Definite integrals and operational methods

An operational method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various types. This technique provides a very flexible and powerful tool yielding new results encompassing different aspects of the special function theory. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.

Differentiability of bizonal positive definite kernels on complex spheres

We prove that any continuous function with domain {z ∈ C: |z| ≤ 1} that generates a bizonal positive definite kernel on the unit sphere in 'C POT.Q' , q ⩾ 3, is continuously differentiable in {z ∈ C: |z| < 1} up to order q − 2, with respect to both z and 'Z BARRA'. In particular, the partial derivatives of the function with respect to x = Re z and y = Im z exist and are continuous in {z ∈ C: |z| < 1} up to the same order.

Convolution roots and differentiability of isotropic positive definite functions on spheres

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d − 1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.

A proposal of algorithm for solving definite descriptions through dialogue structure

En este trabajo proponemos un algoritmo para la resolución de las descripciones definidas en español a través de la estructura del diálogo, mediante la definición de un espacio de accesibilidad anafórico. Este algoritmo está basado en la hipótesis de que la resolución de la anáfora está relacionada con la estructura del diálogo. Así, la resolución de la anáfora mejora si se especifica un espacio de accesibilidad para cada tipo descripción definida según la estructura del diálogo. La utilización de este espacio de accesibilidad anafóico reduce tanto el tiempo de procesamiento como la posibilidad de obtener un antecedente erróneo. Además, la definición de este espacio de accesibilidad depende únicamente de la propia estructura textual del diálogo.

Indefinite determiner introducing definite referent: a special use of 'yi 'one' + classifier' in Chinese

The indefinite determiner yi 'one'+ classifier' is the most approximate to an indefinite article, like the English a, in Chinese. It serves all the functions characteristic of representative stages of grammaticalization from a numeral to a generalized indefinite determiner as elaborated in the literature. It is established in this paper that the Chinese indefinite determiner has developed a special use with definite expressions, serving as a backgrounding device marking entities as of low thematic importance and unlikely to receive subsequent mentions in ensuing discourse. 'yi+ classifier' in the special use with definite expressions displays striking similarities in terms of semantic bleaching and phonological reduction with the same determiner at the advanced stage of grammaticalization characterized by uses with generics, nonspecifics and nonreferentials. An explanation is offered in terms of an implicational relation between nonreferentiality and low thematic importance which characterize the two uses of the indefinite determiner. While providing another piece of evidence in support of the claim that semantically nonreferentials and entities of low thematic importance tend to be encoded in terms of same linguistic devices in language, findings in this paper have shown how an indefinite determiner can undergo a higher degree of grammaticalization than has been reported in the literature-it expands its scope to mark not only indefinite but also definite expressions as semantically nonreferential and/or thematically unimportant. (C) 2003 Elsevier B.V. All rights reserved.

Representations and Positive Definite Functions on Hypergroups

Some relationships between representations of a hypergroup X, its algebras, and positive definite functions on X are studied. Also, various types of convergence of positive definite functions on X are discussed.

Are complex demonstratives synonymous with definite descriptions?

Neste artigo, discuto como o material descritivo dos demonstrativos complexos contribuipara o seu conteúdo literal relativo a um contexto de proferimento. Em filosofia da linguagem, uma hipótese tradicional sobre os demonstrativos complexos prevê que o material descritivo ‘F’ de um demonstrativo complexo faz uma contribuição ao conteúdo literal porque uma descrição definida contendo o nominal ‘F’ determina e expressa o conteúdo literal do demonstrativo complexo relativo ao contexto de proferimento. Assevero que este tipo de hipótese envolve erro porque nenhum tipo de descrição definida, descrições Gödelianas em particular, tem papel efetivo na determinação do conteúdo literal dos demonstrativos complexos. Em vez disso, sou favorável a uma abordagem segundo a qual o conteúdo literal de um demonstrativo complexo é exaustivamente composto pelo conteúdo nãoquantificacional da expressão demonstrativa (e.g., ‘esta’) e pelo conteúdo descritivo de seu nominal (e.g., ‘mesa’). Demonstrativos complexos são, portanto, designadores descritivos, termos que se referem e descrevem sem quantificar. ______________________________________________________________________________________________ ABSTRACT

About The Article: Effect Of Combined Aerobic And Resistance Training Versus Aerobic Training On Arterial Stiffness.

184

A importância das quedas no mesmo nível entre idosos no estado de são paulo

OBJETIVO: Analisar as características das quedas no grupo etário com 60 anos ou mais, com ênfase nas quedas no mesmo nível, residentes no Estado de São Paulo, a partir da análise das diferentes fontes de informação oficiais. MÉTODOS: Foram analisadas as 1.328 mortes registradas no SIM em 2007, 20.726 internações no SIH/SUS em 2008 e os 359 atendimentos realizados em 24 UEs do Estado de São Paulo em 2007. Um teste de regressão logística foi utilizado para testar associações entre variáveis nos atendimentos em emergências. RESULTADOS: O sexo masculino preponderou nas mortes (51,2 %) enquanto o sexo feminino preponderou nas internações (61,1%) e atendimentos em emergências (60,4%). O coeficiente de mortalidade foi 31/100.000 habitantes, aumentando com a idade e atingindo o valor de 110,7/100.000 habitantes na faixa de 80 anos e mais. As quedas no mesmo nível foram responsáveis pela maior proporção de mortes definidas (35%), nas internações (47,5%) e também nas emergências (66%), crescendo de importância com o aumento das faixas etárias. A residência foi o local de ocorrência em 65,8% dos casos atendidos nas emergências. Os traumatismos de cabeça assumem importância nas mortes; as fraturas de fêmur foram as lesões mais frequentes nas internações e emergências. Nas emergências, as mulheres foram 1,55 vezes significativamente mais prováveis de serem atendidas por uma queda do que pelas outras causas externas que os homens. Comparativamente à faixa de 60 a 69 anos, os indivíduos na faixa de 70 a 79 anos foram 2,10 vezes e os indivíduos de 80 anos e mais foram 2,26 vezes significativamente mais prováveis de serem atendidos por uma queda do que pelas outras causas externas. Não houve diferença estatisticamente significante quanto ao sexo ou faixa etária quando se comparou os indivíduos que sofreram quedas no mesmo nível e outros tipos de queda. CONCLUSÃO: Recomenda-se que a prevenção das quedas entre idosos entre na pauta de discussão das políticas públicas sem mais demora.

INFERENCE FOR EIGENVALUES AND EIGENVECTORS OF GAUSSIAN SYMMETRIC MATRICES

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.

An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

The applicability of a meshfree approximation method, namely the EFG method, on fully geometrically exact analysis of plates is investigated. Based on a unified nonlinear theory of plates, which allows for arbitrarily large rotations and displacements, a Galerkin approximation via MLS functions is settled. A hybrid method of analysis is proposed, where the solution is obtained by the independent approximation of the generalized internal displacement fields and the generalized boundary tractions. A consistent linearization procedure is performed, resulting in a semi-definite generalized tangent stiffness matrix which, for hyperelastic materials and conservative loadings, is always symmetric (even for configurations far from the generalized equilibrium trajectory). Besides the total Lagrangian formulation, an updated version is also presented, which enables the treatment of rotations beyond the parameterization limit. An extension of the arc-length method that includes the generalized domain displacement fields, the generalized boundary tractions and the load parameter in the constraint equation of the hyper-ellipsis is proposed to solve the resulting nonlinear problem. Extending the hybrid-displacement formulation, a multi-region decomposition is proposed to handle complex geometries. A criterium for the classification of the equilibrium`s stability, based on the Bordered-Hessian matrix analysis, is suggested. Several numerical examples are presented, illustrating the effectiveness of the method. Differently from the standard finite element methods (FEM), the resulting solutions are (arbitrary) smooth generalized displacement and stress fields. (c) 2007 Elsevier Ltd. All rights reserved.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.