University of California, Berkeley student, Xiao-Yu Fu. The University provides training and mentorship opportunities for local high school students to improve their technological skills, by participating in a robotics competition, during which each student team designs, builds, and programs functional robots. Since 2008, over 20 schools have participated in the program.
Background
Pioneers in Engineering was founded in 2008 by University of California, Berkeley student and Tau Beta Pi member, Xiao-Yu Fu. The organization's office is in UC Berkeley's O'Brien Hall. Staff members, including University of California undergraduates and graduates, design and assemble robotics starter kits for the competition, develop mentors for the program, plan and manufacture the annual competition field, and oversee public relations and internal communications. , the organization has expanded to include 107 staff members.
In preparation for the annual competition, robotic kits are distributed to groups of high schools students, who are paired with undergraduate mentors who assist the teams during the competition. A final tournament is held at the end of the season, allowing the student teams to reveal their work, for which awards are presented.
References
Student organizations in California
Engineering organizations
Organizations established in 2008
2008 establishments in California |
https://en.wikipedia.org/wiki/P%C3%A9ter%20Beke%20%28footballer%2C%20born%201994%29 | Péter Beke (born 6 December 1994) is a Hungarian football player who plays for Kozármisleny.
Club statistics
Updated to games played as of 15 October 2014.
External links
HLSZ
MLSZ
1994 births
Living people
Footballers from Pécs
Hungarian men's footballers
Men's association football midfielders
Pécsi MFC players
Kozármisleny SE footballers
Szeged-Csanád Grosics Akadémia footballers
Dorogi FC footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Nemzeti Bajnokság III players
21st-century Hungarian people |
https://en.wikipedia.org/wiki/Cho%20Min-woo | Cho Min-Woo (趙民宇, born May 13, 1992) is a South Korean football player who currently plays for Pohang Steelers in K League Classic.
Club statistics
Updated to 23 February 2016.
References
External links
Profile at V-Varen Nagasaki
1992 births
Living people
Men's association football central defenders
South Korean men's footballers
South Korean expatriate men's footballers
South Korean expatriate sportspeople in Japan
Expatriate men's footballers in Japan
FC Seoul players
Gangwon FC players
V-Varen Nagasaki players
K League 1 players
K League 2 players
J2 League players
Dongguk University alumni
Sportspeople from Seongnam
Footballers from Gyeonggi Province |
https://en.wikipedia.org/wiki/Kevin%20Houston%20%28mathematician%29 | Kevin Houston is a Professor of Mathematics Education and Public Engagement in the School of Mathematics at the University of Leeds and was previously a lecturer there, a post he held since 2005. Prior to that, he was a lecturer at Middlesex University and a research associate at the University of Liverpool. His research is on singularity theory. He is education secretary of the London Mathematical Society.
Books
Houston is the author of the book
In addition he is an editor of:
References
External links
Living people
21st-century British mathematicians
Date of birth missing (living people)
Academics of the University of Leeds
Academics of the University of Liverpool
Academics of Middlesex University
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Kenya%20Okazaki | is a Japanese football player who currently plays for Montedio Yamagata in the J2 League
Club statistics
Last updated 26 July 2022.
Reserves performance
Honors
Gamba Osaka
J. League Division 1 - 2014
J. League Division 2 - 2013
Emperor's Cup - 2014
J. League Cup - 2014
References
External links
Profile at Tochigi SC
1990 births
Living people
Kansai University alumni
Association football people from Hiroshima Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Gamba Osaka players
Gamba Osaka U-23 players
Ehime FC players
Tochigi SC players
Montedio Yamagata players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Junki%20Kanayama | is a Japanese football player. He currently plays for Fagiano Okayama in J2 League
Club statistics
Updated to 10 August 2022.
1Includes Promotion Playoffs to J1.
References
External links
1988 births
Living people
Ritsumeikan University alumni
Association football people from Shimane Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
V-Varen Nagasaki players
Hokkaido Consadole Sapporo players
Fagiano Okayama players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Park%20Hyung-jin | Park Hyung-jin (, 24 June 1990) is a South Korean football player. He currently plays for Bucheon FC 1995.
His elder brother, Park Jin-soo, is also a football player.
Statistics
Updated to 29 June 2021.
1Includes Japanese Super Cup, K League 1 Final B, K League 1 Final A and FIFA Club World Cup.
References
External links
Profile at V-Varen Nagasaki
Living people
1990 births
South Korean men's footballers
J1 League players
J2 League players
Sanfrecce Hiroshima players
Tochigi SC players
V-Varen Nagasaki players
Fagiano Okayama players
Expatriate men's footballers in Japan
K League 1 players
Suwon Samsung Bluewings players
K League 2 players
Bucheon FC 1995 players
Men's association football defenders
Pocheon Citizen FC players
Footballers from South Gyeongsang Province |
https://en.wikipedia.org/wiki/Paul%C3%A3o%20%28footballer%2C%20born%201989%29 | Luis Paulo da Silva (born 4 December 1989), known as Paulão, is a Brazilian football player. He currently plays for Shanghai Jiading Huilong in China League One.
Club statistics
Updated to 4 December 2022.
References
External links
Living people
1989 births
Brazilian men's footballers
Brazilian expatriate men's footballers
J2 League players
J3 League players
China League One players
Roma Esporte Apucarana players
Associação Esportiva Recreativa Engenheiro Beltrão players
Hokkaido Consadole Sapporo players
Fukushima United FC players
Mito HollyHock players
Tochigi SC players
Albirex Niigata players
FC Gifu players
Shanghai Jiading Huilong F.C. players
Men's association football defenders
Brazilian expatriate sportspeople in Japan
Expatriate men's footballers in Japan
Brazilian expatriate sportspeople in China
Expatriate men's footballers in China |
https://en.wikipedia.org/wiki/Ryota%20Matsumoto | is a Japanese football player. and assistant head coach for Montedio Yamagata in the J2 League.
Club statistics
Updated to 26 July 2022.
References
External links
Profile at Montedio Yamagata
1990 births
Living people
Toyo University alumni
Association football people from Saitama Prefecture
Japanese men's footballers
J2 League players
J3 League players
Hokkaido Consadole Sapporo players
FC Machida Zelvia players
Montedio Yamagata players
Men's association football defenders |
https://en.wikipedia.org/wiki/Yuto%20Horigome%20%28footballer%29 | is a Japanese professional footballer who plays as a left back for club Albirex Niigata.
Club statistics
.
Honours
Albirex Niigata
J2 League : 2022
Individual
J2 League Best XI: 2022
References
External links
Profile at Albirex Niigata
1994 births
Living people
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Hokkaido Consadole Sapporo players
Fukushima United FC players
Albirex Niigata players
Men's association football midfielders
Association football people from Sapporo |
https://en.wikipedia.org/wiki/Ahn%20Young-kyu | Ahn Young-kyu ; is a South Korean football player who plays for Gwangju FC.
Career statistics
References
External links
Living people
1989 births
South Korean men's footballers
South Korean expatriate men's footballers
Suwon Samsung Bluewings players
Giravanz Kitakyushu players
Daejeon Hana Citizen players
Gwangju FC players
Asan Mugunghwa FC players
K League 1 players
K League 2 players
J2 League players
Expatriate men's footballers in Japan
South Korean expatriate sportspeople in Japan
Men's association football midfielders |
https://en.wikipedia.org/wiki/D%C3%A1niel%20Juh%C3%A1sz | Dániel Juhász (born 17 May 1992) is a Hungarian football player who currently plays for Paksi SE.
Club statistics
Updated to games played as of 21 April 2013.
References
HLSZ
MLSZ
1992 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football defenders
Zalaegerszegi TE players
Paksi FC players
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/Joseph%20Boum | Joseph Boum (born 26 September 1989) is a Cameronese footballer who last played for Zira FK as a center back.
Career statistics
Club
References
External links
1986 births
Living people
Men's association football defenders
Cameroonian men's footballers
Mersin Talim Yurdu footballers
Antalyaspor footballers
Zira FK players
Cameroonian expatriate sportspeople in Azerbaijan
Cameroonian expatriate sportspeople in Turkey |
https://en.wikipedia.org/wiki/Lehmer%27s%20totient%20problem | In mathematics, Lehmer's totient problem asks whether there is any composite number n such that Euler's totient function φ(n) divides n − 1. This is an unsolved problem.
It is known that φ(n) = n − 1 if and only if n is prime. So for every prime number n, we have φ(n) = n − 1 and thus in particular φ(n) divides n − 1. D. H. Lehmer conjectured in 1932 that there are no composite numbers with this property.
History
Lehmer showed that if any composite solution n exists, it must be odd, square-free, and divisible by at least seven distinct primes (i.e. ω(n) ≥ 7). Such a number must also be a Carmichael number.
In 1980, Cohen and Hagis proved that, for any solution n to the problem, n > 1020 and ω(n) ≥ 14.
In 1988, Hagis showed that if 3 divides any solution n, then n > 10 and ω(n) ≥ . This was subsequently improved by Burcsi, Czirbusz, and Farkas, who showed that if 3 divides any solution n, then n > 10 and ω(n) ≥ .
A result from 2011 states that the number of solutions to the problem less than is at most .
References
Conjectures
Unsolved problems in number theory
Multiplicative functions |
https://en.wikipedia.org/wiki/Park%20Kwang-il | Park Kwang-il (; born 10 February 1991) is a South Korean footballer who plays as a midfielder for Gyeongnam.
Club statistics
Updated to 28 July 2017.
References
External links
Profile at Ehime FC
1991 births
Living people
South Korean men's footballers
Yonsei University alumni
J2 League players
K League 1 players
Indian Super League players
Matsumoto Yamaga FC players
Selangor F.C. II players
FC Pune City players
Mito HollyHock players
Ehime FC players
Jeonnam Dragons players
Gyeongnam FC players
South Korean expatriate sportspeople in Japan
South Korean expatriate sportspeople in India
Expatriate men's footballers in Japan
Expatriate men's footballers in India
Men's association football wingers
Men's association football fullbacks |
https://en.wikipedia.org/wiki/Park%20Kun | Park Kun (パク・ゴン) is a South Korean football player. He currently plays for Pohang Steelers.
Club statistics
Updated to 23 February 2017.
References
External links
Profile at Thespakusatsu Gunma
Living people
1990 births
South Korean men's footballers
J2 League players
J3 League players
K League 2 players
Avispa Fukuoka players
AC Nagano Parceiro players
Thespakusatsu Gunma players
Bucheon FC 1995 players
Men's association football defenders
People from Gunsan
Sportspeople from North Jeolla Province |
https://en.wikipedia.org/wiki/Geometry%20of%20binary%20search%20trees | In computer science, one approach to the dynamic optimality problem on online algorithms for binary search trees involves reformulating the problem geometrically, in terms of augmenting a set of points in the plane with as few additional points as possible in order to avoid rectangles with only two points on their boundary.
Access sequences and competitive ratio
As typically formulated, the online binary search tree problem involves search trees defined over a fixed key set . An access sequence is a sequence ... where each access belongs to the key set.
Any particular algorithm for maintaining binary search trees (such as the splay tree algorithm or Iacono's working set structure) has a cost for each access sequence that models the amount of time it would take to use the structure to search for each of the keys in the access sequence in turn. The cost of a search is modeled by assuming that the search tree algorithm has a single pointer into a binary search tree, which at the start of each search points to the root of the tree. The algorithm may then perform any sequence of the following operations:
Move the pointer to its left child.
Move the pointer to its right child.
Move the pointer to its parent.
Perform a single tree rotation on the pointer and its parent.
The search is required, at some point within this sequence of operations to move the pointer to a node containing the key, and the cost of the search is the number of operations that are performed in the sequence. The total cost costA(X) for algorithm A on access sequence X is the sum of the costs of the searches for each successive key in the sequence.
As is standard in competitive analysis, the competitive ratio of an algorithm A is defined to be the maximum, over all access sequences, of the ratio of the cost for A to the best cost that any algorithm could achieve:
The dynamic optimality conjecture states that splay trees have constant competitive ratio, but this remains unproven. The geometric view of binary search trees provides a different way of understanding the problem that has led to the development of alternative algorithms that could also (conjecturally) have a constant competitive ratio.
Translation to a geometric point set
In the geometric view of the online binary search tree problem,
an access sequence (sequence of searches performed on a binary search tree (BST) with a key set ) is mapped to the set of points , where the X-axis represents the key space and the Y-axis represents time; to which a set of touched nodes is added. By touched nodes we mean the following. Consider a BST access algorithm with a single pointer to a node in the tree. At the beginning of an access to a given key , this pointer is initialized to the root of the tree. Whenever the pointer moves to or is initialized to a node, we say that the node is touched.
We represent a BST algorithm for a given input sequence by drawing a point for each item that gets touched.
For example, assume the |
https://en.wikipedia.org/wiki/Tunnel%20number | In mathematics, the tunnel number of a knot, as first defined by Bradd Clark, is a knot invariant, given by the minimal number of arcs (called tunnels) that must be added to the knot so that the complement becomes a handlebody. The tunnel number can equally be defined for links. The boundary of a regular neighbourhood of the union of the link and its tunnels forms a Heegaard splitting of the link exterior.
Examples
The unknot is the only knot with tunnel number 0.
The trefoil knot has tunnel number 1. In general, any nontrivial torus knot has tunnel number 1.
Every link L has a tunnel number. This can be seen, for example, by adding a 'vertical' tunnel at every crossing in a diagram of L. It follows from this construction that the tunnel number of a knot is always less than or equal to its crossing number.
References
.
.
.
.
Knot invariants |
https://en.wikipedia.org/wiki/Invariant%20convex%20cone | In mathematics, an invariant convex cone is a closed convex cone in a Lie algebra of a connected Lie group that is invariant under inner automorphisms. The study of such cones was initiated by Ernest Vinberg and Bertram Kostant.
For a simple Lie algebra, the existence of an invariant convex cone forces the Lie algebra to have a Hermitian structure, i.e. the maximal compact subgroup has center isomorphic to the circle group. The invariant convex cone generated by a generator of the Lie algebra of the center is closed and is the minimal invariant convex cone (up to a sign). The dual cone with respect to the Killing form is the maximal invariant convex cone. Any intermediate cone is uniquely determined by its intersection with the Lie algebra of a maximal torus in a maximal compact subgroup. The intersection is invariant under the Weyl group of the maximal torus and the orbit of every point in the interior of the cone intersects the interior of the Weyl group invariant cone.
For the real symplectic group, the maximal and minimal cone coincide, so there is only one invariant convex cone. When one is properly contained in the other, there is a continuum of intermediate invariant convex cones.
Invariant convex cones arise in the analysis of holomorphic semigroups in the complexification of the Lie group, first studied by Grigori Olshanskii. They are naturally associated with Hermitian symmetric spaces and their associated holomorphic discrete series. The semigroup is made up of those elements in the complexification which, when acting on the Hermitian symmetric space of compact type, leave invariant the bounded domain corresponding to the noncompact dual. The semigroup acts by contraction operators on the holomorphic discrete series; its interior acts by Hilbert–Schmidt operators. The unitary part of their polar decomposition is the operator corresponding to an element in the original real Lie group, while the positive part is the exponential of an imaginary multiple of the infinitesimal operator corresponding to an element in the maximal cone. A similar decomposition already occurs in the semigroup.
The oscillator semigroup of Roger Howe concerns the special case of this theory for the real symplectic group. Historically this has been one of the most important applications and has been generalized to infinite dimensions. This article treats in detail the example of the invariant convex cone for the symplectic group and its use in the study of the symplectic Olshanskii semigroup.
Invariant convex cone in symplectic Lie algebra
The Lie algebra of the symplectic group on R2n has a unique invariant convex cone. It is self-dual. The cone and its properties can be derived directly using the description of the symplectic Lie algebra provided by the Weyl calculus in quantum mechanics. Let the variables in R2n be x1, ..., xn, y1, ..., yn. Taking the standard inner product on R2n, the symplectic form corresponds to the matrix
The real polynomials on R2 |
https://en.wikipedia.org/wiki/Bony%E2%80%93Brezis%20theorem | In mathematics, the Bony–Brezis theorem, due to the French mathematicians Jean-Michel Bony and Haïm Brezis, gives necessary and sufficient conditions for a closed subset of a manifold to be invariant under the flow defined by a vector field, namely at each point of the closed set the vector field must have non-positive inner product with any exterior normal vector to the set. A vector is an exterior normal at a point of the closed set if there is a real-valued continuously differentiable function maximized locally at the point with that vector as its derivative at the point. If the closed subset is a smooth submanifold with boundary, the condition states that the vector field should not point outside the subset at boundary points. The generalization to non-smooth subsets is important in the theory of partial differential equations.
The theorem had in fact been previously discovered by Mitio Nagumo in 1942 and is also known as the Nagumo theorem.
Statement
Let F be closed subset of a C2 manifold M and let X be a vector field on M which is Lipschitz continuous. The following conditions are equivalent:
Every integral curve of X starting in F remains in F.
(X(m),v) ≤ 0 for every exterior normal vector v at a point m in F.
Proof
Following , to prove that the first condition implies the second, let c(t) be an integral curve with
c(0) = x in F and dc/dt= X(c). Let g have a local maximum on F at x. Then g(c(t)) ≤ g (c(0)) for t small and positive. Differentiating, this implies that g '(x)⋅X(x) ≤ 0.
To prove the reverse implication, since the result is local, it enough to check it in Rn. In that case X locally satisfies a Lipschitz condition
If F is closed, the distance function D(x) = d(x,F)2 has the following differentiability property:
where the minimum is taken over the closest points z to x in F.
To check this, let
where the minimum is taken over z in F such that d(x,z) ≤ d(x,F) + ε.
Since fε is homogeneous in h and increases uniformly to f0 on any sphere,
with a constant C(ε) tending to 0 as ε tends to 0.
This differentiability property follows from this because
and similarly if |h| ≤ ε
The differentiability property implies that
minimized over closest points z to c(t). For any such z
Since −|y − c(t)|2 has a local maximum on F at y = z, c(t) − z is an exterior normal vector at z. So the first term on the right hand side is non-negative. The Lipschitz condition for X implies the second term is bounded above by 2C⋅D(c(t)). Thus the derivative from the right of
is non-positive, so it is a non-increasing function of t. Thus if c(0) lies in F, D(c(0))=0 and hence D(c(t)) = 0 for t > 0, i.e. c(t) lies in F for t > 0.
References
Literature
, Theorem 8.5.11
See also
Barrier certificate
Ordinary differential equations
Dynamical systems
Manifolds |
https://en.wikipedia.org/wiki/Roland%20Pap | Roland Pap (born 17 August 1990 in Bonyhád) is a Hungarian football player who currently plays for Paksi SE.
Club statistics
Updated to games played as of 1 December 2013.
References
HLSZ
MLSZ
1990 births
Living people
People from Bonyhád
Hungarian men's footballers
Men's association football forwards
Paksi FC players
Vác FC players
Kozármisleny SE footballers
Nemzeti Bajnokság I players
Footballers from Tolna County |
https://en.wikipedia.org/wiki/2006%20Halmstads%20BK%20season | Halmstads BK participated in 2006 in Allsvenskan and Svenska Cupen.
2006 season squad
The 2006 season squad.
Statistics prior to season start only
Transfers
In
Out
Fixtures and results
Allsvenskan
League table
League fixtures and results
References
Footnotes
References
External links
Halmstads BK homepage
Allsvenskan 2006 season SvFF homepage
Halmstads BK seasons
Halmstad |
https://en.wikipedia.org/wiki/Social%20facilitation%20in%20animals | Social facilitation in animals is when the performance of a behaviour by an animal increases the probability of other animals also engaging in that behaviour or increasing the intensity of the behaviour. More technically, it is said to occur when the performance of an instinctive pattern of behaviour by an individual acts as a releaser for the same behaviour in others, and so initiates the same line of action in the whole group. It has been phrased as "The energizing of dominant behaviors by the presence of others."
Social facilitation occurs in a wide variety of species under a range of circumstances. These include feeding, scavenging, teaching, sexual behaviour, coalition formation, group displays, flocking behaviour, and dustbathing. For example, in paper wasp species, Agelaia pallipes, social facilitation is used to recruitment to food resources. By using chemical communication, A. pallipes pool the independent search efforts to locate and defend food sources from other organisms.
Social facilitation is sometimes used to develop successful social scavenging strategies. Griffon vultures are highly specialized scavengers that rely on finding carcasses. When foraging, griffon vultures soar at up to 800 m above the ground. Although some fresh carcasses are located directly by searching birds, the majority of individuals find food by following other vultures, i.e. social facilitation. A chain reaction of information transfer extends from the carcass as descending birds are followed by other birds, which themselves cannot directly see the carcass, ultimately drawing birds from an extensive area over a short period of time.
Moller used a play-back technique to investigate the effects of singing by the black wheatear (Oenanthe leucura) on the behaviour of both conspecifics and heterospecifics. It was found that singing increased in both groups in response to the wheateater and Moller suggested the conspicuous dawn (and dusk) chorus of bird song may be augmented by social facilitation due to the singing of conspecifics as well as heterospecifics.
See also
Behavioral contagion
Social facilitation
References
Ethology
Animal communication |
https://en.wikipedia.org/wiki/List%20of%20Sri%20Lanka%20Premier%20League%20records%20and%20statistics | This is a list of statistics and records of the Sri Lanka Premier League, a Twenty20 cricket competition based in Sri Lanka. The statistics and records included in this article take into account only those matches where two SLPL teams were playing against each other as part of an SLPL season. They do not include the results of trial games, exhibition matches, or games played in other tournaments such as the Champions League Twenty20.
Team records
Result summary
Highest totals
Lowest totals
Highest match aggregates
External links
Sri Lanka Premier League on YouTube
Sri Lanka Premier League
Cricket records and statistics
records |
https://en.wikipedia.org/wiki/OpenIntro%20Statistics | OpenIntro Statistics is an open-source textbook for introductory statistics, written by David Diez, Christopher Barr, and Mine Çetinkaya-Rundel.
The textbook is available online as a free PDF, as LaTeX source and as a royalty-free paperback.
References
Statistics books |
https://en.wikipedia.org/wiki/L-statistic | In statistics, an L-statistic is a statistic (function of a data set) that is a linear combination of order statistics; the "L" is for "linear". These are more often referred to by narrower terms according to use, namely:
L-estimator, using L-statistics as estimators for parameters
L-moment, L-statistic analogs of the conventional moments
Summary statistics |
https://en.wikipedia.org/wiki/Vitalie%20Zlatan | Vitalie Zlatan (born 8 April 1993, Chișinău, Moldova) is a Moldavian football striker who plays for FC Iskra-Stal.
Club statistics
Total matches played in Moldavian First League: 14 matches – 3 goals
References
External links
Profile at Divizia Nationala
Profile at Iskra-Stal FC
1991 births
Living people
Footballers from Chișinău
FC Sfîntul Gheorghe players
FC Iskra-Stal players
Moldovan men's footballers
Men's association football forwards |
https://en.wikipedia.org/wiki/Andrew%20Munro%20%28mathematician%29 | Andrew Munro, M.A., (6 July 1869 – 1 July 1935) was a Scottish lecturer in mathematics, Vice President, Bursar, Steward and Senior Fellow of Queens' College, Cambridge for 45 years from 1893 to 1935. The Munro scholarships and studentships at Queens' College, Cambridge are named in his honour.
Early life
Andrew Munro was born 6 July 1869, in Rosskeen, Ross and Cromarty, Scotland, the son of Andrew Munro and Margaret Small of Invergordon in Ross and Cromarty. His father was a banker, mill owner and farmer, who also served as Chief Magistrate for Invergordon and Justice of the Peace for Ross and Cromarty. The Munros were members of the Clan Munro. His mother was the daughter of John Small (1797–1847), under Librarian of the University of Edinburgh, and the sister of John Small (1828–1886), who succeeded his father as under Librarian and later was appointed Librarian. Munro's mother and family were members of the Smalls of Dirnanean, Perthshire, Scotland.
Academics
Munro initially attended Aberdeen University, Scotland, later transferring to Cambridge. He won a foundation scholarship to Queens' College, Cambridge in 1890, and two years later was designated as the fourth Wrangler.
In 1892, Munro received his Bachelor of Arts degree, followed by a Masters of Arts degree in 1896. In 1893, he was elected a Fellow at Queens' College, Cambridge. For the next 20 years he served as a lecturer, director of studies, and supervisor in mathematics at the college.
In 1913, Munro became Bursar of Queens' College, Cambridge. In this role, Munro advised the college to dispose of most of its farmland after World War I and invest in government stocks, which significantly increased the college's endowments.
Legacy
Andrew Munro died on 1 July 1935 at Dormy House Hotel in Sheringham, Norfolk, England. He was buried in St. Giles Cemetery in Cambridge, now referred to as Parish of the Ascension Burial Ground, on 4 July 1935.
A portion of Munro's estate, upwards of £26,000, was left to Queens' College, Cambridge to fund scholarships in mathematics and physics. These scholarships and studentships are named in Munro's honour.
The Munro Room at Queens' College, Cambridge which faces both Old Court and Walnut Tree Court, is named for Munro. A portrait of Munro, painted by Arthur Trevor Haddon, appropriately hangs in the room.
References
External links
Andrew Munro, Queens' College Portrait
1869 births
1935 deaths
Scottish mathematicians
Alumni of Queens' College, Cambridge
Fellows of Queens' College, Cambridge |
https://en.wikipedia.org/wiki/Complex%20coordinate%20space | In mathematics, the n-dimensional complex coordinate space (or complex n-space) is the set of all ordered n-tuples of complex numbers. It is denoted , and is the n-fold Cartesian product of the complex plane with itself. Symbolically,
or
The variables are the (complex) coordinates on the complex n-space.
Complex coordinate space is a vector space over the complex numbers, with componentwise addition and scalar multiplication. The real and imaginary parts of the coordinates set up a bijection of with the 2n-dimensional real coordinate space, . With the standard Euclidean topology, is a topological vector space over the complex numbers.
A function on an open subset of complex n-space is holomorphic if it is holomorphic in each complex coordinate separately. Several complex variables is the study of such holomorphic functions in n variables. More generally, the complex n-space is the target space for holomorphic coordinate systems on complex manifolds.
See also
Coordinate space
References
Several complex variables
Topological vector spaces |
https://en.wikipedia.org/wiki/Joel%20Sequeira | Joel Sequeira (born 15 March 1988) in Goa is an Indian footballer who last played as a midfielder for ONGC in the I-League.
Career statistics
Club
Statistics accurate as of 11 May 2013
References
External links
Profile at i-league.org.
Indian men's footballers
1988 births
Living people
I-League players
ONGC FC players
Men's association football midfielders
Footballers from Goa |
https://en.wikipedia.org/wiki/Reciprocal%20distribution | In probability and statistics, the reciprocal distribution, also known as the log-uniform distribution, is a continuous probability distribution. It is characterised by its probability density function, within the support of the distribution, being proportional to the reciprocal of the variable.
The reciprocal distribution is an example of an inverse distribution, and the reciprocal (inverse) of a random variable with a reciprocal distribution itself has a reciprocal distribution.
Definition
The probability density function (pdf) of the reciprocal distribution is
Here, and are the parameters of the distribution, which are the lower and upper bounds of the support, and is the natural log. The cumulative distribution function is
Characterization
Relationship between the log-uniform and the uniform distribution
A positive random variable X is log-uniformly distributed if the logarithm of X is uniform distributed,
This relationship is true regardless of the base of the logarithmic or exponential function. If is uniform distributed, then so is , for any two positive numbers . Likewise, if is log-uniform distributed, then so is , where .
Applications
The reciprocal distribution is of considerable importance in numerical analysis, because a computer’s arithmetic operations transform mantissas with initial arbitrary distributions into the reciprocal distribution as a limiting distribution.
References
Continuous distributions |
https://en.wikipedia.org/wiki/Kunal%20Ghosh%20%28footballer%29 | Kunal Ghosh (born 30 March 1986) is an Indian footballer who plays as a midfielder for ONGC in the I-League.
Career statistics
Club
Statistics accurate as of 11 May 2013
References
External links
Profile at I-League
Indian men's footballers
1986 births
Living people
Footballers from West Bengal
I-League players
ONGC FC players
Men's association football midfielders
Calcutta Football League players |
https://en.wikipedia.org/wiki/Artificial%20precision | In numerical mathematics, artificial precision is a source of error that occurs when a numerical value or semantic is expressed with more precision than was initially provided from measurement or user input.
For example, a person enters their birthday as the date 1984-01-01 but it is stored in a database as 1984-01-01T00:00:00Z which introduces the artificial precision of the hour, minute, and second they were born, and may even affect the date, depending on the user's actual place of birth. This is also an example of false precision, which is artificial precision specifically of numerical quantities or measures.
See also
false precision
accuracy and precision
significant figures
References
Computational statistics
Numerical analysis |
https://en.wikipedia.org/wiki/Minkowski%20space%20%28number%20field%29 | In mathematics, specifically the field of algebraic number theory, a Minkowski space is a Euclidean space associated with an algebraic number field.
If K is a number field of degree d then there are d distinct embeddings of K into C. We let KC be the image of K in the product Cd, considered as equipped with the usual Hermitian inner product. If c denotes complex conjugation, let KR denote the subspace of KC fixed by c, equipped with a scalar product. This is the Minkowski space of K.
See also
Geometry of numbers
Footnotes
References
Algebraic number theory |
https://en.wikipedia.org/wiki/Andrew%20Munro | Andrew Munro may refer to:
Andrew Munro (bishop), Bishop of Ross, Scotland in the 15th century
Andrew Munro (mathematician) (1869–1935), Scottish fellow, lecturer in mathematics and bursar of Queens' College, Cambridge
Andrew Munro (footballer) (born 1963), Grenadian international footballer |
https://en.wikipedia.org/wiki/Miriam%20Cohen | Miriam Cohen (born October 1941) is an Israeli mathematician and a professor in the Department of Mathematics at Ben-Gurion University of the Negev whose main areas of research are Hopf algebras, quantum groups and Noncommutative rings.
Biography
Miriam Cohen (née Hirsch) was born in Ramat Gan, British Mandate of Palestine. Her parents Dr. Hanna and Jusin Hirsch fled Nazi Germany to Palestine in 1939. She lived in Petah Tikva and joined the IDF communication corps in 1959. In 1961 she married Yair Cohen and in 1962 they left to study in the US. Miriam received her B.Sc. in Mathematics with High Honors from California State University and continued for her Ph.D. in Mathematics at UCLA where she received her M.Sc. After returning to Israel she completed her Ph.D. at Tel Aviv University under the supervision of Prof. Israel Nathan Herstein from the University of Chicago and Prof. A.A. Klein from Tel Aviv University. During these years the couple had four children (Omer, Ira, Alma and Adaya). In 1978 the family moved for idealistic reasons from Herzliya Pituach to the development town of Yeruham and lived there for 10 years. Miriam joined the faculty of the department of Mathematics at BGU and has been a member ever since. During her time as a researcher and lecturer at BGU she volunteered in educational projects in Yeruham (see below).
In 1983–5 Cohen was a visiting Associate Professor at the University of Southern California and at UCLA in Los Angeles. In 1997–8 she was a visiting professor at the Mathematics Institute of Fudan University in Shanghai.
She was elected as a member of the 2017 class of Fellows of the American Mathematical Society "for contributions to Hopf algebras and their representations, and for service to the mathematical community".
Functions in the Israeli mathematical community
In 1992–94 she served as President of the Israel Mathematical Union.
In 1996 she initiated and established the special track in Bioinformatics in the Department of Mathematics and Computer Sciences Department at BGU.
In 1998–2002 she served as Elected Dean of the Faculty of Natural Sciences at BGU (the first woman in Israel to serve in this capacity) and was a member of the Central Steering Committee and a member of the Executive committee of BGU
In 2001 she founded the Center of Advanced Studies in Mathematics at BGU and has serves as its director since June 2003
She serves as associate editor in Communications in Algebra .
In 1993–95 she served as Chairman of the Mathematics and Computer Science Department
Additional activities
Initiation of the joint Israel Mathematical Union (IMU) and the American Mathematical Society (AMS) International meeting in 1995 and serves as member of the scientific committee of the second IMU and AMS meeting to take place in Israel in 2014.
Since 2002 Chair and member of the Organizing and scientific committee of the Moshe Flato Colloquia series at BGU.
Speaker at the Women Scientists Forum at th |
https://en.wikipedia.org/wiki/Ganita%20Kaumudi | Ganita Kaumudi (Gaṇitakaumudī) is a treatise on mathematics written by Indian mathematician Narayana Pandita in 1356. It was an arithmetical treatise alongside the other algebraic treatise called "Bijganita Vatamsa" by Narayana Pandit.
Contents
Gaṇita Kaumudī contains about 475 verses of sūtra (rules), and 395 verses of udāharaṇa (examples). It is divided into 14 sections (chapters) known as vyavahāras:
1. Prakīrṇaka-vyavahāra
Weights and measures, length, area, volume, etc. It describes addition, subtraction, multiplication, division, square, square root, cube and cube root. The problems of linear and quadratic equations described here are more complex than in earlier works. 63 rules and 82 examples
2. Miśraka-vyavahāra
Mathematics pertaining to daily life: “mixture of materials, interest on a principal, payment in instalments, mixing gold objects with different purities and other problems pertaining to linear indeterminate equations for many unknowns” 42 rules and 49 examples
3. Śreḍhī-vyavahāra
Arithmetic and geometric progressions, sequences and series. The generalization here was crucial for finding the infinite series for sine and cosine. 28 rules and 19 examples.
4. Kṣetra-vyavahāra
Geometry. 149 rules and 94 examples. Includes special material on cyclic quadratilerals, such as the “third diagonal”.
5. Khāta-vyavahāra
Excavations. 7 rules and 9 examples.
6. Citi-vyavahāra
Stacks. 2 rules and 2 examples.
7. Rāśi-vyavahāra
Mounds of grain. 2 rules and 3 examples.
8. Chāyā-vyavahāra
Shadow problems. 7 rules and 6 examples.
9. Kuṭṭaka
Linear integer equations. 69 rules and 36 examples.
10. Vargaprakṛti
Quadratic. 17 rules and 10 examples. Includes a variant of the Chakravala method. Ganita Kaumudi contains many results from continued fractions. In the text Narayana Pandita used the knowledge of simple recurring continued fraction in the solutions of indeterminate equations of the type .
11. Bhāgādāna
Factorization. Contains Fermat's factorization method. 11 rules and 7 examples.
12. Rūpādyaṃśāvatāra
Contains rules for writing a fraction as a sum of unit fractions. 22 rules and 14 examples.
Unit fractions were known in Indian mathematics in the Vedic period: the Śulba Sūtras give an approximation of equivalent to . Systematic rules for expressing a fraction as the sum of unit fractions had previously been given in the Gaṇita-sāra-saṅgraha of Mahāvīra (). Nārāyaṇa's Gaṇita-kaumudi gave a few more rules: the section bhāgajāti in the twelfth chapter named aṃśāvatāra-vyavahāra contains eight rules. The first few are:
Rule 1. To express 1 as a sum of n unit fractions:
Rule 2. To express 1 as a sum of n unit fractions:
Rule 3. To express a fraction as a sum of unit fractions:
Pick an arbitrary number i such that is an integer r, write
and find successive denominators in the same way by operating on the new fraction. If i is always chosen to be the smallest such integer, this is equivalent to the greedy alg |
https://en.wikipedia.org/wiki/Lev%20R.%20Ginzburg | Lev R. Ginzburg (; born 1945) is a mathematical ecologist and the president of the firm Applied Biomathematics.
Biography
Lev Ginzburg was born in 1945 in Moscow, Russia, but grew up in St. Petersburg, at the time Leningrad. He studied mathematics and theoretical mechanics at Leningrad State University (M.S. in 1967) and received his Ph.D. in applied mathematics from the Agrophysical Research Institute in 1970. He worked at this Institute until the Spring of 1975 and emigrated to the United States in December 1975. After several months at the Accademia Nazionale Dei Lincei (Rome, Italy), and one year at the Mathematics Department at Northeastern University (Boston, MA), he was a professor at the Department of Ecology and Evolution at Stony Brook University from 1977 until his retirement in 2015.
In 1982, Ginzburg founded and has since run Applied Biomathematics, a research and software firm focused on conservation biology, ecology, health, engineering and education. The company develops new methods for the assessment of risk and uncertainty in these areas.
Work
Applied Biomathematics is funded primarily by research grants and contracts from the U.S. government and private industry associations. Grants include awards from the National Institutes of Health, United States Department of Agriculture, NASA, National Science Foundation, and the Nuclear Regulatory Commission. Other project funding has come from the Electric Power Research Institute and individual utility companies, healthcare, pharmaceutical and seed companies such as Pfizer, DuPont and Dow, and the U.S. Army Corps of Engineers. Applied Biomathematics translates theoretical concepts from biology and the physical sciences into new mathematical and statistical methods to quantitatively solve practical problems in these areas using risk analysis and reliability assessments. In 2001, Ginzburg testified in the U.S. Senate on the quantitative aspects of endangered species legislation. Ginzburg's work in risk analysis and applied ecology has been conducted at Applied Biomathematics in collaboration with Scott Ferson and Resit Akcakaya, who are now professors at the University of Liverpool, UK, and Stony Brook University, New York, USA respectively. The methods and RAMASsoftware products developed by Applied Biomathematics are used by hundreds of academic institutions around the world, government agencies, and industrial and private labs in over 60 countries.
Ginzburg’s most known academic work is a theory of predation (the ratio-dependent or Arditi-Ginzburg equations) that is an alternative to the classic prey-dependent Lotka-Volterra model. His book, with Roger Arditi, How Species Interact, summarizes their proposed alteration of the standard view. The recent editions of the standard college Ecology textbook devote equal space to the Lotka-Volterra and Arditi-Ginzburg equations. His concept of inertial growth or an explanation of population cycles, based upon maternal effect model, is |
https://en.wikipedia.org/wiki/Symmetric%20cone | In mathematics, symmetric cones, sometimes called domains of positivity, are open convex self-dual cones in Euclidean space which have a transitive group of symmetries, i.e. invertible operators that take the cone onto itself. By the Koecher–Vinberg theorem these correspond to the cone of squares in finite-dimensional real Euclidean Jordan algebras, originally studied and classified by . The tube domain associated with a symmetric cone is a noncompact Hermitian symmetric space of tube type. All the algebraic and geometric structures associated with the symmetric space can be expressed naturally in terms of the Jordan algebra. The other irreducible Hermitian symmetric spaces of noncompact type correspond to Siegel domains of the second kind. These can be described in terms of more complicated structures called Jordan triple systems, which generalize Jordan algebras without identity.
Definitions
A convex cone C in a finite-dimensional real inner product space V is a convex set invariant under multiplication by positive scalars. It spans the subspace C – C and the largest subspace it contains is C ∩ (−C). It spans the whole space if and only if it contains a basis. Since the convex hull of the basis is a polytope with non-empty interior, this happens if and only if C has non-empty interior. The interior in this case is also a convex cone. Moreover, an open convex cone coincides with the interior of its closure, since any interior point in the closure must lie in the interior of some polytope in the original cone. A convex cone is said to be proper if its closure, also a cone, contains no subspaces.
Let C be an open convex cone. Its dual is defined as
It is also an open convex cone and C** = C. An open convex cone C is said to be self-dual if C* = C. It is necessarily proper, since
it does not contain 0, so cannot contain both X and −X.
The automorphism group of an open convex cone is defined by
Clearly g lies in Aut C if and only if g takes the closure of C onto itself. So Aut C is a closed subgroup of GL(V) and hence a Lie group. Moreover, Aut C* = (Aut C)*, where g* is the adjoint of g. C is said to be homogeneous if Aut C acts transitively on C.
The open convex cone C is called a symmetric cone if it is self-dual and homogeneous.
Group theoretic properties
If C is a symmetric cone, then Aut C is closed under taking adjoints.
The identity component Aut0 C acts transitively on C.
The stabilizers of points are maximal compact subgroups, all conjugate, and exhaust the maximal compact subgroups of Aut C.
In Aut0 C the stabilizers of points are maximal compact subgroups, all conjugate, and exhaust the maximal compact subgroups of Aut0 C.
The maximal compact subgroups of Aut0 C are connected.
The component group of Aut C is isomorphic to the component group of a maximal compact subgroup and therefore finite.
Aut C ∩ O(V) and Aut0 C ∩ O(V) are maximal compact subgroups in Aut C and Aut0 C.
C is naturally a Riemannian symmetric space isomorphic to |
https://en.wikipedia.org/wiki/Set%20inversion | In mathematics, set inversion is the problem of characterizing the preimage X of a set Y by a function f, i.e., X = f  −1(Y ) = {x ∈ Rn | f(x) ∈ Y }. It can also be viewed as the problem of describing the solution set of the quantified constraint "Y(f (x))", where Y( y) is a constraint, e.g. an inequality, describing the set Y.
In most applications, f is a function from Rn to Rp and the set Y is a box of Rp (i.e. a Cartesian product of p intervals of R).
When f is nonlinear the set inversion problem can be solved
using interval analysis combined with a branch-and-bound algorithm.
The main idea consists in building a paving of Rp made with non-overlapping boxes. For each box [x], we perform the following tests:
if f ([x]) ⊂ Y we conclude that [x] ⊂ X;
if f ([x]) ∩ Y = ∅ we conclude that [x] ∩ X = ∅;
Otherwise, the box [x] the box is bisected except if its width is smaller than a given precision.
To check the two first tests, we need an interval extension (or an inclusion function) [f ] for f. Classified boxes are stored into subpavings, i.e., union of non-overlapping boxes.
The algorithm can be made more efficient by replacing the inclusion tests by contractors.
Example
The set X = f  −1([4,9]) where f (x1, x2) = x + x is represented on the figure.
For instance, since [−2,1]2 + [4,5]2 = [0,4] + [16,25] = [16,29] does not intersect the interval [4,9], we conclude that the box [−2,1] × [4,5] is outside X. Since [−1,1]2 + [2,]2 = [0,1] + [4,5] = [4,6] is inside [4,9], we conclude that the whole box [−1,1] × [2,] is inside X.
Application
Set inversion is mainly used for path planning, for nonlinear parameter set estimation, for localization
or for the characterization of stability domains of linear dynamical systems.
References
Topology |
https://en.wikipedia.org/wiki/Lists%20of%20shapes | Lists of shapes cover different types of geometric shape and related topics. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools.
Mathematics
List of mathematical shapes
List of two-dimensional geometric shapes
List of triangle topics
List of circle topics
List of curves
List of surfaces
List of polygons, polyhedra and polytopes
List of regular polytopes and compounds
Elsewhere
Solid geometry, including table of major three-dimensional shapes
Box-drawing character
Cuisenaire rods (learning aid)
Geometric shape
Geometric Shapes (Unicode)
Glossary of shapes with metaphorical names
List of symbols
Pattern Blocks (learning aid) |
https://en.wikipedia.org/wiki/Ronald%20Er%C5%91s | Ronald Erős (born 27 January 1993 in Cegléd) is a Hungarian football player. He plays for Ceglédi VSE in the Hungarian NB I.
He played his first league match in 2013.
Club statistics
Updated to games played as of 1 June 2014.
References
MLSZ
1993 births
Living people
People from Cegléd
Hungarian men's footballers
Men's association football defenders
Újpest FC players
Ceglédi VSE footballers
Nemzeti Bajnokság I players
Footballers from Pest County |
https://en.wikipedia.org/wiki/Coordinate%20%28disambiguation%29 | Coordinate may refer to:
An element of a coordinate system in geometry and related domains
Coordinate space in mathematics
Cartesian coordinate system
Coordinate (vector space)
Geographic coordinate system
Coordinate structure in linguistics
Coordinate covalent bond in chemistry
Coordinate descent, an algorithm
See also
Coordination (disambiguation)
Coordinator (disambiguation) |
https://en.wikipedia.org/wiki/Ridgefield%20Christian%20School | Ridgefield Christian School (RCS) is a private, non-denominational Christian school in Jonesboro, Arkansas, United States.
Demographics
According to the National Center for Education Statistics, in the 2019-2020 school year the school had 143 students, 131 or 91.6% of whom were White, 4 or 2.8% Asian, 5 or 3.4% Black, and 3 or 2.1% were Hispanic.
References
External links
Christian schools in Arkansas
Private high schools in Arkansas
Private middle schools in Arkansas
Private elementary schools in Arkansas
Schools in Craighead County, Arkansas
Buildings and structures in Jonesboro, Arkansas |
https://en.wikipedia.org/wiki/Jadson%20%28footballer%2C%20born%201993%29 | Jadson Alves dos Santos (born 30 August 1993), simply known as Jadson, is a Brazilian footballer who plays as defensive midfielder for Juventude.
Career statistics
Honours
Botafogo
Taça Guanabara: 2013
Taça Rio: 2013
Campeonato Carioca: 2013
References
1993 births
Living people
Brazilian men's footballers
Brazil men's youth international footballers
Brazilian expatriate men's footballers
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Botafogo de Futebol e Regatas players
Udinese Calcio players
Club Athletico Paranaense players
Expatriate men's footballers in Italy
Men's association football midfielders
Santa Cruz Futebol Clube players
Associação Atlética Ponte Preta players
Fluminense FC players
Cruzeiro Esporte Clube players
Esporte Clube Bahia players
Esporte Clube Juventude players
Footballers from São Bernardo do Campo |
https://en.wikipedia.org/wiki/Jeremy%20Avigad | Jeremy Avigad is a professor of philosophy and a professor of mathematical sciences at Carnegie Mellon University.
He received a B.A. in mathematics from Harvard University in 1989, and a Ph.D. in mathematics from the University of California at Berkeley in 1995 under the supervision of Jack Silver. He has contributed to the areas of mathematical logic and foundations, formal verification and interactive theorem proving, and the philosophy and history of mathematics. He became Director of the Hoskinson Center for Formal Mathematics at Carnegie Mellon University after Charles Hoskinson donated $20 Million in September 2021 to establish it.
References
20th-century American mathematicians
21st-century American mathematicians
American logicians
Living people
Philosophers of mathematics
Carnegie Mellon University faculty
Harvard College alumni
1968 births
UC Berkeley College of Letters and Science alumni |
https://en.wikipedia.org/wiki/Delzant%27s%20theorem | In mathematics, a Delzant polytope is a convex polytope in such for each vertex , exactly edges meet at , and these edges form a collection of vectors that form a -basis of . Delzant's theorem, introduced by , classifies effective Hamiltonian torus actions on compact connected symplectic manifolds by the image of the associated moment map, which is a Delzant polytope.
The theorem states that there is a bijective correspondence between symplectic toric manifolds (up to torus-equivariant symplectomorphism) and Delzant polytopes -- more precisely, the moment polytope of a symplectic toric manifold is a Delzant polytope, every Delzant polytope is the moment polytope of such a manifold, and any two such manifolds with the equivalent moment polytopes (up to translations) admit a torus-equivariant symplectomorphism between them.
References
Symplectic geometry
Theorems in differential geometry |
https://en.wikipedia.org/wiki/D%C3%A1vid%20Zvara | Dávid Zvara (born 22 July 1994) is a Hungarian football player who plays for Kaposvár.
Club statistics
References
External links
Profile
MLSZ
1994 births
Footballers from Eger
Living people
Hungarian men's footballers
Men's association football midfielders
Egri FC players
Szolnoki MÁV FC footballers
Dunaújváros PASE players
Szeged-Csanád Grosics Akadémia footballers
Tiszakécske FC footballers
Kaposvári Rákóczi FC players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Nemzeti Bajnokság III players
21st-century Hungarian people |
https://en.wikipedia.org/wiki/Mahler%27s%203/2%20problem | In mathematics, Mahler's 3/2 problem concerns the existence of "-numbers".
A -number is a real number such that the fractional parts of
are less than for all positive integers . Kurt Mahler conjectured in 1968 that there are no -numbers.
More generally, for a real number , define as
Mahler's conjecture would thus imply that exceeds . Flatto, Lagarias, and Pollington showed that
for rational in lowest terms.
References
Analytic number theory
Conjectures
Diophantine approximation |
https://en.wikipedia.org/wiki/Shintani%27s%20unit%20theorem | In mathematics, Shintani's unit theorem introduced by is a refinement of Dirichlet's unit theorem and states that a subgroup of finite index of the totally positive units of a number field has a fundamental domain given by a rational polyhedric cone in the Minkowski space of the field .
References
External links
Mathematical pictures by Paul Gunnells
Theorems in algebraic number theory |
https://en.wikipedia.org/wiki/Michael%20D.%20Plummer | Michael David Plummer (born 1937) is a retired mathematics professor from Vanderbilt University. His field of work is in graph theory in which he has produced over a hundred papers and publications. He has also spoken at over a hundred and fifty guest lectures around the world.
Education and career
Plummer was born in Akron, Ohio on August 31, 1937. He grew up in Lima, Ohio where he attended Lima Central High School, graduating in 1955. He then went to Wabash College in Crawfordsville, Indiana on an honor scholarship, with a double major in mathematics and physics. He then took a graduate fellowship in physics at the University of Michigan, but after one year of the program, switched to mathematics; in 1966 he was awarded his Ph.D., with a thesis supervised by Frank Harary.
After postdoctoral studies at Yale University from 1966 to 1968, Plummer took an assistant professorship in the recently formed Department of Computer Science at City College of New York which was part of the School of Engineering.
In 1970 he joined the Department of Mathematics at Vanderbilt University, and remained there until his retirement in 2008.
Contributions
Among his other contributions to graph theory, Plummer is responsible for defining well-covered graphs, for making with László Lovász the now-proven conjecture (generalizing Petersen's theorem) that every bridgeless cubic graph has an exponential number of perfect matchings, and for being one of several mathematicians to conjecture the result now known as Fleischner's theorem on Hamiltonian cycles in squares of graphs.
Awards and honors
Plummer is a Foundation Fellow of the Institute of Combinatorics and its Applications. In 1991, he shared the Niveau Prize of the Publishing House of the Hungarian Academy of Sciences with László Lovász for their book, Matching Theory.
Selected publications
Research papers
.
.
Books
References
Living people
20th-century American mathematicians
21st-century American mathematicians
Graph theorists
City College of New York faculty
Vanderbilt University faculty
University of Michigan alumni
1937 births |
https://en.wikipedia.org/wiki/Dimension%20%28graph%20theory%29 | In mathematics, and particularly in graph theory, the dimension of a graph is the least integer such that there exists a "classical representation" of the graph in the Euclidean space of dimension with all the edges having unit length.
In a classical representation, the vertices must be distinct points, but the edges may cross one another.
The dimension of a graph is written .
For example, the Petersen graph can be drawn with unit edges in , but not in : its dimension is therefore 2 (see the figure to the right).
This concept was introduced in 1965 by Paul Erdős, Frank Harary and William Tutte. It generalises the concept of unit distance graph to more than 2 dimensions.
Examples
Complete graph
In the worst case, every pair of vertices is connected, giving a complete graph.
To immerse the complete graph with all the edges having unit length, we need the Euclidean space of dimension . For example, it takes two dimensions to immerse (an equilateral triangle), and three to immerse (a regular tetrahedron) as shown to the right.
In other words, the dimension of the complete graph is the same as that of the simplex having the same number of vertices.
Complete bipartite graphs
All star graphs , for , have dimension 2, as shown in the figure to the left. Star graphs with equal to 1 or 2 need only dimension 1.
The dimension of a complete bipartite graph , for , can be drawn as in the figure to the right, by placing vertices on a circle whose radius is less than a unit, and the other two vertices one each side of the plane of the circle, at a suitable distance from it. has dimension 2, as it can be drawn as a unit rhombus in the plane.
To summarise:
, depending on the values of and .
Dimension and chromatic number
This proof also uses circles.
We write for the chromatic number of , and assign the integers to the colours. In -dimensional Euclidean space, with its dimensions denoted , we arrange all the vertices of colour arbitrarily on the circle given by .
Then the distance from a vertex of colour to a vertex of colour is given by .
Euclidean dimension
The definition of the dimension of a graph given above says, of the minimal- representation:
if two vertices of are connected by an edge, they must be at unit distance apart;
however, two vertices at unit distance apart are not necessarily connected by an edge.
This definition is rejected by some authors. A different definition was proposed in 1991 by Alexander Soifer, for what he termed the Euclidean dimension of a graph. Previously, in 1980, Paul Erdős and Miklós Simonovits had already proposed it with the name faithful dimension. By this definition, the minimal- representation is one such that two vertices of the graph are connected if and only if their representations are at distance 1.
The figures opposite show the difference between these definitions, in the case of a wheel graph having a central vertex and six peripheral vertices, with one spoke removed. Its |
https://en.wikipedia.org/wiki/Lev%20M.%20Bregman | Lev M. Bregman (1941 - 2023) was a Soviet and Israeli mathematician, most known for the Bregman divergence named after him.
Bregman received his M. Sc. in mathematics in 1963 at Leningrad University and his Ph.D. in mathematics in 1966 at the same institution, under the direction of his advisor Prof. J. V. Romanovsky, for his thesis about relaxation methods for finding a common point of convex sets, which led to one of his most well-known publications.
Bregman's Theorem, proving a 1963 conjecture of Henryk Minc, gives an upper bound on the permanent of a 0-1 matrix.
Bregman was employed at the Institute for Industrial Mathematics, Beer-Sheva, Israel, after having spent one year at Ben-Gurion University of the Negev, Beer-Sheva. Formerly, during 1966-1991, he was senior researcher at the Leningrad University.
Bregman is author of several text books and dozens of publications in international journals.
See also
Institute for Industrial Mathematics, Beer-Sheva, Israel
home page at Institute for Industrial Mathematics, Beer-Sheva, Israel
References
External links
Bregman's Theorem at Theorem of the Day.
1941 births
Mathematicians from Saint Petersburg
Israeli mathematicians
Living people
Saint Petersburg State University alumni |
https://en.wikipedia.org/wiki/List%20of%20largest%20LGBT%20events | The list presents the largest LGBT events (pride parades and festivals) worldwide by attendance. Statistics are announced both by the organizers and authorities (police). In this table, the largest single event by city as well as notable international events such as WorldPride or Europride are indicated. Only referenced statistics are accepted. National parades are generally further supported by nationwide LGBT associations and medias. Certain statistics may include celebrations or festivals that may be exclusive of the parade. They are typically held in late June, in commemoration of the 1969 Stonewall riots.
As of 2022, the NYC Pride March in New York City, considered an epicenter of the global LGBTQIA+ sociopolitical ecosystem, is consistently North America's biggest pride parade, with 2.1 million attendees in 2015 and 2.5 million in 2016; in 2018, and again in 2023, attendance was estimated around two million. During Stonewall 50 – WorldPride NYC 2019, over 5 million took part over the final weekend, with an estimated four million in attendance at the parade.
The São Paulo Gay Pride Parade in Brazil is South America's largest event, and was listed by Guinness World Records as the world's largest Pride parade in 2006 with 2.5 million people. It broke the Guinness record in 2009 with four million attendees, with similar numbers to at least 2016, and up to five million attending in 2017. As of 2019, it has three to five million each year.
Pride Toronto is the largest pride event in Canada. The Tokyo Rainbow Pride in Japan is one of Asia's largest pride events. The most recent Tokyo Rainbow Pride event was held on April 23 and 24, 2022.
As of June 2019, the largest LGBTQ events in other parts of the world include:
in Europe: Madrid Pride, Orgullo Gay de Madrid (MADO), with 3.5 million attendees when it hosted WorldPride in 2017
in Asia: Taiwan Pride in Taipei;
in the Middle East: Tel Aviv Pride in Israel;
in Oceania: Sydney Mardi Gras Parade in Australia;
in Africa: Johannesburg Pride in South Africa
Brooklyn Liberation March, the largest transgender rights demonstration in LGBTQ history, took place on June 14, 2020, stretching from Grand Army Plaza to Fort Greene, Brooklyn in New York City, and focused on supporting Black transgender lives, drawing an estimated 15,000 to 20,000 participants.
On September 7, 2019, London hosted the largest ever Bi Pride celebration, Bi Pride UK, with more than 1,300 people in attendance.
All-time statistics
See also
List of LGBT events
List of LGBT awareness periods
References
Largest
LGBT events |
https://en.wikipedia.org/wiki/1929%E2%80%9330%20Real%20Sociedad%20season | The 1929–30 season was Real Sociedad's second season in La Liga.
This article shows player statistics and all matches that the club played during the 1929–30 season.
Squad
Squad stats
League
Final table
King Alfonso XIII's Cup
Round of 32
Round of 16
External links
Squad and results
Real Sociedad
Real Sociedad seasons |
https://en.wikipedia.org/wiki/Perfectoid%20space | In mathematics, perfectoid spaces are adic spaces of special kind, which occur in the study of problems of "mixed characteristic", such as local fields of characteristic zero which have residue fields of characteristic prime p.
A perfectoid field is a complete topological field K whose topology is induced by a nondiscrete valuation of rank 1, such that the Frobenius endomorphism Φ is surjective on K°/p where K° denotes the ring of power-bounded elements.
Perfectoid spaces may be used to (and were invented in order to) compare mixed characteristic situations with purely finite characteristic ones. Technical tools for making this precise are the tilting equivalence and the almost purity theorem. The notions were introduced in 2012 by Peter Scholze.
Tilting equivalence
For any perfectoid field K there is a tilt K♭, which is a perfectoid field of finite characteristic p. As a set, it may be defined as
Explicitly, an element of K♭ is an infinite sequence (x0, x1, x2, ...) of elements of K such that xi = x. The multiplication in K♭ is defined termwise, while the addition is more complicated. If K has finite characteristic, then K ≅ K♭. If K is the p-adic completion of , then K♭ is the t-adic completion of .
There are notions of perfectoid algebras and perfectoid spaces over a perfectoid field K, roughly analogous to commutative algebras and schemes over a field. The tilting operation extends to these objects. If X is a perfectoid space over a perfectoid field K, then one may form a perfectoid space X♭ over K♭. The tilting equivalence is a theorem that the tilting functor (-)♭ induces an equivalence of categories between perfectoid spaces over K and perfectoid spaces over K♭. Note that while a perfectoid field of finite characteristic may have several non-isomorphic "untilts", the categories of perfectoid spaces over them would all be equivalent.
Almost purity theorem
This equivalence of categories respects some additional properties of morphisms. Many properties of morphisms of schemes have analogues for morphisms of adic spaces. The almost purity theorem for perfectoid spaces is concerned with finite étale morphisms. It's a generalization of Faltings's almost purity theorem in p-adic Hodge theory. The name is alluding to almost mathematics, which is used in a proof, and a distantly related classical theorem on purity of the branch locus.
The statement has two parts. Let K be a perfectoid field.
If X → Y is a finite étale morphism of adic spaces over K and Y is perfectoid, then X also is perfectoid;
A morphism X → Y of perfectoid spaces over K is finite étale if and only if the tilt X♭ → Y♭ is finite étale over K♭.
Since finite étale maps into a field are exactly finite separable field extensions, the almost purity theorem implies that for any perfectoid field K the absolute Galois groups of K and K♭ are isomorphic.
See also
Perfect field
References
External links
Foundations of Perfectoid Spaces by Matthew Morrow
Lean perfectoid sp |
https://en.wikipedia.org/wiki/Endomondo | Endomondo was a social fitness network created by Endomondo LLC which allowed users to track their fitness and health statistics with a mobile application and website. Endomondo launched in 2007 with the goal of motivating people to lead healthier lives.
History
Endomondo started in Denmark in 2007 by Mette Lykke, Christian Birk and Jakob Nordenhof Jønck. In 2011, the company opened an office in Silicon Valley, USA, but kept its research and development department in Denmark. In 2013, Endomondo LLC was listed in Red Herring as a European finalists for promising start-ups. The same year, Christian Birk and Jakob Nordenhof Jønck left the daily operation of the company, but kept co-ownership.
In February 2015, Endomondo LLC was acquired by athletic apparel maker Under Armour for $85 million. Endomondo, at that time, had over 20 million users.
In October 2020, Under Armour announced that Endomondo would be shutting down and selling off MyFitnessPal to the private equity firm Francisco Partners for $345 million. Service stopped on 31 December 2020, giving customers until 15 February 2021 to download an archive of their historic data.
Features
Endomondo could track numerous fitness attributes such as running routes, distance, duration, and calories. The software could help analyze performance and recommend improvements.
There was a free and a paid version available of Endomondo. The free version had advertisements. The paid Premium version was free of advertisements and included additional features such as the possibility to create one's own training plan. The offering of additional features was different between the Android, IOS and Windows platforms, and had significantly better features for tracking performance over time than UnderArmours suggested replacement.
Endomondo offered challenges of various types to the user and allowed users to create their own challenges.
References
External links
GPS sports tracking applications
Mobile social software
American health websites
Fitness apps
IOS software
Android (operating system) software
Windows Phone software
BlackBerry software
Web applications
2007 software |
https://en.wikipedia.org/wiki/Amnon%20Yekutieli | Amnon Yekutieli () is an Israeli mathematician, working in noncommutative algebra, algebraic geometry and deformation quantization. He is a professor of mathematics at the Ben-Gurion University of the Negev.
Professional career
Born in Rehovot, Israel, he earned both his bachelor's and master's degrees at the Hebrew University of Jerusalem. His master thesis was done under the supervision of Shimshon Amitsur. He received his Ph.D. from the Massachusetts Institute of Technology in 1990, after studying there with Michael Artin. Yekutieli received the Alon Fellowship in 1993. He joined the Ben-Gurion University of the Negev in 1999.
Selected publications
References
CV .
External links
1959 births
20th-century Israeli mathematicians
21st-century Israeli mathematicians
Einstein Institute of Mathematics alumni
Massachusetts Institute of Technology alumni
Academic staff of Ben-Gurion University of the Negev
Israeli Jews
Jewish scientists
Living people |
https://en.wikipedia.org/wiki/Mihai%20Cojusea | Mihai Cojusea (born 12 August 1978, Comrat, Moldavian SSR) is a Moldavian football striker who plays for CF Gagauziya.
Club statistics
Total matches played in Moldavian First League: 37 matches – 19 goals
References
External links
Profile at Divizia Nationala
1978 births
People from Comrat
Moldovan men's footballers
Living people
Men's association football forwards
Univer-Oguzsport players |
https://en.wikipedia.org/wiki/Sergiu%20Zacon | Sergiu Zacon (born 13 November 1987) is a Moldavian football striker who plays for FC Nistru Otaci.
Club statistics
Total matches played in Moldavian First League: 109 matches - 11 goals
References
External links
Profile at Divizia Nationala
Profile at UEFA
1987 births
People from Leova District
Moldovan men's footballers
Living people
FC Tighina players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Sergiu%20Gri%C8%9Buc | Sergiu Grițuc (born 6 April 1984, Tiraspol, Moldavian SSR) is a Moldavian football striker who plays for FC Costuleni.
Club statistics
Total matches played in Moldavian First League: 82 matches – 11 goals
References
External links
Profile at Divizia Nationala
Profile at sports.md
1984 births
Sportspeople from Tiraspol
Moldovan men's footballers
Living people
Men's association football forwards
CS Tiligul-Tiras Tiraspol players
FC Nistru Otaci players
FC Costuleni players |
https://en.wikipedia.org/wiki/Bin%20Yu | Bin Yu () is a Chinese-American statistician. She is currently Chancellor's Professor in the Departments of Statistics and of Electrical Engineering & Computer Sciences at the University of California, Berkeley.
Biography
Yu earned a bachelor's degree in mathematics in 1984 from Peking University, and went on to pursue graduate studies in statistics at Berkeley, earning a master's degree in 1987 and a Ph.D. in 1990. Her dissertation, Some Results on Empirical Processes and Stochastic Complexity, was jointly supervised by Lucien Le Cam and Terry Speed.
After postdoctoral studies at the Mathematical Sciences Research Institute and an assistant professorship at the University of Wisconsin–Madison, she returned to Berkeley as a faculty member in 1993, was tenured in 1997, and became Chancellor's Professor in 2006. She also worked at Bell Labs from 1998 to 2000, while on leave from Berkeley, and has held visiting positions at several other universities. She chaired the Department of Statistics at Berkeley from 2009 to 2012, and was president of the Institute of Mathematical Statistics in 2014. In 2023, she was awarded the COPSS Distinguished Achievement Award and Lectureship.
Research
Yu's work leverages computational developments to solve scientific problems by combining statistical machine learning approaches with the domain expertise of many collaborators, spanning many fields including statistics, machine learning, neuroscience, genomics, and remote sensing. Her recent work has focused on solidifying a vision for data science, including a framework for veridical data science and a framework for interpretable machine learning. Yu has also developed a PCS (predictability, computability, and stability) framework for veridical data science to unify, streamline and expand on ideas and best practices of machine learning and statistics. Yu has received recent news coverage regarding her veridical data science framework, investigations into the theoretical foundations of deep learning, and work forecasting COVID-19 severity in the US.
Other research included research in the area of statistical machine learning methods/algorithms (and associated statistical inference problems) such as dictionary learning, non-negative matrix factorization (NMF), EM and deep learning (CNNs and LSTMs), and heterogeneous effect estimation in randomized experiments (X-learner).
Honors and awards
Yu is a fellow of the Institute of Mathematical Statistics, the IEEE, the American Statistical Association, the American Association for the Advancement of Science, the American Academy of Arts and Sciences, and the National Academy of Sciences. In 2012, she was the Tukey Lecturer of the Bernoulli Society for Mathematical Statistics and Probability. In 2018, she was awarded the Elizabeth L. Scott Award. She was invited to give the Breiman lecture at NeurIPS 2019 (formally known as NIPS), on the topic of veridical data science.
References
External links
A conversation with Pro |
https://en.wikipedia.org/wiki/Subpaving | In mathematics, a subpaving is a set of nonoverlapping boxes of R⁺. A subset X of Rⁿ can be approximated by two subpavings X⁻ and X⁺ such that X⁻ ⊂ X ⊂ X⁺.
In R¹ the boxes are line segments, in R² rectangles and in Rⁿ hyperrectangles. A R² subpaving can be also a "non-regular tiling by rectangles", when it has no holes.
Boxes present the advantage of being very easily manipulated by computers, as they form the heart of interval analysis. Many interval algorithms naturally provide solutions that are regular subpavings.
In computation, a well-known application of subpaving in R² is the Quadtree data structure. In image tracing context and other applications is important to see X⁻ as topological interior, as illustrated.
Example
The three figures on the right below show an approximation of the set X = {(x1, x2) ∈ R2 | x + x +
sin(x1 + x2) ∈ [4,9]} with different accuracies. The set X⁻ corresponds to red boxes and the set X⁺ contains all red and yellow boxes.
Combined with interval-based methods, subpavings are used to approximate the solution set of non-linear problems such as set inversion problems.
Subpavings can also be used to prove that a set defined by nonlinear inequalities is path connected,
to provide topological properties of such sets,
to solve piano-mover's problems
or to implement set computation.
References
Topology
Geometry |
https://en.wikipedia.org/wiki/Informal%20inferential%20reasoning | In statistics education, informal inferential reasoning (also called informal inference) refers to the process of making a generalization based on data (samples) about a wider universe (population/process) while taking into account uncertainty without using the formal statistical procedure or methods (e.g. P-values, t-test, hypothesis testing, significance test).
Like formal statistical inference, the purpose of informal inferential reasoning is to draw conclusions about a wider universe (population/process) from data (sample). However, in contrast with formal statistical inference, formal statistical procedure or methods are not necessarily used.
In statistics education literature, the term "informal" is used to distinguish informal inferential reasoning from a formal method of statistical inference.
Informal Inferential Reasoning and Statistical Inference
Since everyday life involves making decisions based on data, making inferences is an important skill to have. However, a number of studies on assessments of students’ understanding statistical inference suggest that students have difficulties in reasoning about inference.
Given the importance of reasoning about statistical inference and difficulties that students have with this type of reasoning, statistics educators and researchers have been exploring alternative approaches towards teaching statistical inference. Recent research suggests that students have some sound intuitions about data and these intuitions can be refined and nudged towards prescriptive theory of inferential reasoning. More of an informal and conceptual approach that build on the previous big ideas and make connection between foundational concepts is therefore favorable.
Recently, informal inferential reasoning has been the focus of research and discussion among researchers and educators in statistics education as it is seen as having a potential to help build fundamental concepts that underlie formal statistical inference. Many advocate that underlying concepts and skills of inference should be introduced early in the course or curriculum as they can help make the formal statistical inference more accessible (see published reaction of Garfield & Zieffler to).
Three essential characteristics
According to Statistical Reasoning, Thinking and Literacy forum, three essential principles to informal inference are:
generalizations (including predictions, parameter estimates, and conclusions) that go beyond describing the given data;
the use of data as evidence for those generalizations; and
conclusions that express a degree of uncertainty, whether or not quantified, accounting for the variability or uncertainty that is unavoidable when generalizing beyond the immediate data to a population or a process.
Core Statistical Ideas
Informal inferential reasoning involved the following related ideas
Properties of aggregates. This includes the ideas of distributions, signal (a stable component of population/process such as |
https://en.wikipedia.org/wiki/Carlos%20Garc%C3%A9s | Carlos Jhon Garcés Acosta (born 1 March 1990) is an Ecuadorian professional footballer who plays as a forward for Cienciano and the Ecuador national team.
Career statistics
Club
Honors
Club
Manta
Serie B: 2008
Delfín
Serie A: 2019
Individual
Ascenso MX top scorer : 2015 Apertura
References
External links
FEF card
1990 births
Living people
Men's association football forwards
Ecuadorian men's footballers
People from Manta, Ecuador
Ecuadorian expatriate men's footballers
Expatriate men's footballers in Mexico
Ecuadorian expatriate sportspeople in Mexico
Manta F.C. footballers
L.D.U. Portoviejo footballers
L.D.U. Quito footballers
S.D. Quito footballers
C.D. Cuenca footballers
Atlante F.C. footballers
Delfín S.C. footballers
9 de Octubre F.C. players
Ecuadorian Serie B players
Ecuadorian Serie A players
Ascenso MX players
Ecuador men's international footballers
2019 Copa América players |
https://en.wikipedia.org/wiki/Igor%20Belyaevski | Igor Konstantinovich Belyaevski () is a retired Kazakhstani professional ice hockey player.
Career statistics
External links
Living people
1963 births
Sportspeople from Almaty
Soviet ice hockey forwards
Kazakhstani ice hockey forwards
Kazakhstani people of Russian descent
Yenbek Almaty players
Kazzinc-Torpedo players
Avangard Omsk players
SKA Saint Petersburg players
Metallurg Novokuznetsk players
HC Izhstal players
HC Spartak Moscow players
HK Acroni Jesenice players
Rubin Tyumen players
Zauralie Kurgan players |
https://en.wikipedia.org/wiki/Complex%20algebraic%20variety | In algebraic geometry, a complex algebraic variety is an algebraic variety (in the scheme sense or otherwise) over the field of complex numbers.
Chow's theorem
Chow's theorem states that a projective analytic variety; i.e., a closed analytic subvariety of the complex projective space is an algebraic variety; it is usually simply referred to as a projective variety.
Hironaka's theorem
Let be a complex algebraic variety. Then there is a projective resolution of singularities .
Relation with similar concepts
Not every complex analytic variety is algebraic, though.
See also
Complete variety
Complex analytic variety
References
Bibliography
Algebraic varieties |
https://en.wikipedia.org/wiki/Konstantin%20Spodarenko | Konstantin Grigorievich Spodarenko (; born April 4, 1972) is a retired Kazakh professional ice hockey player.
Career statistics
External links
1972 births
Energia Kemerovo players
Kazakhstani ice hockey forwards
Kazzinc-Torpedo players
Living people
Neftyanik Almetyevsk players
Soviet ice hockey forwards
Ice hockey people from Oskemen
Yuzhny Ural Orsk players |
https://en.wikipedia.org/wiki/Brownian%20meander | In the mathematical theory of probability, Brownian meander is a continuous non-homogeneous Markov process defined as follows:
Let be a standard one-dimensional Brownian motion, and , i.e. the last time before t = 1 when visits . Then the Brownian meander is defined by the following:
In words, let be the last time before 1 that a standard Brownian motion visits . ( almost surely.) We snip off and discard the trajectory of Brownian motion before , and scale the remaining part so that it spans a time interval of length 1. The scaling factor for the spatial axis must be square root of the scaling factor for the time axis. The process resulting from this snip-and-scale procedure is a Brownian meander. As the name suggests, it is a piece of Brownian motion that spends all its time away from its starting point .
The transition density of Brownian meander is described as follows:
For and , and writing
we have
and
In particular,
i.e. has the Rayleigh distribution with parameter 1, the same distribution as , where is an exponential random variable with parameter 1.
References
Wiener process
Markov processes |
https://en.wikipedia.org/wiki/Linked%20field | In mathematics, a linked field is a field for which the quadratic forms attached to quaternion algebras have a common property.
Linked quaternion algebras
Let F be a field of characteristic not equal to 2. Let A = (a1,a2) and B = (b1,b2) be quaternion algebras over F. The algebras A and B are linked quaternion algebras over F if there is x in F such that A is equivalent to (x,y) and B is equivalent to (x,z).
The Albert form for A, B is
It can be regarded as the difference in the Witt ring of the ternary forms attached to the imaginary subspaces of A and B. The quaternion algebras are linked if and only if the Albert form is isotropic.
Linked fields
The field F is linked if any two quaternion algebras over F are linked. Every global and local field is linked since all quadratic forms of degree 6 over such fields are isotropic.
The following properties of F are equivalent:
F is linked.
Any two quaternion algebras over F are linked.
Every Albert form (dimension six form of discriminant −1) is isotropic.
The quaternion algebras form a subgroup of the Brauer group of F.
Every dimension five form over F is a Pfister neighbour.
No biquaternion algebra over F is a division algebra.
A nonreal linked field has u-invariant equal to 1,2,4 or 8.
References
Field (mathematics)
Quadratic forms
Quaternions |
https://en.wikipedia.org/wiki/Quaternionic%20structure | In mathematics, a quaternionic structure or -structure is an axiomatic system that abstracts the concept of a quaternion algebra over a field.
A quaternionic structure is a triple where is an elementary abelian group of exponent with a distinguished element , is a pointed set with distinguished element , and is a symmetric surjection satisfying axioms
Every field gives rise to a -structure by taking to be , the set of Brauer classes of quaternion algebras in the Brauer group of with the split quaternion algebra as distinguished element and the quaternion algebra .
References
Field (mathematics)
Quadratic forms
Quaternions |
https://en.wikipedia.org/wiki/Isometry%20%28disambiguation%29 | Isometry, in mathematics, refers to a distance-preserving transformation. Isometry may also refer to:
Isometry (quadratic forms)
Isometry (Riemannian geometry)
Isometry group
Quasi-isometry
Dade isometry
Euclidean isometry
Euclidean plane isometry
Itō isometry
See also
Isometric (disambiguation)
Isometries in physics |
https://en.wikipedia.org/wiki/Riesz%20rearrangement%20inequality | In mathematics, the Riesz rearrangement inequality, sometimes called Riesz–Sobolev inequality, states that any three non-negative functions , and satisfy the inequality
where , and are the symmetric decreasing rearrangements of the functions , and respectively.
History
The inequality was first proved by Frigyes Riesz in 1930,
and independently reproved by S.L.Sobolev in 1938. Brascamp, Lieb and Luttinger have shown that can be generalized to arbitrarily (but finitely) many functions acting on arbitrarily many variables.
Applications
The Riesz rearrangement inequality can be used to prove the Pólya–Szegő inequality.
Proofs
One-dimensional case
In the one-dimensional case, the inequality is first proved when the functions , and are characteristic functions of a finite unions of intervals. Then the inequality can be extended to characteristic functions of measurable sets, to measurable functions taking a finite number of values and finally to nonnegative measurable functions.
Higher-dimensional case
In order to pass from the one-dimensional case to the higher-dimensional case, the spherical rearrangement is approximated by Steiner symmetrization for which the one-dimensional argument applies directly by Fubini's theorem.
Equality cases
In the case where any one of the three functions is a strictly symmetric-decreasing function, equality holds only when the other two functions are equal, up to translation, to their symmetric-decreasing rearrangements.
References
Inequalities
Rearrangement inequalities
Real analysis |
https://en.wikipedia.org/wiki/Universal%20geometric%20algebra | In mathematics, a universal geometric algebra is a type of geometric algebra generated by real vector spaces endowed with an indefinite quadratic form. Some authors restrict this to the infinite-dimensional case.
The universal geometric algebra of order is defined as the Clifford algebra of -dimensional pseudo-Euclidean space . This algebra is also called the "mother algebra". It has a nondegenerate signature. The vectors in this space generate the algebra through the geometric product. This product makes the manipulation of vectors more similar to the familiar algebraic rules, although non-commutative.
When , i.e. there are countably many dimensions, then is called simply the universal geometric algebra (UGA), which contains vector spaces such as and their respective geometric algebras .
UGA contains all finite-dimensional geometric algebras (GA).
The elements of UGA are called multivectors. Every multivector can be written as the sum of several -vectors. Some r-vectors are scalars (), vectors () and bivectors ().
One may generate a finite-dimensional GA by choosing a unit pseudoscalar (). The set of all vectors that satisfy
is a vector space. The geometric product of the vectors in this vector space then defines the GA, of which is a member. Since every finite-dimensional GA has a unique (up to a sign), one can define or characterize the GA by it. A pseudoscalar can be interpreted as an n-plane segment of unit area in an n-dimensional vector space.
Vector manifolds
A vector manifold is a special set of vectors in the UGA. These vectors generate a set of linear spaces tangent to the vector manifold. Vector manifolds were introduced to do calculus on manifolds so one can define (differentiable) manifolds as a set isomorphic to a vector manifold. The difference lies in that a vector manifold is algebraically rich while a manifold is not. Since this is the primary motivation for vector manifolds the following interpretation is rewarding.
Consider a vector manifold as a special set of "points". These points are members of an algebra and so can be added and multiplied. These points generate a tangent space of definite dimension "at" each point. This tangent space generates a (unit) pseudoscalar which is a function of the points of the vector manifold. A vector manifold is characterized by its pseudoscalar. The pseudoscalar can be interpreted as a tangent oriented -plane segment of unit area. Bearing this in mind, a manifold looks locally like at every point.
Although a vector manifold can be treated as a completely abstract object, a geometric algebra is created so that every element of the algebra represents a geometric object and algebraic operations such as adding and multiplying correspond to geometric transformations.
Consider a set of vectors in UGA. If this set of vectors generates a set of "tangent" simple -vectors, which is to say
then is a vector manifold, the value of is that of a simple -vector. If one interpre |
https://en.wikipedia.org/wiki/2004%20Maria%20Sharapova%20tennis%20season | Results and statistics from Maria Sharapova's 2004 tennis season.
Yearly summary
Australian Open series
Sharapova began her season at the Australian Open, as the 28th seed. She lost in the third round to Anastasia Myskina.
Indian Wells & Miami
Sharapova played three matches at Indian Wells and three at Miami.
European clay court season
Sharapova reached her first Major quarter-final at the French Open, defeating 2003 quarter-finalist Vera Zvonareva en route. She eventually lost in the quarter-finals to Paola Suárez.
Grass court season
Sharapova won her first title for the year in Birmingham, defeating Tatiana Golovin in the final in three sets. At Wimbledon, Sharapova was seeded 13th, meaning she could have faced a potential fourth round meeting against the French Open champion, Anastasia Myskina, who had defeated her in Australia earlier in the year. However, Sharapova was able to take advantage of Myskina's early exit to reach the quarter-finals, where she dropped her first set of the tournament to Ai Sugiyama, before winning in three sets. In the semi-finals, she faced 1999 champion Lindsay Davenport, trailing by a set and a break before making a comeback to prevail in three sets after the rain appeared to halt Davenport's momentum.
The final saw Sharapova face two-time defending champion Serena Williams, who had defeated her in Miami earlier in the year, in what was their first meeting. Williams entered the match as the favourite, but Sharapova would produce a stunning straight-sets victory to become the third-youngest woman (after Lottie Dod and Martina Hingis) to triumph at Wimbledon. The victory was hailed by the media as "the most stunning upset in memory". By virtue of winning Wimbledon, Sharapova would enter the Top Ten for the first time in her career, and would remain there until January 2009, when she decided not to defend her 2008 Australian Open title due to a serious shoulder injury.
US Open series
Sharapova entered the US Open as the seventh seed, but she was defeated in the third round by Mary Pierce.
Fall series
During the fall of the season Sharapova played and won consecutive titles at the hansol korea open and at the japan tennis championships thus extending her title tally to 4 .She also reached the final of the zurich open defeating venus williams en route but eventually lost to alicia molik in three tight sets.
WTA Tour Championships
Sharapova qualified for the year-end WTA Tour Championships by virtue of her impressive season, which saw her capture four titles for the year to date. She was drawn in the Black Group along with Amélie Mauresmo, US Open champion Svetlana Kuznetsova and Vera Zvonareva. Sharapova won two of her three matches, the only loss coming to Mauresmo in her first match. Sharapova qualified for the semi-finals after finishing second in the group behind Mauresmo; thus, the semi-final saw her drawn against French Open champion and Red Group leader Anastasia Myskina, which she won in three |
https://en.wikipedia.org/wiki/2006%20Maria%20Sharapova%20tennis%20season | Results and statistics from Maria Sharapova's 2006 tennis season.
Yearly summary
Australian Open series
Maria Sharapova began her season at the Australian Open, as the fourth seed. After overcoming a tricky section which included Serena Williams and Daniela Hantuchová, she reached the semi-finals for the second (of four) consecutive year, where she fell in three sets to Justine Henin-Hardenne.
Indian Wells & Miami
Sharapova won her first title of the year at Indian Wells, by defeating compatriot Elena Dementieva in the final in straight sets; it was her first title since she won Birmingham in 2005, and it was the eleventh final out of the last thirteen contested in which she won. Her good form continued into Miami, where she also reached the final for the second consecutive year. However, she was defeated in straight sets by Svetlana Kuznetsova; this marked only the fourth final in which she lost. After the latter defeat, Sharapova took two months off the Tour to recover from a foot injury.
European clay court season
Sharapova was seeded fourth at the French Open. In the first round, she overcame Mashona Washington, saving three match points in the process. She then lost in the fourth round to Dinara Safina (after leading 5–1 in the final set), thus failing to make the quarter-finals of the French Open for the first time since 2003.
Wimbledon
Sharapova was again seeded fourth at Wimbledon, where she reached the semi-finals for the third consecutive year. After winning her first three matches in straight sets, she was more sternly tested by Flavia Pennetta in the fourth round, but still pulled through in three sets.
In the final eight, she faced first-time Wimbledon quarter-finalist Elena Dementieva and won through in straight sets after a streaker briefly interrupted the match in the second set.
In the semi-finals, she lost to Amélie Mauresmo, who eventually captured the title. This marked the fifth time since her Wimbledon victory in 2004 in which she lost to the eventual champion at a Major, and also the fifth time in which she was defeated in the semi-finals of a Major tournament.
US Open series
In the lead-up to the US Open, Sharapova captured her second title of the season by defeating Kim Clijsters in the final of the Acura Classic in San Diego, and in doing so claimed her first victory over the Belgian in five attempts.
Sharapova entered the US Open as the third seed. She defeated Michaëlla Krajicek, Émilie Loit, Elena Likhovtseva, Li Na and Tatiana Golovin all in straight sets, before being tested in three sets by World No. 1 Amélie Mauresmo, who had beaten her at Wimbledon earlier in the year. Sharapova would be too good for the Frenchwoman this time, winning in three sets, two of which were won without dropping a game. In the final, she faced Belgian Justine Henin-Hardenne, who had previously captured the title in 2003 (and would do so again in 2007), and recorded an impressive straight sets victory to claim her second Gra |
https://en.wikipedia.org/wiki/Versor%20%28disambiguation%29 | In mathematics, a versor is a quaternion of norm one (a unit quaternion).
Versor may also refer to:
Hyperbolic versor, a generalization of quaternionic versors
Versor (physics), a vector of norm 1 (unit vector) codirectional with another vector
A product of vectors in geometric algebra |
https://en.wikipedia.org/wiki/Australia%20men%27s%20national%20soccer%20team%20records%20and%20statistics | This article lists various soccer records in relation to the Australia men's national soccer team. The page is updated where necessary after each Australia match, and is correct as of 28 March 2023.
Individual appearances
Appearances
Most appearances
Mark Schwarzer, 109, 31 July 1993 – 7 September 2013
Tim Cahill, 108, 30 March 2004 – 20 November 2018
Lucas Neill, 96, 9 October 1996 – 19 September 2013
Brett Emerton, 95, 7 February 1998 – 9 December 2012
Alex Tobin, 87, 9 March 1988 – 6 November 1998
Marco Bresciano, 84, 1 June 2001 – 22 January 2015
Paul Wade, 84, 3 August 1986 – 1 November 1996
Mark Milligan, 80, 7 June 2006 – 19 October 2019
Mathew Ryan, 80, 5 December 2012 – 24 March 2023
Luke Wilkshire, 80, 9 October 2004 – 26 May 2014
First player to reach 100 appearances
Mark Schwarzer, 6 September 2012, 3–0 vs. Lebanon
Fastest player to reach 100 appearances
Tim Cahill, 30 March 2004 – 25 June 2017
Most consecutive appearances
Alex Tobin, 63, 4 November 1970 – 30 October 1977
Most appearances as a substitute
Archie Thompson, 34, 28 February 2001 – 7 September 2013
Most consecutive appearances as a substitute
Mark Jankovics, 6, 15 June 1980 – 2 December 1980
Most appearances as a substitute without ever starting a game
Jim Campbell, 4, 27 January 1983 – 18 December 1983
Most appearances in competitive matches (World Cup, Confederations Cup, Asian Cup, Nations Cup and qualifier)
Mark Schwarzer, 61, 15 August 1993 – 18 June 2013
Longest Australia career
Mark Schwarzer, 20 years, 38 days, 31 July 1993 – 7 September 2013
Shortest Australia career
Raphael Bove, 1 minute, 6 November 1998, 0–0 vs. United States
Most consecutive appearances comprising entire Australia career
Alan Westwater, 14, 28 May 1967 – 4 April 1968
Youngest player
Duncan Cummings, 17 years, 139 days, 6 August 1975, vs. China
Oldest player
Mark Schwarzer, 40 years, 336 days, 7 September 2013, vs. Brazil
Most appearances at the World Cup finals
Mathew Leckie, 10, 13 June 2014 – 3 December 2022
Mathew Ryan, 10, 13 June 2014 – 3 December 2022
Most appearances without ever playing at the World Cup finals
Alex Tobin, 87, 9 March 1988 – 6 November 1999
Most appearances at the Asian Cup finals
Tim Cahill, 16, 8 July 2007 – 27 January 2015
Most consecutive years of appearances
Tim Cahill, 14, 2004 to 2018 inclusive
Longest gap between appearances
Ted Drain, 8 years, 74 days, 10 May 1947, 1–2 vs. South Africa – 24 September 1955, 0–6 vs. South Africa
Most appearances by a set of brothers
Aurelio and Tony Vidmar, 120, 1991 – 2006
Capped by another country
Ken Hough (New Zealand)
Apostolos Giannou (Greece)
Goals
First goal
William Maunder, 17 June 1922, vs. New Zealand
Most goals
Tim Cahill, 50, 31 May 2004 – 10 October 2017
Most goals in competitive matches (World Cup, Nations Cup, Asian Cup and qualifiers)
Tim Cahill, 39, 2 June 2004 – 10 October 2017
Most goals in a match
Archie Thompson, 13, 11 Apri |
https://en.wikipedia.org/wiki/2013%E2%80%9314%20Stevenage%20F.C.%20season | The 2013–14 season was Stevenage F.C.'s fourth season in the Football League, where the club competed in League One. This article shows statistics of the club's players in the season, and also lists all matches that the club played in the season. Their 18th-place finish during the 2012–13 campaign meant it would be Stevenage's third season of playing in League One, having only spent three years as a Football League club.
Squad details
Last updated on 3 August 2013.
Players information
Management
Manager: Graham Westley
Assistant manager: Dino Maamria
Coach: Jason Goodliffe
Match results
Legend
Pre-season
In June 2013, Stevenage announced that their pre-season campaign would consist of five friendlies to prepare for the 2013–14 season. Two days later, on 20 June, slight amendments were made to the list, with the club facing Championship side Watford at Broadhall Way on 20 July, instead of a trip to Chelmsford City as originally scheduled. One further fixture was added in early July, with a Manchester United XI visiting Broadhall Way on 26 July. Ahead of the pre-season campaign, the team travelled to La Manga in Spain to take part in a four-day training camp.
The club opened the pre-season schedule with a behind-closed-doors friendly against newly promoted League Two side Mansfield Town, winning 5–2 courtesy of goals from Filipe Morais, Dani López, Robin Shroot and a brace from Roarie Deacon. Two days later, Stevenage travelled to another newly promoted team, this time Biggleswade Town of the Southern League Premier Division. The game ended 6–0 in Stevenage's favour, with strikers Oumare Tounkara and Dani López both scoring two apiece, and midfielders Luke Freeman and Matt Ball also netting. The club's first home fixture of pre-season took place on 16 July, entertaining a Queens Park Rangers XI at Broadhall Way. Stevenage won the match 2–0 courtesy of first-half goals from Greg Tansey and Luke Freeman. Back-to-back home defeats to Championship opposition followed. Stevenage's first defeat of pre-season came courtesy of a 2–0 loss to Watford, before a Luke Varney hat-trick gave Leeds United a 3–0 win at Broadhall Way three days later. Three days after the defeat to Leeds, on 26 July, Stevenage entertained a Manchester United XI, with the game ending 2–2 – both of Stevenage's goals coming from Darius Charles after the hosts had trailed by two goals. A day later, the club's pre-season schedule concluded with a 5–0 win at Hitchin Town, with goals coming from Roarie Deacon, Robin Shroot and a Dani López hat-trick.
Note: Stevenage goals come first.
League One
The 2013–14 League One fixtures were released on 19 June 2013, with Stevenage opening their league campaign at home to Oldham Athletic on 3 August 2013. This meant it was the fifth straight season that Stevenage had opened their campaign with a home fixture. The game ended 4–3 in Oldham's favour, with six of the seven goals coming in the second-half. Stevenage's Darius Charles gave the ho |
https://en.wikipedia.org/wiki/2012%E2%80%9313%20GNK%20Dinamo%20Zagreb%20season | This article shows statistics of individual players for the football club Dinamo Zagreb. It also lists all matches that Dinamo Zagreb played in the 2012–13 season.
First-team squad
First team squad
Competitions
Overall
Prva HNL
League table
Results summary
Results by round
Champions league
Group A
Matches
Prva HNL
Champions League
Croatian Cup
Sources: Prva-HNL.hr
Player seasonal records
Competitive matches only. Updated to games played 27 April 2013.
Top scorers
Source: Competitive matches
References
External links
GNK Dinamo Zagreb official website
2012-13
Croatian football clubs 2012–13 season
2012–13 UEFA Champions League participants seasons
2012-13 |
https://en.wikipedia.org/wiki/Gauge%20group%20%28mathematics%29 | A gauge group is a group of gauge symmetries of the Yang–Mills gauge theory of principal connections on a principal bundle. Given a principal bundle with a structure Lie group , a gauge group is defined to be a group of its vertical automorphisms. This group is isomorphic to the group of global sections of the associated group bundle whose typical fiber is a group which acts on itself by the adjoint representation. The unit element of is a constant unit-valued section of .
At the same time, gauge gravitation theory exemplifies field theory on a principal frame bundle whose gauge symmetries are general covariant transformations which are not elements of a gauge group.
In the physical literature on gauge theory, a structure group of a principal bundle often is called the gauge group.
In quantum gauge theory, one considers a normal subgroup of a gauge group which is the stabilizer
of some point of a group bundle . It is called the pointed gauge group. This group acts freely on a space of principal connections. Obviously, . One also introduces the effective gauge group where is the center of a gauge group . This group acts freely on a space of irreducible principal connections.
If a structure group is a complex semisimple matrix group, the Sobolev completion of a gauge group can be introduced. It is a Lie group. A key point is that the action of on a Sobolev completion of a space of principal connections is smooth, and that an orbit space is a Hilbert space. It is a configuration space of quantum gauge theory.
References
Mitter, P., Viallet, C., On the bundle of connections and the gauge orbit manifold in Yang – Mills theory, Commun. Math. Phys. 79 (1981) 457.
Marathe, K., Martucci, G., The Mathematical Foundations of Gauge Theories (North Holland, 1992) .
Mangiarotti, L., Sardanashvily, G., Connections in Classical and Quantum Field Theory (World Scientific, 2000)
See also
Gauge symmetry (mathematics)
Gauge theory
Gauge theory (mathematics)
Principal bundle
Differential geometry
Gauge theories
Theoretical physics |
https://en.wikipedia.org/wiki/Rachel%20Matheson | Rachel Matheson or Mathson may refer to:
Rachel Matheson, character in Under the Mountain (TV miniseries)
Rachel Matheson, character in Revolution (TV series)
Rachel Mathson, beauty pageant contestant |
https://en.wikipedia.org/wiki/Nu%20function | In mathematics, the nu function is a generalization of the reciprocal gamma function of the Laplace transform.
Formally, it can be defined as
where is the Gamma function.
See also
Lambda function (disambiguation)
Mu function
References
External links
Gamma and related functions |
https://en.wikipedia.org/wiki/Cork%E2%80%93Galway%20hurling%20rivalry | The Cork–Galway rivalry is a hurling rivalry between Cork and Galway. The fixture is an irregular one due to both teams playing in separate provinces.
Roots
Statistics
Up to date as of 2023 season
Notable moments
Galway 4-15 : 2-19 Cork (17 August 1975 at Croke Park) - The 1975 All Ireland semi-final took place on one of the hottest days of one of the hottest summers of the century. Cork may have been "a bit rusty" after winning Munster and over-confidence may have been a factor. In any event, Galway hit them hard and hit them fast. They scored a couple of goals early on, they continued to get scores at opportune times and come the end, they had two points in hand, 4-15 to 2-19.
Galway 2-14 : 1-13 Cork (5 August 1979 at Croke Park) - Cork were aiming for an historic four-in-a-row and hence were the defending All-Ireland champions. After a record equalling fifth consecutive Munster title on the back of a final win over Limerick, Cork were expected to see off the Galway challenge comfortably. Galway, on the other hand, were coming with a team of their own backboned by the likes of the Connolly brothers and Noel Lane. In front of a paltry attendance of 12,315, Galway shocked the hurling world by dumping the holders out and progressed to the 1979 decider.
Cork 5-15 : 2-21 Galway (2 September 1990 at Croke Park) - Having recovered from a poor start Galway looked likely winners when holding a seven-points lead early in the second half, but they ceded control at a critical stage. Kevin Hennessy gave Cork a dream start goaling inside the first minute and the last of their five goals, from John Fitzgibbon in the 63rd minute ensured a 27th title.
All-time results
Legend
Senior
Intermediate
Junior
Minor
References
External links
Cork V Galway all-time statistics
Galway
Galway county hurling team rivalries |
https://en.wikipedia.org/wiki/Nonlinear%20realization | In mathematical physics, nonlinear realization of a Lie group G possessing a Cartan subgroup H is a particular induced representation of G. In fact, it is a representation of a Lie algebra of G in a neighborhood of its origin.
A nonlinear realization, when restricted to the subgroup H reduces to a linear representation.
A nonlinear realization technique is part and parcel of many field theories with spontaneous symmetry breaking, e.g., chiral models, chiral symmetry breaking, Goldstone boson theory, classical Higgs field theory, gauge gravitation theory and supergravity.
Let G be a Lie group and H its Cartan subgroup which admits a linear representation in a vector space V. A Lie
algebra of G splits into the sum of the Cartan subalgebra of H and its supplement , such that
(In physics, for instance, amount to vector generators and to axial ones.)
There exists an open neighborhood U of the unit of G such
that any element is uniquely brought into the form
Let be an open neighborhood of the unit of G such that
, and let be an open neighborhood of the
H-invariant center of the quotient G/H which consists of elements
Then there is a local section of
over .
With this local section, one can define the induced representation, called the nonlinear realization, of elements on given by the expressions
The corresponding nonlinear realization of a Lie algebra
of G takes the following form.
Let , be the bases for and , respectively, together with the commutation relations
Then a desired nonlinear realization of in reads
,
up to the second order in .
In physical models, the coefficients are treated as Goldstone fields. Similarly, nonlinear realizations of Lie superalgebras are considered.
See also
Induced representation
Chiral model
References
Giachetta G., Mangiarotti L., Sardanashvily G., Advanced Classical Field Theory, World Scientific, 2009, .
Representation theory
Theoretical physics |
https://en.wikipedia.org/wiki/2005%20Maria%20Sharapova%20tennis%20season | Results and statistics from Maria Sharapova's 2005 tennis season.
Yearly summary
Australian Open series
Sharapova began her season at the Australian Open, as the fourth seed. She reached the semi-finals, defeating Grand Slam debutant Li Na and the previous year's US Open champion Svetlana Kuznetsova en route, before being defeated in the semi-finals by eventual champion Serena Williams in an epic three set thriller on Rod Laver. Sharapova, had several match points in the final set, but ended up losing it 6–8.
Indian Wells & Miami
Sharapova reached the semi-finals at Indian Wells for the first time, but she would suffer the ignominy of a double bagel defeat, failing to win a single game against Lindsay Davenport. This would turn out to be Sharapova's only career defeat against Davenport. She fared much better in Miami though, beating the likes of Justine Henin-Hardenne and Venus Williams en route to the final. In the final, she lost in straight sets to Kim Clijsters.
European clay court season
Sharapova first clay event of the season was the Berlin Open where she was the first seed. She lost in straight sets in the quarters, to eventual champion Justine Henin-Hardenne. Her next tournament was the Internazionali B.N.L D'Italia Open. She lost in the semifinals to Swiss Patty Schnyder, in three sets after winning the first set. Her final clay tournament of the year was the French Open where she reached the quarterfinals. In the quarters she lost to Justine Henin-Hardenne, for the second and final time in the season.
Grass court season
Sharapova successfully defended her title in Birmingham, defeating future rivals Samantha Stosur and Tatiana Golovin, before defeating, future world number one, Jelena Janković in a three set final.
As the defending champion at Wimbledon, Sharapova navigated her way through to the semi-finals without the loss of a set (and serve, with the exception of her third round victory against Katarina Srebotnik), before being defeated by eventual champion Venus Williams; the defeat ending a 22-match winning streak on grass dating back to the 2003 Wimbledon 4th Round.
US Open series
A week before the start of the US Open, Sharapova claimed the World No. 1 ranking for the first time, succeeding Lindsay Davenport. Subsequently, she was named top seed at a Major tournament for the first time, at the US Open, where she reached the semi-finals to complete the feat of having reached at least the quarter-final stage at each of the four Majors.
Sharapova won her first four matches for the loss of just 12 games, before being sternly tested by compatriot Nadia Petrova in the quarter-finals, before winning in three sets. In the semi-finals, she lost to eventual champion Kim Clijsters in three sets. This marked the fourth consecutive Major tournament in which Sharapova was defeated by the eventual champion. Despite this defeat, Sharapova reclaimed the World No. 1 ranking following the tournament, having improved from her third ro |
https://en.wikipedia.org/wiki/Length%20of%20a%20Weyl%20group%20element | In mathematics, the length of an element w in a Weyl group W, denoted by l(w), is the smallest number k so that w is a product of k reflections by simple roots. (So, the notion depends on the choice of a positive Weyl chamber.) In particular, a simple reflection has length one. The function l is then an integer-valued function of W; it is a length function of W. It follows immediately from the definition that l(w−1) = l(w) and that l(ww'−1) ≤ l(w) + l(w' ).
References
Lie groups |
https://en.wikipedia.org/wiki/Okubo%20algebra | In algebra, an Okubo algebra or pseudo-octonion algebra is an 8-dimensional non-associative algebra similar to the one studied by Susumu Okubo. Okubo algebras are composition algebras, flexible algebras (A(BA) = (AB)A), Lie admissible algebras, and power associative, but are not associative, not alternative algebras, and do not have an identity element.
Okubo's example was the algebra of 3-by-3 trace-zero complex matrices, with the product of X and Y given by aXY + bYX – Tr(XY)I/3 where I is the identity matrix and a and b satisfy a + b = 3ab = 1. The Hermitian elements form an 8-dimensional real non-associative division algebra. A similar construction works for any cubic alternative separable algebra over a field containing a primitive cube root of unity. An Okubo algebra is an algebra constructed in this way from the trace-zero elements of a degree-3 central simple algebra over a field.
Construction of Para-Hurwitz algebra
Unital composition algebras are called Hurwitz algebras. If the ground field is the field of real numbers and is positive-definite, then is called a Euclidean Hurwitz algebra.
Scalar product
If has characteristic not equal to 2, then a bilinear form is associated with the quadratic form .
Involution in Hurwitz algebras
Assuming has a multiplicative unity, define involution and right and left multiplication operators by
Evidently is an involution and preserves the quadratic form. The overline notation stresses the fact that complex and quaternion conjugation are partial cases of it. These operators have the following properties:
The involution is an antiautomorphism, i.e.
, , where denotes the adjoint operator with respect to the form
where
, , so that is an alternative algebra
These properties are proved starting from polarized version of the identity :
Setting or yields and . Hence . Similarly . Hence . By the polarized identity so . Applied to 1 this gives . Replacing by gives the other identity. Substituting the formula for in gives .
Para-Hurwitz algebra
Another operation may be defined in a Hurwitz algebra as
The algebra is a composition algebra not generally unital, known as a para-Hurwitz algebra. In dimensions 4 and 8 these are para-quaternion and para-octonion algebras.
A para-Hurwitz algebra satisfies
Conversely, an algebra with a non-degenerate symmetric bilinear form satisfying this equation is either a para-Hurwitz algebra or an eight-dimensional pseudo-octonion algebra. Similarly, a flexible algebra satisfying
is either a Hurwitz algebra, a para-Hurwitz algebra or an eight-dimensional pseudo-octonion algebra.
References
Susumu Okubo & J. Marshall Osborn (1981) "Algebras with nondegenerate associative symmetric bilinear forms permitting composition", Communications in Algebra 9(12): 1233–61, and 9(20): 2015–73 .
Composition algebras
Non-associative algebras |
https://en.wikipedia.org/wiki/Calculus%20of%20concepts | The calculus of concepts is an abstract language and theory, which was developed to simplify the reasons behind effective messaging when delivered to a specific target or set of targets. The theory aims to maximize the likelihood of desired outcomes, by using messaging elements and techniques while analyzing the delivery mechanisms in certain scenarios. The reduction of uncertainty, but not its elimination, is often cost effective and practical.
Empowered by the internet of things (IoT) the framework looks at numerous device such as smart phones, tablets, laptops, hand held gaming devices, GPS devices, automobile Event Data Recorders and other electronic devices as remote sensors capable of providing data channels.
By using elements, the theory discovers underlying key concepts and their relations to better understand how messages can by used to elicit desired behaviors through mental model heuristics and biases. The framework does not serve up spam to potential consumers; it is a new paradigm for effective messaging. The nature of the data produced and consumed by devices in the IoT naturally lends itself to location-based awareness.
Just-in-time and real-time broadcasting of key messages gives the framework an extra dimension, putting it at the forefront of behavioral methodologies. Broadcasting can take place across a number of platforms, text, photographic, video, audio or even direct human contact.
The use of anchoring-and-adjustment, framing and representativeness heuristics provides fertile grounds for “re-wiring” the decision making processes to include either positive or mitigating mental models of a given concept or set of related concepts. The “re-wiring” will often produce results that have a significant impact on later decisions and behaviors on the target audience. The framework analyses key factors that influence the effectiveness of messaging mechanisms and how differing approaches can lead to entirely different results.
Background
The calculus of concepts framework has been practically implemented utilizing a combination of Naive Bayes classification and Support Vector Machines (SVM) algorithms to actively identify the key components of a messaging campaign and its effectiveness. The effectiveness of a communications campaign is often measured by numerous results including reach, frequency and duration.
The training data set for the model implementation utilized the potential messages and delivery mechanisms with Actors, Actions, Objects, Contexts and Indicia as a few examples.
Each concept within the framework is treated by the practical implementation as either an independent or dependent variable (as applicable) and therefore may have a meaningful effect on the outcome of any communication. As with any machine-learning tool the Calculus of Concepts model implementation inputs can be either nominal or ordinal and depending on the particular case.
Practical example
Between 2005 and 2012 one of the largest oil companies |
https://en.wikipedia.org/wiki/2008%20Maria%20Sharapova%20tennis%20season | Results and statistics from Maria Sharapova's 2008 tennis season.
Yearly summary
Australian Open series
Sharapova began her season at the Australian Open, as the 5th seed. She won the tournament without dropping a set (or playing a tie-break set), as she gained redemption following the previous year's heavy defeat in the final to Serena Williams. En route, she defeated Lindsay Davenport in the second round, served three bagels (one each to Elena Vesnina, Elena Dementieva and World No. 1 Justine Henin, whom she defeated very impressively in the quarter-finals) and defeated Jelena Janković (who had defeated the defending champion Williams in the quarter-finals) in the semi-finals, before facing Serbian Ana Ivanovic in the final. In a match dubbed as the "Glam Slam final", Sharapova upset the highly fancied Serb in straight sets to claim her first Australian Open title, and third Major title.
Middle East series
After playing two Fed Cup rubbers for Russia to kick off February, Sharapova then competed at the Qatar Ladies Open. She defeated Galina Voskoboeva, Tamarine Tanasugarn, Caroline Wozniacki and Agnieszka Radwańska (who had benefited from the withdrawal of top seed Ana Ivanovic in the third round) before facing (and defeating in three sets) Vera Zvonareva in the final.
Sharapova then withdrew from Dubai due to a viral infection.
Indian Wells & Miami
Sharapova reached the semi-finals at Indian Wells for the third time in four years, but was defeated there by compatriot and eventual runner-up Svetlana Kuznetsova, bringing an end to her 18-match winning streak to start the season. Following Indian Wells, Sharapova withdrew from Miami, citing a recurring shoulder injury.
Clay court season
American clay court season
After withdrawing from Miami, Sharapova won her first career clay court title in Amelia Island, defeating Dominika Cibulková in the final. At Charleston, she lost to eventual champion Serena Williams in the quarter-finals.
European clay court season
After deciding to skip the 2008 Qatar Telecom German Open, Sharapova next played at the Internazionali BNL d'Italia, reaching the semi-finals before being forced to withdraw from her match against eventual champion Jelena Janković due to a calf injury.
Following Justine Henin's surprise retirement during the same week as the Rome event, Sharapova was elevated to World No. 1 in the rankings. Subsequently, she was named as the top seed at the French Open, which she needed to win to complete a Career Grand Slam (and thus protect her top ranking). After surviving a close final set against compatriot Evgeniya Rodina in the first round, and another three-setter against Bethanie Mattek in the second, Sharapova fell in the fourth round in three sets to eventual finalist Dinara Safina, having held several match points in the second set. As a result, she lost her World No. 1 ranking, after just three weeks, to Ana Ivanovic, who went on to win the tournament.
Wimbledon
Sharapova's 2008 W |
https://en.wikipedia.org/wiki/Supermetric | Supermetric is a mathematical concept used in a number of fields in physics.
See also
Supergeometry
Supergravity
Super Minkowski space
Gauge gravitation theory
References
Further reading
Deligne, P. and Morgan, J. (1999) Notes on supersymmetry (following Joseph Bernstein). In: Quantum Field Theory and Strings: A Course for Mathematicians, Vol. 1 (Providence, RI: Amer. Math. Soc.) pp. 41-97 .
External links
G. Sardanashvily, Lectures on supergeometry, .
Supersymmetry |
https://en.wikipedia.org/wiki/2009%20Maria%20Sharapova%20tennis%20season | Results and statistics from Maria Sharapova's 2009 tennis season.
Yearly summary
Pre-comeback
At the beginning of the year, Sharapova was forced to concede the defence of her Australian Open title, a decision which would see her drop out of the WTA's Top 10 for the first time since winning Wimbledon in 2004. Her continued absence from the Tour also cost her the titles she won in Doha and Amelia Island last year; she also missed both the Premier Mandatory events at Indian Wells and Miami, and subsequently saw her world ranking drop to No. 65.
Sharapova first attempted her comeback by playing doubles with Elena Vesnina at Indian Wells (she did not play in the singles tournament). This decision would backfire, as they lost to fellow Russians Ekaterina Makarova and Tatiana Poutchek in three sets in the first round.
Comeback to tennis
In May, it was announced that she would be making her comeback at the Warsaw Open, which she entered as a wild card entry. She eventually reached the quarter-finals, losing to eventual finalist Alona Bondarenko. In the week during which the tournament was held, though, her world ranking dropped to No. 126, her lowest ranking since 2003, but her run in Warsaw saw her rise to No. 102 in the world rankings.
French Open
Sharapova entered the 2009 French Open unseeded at a Major for the first time since the 2003 US Open. In the second round, she defeated 11th seed Nadia Petrova 6–2, 1–6, 8–6. She went on to reach the quarter-finals, where she suffered her worst defeat at a Major tournament, losing to Dominika Cibulková and winning only two games (she had to defend a match point at 0–6, 0–5 down in the second set, in the process avoiding her second career double bagel defeat). Despite the defeat, Sharapova moved back into the World's Top 100 in the rankings.
Grass court season
Sharapova started her grass court season at Birmingham, where she had won her first grass court title five years earlier. Unseeded, she defeated Stéphanie Dubois, Alexa Glatch, seventh seed and future Wimbledon quarter-finalist Francesca Schiavone and Yanina Wickmayer to reach the semi-finals, before being defeated by Li Na there. Her run in Birmingham brought her ranking back into the Top 60.
As it was in 2008, her Wimbledon campaign would once again turn out to be short-lived, as she was defeated in the second round by Gisela Dulko in three sets.
US Open series
Sharapova next played at the 2009 Bank of the West Classic, where she defeated Ai Sugiyama and Nadia Petrova before being defeated by Venus Williams in the final eight.
She next played at Los Angeles, where she recorded her first career victory against Victoria Azarenka before falling in three sets to eventual champion Flavia Pennetta in the semi-finals. She then reached her first final since April 2008 at the Rogers Cup, falling there to Elena Dementieva in straight sets.
To conclude the US Open series, she competed at the US Open as the 29th seed; this was her lowest seeding at |
https://en.wikipedia.org/wiki/Louis%20Rosenhead | Louis Rosenhead (1 January 1906 – 10 November 1984) was a British mathematician noted for his work on fluid mechanics, and was head of the Department of Applied Mathematics at Liverpool University from 1933 to 1973.
Life
Rosenhead was born in Mabgate, Leeds, on 1 January 1906 to parents from Poland, the first of three children. His parents Abram Rozenkopf (born 1879) and Chaja Nagacz (born 1884) came from adjacent villages in Poland. They were married in Leeds in 1905, adopting the Anglicized versions of their names: Abraham and Ellen Rosenhead. Abraham was a tailor who did his national service in Russia and came to England in 1903; Ellen came in 1902. They were Jewish.
Rosenhead married Esther Brostoff in Leeds in 1932. Together they had two sons, Martin and Jonathan.
Rosenhead died 10 November 1984.
Education
Rosenhead matriculated from Leeds High School and went to the University of Leeds to study medicine, but after four weeks changed his studies to mathematics. His decision was influenced by Selig Brodetsky. Rosenhead graduated with first class honours in 1926, and continuing, eventually to attain a Ph.D. in 1928, studying under Brodetsky. He then earned another Ph.D. at Cambridge University, studying under Harold Jeffreys. This was followed by spending the academic year 1930-31 in Göttingen where Ludwig Prandtl was active. Rosenhead spent time there along with Sydney Goldstein and H. B. Squire, all working on theoretical fluid mechanics.
Career
In 1931 Rosenhead became assistant lecturer in applied mathematics at University College, Swansea. In 1933 he replaced Joseph Proudman as professor of applied mathematics at Liverpool.
During World War II, Rosenhead was superintendent of ballistics at the Projectile Development Establishment and collected a team of mathematicians to work on rocket weapons.
Rosenhead was elected a Fellow of the Royal Society in 1946.
In 1947 he was instrumental in developing statistics and in the appointment of Robin Plackett. His colleagues also included Maurice Bartlett, P. A. P. Moran and D. G. Kendall.
References
1906 births
1984 deaths
British Jews
Jewish scientists
Fluid dynamicists
20th-century English mathematicians
Academics of the University of Liverpool
Fellows of the Royal Society
Scientists from Leeds
Alumni of the University of Leeds |
https://en.wikipedia.org/wiki/Luh%20Dun-jin | Luh Dun-jin () is a Taiwanese politician. He currently serves as the Deputy Minister of the Directorate-General of Budget, Accounting and Statistics (DGBAS) of the Executive Yuan.
Education
Luh obtained his bachelor's degree in economics from Soochow University.
Directorate-General of Budget, Accounting and Statistics
Luh has held several positions in DGBAS such as section chief in 1987–1994, senior executive officer in 1994–1995, deputy director in 1995–1996, chief secretary in 1996–1997, office director of investigation in 1997–1998, controller in 1998-1999 and controller and director of the fourth department in 1999-2005 and of the third department in 2005–2006.
References
Political office-holders in the Republic of China on Taiwan
Living people
Year of birth missing (living people)
Soochow University (Taiwan) alumni |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.