Darboux-Bäcklund transformations and rational solutions of the painlevé IV equation

Rational solutions of the Painlevé IV equation are constructed in the setting of pseudo-differential Lax formalism describing AKNS hierarchy subject to the additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian representations for rational solutions are obtained by successive actions of the Darboux-Bäcklund transformations. ©2010 American Institute of Physics.

On the Bäcklund and Darboux transformations for the Tzitzéica model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation

2000 Mathematics Subject Classification: Primary: 34B40; secondary: 35Q51, 35Q53

TRIHALOMETANOS EM ÁGUA POTÁVEL E RISCOS DE CÂNCER: SIMULAÇÃO USANDO POTENCIAL DE INTERAÇÃO E TRANSFORMAÇÕES DE BÄCKLUND

We briefly investigated the well-known correlation of trihalomethanes, present in fresh water, with cancer hazard in humans. A transient alternative method of chemical simulation using Bäcklund Transformations and Quantum Mechanics is presented. Finally, the method was applied to simulate the interaction between Trichloridemethane and Alanine - as well as its amino and carboxyl groups.

Transformações de Bäcklund para hierarquias integráveis abelianas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On discrete symmetries of the multi-boson KP hierarchies

We show that the multi-boson KP hierarchies possess a class of discrete symmetries linking them to discrete Toda systems. These discrete symmetries are generated by the similarity transformation of the corresponding Lax operator. This establishes a canonical nature of the discrete transformations. The spectral equation, which defines both the lattice system and the corresponding Lax operator, plays a key role in determining pertinent symmetry structure. We also introduce the concept of the square root lattice leading to a family of new pseudo-differential operators with covariance under additional Bäcklund transformations.

Affine Lie algebraic origin of constrained KP hierarchies

An affine sl(n + 1) algebraic construction of the basic constrained KP hierarchy is presented. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and it is shown that these approaches are equivalent. The model is recognized to be the generalized non-linear Schrödinger (GNLS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Bäcklund transformations and interpolate between GNLS and multi-boson KP-Toda hierarchies. Our construction uncovers the origin of the Toda lattice structure behind the latter hierarchy. © 1995 American Institute of Physics.

On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation?

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Type-II defects in integrable classical field theories

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

AFFINE INTERVAL EXCHANGE TRANSFORMATIONS WITH FLIPS AND WANDERING INTERVALS

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips which have wandering intervals and are such that the support of the invariant measure is a Cantor set.

Bacterial communities and biogeochemical transformations of iron and sulfur in a high saltmarsh soil profile

Microbial community structure in saltmarsh soils is stratified by depth and availability of electron acceptors for respiration. However, the majority of the microbial species that are involved in the biogeochemical transformations of iron (Fe) and sulfur (S) in such environments are not known. Here we examined the structure of bacterial communities in a high saltmarsh soil profile and discuss their potential relationship with the geochemistry of Fe and S. Our data showed that the soil horizons Ag (oxic-suboxic), Bg (suboxic), Cri (anoxic with low concentration of pyrite Fe) and Cr-2 (anoxic with high concentrations of pyrite Fe) have distinct geochemical and microbiological characteristics. In general, total S concentration increased with depth and was correlated with the presence of pyrite Fe. Soluble + exchangable-Fe, pyrite Fe and acid volatile sulfide Fe concentrations also increased with depth, whereas ascorbate extractable-Fe concentrations decreased. The occurrence of reduced forms of Fe in the horizon Ag and oxidized Fe in horizon Cr-2 suggests that the typical redox zonation, common to several marine sediments, does not occur in the saltmarsh soil profile studied. Overall, the bacterial community structure in the horizon Ag and Cr-2 shared low levels of similarity, as compared to their adjacent horizons, Bg and Cr-1, respectively. The phylogenetic analyses of bacterial 16S rRNA gene sequences from clone libraries showed that the predominant phylotypes in horizon Ag were related to Alphaproteobacteria and Bacteroidetes. In contrast, the most abundant phylotypes in horizon Cr-2 were related to Deltaproteo-bacteria, Chloroflexi, Deferribacteres and Nitrospira. The high frequency of sequences with low levels of similarity to known bacterial species in horizons Ag and Cr-2 indicates that the bacterial communities in both horizons are dominated by novel bacterial species. (c) 2008 Elsevier Ltd. All rights reserved.

Transformations of taste: Americanisation, generational change and Australian cultural consumption

Researchers within the field of cultural imperialism as well as the more recently developed globalisation paradigm have tended to dwell upon the economic or corporate dimensions of global cultural flows and have been largely indifferent to the domain of the everyday cultural tastes and forms of cultural consumption that exist in particular national contexts. This article seeks to redress this focus through an examination of one particular instance of cultural imperialism, the widely held belief in ?he Americanisation of Australian society. Using data from a major research project inquiring into Australian everyday culture the article focuses on the changes in cultural tastes and preferences that are evident in three generational cohorts: contemporary young adults, a segment of the 'baby-boom' generation now in middle age, and a group of older Australians born in the years following World War I and the 1920s. The article documents a trend in which overseas influences, particularly those originating from America, appear to be increasingly shaping Australians' tastes in a wide range of cultural domains. Nevertheless, despite these changes in cultural taste Australians of ail ages retain a strong sense of a distinctive national identity. Such findings have implications for an understanding of cultural globalisation as a process of hybridisation and intermixing.

On entanglement and Lorentz transformations

We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin 1/2 particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed.