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https://en.wikipedia.org/wiki/2010%20Universitario%20de%20Deportes%20season | The 2010 season was Universitario de Deportes' 82nd season in the Peruvian Primera División and 45th in the Torneo Descentralizado. This article shows player statistics and all matches (official and friendly) that the club played during the 2010 season.
Squad information
Competitions
Torneo Descentralizado
Universitario participates in the Torneo Descentralizado, Peru's highest division.
First stage
The first stage of the Torneo Descentralizado consisted of 16 teams where Universitario played 30 matches; one home game and one away game against each team. The winner of the first stage was eligible to play in first stage of the 2011 Copa Libertadores.
Standings
Summary
Results by round
Matches
Second stage
Universitario finished 5th and played against the teams that placed an odd number at the end of the First stage. The Second stage consisted of 14 matches (7 home and 7 away games) for Universitario. The winner of the group qualified to the 2011 Copa Libertadores.
Standings
Summary
Results by round
Matches
Copa Libertadores
Universitario qualified to the 2010 Copa Libertadores as 2009 season champion. They were drawn into Group 4 with Libertad, which they faced last Copa Libertadores, Lanús, and Clausura champion Blooming. They finished second and advanced to the Round of 16 as the 5th best second-placed team.
Group 4
Round of 16
In the Round of 16, Universitario faced three-time champion São Paulo.
Goalscorers
External links
Universitario.pe Official website
2010
Universitario de Deportes |
https://en.wikipedia.org/wiki/Martin%20Pot%C5%AF%C4%8Dek | Martin Potůček is Czech academic and journalist.
Education
Potůček studied philosophy, mathematics, political science, and sociology at Masaryk University in Brno. He worked as a researcher at the Department of Complex Modelling, Sportpropag, and later in the Institute of Social Medicine and Organisation of Health Services in Prague, until 1989. He received his Ph.D. in management theory in 1989 from the University of Economics, Prague. He subsequently studied at the London School of Economics, receiving an M.Sc. in European social policy in 1991, and participated in a number of professional fellowship and exchange programs, including with the Eisenhower Exchange Fellowship in the United States (1992), Oxford University (1993–1994), the University of Konstanz (1997–2000), the Institute of Human Sciences in Vienna (1998) and Central European University in Budapest (1998–2000).
Career
In 1990 Potůček joined the newly established faculty of social sciences at the Charles University in Prague. He habilitated there in 1992 as associate professor of sociology. In 1999, he became full professor of public and social policy on the new study program he had co-founded. He served as the director of the Institute of Sociological Studies at the same faculty from 1994 to 2003. He established and has run the Center for Social and Economic Strategies there since 2000.
Potůček was elected chairman of the Masaryk Czech Sociological Association in 1995 (vice-chairman, 1994 and 1996) and member of the steering committee of the Network of Institutes and Schools of Public Administration in Central and Eastern Europe (NISPAcee) in 1997. In 2000-2002, he acted as the elected president of this international nonprofit association. He served as the first vice-chairman of the Research and Development Council of the Government of the Czech Republic (1999–2004). He acted as permanent guest professor at the University of Konstanz, Germany (2002–2008). He served as an advisor to Ministers of Labour and Social Affairs (1998–2006) and to the prime minister of the Czech Republic (2002–2004). He has been awarded the Sri Chinmoy International Honour "Lifting Up the World with a Oneness-Heart" (2003) and the NISPAcee Alena Brunovska Award (2004) for teaching excellence in public administration. Since 2008 and from 2004 to 2005 he was a member of Committee for Social Sciences and Humanities, Research and Development Council of the Czech Government.
Potůček ran for Czech president in 2003. He sought the nomination of the Czech Social Democratic Party, but came fourth in the party's presidential primaries and was not nominated.
Bibliography
His work focuses on the teleonomic qualities of differentiated social actors, processes of cultivating and utilising human potential, and factors influencing health and health policy, as well as the processes of public policy formulation and implementation in the Czech Republic. He has published 23 scientific books and three textbooks.
Books
|
https://en.wikipedia.org/wiki/Sturm%20series | In mathematics, the Sturm series associated with a pair of polynomials is named after Jacques Charles François Sturm.
Definition
Let and two univariate polynomials. Suppose that they do not have a common root and the degree of is greater than the degree of . The Sturm series is constructed by:
This is almost the same algorithm as Euclid's but the remainder has negative sign.
Sturm series associated to a characteristic polynomial
Let us see now Sturm series associated to a characteristic polynomial in the variable :
where for in are rational functions in with the coordinate set . The series begins with two polynomials obtained by dividing by where represents the imaginary unit equal to and separate real and imaginary parts:
The remaining terms are defined with the above relation. Due to the special structure of these polynomials, they can be written in the form:
In these notations, the quotient is equal to which provides the condition . Moreover, the polynomial replaced in the above relation gives the following recursive formulas for computation of the coefficients .
If for some , the quotient is a higher degree polynomial and the sequence stops at with .
References
Mathematical series |
https://en.wikipedia.org/wiki/Hurwitz%20determinant | In mathematics, Hurwitz determinants were introduced by , who used them to give a criterion for all roots of a polynomial to have negative real part.
Definition
Consider a characteristic polynomial P in the variable λ of the form:
where , , are real.
The square Hurwitz matrix associated to P is given below:
The i-th Hurwitz determinant is the i-th leading principal minor (minor is a determinant) of the above Hurwitz matrix H. There are n Hurwitz determinants for a characteristic polynomial of degree n.
See also
Transfer matrix
References
Linear algebra
Determinants
de:Hurwitzpolynom#Hurwitz-Kriterium |
https://en.wikipedia.org/wiki/Lajos%20Bertus | Lajos Bertus (born 26 September 1990) is a Hungarian football player who plays for Tiszakécske.
Club statistics
Updated to games played as of 15 May 2021.
References
Player Profile at Kecskemeti TE Official Website
HLSZ
MLSZ
1990 births
Living people
Footballers from Kecskemét
Hungarian men's footballers
Hungary men's under-21 international footballers
Men's association football midfielders
Kecskeméti TE players
Puskás Akadémia FC players
Paksi FC players
Mezőkövesdi SE footballers
Diósgyőri VTK players
Tiszakécske FC footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
21st-century Hungarian people |
https://en.wikipedia.org/wiki/Branislav%20Danilovi%C4%87 | Branislav Danilović (Serbian Cyrillic: Бранислав Даниловић; born 24 June 1988) is a Serbian football goalkeeper who plays for Diósgyőri VTK.
Club statistics
Updated to games played as of 20 May 2021.
External links
UEFA profile
Srbijafudbal profile
1988 births
Living people
Footballers from Belgrade
Serbian men's footballers
Men's association football goalkeepers
Serbia men's under-21 international footballers
FK Rad players
FK BSK Borča players
Puskás Akadémia FC players
Fehérvár FC players
Debreceni VSC players
Diósgyőri VTK players
Serbian SuperLiga players
Nemzeti Bajnokság I players
Serbian expatriate men's footballers
Expatriate men's footballers in Hungary
Serbian expatriate sportspeople in Hungary |
https://en.wikipedia.org/wiki/Saturated%20set | In mathematics, particularly in the subfields of set theory and topology, a set is said to be saturated with respect to a function if is a subset of 's domain and if whenever sends two points and to the same value then belongs to (that is, if then ). Said more succinctly, the set is called saturated if
In topology, a subset of a topological space is saturated if it is equal to an intersection of open subsets of In a T1 space every set is saturated.
Definition
Preliminaries
Let be a map.
Given any subset define its under to be the set:
and define its or under to be the set:
Given is defined to be the preimage:
Any preimage of a single point in 's codomain is referred to as
Saturated sets
A set is called and is said to be if is a subset of 's domain and if any of the following equivalent conditions are satisfied:
There exists a set such that
Any such set necessarily contains as a subset and moreover, it will also necessarily satisfy the equality where denotes the image of
If and satisfy then
If is such that the fiber intersects (that is, if ), then this entire fiber is necessarily a subset of (that is, ).
For every the intersection is equal to the empty set or to
Examples
Let be any function. If is set then its preimage under is necessarily an -saturated set. In particular, every fiber of a map is an -saturated set.
The empty set and the domain are always saturated. Arbitrary unions of saturated sets are saturated, as are arbitrary intersections of saturated sets.
Properties
Let and be any sets and let be any function.
If is -saturated then
If is -saturated then
where note, in particular, that requirements or conditions were placed on the set
If is a topology on and is any map then set of all that are saturated subsets of forms a topology on If is also a topological space then is continuous (respectively, a quotient map) if and only if the same is true of
See also
References
Basic concepts in set theory
General topology
Operations on sets |
https://en.wikipedia.org/wiki/De%20Groot%20dual | In mathematics, in particular in topology, the de Groot dual (after Johannes de Groot) of a topology τ on a set X is the topology τ* whose closed sets are generated by compact saturated subsets of (X, τ).
References
R. Kopperman (1995), Asymmetry and duality in topology. Topology Applications, 66(1), 1–39, 1995.
Topology |
https://en.wikipedia.org/wiki/Volcanic%20hazards | A volcanic hazard is the probability a volcanic eruption or related geophysical event will occur in a given geographic area and within a specified window of time. The risk that can be associated with a volcanic hazard depends on the proximity and vulnerability of an asset or a population of people near to where a volcanic event might occur.
Lava flows
Different forms of effusive lava can provide different hazards. Pahoehoe lava is smooth and ropy while Aa lava is blocky and hard. Lava flows normally follow the topography, sinking into depressions and valleys and flowing down the volcano. Lava flows will bury roads, farmlands and other forms of personal property. This lava could destroy homes, cars, and lives standing in the way. Lava flows are dangerous, however, they are slow moving and this gives people time to respond and evacuate out of immediate areas. People can mitigate this hazard by not moving to valleys or depressed areas around a volcano.
Pyroclastic materials (tephra) and flow
Tephra is a generalized word for the various bits of debris launched out of a volcano during an eruption, regardless of their size. Pyroclastic materials are generally categorized according to size: dust measures at <1/8 mm, ash is 1/8–2 mm, cinders are 2–64 mm, and bombs and blocks are both >64 mm. Different hazards are associated with the different kinds of pyroclastic materials. Dust and ash could coat cars and homes, rendering a car unable to drive with dust accumulation in the engine. They could also layer on homes and add weight to roofs causing a house to collapse. Also, ash and dust inhaled could cause long-term respiratory issues in people inhaling the particles. Cinders are flaming pieces of ejected volcanic material which could set fire to homes and wooded areas. Bombs and blocks run the risk of hitting various objects and people within range of the volcano. Projectiles can be thrown thousands of feet in the air and can be found several miles away from the initial eruption point.
A pyroclastic flow is a fast-moving (up to 700 km/h) extremely hot (~1000 °C) mass of air and tephra that charges down the sides of a volcano during an explosive eruption.
Air travel hazards
Ash thrown into the air by eruptions can present a hazard to aircraft, especially jet aircraft where the particles can be melted by the high operating temperature; the melted particles then adhere to the turbine blades and alter their shape, disrupting the operation of the turbine. Dangerous encounters in 1982 after the eruption of Galunggung in Indonesia, and 1989 after the eruption of Mount Redoubt in Alaska raised awareness of this phenomenon. Nine Volcanic Ash Advisory Centers were established by the International Civil Aviation Organization to monitor ash clouds and advise pilots accordingly. The 2010 eruptions of Eyjafjallajökull caused major disruptions to air travel in Europe.
Mudflows, floods, debris flows and avalanches
When pyroclastic materials mix with water from a near |
https://en.wikipedia.org/wiki/Pairwise%20Stone%20space | In mathematics and particularly in topology, pairwise Stone space is a bitopological space which is pairwise compact, pairwise Hausdorff, and pairwise zero-dimensional.
Pairwise Stone spaces are a bitopological version of the Stone spaces.
Pairwise Stone spaces are closely related to spectral spaces.
Theorem: If is a spectral space, then is a pairwise Stone space, where is the de Groot dual topology of . Conversely, if is a pairwise Stone space, then both and are spectral spaces.
See also
Bitopological space
Duality theory for distributive lattices
Notes
Topology |
https://en.wikipedia.org/wiki/Priestley%20space | In mathematics, a Priestley space is an ordered topological space with special properties. Priestley spaces are named after Hilary Priestley who introduced and investigated them. Priestley spaces play a fundamental role in the study of distributive lattices. In particular, there is a duality ("Priestley duality") between the category of Priestley spaces and the category of bounded distributive lattices.
Definition
A Priestley space is an ordered topological space , i.e. a set equipped with a partial order and a topology , satisfying
the following two conditions:
is compact.
If , then there exists a clopen up-set of such that and . (This condition is known as the Priestley separation axiom.)
Properties of Priestley spaces
Each Priestley space is Hausdorff. Indeed, given two points of a Priestley space , if , then as is a partial order, either or . Assuming, without loss of generality, that , (ii) provides a clopen up-set of such that and . Therefore, and are disjoint open subsets of separating and .
Each Priestley space is also zero-dimensional; that is, each open neighborhood of a point of a Priestley space contains a clopen neighborhood of . To see this, one proceeds as follows. For each , either or . By the Priestley separation axiom, there exists a clopen up-set or a clopen down-set containing and missing . The intersection of these clopen neighborhoods of does not meet . Therefore, as is compact, there exists a finite intersection of these clopen neighborhoods of missing . This finite intersection is the desired clopen neighborhood of contained in .
It follows that for each Priestley space , the topological space is a Stone space; that is, it is a compact Hausdorff zero-dimensional space.
Some further useful properties of Priestley spaces are listed below.
Let be a Priestley space.
(a) For each closed subset of , both and are closed subsets of .
(b) Each open up-set of is a union of clopen up-sets of and each open down-set of is a union of clopen down-sets of .
(c) Each closed up-set of is an intersection of clopen up-sets of and each closed down-set of is an intersection of clopen down-sets of .
(d) Clopen up-sets and clopen down-sets of form a subbasis for .
(e) For each pair of closed subsets and of , if , then there exists a clopen up-set such that and .
A Priestley morphism from a Priestley space to another Priestley space is a map which is continuous and order-preserving.
Let Pries denote the category of Priestley spaces and Priestley morphisms.
Connection with spectral spaces
Priestley spaces are closely related to spectral spaces. For a Priestley space , let denote the collection of all open up-sets of . Similarly, let denote the collection of all open down-sets of .
Theorem:
If is a Priestley space, then both and are spectral spaces.
Conversely, given a spectral space , let denote the patch topology on ; that is, the topology generated by the subbasis consisting |
https://en.wikipedia.org/wiki/Duality%20theory%20for%20distributive%20lattices | In mathematics, duality theory for distributive lattices provides three different (but closely related) representations of bounded distributive lattices via Priestley spaces, spectral spaces, and pairwise Stone spaces. This duality, which is originally also due to Marshall H. Stone, generalizes the well-known Stone duality between Stone spaces and Boolean algebras.
Let be a bounded distributive lattice, and let denote the set of prime filters of . For each , let . Then is a spectral space, where the topology on is generated by . The spectral space is called the prime spectrum of .
The map is a lattice isomorphism from onto the lattice of all compact open subsets of . In fact, each spectral space is homeomorphic to the prime spectrum of some bounded distributive lattice.
Similarly, if and denotes the topology generated by , then is also a spectral space. Moreover, is a pairwise Stone space. The pairwise Stone space is called the bitopological dual of . Each pairwise Stone space is bi-homeomorphic to the bitopological dual of some bounded distributive lattice.
Finally, let be set-theoretic inclusion on the set of prime filters of and let . Then is a Priestley space. Moreover, is a lattice isomorphism from onto the lattice of all clopen up-sets of . The Priestley space is called the Priestley dual of . Each Priestley space is isomorphic to the Priestley dual of some bounded distributive lattice.
Let Dist denote the category of bounded distributive lattices and bounded lattice homomorphisms. Then the above three representations of bounded distributive lattices can be extended to dual equivalence between Dist and the categories Spec, PStone, and Pries of spectral spaces with spectral maps, of pairwise Stone spaces with bi-continuous maps, and of Priestley spaces with Priestley morphisms, respectively:
Thus, there are three equivalent ways of representing bounded distributive lattices. Each one has its own motivation and advantages, but ultimately they all serve the same purpose of providing better understanding of bounded distributive lattices.
See also
Representation theorem
Birkhoff's representation theorem
Stone's representation theorem for Boolean algebras
Stone duality
Esakia duality
Notes
References
Priestley, H. A. (1970). Representation of distributive lattices by means of ordered Stone spaces. Bull. London Math. Soc., (2) 186–190.
Priestley, H. A. (1972). Ordered topological spaces and the representation of distributive lattices. Proc. London Math. Soc., 24(3) 507–530.
Stone, M. (1938). Topological representation of distributive lattices and Brouwerian logics. Casopis Pest. Mat. Fys., 67 1–25.
Cornish, W. H. (1975). On H. Priestley's dual of the category of bounded distributive lattices. Mat. Vesnik, 12(27) (4) 329–332.
M. Hochster (1969). Prime ideal structure in commutative rings. Trans. Amer. Math. Soc., 142 43–60
Johnstone, P. T. (1982). Stone spaces. Cambridge University Press, Cambridge. .
Jung, A. |
https://en.wikipedia.org/wiki/Esakia%20space | In mathematics, Esakia spaces are special ordered topological spaces introduced and studied by Leo Esakia in 1974. Esakia spaces play a fundamental role in the study of Heyting algebras, primarily by virtue of the Esakia duality—the dual equivalence between the category of Heyting algebras and the category of Esakia spaces.
Definition
For a partially ordered set and for , let } and let }. Also, for , let } and }.
An Esakia space is a Priestley space such that for each clopen subset of the topological space , the set is also clopen.
Equivalent definitions
There are several equivalent ways to define Esakia spaces.
Theorem: Given that is a Stone space, the following conditions are equivalent:
(i) is an Esakia space.
(ii) is closed for each and is clopen for each clopen .
(iii) is closed for each and for each (where denotes the closure in ).
(iv) is closed for each , the least closed set containing an up-set is an up-set, and the least up-set containing a closed set is closed.
Since Priestley spaces can be described in terms of spectral spaces, the Esakia property can be expressed in spectral space terminology as follows:
The Priestley space corresponding to a spectral space is an Esakia space if and only if the closure of every constructible subset
of is constructible.
Esakia morphisms
Let and be partially ordered sets and let be an order-preserving map. The map is a bounded morphism (also known as p-morphism) if for each and , if , then there exists such that and .
Theorem: The following conditions are equivalent:
(1) is a bounded morphism.
(2) for each .
(3) for each .
Let and be Esakia spaces and let be a map. The map is called an Esakia morphism if is a continuous bounded morphism.
Notes
References
Esakia, L. (1974). Topological Kripke models. Soviet Math. Dokl., 15 147–151.
Esakia, L. (1985). Heyting Algebras I. Duality Theory (Russian). Metsniereba, Tbilisi.
General topology |
https://en.wikipedia.org/wiki/Esakia%20duality | In mathematics, Esakia duality is the dual equivalence between the category of Heyting algebras and the category of Esakia spaces. Esakia duality provides an order-topological representation of Heyting algebras via Esakia spaces.
Let Esa denote the category of Esakia spaces and Esakia morphisms.
Let be a Heyting algebra, denote the set of prime filters of , and denote set-theoretic inclusion on the prime filters of . Also, for each , let }, and let denote the topology on generated by }.
Theorem: is an Esakia space, called the Esakia dual of . Moreover, is a Heyting algebra isomorphism from onto the Heyting algebra of all clopen up-sets of . Furthermore, each Esakia space is isomorphic in Esa to the Esakia dual of some Heyting algebra.
This representation of Heyting algebras by means of Esakia spaces is functorial and yields a dual equivalence between the categories
HA of Heyting algebras and Heyting algebra homomorphisms
and
Esa of Esakia spaces and Esakia morphisms.
Theorem: HA is dually equivalent to Esa.
The duality can also be expressed in terms of spectral spaces, where it says that the category of Heyting algebras is dually equivalent
to the category of Heyting spaces.
See also
Duality theory for distributive lattices
References
Topology
Lattice theory
Duality theories |
https://en.wikipedia.org/wiki/Baron%20%28footballer%29 | Marcelo Baron Polanczyk (born 19 January 1974), known as just Baron, is a former Brazilian football player.
Club statistics
Honors
Club
Sampaio Corrêa Futebol Clube
Campeonato Brasileiro Série C: 1997
Campeonato Maranhense: 1997
Shimizu S-Pulse
Emperor's Cup: 2001
Japanese Super Cup: 2001, 2002
Individual
Campeonato Brasileiro Série C Top goalscorer: 1997
References
External links
Avispa Fukuoka news release
Marcelo Baron Polanczyk at TheFinalBall.com
Marcelo Baron Polanczyk at J.League (in Japanese)
1974 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J1 League players
J2 League players
Japan Football League (1992–1998) players
Ventforet Kofu players
JEF United Chiba players
Shimizu S-Pulse players
Cerezo Osaka players
Kashima Antlers players
Vegalta Sendai players
Vissel Kobe players
Avispa Fukuoka players
Sport Club Internacional players
Associação Chapecoense de Futebol players
Santa Cruz Futebol Clube players
América Futebol Clube (SP) players
Men's association football forwards |
https://en.wikipedia.org/wiki/Koji%20Matsuura | is a former Japanese football player.
Club statistics
References
External links
1980 births
Living people
Hannan University alumni
Association football people from Hyōgo Prefecture
Japanese men's footballers
J1 League players
J2 League players
Sanfrecce Hiroshima players
Vegalta Sendai players
Tokyo Verdy players
Fagiano Okayama players
Thespakusatsu Gunma players
Men's association football forwards |
https://en.wikipedia.org/wiki/Goshi%20Okubo | is a Japanese football player.
Club statistics
References
External links
1986 births
Living people
Association football people from Miyagi Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Vegalta Sendai players
Sony Sendai FC players
Montedio Yamagata players
Goshi Okubo
Goshi Okubo
Expatriate men's footballers in Thailand
Japanese expatriate men's footballers
Japanese expatriate sportspeople in Thailand
Men's association football forwards
Goshi Okubo |
https://en.wikipedia.org/wiki/Ryuji%20Akiba | is a former Japanese football player.
Club statistics
References
External links
1984 births
Living people
Association football people from Shizuoka Prefecture
Japanese men's footballers
J1 League players
J2 League players
Nagoya Grampus players
Vegalta Sendai players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Marcos%20%28footballer%2C%20born%201974%29 | Marcos Paulo Souza Ribeiro (born 21 March 1974) is a former Brazilian football player.
Club statistics
Honours
J2. League Top Scorer: 2001
References
External links
Vegalta Sendai
1974 births
Living people
Brazilian men's footballers
Santa Cruz Futebol Clube players
Joinville Esporte Clube players
Esporte Clube Bahia players
Criciúma Esporte Clube players
Grêmio Foot-Ball Porto Alegrense players
J1 League players
J2 League players
Vegalta Sendai players
Men's association football forwards |
https://en.wikipedia.org/wiki/Jozef%20Ga%C5%A1par | Jozef Gašpar () (born 23 August 1977 in Rožňava) is a professional Slovak football player of Hungarian ethnicity. He currently plays for Vasas SC.
Club statistics
References
External links
Vegalta Sendai
HLSZ
1977 births
Living people
People from Rožňava
Hungarians in Slovakia
Slovak men's footballers
Men's association football defenders
Slovak expatriate men's footballers
FK Inter Bratislava players
J2 League players
Vegalta Sendai players
ŠK Slovan Bratislava players
Diósgyőri VTK players
Panionios F.C. players
A.O. Kerkyra players
Ethnikos Asteras F.C. players
Expatriate men's footballers in Japan
Slovak expatriate sportspeople in Japan
Expatriate men's footballers in Hungary
Slovak expatriate sportspeople in Hungary
Expatriate men's footballers in Greece
Slovak expatriate sportspeople in Greece |
https://en.wikipedia.org/wiki/Ricardo%20%28footballer%2C%20born%201977%29 | Ricardo Cavalcante Ribeiro (born 23 February 1977) is a Brazilian football player.
Club statistics
References
External links
biglobe.ne.jp
1977 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J1 League players
J2 League players
Kashima Antlers players
Vegalta Sendai players
Sanfrecce Hiroshima players
Kyoto Sanga FC players
Joinville Esporte Clube players
Esporte Clube Juventude players
Men's association football defenders |
https://en.wikipedia.org/wiki/%C3%89der%20Ceccon | Éder Ceccon (born 13 April 1983) is a Brazilian football player.
Club statistics
References
External links
Vegalta Sendai
1983 births
Living people
Brazilian men's footballers
São Paulo FC players
Avaí FC players
Clube Atlético Sorocaba players
Santos FC players
Paysandu Sport Club players
Esporte Clube Juventude players
Criciúma Esporte Clube players
Konyaspor footballers
Vegalta Sendai players
J1 League players
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Expatriate men's footballers in Turkey
Men's association football forwards |
https://en.wikipedia.org/wiki/Binary%20form%20%28disambiguation%29 | Binary form may refer to:
In music, binary form is a form (structure) consisting of two related parts.
In computer science and mathematics, number in the binary form refers to the use of binary numeral system.
In mathematics, a binary form is a homogeneous polynomial in two variables.
The article binary quadratic form discusses binary forms of degree two.
The article invariant of a binary form discusses binary forms of higher degree.
Binary form is another name for a binary quantic |
https://en.wikipedia.org/wiki/Akira%20Oba | is a former Japanese football player.
Club statistics
References
External links
jsgoal
1976 births
Living people
Association football people from Fukuoka Prefecture
Japanese men's footballers
J2 League players
Japan Football League (1992–1998) players
Japan Football League players
Tokushima Vortis players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Robert%20Iacob | Robert Mihai Iacob (born 24 June 1981 in Bucharest) is a former Romanian football player.
External links
Robert Iacob's profile and career statistics
1981 births
Living people
Romanian men's footballers
AFC Rocar București players
FCV Farul Constanța players
FC Universitatea Cluj players
FC Bihor Oradea (1958) players
CF Liberty Oradea players
Men's association football defenders
Footballers from Bucharest |
https://en.wikipedia.org/wiki/Unital | Unital may refer to:
A unital algebra – an algebra that contains a multiplicative identity element.
A geometric unital – a block design for integer .
A unital algebraic structure, such as a unital magma.
A unital map on C*-algebras – a map that preserves the identity element. |
https://en.wikipedia.org/wiki/Normal-exponential-gamma%20distribution | In probability theory and statistics, the normal-exponential-gamma distribution (sometimes called the NEG distribution) is a three-parameter family of continuous probability distributions. It has a location parameter , scale parameter and a shape parameter .
Probability density function
The probability density function (pdf) of the normal-exponential-gamma distribution is proportional to
,
where D is a parabolic cylinder function.
As for the Laplace distribution, the pdf of the NEG distribution can be expressed as a mixture of normal distributions,
where, in this notation, the distribution-names should be interpreted as meaning the density functions of those distributions.
Within this scale mixture, the scale's mixing distribution (an exponential with a gamma-distributed rate) actually is a Lomax distribution.
Applications
The distribution has heavy tails and a sharp peak at and, because of this, it has applications in variable selection.
See also
Compound probability distribution
Lomax distribution
References
Continuous distributions
Compound probability distributions |
https://en.wikipedia.org/wiki/F%C3%A1bio%20Nunes%20%28Brazilian%20footballer%29 | Fábio Nunes Fernandes (born 15 January 1980) is a Brazilian former football player.
Club statistics
References
External links
Vegalta Sendai
1980 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Liga Portugal 2 players
Liga I players
J2 League players
Associação Chapecoense de Futebol players
Santa Cruz Futebol Clube players
Vegalta Sendai players
S.C. Beira-Mar players
Uberlândia Esporte Clube players
C.F. Estrela da Amadora players
CS Pandurii Târgu Jiu players
Expatriate men's footballers in Portugal
Expatriate men's footballers in Japan
Expatriate men's footballers in Romania
Brazilian expatriate sportspeople in Romania
Men's association football forwards
Footballers from Porto Alegre |
https://en.wikipedia.org/wiki/List%20of%20Ligue%201%20records%20and%20statistics | The following is a list of records attained in French Football Ligue 1 since the league foundation in 1932.
Club statistics
Titles and points
Most titles: 11, Paris Saint-Germain
Most consecutive titles: 7, Lyon (2002–2008)
Most points in a single season: 96, Paris Saint-Germain (2015–16)
Wins and unbeaten runs
Most wins in a single season:
38-match season: 30, Paris Saint-Germain (2015–16) and Monaco (2016–17)
34-match season: 25, Saint-Étienne (1969–70)
Most home victories in a single season: 19, Saint-Étienne (1974–75)
Most away victories in a single season: 15, Paris Saint-Germain (2015–16)
Most consecutive victories: 16, Monaco (between 25 February 2017 and 17 August 2017)
Most consecutive victories in a single season: 14, Paris Saint-Germain (2018–19)
Most consecutive home victories: 28, Saint-Étienne (between 13 March 1974 and 27 August 1975)
Most consecutive away victories: 9, Marseille (between 15 February 2009 and 8 August 2009)
Biggest win: Sochaux 12–1 Valenciennes (1 July 1935)
Biggest away win: Troyes 0–9 Paris Saint-Germain (13 March 2016)
Longest unbeaten run within a single season: 32 matches, Nantes (1994–95)
Longest home unbeaten run: 92 matches, Nantes (between 15 May 1976 and 7 April 1981)
Longest unbeaten run: 36 matches, Paris Saint-Germain (between 15 March 2015 and 20 February 2016)
Losses
Fewest losses in a single season: 1, Nantes (1994–95)
Fewest home losses in a single season: 0 (53 times)
Fewest away losses in a single season: 1, Sochaux (1934–35), Saint-Étienne (1969–70), Nantes (1994–95), Marseille (2008–09) and Paris Saint-Germain (2015–16)
Top flight appearances
Most seasons in top flight: 72, Marseille
Most consecutive seasons in top flight: 49, Paris Saint-Germain (1974–present)
Goals
Highest-scoring season:
38-match season: 1946–47 (134 goals; 3.51 average per match)
34-match season: 1948–49 (113 goals; 3.71 average per match)
Most goals scored by a team in a single season:
38-match season: 118, RC Paris (1959–60)
34-match season: 102, Lille (1948–49)
Most goals in a single match: 13
Sochaux 12–1 Valenciennes (1 July 1935)
Marseille 3–10 Saint-Étienne (16 September 1951)
RC Paris 11–2 Metz (19 November 1961)
Fewest goals conceded by a team in a single season: 19, Paris Saint-Germain (2015–16)
Fewest home goals conceded by a team in a single season: 4, Saint-Étienne (2007–08)
Fewest away goals conceded by a team in a single season: 7, Paris Saint-Germain (2015–16)
Best goal difference in a single season:
38-match season: +83, Paris Saint-Germain (2015–16)
34-match season: +62, Lille (1948–49)
Disciplinary
Most yellow cards in a season: 654 (2002–03)
Most red cards in a season: 131 (2002–03)
Most red cards by a team in a single season: 14, Montpellier (2013–14)
Manager
Most matches managed: 894, Guy Roux (890 for Auxerre (1961–2000, 2001–2005) and 4 for Lens (2007–2008))
Attendance
Highest overall attendance in a season: 8,676,490 (2018–19; 38-match season)
Highest average attendance in a season: |
https://en.wikipedia.org/wiki/Sidmar%20%28footballer%29 | Sidmar Antônio Martins (born 13 June 1962) is a former Brazilian football player who played as a goalkeeper. He is currently head coach of Fujieda MYFC.
Club statistics
References
External links
geocities.jp
1962 births
Living people
Brazilian men's footballers
J1 League players
J3 League players
Guarani FC players
Esporte Clube Bahia players
Associação Portuguesa de Desportos players
Grêmio Foot-Ball Porto Alegrense players
Esporte Clube XV de Novembro (Piracicaba) players
Shimizu S-Pulse players
Fujieda MYFC players
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/C%C3%A9sar%20Quintero%20%28footballer%29 | César Alexander Quintero Jiménez (born November 29, 1988, in Medellín) is a Colombian football player who last played for Deportivo Pasto.
Club statistics
Updated to games played as of 8 December 2013.
References
Profile at HLSZ
1988 births
Living people
Footballers from Medellín
Colombian men's footballers
Men's association football defenders
Independiente Medellín footballers
Pápai FC footballers
Atlético Nacional footballers
Atlético Huila footballers
Once Caldas footballers
Deportes Tolima footballers
Atlético Bucaramanga footballers
Deportivo Pasto footballers
Categoría Primera A players
Nemzeti Bajnokság I players
Colombian expatriate men's footballers
Expatriate men's footballers in Hungary
Colombian expatriate sportspeople in Hungary |
https://en.wikipedia.org/wiki/Celso%20Vieira | Celso Vieira (born 25 September 1974) is a former Brazilian football player.
Club statistics
References
External links
Vegalta Sendai
1974 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Brazil men's youth international footballers
J2 League players
Sport Club Internacional players
Ituano FC players
Associação Portuguesa de Desportos players
Vegalta Sendai players
Expatriate men's footballers in Japan
Men's association football midfielders |
https://en.wikipedia.org/wiki/Bentinho | Antônio Bento dos Santos (born 18 December 1971), known as just Bentinho, is a former Brazilian football player.
Club statistics
References
External links
jsgoal
1971 births
Living people
Brazilian men's footballers
Brazil men's youth international footballers
Brazilian expatriate men's footballers
Saudi Pro League players
J1 League players
J2 League players
São José Esporte Clube players
Associação Portuguesa de Desportos players
São Paulo FC players
Botafogo de Futebol e Regatas players
Cruzeiro Esporte Clube players
Club Athletico Paranaense players
Tokyo Verdy players
Al Hilal SFC players
Kashiwa Reysol players
Oita Trinita players
Kawasaki Frontale players
Avispa Fukuoka players
Expatriate men's footballers in Japan
Brazilian expatriate sportspeople in Saudi Arabia
Expatriate men's footballers in Saudi Arabia
Men's association football forwards
People from Montes Claros |
https://en.wikipedia.org/wiki/Shintani%20zeta%20function | In mathematics, a Shintani zeta function or Shintani L-function is a generalization of the Riemann zeta function. They were first studied by . They include Hurwitz zeta functions and Barnes zeta functions.
Definition
Let be a polynomial in the variables with real coefficients such that is a product of linear polynomials with positive coefficients, that is, , where where , and . The Shintani zeta function in the variable is given by (the meromorphic continuation of)
The multi-variable version
The definition of Shintani zeta function has a straightforward generalization to a zeta function in several variables given byThe special case when k = 1 is the Barnes zeta function.
Relation to Witten zeta functions
Just like Shintani zeta functions, Witten zeta functions are defined by polynomials which are products of linear forms with non-negative coefficients. Witten zeta functions are however not special cases of Shintani zeta functions because in Witten zeta functions the linear forms are allowed to have some coefficients equal to zero. For example, the polynomial defines the Witten zeta function of but the linear form has -coefficient equal to zero.
References
Zeta and L-functions |
https://en.wikipedia.org/wiki/Multiple%20gamma%20function | In mathematics, the multiple gamma function is a generalization of the Euler gamma function and the Barnes G-function. The double gamma function was studied by . At the end of this paper he mentioned the existence of multiple gamma functions generalizing it, and studied these further in .
Double gamma functions are closely related to the q-gamma function, and triple gamma functions are related to the elliptic gamma function.
Definition
For , let
where is the Barnes zeta function. (This differs by a constant from Barnes's original definition.)
Properties
Considered as a meromorphic function of , has no zeros. It has poles at for non-negative integers . These poles are simple unless some of them coincide. Up to multiplication by the exponential of a polynomial, is the unique meromorphic function of finite order with these zeros and poles.
In the case of the double Gamma function, the asymptotic behaviour for is known, and the leading factor is
Infinite product representation
The multiple gamma function has an infinite product representation that makes it manifest that it is meromorphic, and that also makes the positions of its poles manifest. In the case of the double gamma function, this representation is
where we define the -independent coefficients
where is an -th order residue at .
Another representation as a product over leads to an algorithm for numerically computing the double Gamma function.
Reduction to the Barnes G-function
The double gamma function with parameters obeys the relations
It is related to the Barnes G-function by
The double gamma function and conformal field theory
For and , the function
is invariant under , and obeys the relations
For , it has the integral representation
From the function , we define the double Sine function and the Upsilon function by
These functions obey the relations
plus the relations that are obtained by . For they have the integral representations
The functions and appear in correlation functions of two-dimensional conformal field theory, with the parameter being related to the central charge of the underlying Virasoro algebra. In particular, the three-point function of Liouville theory is written in terms of the function .
References
Further reading
Gamma and related functions |
https://en.wikipedia.org/wiki/Barnes%20zeta%20function | In mathematics, a Barnes zeta function is a generalization of the Riemann zeta function introduced by . It is further generalized by the Shintani zeta function.
Definition
The Barnes zeta function is defined by
where w and aj have positive real part and s has real part greater than N.
It has a meromorphic continuation to all complex s, whose only singularities are simple poles at s = 1, 2, ..., N. For N = w = a1 = 1 it is the Riemann zeta function.
References
Zeta and L-functions |
https://en.wikipedia.org/wiki/Yusuke%20Gondo | is a former Japanese football player.
Club statistics
References
External links
1982 births
Living people
Seisa Dohto University alumni
Association football people from Tokyo
Japanese men's footballers
J2 League players
Hokkaido Consadole Sapporo players
Mito HollyHock players
Zweigen Kanazawa players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Taguig%20Science%20High%20School | Taguig Science High School (commonly called as TagSci) is a public specialized secondary science school in the Philippines that specializes in science, english, and mathematics curriculum.
Formerly known as a Science Special class, Taguig Science High School is located at its Annex branch in C.P. Tiñga Sports Complex, Hagonoy, Taguig City and Main branch in Brgy. San Miguel, Taguig City. Its establishment was made possible by the City Mayor Hon. Sigfrido R. Tiñga in collaboration with the Department of Education (Philippines)- Division of Taguig and Pateros, then Schools Division Superintendent, Jovita O. Calixihan.
School History
June 2002
Taguig Science was formerly known as a Special Science class which initially housed 35 students each section on its academic year 2002-2003 which were temporarily housed at Signal Village National High School.
October 22, 2003
A resolution endorsing the creation of Taguig Science High School was approved by the Office of the Division of Taguig and Pateros (TaPat) signed by the President of TAPASPA and PESPA and the Assistant Schools Division Superintendent and OIC Dr. Estrellita Putian.
November 10, 2003
Dr. Estrellita Putian, OIC, submitted the Feasibility Study for the creation of Taguig Science High School to Councilor Myla Rodriguez Valencia, Chairman, Committee on Education, Municipality of Taguig.
December 9, 2003
The Municipality of Taguig enacted Ordinance No. 104, s. 2003, an Ordinance establishing the Taguig Science High School to be funded by the Local School Board of Taguig.
February 13, 2004
The Division Office of Taguig and Pateros through Dr. Rolando Magno, Schools Division Superintendent, forward a copy of the said ordinance to Hon. Edilberto de Jesus, Secretary of Education.
March 12, 2004
The request of the local government for allocation of funds in the amount of Thirty Million Pesos (P30.0 M) for the construction of a two-storey (12 classrooms) school building with laboratories for the proposed Taguig Science and Technology Multi-Purpose Hall was referred to the DepEd-NCR by the Planning Office of DepEd, Central Office.
March 29, 2004
The Regional Office denied the request of the local government re: the appropriation for the construction of the proposed Taguig Science High School.
April 1, 2004
The Regional Office acknowledged the receipt of Ordinance No. 104, s. 2003 and requested the Division Office to submit the requirements for the establishment of Taguig Science High School as stipulated in DepEd Order No. 5, s. 1989.
June 4, 2004
Additional requirements for the establishment of Taguig Science High School were requested from the Division Office by the Regional Office.
August 9, 2004
The Division Office submitted to the regional Office the evaluated documents of the Taguig Science High School.
September 8, 2004
An ocular inspection of the school was conducted by Dr. Luz Rojo, Chief of Secondary Education division and Mrs. Aurora A. Franco, Education |
https://en.wikipedia.org/wiki/Venvaroha | Veṇvāroha is a work in Sanskrit composed by Mādhava of Sangamagrāma ( – ), the founder of the Kerala school of astronomy and mathematics. It is a work in 74 verses describing methods for the computation of the true positions of the Moon at intervals of about half an hour for various days in an anomalistic cycle. This work is an elaboration of an earlier and shorter work of Mādhava himself titled Sphutacandrāpti. Veṇvāroha is the most popular astronomical work of Mādhava.
Etymology
The title Veṇvāroha literally means 'Bamboo Climbing' (Veṇu 'bamboo' + āroha 'climbing') and it is indicative of the computational procedure expounded in the text. The computational scheme is like climbing a bamboo tree, going up and up step by step at measured equal heights.
Overview
It is dated 1403 CE. Acyuta Piṣārati (1550–1621), another prominent mathematician/astronomer of the Kerala school, has composed a Malayalam commentary on Veṇvāroha. This astronomical treatise is of a type generally described as Karaṇa texts in India. Such works are characterized by the fact that they are compilations of computational methods of practical astronomy.
The novelty and ingenuity of the method attracted the attention of several of the followers of Mādhava and they composed similar texts thereby creating a genre of works in Indian mathematical tradition collectively referred to as ‘veṇvāroha texts’. These include Drik-veṇvārohakriya of unknown authorship of epoch 1695 and Veṇvārohastaka of Putuman Somāyaji.
In the technical terminology of astronomy, the ingenuity introduced by Mādhava in Veṇvāroha can be explained thus: Mādhava has endeavored to compute the true longitude of the Moon by making use of the true motions rather than the epicyclic astronomy of the Aryabhata tradition. He made use of the anomalistic revolutions for computing the true positions of the Moon using the successive true daily velocity specified in Candravākyas (Table of Moon-mnemonics) for easy memorization and use.
Veṇvāroha has been studied from a modern perspective and the process is explained using the properties of periodic functions.
See also
Indian mathematics
Indian mathematicians
Kerala school of astronomy and mathematics
Madhava of Sangamagrama
References
Further reading
For a fuller technical account of the contents of Veṇvāroha see :
Veṇvāroha with the Malayalam commentary of Achyuta Pisharati has been edited by K.V. Sarma and published by Sanskrit College, Thrippunithura, Kerala, India in 1956.
Hindu astronomy
History of mathematics
Kerala school of astronomy and mathematics
Indian astronomy texts |
https://en.wikipedia.org/wiki/Gy%C3%B6rgy%20Elekes | György Elekes (19 May 1949 – 29 September 2008) was a Hungarian mathematician and computer scientist who specialized in Combinatorial geometry and Combinatorial set theory. He may be best known for his work in the field that would eventually be called Additive Combinatorics. Particularly notable was his "ingenious" application of the Szemerédi–Trotter theorem to improve the best known lower bound for the sum-product problem. He also proved that any polynomial-time algorithm approximating the volume of convex bodies must have a multiplicative error, and the error grows exponentially on the dimension. With Micha Sharir he set up a framework which eventually led Guth and Katz to the solution of the Erdős distinct distances problem. (See below.)
Life
After graduating from the mathematics program at Fazekas Mihály Gimnázium (i.e., "Fazekas Mihály high school" in Budapest, which is known for its excellence, especially in mathematics), Elekes studied mathematics at the Eötvös Loránd University. Upon completing his degree, he joined the faculty in the Department of Analysis at the university. In 1984, he joined the newly forming Department of Computer Science, which was being headed by László Lovász. Elekes was promoted to full professor in 2005. He received the Doctor of Mathematical Sciences title from the Hungarian Academy of Sciences in 2001.
Work
Elekes started his mathematical work in combinatorial set theory, answering some questions posed by Erdős and Hajnal. One of his results states that if the set of infinite subsets of the set of natural numbers is split into countably many parts, then in one of them, there is a solution of the equation A∪B=C. His interest later switched to another favorite topic of Erdős, discrete geometry and geometric algorithm theory. In 1986 he proved that if a deterministic polynomial algorithm computes a number V(K) for every convex body K in any Euclidean space given by a separation oracle such that V(K) always at least vol(K), the volume of K, then for every large enough dimension n, there is a convex body in the n-dimensional Euclidean space such that V(K)>20.99nvol(K). That is, any polynomial-time estimator of volume over K must be inaccurate by at least an exponential factor.
Not long before his death he developed new tools in Algebraic geometry and used them to obtain results in Discrete geometry, proving Purdy's Conjecture. Micha Sharir organized, extended and published Elekes's posthumous notes on these methods. Then Nets Katz and Larry Guth used them to solve (apart from a factor of (log n) 1/2 ) the Erdős distinct distances problem, posed in 1946.
References
External links
Elekes' home page
Number theorists
Combinatorialists
Researchers in geometric algorithms
20th-century Hungarian mathematicians
21st-century Hungarian mathematicians
Hungarian computer scientists
1949 births
2008 deaths |
https://en.wikipedia.org/wiki/Stevedore%20knot%20%28mathematics%29 | In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. The stevedore knot is listed as the 61 knot in the Alexander–Briggs notation, and it can also be described as a twist knot with four half twists, or as the (5,−1,−1) pretzel knot.
The mathematical stevedore knot is named after the common stevedore knot, which is often used as a stopper at the end of a rope. The mathematical version of the knot can be obtained from the common version by joining together the two loose ends of the rope, forming a knotted loop.
The stevedore knot is invertible but not amphichiral. Its Alexander polynomial is
its Conway polynomial is
and its Jones polynomial is
The Alexander polynomial and Conway polynomial are the same as those for the knot 946, but the Jones polynomials for these two knots are different. Because the Alexander polynomial is not monic, the stevedore knot is not fibered.
The stevedore knot is a ribbon knot, and is therefore also a slice knot.
The stevedore knot is a hyperbolic knot, with its complement having a volume of approximately 3.16396.
See also
Figure-eight knot (mathematics)
References
Double torus knots and links |
https://en.wikipedia.org/wiki/Cyclic%20polytope | In mathematics, a cyclic polytope, denoted C(n,d), is a convex polytope formed as a convex hull of n distinct points on a rational normal curve in Rd, where n is greater than d. These polytopes were studied by Constantin Carathéodory, David Gale, Theodore Motzkin, Victor Klee, and others. They play an important role in polyhedral combinatorics: according to the upper bound theorem, proved by Peter McMullen and Richard Stanley, the boundary Δ(n,d) of the cyclic polytope C(n,d) maximizes the number fi of i-dimensional faces among all simplicial spheres of dimension d − 1 with n vertices.
Definition
The moment curve in is defined by
.
The -dimensional cyclic polytope with vertices is the convex hull
of distinct points with on the moment curve.
The combinatorial structure of this polytope is independent of the points chosen, and the resulting polytope has dimension d and n vertices. Its boundary is a (d − 1)-dimensional simplicial polytope denoted Δ(n,d).
Gale evenness condition
The Gale evenness condition provides a necessary and sufficient condition to determine a facet on a cyclic polytope.
Let . Then, a -subset forms a facet of iff any two elements in are separated by an even number of elements from in the sequence .
Neighborliness
Cyclic polytopes are examples of neighborly polytopes, in that every set of at most d/2 vertices forms a face. They were the first neighborly polytopes known, and Theodore Motzkin conjectured that all neighborly polytopes are combinatorially equivalent to cyclic polytopes, but this is now known to be false.
Number of faces
The number of i-dimensional faces of the cyclic polytope Δ(n,d) is given by the formula
and completely determine via the Dehn–Sommerville equations.
Upper bound theorem
The upper bound theorem states that cyclic polytopes have the maximum possible number of faces for a given dimension and number of vertices: if Δ is a simplicial sphere of dimension d − 1 with n vertices, then
The upper bound conjecture for simplicial polytopes was proposed by Theodore Motzkin in 1957 and proved by Peter McMullen in 1970. Victor Klee suggested that the same statement should hold for all simplicial spheres and this was indeed established in 1975 by Richard P. Stanley using the notion of a Stanley–Reisner ring and homological methods.
See also
Combinatorial commutative algebra
References
Polyhedral combinatorics |
https://en.wikipedia.org/wiki/Takuro%20Shintani | was a Japanese mathematician working in number theory who introduced Shintani zeta functions and Shintani's unit theorem. Shintani died by suicide at the age of 37 on 14 November 1980.
Notes
References
1943 births
1980 deaths
20th-century Japanese mathematicians |
https://en.wikipedia.org/wiki/PSTN%20network%20topology | PSTN network topology is the switching network topology of a telephone network connected to the public switched telephone network (PSTN).
In the United States and Canada, the Bell System network topology was the switching system hierarchy implemented and operated from c. 1930 to the 1980s for the purpose of integrating the diverse array of local telephone companies and telephone numbering plans to achieve nationwide Direct Distance Dialing (DDD) by telephone subscribers. It was the precursor of the world-wide interconnected public switched telephone network (PSTN) and originated in the efforts of the General Toll Switching Plan that by 1929 formulated the technical infrastructure and the operating principles for connecting long-distance telephone calls in North America.
The ideas were first developed in the Bell System in the United States, but were soon adopted by other countries where telephone companies were facing similar issues, even when servicing smaller geographic areas. The system in the United Kingdom implemented by the General Post Office resulted in fewer switching levels than in the Bell System.
Bell System
In the late 1940s the Bell System devised plans to consolidate the various incompatible local telephone numbering plans of affiliated and independent service provides in North America into a unified numbering and routing system, that later became known as the North American Numbering Plan (NANP). Initially designed for use in Operator Toll Dialing, the reorganization was also a prerequisite for Direct Distance Dialing (DDD) by customers, first implemented in Englewood, New Jersey in 1951. In addition to devising a unified numbering plan, the American Telephone and Telegraph Company (AT&T) reorganized the switching and routing plan under management by AT&T Long Lines into a hierarchical network with five levels, termed "classes of switching systems.
The newly devised hierarchy was maintained into the early 1980s, when technological advances and business models rendered it increasingly obsolete, but the hierarchical features live on in terms, such as Class 4 and Class 5 telephone switch, referring to tandem and end-office switches, respectively. The PSTN in the United States was essentially restructured with the 1984 divestiture of AT&T. The old Long Lines network remained with AT&T, but its internal routing became non-hierarchical with the introduction of advanced computer-controlled switching. Each major long-distance carrier can have its own internal routing policies, though they generally start with the same principles and even components.
With Bell System divestiture, the network in the US was divided into local access and transport areas (LATAs). Calls within LATAs were carried by Local Exchange Carriers (LECs), while calls between them were carried by interexchange carriers (IXCs). LATAs generally have one or more tandem switches which interconnect end office switches.
While the following discussion refers to AT&T an |
https://en.wikipedia.org/wiki/Square%20knot%20%28mathematics%29 | In knot theory, the square knot is a composite knot obtained by taking the connected sum of a trefoil knot with its reflection. It is closely related to the granny knot, which is also a connected sum of two trefoils. Because the trefoil knot is the simplest nontrivial knot, the square knot and the granny knot are the simplest of all composite knots.
The square knot is the mathematical version of the common reef knot.
Construction
The square knot can be constructed from two trefoil knots, one of which must be left-handed and the other right-handed. Each of the two knots is cut, and then the loose ends are joined together pairwise. The resulting connected sum is the square knot.
It is important that the original trefoil knots be mirror images of one another. If two identical trefoil knots are used instead, the result is a granny knot.
Properties
The square knot is amphichiral, meaning that it is indistinguishable from its own mirror image. The crossing number of a square knot is six, which is the smallest possible crossing number for a composite knot.
The Alexander polynomial of the square knot is
which is simply the square of the Alexander polynomial of a trefoil knot. Similarly, the Alexander–Conway polynomial of a square knot is
These two polynomials are the same as those for the granny knot. However, the Jones polynomial for the square knot is
This is the product of the Jones polynomials for the right-handed and left-handed trefoil knots, and is different from the Jones polynomial for a granny knot.
The knot group of the square knot is given by the presentation
This is isomorphic to the knot group of the granny knot, and is the simplest example of two different knots with isomorphic knot groups.
Unlike the granny knot, the square knot is a ribbon knot, and it is therefore also a slice knot.
References |
https://en.wikipedia.org/wiki/Granny%20knot%20%28mathematics%29 | In knot theory, the granny knot is a composite knot obtained by taking the connected sum of two identical trefoil knots. It is closely related to the square knot, which can also be described as a connected sum of two trefoils. Because the trefoil knot is the simplest nontrivial knot, the granny knot and the square knot are the simplest of all composite knots.
The granny knot is the mathematical version of the common granny knot.
Construction
The granny knot can be constructed from two identical trefoil knots, which must either be both left-handed or both right-handed. Each of the two knots is cut, and then the loose ends are joined together pairwise. The resulting connected sum is the granny knot.
It is important that the original trefoil knots be identical to each another. If mirror-image trefoil knots are used instead, the result is a square knot.
Properties
The crossing number of a granny knot is six, which is the smallest possible crossing number for a composite knot. Unlike the square knot, the granny knot is not a ribbon knot or a slice knot.
The Alexander polynomial of the granny knot is
which is simply the square of the Alexander polynomial of a trefoil knot. Similarly, the Conway polynomial of a granny knot is
These two polynomials are the same as those for the square knot. However, the Jones polynomial for the (right-handed) granny knot is
This is the square of the Jones polynomial for the right-handed trefoil knot, and is different from the Jones polynomial for a square knot.
The knot group of the granny knot is given by the presentation
This is isomorphic to the knot group of the square knot, and is the simplest example of two different knots with isomorphic knot groups.
References
Composite knots and links |
https://en.wikipedia.org/wiki/Hypercomplex%20analysis | In mathematics, hypercomplex analysis is the extension of complex analysis to the hypercomplex numbers. The first instance is functions of a quaternion variable, where the argument is a quaternion (in this case, the sub-field of hypercomplex analysis is called quaternionic analysis). A second instance involves functions of a motor variable where arguments are split-complex numbers.
In mathematical physics, there are hypercomplex systems called Clifford algebras. The study of functions with arguments from a Clifford algebra is called Clifford analysis.
A matrix may be considered a hypercomplex number. For example, the study of functions of 2 × 2 real matrices shows that the topology of the space of hypercomplex numbers determines the function theory. Functions such as square root of a matrix, matrix exponential, and logarithm of a matrix are basic examples of hypercomplex analysis.
The function theory of diagonalizable matrices is particularly transparent since they have eigendecompositions. Suppose where the Ei are projections. Then for any polynomial ,
The modern terminology for a "system of hypercomplex numbers" is an algebra over the real numbers, and the algebras used in applications are often Banach algebras since Cauchy sequences can be taken to be convergent. Then the function theory is enriched by sequences and series. In this context the extension of holomorphic functions of a complex variable is developed as the holomorphic functional calculus. Hypercomplex analysis on Banach algebras is called functional analysis.
See also
Giovanni Battista Rizza
References
Sources
Daniel Alpay (ed.) (2006) Wavelets, Multiscale systems and Hypercomplex Analysis, Springer, .
Enrique Ramirez de Arellanon (1998) Operator theory for complex and hypercomplex analysis, American Mathematical Society (Conference proceedings from a meeting in Mexico City in December 1994).
J. A. Emanuello (2015) Analysis of functions of split-complex, multi-complex, and split-quaternionic variables and their associated conformal geometries, Ph.D. Thesis, Florida State University
Sorin D. Gal (2004) Introduction to the Geometric Function theory of Hypercomplex variables, Nova Science Publishers, .
R. Lavika & A.G. O’Farrell & I. Short (2007) "Reversible maps in the group of quaternionic Möbius transformations", Mathematical Proceedings of the Cambridge Philosophical Society 143:57–69.
Irene Sabadini and Franciscus Sommen (eds.) (2011) Hypercomplex Analysis and Applications, Birkhauser Mathematics.
Irene Sabadini & Michael V. Shapiro & F. Sommen (editors) (2009) Hypercomplex Analysis, Birkhauser .
Sabadini, Sommen, Struppa (eds.) (2012) Advances in Hypercomplex Analysis, Springer.
Functions and mappings
Hypercomplex numbers
Mathematical analysis |
https://en.wikipedia.org/wiki/Israel%20Institute%20for%20Advanced%20Studies | The Israel Institute for Advanced Studies (; IIAS, or IAS in Israel) is a research institute in Jerusalem, Israel, devoted to academic research in physics, mathematics, the life sciences, economics, and comparative religion. It is a self-governing body, both in its administrative function as well as its academic pursuits. It is one of the nine members of the symposium Some Institutes for Advanced Study (SIAS).
The IIAS is located at the Edmond J. Safra Campus of the Hebrew University of Jerusalem in Givat Ram. The Institute brings together scholars from around the world to engage in collaborative research projects for periods of four to twelve months. Throughout over forty years of existence it has been dedicated to unrestricted academic research.
History
The Institute for Advanced Studies in Jerusalem was founded in 1975 by Israeli mathematician Aryeh Dvoretzky, winner of the Israel Prize for Mathematics. Visits to the Institute for Advanced Study in Princeton, New Jersey inspired Prof. Dvoretzky to establish an IAS in Jerusalem in 1975. In March, 1976 Dvoretzky wrote:
In 1982, Yuval Ne'eman, Professor of Physics and Minister of Science, established the first School in Theoretical Physics at the Jerusalem IAS. Prof. Steven Weinberg, Nobel laureate in Physics, was asked to become the director of the School, a post he held for twelve years. Four additional Schools were established, based on the same model, in the following fields: Economics, Life Sciences, Jewish Studies and Comparative Religion, and Mathematics. Each School is headed by a preeminent scholar in his or her field.
Directors
Aryeh Dvoretzky (1975–1985)
Menahem Yaari (1986-1989, 1990-1992)
Hanoch Gutfreund (1989-1990)
David Dean Shulman (1992–1998)
Alexander Levitzki (1998–2001)
Benjamin Z. Kedar (2001–2005)
Eliezer Rabinovici (2005–2012)
Michal Linial (2012–2018)
Yitzhak Hen (2018–present)
Advanced schools
The Institute annually hosts five schools under the auspices of the Victor Rothschild Memorial Symposia. Each lasts seven to twelve days, and is headed by an internationally preeminent scholar, working alongside an Israeli co-director. Attendees include senior scholars, doctoral students, and postdoctoral researchers. The Institute subsidizes participants in the form of travel grants, tuition or hotel expenses. The Israeli coordinator allocates scholarships to candidates and assumes responsibility for technical arrangements. Scholars have come to the institute from Western and Eastern Europe, South and North America, East Asia, and North Africa.
The IIAS also hosts conferences and lecture series, sometimes associated with schools, such as the Ada Lovelace Bicentenary Lectures on Computability during 2015–16.
Current directors of the advanced schools are as follows:
School in Theoretical physics: David Gross
School in Economics Theory: Eric Maskin
Midrasha Mathematicae: Peter Sarnak
School in Jewish Studies and Comparative Religion: Haym Soloveitchik
School in |
https://en.wikipedia.org/wiki/Takamichi%20Seki | is a former Japanese football player.
Club statistics
References
External links
1981 births
Living people
Toyo University alumni
Association football people from Chiba Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Omiya Ardija players
Mito HollyHock players
Hokkaido Consadole Sapporo players
Fagiano Okayama players
FC Ryukyu players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Yuhei%20Ono | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Association football people from Osaka Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Tokyo Verdy players
Tokushima Vortis players
Fagiano Okayama players
Fukushima United FC players
Iwate Grulla Morioka players
Expatriate men's footballers in Thailand
Men's association football midfielders |
https://en.wikipedia.org/wiki/Kohei%20Kiyama | is a Japanese football player. He plays for Fagiano Okayama.
Club career statistics
Updated to 10 August 2022.
References
External links
Fagiano Okayama
1988 births
Living people
Association football people from Tokyo
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Tokyo Verdy players
Fagiano Okayama players
Kamatamare Sanuki players
Matsumoto Yamaga FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Herglotz%E2%80%93Zagier%20function | In mathematics, the Herglotz–Zagier function, named after Gustav Herglotz and Don Zagier, is the function
introduced by who used it to obtain a Kronecker limit formula for real quadratic fields.
References
Special functions |
https://en.wikipedia.org/wiki/Additional%20Mathematics | Additional Mathematics is a qualification in mathematics, commonly taken by students in high-school (or GCSE exam takers in the United Kingdom). It features a range of problems set out in a different format and wider content to the standard Mathematics at the same level.
Additional Mathematics in Singapore
In Singapore, Additional Mathematics is an optional subject offered to pupils in secondary school—specifically those who have an aptitude in Mathematics and are in the Normal (Academic) stream or Express stream. The syllabus covered is more in-depth as compared to Elementary Mathematics, with additional topics including Algebra binomial expansion, proofs in plane geometry, differential calculus and integral calculus. Additional Mathematics is also a prerequisite for students who are intending to offer H2 Mathematics and H2 Further Mathematics at A-level (if they choose to enter a Junior College after secondary school). Students without Additional Mathematics at the 'O' level will usually be offered H1 Mathematics instead.
Examination Format
The syllabus was updated starting with the 2021 batch of candidates. There are two written papers, each comprising half of the weightage towards the subject. Each paper is 2 hours 15 minutes long and worth 90 marks. Paper 1 has 12 to 14 questions, while Paper 2 has 9 to 11 questions. Generally, Paper 2 would have a graph plotting question based on linear law.
GCSE Additional Mathematics in Northern Ireland
In Northern Ireland, Additional Mathematics was offered as a GCSE subject by the local examination board, CCEA. There were two examination papers: one which tested topics in Pure Mathematics, and one which tested topics in Mechanics and Statistics. It was discontinued in 2014 and replaced with GCSE Further Mathematics—a new qualification whose level exceeds both those offered by GCSE Mathematics, and the analogous qualifications offered in England.
Further Maths IGCSE and Additional Maths FSMQ in England
Starting from 2012, Edexcel and AQA have started a new course which is an IGCSE in Further Maths. Edexcel and AQA both offer completely different courses, with Edexcel including the calculation of solids formed through integration, and AQA not including integration.
AQA's syllabus mainly offers further algebra, with the factor theorem and the more complex algebra such as algebraic fractions. It also offers differentiation up to—and including—the calculation of normals to a curve. AQA's syllabus also includes a wide selection of matrices work, which is an AS Further Mathematics topic.
AQA's syllabus is much more famous than Edexcel's, mainly for its controversial decision to award an A* with Distinction (A^), a grade higher than the maximum possible grade in any Level 2 qualification; it is known colloquially as a Super A* or A**.
A new Additional Maths course from 2018 is OCR Level 3 FSMQ: Additional Maths (6993). In addition to algebra, coordinate geometry, Pythagorean theorem, trigonometry a |
https://en.wikipedia.org/wiki/Gregory%20R.%20Hancock | Gregory Robert Hancock (born April 18, 1963 in Seattle, Washington, USA) is a Professor of Measurement, Statistics and Evaluation. He is the current University of Maryland head of the Educational Department of Measurement and Statistics (EDMS) program. Hancock also co-hosts the podcast Quantitude with Patrick Curran. He is internationally known for the voice of Jiffy from the podcast.
References
External links
University of Maryland EDMS website
Website for the Center for Integrated Latent Variable Research
1963 births
Living people
University of Maryland, College Park faculty |
https://en.wikipedia.org/wiki/Klaus%20Fischer%20%28mathematician%29 | Klaus Gunter Fischer (November 12, 1943 – July 2, 2009) was a German-American mathematician of German origin. He worked on a wide range of problems in algebraic geometry, commutative algebra, graph theory, and combinatorics.
Fischer was chair of the Mathematics Department at George Mason University at the time of his death.
References
External links
1943 births
2009 deaths
20th-century American mathematicians
21st-century American mathematicians
20th-century German mathematicians
21st-century German mathematicians
Group theorists
George Mason University faculty
Northwestern University alumni |
https://en.wikipedia.org/wiki/Witten%20zeta%20function | In mathematics, the Witten zeta function, is a function associated to a root system that encodes the degrees of the irreducible representations of the corresponding Lie group. These zeta functions were introduced by Don Zagier who named them after Edward Witten's study of their special values (among other things). Note that in, Witten zeta functions do not appear as explicit objects in their own right.
Definition
If is a compact semisimple Lie group, the associated Witten zeta function is (the meromorphic continuation of) the series
where the sum is over equivalence classes of irreducible representations of .
In the case where is connected and simply connected, the correspondence between representations of and of its Lie algebra, together with the Weyl dimension formula, implies that can be written as
where denotes the set of positive roots, is a set of simple roots and is the rank.
Examples
, the Riemann zeta function.
Abscissa of convergence
If is simple and simply connected, the abscissa of convergence of is , where is the rank and . This is a theorem due to Alex Lubotzky and Michael Larsen. A new proof is given by Jokke Häsä and Alexander Stasinski
which yields a more general result, namely it gives an explicit value (in terms of simple combinatorics) of the abscissa of convergence of any "Mellin zeta function" of the form
where is a product of linear polynomials with non-negative real coefficients.
Singularities and values of the Witten zeta function associated to SU(3)
is absolutely convergent in , and it can be extended meromorphicaly in . Its singularities are in and all of those singularities are simple poles. In particular, the values of are well defined at all integers, and have been computed by Kazuhiro Onodera.
At , we have and
Let be a positive integer. We have
If a is odd, then has a simple zero at and
If a is even, then has a zero of order at and
References
Zeta and L-functions |
https://en.wikipedia.org/wiki/Tests%20of%20Engineering%20Aptitude%2C%20Mathematics%2C%20and%20Science | Tests of Engineering Aptitude, Mathematics, and Science (TEAMS) is an annual competition originally organized by the Junior Engineering Technical Society (JETS). TEAMS is an annual theme-based competition for students in grades 9–12, aimed at giving them the opportunity to discover engineering and how they can make a difference in the world.
History
The TEAMS competition was created in 1975 at the University of Illinois for the state of Illinois. In 1978, JETS expanded TEAMS to become a national competition. In 1993, the TEAMS test changed format into a format very similar to the one used today. Since 2008, the TEAMS competitions have had a theme.
The 2010 theme for the TEAMS competition delved in the problems engineers face while providing access to clean water. It was named for Samuel Taylor Coleridge's famous quote, "Water, water, everywhere, / Nor any drop to drink."
Format
This competition is divided in two parts. The first part, lasting an hour and a half, has 80 multiple choice questions. Each group of ten questions is related to a specific problem relating to the overall theme. The second part consists of eight open-ended tasks that are aimed at encouraging teamwork to develop the best answer. This competition is taken part by each participating school in a regional competition; the scores at that date determine the standings in the regional, state, and national level. There are six school divisions, one home division, one group division and two levels (9th/10th grade level & 11th/12th grade level).
Each team consists of eight high school students. A school may submit multiple teams. Thousands of teams participate in this competition each year.
References
Engineering competitions |
https://en.wikipedia.org/wiki/Induce | Induce may refer to:
Induced consumption
Induced innovation
Induced character
Induced coma
Induced menopause
Induced metric
Induced path
Induced topology
Induce (musician), American musician
Labor induction, stimulation of childbirth
See also
Inducement (disambiguation)
Induction (disambiguation) |
https://en.wikipedia.org/wiki/1994%E2%80%9395%20SS%20Lazio%20season | S.S. Lazio finished in second place in Serie A this season and reached the quarter-final of the UEFA Cup.
Squad
Transfers
Winter
Serie A
League table
Results by round
Matches
Statistics
Players statistics
Top scorers
Giuseppe Signori 17 (3)
Pierluigi Casiraghi 11 (1)
Alen Bokšić 9
Diego Fuser 5
Aron Winter 5
References
SS Lazio seasons
Lazio |
https://en.wikipedia.org/wiki/Brazil%20national%20football%20team%20records%20and%20statistics | This is a list of the Brazil national football team's competitive records and statistics.
Honours
Senior team
Major competitions
FIFA World Cup:
Winners (5): 1958, 1962, 1970, 1994, 2002
Runners-up (2): 1950, 1998
Third place (2): 1938, 1978
Fourth place (2): 1974, 2014
South American Championship / Copa América:
Winners (9): 1919, 1922, 1949, 1989, 1997, 1999, 2004, 2007, 2019
Runners-up (12): 1921, 1925, 1937, 1945, 1946, 1953, 1957, 1959 (Argentina), 1983, 1991, 1995, 2021
Third place (7): 1916, 1917, 1920, 1942, 1959 (Ecuador), 1975, 1979
Fourth place (3): 1923, 1956, 1963
FIFA Confederations Cup:
Winners (4): 1997, 2005, 2009, 2013
Runners-up: 1999
Fourth place: 2001
Panamerican Championship:
Winners (2): 1952, 1956
Runners-up: 1960
CONCACAF Gold Cup:
Runners-up (2): 1996, 2003
Third place: 1998
Awards
FIFA Team of the Year:
Winners (12): 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2003, 2004, 2005, 2006
World Soccer Team of the Year
Winners (2): 1982, 2002
FIFA World Cup Fair Play Trophy:
Winners (4): 1982, 1986, 1994, 2006
FIFA Confederations Cup Fair Play Trophy:
Winners (2): 1999, 2009
Copa América Fair Play Trophy:
Winners (1) : 2019
South-American National Teams Tournaments
Roca Cup / Superclásico de las Américas (vs ):
Winners (12): 1914, 1922, 1945, 1957, 1960, 1963, 1971 (shared), 1976, 2011, 2012, 2014, 2018
Copa Confraternidad (vs ):
Winners: 1923
Copa 50imo Aniversario de Clarín (vs ):
Winners: 1995
Copa Río Branco (vs ):
Winners (7): 1931, 1932, 1947, 1950, 1967 (shared), 1968, 1976
Copa Rodrigues Alves (vs ):
Winners (2): 1922, 1923
Taça Oswaldo Cruz (vs ):
Winners (8): 1950, 1955, 1956, 1958, 1961, 1962, 1968, 1976
Copa Bernardo O'Higgins (vs ):
Winners (4): 1955, 1959, 1961, 1966 (shared)
Copa Teixeira (vs ):
Winners: 1990 (shared)
Taça Jorge Chavéz / Santos Dumont (vs ):
Winners: 1968
Friendlies
Taça Interventor Federal (vs EC Bahia):
Winners: 1934
Taça Dois de Julho (vs Bahia XI):
Winners: 1934
Copa Emílio Garrastazú Médici (vs ):
Winners: 1970
Taça Independência:
Winners: 1972
Taça do Atlântico:
Winners (3): 1956, 1970, 1976
U.S.A. Bicentennial Cup Tournament:
Winners: 1976
Taça Centenário Jornal O Fluminense (vs Rio de Janeiro XI):
Winners: 1978
Saudi Crown Prince Trophy (vs Al Ahli Saudi FC):
Winners: 1978
Rous Cup:
Winners: 1987
Australia Bicentenary Gold Cup:
Winners: 1988
Amistad Cup:
Winners: 1992
Umbro Cup:
Winners: 1995
Nelson Mandela Challenge:
Winners: 1996
Lunar New Year Cup:
Winners: 2005
Kirin Challenge Cup:
Winners: 2022
Olympic and Pan American Team
Summer Olympics:
Gold medalists (2): 2016, 2020
Silver medalists (3): 1984, 1988, 2012
Bronze medalists (2): 1996, 2008
Fourth place: 1976
Pan American Games:
Gold medalists (4): 1963, 1975 (shared), 1979, 1987
Silver medalists (3): 1959, 1983, 2003
Bronze medalists (1): 2015
CONMEBOL Pre-Olympic Tournament:
Winners (7): 1968, 1971, 1976, 1984, 1987, 1996, 2000
|
https://en.wikipedia.org/wiki/Noh%20Yong-hun | Noh Yong-Hoon (; born 29 March 1986) is a South Korean football player who last played for Daejeon Citizen.
Career statistics
External links
1986 births
Living people
Men's association football defenders
South Korean men's footballers
Gyeongnam FC players
Busan IPark players
Daejeon Hana Citizen players
Gangwon FC players
K League 1 players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Peter%20J.%20Bickel | Peter John Bickel (born 1940) is an American statistician and Professor of Statistics at the University of California, Berkeley.
Education and career
Bickel studied physics at the California Institute of Technology. He graduated from University of California, Berkeley, with a Ph.D., in 1963, where he studied under Erich Leo Lehmann.
His students include C.F. Jeff Wu, Jianqing Fan, Katerina Kechris, Elizaveta Levina, and Donald Andrews.
Personal
He married Nancy Kramer in 1964; they have two children.
Awards
1970 Guggenheim Fellow
1973 Fellow of the American Statistical Association
1981 the recipient of COPSS Presidents' Award
1984 MacArthur Fellow
1986 Fellow of the American Academy of Arts and Sciences
1986 Member of the National Academy of Sciences
1986 Honorary Doctorate degree from Hebrew University, Jerusalem
1995 Foreign member of the Royal Netherlands Academy of Arts and Sciences
2006 Commander of the Order of Orange-Nassau
2013 R. A. Fisher Lectureship
2014 Honorary Doctorate degree from ETH Zurich
References
Further reading
External links
Homepage
1940 births
American statisticians
Romanian emigrants to the United States
California Institute of Technology alumni
University of California, Berkeley College of Letters and Science faculty
University of California, Berkeley alumni
MacArthur Fellows
Living people
Fellows of the American Academy of Arts and Sciences
Fellows of the American Statistical Association
Members of the Royal Netherlands Academy of Arts and Sciences
Members of the United States National Academy of Sciences
Presidents of the Institute of Mathematical Statistics
Commanders of the Order of Orange-Nassau
Mathematical statisticians
Network scientists |
https://en.wikipedia.org/wiki/Harmonic%20differential | In mathematics, a real differential one-form ω on a surface is called a harmonic differential if ω and its conjugate one-form, written as ω∗, are both closed.
Explanation
Consider the case of real one-forms defined on a two dimensional real manifold. Moreover, consider real one-forms that are the real parts of complex differentials. Let , and formally define the conjugate one-form to be .
Motivation
There is a clear connection with complex analysis. Let us write a complex number z in terms of its real and imaginary parts, say x and y respectively, i.e. . Since , from the point of view of complex analysis, the quotient tends to a limit as dz tends to 0. In other words, the definition of ω∗ was chosen for its connection with the concept of a derivative (analyticity). Another connection with the complex unit is that (just as ).
For a given function f, let us write , i.e. , where ∂ denotes the partial derivative. Then . Now d((df)∗) is not always zero, indeed , where .
Cauchy–Riemann equations
As we have seen above: we call the one-form ω harmonic if both ω and ω∗ are closed. This means that (ω is closed) and (ω∗ is closed). These are called the Cauchy–Riemann equations on . Usually they are expressed in terms of as and .
Notable results
A harmonic differential (one-form) is precisely the real part of an (analytic) complex differential. To prove this one shows that satisfies the Cauchy–Riemann equations exactly when is locally an analytic function of . Of course an analytic function is the local derivative of something (namely ∫w(z) dz).
The harmonic differentials ω are (locally) precisely the differentials df of solutions f to Laplace's equation .
If ω is a harmonic differential, so is ω∗.
See also
De Rham cohomology
References
Mathematical analysis |
https://en.wikipedia.org/wiki/Twist%20knot | In knot theory, a branch of mathematics, a twist knot is a knot obtained by repeatedly twisting a closed loop and then linking the ends together. (That is, a twist knot is any Whitehead double of an unknot.) The twist knots are an infinite family of knots, and are considered the simplest type of knots after the torus knots.
Construction
A twist knot is obtained by linking together the two ends of a twisted loop. Any number of half-twists may be introduced into the loop before linking, resulting in an infinite family of possibilities. The following figures show the first few twist knots:
Properties
All twist knots have unknotting number one, since the knot can be untied by unlinking the two ends. Every twist knot is also a 2-bridge knot. Of the twist knots, only the unknot and the stevedore knot are slice knots. A twist knot with half-twists has crossing number . All twist knots are invertible, but the only amphichiral twist knots are the unknot and the figure-eight knot.
Invariants
The invariants of a twist knot depend on the number of half-twists. The Alexander polynomial of a twist knot is given by the formula
and the Conway polynomial is
When is odd, the Jones polynomial is
and when is even, it is
References
Twist knots
Double torus knots and links |
https://en.wikipedia.org/wiki/Matsumoto%20zeta%20function | In mathematics, Matsumoto zeta functions are a type of zeta function introduced by Kohji Matsumoto in 1990. They are functions of the form
where p is a prime and Ap is a polynomial.
References
Zeta and L-functions |
https://en.wikipedia.org/wiki/Ingram%20Olkin | Ingram Olkin (July 23, 1924 – April 28, 2016) was a professor emeritus and chair of statistics and education at Stanford University and the Stanford Graduate School of Education. He is known for developing statistical analysis for evaluating policies, particularly in education, and for his contributions to meta-analysis, statistics education, multivariate analysis, and majorization theory.
Biography
Olkin was born in 1924 in Waterbury, Connecticut. He received a B.S. in mathematics at the City College of New York, an M.A. from Columbia University, and his Ph.D. from the University of North Carolina. Olkin also studied with Harold Hotelling. Olkin's advisor was S. N. Roy and his Ph.D. thesis was "On distribution problems in multivariate analysis" submitted in 1951.
Olkin died from complications of colorectal cancer at his home in Palo Alto, California on April 28, 2016, aged 91.
Honors and awards
Olkin was awarded the fourth biennial Elizabeth Scott Award in 1998 from the American Statistical Association for his achievements in supporting women in statistics. Of the 14 recipients thus far, he is the only man.
In 1962 he was elected as a Fellow of the American Statistical Association.
In 1984, he was President of the Institute of Mathematical Statistics. Olkin is a Guggenheim, Fulbright, and Lady Davis Fellow, with an honorary doctorate from De Montfort University.
Publications and editing
Olkin has written many books including Statistical methods for meta-analysis, Probability theory, and Education in a Research University. Olkin's coauthors include S. S. Shrikhande and Larry V. Hedges. Olkin has written two books with Albert W. Marshall, Inequalities: Theory of Majorization and its Applications (1979) and Life distributions: Structure of nonparametric, semiparametric, and parametric families (2007). In nonparametric statistics and decision theory, Olkin wrote Selecting and ordering populations: A new statistical methodology with Jean Dickinson Gibbons and Milton Sobel (1977, 1999).
Ingram was Editor of the Annals of Mathematical Statistics and served as the first editor of the Annals of Statistics, both published by the Institute of Mathematical Statistics. He was a primary force in the founding of the Journal of Educational Statistics, which is published with the American Statistical Association. Olkin was also an editor with the mathematics journal, Linear Algebra and its Applications, and has been active in supporting a series of international conferences on matrix theory, linear algebra, and statistics.
Bibliography
Inequalities: Theory of Majorization and Its Applications (2011) Albert W. Marshall, Ingram Olkin, Barry Arnold, Springer,
Inequalities: Theory of Majorization and Its Applications (1979) Albert W. Marshall, Ingram Olkin, Academic Press,
"A Guide to Probability Theory and Application" (1973), with L. Gleser and C. Derman, Holt, Rinehart and Winston.
"Probability Models and Application" (1994), with L. Gleser and C. |
https://en.wikipedia.org/wiki/Eulerian%20poset | In combinatorial mathematics, an Eulerian poset is a graded poset in which every nontrivial interval has the same number of elements of even rank as of odd rank. An Eulerian poset which is a lattice is an Eulerian lattice. These objects are named after Leonhard Euler. Eulerian lattices generalize face lattices of convex polytopes and much recent research has been devoted to extending known results from polyhedral combinatorics, such as various restrictions on f-vectors of convex simplicial polytopes, to this more general setting.
Examples
The face lattice of a convex polytope, consisting of its faces, together with the smallest element, the empty face, and the largest element, the polytope itself, is an Eulerian lattice. The odd–even condition follows from Euler's formula.
Any simplicial generalized homology sphere is an Eulerian lattice.
Let L be a regular cell complex such that |L| is a manifold with the same Euler characteristic as the sphere of the same dimension (this condition is vacuous if the dimension is odd). Then the poset of cells of L, ordered by the inclusion of their closures, is Eulerian.
Let W be a Coxeter group with Bruhat order. Then (W,≤) is an Eulerian poset.
Properties
The defining condition of an Eulerian poset P can be equivalently stated in terms of its Möbius function:
The dual of an Eulerian poset with a top element, obtained by reversing the partial order, is Eulerian.
Richard Stanley defined the toric h-vector of a ranked poset, which generalizes the h-vector of a simplicial polytope.<ref>Enumerative combinatorics, 3.14, p. 138; formerly called the generalized h-vector.</ref> He proved that the Dehn–Sommerville equations
hold for an arbitrary Eulerian poset of rank d + 1. However, for an Eulerian poset arising from a regular cell complex or a convex polytope, the toric h-vector neither determines, nor is neither determined by the numbers of the cells or faces of different dimension and the toric h''-vector does not have a direct combinatorial interpretation.
Notes
References
Richard P. Stanley, Enumerative Combinatorics, Volume 1. Cambridge University Press, 1997
See also
Abstract polytope
Star product, a method for combining posets while preserving the Eulerian property
Algebraic combinatorics |
https://en.wikipedia.org/wiki/Masaki%20Kinoshita | is a former Japanese football player.
Club statistics
References
External links
1989 births
Living people
Association football people from Hyōgo Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Gamba Osaka players
Roasso Kumamoto players
Ventforet Kofu players
AC Nagano Parceiro players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/D%C3%A1niel%20Vadnai | Dániel Vadnai (born 19 February 1988) is a Hungarian football player who plays for MTK Budapest.
Career
On 3 February 2023, Vadnai returned to MTK Budapest.
Club statistics
Updated to games played as of 10 May 2021.
Debreceni VSC
On 16 August 2013, Vadnai signed a four-year contract with Debreceni VSC.
References
External links
MLSZ
HLSZ
1988 births
Footballers from Budapest
Living people
Hungarian men's footballers
Men's association football defenders
MTK Budapest FC players
Debreceni VSC players
Mezőkövesdi SE footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/List%20of%20career%20achievements%20by%20Carmelo%20Anthony | This page details the records, statistics and career achievements of American basketball player Carmelo Anthony. Anthony is an American basketball forward and is currently playing for the Los Angeles Lakers of the National Basketball Association.
NBA career statistics
Statistics are correct as at March 11, 2020.
Regular season
Playoffs
Career-highs
Awards and accomplishments
NBA
NBA Scoring Leader: 2013
NBA Minutes leader: 2014
7x All-NBA selection:
Second All-NBA team: 2010, 2013, 2010s Decade
Third All-NBA team: 2006, 2007, 2009, 2012
10x NBA All-Star: 2007, 2008, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017
NBA Rookie Challenge MVP: 2005
NBA All-Rookie selection:
First Rookie team: 2004
3x NBA Western Conference Player of the Month
3x NBA Eastern Conference Player of the Month
11x NBA Western Conference Player of the Week
8x NBA Eastern Conference Player of the Week
6x NBA Western Conference Player of the Month
9th Leading Scorer In NBA History
United States National Team
4x Olympic medalist:
Gold: 2008, 2012, 2016
Bronze: 2004
FIBA World Championship medalist:
Bronze: 2006
FIBA Americas Championship medalist:
Gold: 2007
FIBA Americas Under-18 Championship medalist:
Bronze: 2002
USA Basketball Male Athlete of the Year: 2006, 2016
Individual single-game records
Points (Olympics): 37
3-point field goals made: 10
Free throws made: 13
Career total records:
Games played (Olympics): 31
Second all-time in points (Olympics): 336
Field goals attempted (Olympics): 272
Second all-time in 3-point field goals attempted (Olympics): 139
Second all-time in 3-point field goals made (Olympics): 57
Rebounds (Olympics): 125
College
NCAA champion: 2003
Final Four Most Outstanding Player: 2003
Consensus second team All-American: 2003
NCAA East Regional Most Valuable Player: 2003
Consensus Big East Conference Rookie of the Year: 2003
USBWA National Freshman of the Year: 2003
All-Big East First Team: 2003
All-Big East Rookie Team: 2003
10x Big East Rookie of the Week
#15 retired at Syracuse University
High school
USA Today All-USA First Team: 2002
Parade First Team All-American: 2002
McDonald's High School All-American: 2002
Sprite Slam Jam dunk contest champion: 2002
Les Schwab Invitational Most Valuable Player: 2002
Baltimore Catholic League Player of the Year: 2001
Baltimore Sun All-Metropolitan Player of the Year: 2001
Baltimore County Player of the Year: 2001
NBA records
Youngest player to log a double double in a playoff game: (19 years, 331 days)
First player in NBA history to start first 1000 games (accomplished December 9, 2017 at Memphis Grizzlies)
NBA achievements
One of three players in NBA history to have a 20-20 game as a small forward
Includes Shawn Marion and Giannis Antetokounmpo.
One of two players in NBA history to lead their team in playoff points per game as a rookie
Includes David Robinson
Only player in NBA history to score at least 50 points with no points in the paint.
Only player in NBA history to score 62+ points in Madis |
https://en.wikipedia.org/wiki/Agricultural%20Science%20and%20Technology%20Indicators | The Agricultural Science and Technology Indicators (ASTI) is a comprehensive source of information on agricultural research and development (R&D) statistics.
Overview
ASTI compiles, analyzes, and publicizes data on institutional developments, investments, and capacity trends in agricultural R&D in low- and middle-income countries worldwide. ASTI has published a broad set of country briefs and regional synthesis reports that describe general human and financial capacity trends in agricultural R&D at national, regional, and global levels.
ASTI comprises a network of national, regional, and international agricultural R&D agencies and is hosted and facilitated by the International Food Policy Research Institute (IFPRI). ASTI is currently funded by the Bill & Melinda Gates Foundation.
Importance of agricultural R&D data
Greater investment in agricultural research could make a significant contribution to increasing agricultural production to the levels required to feed the world’s growing population. Furthermore, additional investments in agricultural research are required to address emerging challenges, such as increasing weather variability, adaptation to climate change, water scarcity, and increased price volatility in global markets. Despite this growing attention to the agricultural sector and the role of agricultural research, many low- and middle-income countries continue to struggle with serious and deepening capacity and funding constraints in their agricultural research and higher education systems.
Quantitative information is fundamental to understanding the contribution of agricultural science and technology (S&T) to agricultural growth. Indicators derived from such information allow the performance, inputs, and outcomes of agricultural S&T systems to be measured, monitored, and benchmarked. These indicators assist S&T stakeholders in formulating policy, setting priorities, and undertaking strategic planning, monitoring, and evaluation. They also provide information to governments, policy research institutes, universities, and private-sector organizations involved in public debate on the state of agricultural S&T at national, regional, and international levels.
Activities
ASTI’s recent work has primarily focused on the following activities:
initiating institutional survey rounds in Subsaharan Africa, Latin America and the Caribbean, the Asia Pacific, and the Middle East and North Africa;
developing and maintaining a comprehensive, user-friendly website offering access to primary data sources; and
building a network of national, regional and international partners to facilitate data collection efforts and the dissemination of outputs.
Products
In 2009 ASTI launched a web application that allows its users to display different ASTI indicators by country and plot two indicators against each other.
ASTI’s current indicators include
trend data on agricultural scientist numbers and total investments in agricultural research by the |
https://en.wikipedia.org/wiki/Local%20duality | In mathematics, local duality may refer to:
Local Tate duality of modules over a Galois group of a local field
Grothendieck local duality of modules over local rings |
https://en.wikipedia.org/wiki/List%20of%20the%20busiest%20airports%20in%20the%20Republic%20of%20Ireland | The following tables show 2008 to 2019 passenger traffic statistics for all airports in the Republic of Ireland, ranked by total passenger traffic each year. The data also shows available total aircraft movements at each airport based on statistics published by the Irish Aviation Authority.
Dublin Airport is the largest airport in Ireland, and in 2018 was the 13th busiest airport in Europe. Ireland has four main airports: Cork, Dublin, Shannon and Knock. There are also smaller regional airports at Donegal, Kerry, Galway, Sligo and Waterford. The latter three, as of July 2019, do not have any scheduled flights.
Many airlines serve Ireland with Aer Lingus, Aer Lingus Regional and Ryanair having a significant presence at Irish airports. North American airlines serving Ireland include Air Canada, American Airlines, Delta Air Lines and United Airlines.
Ireland is well connected with Europe mainly through Dublin, Shannon and Cork Airports. The United Kingdom is the most flown to country from Ireland. Transatlantic flights are available at Dublin Airport and Shannon Airports. US preclearance is available at both Dublin and Shannon Airports, two of fifteen US preclearance airports in the world.
At a glance
The graph shows the yearly total passenger numbers handled by Irish airports.
Table per year
2022 data
2021 data
2020 data
2019 data
2018 data
2017 data
2016 data
2015 data
2014 data
2013 data
2012 data
2011 data
2010 data
2009 data
See also
List of the busiest airports in Europe
Busiest airports in the United Kingdom by total passenger traffic
List of the busiest airports in the Nordic countries
List of the busiest airports in the Baltic states
References
Ireland, Republic of |
https://en.wikipedia.org/wiki/Ebrahim%20Karimi | Ebrahim Karimi (; born March 6, 1986) is an Iranian footballer who plays for Mashhad in the Iran Premier League.
Club career
Karimi has played his entire career with Rah Ahan.
Club career statistics
International career
He made his debut against Mauritania in April 2012 under Carlos Queiroz.
References
1986 births
Living people
People from Ray, Iran
Sportspeople from Tehran province
Persian Gulf Pro League players
Rah Ahan Tehran F.C. players
Iranian men's footballers
Iran men's international footballers
Men's association football central defenders |
https://en.wikipedia.org/wiki/Javad%20Ashtiani | Javad Ashtiani (born 20 August 1981) is an Iranian footballer who plays for Saipa in the IPL.
Club career
Ashtiani has played for Saipa F.C. since 2005.
Club career statistics
Last Update 4 August 2011
Assist Goals
References
1981 births
Living people
Saipa F.C. players
Iranian men's footballers
Men's association football midfielders
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/Gauss%20iterated%20map | In mathematics, the Gauss map (also known as Gaussian map or mouse map), is a nonlinear iterated map of the reals into a real interval given by the Gaussian function:
where α and β are real parameters.
Named after Johann Carl Friedrich Gauss, the function maps the bell shaped Gaussian function similar to the logistic map.
Properties
In the parameter real space can be chaotic. The map is also called the mouse map because its bifurcation diagram resembles a mouse (see Figures).
References
Chaotic maps |
https://en.wikipedia.org/wiki/Mathematical%20instrument | A mathematical instrument is a tool or device used in the study or practice of mathematics. In geometry, construction of various proofs was done using only a compass and straightedge; arguments in these proofs relied only on idealized properties of these instruments and literal construction was regarded as only an approximation. In applied mathematics, mathematical instruments were used for measuring angles and distances, in astronomy, navigation, surveying and in the measurement of time.
Overview
Instruments such as the astrolabe, the quadrant, and others were used to measure and accurately record the relative positions and movements of planets and other celestial objects. The sextant and other related instruments were essential for navigation at sea.
Most instruments are used within the field of geometry, including the ruler, dividers, protractor, set square, compass, ellipsograph, T-square and opisometer. Others are used in arithmetic (for example the abacus, slide rule and calculator) or in algebra (the integraph). In astronomy, many have said the pyramids (along with Stonehenge) were actually instruments used for tracking the stars over long periods or for the annual planting seasons.
In schools
The Oxford Set of Mathematical Instruments is a set of instruments used by generations of school children in the United Kingdom and around the world in mathematics and geometry lessons. It includes two set squares, a 180° protractor, a 15 cm ruler, a metal compass, a 9 cm pencil, a pencil sharpener, an eraser and a 10mm stencil.
See also
The Construction and Principal Uses of Mathematical Instruments
Dividing engine
Measuring instrument
Planimeter
Integraph
References
External reading
J. L. Heilbron (ed.), The Oxford Companion To the History of Modern Science (Oxford University Press, 2003) , Instruments and Instrument Making, pp. 408–411
Mathematical tools
Articles containing video clips |
https://en.wikipedia.org/wiki/Kunihiro%20Yamashita | is a Japanese football player. He plays as a centre back.
Honours
Club
Tampines Rovers
Singapore League Cup: 2011
Yangon United
MFF Charity Cup: 2016
Career statistics
As of 23 June 2019
References
External links
1986 births
Living people
People from Kashiwa
Ryutsu Keizai University alumni
Association football people from Chiba Prefecture
Japanese men's footballers
J2 League players
Singapore Premier League players
Myanmar National League players
Liga 1 (Indonesia) players
Roasso Kumamoto players
Albirex Niigata Singapore FC players
Tampines Rovers FC players
Hougang United FC players
Yangon United F.C. players
Borneo F.C. Samarinda players
Perseru Serui players
Badak Lampung F.C. players
Japanese expatriate men's footballers
Expatriate men's footballers in Singapore
Expatriate men's footballers in Myanmar
Expatriate men's footballers in Indonesia
Japanese expatriate sportspeople in Singapore
Japanese expatriate sportspeople in Myanmar
Japanese expatriate sportspeople in Indonesia
Men's association football central defenders |
https://en.wikipedia.org/wiki/Mizan%20Rahman | Mizan Rahman (September 16, 1932 – January 5, 2015) was a Bangladeshi Canadian mathematician and writer. He specialized in fields of mathematics such as hypergeometric series and orthogonal polynomials. He also had interests encompassing literature, philosophy, scientific skepticism, freethinking and rationalism. He co-authored Basic Hypergeometric Series with George Gasper. This book is widely considered as the standard work of choice for that subject of study. He also published ten Bengali books.
Education and career
Rahman was born and grew up in East Bengal, British India (nowadays Bangladesh). He studied at the University of Dhaka, where he obtained his B.Sc degree in Mathematics and Physics in 1953, and his M.Sc in Applied Mathematics in 1954. He received a B.A in Mathematics from the University of Cambridge in 1958, and an M.A. in mathematics from the same university in 1963. He was a senior lecturer at the University of Dhaka from 1958 until 1962. Rahman went to the University of New Brunswick of Canada in 1962 and received his Ph.D in 1965 with a thesis on the kinetic theory of plasma using singular integral equation techniques. After his Ph.D, he became an assistant professor, later a full professor, at Carleton University, where he spent the rest of his career, after his retirement as a Distinguished Professor Emeritus. He unexpectedly died in Ottawa on January 5, 2015, at the age of 82.
Writing and other activities
Apart from his teaching and academic activities, Rahman wrote on various issues, particularly on those related to Bangladesh. He contributed to Internet blogs and various internet e-magazines, mainly in the Bengali language, covering his interests. He was a prolific writer and a regular contributor to Porshi, a Bengali monthly publication based in Silicon Valley, California.
He was also the member of the advisory board of the Mukto-Mona, an Internet congregation of freethinkers, rationalists, skeptics, atheists and humanists of mainly Bengali and South Asian descent.
Honors and awards
Best Teaching Award (1986)
Life-time membership in the Bharat Ganita Parishad (Indian Mathematical Society)
Fellow of the Bangladesh Academy of Sciences (2002)
Award of Excellence from Bangladesh Publications (Ottawa) (1996)
Books
English
Basic Hypergeometric Series (co-author)
Special Functions, q-Series and Related Topics (co-editor)
The Little Garden in the Corner (prose)
Bengali
তীর্থ আমার গ্রাম (Tirtha is my village) (1994)
লাল নদী (The Red River) (2001)
অ্যালবাম (Album) (2002)
প্রসঙ্গ নারী (Context - Women) (2002)
অনন্যা আমার দেশ (Ananya is my country) (2004)
আনন্দ নিকেতন (Ananda Niketan) (2006)
দুর্যোগের পূর্বাভাস (Premonition) (2007)
শুধু মাটি নয় (Not just soil) (2009)
ভাবনার আত্মকথন (Autobiography of thought) (2010)
শূন্য (Zero) (2012)
শূন্য থেকে মহাবিশ্ব With Avijit Roy(The universe from zero)(2015)
References
External links
OP-SF NET 22.1, January 2015. Topic #1: Mizan Rahman 1932–2015 (a short obituary by Martin Muld |
https://en.wikipedia.org/wiki/Robert%20D.%20Macredie | Robert Duncan Macredie (born 31 July 1968) is a British computer scientist. He served as Professor, Head of department, and Head of the School of Information Systems, Computing and Mathematics at Brunel University, Uxbridge, west London and was, until February 2010, Pro-Vice-Chancellor for Student Experience at Brunel University. Macredie was founder and is editor-in-chief, of the Springer research journal Virtual Reality. He has held a number of UK Research Council and EU Framework grants in the areas of computer science and information systems. He is Governor of the Crest Girls' Academy in Brent, West London.
Biography
Macredie was born in Rotherham, West Riding of Yorkshire and attended Broom Valley junior and infants' school, Oakwood Comprehensive School, and Rotherham College of Arts and Technology, before an undergraduate degree in Physics and Computer Science at the University of Hull. He graduated in 1989, and subsequently completed an SERC-funded PhD in Computer Science before joining the Virtual Environments Research Group (VERG) (now HIVE) at the University of Hull. In 1994 he joined Brunel University as a lecturer, and became full Professor in 1999, Head of department in 2001, Dean of Faculty and Head of School in 2004 and Pro-Vice-Chancellor for the Student Experience in 2006.
Publications
References
1968 births
Alumni of the University of Hull
Living people
Academics of Brunel University London |
https://en.wikipedia.org/wiki/Beppo-Levi%20space | In functional analysis, a branch of mathematics, a Beppo Levi space, named after Beppo Levi, is a certain space of generalized functions.
In the following, is the space of distributions, is the space of tempered distributions in , the differentiation operator with a multi-index, and is the Fourier transform of .
The Beppo Levi space is
where denotes the Sobolev semi-norm.
An alternative definition is as follows: let such that
and define:
Then is the Beppo-Levi space.
References
Wendland, Holger (2005), Scattered Data Approximation, Cambridge University Press.
Rémi Arcangéli; María Cruz López de Silanes; Juan José Torrens (2007), "An extension of a bound for functions in Sobolev spaces, with applications to (m,s)-spline interpolation and smoothing" Numerische Mathematik
Rémi Arcangéli; María Cruz López de Silanes; Juan José Torrens (2009), "Estimates for functions in Sobolev spaces defined on unbounded domains" Journal of Approximation Theory
External links
L. Brasco, D. Gómez-Castro, J.L. Vázquez, Characterisation of homogeneous fractional Sobolev spaces https://link.springer.com/content/pdf/10.1007/s00526-021-01934-6.pdf
J. Deny, J.L. Lions, Les espaces du type de Beppo-Levy https://aif.centre-mersenne.org/item/10.5802/aif.55.pdf
R. Adams, J. Fournier, Sobolev Spaces (2003), Academic press -- Theorem 4.31
Functional analysis |
https://en.wikipedia.org/wiki/David%20Levy%20%28economist%29 | David A. Levy is an American economist and author. He is chairman of the Jerome Levy Forecasting Center LLC, an economic consultancy.
Education
Levy holds a B.A. in Mathematics from Williams College and a Master's degree in Business Administration from Columbia University.
Career
Levy was appointed by President Clinton to the Commission to Study Capital Budgeting in 1997 and served on the federal government’s Competitive Policy Council Infrastructure Subcouncil. He has given briefings and testimony to members of Congress.
Publications
Levy is the coauthor, with Jay Levy, of Profits and the Future of American Society, published by HarperCollins in 1983. Forbes magazine praised the book for explaining "why squeezing business profits for the alleged benefit of the poor or of the working man is a self-defeating exercise. It leads not to the satisfaction of human needs but to inflation and unemployment."
Uncle Sam Won’t Go Broke - The Misguided Sovereign Debt Hysteria (2010), co-author Srinivas Thiruvadanthai, The Jerome Levy Forecasting Center
Profits and the Future of American Society, (1983), HarperCollins
References
American economists
Living people
Year of birth missing (living people)
Columbia Business School alumni
Williams College alumni |
https://en.wikipedia.org/wiki/Summation%20equation | In mathematics, a summation equation or discrete integral equation is an equation in which an unknown function appears under a summation sign. The theories of summation equations and integral equations can be unified as integral equations on time scales using time scale calculus. A summation equation compares to a difference equation as an integral equation compares to a differential equation.
The Volterra summation equation is:
where x is the unknown function, and s, a, t are integers, and f, k are known functions.
References
Summation equations or discrete integral equations
Integral equations |
https://en.wikipedia.org/wiki/Airy%20zeta%20function | In mathematics, the Airy zeta function, studied by , is a function analogous to the Riemann zeta function and related to the zeros of the Airy function.
Definition
The Airy function
is positive for positive x, but oscillates for negative values of x. The Airy zeros are the values at which , ordered by increasing magnitude: .
The Airy zeta function is the function defined from this sequence of zeros by the series
This series converges when the real part of s is greater than 3/2, and may be extended by analytic continuation to other values of s.
Evaluation at integers
Like the Riemann zeta function, whose value is the solution to the Basel problem,
the Airy zeta function may be exactly evaluated at s = 2:
where is the gamma function, a continuous variant of the factorial.
Similar evaluations are also possible for larger integer values of s.
It is conjectured that the analytic continuation of the Airy zeta function evaluates at 1 to
References
External links
Zeta and L-functions |
https://en.wikipedia.org/wiki/Jacobi%20zeta%20function | In mathematics, the Jacobi zeta function Z(u) is the logarithmic derivative of the Jacobi theta function Θ(u). It is also commonly denoted as
Where E, K, and F are generic Incomplete Elliptical Integrals of the first and second kind. Jacobi Zeta Functions being kinds of Jacobi theta functions have applications to all their relevant fields and application.
This relates Jacobi's common notation of, , , . to Jacobi's Zeta function.
Some additional relations include ,
References
https://booksite.elsevier.com/samplechapters/9780123736376/Sample_Chapters/01~Front_Matter.pdf Pg.xxxiv
http://mathworld.wolfram.com/JacobiZetaFunction.html
Special functions |
https://en.wikipedia.org/wiki/Gopal%20Prasad | Gopal Prasad (born 31 July 1945 in Ghazipur, India) is an Indian-American mathematician. His research interests span the fields of Lie groups, their discrete subgroups, algebraic groups, arithmetic groups, geometry of locally symmetric spaces, and representation theory of reductive p-adic groups.
He is the Raoul Bott Professor of Mathematics at the University of Michigan in Ann Arbor.
Education
Prasad earned his bachelor's degree with honors in Mathematics from Magadh University in 1963. Two years later, in 1965, he received his master's degree in Mathematics from Patna University. After a brief stay at the Indian Institute of Technology Kanpur in their Ph.D. program for Mathematics, Prasad entered the Ph.D. program at the Tata Institute of Fundamental Research (TIFR) in 1966. There he began a long and extensive collaboration with his advisor M. S. Raghunathan on several topics including the study of lattices in semi-simple Lie groups and the congruence subgroup problem. In 1976, Prasad received his Ph.D. from the University of Mumbai. Prasad became an associate professor at TIFR in 1979, and a professor in 1984. In 1992 he left TIFR to join the faculty at the University of Michigan in Ann Arbor, where he is the Raoul Bott Professor Emeritus of Mathematics.
Family
Gopal Prasad's parents were Ram Krishna Prasad and Lakshmi Devi. Ram Krishna Prasad was a social worker, philanthropist, and was jailed by the British for his participation in the Indian freedom struggle against British rule. The family was involved in retail, and wholesale businesses. In 1969, he married Indu Devi (née Poddar) of Deoria. Gopal Prasad and Indu Devi have a son, Anoop Prasad, who is managing director at D.E. Shaw & Co, and a daughter, Ila Fiete, who is Professor of Neuroscience at MIT, and five grandchildren. Shrawan Kumar, Professor of Mathematics at the University of North Carolina at Chapel Hill, Pawan Kumar, Professor of Astrophysics at the University of Texas, Austin and Dipendra Prasad, Professor of Mathematics at the Indian Institute of Technology, Mumbai, are his younger brothers.
Some contributions to mathematics
Prasad's early work was on discrete subgroups of real and p-adic semi-simple groups. He proved the "strong rigidity" of lattices in real semi-simple groups of rank 1 and also of lattices in p-adic groups, see [1] and [2]. He then tackled group-theoretic and arithmetic questions on semi-simple algebraic groups. He proved the "strong approximation" property for simply connected semi-simple groups over global function fields [3]. Prasad determined the topological central extensions of these groups and computed the "metaplectic kernel" for isotropic groups in collaboration with M. S. Raghunathan, see [11], [12] and [10]. Prasad and Raghunathan have also obtained results on the Kneser-Tits problem, [13]. Later, together with Andrei Rapinchuk, Prasad gave a precise computation of the metaplectic kernel for all simply connected semi-simple groups, see [ |
https://en.wikipedia.org/wiki/Number%20bond | In mathematics education at primary school level, a number bond (sometimes alternatively called an addition fact) is a simple addition sum which has become so familiar that a child can recognise it and complete it almost instantly, with recall as automatic as that of an entry from a multiplication table in multiplication.
For example, a number bond looks like
A child who "knows" this number bond should be able to immediately fill in any one of these three numbers if it were missing, given the other two, without having to "work it out".
Number bonds are often learned in sets for which the sum is a common round number such as 10 or 20. Having acquired some familiar number bonds, children should also soon learn how to use them to develop strategies to complete more complicated sums, for example by navigating from a new sum to an adjacent number bond they know, i.e. 5 + 2 and 4 + 3 are both number bonds that make 7; or by strategies like "making ten", for example recognising that 7 + 6 = (7 + 3) + 3 = 13.
The term "number bond" is also used to refer to a pictorial representation of part-part-whole relationships, often found in the Singapore mathematics curriculum. Number bonds consist of a minimum of 3 circles that are connected by lines. The “whole” is written in the first circle and its “parts” are written in the adjoining circles.
Number bonds are used to build deeper understanding of math facts.
History
The term "number bond" is sometimes derided as a piece of unnecessary new mathematical jargon, adding an element of pointless abstraction or incomprehensibility for those not familiar with it (such as children's parents) to a subject even as simple as primary school addition. The term has been used at least since the 1920s and formally entered the primary curriculum in Singapore in the early 1970s.
In the U.K. the phrase came into widespread classroom use from the late 1990s when the National Numeracy Strategy brought in an emphasis on in-classroom discussion of strategies for developing mental arithmetic in its "numeracy hour".
See also
and
References
External links
What is a Number Bond? - visual explanation of number bonds, and link to free printables.
Let's play math: Number bonds
Number Bond Worksheet
Number Bonds to 20 - Free printable PDF number bonds to 20 worksheet (number bonds to 10 and to 100 also available)
Making sense of number bonds. - A detailed explanation of what number bonds are.
Mathematics education
Elementary arithmetic
Primary education |
https://en.wikipedia.org/wiki/Fritz%20John%20conditions | The Fritz John conditions (abbr. FJ conditions), in mathematics, are a necessary condition for a solution in nonlinear programming to be optimal. They are used as lemma in the proof of the Karush–Kuhn–Tucker conditions, but they are relevant on their own.
We consider the following optimization problem:
where ƒ is the function to be minimized, the inequality constraints and the equality constraints, and where, respectively, , and are the indices sets of inactive, active and equality constraints and is an optimal solution of , then there exists a non-zero vector such that:
if the and are linearly independent or, more generally, when a constraint qualification holds.
Named after Fritz John, these conditions are equivalent to the Karush–Kuhn–Tucker conditions in the case . When , the condition is equivalent to the violation of Mangasarian–Fromovitz constraint qualification (MFCQ). In other words, the Fritz John condition is equivalent to the optimality condition KKT or not-MFCQ.
References
Further reading
Mathematical optimization |
https://en.wikipedia.org/wiki/Sharafutdinov%27s%20retraction | In mathematics, Sharafutdinov's retraction is a construction that gives a retraction of an open non-negatively curved Riemannian manifold onto its soul.
It was first used by Sharafutdinov to show that any two souls of a complete Riemannian manifold with non-negative sectional curvature are isometric. Perelman later showed that in this setting, Sharafutdinov's retraction is in fact a submersion, thereby essentially settling the soul conjecture.
For open non-negatively curved Alexandrov space, Perelman also showed that there exists a Sharafutdinov retraction from the entire space to the soul. However it is not yet known whether this retraction is submetry or not.
References
Riemannian geometry |
https://en.wikipedia.org/wiki/Shrawan%20Kumar%20%28mathematician%29 | Shrawan Kumar is the John R. and Louise S. Parker distinguished professor of mathematics at the University of North Carolina at Chapel Hill. He has written two books: Kac-Moody groups, their flag varieties, and representation theory and Frobenius splitting methods in geometry and representation theory (jointly with ).
Born and raised in Ghazipur, India, Shrawan Kumar earned a Ph.D. in mathematics from the University of Mumbai and the Tata Institute of Fundamental Research (TIFR), Mumbai in 1986. His advisor was S. Ramanan. Shrawan Kumar is the younger brother of Gopal Prasad, a professor of mathematics at the University of Michigan, and the elder brother of Dipendra Prasad, a professor of mathematics at the Tata Institute of Fundamental Research.
In 2012 he became a fellow of the American Mathematical Society.
References
External links
1953 births
Living people
20th-century Indian mathematicians
University of Mumbai alumni
University of North Carolina at Chapel Hill faculty
Tata Institute of Fundamental Research alumni
Fellows of the American Mathematical Society
People from Ghazipur
Scientists from Uttar Pradesh |
https://en.wikipedia.org/wiki/Imaginary%20%28exhibition%29 | IMAGINARY is an open platform dedicated to the communication of modern mathematics. With over 100 different exhibits, software, films, texts, and images for free use and editing, IMAGINARY connects users from over 50 countries. Science museums such as the German Museum in Munich or the Museum of Mathematics (MoMath) in New York have some of the exhibits in their collections. IMAGINARY also acted as an independent organizer of exhibitions.
History
IMAGINARY was founded at the Mathematisches Forschungsinstitut Oberwolfach (MFO) in 2007 by Gert-Martin Greuel and Andreas Matt with an exhibition of the same name, supported by Klaus Tschira Foundation.
In 2013 Gert-Martin Greuel and Andreas Matt received the Media Prize Mathematics of the German Mathematicians Association for IMAGINARY.
From 2019 to 2019, IMAGINARY was funded by the Leibniz Association as an impetus to found a non-profit organisation. Since September 2017, IMAGINARY has been independent with an office in Berlin and regional representatives in numerous countries such as Spain, Uruguay, France, Turkey, South Korea, and China.
Exhibitions
IMAGINARY - Through the eyes of mathematics 2007
The IMAGINARY exhibition aimed to convey abstract mathematics through images and visualizations. In the Surfer exhibit, a real-time ray tracer for generating algebraic surfaces, users can enter and edit polynomial equations with three variables, as well as rotate and color the resulting surfaces. Together with the science magazine Spectrum, a competition was created at the MFO to promote the creation of artistic images made in Surfer.
MPE - Mathematics of Planet Earth
As part of the theme year “Mathematics of Planet Earth”, announced by UNESCO, the International Science Council ICSU and the International Council for Applied Mathematics ICIAM, IMAGINARY organized a competition on the topic. The best submissions were part of an exhibition in the German Museum of Technology in Berlin. These included an interactive simulation from the University of Freiburg that calculates the movements of ash clouds, and an exhibit from the Free University of Berlin that introduces the scientific prognosis of glacier changes.
La La Lab - The Mathematics of Music
The La La Lab exhibition was opened in 2019 in cooperation with the Heidelberg Laureate Forum Foundation in the Mathematik-Informatik-Station (MAINS) and communicates the research results from mathematics and music. The 20 interactive stations include, among others, an exhibit using a 3D printer, art objects, laser installation.
I AM A.I. 2020/2021
The I.AM.AI exhibition was created in 2020 with the financial support of the Carl Zeiss Foundation with the aim of communicating current AI research to a general audience. Due to the corona pandemic, I.AM.AI initially celebrated its launch as a virtual exhibition. The physical exhibition has been postponed to the year 2021 and will visit three venues with the Friedrich Schiller University Jena, the Heidelberg L |
https://en.wikipedia.org/wiki/Reciprocal%20length | Reciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics, defined as the reciprocal of length.
Common units used for this measurement include the reciprocal metre or inverse metre (symbol: m−1), the reciprocal centimetre or inverse centimetre (symbol: cm−1).
In optics, the dioptre is a unit equivalent to reciprocal metre.
List of quantities
Quantities measured in reciprocal length include:
absorption coefficient or attenuation coefficient, in materials science
curvature of a line, in mathematics
gain, in laser physics
magnitude of vectors in reciprocal space, in crystallography
more generally any spatial frequency e.g. in cycles per unit length
optical power of a lens, in optics
rotational constant of a rigid rotor, in quantum mechanics
wavenumber, or magnitude of a wavevector, in spectroscopy
density of a linear feature in hydrology and other fields; see kilometre per square kilometre
surface area to volume ratio
Measure of energy
In some branches of physics, the universal constants c, the speed of light, and ħ, the reduced Planck constant, are treated as being unity (i.e. that c = ħ = 1), which leads to mass, energy, momentum, frequency and reciprocal length all having the same unit. As a result, reciprocal length is used as a measure of energy. The frequency of a photon yields a certain photon energy, according to the Planck–Einstein relation, and the frequency of a photon is related to its spatial frequency via the speed of light. Spatial frequency is a reciprocal length, which can thus be used as a measure of energy, usually of a particle. For example, the reciprocal centimetre, , is an energy unit equal to the energy of a photon with a wavelength of 1 cm. That energy amounts to approximately or .
The energy is inversely proportional to the size of the unit of which the reciprocal is used, and is proportional to the number of reciprocal length units. For example, in terms of energy, one reciprocal metre equals (one hundredth) as much as a reciprocal centimetre. Five reciprocal metres are five times as much energy as one reciprocal metre.
See also
Lineic quantity
Reciprocal second
Further reading
SI derived units
Length-specific quantities |
https://en.wikipedia.org/wiki/CDNF | CDNF may refer to:
Canonical disjunctive normal form, a form of expression in Boolean algebra
Cerebral dopamine neurotrophic factor, a protein encoded by the CDNF gene |
https://en.wikipedia.org/wiki/List%20of%20most%20common%20surnames%20in%20Oceania | This is a list of the most common surnames in Oceania.
Australia
Statistics are drawn from Australian government records of 2007, however they may have changed.
Fiji
Statistics are based on the genealogy resources and vital statistics in Fiji during 2014.
New Zealand
Statistics are based on births registered in New Zealand during 2021.
See also
List of family name affixes
List of most popular given names
Lists of most common surnames, for other continents
References
Oceania
Surnames, most common |
https://en.wikipedia.org/wiki/Maxwell%20Rosenlicht | Maxwell Alexander Rosenlicht (April 15, 1924 – January 22, 1999) was an American mathematician known for works in algebraic geometry, algebraic groups, and differential algebra.
Rosenlicht went to school in Brooklyn (Erasmus High School) and studied at Columbia University (B.A. 1947) and at Harvard University, where he studied under Zariski. He became a Putnam fellow twice, in 1946 and 1947. He was awarded in his doctorate on an Algebraic Curve Equivalence Concepts in 1950. In 1952, he went to Northwestern University. From 1958 until his retirement in 1991, he was a professor at Berkeley. He was also a visiting professor in Mexico City, IHÉS, Rome, Leiden, and Harvard University.
In 1960, he shared the Cole Prize in algebra with Serge Lang for his work on generalized Jacobian varieties. He also studied the algorithmic algebraic theory of integration.
Rosenlicht was a Fulbright Fellow and 1954 Guggenheim Fellow.
He died of neurological disease on a trip to Hawaii. Rosenlicht married in 1954 and had four children.
Publications
References
The article was initially created as a translation (by Google) of the corresponding article in German Wikipedia.
External links
Obituary, Berkeley
Rosenlicht at University of California, Berkeley
1924 births
1999 deaths
20th-century American mathematicians
Harvard University alumni
University of California, Berkeley faculty
Mathematicians from New York (state)
Erasmus Hall High School alumni
Putnam Fellows |
https://en.wikipedia.org/wiki/Diagonalizable%20group | In mathematics, an affine algebraic group is said to be diagonalizable if it is isomorphic to a subgroup of Dn, the group of diagonal matrices. A diagonalizable group defined over a field k is said to split over k or k-split if the isomorphism is defined over k. This coincides with the usual notion of split for an algebraic group. Every diagonalizable group splits over the separable closure ks of k. Any closed subgroup and image of diagonalizable groups are diagonalizable. The torsion subgroup of a diagonalizable group is dense.
The category of diagonalizable groups defined over k is equivalent to the category of finitely generated abelian groups with Gal(ks/k)-equivariant morphisms without p-torsion, if k is of characteristic p. This is an analog of Poincaré duality and motivated the terminology.
A diagonalizable k-group is said to be anisotropic if it has no nontrivial k-valued character.
The so-called "rigidity" states that the identity component of the centralizer of a diagonalizable group coincides with the identity component of the normalizer of the group. The fact plays a crucial role in the structure theory of solvable groups.
A connected diagonalizable group is called an algebraic torus (which is not necessarily compact, in contrast to a complex torus). A k-torus is a torus defined over k. The centralizer of a maximal torus is called a Cartan subgroup.
See also
Diagonal subgroup
References
Borel, A. Linear algebraic groups, 2nd ed.
Algebraic groups |
https://en.wikipedia.org/wiki/Gustaf%20Enestr%C3%B6m | Gustaf Hjalmar Eneström (5 September 1852 – 10 June 1923) was a Swedish mathematician, statistician and historian of mathematics known for introducing the Eneström index, which is used to identify Euler's writings. Most historical scholars refer to the works of Euler by their Eneström index.
Eneström received a Bachelor of Science (filosofie kandidat) degree from Uppsala university in 1871, received a position at Uppsala University Library in 1875, and at the National Library of Sweden in 1879.
From 1884 to 1914, he was the publisher of the mathematical-historical journal Bibliotheca Mathematica, which he had founded and partially funded with his own means. Concerning the history of mathematics, he was known as critical to Moritz Cantor.
With Soichi Kakeya, he is known for the Eneström-Kakeya theorem which determines an annulus containing the roots of a real polynomial.
In 1923 George Sarton wrote, "No one has done more for the sound development of our studies". Sarton went on: "the very presence of Eneström obliged every scholar devoting himself to the history of mathematics to increase his circumspection and improve his work."
Enestrom has also developed an election method similar to Phragmen's voting rules.
Notes
References
Swedish mathematicians
Historians of mathematics
Uppsala University alumni
1852 births
1923 deaths |
https://en.wikipedia.org/wiki/Robertinho%20%28footballer%2C%20born%201988%29 | Roberto Soares Anghinetti (or simply Robertinho) (born June 13, 1988) is Brazilian football player. He is a winger who plays for Estrela do Norte.
Career statistics
Last edit: March 3, 2013
External links
FC Dinamo Tbilisi player profile
1988 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football forwards
América Futebol Clube (MG) players
Expatriate men's footballers in Georgia (country)
FC Dinamo Tbilisi players
Shamakhi FK players
Brazilian expatriate sportspeople in Azerbaijan
Brazilian expatriate sportspeople in Georgia (country)
Estrela do Norte Futebol Clube players
Men's association football midfielders
Footballers from Belo Horizonte |
https://en.wikipedia.org/wiki/List%20of%20VFL%20debuts%20in%201969 | This is a listing of Australian rules footballers who made their senior debut for a Victorian Football League (VFL) club in 1969.
Debuts
References
Australian rules football records and statistics
Australian rules football-related lists
1969 in Australian rules football |
https://en.wikipedia.org/wiki/De%20Bruijn%E2%80%93Erd%C5%91s%20theorem%20%28incidence%20geometry%29 | In incidence geometry, the De Bruijn–Erdős theorem, originally published by , states a lower bound on the number of lines determined by n points in a projective plane. By duality, this is also a bound on the number of intersection points determined by a configuration of lines.
Although the proof given by De Bruijn and Erdős is combinatorial, De Bruijn and Erdős noted in their paper that the analogous (Euclidean) result is a consequence of the Sylvester–Gallai theorem, by an induction on the number of points.
Statement of the theorem
Let P be a configuration of n points in a projective plane, not all on a line. Let t be the number of lines determined by P. Then,
t ≥ n, and
if t = n, any two lines have exactly one point of P in common. In this case, P is either a projective plane or P is a near pencil, meaning that exactly n - 1 of the points are collinear.
Euclidean proof
The theorem is clearly true for three non-collinear points. We proceed by induction.
Assume n > 3 and the theorem is true for n − 1.
Let P be a set of n points not all collinear.
The Sylvester–Gallai theorem states that there is a line containing exactly two points of P. Such two point lines are called ordinary lines.
Let a and b be the two points of P on an ordinary line.
If the removal of point a produces a set of collinear points then P generates a near pencil of n lines (the n - 1 ordinary lines through a plus the one line containing the other n - 1 points).
Otherwise, the removal of a produces a set, P' , of n − 1 points that are not all collinear.
By the induction hypothesis, P' determines at least n − 1 lines. The ordinary line determined by a and b is not among these, so P determines at least n lines.
J. H. Conway's proof
John Horton Conway has a purely combinatorial proof which consequently also holds for points and lines over the complex numbers, quaternions and octonions.
References
Sources
.
Theorems in projective geometry
Euclidean plane geometry
Theorems in discrete geometry
Incidence geometry
Paul Erdős |
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