Approximation of planar BV homeomorphisms by diffeomorphisms

We show that a planar BV homeomorphism can be approximated in the area strict sense, together with its inverse, with smooth or piecewise affine homeomorphisms.     

Spin polarization and temperature dependence of electron effective mass in quantum wires

The electron effective mass in GaAs quantum wires has been estimated by using a full dynamical random-phase approximation to examine its properties versus spin polarization, temperature, and carrier density. A decrease of mass with spin polarization is seen. The minority mass increases with the polarization while the majority mass decreases and this behaviour is seen for all densities. A maximal enhancement of mass at moderate temperature around 25 K is also presented. These calculations show a qualitative consistence with results in two-dimensional systems and help to control the electronic transport in quantum wires.     

Continuous dependence on data for bilocal difference equations

The continuous dependence on data is studied for a class of second order difference equations governed by a maximal monotone operator A in a Hilbert space. A nonhomogeneous term f appears in the equation and some bilocal boundary conditions a, b are added. One shows that the function which associates to {a, b, A, f} the solution of this boundary value problem is continuous in a specific sense. One uses the convergence of a sequence of operators in the sense of the resolvent. The problem studied here is the discrete variant of a problem from the continuous case.     

How Fast Is the Bandit?

Abstract

In this article we investigate the rate of convergence of the so-called two-armed bandit algorithm. The behavior of the algorithm turns out to be highly non standard: no central limit theorem, possible occurrence of two different rates of convergence with positive probability.     

Product Inhibited Enzymatic Reactions on the Rotating Disk Electrodes

A model of cyclic staircase voltammetry of enzymatic reactions on the rotating disk electrode is developed and the inhibition by the product is investigated. The responses are mostly time – dependent current – potential curves with maxima in the forward but not in the backward branch. If the maxima appear in both branches, the inhibition is potential – dependent either directly or indirectly. The source of the second maximum is explained.     

Wavespeed analysis: Approximating Arrhenius kinetics with step-function kinetics

The accuracy of using step-function approximations to the Arrhenius exponential in computing the wavespeed in combustion wave propagation is investigated. Gaseous and gasless combustion, and first- and second-order reactions are included in the study. The theoretical analysis is based on Melnikov theory from dynamical systems. The error is shown to be small in most instances. The analytical results are supported with numerical simulations.