A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

An analytical relation between entropy production and quantum Lyapunov exponents for Gaussian bipartite systems

We study and compare the information loss of a large class of Gaussian bipartite systems. It includes the usual Caldeira-Leggett-type model as well as Anosov models ( parametric oscillators, the inverted oscillator environment, etc), which exhibit instability, one of the most important characteristics of chaotic systems. We establish a rigorous connection between the quantum Lyapunov exponents and coherence loss, and show that in the case of unstable environments coherence loss is completely determined by the upper quantum Lyapunov exponent, a behavior which is more universal than that of the Caldeira-Leggett-type model.

Approximations for the generalized temperature integral: a method based on quadrature rules

The generalized temperature integral I(m, x) appears in non-isothermal kinetic analysis when the frequency factor depends on the temperature. A procedure based on Gaussian quadrature to obtain analytical approximations for the integral I(m, x) was proposed. The results showed good agreement between the obtained approximation values and those obtained by numerical integration. Unless other approximations found in literature, the methodology presented in this paper can be easily generalized in order to obtain approximations with the maximum of accurate.

ANOTHER QUADRATURE RULE OF HIGHEST ALGEBRAIC DEGREE OF PRECISION

We consider certain quadrature rules of highest algebraic degree of precision that involve strong Stieltjes distributions (i.e., strong distributions on the positive real axis). The behavior of the parameters of these quadrature rules, when the distributions are strong c-inversive Stieltjes distributions, is given. A quadrature rule whose parameters have explicit expressions for their determination is presented. An application of this quadrature rule for the evaluation of a certain type of integrals is also given.

Enhanced emission from Eu(III) beta-diketone complex combined with ether-type oxygen atoms of di-ureasil organic-inorganic hybrids

Organic-inorganic hybrids, named di-ureasils and described by polyether-based chains grafted to both ends to a siliceous backbone through urea cross linkages, were used as hosts for incorporation of the well-known coordination complex of trivalent europium (Eu3+) ions described by the formula [Eu(TTA)(3)(H2O)(2)] (where TTA stands for thenoyltrifluoroacetone). By comparing with Eu3+-doped di-ureasil without complex form the new materials prepared here enhanced the quantum efficiency for photoemission of Eu3+ ions. The enhancement can be explained by the coordination ability of the organic counterpart of the host structure which is strong enough to displace water molecules in [Eu(TTA)(3)(H2O)(2)] from the rare earth neighbourhood after the incorporation process. High intensity of Eu3+ emission was observed with a low non-radiative decay rate under ultraviolet excitation. The quantum efficiency calculated from the decay of D-5(0) emission was 74%, which in the same range of values previously obtained for the most efficient Eu3+ coordination compounds reported in literature. Luminescence, X-ray absorption and infrared absorption results considered together leads to a picture where the first coordination shell of Eu3+ is composed of the 6 oxygen atoms of the 3 beta-diketonate ligands and 2 ether-like oxygen atoms of the host. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.

Magnetic properties of spinel-type oxides NiMn2-xMexO4

New materials, based on the well-known spinel compound NiMn 2O4, have been synthesized and characterized from the magnetic point of view. The manganese cation was partially substituted in the general formula NiMn2-xMexO4, by nonmagnetic and magnetic elements, such as Me = Ga, Zn, Ni and Cr (0 × 1). Prior to the determination of their magnetic properties, the non-substituted spinel NiMn2O4 was carefully characterized and studied as a function of the oxygen stoichiometry, based on the influence of the annealing atmosphere and quenching rate. The ferrimagnetic character was observed in all samples, with a paramagnetic-to-ferromagnetic transition temperature T c stabilized at 110 K, and well defined long-range antiferromagnetic interactions at lower temperatures, which depend on the applied field and the substitute concentration. © 2006 Sociedad Chilena de Química.

Migração 3-D Kirchhoff-Gaussian-Beam (KGB) pré-empilhamento no domínio da profundidade

O Feixe Gaussiano (FG) é uma solução assintótica da equação da elastodinâmica na vizinhança paraxial de um raio central, a qual se aproxima melhor do campo de ondas do que a aproximação de ordem zero da Teoria do Raio. A regularidade do FG na descrição do campo de ondas, assim como a sua elevada precisão em algumas regiões singulares do meio de propagação, proporciona uma forte alternativa na solução de problemas de modelagem e imageamento sísmicos. Nesta Tese, apresenta-se um novo procedimento de migração sísmica pré-empilhamento em profundidade com amplitudes verdadeiras, que combina a flexibilidade da migração tipo Kirchhoff e a robustez da migração baseada na utilização de Feixes Gaussianos para a representação do campo de ondas. O algoritmo de migração proposto é constituído por dois processos de empilhamento: o primeiro é o empilhamento de feixes (“beam stack”) aplicado a subconjuntos de dados sísmicos multiplicados por uma função peso definida de modo que o operador de empilhamento tenha a mesma forma da integral de superposição de Feixes Gaussianos; o segundo empilhamento corresponde à migração Kirchhoff tendo como entrada os dados resultantes do primeiro empilhamento. Pelo exposto justifica-se a denominação migração Kirchhoff-Gaussian-Beam (KGB). As principais características que diferenciam a migração KGB, durante a realização do primeiro empilhamento, de outros métodos de migração que também utilizam a teoria dos Feixes Gaussianos, são o uso da primeira zona de Fresnel projetada para limitar a largura do feixe e a utilização, no empilhamento do feixe, de uma aproximação de segunda ordem do tempo de trânsito de reflexão. Como exemplos são apresentadas aplicações a dados sintéticos para modelos bidimensionais (2-D) e tridimensionais (3-D), correspondentes aos modelos Marmousi e domo de sal da SEG/EAGE, respectivamente.

Análise do efeito da discretização do modelo de velocidades nas migrações Kirchhoff e Kirchhoff-Gaussian- Beam 2D pré-empilhamento em profundidade

O Feixe Gaussiano (FG) é uma solução assintótica da equação da elastodinâmica na vizinhança paraxial de um raio central, a qual se aproxima melhor do campo de ondas do que a aproximação de ordem zero da Teoria do Raio. A regularidade do FG na descrição do campo de ondas, assim como a sua elevada precisão em algumas regiões singulares do meio de propagação, proporciona uma forte alternativa no imageamento sísmicos. Nesta dissertação, apresenta-se um novo procedimento de migração sísmica pré-empilhamento em profundidade com amplitudes verdadeiras, que combina a flexibilidade da migração tipo Kirchhoff e a robustez da migração baseada na utilização de Feixes Gaussianos para a representação do campo de ondas. O algoritmo de migração proposto é constituído por dois processos de empilhamento: o primeiro é o empilhamento de feixes (“beam stack”) aplicado a subconjuntos de dados sísmicos multiplicados por uma função peso definida de modo que o operador de empilhamento tenha a mesma forma da integral de superposição de Feixes Gaussianos; o segundo empilhamento corresponde à migração Kirchhoff tendo como entrada os dados resultantes do primeiro empilhamento. Pelo exposto justifica-se a denominação migração Kirchhoff-Gaussian-Beam (KGB).Afim de comparar os métodos Kirchhoff e KGB com respeito à sensibilidade em relação ao comprimento da discretização, aplicamos no conjunto de dados conhecido como Marmousi 2-D quatro grids de velocidade, ou seja, 60m, 80m 100m e 150m. Como resultado, temos que ambos os métodos apresentam uma imagem muito melhor para o menor intervalo de discretização da malha de velocidade. O espectro de amplitude das seções migradas nos fornece o conteúdo de frequência espacial das seções das imagens obtidas.

Zero sets of bivariate Hermite polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Synthesis, characterization and thermal behavior of heterobimetallic carbonyl compounds of the type [W(CO)(4)(bipy)(CuX)] (X=Cl, N-3, ClO4 and BF4)

Four new heterobimetallic metal carbonyls were synthesized by the reaction of [W(CO)4(bipy)] (1) with copper(I) compounds leading to species with the general formula [W(CO)4(bipy)(CuX)] (X = Cl, N3, ClO4, BF4) (2-5). The metal carbonyl compounds were characterized by elemental analysis, infrared and UV -visible electronic spectroscopy and thermogravimetric analysis. The IR data for 2-5 show carbonyl stretching band patterns similar to compound 1 ; ie they exhibit the same number of bands. The UV - vis results show a dissociation reaction generating the starting compound 1 and CuX as consequence of a weak interaction between 1 and CuX. Thermal decomposition mechanisms as well as the thermal stability are influenced by the CuX fragments. The thermal stability decreases in the order [W(CO)4(bipy)] > [W(CO)4(bipy)(CuCl)] > [W(CO)4(bipy) (CuBF4)]. The X-ray results show the formation of WO3, CuWO4, Cu2O and CuO as final decomposition products.

The tangential variation of a localized flux-type eigenvalue problem

In this work the differentiability of the principal eigenvalue lambda = lambda(1)(Gamma) to the localized Steklov problem -Delta u + qu = 0 in Omega, partial derivative u/partial derivative nu = lambda chi(Gamma)(x)u on partial derivative Omega, where Gamma subset of partial derivative Omega is a smooth subdomain of partial derivative Omega and chi(Gamma) is its characteristic function relative to partial derivative Omega, is shown. As a key point, the flux subdomain Gamma is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of lambda(1) (Gamma) with respect to Gamma is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H(1)(Omega). The study is of interest in mathematical models in morphogenesis. (C) 2011 Elsevier Inc. All rights reserved.

Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Estimating the number of motor units using random sums with independently thinned terms

The problem of estimating the numbers of motor units N in a muscle is embedded in a general stochastic model using the notion of thinning from point process theory. In the paper a new moment type estimator for the numbers of motor units in a muscle is denned, which is derived using random sums with independently thinned terms. Asymptotic normality of the estimator is shown and its practical value is demonstrated with bootstrap and approximative confidence intervals for a data set from a 31-year-old healthy right-handed, female volunteer. Moreover simulation results are presented and Monte-Carlo based quantiles, means, and variances are calculated for N in{300,600,1000}.

Boron-Bearing Kornerupine from Fiskenaesset, West Greenland: A Reexamination of Specimens from the Type Locality

In 1884, Lorenzen proposed the formula MgAI2SiO6 for his new mineral kornerupine from Fiskenæsset and did not suspect it to contain boron. Lacroix and de Gramont (1919) reported boron in Fiskenæsset kornerupine, while Herd (1973) found none. New analyses (ion microprobe mass analyser and spectrophotometric) of kornerupine in three specimens from the type locality, including the specimens analysed by Lorenzen and Herd, indicate the presence of boron in all three, in amounts ranging from 0.50 to 1.44 wt.% B203, e.g. (Li0.04 Na0.01 Ca0.01) (Mg3.49 Mn0.01 Fe0.17 Ti0.01 Al5.64)Σ9.30 (Si3.67 Al1.02 B0.31)Σ5 O21 (OH0.99 F0.01) for Lorenzen's specimen. Textures and chemical compositions suggest that kornerupine crystallized in equilibrium in the following assemblages, all with anorthite (An 92-95) and phlogopite (XFe = atomic Fe/(Fe + Mg) = 0.028-0.035): (1) kornerupine (0.045)-gedrite (0.067); (2) kornerupine (0.038-0.050)-sapphirine (0.032-0.035); and (3) kornerupine (0.050)-hornblende. Fluorine contents of kornerupine range from 0.01 to 0.06%, of phlogopite, from 0.09 to 0.10%. In the first assemblage, sapphirine (0.040) and corundum are enclosed in radiating bundles of kornerupine; additionally sapphirine, corundum, and/or gedrite occur with chlorite and pinite (cordierite?) as breakdown products of kornerupine. Kornerupine may have formed by reactions such as: gedrite + sapphirine + corundum + B203 (in solution) + H20 = kornerupine + anorthite + Na-phlogopite under conditions of the granulite facies. Boron for kornerupine formation was most likely remobilized by hydrous fluids from metasedimentary rocks occurring along the upper contact of the Fiskenæsset gabbro-anorthosite complex with amphibolite.