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Applied Mathematics Research eXpress Volume 2008: January

Subject Areas:
Publisher: Oxford University Press - Oxford University Press
ISSN: 1687-1200

LitStream

Journal Article

Operators That Commute with Slant Toeplitz Operators

Ho, Mark C.; Wong, Mu Ming

2008 Applied Mathematics Research eXpress

doi:10.1093/amrx/abn003

Let be a separable Hilbert space and be an orthonormal basis in . A bounded operator is called the slant Toeplitz operator if , where cn is the nth Fourier coefficient of a bounded Lebesgue measurable function on the unit circle . It has been shown [9], with some assumption on the smoothness...
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Journal Article

Evolution of a Mixing Zone in Granular Avalanches

McIntyre, Meghan; Rowe, Edward L.; Shearer, Michael; Gray, J. M. N. T.; Thornton, Anthony R.

2008 Applied Mathematics Research eXpress

doi:10.1093/amrx/abm008

A nonlinear first-order partial differential equation in two space variables and time describes the process of kinetic sieving in an avalanche, in which larger particles tend to rise to the surface while smaller particles descend, quickly leading to completely segregated layers. The interface...
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Journal Article

Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation

Davie, A. M.

2008 Applied Mathematics Research eXpress

doi:10.1093/amrx/abm009

A theory of systems of differential equations of the form dyi jfij(y)dxi, where the driving path x(t) is nondifferentiable, has recently been developed by Lyons. I develop an alternative approach to this theory, using (modified) Euler approximations, and investigate its applicability to...
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Journal Article

Convergence of Leray-type Solutions of Inhomogeneous MHD Systems

Ghazel, Malek; Benameur, Jamel

2008 Applied Mathematics Research eXpress

doi:10.1093/amrx/abm011

In this paper, we study the convergence of Leray-type solutions of a magneto-hydro-dynamic system as the Rossby number approaches zero. The proofs are based on weak compactness arguments, interpolation estimates, and linear algebra methods.
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Journal Article

A Coupled System of PDEs and ODEs Arising in Electrocardiograms Modeling

Boulakia, Muriel; Fernndez, Miguel Angel; Gerbeau, Jean-Frdric; Zemzemi, Nejib

2008 Applied Mathematics Research eXpress

doi:10.1093/amrx/abn002

We study the well-posedness of a coupled system of PDEs and ODEs arising in the numerical simulation of electrocardiograms. It consists of a system of degenerate reactiondiffusion equations, the so-called bidomain equations, governing the electrical activity of the heart, and a diffusion equation...
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Journal Article

Stochastic Diffeomorphisms and Homogenization of Multiple Integrals

Gloria, Antoine

2008 Applied Mathematics Research eXpress

doi:10.1093/amrx/abn001

In 4, Blanc, Le Bris, and Lions have introduced the notion of stochastic diffeomorphism together with a variant of stochastic homogenization theory for linear and monotone elliptic operators. Their proofs rely on the ergodic theorem and on the analysis of the associated corrector equation. In the...
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Journal Article

Complete Solution of a Differential Game with Linear Dynamics and Bounded Controls

Glizer, Valery Y.; Turetsky, Vladimir

2008 Applied Mathematics Research eXpress

doi:10.1093/amrx/abm012

A zero-sum finite-horizon differential game with linear dynamics and bounded controls is considered. The target set is a given hyperplane in the state space. The cost function is the distance between the terminal state and this hyperplane. The complete game solution is obtained in two classes of...
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Journal Article

Sampling Constraints in Average: The Example of Hugoniot Curves

Maillet, Jean-Bernard; Stoltz, Gabriel

2008 Applied Mathematics Research eXpress

doi:10.1093/amrx/abn004

We present a method for sampling microscopic configurations of a physical system distributed according to a canonical (BoltzmannGibbs) measure, with a constraint holding in average. Assuming that the constraint can be controlled by the volume and/or the temperature of the system, and considering...

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