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A DUALITY PRINCIPLE FOR GROUPS
, 902
"... Abstract. The duality principle for Gabor frames states that a Gabor sequence obtained by a timefrequency lattice is a frame for L 2 (R d) if and only if the associated adjoint Gabor sequence is a Riesz sequence. We prove that this duality principle extends to any dual pairs of projective unitary r ..."
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Cited by 3 (2 self)
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Abstract. The duality principle for Gabor frames states that a Gabor sequence obtained by a timefrequency lattice is a frame for L 2 (R d) if and only if the associated adjoint Gabor sequence is a Riesz sequence. We prove that this duality principle extends to any dual pairs of projective unitary
The quantum duality principle
 Ann. Inst. Fourier (Grenoble
, 2002
"... Abstract. The "quantum duality principle " states that the quantisation of a Lie bialgebra  via a quantum universal enveloping algebra (in short, QUEA)  also provides a quantisation of the dual Lie bialgebra (through its associated formal Poisson group)  via a quantum formal series H ..."
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Cited by 11 (5 self)
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Abstract. The "quantum duality principle " states that the quantisation of a Lie bialgebra  via a quantum universal enveloping algebra (in short, QUEA)  also provides a quantisation of the dual Lie bialgebra (through its associated formal Poisson group)  via a quantum formal series
Machine Intelligibility and the Duality Principle
, 1996
"... The scale and diversity of networked sources of data and computer programs is rapidly swamping human abilities to digest and even locate relevant information. The high speed of computing has compounded this problem by the generation of even larger amounts of data, derived in ways that are generally ..."
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Cited by 3 (0 self)
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that lack of machine intelligibility in humancomputer interactions can be traced directly to present approaches to software design. According to the duality principle in this paper, software involved in humancomputer interaction should contain two distinct layers: a declarative knowledgelevel layer and a
DUALITY PRINCIPLE OF W. SIERPIŃSKI
"... Abstract. Let ^ be an 'JJJfamily of subsets of X and — the family of its “first category” sets. It is proven that one and only one of the following conditions is satisfied: (*) each ^ ise t is at most countable; (**) X is the union o f ^ ise t and a set having property (L), which are disjoi ..."
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are disjoint; (***) each ^residual set contains an uncountable ^fiset. Moreover, a n d @ C 2 y are two 9J}families, the “duality principle ” holds (i.e. there exists a bijection / : X * Y transforming 'if,sets onto ££>isets) ifF* ^ and satisfy the same of the conditions above. Also, some
Duality Principles And Reduction Theorems
, 2000
"... . We introduce a fairly general class of Banach function spaces X given by kfk X := kf k X , where f is defined on a totally oefinite nonatomic measure space (R; ), f is the nonincreasing rearrangement of f with respect to and X is certain rearrangementinvariant space over the inter ..."
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Cited by 3 (0 self)
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the interval (0; (R)). This class contains for example classical Lorentz spaces. We prove a general duality principle for these spaces and present several applications. In particular, we prove theorems which enable us to reduce weighted inequalities involving integral operators restricted to monotone functions
A Duality Principle for the Legendre Transform
"... We present a duality principle for the Legendre transform that yields the shortest path between the graphs of functions and embodies the underlying Nash equilibrium. A useful feature of the algorithm for the shortest path obtained in this way is that its implementation has a local character in the s ..."
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Cited by 8 (4 self)
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We present a duality principle for the Legendre transform that yields the shortest path between the graphs of functions and embodies the underlying Nash equilibrium. A useful feature of the algorithm for the shortest path obtained in this way is that its implementation has a local character
Duality principle and braided geometry
 Lec. Notes in Physics 447
, 1995
"... Abstract We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes correspondi ..."
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Cited by 12 (8 self)
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Abstract We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semiclassical level of PoissonLie groups and at the level of braided groups and braided geometry.
DUALITY PRINCIPLE AND SPECIAL OSSERMAN MANIFOLDS
"... Abstract. We investigate the connection between the duality principle and the Osserman condition in a pseudoRiemannian setting. We prove that a connected pointwise twoleaves Osserman manifold of dimension n> 5 is globally Osserman and investigate the relation between the special Osserman condi ..."
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Abstract. We investigate the connection between the duality principle and the Osserman condition in a pseudoRiemannian setting. We prove that a connected pointwise twoleaves Osserman manifold of dimension n> 5 is globally Osserman and investigate the relation between the special Osserman
DUALITY PRINCIPLE AND BRAIDED GEOMETRY
, 1994
"... Abstract We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes correspondin ..."
Abstract
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Abstract We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semiclassical level of PoissonLie groups and at the level of braided groups and braided geometry.
DUALITY PRINCIPLE AND BRAIDED GEOMERTY
, 1994
"... Abstract We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes correspondin ..."
Abstract
 Add to MetaCart
Abstract We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semiclassical level of PoissonLie groups and at the level of braided groups and braided geometry.
Results 1  10
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80,245