Some applications of duality relations

1991 ◽  
pp. 13-40 ◽  
Author(s):  
V. Milman
Keyword(s):  
Duality Relations

scholarly journals Duality of positive and negative integrable hierarchies via relativistically invariant fields

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
S. Y. Lou ◽  
X. B. Hu ◽  
Q. P. Liu
Keyword(s):  
Integrable Hierarchies ◽  
Gordon Equation ◽  
Formal Series ◽  
Two Dimensional ◽  
Relativistic Invariance ◽  
Sine Gordon Equation ◽  
Recursion Operators ◽  
Symmetry Approach ◽  
Duality Relations ◽  
Duality Problem

Abstract It is shown that the relativistic invariance plays a key role in the study of integrable systems. Using the relativistically invariant sine-Gordon equation, the Tzitzeica equation, the Toda fields and the second heavenly equation as dual relations, some continuous and discrete integrable positive hierarchies such as the potential modified Korteweg-de Vries hierarchy, the potential Fordy-Gibbons hierarchies, the potential dispersionless Kadomtsev-Petviashvili-like (dKPL) hierarchy, the differential-difference dKPL hierarchy and the second heavenly hierarchies are converted to the integrable negative hierarchies including the sG hierarchy and the Tzitzeica hierarchy, the two-dimensional dispersionless Toda hierarchy, the two-dimensional Toda hierarchies and negative heavenly hierarchy. In (1+1)-dimensional cases the positive/negative hierarchy dualities are guaranteed by the dualities between the recursion operators and their inverses. In (2+1)-dimensional cases, the positive/negative hierarchy dualities are explicitly shown by using the formal series symmetry approach, the mastersymmetry method and the relativistic invariance of the duality relations. For the 4-dimensional heavenly system, the duality problem is studied firstly by formal series symmetry approach. Two elegant commuting recursion operators of the heavenly equation appear naturally from the formal series symmetry approach so that the duality problem can also be studied by means of the recursion operators.

Duality relations and optimality conditions in linear stochastic programming

Cybernetics ◽  
1987 ◽  
Vol 23 (1) ◽  
pp. 128-135
Author(s):  
A. I. Yastremskii
Keyword(s):  
Stochastic Programming ◽  
Optimality Conditions ◽  
Duality Relations

scholarly journals Generalized fractional programming duablity: a ratio game approach

1986 ◽  
Vol 28 (2) ◽  
pp. 170-180 ◽  
Author(s):  
S. Chandra ◽  
B. D. Craven ◽  
B. Mond
Keyword(s):  
Objective Function ◽  
Programming Problem ◽  
Fractional Programming ◽  
Generalized Fractional Programming ◽  
Fractional Programming Problem ◽  
Fractional Programs ◽  
Duality Relations

AbstractA ratio game approach to the generalized fractional programming problem is presented and duality relations established. This approach suggests certain solution procedures for solving fractional programs involving several ratios in the objective function.

scholarly journals Irreducible representations of E theory

2019 ◽  
Vol 34 (24) ◽  
pp. 1950133 ◽  
Author(s):  
Peter West
Keyword(s):  
Irreducible Representation ◽  
Direct Product ◽  
Simple Form ◽  
Light Cone ◽  
Degrees Of Freedom ◽  
Irreducible Representations ◽  
Vector Representation ◽  
Maximal Supergravity ◽  
Duality Relations ◽  
Cartan Involution

We construct the [Formula: see text] theory analogue of the particles that transform under the Poincaré group, that is, the irreducible representations of the semi-direct product of the Cartan involution subalgebra of [Formula: see text] with its vector representation. We show that one such irreducible representation has only the degrees of freedom of 11-dimensional supergravity. This representation is most easily discussed in the light cone formalism and we show that the duality relations found in [Formula: see text] theory take a particularly simple form in this formalism. We explain that the mysterious symmetries found recently in the light cone formulation of maximal supergravity theories are part of [Formula: see text]. We also argue that our familiar space–times have to be extended by additional coordinates when considering extended objects such as branes.

scholarly journals Algebraic differential formulas for the shuffle, stuffle and duality relations of iterated integrals

2020 ◽  
Vol 556 ◽  
pp. 363-384
Author(s):  
Minoru Hirose ◽  
Nobuo Sato
Keyword(s):  
Iterated Integrals ◽  
Duality Relations

scholarly journals Duality relations for hypergeometric series

2015 ◽  
Vol 47 (2) ◽  
pp. 343-358 ◽  
Author(s):  
Frits Beukers ◽  
Frédéric Jouhet
Keyword(s):  
Hypergeometric Series ◽  
Duality Relations

Duality relations for models with quenched random interactions

1981 ◽  
Vol 24 (1) ◽  
pp. 313-318 ◽  
Author(s):  
H. R. Jauslin ◽  
R. H. Swendsen
Keyword(s):  
Random Interactions ◽  
Duality Relations

MONTE-CARLO ANALYSIS OF THE ABELIAN SURFACE GAUGE MODEL

1992 ◽  
Vol 07 (18) ◽  
pp. 1601-1607 ◽  
Author(s):  
M. BAIG ◽  
A. TRIAS
Keyword(s):  
Monte Carlo ◽  
Phase Structure ◽  
Three Dimensional ◽  
Monte Carlo Analysis ◽  
Abelian Surface ◽  
Gauge Model ◽  
Monte Carlo Techniques ◽  
Gauge Models ◽  
Lattice Gauge ◽  
Duality Relations

We present the first numerical results from a lattice formulation of the Abelian surface gauge model which accounts for three-index fields required in theories based on an antisymmetrical potential. For this purpose we have defined a lattice gauge model in such a way that field variables are assigned to the plaquettes and the interaction is defined through elementary three-dimensional cubes. The phase structure of the Abelian Z(2) case has been determined using Monte-Carlo techniques. Duality relations to spin and gauge models are also studied.

Duality relations and the replica method for Ising models

1980 ◽  
Vol 13 (16) ◽  
pp. L407-L414 ◽  
Author(s):  
A Aharony ◽  
M J Stephen
Keyword(s):  
Ising Models ◽  
Replica Method ◽  
Duality Relations
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