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Toda lattice realization of integrable hierarchies
(Kluwer Academic Publ, 1996-12-01)
We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy. In other words, we show on a large number of examples that an integrable hierarchy, defined by a pseudo-differential Lax ...
Modified Korteweg-de Vries hierarchy with hodograph transformation: Camassa-Holm and Harry-Dym hierarchies
(Elsevier B.V., 2001-03-15)
In this paper, we present relations between Camassa-Holm (CH), Harry-Dym (HD) and modified Korteweg-de Vries (mKdV) hierarchies, which are given by the hodograph type transformation. (C) 2001 IMACS. Published by Elsevier ...
Toda lattice realization of integrable hierarchies
(Kluwer Academic Publ, 2014)
The higher grading structure of the WKI hierarchy and the two-component short pulse equation
(Springer, 2012-08-01)
A higher grading affine algebraic construction of integrable hierarchies, containing the Wadati-Konno-Ichikawa (WKI) hierarchy as a particular case, is proposed. We show that a two-component generalization of the Schafer-Wayne ...
Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations
(2018-01-01)
The integrability of the N= 1 supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super Bäcklund transformation. The construction of such ...
Construction of type-II Bäcklund transformation for the mKdV hierarchy
(2015-09-14)
From an algebraic construction of the mKdV hierarchy we observe that the space component of the Lax operator plays the role of a universal algebraic object. This fact induces the universality of a gauge transformation that ...
Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups
(1996-10-31)
In analogy with the Liouville case we study the sl3 Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete W3 algebra. We define an integrable system with respect to the ...
Normal numbers and the Borel hierarchy
(Polish Academy of Sciences. Institute of Mathematics, 2014-02)
We show that the set of absolutely normal numbers is Π03-complete in the Borel hierarchy of subsets of real numbers. Similarly, the set of absolutely normal numbers is Π03-complete in the effective Borel hierarchy.
Using topic hierarchies with privileged information to improve context-aware recommender systems
(Universidade de São Paulo - USPUniversidade Federal de São Carlos - UFSCarCentro de Robótica de São Carlos - CROBSociedade Brasileira de Computação - SBCSociedade Brasileira de Automática - SBASão Carlos, 2014-10)
Recommender systems are designed to assist individuals to identify items of interest in a set of options. A context-aware recommender system makes recommendations by incorporating available contextual information into the ...