Some applications of duality relations

Author(s):  
V. Milman
Keyword(s):  

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
S. Y. Lou ◽  
X. B. Hu ◽  
Q. P. Liu

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.



Cybernetics ◽  
1987 ◽  
Vol 23 (1) ◽  
pp. 128-135
Author(s):  
A. I. Yastremskii


Author(s):  
S. Chandra ◽  
B. D. Craven ◽  
B. Mond

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.



2019 ◽  
Vol 34 (24) ◽  
pp. 1950133 ◽  
Author(s):  
Peter West

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.





2015 ◽  
Vol 47 (2) ◽  
pp. 343-358 ◽  
Author(s):  
Frits Beukers ◽  
Frédéric Jouhet


1981 ◽  
Vol 24 (1) ◽  
pp. 313-318 ◽  
Author(s):  
H. R. Jauslin ◽  
R. H. Swendsen


1992 ◽  
Vol 07 (18) ◽  
pp. 1601-1607 ◽  
Author(s):  
M. BAIG ◽  
A. TRIAS

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.



1980 ◽  
Vol 13 (16) ◽  
pp. L407-L414 ◽  
Author(s):  
A Aharony ◽  
M J Stephen


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