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https://en.wikipedia.org/wiki/Heinrich%20Gustav%20Fl%C3%B6rke | Heinrich Gustav Flörke (24 December 1764, in Altenkalden in Mecklenburg – 11 June 1835) was a German botanist and lichenologist.
He initially studied theology and mathematics in Bützow, later studying medicine at the University of Jena. In 1816 he succeeded Ludolph Christian Treviranus (1779–1864) as professor of natural history at the University of Rostock, where he remained for the rest of his life.
He specialized in the field of lichenology, being known for his investigations of the genus Cladonia. During his career, he was highly critical of Swedish botanist Erik Acharius's work; e.g. Kritische Anmerkungen zu den Becherflechten in der Lichenographia universalis des Herrn Doctors und Ritters Erik Acharius (1810) - (Critical comments on the cup lichen in Lichenographia universalis of Erik Acharius).
For a number of years Flörke was an editor of "Oekonomische Encyklopädie", an encyclopedia initiated by Johann Georg Krünitz (1728–1796). His name is associated with the wildflower genus Floerkea, and also the lichen species Cladonia floerkeana.
Selected writings
Beschreibung der deutschen staubflechten, 1807
Deutsche Lichenen gesammelt und mit Ammerkungen, 1815
De Cladoniis : difficillimo lichenum genere, commentatio nova, 1828.
See also
:Category:Taxa named by Heinrich Gustav Flörke
References
1764 births
1835 deaths
Academic staff of the University of Rostock
University of Jena alumni
19th-century German botanists
German lichenologists
18th-century German botanists |
https://en.wikipedia.org/wiki/1986%E2%80%9387%20Galatasaray%20S.K.%20season | The 1986–87 season was Galatasaray's 83rd in existence and the 29th consecutive season in the 1. Lig. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
Players in / out
In
Out
1. Lig
Standings
Matches
Türkiye Kupası
Kick-off listed in local time (EET)
5th round
6th round
1/4 final
UEFA Cup
1st round
Süper Kupa-Cumhurbaşkanlığı Kupası
Kick-off listed in local time (EET)
Friendly Matches
Kick-off listed in local time (EET)
TSYD Kupası
Attendance
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1986–87 season
Turkish football championship-winning seasons
1980s in Istanbul
Galatasaray Sports Club 1986–87 season |
https://en.wikipedia.org/wiki/2012%E2%80%9313%20RNK%20Split%20season | This article shows statistics of individual players for the RNK Split football club. It also lists all matches that RNK Split played in the 2012–13 season.
First-team squad
Competitions
Prva HNL
Classification
Results summary
Results by round
Matches
Prva HNL
Croatian Cup
Split-Dalmatia County Cup
Sources: Prva-HNL.hr
Player seasonal records
Competitive matches only. Updated to games played 30 November 2012.
Top scorers
Source: Competitive matches
Appearances and goals
Sources: Prva-HNL.hr
References
2012-13
Croatian football clubs 2012–13 season |
https://en.wikipedia.org/wiki/1987%E2%80%9388%20Galatasaray%20S.K.%20season | The 1987–88 season was Galatasaray's 84th in existence and the 30th consecutive season in the 1. Lig. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
Players in / out
In
Out
1. Lig
Standings
Matches
Kick-off listed in local time (EET)
Türkiye Kupası
Kick-off listed in local time (EET)
3rd round
4th round
European Cup
1st round
Süper Kupa-Cumhurbaşkanlığı Kupası
Kick-off listed in local time (EET)
Friendly Matches
Kick-off listed in local time (EET)
TSYD Kupası
Attendance
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Galatasaray
Turkish football championship-winning seasons
1980s in Istanbul
Galatasaray Sports Club 1987–88 season |
https://en.wikipedia.org/wiki/Matroid%20oracle | In mathematics and computer science, a matroid oracle is a subroutine through which an algorithm may access a matroid, an abstract combinatorial structure that can be used to describe the linear dependencies between vectors in a vector space or the spanning trees of a graph, among other applications.
The most commonly used oracle of this type is an independence oracle, a subroutine for testing whether a set of matroid elements is independent. Several other types of oracle have also been used; some of them have been shown to be weaker than independence oracles, some stronger, and some equivalent in computational power.
Many algorithms that perform computations on matroids have been designed to take an oracle as input, allowing them to run efficiently without change on many different kinds of matroids, and without additional assumptions about what kind of matroid they are using. For instance, given an independence oracle for any matroid, it is possible to find the minimum weight basis of the matroid by applying a greedy algorithm that adds elements to the basis in sorted order by weight, using the independence oracle to test whether each element can be added.
In computational complexity theory, the oracle model has led to unconditional lower bounds proving that certain matroid problems cannot be solved in polynomial time, without invoking unproved assumptions such as the assumption that P ≠ NP. Problems that have been shown to be hard in this way include testing whether a matroid is binary or uniform, or testing whether it contains certain fixed minors.
Why oracles?
Although some authors have experimented with computer representations of matroids that explicitly list all independent sets or all basis sets of the matroid, these representations are not succinct: a matroid with elements may expand into a representation that takes space exponential in . Indeed, the number of distinct matroids on elements grows doubly exponentially as
from which it follows that any explicit representation capable of handling all possible matroids would necessarily use exponential space.
Instead, different types of matroids may be represented more efficiently from the other structures from which they are defined: uniform matroids from their two numeric parameters, graphic matroids, bicircular matroids, and gammoids from graphs, linear matroids from matrices, etc. However, an algorithm for performing computations on arbitrary matroids needs a uniform method of accessing its argument, rather than having to be redesigned for each of these matroid classes. The oracle model provides a convenient way of codifying and classifying the kinds of access that an algorithm might need.
History
Starting with , "independence functions" or "-functions" have been studied as one of many equivalent ways of axiomatizing matroids. An independence function maps a set of matroid elements to the number if the set is independent or if it is dependent; that is, it is the indicator funct |
https://en.wikipedia.org/wiki/Patricio%20Guill%C3%A9n | Patricio Damián Guillén Gandini (born 28 December 1984 in Montevideo) is an Uruguayan footballer who plays as a goalkeeper for Spanish club SD Compostela.
Career statistics
Club
References
External links
1984 births
Living people
Uruguayan people of Spanish descent
Uruguayan men's footballers
Men's association football goalkeepers
Club Atlético River Plate (Montevideo) players
C.A. Cerro players
Racing Club de Montevideo players
Segunda División B players
Tercera División players
CD Ourense footballers
Barakaldo CF footballers
SD Compostela footballers
Uruguayan expatriate men's footballers
Uruguayan expatriate sportspeople in Spain
Expatriate men's footballers in Spain
CD Binéfar players
Atlético Monzón players
Footballers from Montevideo |
https://en.wikipedia.org/wiki/V%C3%A1mos%20matroid | In mathematics, the Vámos matroid or Vámos cube is a matroid over a set of eight elements that cannot be represented as a matrix over any field. It is named after English mathematician Peter Vámos, who first described it in an unpublished manuscript in 1968.
Definition
The Vámos matroid has eight elements, which may be thought of as the eight vertices of a cube or cuboid. The matroid has rank 4: all sets of three or fewer elements are independent, and 65 of the 70 possible sets of four elements are also independent. The five exceptions are four-element circuits in the matroid. Four of these five circuits are formed by faces of the cuboid (omitting two opposite faces). The fifth circuit connects two opposite edges of the cuboid, each of which is shared by two of the chosen four faces.
Another way of describing the same structure is that it has two elements for each vertex of the diamond graph, and a four-element circuit for each edge of the diamond graph.
Properties
The Vámos matroid is a paving matroid, meaning that all of its circuits have size at least equal to its rank.
The Vámos matroid is isomorphic to its dual matroid, but it is not identically self-dual (the isomorphism requires a nontrivial permutation of the matroid elements).
The Vámos matroid cannot be represented over any field. That is, it is not possible to find a vector space, and a system of eight vectors within that space, such that the matroid of linear independence of these vectors is isomorphic to the Vámos matroid. Indeed, it is one of the smallest non-representable matroids, and served as a counterexample to a conjecture of Ingleton that the matroids on eight or fewer elements were all representable.
The Vámos matroid is a forbidden minor for the matroids representable over a field , whenever has five or more elements. However, it is not possible to test in polynomial time whether it is a minor of a given matroid , given access to through an independence oracle.
The Vámos matroid is not algebraic. That is, there do not exist a field extension and a set of eight elements of , such that the transcendence degree of sets of these eight elements equals the rank function of the matroid.
The Vámos matroid is not a secret-sharing matroid. Secret-sharing matroids describe "ideal" secret sharing schemes in which any coalition of users who can gain any information about a secret key can learn the whole key (these coalitions are the dependent sets of the matroid), and in which the shared information contains no more information than is needed to represent the key. These matroids also have applications in coding theory.
The Vámos matroid has no adjoint. This means that the dual lattice of the geometric lattice of the Vámos matroid cannot be order-embedded into another geometric lattice of the same rank.
The Vámos matroid can be oriented. In oriented matroids, a form of the Hahn–Banach theorem follows from a certain intersection property of the flats of the matroid; the Vámos matroi |
https://en.wikipedia.org/wiki/Bipartite%20matroid | In mathematics, a bipartite matroid is a matroid all of whose circuits have even size.
Example
A uniform matroid is bipartite if and only if is an odd number, because the circuits in such a matroid have size .
Relation to bipartite graphs
Bipartite matroids were defined by as a generalization of the bipartite graphs, graphs in which every cycle has even size. A graphic matroid is bipartite if and only if it comes from a bipartite graph.
Duality with Eulerian matroids
An Eulerian graph is one in which all vertices have even degree; Eulerian graphs may be disconnected. For planar graphs, the properties of being bipartite and Eulerian are dual: a planar graph is bipartite if and only if its dual graph is Eulerian. As Welsh showed, this duality extends to binary matroids: a binary matroid is bipartite if and only if its dual matroid is an Eulerian matroid, a matroid that can be partitioned into disjoint circuits.
For matroids that are not binary, the duality between Eulerian and bipartite matroids may break down. For instance, the uniform matroid is non-bipartite but its dual is Eulerian, as it can be partitioned into two 3-cycles. The self-dual uniform matroid is bipartite but not Eulerian.
Computational complexity
It is possible to test in polynomial time whether a given binary matroid is bipartite. However, any algorithm that tests whether a given matroid is Eulerian, given access to the matroid via an independence oracle, must perform an exponential number of oracle queries, and therefore cannot take polynomial time.
References
Matroid theory |
https://en.wikipedia.org/wiki/1988%E2%80%9389%20Galatasaray%20S.K.%20season | The 1988–89 season was Galatasaray's 85th in existence and the 31st consecutive season in the 1. Lig. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
Players in / out
In
Out
1. Lig
Standings
Matches
Turkish Cup
Kick-off listed in local time (EET)
3rd round
4th round
Quarter-finals
European Cup
1st round
2nd round
Quarter-finals
Semi-finals
Steaua București won 5–1 on aggregate.
Friendly Matches
Kick-off listed in local time (EET)
TSYD Kupası
Attendance
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Galatasaray
1980s in Istanbul
Galatasaray Sports Club 1988–89 season |
https://en.wikipedia.org/wiki/Biregular%20graph | In graph-theoretic mathematics, a biregular graph or semiregular bipartite graph is a bipartite graph for which every two vertices on the same side of the given bipartition have the same degree as each other. If the degree of the vertices in is and the degree of the vertices in is , then the graph is said to be -biregular.
Example
Every complete bipartite graph is -biregular.
The rhombic dodecahedron is another example; it is (3,4)-biregular.
Vertex counts
An -biregular graph must satisfy the equation . This follows from a simple double counting argument: the number of endpoints of edges in is , the number of endpoints of edges in is , and each edge contributes the same amount (one) to both numbers.
Symmetry
Every regular bipartite graph is also biregular.
Every edge-transitive graph (disallowing graphs with isolated vertices) that is not also vertex-transitive must be biregular. In particular every edge-transitive graph is either regular or biregular.
Configurations
The Levi graphs of geometric configurations are biregular; a biregular graph is the Levi graph of an (abstract) configuration if and only if its girth is at least six.
References
Bipartite graphs |
https://en.wikipedia.org/wiki/Charlotte%20Barnum | Charlotte Cynthia Barnum (May 17, 1860 – March 27, 1934), mathematician and social activist, was the first woman to receive a Ph.D. in mathematics from Yale University.
Early life and education
Charlotte Barnum was born in Phillipston, Massachusetts, the third of four children of the Reverend Samuel Weed Barnum (1820–1891) and Charlotte Betts (1823–1899). Education was important in her family: two uncles had received medical degrees from Yale and her father had graduated from there with a Bachelor of Arts and a Bachelor of Divinity. Her brothers Samuel and Thomas would both graduate from Yale, and her sister Clara would attend Yale graduate school after graduating from Vassar.
After graduating from Hillhouse High School in New Haven, Connecticut Charlotte attended Vassar College, where she graduated in 1881. From 1881 to 1886 she taught at a boys’ preparatory school, Betts Academy, in Stamford, Connecticut and at Hillhouse High School. She also did computing work for the Yale Observatory 1883–1885 and worked on a revision of James Dwight Dana’s System of Mineralogy. Charlotte was an editorial writer for Webster's International Dictionary from 1886 to 1890, and then taught astronomy at Smith College for the academic year 1889–90.
In 1890 Charlotte applied for graduate studies at Johns Hopkins University, but was turned down because they did not accept women. She persisted and with the support of Simon Newcomb, professor of mathematics and astronomy at the university, she won approval to attend lectures without enrollment and without charge. Two years later, she moved to New Haven to pursue her graduate studies at Yale. In 1895 she was the first woman to receive a Ph.D. in mathematics from that institution. Her thesis was titled "Functions Having Lines or Surfaces of Discontinuity". The identity of her adviser is unclear from the record.
Later career
After receiving her Ph.D., Charlotte Barnum taught at Carleton College in Northfield, Minnesota for one year. She then left academia, and did civilian and governmental applied mathematics and editorial work the remainder of her career.
In 1898 she joined the American Academy of Actuaries and until 1901 worked as an actuarial computer for the Massachusetts Mutual Life Insurance Company, Springfield, Massachusetts and the Fidelity Mutual Life Insurance Company in Philadelphia, Pennsylvania.
In 1901 she moved to Washington D.C. to work as a computer for US Naval Observatory. She subsequently did the same work for the tidal division of the US Coast and Geodetic Survey until 1908 and then was editorial assistant in the biological survey section of the US Department of Agriculture through 1913.
She left government employment and returned to New Haven in 1914 where she did editorial work for Yale Peruvian Expeditions, the Yale University secretary's office, and the Yale University Press.
Starting in 1917 she worked in various organizations and academic institutions in Connecticut, New York and Mas |
https://en.wikipedia.org/wiki/1989%E2%80%9390%20Galatasaray%20S.K.%20season | The 1989–90 season was Galatasaray's 86th in existence and the 32nd consecutive season in the 1. Lig. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
Players in / out
In
Out
1. Lig
Standings
Matches
Türkiye Kupası
Kick-off listed in local time (EET)
5th round
UEFA Cup
1st round
Başbakanlık Kupası
Kick-off listed in local time (EET)
Friendly Matches
Kick-off listed in local time (EET)
TSYD Kupası
Attendance
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Galatasaray
1980s in Istanbul
1990s in Istanbul
Galatasaray Sports Club 1989–90 season |
https://en.wikipedia.org/wiki/Kikas%20%28Angolan%20footballer%29 | Francisco Caetano Monteiro de Assis also known as Kikas (born October 21, 1981) is an Angolan football player. He has played for Angola national team.
National team statistics
References
External links
1981 births
Living people
Angolan men's footballers
Angola men's international footballers
Men's association football defenders |
https://en.wikipedia.org/wiki/Fractal%20canopy | In geometry, a fractal canopy, a type of fractal tree, is one of the easiest-to-create types of fractals. Each canopy is created by splitting a line segment into two smaller segments at the end (symmetric binary tree), and then splitting the two smaller segments as well, and so on, infinitely. Canopies are distinguished by the angle between concurrent adjacent segments and ratio between lengths of successive segments.
A fractal canopy must have the following three properties:
The angle between any two neighboring line segments is the same throughout the fractal.
The ratio of lengths of any two consecutive line segments is constant.
Points all the way at the end of the smallest line segments are interconnected, which is to say the entire figure is a connected graph.
The pulmonary system used by humans to breathe resembles a fractal canopy, as do trees, blood vessels, viscous fingering, electrical breakdown, and crystals with appropriately adjusted growth velocity from seed.
See also
Brownian tree
Dendrite (crystal)
Lichtenberg figure
H tree
References
External links
from a student-generated Oracle Thinkquest website
Fractals
L-systems |
https://en.wikipedia.org/wiki/Din%20Gabay | Din Gabay (born September 19, 1992) is a retired Israeli footballer. He is the son of Ronen Gabay.
Club career statistics
(correct as of August 2012)
References
External links
1992 births
Living people
Israeli men's footballers
Beitar Nes Tubruk F.C. players
Maccabi Netanya F.C. players
Beitar Tel Aviv Bat Yam F.C. players
Hakoah Amidar Ramat Gan F.C. players
Israeli Premier League players
Liga Leumit players
Footballers from Netanya
Men's association football defenders |
https://en.wikipedia.org/wiki/Hasan%20Sarhan | Hasan Sarhan (, ; born 30 April 1993) is a Palestinian footballer.
Club career statistics
(correct as of August 2012)
References
External links
1993 births
Living people
Israeli men's footballers
Arab-Israeli footballers
Palestinian men's footballers
Palestine men's international footballers
Maccabi Netanya F.C. players
Ihud Bnei Majd al-Krum F.C. players
Shabab Al-Dhahiriya SC players
Hapoel Iksal F.C. players
Hapoel Bnei Rameh F.C. players
West Bank Premier League players
Footballers from Majd al-Krum
Men's association football forwards |
https://en.wikipedia.org/wiki/Gauge%20theory%20gravity | Gauge theory gravity (GTG) is a theory of gravitation cast in the mathematical language of geometric algebra. To those familiar with general relativity, it is highly reminiscent of the tetrad formalism although there are significant conceptual differences. Most notably, the background in GTG is flat, Minkowski spacetime. The equivalence principle is not assumed, but instead follows from the fact that the gauge covariant derivative is minimally coupled. As in general relativity, equations structurally identical to the Einstein field equations are derivable from a variational principle. A spin tensor can also be supported in a manner similar to Einstein–Cartan–Sciama–Kibble theory. GTG was first proposed by Lasenby, Doran, and Gull in 1998 as a fulfillment of partial results presented in 1993. The theory has not been widely adopted by the rest of the physics community, who have mostly opted for differential geometry approaches like that of the related gauge gravitation theory.
Mathematical foundation
The foundation of GTG comes from two principles. First, position-gauge invariance demands that arbitrary local displacements of fields not affect the physical content of the field equations. Second, rotation-gauge invariance demands that arbitrary local rotations of fields not affect the physical content of the field equations. These principles lead to the introduction of a new pair of linear functions, the position-gauge field and the rotation-gauge field. A displacement by some arbitrary function f
gives rise to the position-gauge field defined by the mapping on its adjoint,
which is linear in its first argument and a is a constant vector. Similarly, a rotation by some arbitrary rotor R gives rise to the rotation-gauge field
We can define two different covariant directional derivatives
or with the specification of a coordinate system
where × denotes the commutator product.
The first of these derivatives is better suited for dealing directly with spinors whereas the second is better suited for observables. The GTG analog of the Riemann tensor is built from the commutation rules of these derivatives.
Field equations
The field equations are derived by postulating the Einstein–Hilbert action governs the evolution of the gauge fields, i.e.
Minimizing variation of the action with respect to the two gauge fields results in the field equations
where is the covariant energy–momentum tensor and is the covariant spin tensor. Importantly, these equations do not give an evolving curvature of spacetime but rather merely give the evolution of the gauge fields within the flat spacetime.
Relation to general relativity
For those more familiar with general relativity, it is possible to define a metric tensor from the position-gauge field in a manner similar to tetrads. In the tetrad formalism, a set of four vectors are introduced. The Greek index μ is raised or lowered by multiplying and contracting with the spacetime's metric tensor. The |
https://en.wikipedia.org/wiki/Dominik%20Furman | Dominik Grzegorz Furman (born 6 July 1992) is a Polish professional footballer who plays as a midfielder.
Career
Furman started his career with Legia Warsaw.
Career statistics
Honours
Legia Warsaw
Polish Cup: 2011–12, 2012–13, 2014–15, 2015–16
Ekstraklasa: 2012–13, 2013–14, 2015–16
References
External links
1992 births
Living people
People from Szydłowiec
Jewish Polish sportspeople
Polish men's footballers
Ekstraklasa players
Ligue 1 players
Serie A players
Süper Lig players
Legia Warsaw players
Toulouse FC players
Hellas Verona FC players
Wisła Płock players
Gençlerbirliği S.K. footballers
Polish expatriate men's footballers
Expatriate men's footballers in France
Expatriate men's footballers in Italy
Expatriate men's footballers in Turkey
Polish expatriate sportspeople in France
Polish expatriate sportspeople in Italy
Polish expatriate sportspeople in Turkey
Men's association football midfielders
Poland men's international footballers
Poland men's youth international footballers
Poland men's under-21 international footballers |
https://en.wikipedia.org/wiki/Keisuke%20Harada | is a former Japanese football player.
Club statistics
Updated to 11 December 2014.
References
External links
J. League (#28)
1988 births
Living people
University of Tsukuba alumni
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Vegalta Sendai players
Tochigi SC players
FC Machida Zelvia players
Men's association football defenders
Association football people from Sapporo |
https://en.wikipedia.org/wiki/Keiki%20Shimizu | is a Japanese football player who plays for Thespakusatsu Gunma.
Club statistics
Updated to 23 February 2020.
References
External links
Profile at Thespakusatsu Gunma
Profile at Omiya Ardija
1985 births
Living people
Ryutsu Keizai University alumni
Association football people from Gunma Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Omiya Ardija players
Thespakusatsu Gunma players
Blaublitz Akita players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Kweon%20Han-jin | Kweon Han-Jin (; born May 19, 1988) is a South Korean football player who plays for Daejeon Hana Citizen FC.
Club statistics
References
External links
J. League (#14)
1988 births
Living people
South Korean men's footballers
South Korean expatriate men's footballers
J1 League players
J2 League players
K League 1 players
Kashiwa Reysol players
Shonan Bellmare players
Thespakusatsu Gunma players
Roasso Kumamoto players
Jeju United FC players
Expatriate men's footballers in Japan
South Korean expatriate sportspeople in Japan
Men's association football defenders |
https://en.wikipedia.org/wiki/Hirotaka%20Mita | Hirotaka Mita (三田 啓貴, born September 14, 1990) is a Japanese professional footballer who plays as an attacking midfielder for club Yokohama FC.
Club statistics
.
Honours
Club
FC Tokyo
J.League Cup: 2020
References
External links
Profile at Yokohama FC
Profile at Vissel Kobe
Profile at Vegalta Sendai
1990 births
Living people
Meiji University alumni
Association football people from Tokyo
Japanese men's footballers
J1 League players
FC Tokyo players
Vegalta Sendai players
Vissel Kobe players
Yokohama FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Kyotaro%20Yamakoshi | is a Japanese football player for Tochigi SC.
Club statistics
Updated to 23 February 2016.
References
External links
Profile at Tochigi SC
1991 births
Living people
University of Tsukuba alumni
Association football people from Tochigi Prefecture
Japanese men's footballers
J1 League players
J3 League players
Kawasaki Frontale players
Tochigi SC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Akito%20Tachibana | is a former Japanese football player.
Club statistics
References
External links
J. League (#22)
1988 births
Living people
Osaka Sangyo University alumni
Association football people from Hyōgo Prefecture
Japanese men's footballers
J1 League players
J2 League players
Shimizu S-Pulse players
Matsumoto Yamaga FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Makoto%20Shibahara | is a former Japanese football player.
Club statistics
References
External links
J. League (#24)
1992 births
Living people
Association football people from Shizuoka Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Shimizu S-Pulse players
FC Gifu players
Fukushima United FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Tomoya%20Inukai | is a Japanese footballer who plays for J1 League club Kashiwa Reysol, on loan from Urawa Red Diamonds.
Club statistics
.
Honours
Club
Urawa Red Diamonds
Japanese Super Cup: 2022
AFC Champions League: 2022
References
External links
Profile at Kashima Antlers
1993 births
Living people
Association football people from Shizuoka Prefecture
Japanese men's footballers
J1 League players
J2 League players
Shimizu S-Pulse players
Matsumoto Yamaga FC players
Kashima Antlers players
Urawa Red Diamonds players
Kashiwa Reysol players
Men's association football defenders |
https://en.wikipedia.org/wiki/Yuji%20Senuma | is a Japanese football player for Tochigi SC.
Club statistics
Updated to 1 March 2019.
1Includes Promotion Playoffs to J1.
References
External links
Profile at Montedio Yamagata
1990 births
Living people
University of Tsukuba alumni
Association football people from Kanagawa Prefecture
Japanese men's footballers
J1 League players
J2 League players
Shimizu S-Pulse players
Tochigi SC players
Ehime FC players
Montedio Yamagata players
Yokohama FC players
Zweigen Kanazawa players
Men's association football forwards
FISU World University Games gold medalists for Japan
Universiade medalists in football
Medalists at the 2011 Summer Universiade
Sportspeople from Sagamihara |
https://en.wikipedia.org/wiki/Akihiko%20Takeshige | is a Japanese football player who currently plays for SC Sagamihara.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Tochigi SC
1987 births
Living people
Hannan University alumni
Association football people from Yamaguchi Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Júbilo Iwata players
Albirex Niigata players
Tochigi SC players
Yokohama FC players
SC Sagamihara players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Ryota%20Tanabe | Ryota Tanabe (田鍋 陵太, born 10 April 1993) is a Japanese football player for Tokyo United FC.
Career statistics
Club
Updated to 31 January 2018.
References
External links
1993 births
Living people
Association football people from Tokyo
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Nagoya Grampus players
J.League U-22 Selection players
Roasso Kumamoto players
Tokyo United FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Takuya%20Masuda | Takuya Masuda (増田 卓也, born 29 June 1989) is a Japanese professional football goalkeeper who plays for Roasso Kumamoto.
Club statistics
Updated to end of 2018 season.
1Includes Japanese Super Cup, FIFA Club World Cup and J. League Championship.
References
External links
Profile at V-Varen Nagasaki
1989 births
Living people
Ryutsu Keizai University alumni
Association football people from Hiroshima Prefecture
Japanese men's footballers
J1 League players
J2 League players
Sanfrecce Hiroshima players
V-Varen Nagasaki players
FC Machida Zelvia players
Roasso Kumamoto players
Asian Games medalists in football
Footballers at the 2010 Asian Games
Men's association football goalkeepers
Asian Games gold medalists for Japan
Medalists at the 2010 Asian Games
FISU World University Games gold medalists for Japan
Universiade medalists in football
Medalists at the 2011 Summer Universiade |
https://en.wikipedia.org/wiki/Kota%20Sameshima | is a Japanese football player for Fujieda MYFC.
Club statistics
Updated to 23 February 2018.
1Includes Emperor's Cup.
2Includes J. League Cup.
3Includes AFC Champions League.
4Includes FIFA Club World Cup.
References
External links
Profile at Fujieda MYFC
1992 births
Living people
Association football people from Kagoshima Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Sanfrecce Hiroshima players
Gainare Tottori players
AC Nagano Parceiro players
Fujieda MYFC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Gakuto%20Notsuda | is a Japanese football player who plays as a midfielder for Sanfrecce Hiroshima and the Japan national team.
Club statistics
International
Gakuto got called up to the senior Japan squad for the 2022 EAFF E-1 Football Championship. On 24 July 2022, he make his international debut against China playing the entire 90 minute. He helped Japan to win the tournament at the Toyota Stadium.
1Includes Japanese Super Cup and FIFA Club World Cup.
Honours
Club
Sanfrecce Hiroshima
J. League Division 1 (3) : 2012, 2013, 2015
J.League Cup (1) : 2022
Japanese Super Cup (2) : 2013, 2014
International
EAFF E-1 Football Championship: 2022
References
External links
Profile at Vegalta Sendai
Profile at Shimizu S-Pulse
1994 births
Living people
Japanese men's footballers
Japan men's youth international footballers
J1 League players
J3 League players
Sanfrecce Hiroshima players
Albirex Niigata players
Shimizu S-Pulse players
J.League U-22 Selection players
Vegalta Sendai players
Footballers at the 2014 Asian Games
Men's association football midfielders
Asian Games competitors for Japan
Association football people from Hiroshima |
https://en.wikipedia.org/wiki/Yuki%20Yamamura | is a Japanese football player who currently plays for Tochigi City FC.
Club statistics
Updated to 23 February 2018.
References
External links
1990 births
Living people
Meiji University alumni
Association football people from Kanagawa Prefecture
Japanese men's footballers
J2 League players
Mito HollyHock players
Tochigi City FC players
Men's association football forwards |
https://en.wikipedia.org/wiki/Daichi%20Inui | is a Japanese football player currently playing for Tochigi SC on loan from Matsumoto Yamaga FC.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at V-Varen Nagasaki
1989 births
Living people
Ryutsu Keizai University alumni
Association football people from Gunma Prefecture
Japanese men's footballers
J1 League players
J2 League players
Thespakusatsu Gunma players
V-Varen Nagasaki players
Sagan Tosu players
Yokohama FC players
Tochigi SC players
Matsumoto Yamaga FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Bae%20Dae-won | Bae Dae-Won (born July 6, 1988) is a South Korean football player who currently plays for Gimhae FC.
Club statistics
References
External links
1988 births
Living people
South Korean men's footballers
South Korean expatriate men's footballers
Suwon Samsung Bluewings players
Tokyo Verdy players
FC Machida Zelvia players
K League 1 players
Korea National League players
J2 League players
J3 League players
Japan Football League players
South Korean expatriate sportspeople in Japan
Expatriate men's footballers in Japan
Hanyang University alumni
Men's association football defenders |
https://en.wikipedia.org/wiki/Ryuto%20Otake | is a Japanese football player for J.FC Miyazaki.
Club statistics
Updated to 1 January 2020.
References
External links
Profile at Fujieda MYFC
1988 births
Living people
Kokushikan University alumni
Association football people from Tokyo
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
FC Machida Zelvia players
Fujieda MYFC players
Veroskronos Tsuno players
Men's association football defenders
People from Meguro |
https://en.wikipedia.org/wiki/Katsuya%20Senzaki | is a former Japanese football player.
Club statistics
References
External links
J. League (#24)
1987 births
Living people
Kokushikan University alumni
Association football people from Kanagawa Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Vanraure Hachinohe players
FC Machida Zelvia players
FC Ryukyu players
Kagoshima United FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Kohei%20Mihara%20%28footballer%29 | is a Japanese football player for Nankatsu SC.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Nankatsu SC
1989 births
Living people
Kanagawa University alumni
Association football people from Kagawa Prefecture
Japanese men's footballers
J2 League players
Shonan Bellmare players
Ehime FC players
Vonds Ichihara players
Nankatsu SC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Lee%20Min-soo | Lee Min-Soo (; born January 11, 1992) is a South Korean football player.
Club statistics
References
External links
1992 births
Living people
Hannam University alumni
South Korean men's footballers
South Korean expatriate men's footballers
J1 League players
J2 League players
J3 League players
Korea National League players
K League 1 players
Shonan Bellmare players
Shimizu S-Pulse players
Tochigi SC players
FC Machida Zelvia players
Daejeon Korail FC players
Gangwon FC players
Expatriate men's footballers in Japan
South Korean expatriate sportspeople in Japan
Men's association football midfielders |
https://en.wikipedia.org/wiki/Renato%20%28footballer%2C%20born%201992%29 | Renato Piau de Sa (born December 19, 1992) is a Brazilian football player.
Club statistics
References
External links
1992 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J2 League players
Ventforet Kofu players
Men's association football forwards |
https://en.wikipedia.org/wiki/Hidetoshi%20Miyuki | is a Japanese professional footballer who plays as a midfielder for J.League club Omiya Ardija.
Club statistics
Updated to end of 2018 season.
References
External links
Profile at Omiya Ardija
1993 births
Living people
Association football people from Chiba Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Ventforet Kofu players
SC Sagamihara players
Renofa Yamaguchi FC players
Shonan Bellmare players
Omiya Ardija players
Men's association football midfielders |
https://en.wikipedia.org/wiki/1990%E2%80%9391%20Galatasaray%20S.K.%20season | The 1990–91 season was Galatasaray's 87th in existence and the 33rd consecutive season in the 1. Lig. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
Players in / out
In
Out
1. Lig
Standings
Matches
Türkiye Kupası
Kick-off listed in local time (EET)
6th round
1/4 final
1/2 final
Final
Süper Kupa-Cumhurbaşkanlığı Kupası
Kick-off listed in local time (EET)
Friendly Matches
Kick-off listed in local time (EET)
TSYD Kupası
Attendance
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Galatasaray
1990s in Istanbul
Galatasaray Sports Club 1990–91 season |
https://en.wikipedia.org/wiki/Shota%20Imai | is a former Japanese football player.
Club statistics
References
External links
Football News
1984 births
Living people
Biwako Seikei Sport College alumni
Association football people from Nagano Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Matsumoto Yamaga FC players
Blaublitz Akita players
Reilac Shiga FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Yuto%20Shirai | Yuto Shirai (白井 裕人, born June 19, 1988) is a Japanese football player for Zweigen Kanazawa.
Club statistics
Updated to end of 2018 season.
References
External links
Profile at Zweigen Kanazawa
1988 births
Living people
People from Kashiwa
Ryutsu Keizai University alumni
Association football people from Chiba Prefecture
Japanese men's footballers
J1 League players
J2 League players
Matsumoto Yamaga FC players
Zweigen Kanazawa players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Yoon%20Sung-yeul | Yoon Sung-yeul (born December 22, 1987) is a South Korean football player who plays for Seoul E-Land.
Club statistics
References
External links
1987 births
Living people
South Korean men's footballers
Men's association football midfielders
Men's association football fullbacks
South Korean expatriate men's footballers
FC Machida Zelvia players
Matsumoto Yamaga FC players
Seoul E-Land FC players
J2 League players
Japan Football League players
K League 2 players
South Korean expatriate sportspeople in Japan
Expatriate men's footballers in Japan |
https://en.wikipedia.org/wiki/Choi%20Su-bin | Choi Su-bin (born October 14, 1988) is a South Korean football player who currently plays for Mokpo City.
Club statistics
References
External links
1988 births
Living people
South Korean men's footballers
South Korean expatriate men's footballers
Incheon United FC players
Matsumoto Yamaga FC players
K League 1 players
Korea National League players
J2 League players
South Korean expatriate sportspeople in Japan
Expatriate men's footballers in Japan
Men's association football forwards |
https://en.wikipedia.org/wiki/Kazuki%20Mine | is a Japanese football player. He is currently playing for Vanraure Hachinohe.
Club statistics
Updated to 20 February 2017.
References
External links
Profile at Vanraure Hachinohe
1993 births
Living people
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Kyoto Sanga FC players
Kataller Toyama players
AC Nagano Parceiro players
J.League U-22 Selection players
Vanraure Hachinohe players
Men's association football forwards
Association football people from Osaka |
https://en.wikipedia.org/wiki/Hiroaki%20Kamijo | is a former Japanese football player.
Club statistics
References
External links
J. League (#35)
1989 births
Living people
Ryutsu Keizai University alumni
Association football people from Chiba Prefecture
Japanese men's footballers
J2 League players
Fagiano Okayama players
Men's association football forwards |
https://en.wikipedia.org/wiki/Makoto%20Mimura | Makoto Mimura (三村 真, born March 30, 1989) is a Japanese football player.
Club statistics
Updated to end of 2018 season.
References
External links
1989 births
Living people
Takushoku University alumni
Association football people from Okayama Prefecture
Japanese men's footballers
J2 League players
Fagiano Okayama players
Men's association football forwards
Association football people from Hiroshima |
https://en.wikipedia.org/wiki/Kohei%20Kawata | is a Japanese football player for Ventforet Kofu.
Club statistics
Updated to end of 2018 season.
Honours
Club
Ventforet Kofu
Emperor's Cup: 2022
References
External links
Profile at Ventforet Kofu
1987 births
Living people
Fukuoka University alumni
Association football people from Ōita Prefecture
Japanese men's footballers
J1 League players
J2 League players
Gamba Osaka players
Avispa Fukuoka players
Ventforet Kofu players
Men's association football goalkeepers
Universiade bronze medalists for Japan
Universiade medalists in football
Medalists at the 2009 Summer Universiade
Sportspeople from Ōita (city) |
https://en.wikipedia.org/wiki/1991%E2%80%9392%20Galatasaray%20S.K.%20season | The 1991–92 season was Galatasaray's 88th in existence and the 34th consecutive season in the 1. Lig. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
Players in / out
In
Out
1. Lig
Standings
Matches
Türkiye Kupası
Kick-off listed in local time (EET)
6th round
1/4 final
European Cup Winners' Cup
First round
Second round
Quarter-finals
Friendly Matches
Kick-off listed in local time (EET)
TSYD Kupası
Attendance
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Galatasaray
1990s in Istanbul
Galatasaray Sports Club 1991–92 season |
https://en.wikipedia.org/wiki/AStA%20Wirtschafts-%20und%20Sozialstatistisches%20Archiv | (English: AStA Economical and Social Statistics Archive) is a quarterly peer-reviewed scientific journal of statistics published quarterly by Springer Science+Business Media. It was established in 2007 and covers statistical analysis. Articles are in German or English. The journal evolved from the Allgemeines Statistisches Archiv, established in 1890.
Abstracting and indexing
The journal is abstracted and indexed in:
Scopus
Academic OneFile
Expanded Academic
Research Papers in Economics
References
External links
Statistics journals
Academic journals established in 2007
Multilingual journals
Academic journals of Germany
Quarterly journals
Springer Science+Business Media academic journals |
https://en.wikipedia.org/wiki/Sirari | Sirari is a town and ward in Tarime District, Mara Region of northern Tanzania, East Africa. In 2016 the Tanzania National Bureau of Statistics report there were 17,564 people in the ward, from 15,917 in 2012.
Villages / neighborhoods
The ward has 4 villages and 15 hamlets.
Sokoni
Majengo mapya
Mlimani
Nyairoma
Sokoni
Buriba
Kenanso
Nyasoko
Nyatiti
Sirari
Mpakani
Bondeni
Forodhani
Kemwita Wahende
Nyamorege
Kanisani
Gwitanka
Kanisani
Nyatoraha
References
Populated places in Mara Region
Tarime District |
https://en.wikipedia.org/wiki/University%20of%20Texas%20at%20Brownsville%20College%20of%20Science%2C%20Mathematics%2C%20and%20Technology | The College of Science, Mathematics, and Technology (abbreviated as CSMT) was the science college of the former (1992-2015) University of Texas at Brownsville. It consisted of six academic departments. The six departments employ diverse faculty members - many of whom are leading experts in the fields - who have received funding from a variety of funding agencies, including the National Science Foundation, the National Institutes of Health, the Department of Education, and the Department of Defense, among others. The average active ongoing external funding is about 25-30 million dollars. In 2002 the Center for Gravitational Wave Astronomy (CGWA) research center was founded to help "develop excellence in research and education in areas related to gravitational wave astronomy."
CSMT had partnership agreements for scientific collaboration and students exchange with universities in Europe, Asia and Australia.As of 2012, the college hosted more than 1000 students enrolled in twenty-eight undergraduate and seven graduate programs. The programs offer a range of degree plans from certificates and associate degrees up to cooperative Ph.D. degrees with University of Texas at San Antonio. The college hosts annual national/international conferences and workshops in discrete geometry and gravitational waves among others. In 2012, CSMT initiated its own cohort program and student advisory council.
Departments
Department of Biological Sciences
The Department of Biological Sciences at the University of Texas at Brownsville undertakes teaching, research, and community service. The department offers courses that cover a range of biological topics at both the undergraduate and graduate levels. Current research interests cover a broad range of taxonomic groups (e.g. all things aquatic) to a variety of ecosystems (e.g., coastal marine, subtropical, thorn scrub, and freshwater).
Bachelor's Degrees
Biology
Biology – 8th-12th Grade Teaching
Graduate Degrees
Master of Science in Biology
Master of Science in Interdisciplinary Studies concentration in Biology
Department of Chemistry and Environmental Sciences
The Department of Chemistry and Environmental Sciences at the University of Texas at Brownsville undertakes teaching and research. Current research projects include wetland restoration at the Bahia Grande Unit of Laguna Atascosa National Wildlife Refuge, artificial reef monitoring in the Gulf of Mexico, and the impacts of the US-Mexico border fence. Students work with organic molecules, assembling them at the thicknesses of a single molecule as well as nanotechnology. The department has also looked into the recent swine flu epidemic, and work on furthered understanding of how indigenous medicinal plants used in the US-Mexico Border region may be used in the treatment of diabetes.
Bachelor's Degrees
Chemistry
Environmental Sciences
Chemistry – 8th-12th Grade Teaching
Environmental Sciences – 8th-12th Grade Teaching
Department of Computer and In |
https://en.wikipedia.org/wiki/Singular%20integral%20operators%20on%20closed%20curves | In mathematics, singular integral operators on closed curves arise in problems in analysis, in particular complex analysis and harmonic analysis. The two main singular integral operators, the Hilbert transform and the Cauchy transform, can be defined for any smooth Jordan curve in the complex plane and are related by a simple algebraic formula. In the special case of Fourier series for the unit circle, the operators become the classical Cauchy transform, the orthogonal projection onto Hardy space, and the Hilbert transform a real orthogonal linear complex structure. In general the Cauchy transform is a non-self-adjoint idempotent and the Hilbert transform a non-orthogonal complex structure. The range of the Cauchy transform is the Hardy space of the bounded region enclosed by the Jordan curve. The theory for the original curve can be deduced from that of the unit circle, where, because of rotational symmetry, both operators are classical singular integral operators of convolution type. The Hilbert transform satisfies the jump relations of Plemelj and Sokhotski, which express the original function as the difference between the boundary values of holomorphic functions on the region and its complement. Singular integral operators have been studied on various classes of functions, including Hölder spaces, Lp spaces and Sobolev spaces. In the case of L2 spaces—the case treated in detail below—other operators associated with the closed curve, such as the Szegő projection onto Hardy space and the Neumann–Poincaré operator, can be expressed in terms of the Cauchy transform and its adjoint.
Operators on the unit circle
If f is in L2(T), then it has a Fourier series expansion
Hardy space H2(T) consists of the functions for which the negative coefficients vanish, an = 0 for n < 0. These are precisely the square-integrable functions that arise as boundary values of holomorphic functions in the unit disk |z| < 1. Indeed, f is the boundary value of the function
in the sense that the functions
defined by the restriction of F to the concentric circles |z| = r, satisfy
The orthogonal projection P of L2(T) onto H2(T) is called the Szegő projection. It is a bounded operator on L2(T) with operator norm 1.
By Cauchy's theorem
Thus
When r equals 1, the integrand on the right hand side has a singularity at θ = 0. The truncated Hilbert transform is defined by
where δ = |1 – eiε|. Since it is defined as convolution with a bounded function, it is a bounded operator on L2(T). Now
If f is a polynomial in z then
By Cauchy's theorem the right hand side tends to 0 uniformly as ε, and hence δ, tends to 0. So
uniformly for polynomials. On the other hand, if u(z) = z it is immediate that
Thus if f is a polynomial in z−1 without constant term
uniformly.
Define the Hilbert transform on the circle by
Thus if f is a trigonometric polynomial
uniformly.
It follows that if f is any L2 function
in the L2 norm.
This is a consequence of the result for trigonometric |
https://en.wikipedia.org/wiki/Tibor%20Nagy%20%28footballer%2C%20born%201991%29 | Tibor Nagy (born 14 August 1991) is a Hungarian football player who plays for Monor.
Club statistics
Updated to games played as of 7 February 2022.
References
External links
Profile at HLSZ
1991 births
Living people
Footballers from Nyíregyháza
Hungarian men's footballers
Hungary men's youth international footballers
Men's association football defenders
MTK Budapest FC players
Szigetszentmiklósi TK footballers
Újpest FC players
Diósgyőri VTK players
III. Kerületi TVE footballers
Monori SE players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/Rich%C3%A1rd%20Horv%C3%A1th | Richárd Horváth (born 11 May 1992, in Budapest) is a Hungarian striker player who currently plays for Újpest FC.
Club statistics
Updated to games played as of 1 June 2014.
External links
Nemzeti sport
HLSZ
Living people
1992 births
Footballers from Budapest
Hungarian men's footballers
Men's association football forwards
Újpest FC players
Pápai FC footballers
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/Gianni%20Pelletier | Giovanni "Gianni" Pelletier is an Italian former professional Grand Prix motorcycle racer.
Career statistics
By season
References
External links
Profile on motogp.com
Living people
1954 births
Italian motorcycle racers
350cc World Championship riders
500cc World Championship riders
Sportspeople from Rome |
https://en.wikipedia.org/wiki/Allen%20Tannenbaum | Allen Robert Tannenbaum (born January 25, 1953) is an is an American applied mathematician who is presently the Distinguished Professor of Computer Science and Applied Mathematics & Statistics at the State University of New York at Stony Brook. He is also Visiting Investigator of Medical Physics at Memorial Sloan Kettering Cancer Center in New York City. He has held a number of other positions in the United States, Israel, and Canada including the Bunn Professorship of Electrical and Computer Engineering and Interim Chair, and Senior Scientist at the Comprehensive Cancer Center at the University of Alabama, Birmingham. He received his B.A. from Columbia University in 1973 and Ph.D. with thesis advisor Heisuke Hironaka at the Harvard University in 1976.
Tannenbaum has done research in numerous areas including robust control, computer vision, and biomedical imaging, having almost 500 publications. He pioneered the field of robust control with the solution of the gain margin and phase margin problems using techniques from Nevanlinna–Pick interpolation theory, which was the first H-infinity type control problem solved. Tannenbaum used techniques from elliptic curves to show that the reachability does not imply pole assignability for systems defined over polynomial rings in two or more variables over an arbitrary field. He pioneered the use of partial differential equations in computer vision and biomedical imaging co-inventing with Guillermo Sapiro an affine-invariant heat equation for image enhancement. Tannenbaum further formulated a new approach to optimal mass transport (Monge-Kantorovich) theory in joint work with Steven Haker and Sigurd Angenent. In recent work, he has developed techniques using graph curvature ideas for analyzing the robustness of complex networks.
His work has won several awards including IEEE Fellow in 2008, O. Hugo Schuck Award of the American Automatic Control Council in 2007 (shared with S. Dambreville and Y. Rathi), and the George Taylor Award for Distinguished Research from the University of Minnesota in 1997. He has given numerous plenary talks at major conferences including the Society for Industrial and Applied Mathematics (SIAM) Conference on Control in 1998, IEEE Conference on Decision and Control of the IEEE Control Systems Society in 2000, and the International Symposium on the Mathematical Theory of Networks and Systems (MTNS) in 2012. He is also well known as one of the authors of the textbook Feedback Control Theory (with John Doyle and Bruce Francis), which is currently a standard introduction to robust control at the graduate level.
His wife Rina Tannenbaum is a chemist and his son Emmanuel David Tannenbaum was a biophysicist and applied mathematician.
Georgia Tech/Technion employment controversy
In 2011 an audit by Georgia Tech accused professors Allen Tannenbaum and his wife Rina Tannenbaum that they violated Georgia Institute of Technology and State policies by working simultaneously at Georgia Tech |
https://en.wikipedia.org/wiki/Sukhrob%20Khamidov | Sukhrob Hamidov (born 14 August 1975) is a retired Tajikistan footballer who played as a forward.
Career statistics
International
Statistics accurate as of match played 11 September 2015
Honours
Club
Varzob Dushanbe
Tajik League (2): 1998, 1999
Tajik Cup (2): 1998, 1999
Regar-TadAZ
Tajik League (2): 2004, 2007
Tajik Cup (1): 2005
Individual
Tajik League Top Goalscorer 2004: 33
Tajik League Top Goalscorer 2007: 21
References
External links
1975 births
Living people
Tajikistani men's footballers
Tajikistani expatriate men's footballers
Tajikistan men's international footballers
Expatriate men's footballers in Kazakhstan
Tajikistani expatriate sportspeople in Kazakhstan
Expatriate men's footballers in Belarus
FC Shakhtyor Soligorsk players
Men's association football forwards
Tajikistan Higher League players |
https://en.wikipedia.org/wiki/Irreligion%20in%20Brazil | Irreligion in Brazil has increased in the last few decades. In the 2010 census, 8% of the population identified as "irreligious". Since 1970, the Brazilian Institute of Geography and Statistics has included sem religião (Portuguese for no religion) as a self-description option in their decennial census, for people who do not consider themselves members of any specific religion, including non-affiliated theists and deists. In the 2010 census, 8.0% of the population declared themselves "irreligious".
The Constitution grants freedom of religion and thought to its citizens (Art. 5, VI). In 2008, the Brazilian Association of Atheists and Agnostics was founded; it promotes secularism and supports irreligious victims of prejudice.
Although the Federal Constitution guarantees religious tolerance to all its citizens (see article 5, item VI), it expressly prohibits all entities that make up the Federation to found and finance public cults and state churches controlled and coordinated by the Government – (see article 19, I), since until now the Brazilian State recognizes the "peculiar character" of the Catholic Church under the other religions in its legal system (see Article 16 of Decree 7107/2010), which is why the law recognizes the Virgin Mary, the mother of Jesus, as the "patroness of Brazil" (see Article 1 of Law 6,802 / 1980); the Constitution is sworn "under the protection of God" (see Preamble of the Federal Constitution); Catholic holidays (such as the day of Our Lady of Aparecida and the day of our Lord's birth) are recognized as national holidays by law (see Law 10.607 / 2002, Law 6.802 / 1980); the Catholic religion has an exclusive status for itself (see Decree 7107/2010); cities and states bear the name of Catholic saints; Catholic statues are exposed in public offices; the expression "God be praised" is present in all Real notes; and religious teaching exclusively Catholic in public schools is permitted in the country (see ADI 4439).
A 2009 survey showed that atheists were the most hated demographic group in Brazil, among several other minorities polled. According to the survey, 17% of the interviewees stated they felt either hatred or repulsion for atheists, while 25% felt antipathy and 29% were indifferent.
In 2022 a Datafolha survey found that non-religious people account for 25% of the Brazilian youth (aged between 16 and 24 year-old) nationwide. In the country's two largest cities of São Paulo and Rio de Janeiro the non-religious represent 30% and 34% of the people of the same age respectively, outnumbering evangelical, catholic and other religions youth. According to professors Ricardo Mariano and Silvia Fernandes there's a growing trend in Brazil of religious disaffiliation among young people because of social liberalization and their individualistic beliefs often seen as conflicting with often harsh moral dogmas, strict codes of conduct and the increasing politicization of religions by the churches, especially the evangelicals.
|
https://en.wikipedia.org/wiki/1992%E2%80%9393%20Galatasaray%20S.K.%20season | The 1992–93 season was Galatasaray's 89th in existence and the 35th consecutive season in the 1. Lig. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
Players in / out
In
Out
1. Lig
Standings
Matches
Türkiye Kupası
Kick-off listed in local time (EET)
6th round
1/4 final
1/2 final
Final
UEFA Cup
1st round
2nd round
3rd round
Friendly Matches
Kick-off listed in local time (EET)
TSYD Kupası
Attendance
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Galatasaray
Turkish football championship-winning seasons
1990s in Istanbul
Galatasaray Sports Club 1992–93 season |
https://en.wikipedia.org/wiki/List%20of%20Champions%20League%20Twenty20%20records%20and%20statistics | This is a list of statistics and records of the Champions League Twenty20, a Twenty20 cricket competition.
Team records
Results summary
The table below provides an overview of the performances of teams over past editions of the Champions League Twenty20. League and group stages are considered equivalent.
Note: List includes qualifier results also.
Tie+W and Tie+L indicates matches tied and then won or lost by "Super Over"
Apprd = No. of times teams participated in the tournament
The above table is sorted by no. of matches, then no. of wins, less no. of defeats, win%, no. of appearances and then by alphabetical order
Source: Results Summary
Highest totals
Full Table on Cricinfo
Lowest totals
Full Table on Cricinfo
Batting Records
Most runs
Full Table on Cricinfo
Highest individual score
Full Table on Cricinfo
Most sixes
Full Table on Cricinfo
Most Fifties
Full Table on Cricinfo
Most hundreds
Note: Team in brackets represents for which the batsman scored century
Full Table on Cricinfo
Best strike rates
Minimum 100 balls faced
Full Table on Cricinfo
Highest averages
Minimum of 10 innings
Full Table on Cricinfo
Bowling Records
Most wickets
Full Table on Cricinfo
Best bowling figures in an innings
Full Table on Cricinfo
Best economy rates
Minimum 10 overs bowled
Full Table on Cricinfo
Hat-tricks
Wicketkeeping and Fielding records
Most dismissals
Full Table on Cricinfo
Most catches (fielder)
Full Table on Cricinfo
Miscellaneous records
External links
Champions League Twenty20 records on ESPN CricInfo
References
records and statistics
Cricket records and statistics
Champions League Twenty20 records and statistics |
https://en.wikipedia.org/wiki/Xin%20Zhou | Xin Zhou is a mathematician known for his contributions in scattering theory, integrable systems, random matrices and Riemann–Hilbert problems.
He is Professor Emeritus of Mathematics at Duke University. Zhou had obtained M.Sc. from the University of the Chinese Academy of Sciences in 1982 and then got his Ph.D. in 1988 from the University of Rochester. He received the Pólya prize in 1998 and was awarded with the Guggenheim Fellowship in 1999. He is most well known for his work with Percy Deift on the steepest descent method for oscillatory Riemann–Hilbert problems.
References
20th-century births
Living people
Mathematical analysts
Duke University faculty
University of Rochester alumni
American people of Chinese descent
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Shinichi%20Mochizuki | is a Japanese mathematician working in number theory and arithmetic geometry. He is one of the main contributors to anabelian geometry. His contributions include his solution of the Grothendieck conjecture in anabelian geometry about hyperbolic curves over number fields. Mochizuki has also worked in Hodge–Arakelov theory and p-adic Teichmüller theory. Mochizuki developed inter-universal Teichmüller theory, which has attracted attention from non-mathematicians due to claims it provides a resolution of the abc conjecture.
Biography
Early life
Shinichi Mochizuki was born to parents Kiichi and Anne Mochizuki. When he was five years old, Shinichi Mochizuki and his family left Japan to live in the United States. His father was Fellow of the Center for International Affairs and Center for Middle Eastern Studies at Harvard University (1974–76). Mochizuki attended Phillips Exeter Academy and graduated in 1985.
Mochizuki entered Princeton University as an undergraduate student at the age of 16 and graduated as salutatorian with an A.B. in mathematics in 1988. He completed his senior thesis, titled "Curves and their deformations," under the supervision of Gerd Faltings.
He remained at Princeton for graduate studies and received his Ph.D. in mathematics in 1992 after completing his doctoral dissertation, titled "The geometry of the compactification of the Hurwitz scheme," also under the supervision of Faltings.
After his graduate studies, Mochizuki spent two years at Harvard University and then in 1994 moved back to Japan to join the Research Institute for Mathematical Sciences (RIMS) at Kyoto University in 1992, and was promoted to professor in 2002.
Career
Mochizuki proved Grothendieck's conjecture on anabelian geometry in 1996. He was an invited speaker at the International Congress of Mathematicians in 1998. In 2000–2008 he discovered several new theories including the theory of frobenioids, mono-anabelian geometry and the etale theta theory for line bundles over tempered covers of the Tate curve.
On August 30, 2012 Mochizuki released four preprints, whose total size was about 500 pages, that developped inter-universal Teichmüller theory and applied it in an attempt to prove several very famous problems in Diophantine geometry. These include the strong Szpiro conjecture, the hyperbolic Vojta conjecture and the abc conjecture over every number field. In September 2018, Mochizuki posted a report on his work by Peter Scholze and Jakob Stix asserting that the third preprint contains an irreparable flaw; he also posted several documents containing his rebuttal of their criticism. The majority of number theorists have found Mochizuki's preprints very difficult to follow and have not accepted the conjectures as settled, although there are a few prominent exceptions, including Go Yamashita, Ivan Fesenko, and Yuichiro Hoshi, who vouch for the work and have written expositions of the theory.
On April 3, 2020, two Japanese mathematicians, Masaki Kashi |
https://en.wikipedia.org/wiki/Daniel%20Buchanan | Daniel Buchanan may refer to:
Daniel Buchanan (Shortland Street), a character from the soap opera Shortland Street
Daniel Buchanan (mathematician) (1880–1950), Canadian mathematics and astronomy professor |
https://en.wikipedia.org/wiki/Umed%20Khabibulloyev | Umed Khabibulloyev (born 12 November 1978) is a Tajikistani footballer who plays as a defender most recently for FC Istiklol and the Tajikistan national football team.
Career statistics
International
Statistics accurate as of match played 6 September 2011
Honors
Varzob Dushanbe
Tajik League (3): 1998, 1999, 2000
Tajik Cup (2): 1998, 1999
Khujand
Tajik Cup (2): 2008
Istiklol
Tajik League (2): 2010, 2011
Tajik Cup (1): 2010
References
External links
1978 births
Living people
Tajikistani men's footballers
Tajikistan men's international footballers
Men's association football defenders |
https://en.wikipedia.org/wiki/Mahmadali%20Sodikov | Mahmadali Sodikov (born 20 March 1984) is a Tajikistani footballer who plays as a forward for CSKA Pamir Dushanbe and the Tajikistan national football team.
Career statistics
Club
International
Statistics accurate as of match played 21 March 2013
Honors
Khujand
Tajik Cup (1): 2008
Istiklol
Tajik League (1): 2011
AFC President's Cup (1): 2012
References
External links
1984 births
Living people
Tajikistani men's footballers
FC Khatlon players
Men's association football forwards
Tajikistan Higher League players
Tajikistan men's international footballers |
https://en.wikipedia.org/wiki/G.%20V.%20Belyi | Gennadii Vladimirovich Belyi (1951–2001, , ) was a Soviet, Ukrainian, and Russian mathematician, known for Belyi's theorem on the representation of algebraic curves as Riemann surfaces and for the Belyi functions arising in that theorem.
Belyi was born on February 2, 1951, in Magnitogorsk, Russia, then part of the Soviet Union. His family moved from there to Ukraine, and he began his studies at the Kiev Physics and Mathematics School but moved from there to Moscow State University. After completing his studies in 1973 he returned to Ukraine, working in Kiev and then Lviv. He became a graduate student at the Steklov Institute of Mathematics in Moscow in 1975, and studied there under the supervision of Igor Shafarevich, earning a candidate degree in 1979. He then took a faculty position at Vladimir State University, in Vladimir, Russia, where he remained for the remainder of his career. He died on January 29, 2001, in Vladimir.
Belyi won a prize of the Moscow Mathematical Society in 1981, and was an invited speaker at the International Congress of Mathematicians in 1986.
References
1951 births
2001 deaths
Ukrainian mathematicians |
https://en.wikipedia.org/wiki/Near-horizon%20metric | The near-horizon metric (NHM) refers to the near-horizon limit of the global metric of a black hole. NHMs play an important role in studying the geometry and topology of black holes, but are only well defined for extremal black holes. NHMs are expressed in Gaussian null coordinates, and one important property is that the dependence on the coordinate is fixed in the near-horizon limit.
NHM of extremal Reissner–Nordström black holes
The metric of extremal Reissner–Nordström black hole is
Taking the near-horizon limit
and then omitting the tildes, one obtains the near-horizon metric
NHM of extremal Kerr black holes
The metric of extremal Kerr black hole () in Boyer–Lindquist coordinates can be written in the following two enlightening forms,
where
Taking the near-horizon limit
and omitting the tildes, one obtains the near-horizon metric (this is also called extremal Kerr throat )
NHM of extremal Kerr–Newman black holes
Extremal Kerr–Newman black holes () are described by the metric
where
Taking the near-horizon transformation
and omitting the tildes, one obtains the NHM
NHMs of generic black holes
In addition to the NHMs of extremal Kerr–Newman family metrics discussed above, all stationary NHMs could be written in the form
where the metric functions are independent of the coordinate r, denotes the intrinsic metric of the horizon, and are isothermal coordinates on the horizon.
Remark: In Gaussian null coordinates, the black hole horizon corresponds to .
See also
Extremal black hole
Reissner–Nordström metric
Kerr metric
Kerr–Newman metric
References
General relativity
Black holes |
https://en.wikipedia.org/wiki/Power%20residue%20symbol | In algebraic number theory the n-th power residue symbol (for an integer n > 2) is a generalization of the (quadratic) Legendre symbol to n-th powers. These symbols are used in the statement and proof of cubic, quartic, Eisenstein, and related higher reciprocity laws.
Background and notation
Let k be an algebraic number field with ring of integers that contains a primitive n-th root of unity
Let be a prime ideal and assume that n and are coprime (i.e. .)
The norm of is defined as the cardinality of the residue class ring (note that since is prime the residue class ring is a finite field):
An analogue of Fermat's theorem holds in If then
And finally, suppose These facts imply that
is well-defined and congruent to a unique -th root of unity
Definition
This root of unity is called the n-th power residue symbol for and is denoted by
Properties
The n-th power symbol has properties completely analogous to those of the classical (quadratic) Legendre symbol ( is a fixed primitive -th root of unity):
In all cases (zero and nonzero)
Relation to the Hilbert symbol
The n-th power residue symbol is related to the Hilbert symbol for the prime by
in the case coprime to n, where is any uniformising element for the local field .
Generalizations
The -th power symbol may be extended to take non-prime ideals or non-zero elements as its "denominator", in the same way that the Jacobi symbol extends the Legendre symbol.
Any ideal is the product of prime ideals, and in one way only:
The -th power symbol is extended multiplicatively:
For then we define
where is the principal ideal generated by
Analogous to the quadratic Jacobi symbol, this symbol is multiplicative in the top and bottom parameters.
If then
Since the symbol is always an -th root of unity, because of its multiplicativity it is equal to 1 whenever one parameter is an -th power; the converse is not true.
If then
If then is not an -th power modulo
If then may or may not be an -th power modulo
Power reciprocity law
The power reciprocity law, the analogue of the law of quadratic reciprocity, may be formulated in terms of the Hilbert symbols as
whenever and are coprime.
See also
Modular_arithmetic#Residue_class
Quadratic_residue#Prime_power_modulus
Artin symbol
Gauss's lemma
Notes
References
Algebraic number theory |
https://en.wikipedia.org/wiki/Gino%20Loria | Gino Benedetto Loria (19 May 1862, Mantua – 30 January 1954, Genoa) was a Jewish-Italian mathematician and historian of mathematics.
Loria studied mathematics in Mantua, Turin, and Pavia and received his doctorate in 1883 from the University of Turin under the direction of Enrico D'Ovidio. For several years he was D'Ovidio's assistant in Turin. Starting in 1886 he became, as a result of winning a then-customary competition, Professor for Algebra and Analytic Geometry at the University of Genoa, where he stayed for the remainder of his career.
Loria did research on projective geometry, special curves and rational transformations in algebraic geometry, and elliptic functions. At the International Congress of Mathematicians he was an invited speaker in 1897 in Zürich, 1904 in Heidelberg, in 1908 in Rome, in 1912 in Cambridge, UK, in 1924 in Toronto, in 1928 in Bologna, and in 1932 in Zürich.
In 1897 he became editor of Bolletino di Bibliografia e Storia delle Science Matematiche. In 1916 he published a guide to the study of history of mathematics. A reviewer noted
The amount of information given is really remarkable, and it is well up to date; the author, too, has not shrunk from the disagreeable duty of pointing out works ... which must be used with caution.
Loria wrote a history of mathematics and was especially concerned with the history of mathematics in Italy and among the ancient Greeks.
After the German seized control of Italy in World War II, Waldensians helped Loria (endangered as a Jew) hide in Torre Pellice.
Loria was elected to the Accademia dei Lincei and the Turin Academy of Sciences. An asteroid (27056 Ginoloria) is named after him.
Books
Il passato ed il presente delle principali teorie geometriche, storiae e bibliografia; (1896, 2nd edn., 1907, 3rd edn.; Torino: Carlo Clausen);, 1931, 4th edn., Padova: A. Milani
Spezielle algebraische und transscendente ebene kurven. Theorie und Geschichte., Leipzig: B. G. Teubner, 1902.
Curve sghembe speciali algebriche e trascendenti, 2 vols., Bologna, Zanichelli 1925
Le scienze esatte nell' antica Grecia, Mailand, U. Hoepli, 1914
Storia della Geometria Descrittiva dalle Origini sino ai Giorni Nostri. (1921, Milano: Ulrico Hoepli)
Storia delle matematiche dall'alba della civiltà al tramonto del secolo XIX, Mailand, U. Hoepli, 1950, 1st edn. Turin 1929 to 1933 in three vols.
Vorlesungen über Darstellende Geometrie, 2 vols., Teubner 1907
Die hauptsachlichsten Theorien der Geometrie in ihrer fruheren und heutigen Entwickelung, Teubner 1907
with G. Kohn Spezielle ebene algebraische Kurven, Enzyklopädie der mathematischen Wissenschaften
Spezielle ebene algebraische Kurven von höherer als vierter Ordnung, Enzyklopädie der mathematischen Wissenschaften
Articles
"The Philosophical Magazine and History of Mathematics" (1916) Mathematical Gazette 8:325–9.
La scienza nel secolo 18. In: Scientia, 45, 1929, pp. 1–12.
Lo sviluppo delle matematiche pure durante il secolo 19. Parte 1: La Geo |
https://en.wikipedia.org/wiki/Eric%20Gasana | Eric Gasana (born May 15, 1986) is a Rwandan footballer who plays as a right-back. He participated at 2012 Africa Cup of Nations with the Rwanda national team.
Career statistics
Scores and results list Rwanda's goal tally first, score column indicates score after each Gasana goal.
References
External links
Living people
1986 births
Rwandan men's footballers
Men's association football fullbacks
Rwanda men's international footballers
Footballers from Kinshasa
2011 African Nations Championship players
Rwanda men's A' international footballers |
https://en.wikipedia.org/wiki/Luan%20Garcia | Luan Garcia Teixeira (born 10 May 1993), simply known as Luan, is a Brazilian footballer who plays as a centre back for Palmeiras.
Career statistics
Honours
Club
Vasco da Gama
Campeonato Carioca: 2015, 2016
Palmeiras
Campeonato Brasileiro Série A: 2018, 2022
Campeonato Paulista: 2020, 2022, 2023
Copa do Brasil: 2020
Copa Libertadores: 2020, 2021
Recopa Sudamericana: 2022
Supercopa do Brasil: 2023
International
Brazil
Olympic Gold Medal: 2016
Brazil U20
8 Nations International Tournament: 2012
Individual
Campeonato Carioca Team of the year: 2014, 2015, 2016
Campeonato Brasileiro Série B Best Defender: 2016
References
1993 births
Living people
Sportspeople from Vitória, Espírito Santo
Brazilian men's footballers
Men's association football defenders
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
CR Vasco da Gama players
Sociedade Esportiva Palmeiras players
Copa Libertadores-winning players
Brazil men's under-20 international footballers
Footballers at the 2015 Pan American Games
Pan American Games bronze medalists for Brazil
Olympic footballers for Brazil
Footballers at the 2016 Summer Olympics
Olympic gold medalists for Brazil
Olympic medalists in football
Medalists at the 2016 Summer Olympics
Pan American Games medalists in football
Medalists at the 2015 Pan American Games
Footballers from Espírito Santo |
https://en.wikipedia.org/wiki/Eisenstein%20reciprocity | In algebraic number theory Eisenstein's reciprocity law is a reciprocity law that extends the law of quadratic reciprocity and the cubic reciprocity law to residues of higher powers. It is one of the earliest and simplest of the higher reciprocity laws, and is a consequence of several later and stronger reciprocity laws such as the Artin reciprocity law. It was introduced by , though Jacobi had previously announced (without proof) a similar result for the special cases of 5th, 8th and 12th powers in 1839.
Background and notation
Let be an integer, and let be the ring of integers of the m-th cyclotomic field where is a
primitive m-th root of unity.
The numbers are units in (There are other units as well.)
Primary numbers
A number is called primary if it is not a unit, is relatively prime to , and is congruent to a rational (i.e. in ) integer
The following lemma shows that primary numbers in are analogous to positive integers in
Suppose that and that both and are relatively prime to Then
There is an integer making primary. This integer is unique
if and are primary then is primary, provided that is coprime with .
if and are primary then is primary.
is primary.
The significance of
which appears in the definition is most easily seen when
is a prime. In that case
Furthermore, the prime ideal
of
is totally ramified in
and the ideal
is prime of degree 1.Lemmermeyer, prop. 3.1
m-th power residue symbol
For the m-th power residue symbol for is either zero or an m-th root of unity:
It is the m-th power version of the classical (quadratic, m = 2) Jacobi symbol (assuming and are relatively prime):
If and then
If then is not an m-th power
If then may or may not be an m-th power
Statement of the theorem
Let be an odd prime and an integer relatively prime to Then
First supplement
Second supplement
Eisenstein reciprocity
Let be primary (and therefore relatively prime to ), and assume that is also relatively prime to . Then
Proof
The theorem is a consequence of the Stickelberger relation.
gives a historical discussion of some early reciprocity laws, including a proof of Eisenstein's law using Gauss and Jacobi sums that is based on Eisenstein's original proof.
Generalization
In 1922 Takagi proved that if is an arbitrary algebraic number field containing the -th roots of unity for a prime , then Eisenstein's law for -th powers holds in
Applications
First case of Fermat's Last Theorem
Assume that
is an odd prime, that
for pairwise relatively prime integers
(i.e. in
)
and that
This is the first case of Fermat's Last Theorem. (The second case is when ) Eisenstein reciprocity can be used to prove the following theorems
(Wieferich 1909) Under the above assumptions,
The only primes below 6.7×1015 that satisfy this are 1093 and 3511. See Wieferich primes for details and current records.
(Mirimanoff 1911) |
https://en.wikipedia.org/wiki/Suicide%20in%20Guyana | Suicide in Guyana is a serious social problem, as Guyana is ranked worst in suicides per capita worldwide among sovereign nations.
Statistics
Domestic data on suicide in Guyana is limited, as the country's available health literature is focused mainly on infectious tropical diseases. A 2012 World Health Organization report indicated that Guyana had a suicide rate of 44.2 per 100,000 people, and that for every single female suicide, there were 3.2 male suicides. By comparison, neighboring Suriname had a suicide rate of 27.8 per 100,000, and Venezuela's rate was 2.6 per 100,000.
Sucides appear to be significantly higher among Indo-Guyanese than other ethnic groups, accounting for around 80% of total suicides. Most of suicides result from poisioning, primarily from agricultural pesticides.
Legal issues
Attempts by the government to address the issue have been stymied by political divisions. A bill was voted down in 2016 which would have amended the country's laws in order to decriminalize suicide, implemented the 2014 Mental Health Strategic Plan and a 5-year National Suicide Prevention Plan which were both crafted by the previous government, and allocated funds to treat mental health and suicide as national priorities. Speakers for the parliamentary majority argued that the manner in which the legislation was framed both politicized and trivialized the issue.
See also
Health in Guyana
Jonestown massacre, the largest mass suicide in the history
List of countries by suicide rate
References
Health in Guyana |
https://en.wikipedia.org/wiki/Strangulated%20graph | In graph theoretic mathematics, a strangulated graph is a graph in which deleting the edges of any induced cycle of length greater than three would disconnect the remaining graph. That is, they are the graphs in which every peripheral cycle is a triangle.
Examples
In a maximal planar graph, or more generally in every polyhedral graph, the peripheral cycles are exactly the faces of a planar embedding of the graph, so a polyhedral graph is strangulated if and only if all the faces are triangles, or equivalently it is maximal planar. Every chordal graph is strangulated, because the only induced cycles in chordal graphs are triangles, so there are no longer cycles to delete.
Characterization
A clique-sum of two graphs is formed by identifying together two equal-sized cliques in each graph, and then possibly deleting some of the clique edges. For the version of clique-sums relevant to strangulated graphs, the edge deletion step is omitted. A clique-sum of this type between two strangulated graphs results in another strangulated graph, for every long induced cycle in the sum must be confined to one side or the other (otherwise it would have a chord between the vertices at which it crossed from one side of the sum to the other), and the disconnected parts of that side formed by deleting the cycle must remain disconnected in the clique-sum. Every chordal graph can be decomposed in this way into a clique-sum of complete graphs, and every maximal planar graph can be decomposed into a clique-sum of 4-vertex-connected maximal planar graphs.
As show, these are the only possible building blocks of strangulated graphs: the strangulated graphs are exactly the graphs that can be formed as clique-sums of complete graphs and maximal planar graphs.
See also
Line perfect graph, a graph in which every odd cycle is a triangle
References
.
Graph families
Planar graphs |
https://en.wikipedia.org/wiki/P-adic%20Teichm%C3%BCller%20theory | In mathematics, p-adic Teichmüller theory describes the "uniformization" of p-adic curves and their moduli, generalizing the usual Teichmüller theory that describes the uniformization of Riemann surfaces and their moduli. It was introduced and developed by .
The first problem is to reformulate the Fuchsian uniformization of a complex Riemann surface (an isomorphism from the upper half plane to a universal covering space of the surface) in a way that makes sense for p-adic curves. The existence of a Fuchsian uniformization is equivalent to the existence of a canonical indigenous bundle over the Riemann surface: the unique indigenous bundle that is invariant under complex conjugation and whose monodromy representation is quasi-Fuchsian. For p-adic curves the analogue of complex conjugation is the Frobenius endomorphism, and the analogue of the quasi-Fuchsian condition is an integrality condition on the indigenous line bundle. So p-adic Teichmüller theory, the p-adic analogue the Fuchsian uniformization of Teichmüller theory, is the study of integral Frobenius invariant indigenous bundles.
See also
Inter-universal Teichmüller theory
Anabelian geometry
References
Algebraic geometry
Number theory
p-adic numbers |
https://en.wikipedia.org/wiki/1993%E2%80%9394%20Galatasaray%20S.K.%20season | The 1993–94 season was Galatasaray's 90th in existence and the 36th consecutive season in the 1. Lig. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
Players in / out
In
Out
1. Lig
Standings
Matches
Türkiye Kupası
Kick-off listed in local time (EET)
6th round
1/4 final
1/2 final
Final
UEFA Champions League
1st round
2nd round
Group stage
Süper Kupa-Cumhurbaşkanlığı Kupası
Kick-off listed in local time (EET)
1993
1994
Friendly Matches
Kick-off listed in local time (EET)
TSYD Kupası
Attendance
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Galatasaray
Turkish football championship-winning seasons
1990s in Istanbul
Galatasaray Sports Club 1993–94 season |
https://en.wikipedia.org/wiki/Indigenous%20bundle | In mathematics, an indigenous bundle on a Riemann surface is a fiber bundle with a flat connection associated to some complex projective structure. Indigenous bundles were introduced by . Indigenous bundles for curves over p-adic fields were introduced by in his study of p-adic Teichmüller theory.
References
Riemann surfaces |
https://en.wikipedia.org/wiki/Vittorio%20Gr%C3%BCnwald | Vittorio Grünwald (Verona, Italy, 13 June 1855 – Florence, Italy, March 1943) was an Italian professor of mathematics and German language. His father Guglielmo (Willhelm) Grünwald (son of Aronne and Regina) was Hungarian, his mother Fortuna Marini (daughter of Mandolino Marini and Ricca Bassani) was Italian. In 1861 he moved to Hungary with his family, then came back in 1877 to Verona, later in November 1885 they moved to Brescia, and then to Venice. He studied at the Technische Universität Wien, where he graduated in mathematics. After coming back to Italy, he taught mathematics and German language in several schools (such as in Livorno and Venice), and then he settled in Florence.
He married Dora Olschky, born in Berlin, and had three kids: Marta Grünwald, Beniamino (Benno) Grünwald, and Emanuele Grünwald.
He was a librarian and a teacher at the Rabbinical College of Florence. He died at 88 in Florence, a few months before Nazi's persecutions hit Jewish families in Central Italy. He published several contributions in mathematics, including a seminal work on negative numerical bases. He also published an Italian-German vocabulary.
References
Vittorio Grünwald. Saggio di aritmetica non decimale con applicazioni del calcolo duodecima/e e trigesimale a problemi sui numeri complessi (Verona, 1884)
Vittorio Grünwald. Intorno all'aritmetica dei sistemi numerici a base negativa con particolare riguardo al sistema numerico a base negativo-decimale per lo studio delle sue analogie coll'aritmetica ordinaria (decimale), Giornale di Matematiche di Battaglini (1885), 203-221, 367
Vittorio Grünwald and Garibaldi Menotti Gatti, Vocabolario delle lingue Italiana e Tedesca. Ed. Belforte.
Gianfranco Di Segni, In ricordo del prof. Vittorio Grünwald, Firenze Ebraica, Anno 25 n. 5, Settembre-Ottobre 2012.
1855 births
1943 deaths
Italian mathematicians
Scientists from Verona |
https://en.wikipedia.org/wiki/Hans-Joachim%20Nastold | Hans-Joachim Nastold (13 July 1929 – 26 January 2004) was a German mathematician, who made notable contributions to algebra and number theory.
Born in Stuttgart, Nastold earned his Abitur in Göppingen. He attended the University of Heidelberg, earning his doctorate in 1957, under supervision of Friedrich Karl Schmidt.
References
External links
1929 births
2004 deaths
20th-century German mathematicians
21st-century German mathematicians
Heidelberg University alumni
Academic staff of the University of Münster |
https://en.wikipedia.org/wiki/Nigel%20Boston | Nigel Boston (born July 20, 1961) is a British-American mathematician, who has made notable contributions to algebraic number theory, group theory, and arithmetic geometry.
He attended Harvard University, earning his doctorate in 1987, under supervision of Barry Mazur. He is a Professor Emeritus at the University of Wisconsin–Madison. In 2012, he became a fellow of the American Mathematical Society.
References
External links
1961 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Harvard University alumni
University of Wisconsin–Madison faculty
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Frobenioid | In arithmetic geometry, a Frobenioid is a category with some extra structure that generalizes the theory of line bundles on models of finite extensions of global fields. Frobenioids were introduced by . The word "Frobenioid" is a portmanteau of Frobenius and monoid, as certain Frobenius morphisms between Frobenioids are analogues of the usual Frobenius morphism, and some of the simplest examples of Frobenioids are essentially monoids.
The Frobenioid of a monoid
If M is a commutative monoid, it is acted on naturally by the monoid N of positive integers under multiplication, with an element n of N multiplying an element of M by n. The Frobenioid of M is the semidirect product of M and N. The underlying category of this Frobenioid is category of the monoid, with one object and a morphism for each element of the monoid. The standard Frobenioid is the special case of this construction when M is the additive monoid of non-negative integers.
Elementary Frobenioids
An elementary Frobenioid is a generalization of the Frobenioid of a commutative monoid, given by a sort of semidirect product of the monoid of positive integers by a family Φ of commutative monoids over a base category D. In applications the category D is sometimes the category of models of finite separable extensions of a global field, and Φ corresponds to the line bundles on these models, and the action of a positive integers n in N is given by taking the nth power of a line bundle.
Frobenioids and poly-Frobenioids
A Frobenioid consists of a category C together with a functor to an elementary Frobenioid, satisfying some complicated conditions related to the behavior of line bundles and divisors on models of global fields. One of Mochizuki's fundamental theorems states that under various conditions a Frobenioid can be reconstructed from the category C. A poly-Frobenioid is an extension of a Frobenioid.
See also
Category theory
Anabelian geometry
Inter-universal Teichmüller theory
References
External links
What is an étale theta function?
Algebraic geometry
Number theory |
https://en.wikipedia.org/wiki/Albanians%20in%20the%20United%20Kingdom | Albanians in the United Kingdom () include immigrants from Albania and ethnic Albanians from Kosovo. According to estimates from the Office for National Statistics, there were 47,000 Albanian-born residents of the United Kingdom in 2019.
History
Albanians in the United Kingdom were first mentioned as merchants and seamen on the coasts of England during the 14th and 15th centuries.
Albanian stradioti mercenaries during the 16th century served the English king in his wars against the Kingdom of Scotland.
The history of modern-day Albanians in the UK began in the early 20th century, when a small group of Albanians arrived in this country. Among them was one of the greatest Albanian intellectuals, Faik Konica, who moved to London and continued to publish the magazine Albania, which he had founded in Brussels. Shortly after World War II, there were about 100 Albanians in Britain.
The 1991 census recorded only 338 Albanians in England. In 1993, the figure had risen to 2,500. Many were young Kosovars who avoided recruiting into the Yugoslav Army, who had sought political asylum. In June 1996, a Supreme Court decision accepted that Kosovo Albanians were persecuted in the former Yugoslavia. This meant that all Kosovo Albanians should be granted residence permits in Britain. After this decision, Britain faced a huge and unexpected influx of Albanians from Kosovo, Albania, the Republic of Macedonia, Montenegro and Serbia. By the end of 1997, around 30,000 Albanians lived in Britain.
Many Albanians are reported to have moved to the UK by pretending to be Kosovans fleeing the Kosovo War.
Demography
A mapping exercise published by the International Organization for Migration in September 2008 states that there were no official estimates of the total number of ethnic Albanians in the UK at the time. The majority of respondents interviewed for the exercise estimated the population to lie between 70,000 and 100,000.
The 2011 Census recorded 13,295 Albanian-born residents in England and 120 in Wales, The censuses of Scotland and Northern Ireland recorded 196 and 55 Albanian-born residents respectively. The census recorded 28,390 Kosovo-born residents (including people all ethnicities) in England and 56 in Wales. The censuses of Scotland and Northern Ireland recorded 215 and 44 Kosovo-born residents respectively. In 2019, the Office for National Statistics estimated that 47,000 people born in Albania and 29,000 people born in Kosovo were resident in the UK.
The 2021 Census recorded 67,957 usual residents of England and 715 of Wales who were born in Albania. In Northern Ireland, the figure was 142. The number of residents of England born in Kosovo was 30,427, with 90 recorded in Wales and 60 in Northern Ireland.
Religious demography
Of the Albanian-born community residing in England and Wales, approximately 34.2% identified as Christian in the 2021 census and around 29.8% as Muslim, with 26.1% specifying "no religion". 9.3% did not provide a response rega |
https://en.wikipedia.org/wiki/Farrell%E2%80%93Markushevich%20theorem | In mathematics, the Farrell–Markushevich theorem, proved independently by O. J. Farrell (1899–1981) and A. I. Markushevich (1908–1979) in 1934, is a result concerning the approximation in mean square of holomorphic functions on a bounded open set in the complex plane by complex polynomials. It states that complex polynomials form a dense subspace of the Bergman space of a domain bounded by a simple closed Jordan curve. The Gram–Schmidt process can be used to construct an orthonormal basis in the Bergman space and hence an explicit form of the Bergman kernel, which in turn yields an explicit Riemann mapping function for the domain.
Proof
Let Ω be the bounded Jordan domain and let Ωn be bounded Jordan domains decreasing to Ω, with Ωn containing the closure of Ωn + 1. By the Riemann mapping theorem there is a conformal mapping fn of Ωn onto Ω, normalised to fix a given point in Ω with positive derivative there. By the Carathéodory kernel theorem fn(z) converges uniformly on compacta in Ω to z. In fact Carathéodory's theorem implies that the inverse maps tend uniformly on compacta to z. Given a subsequence of fn, it has a subsequence, convergent on compacta in Ω. Since the inverse functions converge to z, it follows that the subsequence converges to z on compacta. Hence fn converges to z on compacta in Ω.
As a consequence the derivative of fn tends to 1 uniformly on compacta.
Let g be a square integrable holomorphic function on Ω, i.e. an element of the Bergman space A2(Ω). Define gn on Ωn by gn(z) = g(fn(z))fn'(z). By change of variable
Let hn be the restriction of gn to Ω. Then the norm of hn is less than that of gn. Thus these norms are uniformly bounded. Passing to a subsequence if necessary, it can therefore be assumed that hn has a weak limit in A2(Ω). On the other hand, hn tends uniformly on compacta
to g. Since the evaluation maps are continuous linear functions on A2(Ω), g is the weak limit of hn. On the other hand, by Runge's theorem, hn lies in the closed subspace K of A2(Ω) generated by complex polynomials. Hence g lies in the weak closure of K, which is K itself.
See also
Mergelyan's theorem
Notes
References
Theorems in functional analysis
Operator theory
Theorems in complex analysis |
https://en.wikipedia.org/wiki/Ralph%20Greenberg | Ralph Greenberg (born 1944) is an American mathematician who has made contributions to number theory, in particular Iwasawa theory.
He was born in Chester, Pennsylvania and studied at the University of Pennsylvania, earning a B.A. in 1966, after which he attended Princeton University, earning his doctorate in 1971 under the supervision of Kenkichi Iwasawa.
Greenberg's results include a proof (joint with Glenn Stevens) of the Mazur–Tate–Teitelbaum conjecture as well as a formula for the derivative of a p-adic Dirichlet L-function at (joint with Bruce Ferrero). Greenberg is also well known for his many conjectures. In his PhD thesis, he conjectured that the Iwasawa μ- and λ-invariants of the cyclotomic -extension of a totally real field are zero, a conjecture that remains open as of September 2012. In the 1980s, he introduced the notion of a Selmer group for a p-adic Galois representation and generalized the "main conjectures" of Iwasawa and Barry Mazur to this setting. He has since generalized this setup to present Iwasawa theory as the theory of p-adic deformations of motives. He also provided an arithmetic theory of L-invariants generalizing his aforementioned work with Stevens.
Greenberg was an invited speaker in International Congress of Mathematicians 2010, Hyderabad on the topic of "Number Theory."
In 2012, he became a fellow of the American Mathematical Society.
In the late 1990s and early 2000s, Greenberg publicly disputed NASA conspiracy theorist and pseudoscientist Richard C. Hoagland's mathematical interpretations of the so-called "D&M Pyramid" and surrounding features found on the Cydonia Planitia region of Mars as being conclusive signs of extraterrestrial intelligence and challenged him to a public debate. Hoagland has yet to respond.
References
External links
1944 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Princeton University alumni
University of Washington faculty
Fellows of the American Mathematical Society
Number theorists
People from Chester, Pennsylvania
Mathematicians from Pennsylvania
University of Pennsylvania alumni |
https://en.wikipedia.org/wiki/Mojtaba%20Mobini%20Pour | Mojtaba Mobinipour (; born 25 December 1990) is an Iranian professional footballer.
Career statistics
References
1990 births
Living people
Sportspeople from Qom
Iranian men's footballers
Saba Qom F.C. players
Persian Gulf Pro League players
Azadegan League players
Men's association football central defenders |
https://en.wikipedia.org/wiki/Chemical%20reaction%20network%20theory | Chemical reaction network theory is an area of applied mathematics that attempts to model the behaviour of real-world chemical systems. Since its foundation in the 1960s, it has attracted a growing research community, mainly due to its applications in biochemistry and theoretical chemistry. It has also attracted interest from pure mathematicians due to the interesting problems that arise from the mathematical structures involved.
History
Dynamical properties of reaction networks were studied in chemistry and physics after the invention of the law of mass action. The essential steps in this study were introduction of detailed balance for the complex chemical reactions by Rudolf Wegscheider (1901), development of the quantitative theory of chemical chain reactions by Nikolay Semyonov (1934), development of kinetics of catalytic reactions by Cyril Norman Hinshelwood, and many other results.
Three eras of chemical dynamics can be revealed in the flux of research and publications. These eras may be associated with leaders: the first is the van 't Hoff era, the second may be called the Semenov–Hinshelwood era and the third is definitely the Aris era.
The "eras" may be distinguished based on the main focuses of the scientific leaders:
van’t Hoff was searching for the general law of chemical reaction related to specific chemical properties. The term "chemical dynamics" belongs to van’t Hoff.
The Semenov-Hinshelwood focus was an explanation of critical phenomena observed in many chemical systems, in particular in flames. A concept chain reactions elaborated by these researchers influenced many sciences, especially nuclear physics and engineering.
Aris’ activity was concentrated on the detailed systematization of mathematical ideas and approaches.
The mathematical discipline "chemical reaction network theory" was originated by Rutherford Aris, a famous expert in chemical engineering, with the support of Clifford Truesdell, the founder and editor-in-chief of the journal Archive for Rational Mechanics and Analysis. The paper of R. Aris in this journal was communicated to the journal by C. Truesdell. It opened the series of papers of other authors (which were communicated already by R. Aris). The well known papers of this series are the works of Frederick J. Krambeck, Roy Jackson, Friedrich Josef Maria Horn, Martin Feinberg and others, published in the 1970s. In his second "prolegomena" paper, R. Aris mentioned the work of N.Z. Shapiro, L.S. Shapley (1965), where an important part of his scientific program was realized.
Since then, the chemical reaction network theory has been further developed by a large number of researchers internationally.<ref>P. De Leenheer, D. Angeli and E. D. Sontag, "Monotone chemical reaction networks" , J. Math. Chem.', 41(3):295–314, 2007.</ref>G. Craciun and C. Pantea, "Identifiability of chemical reaction networks", J. Math. Chem., 44:1, 2008.A. N. Gorban and G. S. Yablonsky, "Extended detailed balance for systems with |
https://en.wikipedia.org/wiki/Daniela%20K%C3%BChn | Daniela Kühn (born 1973) is a German mathematician and the Mason Professor in Mathematics at the University of Birmingham in Birmingham, England. She is known for her research in combinatorics, and particularly in extremal combinatorics and graph theory.
Biography
Kühn earned the Certificate of Advanced Studies in Mathematics (Cambridge Mathematical Tripos) from Cambridge University in 1997 and a Diploma in Mathematics from the Chemnitz University of Technology in 1999, followed by her doctorate from the University of Hamburg in 2001, under the supervision of Reinhard Diestel. After working as a postdoctoral researcher at Hamburg and the Free University of Berlin, she moved to the University of Birmingham as a lecturer in 2004, and was awarded the Mason Professorship of Mathematics in 2010.
Research
In 2004 Kühn published a pair of papers in Combinatorica with her thesis advisor, Reinhard Diestel, concerning the cycle spaces of infinite graphs. In these graphs the appropriate generalizations of cycles and spanning trees hinge on a proper treatment of the ends of the graph. Reviewer R. Bruce Richter writes that "the results are extremely satisfactory, in the sense that standard theorems for finite graphs have perfect analogues" but that "there is nothing simple about any aspect of this work. It is a nice mix of graph-theoretic and topological ideas."
In 2011, Kühn and her co-authors published a proof of Sumner's conjecture, that every n-vertex polytree forms a subgraph of every (2n − 2)-vertex tournament, for all but finitely many values of n. MathSciNet reviewer K. B. Reid wrote that their proof "is an important and welcome development in tournament theory".
Awards and honours
In 2002, Kühn won the Richard Rado Prize, a biennial best dissertation award given by the Section for Discrete Mathematics of the German Mathematical Society. Together with Deryk Osthus and Alain Plagne, she was one of the first winners of the European Prize in Combinatorics in 2003. Together with Osthus, she was a recipient of the 2014 Whitehead Prize of the London Mathematical Society for "their many results in extremal graph theory and related areas. Several of their papers resolve long-standing open problems in the area." She was an Invited Speaker at the 2014 International Congress of Mathematicians, in Seoul. and appointed as a Royal Society Wolfson Research Merit Award holder in 2015.
References
Living people
21st-century German mathematicians
German women mathematicians
Graph theorists
University of Hamburg alumni
Academics of the University of Birmingham
Whitehead Prize winners
1973 births
Royal Society Wolfson Research Merit Award holders
21st-century women mathematicians
21st-century German women |
https://en.wikipedia.org/wiki/Graeme%20Geddes | Graeme Geddes is a former Grand Prix motorcycle racer from Australia.
Career statistics
By season
References
External links
Profile on motogp.com
Living people
1960 births
Australian motorcycle racers
250cc World Championship riders
350cc World Championship riders |
https://en.wikipedia.org/wiki/Victor%20Soussan | Victor Soussan (born 28 March 1946 in Casablanca) is an Australian private former Grand Prix motorcycle racer of French Moroccan descent.
Career statistics
By season
References
External links
Official website
Profile on motogp.com
1946 births
Living people
Sportspeople from Casablanca
Australian people of Moroccan descent
Australian motorcycle racers
250cc World Championship riders
350cc World Championship riders |
https://en.wikipedia.org/wiki/Hodge%E2%80%93Arakelov%20theory | In mathematics, Hodge–Arakelov theory of elliptic curves is an analogue of classical and p-adic Hodge theory for elliptic curves carried out in the framework of Arakelov theory. It was introduced by . It bears the name of two mathematicians, Suren Arakelov and W. V. D. Hodge.
The main comparison in his theory remains unpublished as of 2019.
Mochizuki's main comparison theorem in Hodge–Arakelov theory states (roughly) that the space of polynomial functions of degree less than d on the universal extension of a smooth elliptic curve in characteristic 0 is naturally isomorphic (via restriction) to the d2-dimensional space of functions on the d-torsion points.
It is called a 'comparison theorem' as it is an analogue for Arakelov theory of comparison theorems in cohomology relating de Rham cohomology to singular cohomology of complex varieties or étale cohomology of p-adic varieties.
In and he pointed out that arithmetic Kodaira–Spencer map and Gauss–Manin connection may give some important hints for Vojta's conjecture, ABC conjecture and so on; in 2012, he published his Inter-universal Teichmuller theory, in which he didn't use Hodge-Arakelov theory but used the theory of frobenioids, anabelioids and mono-anabelian geometry.
See also
Hodge theory
Arakelov theory
P-adic Hodge theory
Inter-universal Teichmüller theory
References
Number theory
Algebraic geometry |
https://en.wikipedia.org/wiki/Inertial%20manifold | In mathematics, inertial manifolds are concerned with the long term behavior of the solutions of dissipative dynamical systems. Inertial manifolds are finite-dimensional, smooth, invariant manifolds that contain the global attractor and attract all solutions exponentially quickly. Since an inertial manifold is finite-dimensional even if the original system is infinite-dimensional, and because most of the dynamics for the system takes place on the inertial manifold, studying the dynamics on an inertial manifold produces a considerable simplification in the study of the dynamics of the original system.
In many physical applications, inertial manifolds express an interaction law between the small and large wavelength structures. Some say that the small wavelengths are enslaved by the large (e.g. synergetics). Inertial manifolds may also appear as slow manifolds common in meteorology, or as the center manifold in any bifurcation. Computationally, numerical schemes for partial differential equations seek to capture the long term dynamics and so such numerical schemes form an approximate inertial manifold.
Introductory Example
Consider the dynamical system in just two variables and and with parameter :
It possesses the one dimensional inertial manifold of (a parabola).
This manifold is invariant under the dynamics because on the manifold
which is the same as
The manifold attracts all trajectories in some finite domain around the origin because near the origin (although the strict definition below requires attraction from all initial conditions).
Hence the long term behavior of the original two dimensional dynamical system is given by the 'simpler' one dimensional dynamics on the inertial manifold , namely .
Definition
Let denote a solution of a dynamical system. The solution may be an evolving vector in or may be an evolving function in an infinite-dimensional Banach space .
In many cases of interest the evolution of is determined as the solution of a differential equation in , say with initial value .
In any case, we assume the solution of the dynamical system can be written in terms of a semigroup operator, or state transition matrix, such that for all times and all initial values .
In some situations we might consider only discrete values of time as in the dynamics of a map.
An inertial manifold for a dynamical semigroup is a smooth manifold such that
is of finite dimension,
for all times ,
attracts all solutions exponentially quickly, that is, for every initial value there exist constants such that .
The restriction of the differential equation to the inertial manifold is therefore a well defined finite-dimensional system called the inertial system.
Subtly, there is a difference between a manifold being attractive, and solutions on the manifold being attractive.
Nonetheless, under appropriate conditions the inertial system possesses so-called asymptotic completeness: that is, every solution of the |
https://en.wikipedia.org/wiki/Katsumi%20Nomizu | was a Japanese-American mathematician known for his work in differential geometry.
Life and career
Nomizu was born in Osaka, Japan on the first day of December, 1924. He studied mathematics at Osaka University, graduating in 1947 with a Master of Science then traveled to the United States on a U.S. Army Fulbright Scholarship. He studied first at Columbia University and then at the University of Chicago where in 1953 he became the first student to earn a Ph.D. under the thesis direction of Shiing-Shen Chern. The subject was affine differential geometry, a topic to which he would return much later in his career. He presented his thesis, Invariant affine connections on homogeneous spaces in 1953.
Returning to Japan, he studied at Nagoya University, obtaining a doctor of science in 1955. He published his first volume, Lie Groups and Differential Geometry dedicated to his wife Kimiko whom he had married that same year. Nomizu taught at Nagoya University until 1958 when he accepted a position at Catholic University in Washington D.C. His first Ph.D. student there was Fr. Andrew Whitman, SJ, founder of the Clavius Research Group, who maintained a close relationship with his advisor over the years.
In 1960 he began his thirty-five-year career with Brown University, first as associate professor, then becoming full professor in 1963. During this time he embarked on a major collaborative project with Professor Shoshichi Kobayashi at the University of California, Berkeley, resulting in the classic two-volume work, Foundations of Differential Geometry in 1963. A second volume completed the project in 1969. A mark of the style of these two mathematicians is that in the more than 700 pages in this work on geometry, there is not a single diagram or picture.
Katsumi Nomizu was well known for his devotion to meticulous exposition in a very formal style and to high-quality teaching at the undergraduate level. His 1966 text, Fundamentals of Linear Algebra includes these words in the dedication, "It is my hope that this book will continue to serve those students of mathematics and science for whom a more than rudimentary background in linear algebra is an indispensable part of their training." When the book came out in a new edition in 1979, Nomizu specifically acknowledged help from a student, Marty Magid, who started as a freshman at Brown in his linear algebra class and ended up writing a Ph.D. thesis under his direction in 1978.
Over the course of his career, Katsumi Nomizu was influential in determining the course of differential geometry by stressing what he called the structural approach. In 1965, he edited the Proceedings of a United States-Japan Seminar in Differential Geometry that he helped to organize for the National Science Foundation. He was invited to visiting positions in Berlin, Bonn, Strasbourg, and Rio de Janeiro. Among his nearly one hundred papers and articles and seven books, he had twenty-three co-authors from Belgium, Brazil, China, Ge |
https://en.wikipedia.org/wiki/Associate%20family | In differential geometry, the associate family (or Bonnet family) of a minimal surface is a one-parameter family of minimal surfaces which share the same Weierstrass data. That is, if the surface has the representation
the family is described by
where indicates the real part of a complex number.
For θ = π/2 the surface is called the conjugate of the θ = 0 surface.
The transformation can be viewed as locally rotating the principal curvature directions. The surface normals of a point with a fixed ζ remains unchanged as θ changes; the point itself moves along an ellipse.
Some examples of associate surface families are: the catenoid and helicoid family, the Schwarz P, Schwarz D and gyroid family, and the Scherk's first and second surface family. The Enneper surface is conjugate to itself: it is left invariant as θ changes.
Conjugate surfaces have the property that any straight line on a surface maps to a planar geodesic on its conjugate surface and vice versa. If a patch of one surface is bounded by a straight line, then the conjugate patch is bounded by a planar symmetry line. This is useful for constructing minimal surfaces by going to the conjugate space: being bound by planes is equivalent to being bound by a polygon.
There are counterparts to the associate families of minimal surfaces in higher-dimensional spaces and manifolds.
References
Differential geometry
Minimal surfaces |
https://en.wikipedia.org/wiki/Koecher%E2%80%93Vinberg%20theorem | In operator algebra, the Koecher–Vinberg theorem is a reconstruction theorem for real Jordan algebras. It was proved independently by Max Koecher in 1957 and Ernest Vinberg in 1961. It provides a one-to-one correspondence between formally real Jordan algebras and so-called domains of positivity. Thus it links operator algebraic and convex order theoretic views on state spaces of physical systems.
Statement
A convex cone is called regular if whenever both and are in the closure .
A convex cone in a vector space with an inner product has a dual cone . The cone is called self-dual when . It is called homogeneous when to any two points there is a real linear transformation that restricts to a bijection and satisfies .
The Koecher–Vinberg theorem now states that these properties precisely characterize the positive cones of Jordan algebras.
Theorem: There is a one-to-one correspondence between formally real Jordan algebras and convex cones that are:
open;
regular;
homogeneous;
self-dual.
Convex cones satisfying these four properties are called domains of positivity or symmetric cones. The domain of positivity associated with a real Jordan algebra is the interior of the 'positive' cone .
Proof
For a proof, see or .
References
Non-associative algebras
Theorems in algebra |
https://en.wikipedia.org/wiki/Nilcurve | In mathematics, a nilcurve is a pointed stable curve over a finite field with an indigenous bundle whose p-curvature is square nilpotent. Nilcurves were introduced by as a central concept in his theory of p-adic Teichmüller theory.
The nilcurves form a stack over the moduli stack of stable genus g curves with r marked points in characteristic p, of degree
p3g–3+r.
References
Algebraic geometry |
https://en.wikipedia.org/wiki/David%20Nualart | David Nualart (born 21 March 1951) is a Spanish mathematician working in the field of probability theory, in particular on aspects of stochastic processes and stochastic analysis.
He obtained his PhD titled "Contribución al estudio de la integral estocástica" in 1975 at the University of Barcelona under the supervision of Francesc d'Assís Sales Vallès.
After positions at the University of Barcelona and the Polytechnique University of Barcelona he took up a professorship at the University of Kansas and is currently the Black-Babcock Distinguished Professor in its Mathematics Department.
He published hundreds of scientific articles in his field, served on several scientific committees, has been an associate editor of many journals and from 2006 to 2008 was the Chief Editor of Electronic Communications in Probability.
Recognition
He has been elected a Fellow of the Institute of Mathematical Statistics in 1997.
He received a Doctor Honoris Causa by the Université Blaise Pascal of Clermond-Ferrand in 1998.
He received the Prize IBERDROLA de Ciencia y Tecnologia in 1999.
He has been a Corresponding Member of the Real Academia de Ciencias Exactas Fisicas y Naturales of
Madrid since 2003.
He has been a member of the Reial Academia de Ciencies i Arts of Barcelona since 2003.
He received the Research Prize of the Real Academia de Ciencias de Madrid in 1991.
In March 2011 the International Conference on Malliavin Calculus and Stochastic Analysis in honor of David
Nualart took place at University of Kansas.
He was named to the 2023 class of Fellows of the American Mathematical Society, "for contributions to Malliavin calculus, stochastic PDE's, and fractional Brownian motion".
References
https://web.archive.org/web/20120331065622/http://www.math.ku.edu/~nualart/cv.pdf
External links
https://web.archive.org/web/20120331065603/http://www.math.ku.edu/~nualart/ - Webpage of David Nualart at Kansas University
1951 births
Living people
20th-century Spanish mathematicians
Mathematical analysts
University of Barcelona alumni
21st-century Spanish mathematicians
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Lidinoid | In differential geometry, the lidinoid is a triply periodic minimal surface. The name comes from its Swedish discoverer Sven Lidin (who called it the HG surface).
It has many similarities to the gyroid, and just as the gyroid is the unique embedded member of the associate family of the Schwarz P surface the lidinoid is the unique embedded member of the associate family of a Schwarz H surface. It belongs to space group 230(Ia3d).
The Lidinoid can be approximated as a level set:
References
External images
The lidinoid at the minimal surface archive
The lidinoid in the Scientific Graphic Project
Minimal surfaces
Differential geometry of surfaces |
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