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Vladimir Retakh
Vladimir Solomonovich Retakh (russian: Ретах Владимир Соломонович; 20 May 1948) is a Russian-American mathematician who made important contributions to Noncommutative algebra and combinatorics among other areas. Biography Retakh graduated in 1970 from the Moscow State Pedagogical University. Beginning as an undergraduate Retakh regularly attended lectures and seminars at the Moscow State University most notably the Gelfand seminars. He obtained his PhD in 1973 under the mentorship of Dmitrii Abramovich Raikov. He joined the Gelfand group in 1986. His first position was at the central Research Institute for Engineering Buildings and later obtained his first academic position at the Council for Cybernetics of the Soviet Academy of Sciences in 1989. While at the Council for Cybernetics of the Soviet Academy of Sciences in 1990, Retakh had started working with Gelfand on their new program on Noncommutative determinants. Prior to immigrating to the US in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rutgers University
Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College, and was affiliated with the Reformed Church in America, Dutch Reformed Church. It is the eighth-oldest college in the United States, the second-oldest in New Jersey (after Princeton University), and one of the nine U.S. colonial colleges that were chartered before the American Revolution.Stoeckel, Althea"Presidents, professors, and politics: the colonial colleges and the American revolution", ''Conspectus of History'' (1976) 1(3):45–56. In 1825, Queen's College was renamed Rutgers College in honor of Colonel Henry Rutgers, whose substantial gift to the school had stabilized its finances during a period of uncertainty. For most of its existence, Rutgers was a Private university, private liberal arts college but it has evolved int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian Mathematicians
Russian(s) refers to anything related to Russia, including: *Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *Rossiyane (), Russian language term for all citizens and people of Russia, regardless of ethnicity *Russophone, Russian-speaking person (, ''russkogovoryashchy'', ''russkoyazychny'') *Russian language, the most widely spoken of the Slavic languages *Russian alphabet *Russian cuisine *Russian culture *Russian studies Russian may also refer to: *Russian dressing *''The Russians'', a book by Hedrick Smith *Russian (comics), fictional Marvel Comics supervillain from ''The Punisher'' series *Russian (solitaire), a card game * "Russians" (song), from the album ''The Dream of the Blue Turtles'' by Sting *"Russian", from the album ''Tubular Bells 2003'' by Mike Oldfield *"Russian", from the album '' '' by Caravan Palace *Nik Russian, the perpetrator of a con committed in 2002 *The South African name for a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1948 Births
Events January * January 1 ** The General Agreement on Tariffs and Trade (GATT) is inaugurated. ** The Constitution of New Jersey (later subject to amendment) goes into effect. ** The railways of Britain are nationalized, to form British Railways. * January 4 – Burma gains its independence from the United Kingdom, becoming an independent republic, named the ''Union of Burma'', with Sao Shwe Thaik as its first President, and U Nu its first Prime Minister. * January 5 ** Warner Brothers shows the first color newsreel (''Tournament of Roses Parade'' and the ''Rose Bowl Game''). ** The first Kinsey Reports, Kinsey Report, ''Sexual Behavior in the Human Male'', is published in the United States. * January 7 – Mantell UFO incident: Kentucky Air National Guard pilot Thomas Mantell crashes while in pursuit of an unidentified flying object. * January 12 – Mahatma Gandhi begins his fast-unto-death in Delhi, to stop communal violence during the Partition of India. * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integrable System
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals, such that its behaviour has far fewer degrees of freedom than the dimensionality of its phase space; that is, its evolution is restricted to a submanifold within its phase space. Three features are often referred to as characterizing integrable systems: * the existence of a ''maximal'' set of conserved quantities (the usual defining property of complete integrability) * the existence of algebraic invariants, having a basis in algebraic geometry (a property known sometimes as algebraic integrability) * the explicit determination of solutions in an explicit functional form (not an intrinsic property, but something often referred to as solvability) Integrable systems may be seen as very different in qualitative character from mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plücker Coordinates
In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3-space, P3. Because they satisfy a quadratic constraint, they establish a one-to-one correspondence between the 4-dimensional space of lines in P3 and points on a quadric in P5 (projective 5-space). A predecessor and special case of Grassmann coordinates (which describe ''k''-dimensional linear subspaces, or ''flats'', in an ''n''-dimensional Euclidean space), Plücker coordinates arise naturally in geometric algebra. They have proved useful for computer graphics, and also can be extended to coordinates for the screws and wrenches in the theory of kinematics used for robot control. Geometric intuition A line L in 3-dimensional Euclidean space is determined by two distinct points that it contains, or by two distinct planes that contain it. Consider the first case, with points x=(x_1,x_2,x_3) and y=(y_1,y_2,y_3). The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noncommutative Symmetric Function
In mathematics, the noncommutative symmetric functions form a Hopf algebra NSymm analogous to the Hopf algebra of symmetric functions. The Hopf algebra NSymm was introduced by Israel M. Gelfand, Daniel Krob, Alain Lascoux, Bernard Leclerc, Vladimir Retakh, and Jean-Yves Thibon. It is noncommutative but cocommutative graded Hopf algebra. It has the Hopf algebra of symmetric functions as a quotient, and is a subalgebra of the Hopf algebra of permutations, and is the graded dual of the Hopf algebra of quasisymmetric function. Over the rational numbers it is isomorphic as a Hopf algebra to the universal enveloping algebra of the free Lie algebra on countably many variables. Definition The underlying algebra of the Hopf algebra of noncommutative symmetric functions is the free ring Z⟨''Z''1, ''Z''2,...⟩ generated by non-commuting variables ''Z''1, ''Z''2, ... The coproduct takes ''Z''''n'' to Σ ''Z''''i'' ⊗ ''Z''''n''–''i'', where ''Z'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasideterminant
In mathematics, the quasideterminant is a replacement for the determinant for matrices with noncommutative entries. Example 2 × 2 quasideterminants are as follows: : \left, \begin a_ & a_ \\ a_ & a_ \end \_ = a_ - a_^a_ \qquad \left, \begin a_ & a_ \\ a_ & a_ \end \_ = a_ - a_^a_. In general, there are ''n''2 quasideterminants defined for an ''n'' × ''n'' matrix (one for each position in the matrix), but the presence of the inverted terms above should give the reader pause: they are not always defined, and even when they are defined, they do not reduce to determinants when the entries commute. Rather, : \left, A\_ = (-1)^ \frac , where A^ means delete the ''i''th row and ''j''th column from ''A''. The 2\times2 examples above were introduced between 1926 and 1928 by Richardson and Heyting, but they were marginalized at the time because they were not polynomials in the entries of A. These examples were redisc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Hypergeometric Function
In mathematics, a general hypergeometric function or Aomoto–Gelfand hypergeometric function is a generalization of the hypergeometric function that was introduced by . The general hypergeometric function is a function that is (more or less) defined on a Grassmannian In mathematics, the Grassmannian is a space that parameterizes all -Dimension, dimensional linear subspaces of the -dimensional vector space . For example, the Grassmannian is the space of lines through the origin in , so it is the same as the ..., and depends on a choice of some complex numbers and signs. References *{{Citation , last1=Gelfand , first1=I. M. , authorlink=Israel Gelfand , title=General theory of hypergeometric functions , mr=841131 , year=1986 , journal=Doklady Akademii Nauk SSSR , issn=0002-3264 , volume=288 , issue=1 , pages=14–18 (English translation in collected papers, volume III.) * Aomoto, K. (1975), "Les équations aux différences linéaires et les intégrales des fonct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow State V
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million residents within the city limits, over 17 million residents in the urban area, and over 21.5 million residents in the metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's largest cities; being the most populous city entirely in Europe, the largest urban and metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow grew to become a prosperous and powerful city that served as the capital of the Grand Duchy that bears its name. When the Grand Duchy of Moscow evolved into the Tsardom of Russia, Moscow remained the political and economic center for most of the Tsardom's history. When the Ts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
