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Four Dimensional Lie Symmetry Algebras and Fourth Order Ordinary Differential Equations
, 2002
"... Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary di#erential equations which admit such Lie symmetry algebras are derived. The route to their integration is described. ..."
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Cited by 3 (0 self)
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Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary di#erential equations which admit such Lie symmetry algebras are derived. The route to their integration is described.
The string dual of a confining fourdimensional gauge theory
, 2000
"... We study N = 1 gauge theories obtained by adding finite mass terms to N = 4 YangMills theory. The Maldacena dual is nonsingular: in each of the many vacua, there is an extended brane source, arising from Myers’ dielectric effect. The source consists of one or more (p,q) 5branes. In particular, the ..."
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Cited by 359 (8 self)
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, the confining vacuum contains an NS5brane; the confining flux tube is a fundamental string bound to the 5brane. The system admits a simple quantitative description as a perturbation of a state on the N = 4 Coulomb branch. Various nonperturbative phenomena, including flux tubes, baryon vertices, domain walls
String theory and noncommutative geometry
 JHEP
, 1999
"... We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from ..."
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Cited by 801 (8 self)
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this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary DiracBornInfeld theory with its noncommutative
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
The FourthOrder Type Linear Ordinary Differential Equations
, 2006
"... Abstract. This note reports on the recent advancements in the search for explicit representation, in classical special functions, of the solutions of the fourthorder linear ordinary differential equations named Besseltype, Jacobitype, Laguerretype, Legendretype. Contents ..."
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Cited by 5 (3 self)
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Abstract. This note reports on the recent advancements in the search for explicit representation, in classical special functions, of the solutions of the fourthorder linear ordinary differential equations named Besseltype, Jacobitype, Laguerretype, Legendretype. Contents
The Inverse Problem Of The Calculus Of Variations For Scalar FourthOrder Ordinary Differential Equations
, 1996
"... . A simple invariant characterization of the scalar fourthorder ordinary differential equations which admit a variational multiplier is given. The necessary and sufficient conditions for the existence of a multiplier is expressed in terms of the vanishing of two relative invariants which can be ass ..."
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Cited by 8 (0 self)
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. A simple invariant characterization of the scalar fourthorder ordinary differential equations which admit a variational multiplier is given. The necessary and sufficient conditions for the existence of a multiplier is expressed in terms of the vanishing of two relative invariants which can
Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares pr ..."
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Cited by 973 (4 self)
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squares problem for three or more points. Currently various empirical, graphical, and numerical iterative methods are in use. Derivation of the solution is simplified by use of unit quaternions to represent rotation. I emphasize a symmetry property that a solution to this problem ought to possess. The best
Least angle regression
 Ann. Statist
"... The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to s ..."
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Cited by 1308 (43 self)
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implements the Lasso, an attractive version of ordinary least squares that constrains the sum of the absolute regression coefficients; the LARS modification calculates all possible Lasso estimates for a given problem, using an order of magnitude less computer time than previous methods. (2) A different LARS
Results 1  10
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