Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in

We study the Riemann boundary value problem , for analytic functions in the class of analytic functions represented by the Cauchy-type integrals with density in the spaces with variable exponent. We consider both the case when the coefficient is piecewise continuous and it may be of a more general nature, admitting its oscillation. The explicit formulas for solutions in the variable exponent setting are given. The related singular integral equations in the same setting are also investigated. As an application there is derived some extension of the Szegö-Helson theorem to the case of variable exponents.

Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered. (C) 2012 Elsevier Ltd. All rights reserved.

Boundary element formulation for elastoplastic analysis of axisymmetric bodies

The complete formulation of B.E.M. applied to the analysis of axisymmetric bodies acting in the plastic range is presented in this paper. The concept of derivative of a singular integral given by Mikhlin has been used in order to calculate the stresses in internal points. Also a semianalytical approach is proposed to compute the matrix coefficients, presenting the way in which it can be done and the results obtained.

On a Hypersingular Equation of a Problem, for a Crack in Elastic Media

Mathematics Subject Classification 2010: 45DB05, 45E05, 78A45.

On the approximation by convolution operators in homogeneous Banach spaces on R^d

AMS Subject Classification 2010: 41A25, 41A35, 41A40, 41A63, 41A65, 42A38, 42A85, 42B10, 42B20

On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions

AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.

Certain Aspects Related To Computation By Modified Crack Closure Integral(MCCI)

This paper presents the proper computational approach for the estimation of strain energy release rates by modified crack closure integral (MCCI). In particular, in the estimation of consistent nodal force vectors used in the MCCI expressions for quarter-point singular elements (wherein all the nodal force vectors participate in computation of strain energy release rates by MCCI). The numerical example of a centre crack tension specimen under uniform loading is presented to illustrate the approach.

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

Existence results for elliptic equations with singular terms

Esta dissertação estuda em detalhe três problemas elípticos: (I) uma classe de equações que envolve o operador Laplaciano, um termo singular e nãolinearidade com o exponente crítico de Sobolev, (II) uma classe de equações com singularidade dupla, o expoente crítico de Hardy-Sobolev e um termo côncavo e (III) uma classe de equações em forma divergente, que envolve um termo singular, um operador do tipo Leray-Lions, e uma função definida nos espaços de Lorentz. As não-linearidades consideradas nos problemas (I) e (II), apresentam dificuldades adicionais, tais como uma singularidade forte no ponto zero (de modo que um "blow-up" pode ocorrer) e a falta de compacidade, devido à presença do exponente crítico de Sobolev (problema (I)) e Hardy-Sobolev (problema (II)). Pela singularidade existente no problema (III), a definição padrão de solução fraca pode não fazer sentido, por isso, é introduzida uma noção especial de solução fraca em subconjuntos abertos do domínio. Métodos variacionais e técnicas da Teoria de Pontos Críticos são usados para provar a existência de soluções nos dois primeiros problemas. No problema (I), são usadas uma combinação adequada de técnicas de Nehari, o princípio variacional de Ekeland, métodos de minimax, um argumento de translação e estimativas integrais do nível de energia. Neste caso, demonstramos a existência de (pelo menos) quatro soluções não triviais onde pelo menos uma delas muda de sinal. No problema (II), usando o método de concentração de compacidade e o teorema de passagem de montanha, demostramos a existência de pelo menos duas soluções positivas e pelo menos um par de soluções com mudança de sinal. A abordagem do problema (III) combina um resultado de surjectividade para operadores monótonos, coercivos e radialmente contínuos com propriedades especiais do operador de tipo Leray- Lions. Demonstramos assim a existência de pelo menos, uma solução no espaço de Lorentz e obtemos uma estimativa para esta solução.

Universidad y participación: la formación integral a través de actividades complementarias

En las últimas décadas, se han producido enormes cambios sociales, económicos y culturales en la sociedad. Del mismo modo las universidades, en muchos casos como reflejo de esos cambios, se han enfrentado a su vez a importantes transformaciones, tanto en su propio contexto como en sus relaciones con la sociedad en la que se encuentran. Se incide con mayor frecuencia y profundidad en los cambios científico-tecnológicos y en los económicos haciendo especial hincapié en la globalización y en la era de la comunicación. Sin embargo, no menos importante resultan los cambios producidos a nivel social y cultural, como la democratización de las sociedades, el importante aumento de la multiculturalidad o el interés por los derechos humanos y por la promoción de la calidad de vida y de los pilares básicos que la sustentan. Estos últimos engloban a la educación, la salud, la paz, la igualdad, etc. (González, 2007). Todos estos cambios han confluido, en gran medida, en la configuración del EEES. Las posibilidades que supone la formación complementaria en la universidad es el tema central de este trabajo, y sus posibilidades en el desarrollo de valores y actitudes, esenciales en una educación integral y adecuada a la sociedad de la información, ya que creemos que la formación axiológica y actitudinal en la universidad, además de la instructiva, es ineludible. Así mismo se hace un análisis de los servicios de la Universidad de Santiago de Compostela destinados a la formación complementaria de nuestro alumnado y se describe una experiencia enmarcada en el programa Móvete’09, organizada por el Servicio de Voluntariado. Por lo tanto, todo el conjunto de servicios y actividades paralelas a la formación curricular tiene un papel de singular importancia en la promoción y fomento de la cultura en la comunidad universitaria y en el entorno en general, ya que muchos de estos servicios están abiertos a población no universitaria. Por ello debe ser gestionado con profesionalidad y sentido de responsabilidad institucional compartida, porque la cultura no es competencia exclusiva de ninguna institución, sino que tiene carácter público y social

L'IES Joaquim Blume, un centre singular per a la formació d'esportistes. 'El IES Joaquim Blume, un centro singular para la formación de deportistas'.

Resumen del autor en catalán

La reparación integral: un estudio desde su aplicación en acciones de protección el Ecuador

Las características de la reparación integral que se manifiestan en el ámbito nacional dentro de las acciones de protección, revelan la existencia de marcadas diferencias respecto a los parámetros y estándares trazados por la doctrina y jurisprudencia internacional. En función a los elementos que se presentan en el escenario jurídico local, la reparación integral atraviesa por un proceso de trasmutación en el cual puede distorsionarse sin que esto implique la pérdida de su naturaleza jurídica. En este sentido se manifiesta que la reparación integral en el Ecuador adquiere un contenido singular a consecuencia de su traslado normativo al ordenamiento interno y al proceso de adecuación que atraviesa durante su aplicación. Estas diferencias y peculiaridades que se identifican en la práctica jurídica interna, responden principalmente a la naturaleza de las afectaciones que se ventilan en las acciones de protección, por lo tanto no constituyen fundamentos para la desvalorización de la reparación integral prevista en el ámbito nacional que lejos de alcanzar el estereotipo internacional de reparación integral, puede cumplir su finalidad garantista. Con el propósito de desentrañar y descubrir el contenido de la reparación integral en la realidad nacional, identificar los fenómenos que se generan en la práctica jurídica y establecer las diferencias que se presentan en la aplicación de esta institución en el contexto local, se recurre a contrastar la doctrina y jurisprudencia internacional con los resultados empíricos extraídos de las resoluciones judiciales de una de las garantías jurisdiccionales encargadas de precautelar el respeto de todos los derechos constitucionales, esta es la acción de protección. De esta manera es posible presentar a través de las sentencias constitucionales y dar a conocer la forma en que esta institución es concebida y aplicada por autoridades judiciales del Ecuador y a partir de dicha realidad, construir un contenido propio y reflejar el estado de desarrollo de la reparación integral en el contexto nacional.

Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

Uma experiência baseada no Apoio Matricial em Saúde Mental: estratégia para um atendimento integral

Pós-graduação em Psicologia - FCLAS

Impedance of foundations using the Boundary Integral Equation Method

Dynamic soil-structure interaction has been for a long time one of the most fascinating areas for the engineering profession. The building of large alternating machines and their effects on surrounding structures as well as on their own functional behavior, provided the initial impetus; a large amount of experimental research was done,and the results of the Russian and German groups were especially worthwhile. Analytical results by Reissner and Sehkter were reexamined by Quinlan, Sung, et. al., and finally Veletsos presented the first set of reliable results. Since then, the modeling of the homogeneous, elastic halfspace as a equivalent set of springs and dashpots has become an everyday tool in soil engineering practice, especially after the appearance of the fast Fourier transportation algorithm, which makes possible the treatment of the frequency-dependent characteristics of the equivalent elements in a unified fashion with the general method of analysis of the structure. Extensions to the viscoelastic case, as well as to embedded foundations and complicated geometries, have been presented by various authors. In general, they used the finite element method with the well known problems of geometric truncations and the subsequent use of absorbing boundaries. The properties of boundary integral equation methods are, in our opinion, specially well suited to this problem, and several of the previous results have confirmed our opinion. In what follows we present the general features related to steady-state elastodynamics and a series of results showing the splendid results that the BIEM provided. Especially interesting are the outputs obtained through the use of the so-called singular elements, whose description is incorporated at the end of the paper. The reduction in time spent by the computer and the small number of elements needed to simulate realistically the global properties of the halfspace make this procedure one of the most interesting applications of the BIEM.