Radiative isotropic cosmologies with extra dimensions

We solve Einsteins equations in an n-dimensional vacuum with the simplest ansatz leading to a Friedmann-Robertson-Walker (FRW) four-dimensional space time. We show that the FRW model must be of radiation. For the open models the extra dimensions contract as a result of cosmological evolution. For flat and closed models they contract only when there is one extra dimension.

Existência de solução de equações integrais não lineares em escalas temporais sobre espaços de Banach

Pós-graduação em Matemática - IBILCE

A mathematical model of integrin-mediated haptotactic cell migration

Haptotactic cell migration, a directed response to gradients of cell—extracellular matrix adhesion, is an important process in a number of biological phenomena such as wound healing and tumour cell invasion. Previously, mathematical models of haptotaxis have been developed on the premise that cells migrate in response to gradients in the density of the extracellular matrix. In this paper, we develop a novel mathematical model of haptotaxis which includes the adhesion receptors known as integrins and a description of their functional activation, local recruitment and protrusion as part of lamellipodia. Through the inclusion of integrins, the modelled cell matter is able to respond to a true gradient of cell–matrix adhesion, represented by functionally active integrins. We also show that previous matrix-mediated models are in fact a subset of the novel integrin-mediated models, characterised by specific choices of diffusion and haptotaxis coefficients in their model equations. Numerical solutions suggest the existence of travelling waves of cell migration that are confirmed via a phase plane analysis of a simplified model.

Una primera lección de Geometría algebraica

En este artículo se explica cómo aparece la Geometría Algebraica, partiendo del estudio de los conjuntos de soluciones de sistemas algebraicos

Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Asymptotic soliton train solutions of Kaup-Boussinesq equations

Asymptotic soliton trains arising from a 'large and smooth' enough initial pulse are investigated by the use of the quasiclassical quantization method for the case of Kaup-Boussinesq shallow water equations. The parameter varying along the soliton train is determined by the Bohr-Sommerfeld quantization rule which generalizes the usual rule to the case of 'two potentials' h(0)(x) and u(0)(x) representing initial distributions of height and velocity, respectively. The influence of the initial velocity u(0)(x) on the asymptotic stage of the evolution is determined. Excellent agreement of numerical solutions of the Kaup-Boussinesq equations with predictions of the asymptotic theory is found. (C) 2003 Elsevier B.V. All rights reserved.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Global solutions for abstract neutral differential equations

We study the existence of global solutions for a class of abstract neutral differential equation defined on the whole real axis. Some concrete applications related to ordinary and partial differential equations are considered. (C) 2009 Elsevier Ltd. All rights reserved.

The existence of solutions for impulsive neutral functional differential equations

This work deals with the existence of mild solutions for a class of impulsive functional differential equations of the neutral type associated with the family of linear closed (not necessarily bounded) operators {A(t) : t is an element of 1}. (C) 2009 Elsevier Ltd. All rights reserved.

Global solutions for abstract impulsive neutral differential equations

We study the existence of mild solutions for a class of impulsive neutral functional differential equation defined on the whole real axis. Some concrete applications to ordinary and partial neutral differential equations with impulses are considered. (C) 2010 Elsevier Ltd. All rights reserved.