General soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equations

We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons. Our soliton matrices explicitly give all higher-order multisoliton solutions to the nonlinear partial differential equations integrable through the matrix Riemann-Hilbert problem. We have applied these general results to the three-wave interaction system, and derived new classes of higher-order soliton and two-soliton solutions, in complement to those from our previous publication [Stud. Appl. Math. 110, 297 (2003)], where only the elementary higher-order zeros were considered. The higher-order solitons corresponding to nonelementary zeros generically describe the simultaneous breakup of a pumping wave (u(3)) into the other two components (u(1) and u(2)) and merger of u(1) and u(2) waves into the pumping u(3) wave. The two-soliton solutions corresponding to two simple zeros generically describe the breakup of the pumping u(3) wave into the u(1) and u(2) components, and the reverse process. In the nongeneric cases, these two-soliton solutions could describe the elastic interaction of the u(1) and u(2) waves, thus reproducing previous results obtained by Zakharov and Manakov [Zh. Eksp. Teor. Fiz. 69, 1654 (1975)] and Kaup [Stud. Appl. Math. 55, 9 (1976)]. (C) 2003 American Institute of Physics.

Structural refinement and photoluminescence properties of irregular cube-like (Ca-1_Cu-x(x))TiO3 microcrystals synthesized by the microwave-hydrothermal method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Structural refinement and photoluminescence properties of cube-like (Ca 1-xCu x)TiO 3 crystals synthesized by the microwave-hydrothermal method

In this work, (Ca 1-xCu x)TiO 3 crystals with (x = 0, 0.01 and 0.02), labeled as CTO, CCTO1 and CCTO2, were synthesized by the microwave-hydrothermal method at 140°C for 32 min. XRD patterns (Fig. 1), Rietveld refinement and FT-Raman spectroscopy indicated that these crystals present orthorhombic structure Pbnm. Micro-Raman and XANES spectra suggested that the substitution of Ca by Cu in A-site promoted a displacement of the [TiO6]-[TiO6] clusters adjacent from its symmetric center, which leads distortions on the [CaO 12] clusters neighboring and consequently cause the strains into the CaTiO3 lattice. FE-SEM images showed that these crystals have an irregular shape as cube like probably indicating an Ostwald-ripening and self-assemble as dominant mechanisms to crystals growth. The powders presented an intense PL blue-emission.

Universalidade em matrizes aleatórias via problemas de Riemann-Hilbert

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

Problemas de Riemann-Hilbert

Pós-graduação em Matemática - IBILCE

Terceiro problema de Hilbert e Teorema de Dehn

Pós-graduação em Matemática em Rede Nacional - IBILCE

Espaço de Hilbert e quantificação de emaranhamento via entropia não extensiva

Pós-graduação em Matemática - IBILCE

Desenvolvimento de um instrumento portátil para detectar falha em rolamento de motor de indução, pela técnica do envelope, usando um DSP de 16 bits e a transformada de Hilbert

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Long-range and short-range structures of cube-like shape SrTiO3 powders: microwave-assisted hydrothermal synthesis and photocatalytic activity

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Hilbert space of curved βγ systems on quadric cones

We clarify the structure of the Hilbert space of curved βγ systems defined by a quadratic constraint. The constraint is studied using intrinsic and BRST methods, and their partition functions are shown to agree. The quantum BRST cohomology is non-empty only at ghost numbers 0 and 1, and there is a one-to-one mapping between these two sectors. In the intrinsic description, the ghost number 1 operators correspond to the ones that are not globally defined on the constrained surface. Extension of the results to the pure spinor superstring is discussed in a separate work.

Husserl's two notions of completeness: husserl and hilbert on completeness and imaginary elements in mathematics

In this paper I discuss Husserl's solution of the problem of imaginary elements in mathematics as presented in the drafts for two lectures he gave in Göttingen in 1901 and other related texts of the same period, a problem that had occupied Husserl since the beginning of 1890, when he was planning a never published sequel to Philosophie der Arithmetik (1891). In order to solve the problem of imaginary entities Husserl introduced, independently of Hilbert, two notions of completeness (definiteness in Husserl's terminology) for a formal axiomatic system. I present and discuss these notions here, establishing also parallels between Husserl's and Hilbert's notions of completeness. © 2000 Kluwer Academic Publishers.

A comparison of statistical methods for genomic selection in a mice population

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