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The duality between color and kinematics and its applications
Journal of Physics A: Mathematical and Theoretical, 2019This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories.
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Journal of Optimization Theory and Applications, 2007
The authors consider a convex programming problem involving inequality, equality and set constraints with functions defined on a Hausdorff locally convex topological vector space together with its Lagrangian dual. They prove the basic connections between the set of \(\epsilon\)-minimizers, the set of \(\epsilon\)-Kuhn-Tucker vectors, the set of points ...
Scovel, C., Hush, D., Steinwart, I.
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The authors consider a convex programming problem involving inequality, equality and set constraints with functions defined on a Hausdorff locally convex topological vector space together with its Lagrangian dual. They prove the basic connections between the set of \(\epsilon\)-minimizers, the set of \(\epsilon\)-Kuhn-Tucker vectors, the set of points ...
Scovel, C., Hush, D., Steinwart, I.
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Journal of Algebra and Its Applications, 2002
Let R anf T be rings, and let U be a faithful R-T-bimodule. We show that the triple (R, U, T) has a Morita duality if and only if RR and TT are linearly compact, and there is a duality between the semisimple factors R/J(R) and T/J(T) induced by the socle of U. The main tool to prove this result is proving that lattice anti-isomorphisms can be patched
Ánh, Pham Ngoc, Herbera, Dolors
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Let R anf T be rings, and let U be a faithful R-T-bimodule. We show that the triple (R, U, T) has a Morita duality if and only if RR and TT are linearly compact, and there is a duality between the semisimple factors R/J(R) and T/J(T) induced by the socle of U. The main tool to prove this result is proving that lattice anti-isomorphisms can be patched
Ánh, Pham Ngoc, Herbera, Dolors
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Symmetric Duality via Conjugate Duality
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1977AbstractSymmetric pairs of programming problems involving square roots of quadratic forms have been studied by a number of authors. By applying the methods of conjugate duality theory to generalizations of these problems we readily obtain extensions of most known results guaranteeing duality of this pair.
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Annals of Global Analysis and Geometry, 2000
Let \(G\) be a complex semi-simple group, \(Q\) a parabolic subgroup and \(Z=G/Q\) the associated flag manifold. If \(G_0\) is a real form, then it has open orbits in \(Z\). The authors introduce a duality on complex flag manifolds which is an extension of the usual point-hyperplane duality of complex projective spaces.
Huckleberry, Alan T., Wolf, Joseph A.
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Let \(G\) be a complex semi-simple group, \(Q\) a parabolic subgroup and \(Z=G/Q\) the associated flag manifold. If \(G_0\) is a real form, then it has open orbits in \(Z\). The authors introduce a duality on complex flag manifolds which is an extension of the usual point-hyperplane duality of complex projective spaces.
Huckleberry, Alan T., Wolf, Joseph A.
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Fehchel duality from LP duality
Mathematische Operationsforschung und Statistik. Series Optimization, 1980Let f closed - grcoer convex functions. We derive Fenchel duality theorem from LP duality by finding polyhedral approximations f iand g ito f iand g ito fand gsuch that (under the conditions of the Fenchel theorem). (i)the problems to find inf {f i–g iand sup correspond to a pair of mutually dual linear programs. (ii)inf{f i–g i}→{f–g i} and sup . (iii)
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Optimization, 1991
We introduce and study dualities △:[Rbar]x → [Rbar]w (i.e., mappings f e [Rbar]x → f △ e [Rbar]w such that for all {fi }ie1 ∈ Rx and all index sets I), which satisfy the additional condition and their duals, which are characterized as those dualities △*:Rx → Rw for which , where ⊥ and ⊺ are two new binary operations on [Rbar], which we introduce here ...
J.E. Martínez-Legaz, I. Singer
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We introduce and study dualities △:[Rbar]x → [Rbar]w (i.e., mappings f e [Rbar]x → f △ e [Rbar]w such that for all {fi }ie1 ∈ Rx and all index sets I), which satisfy the additional condition and their duals, which are characterized as those dualities △*:Rx → Rw for which , where ⊥ and ⊺ are two new binary operations on [Rbar], which we introduce here ...
J.E. Martínez-Legaz, I. Singer
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Directional duality theory Directional duality theory
Economic Theory, 2005In [Can. J. Math. 5, 364--383 (1953; Zbl 0052.16403)] \textit{G. C. Shephard} introduced radial distance functions as representations of a firm's technology. \textit{R. G. Chambers}, \textit{Y. Chung} and \textit{R. Färe} [J. Econ. Theory 70, No. 2, 407--419 (1996; Zbl 0866.90027) and \textit{R. G. Chambers}, \textit{R. Färe}, \textit{E. Jaenicke} and \
Färe, Rolf, Primont, Daniel
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1998
The wide use of duality in economics arises from the theoretical insights that it provides and from its usefulness for empirical work. The economic implications of the optimization problem and the restrictions that have to be imposed on functional relations to enable econometric estimation become more transparent in the dual than in the original ...
Ryuzo Sato, Rama V. Ramachandran
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The wide use of duality in economics arises from the theoretical insights that it provides and from its usefulness for empirical work. The economic implications of the optimization problem and the restrictions that have to be imposed on functional relations to enable econometric estimation become more transparent in the dual than in the original ...
Ryuzo Sato, Rama V. Ramachandran
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Mesh duality and Legendre duality
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1990We describe a sense in which mesh duality is equivalent to Legendre duality. That is, a general pair of meshes, which satisfy a definition of duality for meshes, are shown to be the projection of a pair of piecewise linear functions that are dual to each other in the sense of a Legendre dual transformation. In applications the latter functions can be a
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