Invariant integrals applied to nematic liquid crystals with small Ericksen number and topological defects

Invariant integrals are derived for nematic liquid crystals and applied to materials with small Ericksen number and topological defects. The nematic material is confined between two infinite plates located at y = -h and y = h (h is an element of R+) with a semi-infinite plate at y = 0 and x < 0. Planar and homeotropic strong anchoring boundary conditions to the director field are assumed at these two infinite and semi-infinite plates, respectively. Thus, a line disclination appears in the system which coincides with the z-axis. Analytical solutions to the director field in the neighbourhood of the singularity are obtained. However, these solutions depend on an arbitrary parameter. The nematic elastic force is thus evaluated from an invariant integral of the energy-momentum tensor around a closed surface which does not contain the singularity. This allows one to determine this parameter which is a function of the nematic cell thickness and the strength of the disclination. Analytical solutions are also deduced for the director field in the whole region using the conformal mapping method. (C) 2013 Elsevier Ltd. All rights reserved.

Factorization by invariant embedding of elliptic problems: circular and star-shaped domains

Dissertação apresentada para obtenção do grau de Doutor em Matemática na especialidade de Equações Diferenciais, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

Delay approximation of fractional integrals

This paper explores the calculation of fractional integrals by means of the time delay operator. The study starts by reviewing the memory properties of fractional operators and their relationship with time delay. Based on the time response of the Mittag-Leffler function an approximation of fractional integrals consisting of time delayed samples is proposed. The tuning of the approximation is optimized by means of a genetic algorithm. The results demonstrate the feasibility of the new perspective and the limits of their application.

Factorization of elliptic boundary value problems by invariant embedding and application to overdetermined problems

Dissertação para obtenção do Grau de Doutor em Matemática

Quasi-integrals and the origin of bursting pH oscillations in an enzyme model system

Bursting Oscillation, Mixed-Mode oscillation, Slow Manifold, Quasi-Integral, slow-fast analysis, QSSA

Existence, multiplicity and behaviour of solutions of some elliptic differential equations of higher order

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009

A note on the application of integrals involving cyclic products kernels

A l'estadística de processos estocàstics i camps aleatoris, una funció de moments o un cumulant d'un estimador de la funció de correlació o de la densitat espectral sovint pot contenir una integral amb un producte cíclic de nuclis. En aquest treball es defineix i s'investiga aquesta classe d'integrals i es demostra la desigualtat de Young-Hölder que permet estudiar el comportament asimptòtic de les esmentades integrals en la situació quan els nuclis depenen d'un pàràmetre. Es considera una aplicació al problema d'estimació de la funció de resposta en un sistema de Volterra.

Convergence of singular integrals with general measures

We show that L2-bounded singular integrals in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost everywhere existence of principal values.

On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

Rational first integrals in the Darboux theory of integrability in Cn

"Vegeu el resum a l'inici del document del fitxer adjunt."

Known and new results on absolute convergence of Fourier integrals

New sufficient conditions for representation of a function via the absolutely convergent Fourier integral are obtained in the paper. In the main result, Theorem 1.1, this is controlled by the behavior near infinity of both the function and its derivative. This result is extended to any dimension d &= 2.

Singular integrals on Ahlfors-David regular subsets of the Heisenberg group

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