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Gennadi Sardanashvily
Gennadi Sardanashvily (; March 13, 1950 – September 1, 2016) was a theoretical physicist, a principal research scientist of Moscow State University. Biography Gennadi Sardanashvily graduated from Moscow State University (MSU) in 1973, he was a Ph.D. student of the Department of Theoretical Physics ( MSU) in 1973–76, where he held a position in 1976. He attained his Ph.D. degree in physics and mathematics from MSU, in 1980, with Dmitri Ivanenko as his supervisor, and his D.Sc. degree in physics and mathematics from MSU, in 1998. Gennadi Sardanashvily was the founder and Managing Editor (2003 - 2013) of the International Journal of Geometric Methods in Modern Physics (IJGMMP). He was a member of Lepage Research Institute (Slovakia). Research area Gennadi Sardanashvily research area is geometric method in classical and quantum mechanics and field theory, gravitation theory. His main achievement is geometric formulation of classical field theory and non-autonom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow
Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents within the city limits, over 19.1 million residents in the urban area, and over 21.5 million residents in Moscow metropolitan area, its 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 List of largest cities, largest cities, being the List of European cities by population within city limits, most populous city entirely in Europe, the largest List of urban areas in Europe, urban and List of metropolitan areas in Europe, metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow became the capital of the Grand Principality of Moscow, which led the unification of the Russian lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jet Bundle
In differential topology, the jet bundle is a certain construction that makes a new smooth fiber bundle out of a given smooth fiber bundle. It makes it possible to write differential equations on sections of a fiber bundle in an invariant form. Jets may also be seen as the coordinate free versions of Taylor expansions. Historically, jet bundles are attributed to Charles Ehresmann, and were an advance on the method ( prolongation) of Élie Cartan, of dealing ''geometrically'' with higher derivatives, by imposing differential form conditions on newly introduced formal variables. Jet bundles are sometimes called sprays, although sprays usually refer more specifically to the associated vector field induced on the corresponding bundle (e.g., the geodesic spray on Finsler manifolds.) Since the early 1980s, jet bundles have appeared as a concise way to describe phenomena associated with the derivatives of maps, particularly those associated with the calculus of variations. Conseq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Staff Of Moscow State University
An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of tertiary education. The name traces back to Plato's school of philosophy, founded approximately 386 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and skill, north of Athens, Greece. The Royal Spanish Academy defines academy as scientific, literary or artistic society established with public authority and as a teaching establishment, public or private, of a professional, artistic, technical or simply practical nature. Etymology The word comes from the ''Academy'' in ancient Greece, which derives from the Athenian hero, ''Akademos''. Outside the city walls of Athens, the gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive grove, hence the expression "the groves of Academe". In these gardens, the philosopher Plato conversed with followers. Plato developed his sessions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian Physicists
This list of Russian physicists includes the famous physicists from the Russian Empire, the Soviet Union and the Russian Federation. Alphabetical list __NOTOC__ A *Alexei Alexeyevich Abrikosov, Alexei Abrikosov, discovered how magnetic flux can penetrate a superconductor (the Abrikosov vortex), Nobel Prize winner *Franz Aepinus, related electricity and magnetism, proved the electric nature of pyroelectricity, explained electric polarization and electrostatic induction, invented Achromatic lens, achromatic microscope *Zhores Alferov, inventor of modern heterotransistor, Nobel Prize winner *Sergey Alekseenko, director of the Kutateladze Institute of Thermophysics, Global Energy Prize recipient *Artem Alikhanian, a prominent researcher of cosmic rays, inventor of wide-gap track spark chamber *Abram Alikhanov, nuclear physicist, a prominent researcher of cosmic rays, built the first nuclear reactors in the USSR, founder of Institute for Theoretical and Experimental Physics (ITEP) *S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2016 Deaths
This is a list of lists of deaths of notable people, organized by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked below. 2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 1986 Earlier years ''Deaths in years earlier than this can usually be found in the main articles of the years.'' See also * Lists of deaths by day * Deaths by year (category) {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1950 Births
Events January * January 1 – The International Police Association (IPA) – the largest police organization in the world – is formed. * January 5 – 1950 Sverdlovsk plane crash, Sverdlovsk plane crash: ''Aeroflot'' Lisunov Li-2 crashes in a snowstorm. All 19 aboard are killed, including almost the entire national ice hockey team (VVS Moscow) of the Soviet Air Force – 11 players, as well as a team doctor and a masseur. * January 6 – The UK recognizes the People's Republic of China; the Republic of China severs diplomatic relations with Britain in response. * January 7 – A fire in the St Elizabeth's Ward of Mercy Hospital in Davenport, Iowa, United States, kills 41 patients. * January 9 – The Israeli government recognizes the People's Republic of China. * January 12 – Submarine collides with Sweden, Swedish oil tanker ''Divina'' in the Thames Estuary and sinks; 64 die. * January 13 – Finland forms diplomatic relations with the People's Republic of Chin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graded Manifold
In algebraic geometry, graded manifolds are extensions of the concept of manifolds based on ideas coming from supersymmetry and supercommutative algebra. Both graded manifolds and supermanifolds are phrased in terms of sheaves of graded commutative algebras. However, graded manifolds are characterized by sheaves on smooth manifolds, while supermanifolds are constructed by gluing of sheaves of supervector spaces. Graded manifolds A graded manifold of dimension (n,m) is defined as a locally ringed space (Z,A) where Z is an n-dimensional smooth manifold and A is a C^\infty_Z-sheaf of Grassmann algebras of rank m where C^\infty_Z is the sheaf of smooth real functions on Z. The sheaf A is called the structure sheaf of the graded manifold (Z,A), and the manifold Z is said to be the body of (Z,A). Sections of the sheaf A are called graded functions on a graded manifold (Z,A). They make up a graded commutative C^\infty(Z)-ring A(Z) called the structure ring of (Z,A). The well-known Batc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superintegrable Hamiltonian System
In mathematics, a superintegrable Hamiltonian system is a Hamiltonian system on a 2n-dimensional symplectic manifold for which the following conditions hold: (i) There exist k>n independent integrals F_i of motion. Their level surfaces (invariant submanifolds) form a fibered manifold F:Z\to N=F(Z) over a connected open subset N\subset\mathbb R^k. (ii) There exist smooth real functions s_ on N such that the Poisson bracket of integrals of motion reads \= s_\circ F. (iii) The matrix function s_ is of constant corank m=2n-k on N. If k=n, this is the case of a completely integrable Hamiltonian system. The Mishchenko-Fomenko theorem for superintegrable Hamiltonian systems generalizes the Liouville-Arnold theorem on action-angle coordinates of completely integrable Hamiltonian system as follows. Let invariant submanifolds of a superintegrable Hamiltonian system be connected compact and mutually diffeomorphic. Then the fibered manifold F is a fiber bundle in tori T^m. There exists a ... [...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, that its motion is confined to a submanifold of much smaller dimensionality than that of 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 more ''generic'' dynamical systems, which are more typically chaotic syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian System
In mathematics, a Lagrangian system is a pair , consisting of a smooth fiber bundle and a Lagrangian density , which yields the Euler–Lagrange differential operator acting on sections of . In classical mechanics, many dynamical systems are Lagrangian systems. The configuration space of such a Lagrangian system is a fiber bundle Q \rarr \mathbb over the time axis \mathbb. In particular, Q = \mathbb \times M if a reference frame is fixed. In classical field theory, all field systems are the Lagrangian ones. Lagrangians and Euler–Lagrange operators A Lagrangian density (or, simply, a Lagrangian) of order is defined as an -form, , on the -order jet manifold of . A Lagrangian can be introduced as an element of the variational bicomplex of the differential graded algebra of exterior forms on jet manifolds of . The coboundary operator of this bicomplex contains the variational operator which, acting on , defines the associated Euler–Lagrange operator . In coor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether Identities
In mathematics, Noether identities characterize the degeneracy of a Lagrangian system. Given a Lagrangian system and its Lagrangian ''L'', Noether identities can be defined as a differential operator whose kernel contains a range of the Euler–Lagrange operator of ''L''. Any Euler–Lagrange operator obeys Noether identities which therefore are separated into the trivial and non-trivial ones. A Lagrangian ''L'' is called degenerate if the Euler–Lagrange operator of ''L'' satisfies non-trivial Noether identities. In this case Euler–Lagrange equations are not independent. Noether identities need not be independent, but satisfy first-stage Noether identities, which are subject to the second-stage Noether identities and so on. Higher-stage Noether identities also are separated into trivial and non-trivial cases. A degenerate Lagrangian is called reducible if there exist non-trivial higher-stage Noether identities. Yang–Mills gauge th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether's Second Theorem
In mathematics and theoretical physics, Noether's second theorem relates symmetries of an action functional with a system of differential equations. :Translated in The theorem is named after its discoverer, Emmy Noether. The action ''S'' of a physical system is an integral of a so-called Lagrangian function ''L'', from which the system's behavior can be determined by the principle of least action. Specifically, the theorem says that if the action has an infinite-dimensional Lie algebra of infinitesimal symmetries parameterized linearly by ''k'' arbitrary functions and their derivatives up to order ''m'', then the functional derivatives of ''L'' satisfy a system of ''k'' differential equations. Noether's second theorem is sometimes used in gauge theory. Gauge theories are the basic elements of all modern field theories of physics, such as the prevailing Standard Model. Mathematical formulation First variation formula Suppose that we have a dynamical system specified in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
