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4,176
Quantum field theory on noncommutative spaces
"... A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommuta ..."
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Cited by 397 (26 self)
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A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative YangMills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an indepth study of the gauge group of noncommutative YangMills theory. Some of the more mathematical ideas and
On conformal field theories
 in fourdimensions,” Nucl. Phys. B533
, 1998
"... We review the generalization of field theory to spacetime with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last ..."
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Cited by 366 (1 self)
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. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, both on the classical and quantum level. Submitted to Reviews of Modern Physics.
Nonholonomic motion planning: Steering using sinusoids
 IEEE fins. Auto. Control
, 1993
"... AbstractIn this paper, we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vec ..."
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Cited by 353 (15 self)
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vector fields and their first order Lie brackets. Using Brockett’s result as motivation, we derive suboptimal trajectories for systems which are not in canonical form and consider systems in which it takes more than one level of bracketing to achieve controllability. These trajectories use sinusoids
Generalized complex geometry
"... Generalized complex geometry encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deformation theory, relation to Poisson geometry, and local structure theory. We also define and s ..."
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Cited by 302 (7 self)
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Generalized complex geometry encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deformation theory, relation to Poisson geometry, and local structure theory. We also define and study generalized complex branes, which interpolate between flat bundles on
On the center problem for ordinary differential equation
, 2003
"... The classical CenterFocus problem posed by H. Poincaré in 1880’s asks about the characterization of planar polynomial vector fields such that all their integral trajectories are closed curves whose interiors contain a fixed point, a center. In this paper we describe a new general approach to the Ce ..."
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Cited by 10 (6 self)
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The classical CenterFocus problem posed by H. Poincaré in 1880’s asks about the characterization of planar polynomial vector fields such that all their integral trajectories are closed curves whose interiors contain a fixed point, a center. In this paper we describe a new general approach
How algebraic Bethe ansatz works for integrable model
 In: Symétries quantiques (Les Houches
, 1996
"... In my Les–Houches lectures of 1982 I described the inverse scattering method of solving the integrable field–theoretical models in 1+1 dimensional space–time. Both classical case, stemming from the famous paper by Gardner, Green, Kruskal and Miura of 1967 on KdV equation, and its quantum counterpart ..."
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Cited by 273 (4 self)
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In my Les–Houches lectures of 1982 I described the inverse scattering method of solving the integrable field–theoretical models in 1+1 dimensional space–time. Both classical case, stemming from the famous paper by Gardner, Green, Kruskal and Miura of 1967 on KdV equation, and its quantum
The Painlevé approach to nonlinear ordinary differential equations
 CRM SERIES IN MATHEMATICAL PHYSICS
, 1999
"... The “Painlevé analysis” is quite often perceived as a collection of tricks reserved to experts. The aim of this course is to demonstrate the contrary and to unveil the simplicity and the beauty of a subject which is in fact the theory of the (explicit) integration of nonlinear differential equatio ..."
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Cited by 32 (13 self)
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equations. To achieve our goal, we will not start the exposition with a more or less precise “Painlevé test”. On the contrary, we will finish with it, after a gradual introduction to the rich world of singularities of nonlinear differential equations, so as to remove any cooking recipe. The emphasis is put
Nonlinear Ordinary and Partial Differential Equations
"... The automation of the traditional Painlevé test in Mathematica is discussed. The package PainleveTest.m allows for the testing of polynomial systems of nonlinear ordinary and partial differential equations which may be parameterized by arbitrary functions (or constants). Except where limited by memo ..."
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The automation of the traditional Painlevé test in Mathematica is discussed. The package PainleveTest.m allows for the testing of polynomial systems of nonlinear ordinary and partial differential equations which may be parameterized by arbitrary functions (or constants). Except where limited
On The Darboux Transformation II
, 1995
"... . Automorphisms of the family of all SturmLiouville equations y 00 = qy are investigated. The classical Darboux transformation arises as a particular case of a general result. 1. Introduction To make this part independent of [7], we recall the classical Darboux result. Let nonvanishing functio ..."
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functions y = y(x), z = z(x) be solutions of the SturmLiouville equations (1) y 00 = p(x)y; z 00 = q(x)z where the potentials p(x); q(x) differ by a constant: p \Gamma q = 2 R. Then the function ~ y = y 0 \Gamma yz 0 =z satisfies the SturmLiouville equation (2) ~ y 00 = ~ p(x)~y (~p = p
Results 1  10
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4,176