Wave attenuation model for dephasing and measurement of conditional times

Inelastic scattering induces dephasing in mesoscopic systems. An analysis of previous models to simulate inelastic scattering in such systems is presented and a relatively new model based on wave attenuation is introduced. The problem of Aharonov-Bohm (AB) oscillations in conductance of a mesoscopic ring is studied. We show that the conductance is symmetric under flux reversal and the visibility of AB oscillations decays to zero as a function of the incoherence parameter, signaling dephasing. Further the wave attenuation model is applied to a fundamental problem in quantum mechanics, that of the conditional (reflection/transmission) times spent in a given region of space by a quantum particle before scattering off from that region.     

How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

Mathematical modeling of the dynamics of the human gait in the saggital plane

We propose a new formulation of the problem of mathematical modeling of the human gait as an optimal control problem for a nonlinear multidimensional mechanical system with phase constraints given by expeimental data. We give the results of a solution of this optimal control problem obtained using Fourier-spline approximation of independently varying functions and minimizing an objective function over maximally likely directions.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 127–138.This work was carried out in collaboration with the firm Ukprotez of Kiev and Swedish Institute and Wenner Gren Center Foundation, Stockholm, Sweden.     

DNA vaccine containing the mycobacterial hsp65 gene prevented insulitis in MLD-STZ diabetes

Background  

Our group previously demonstrated that a DNA plasmid encoding the mycobacterial 65-kDa heat shock protein (DNA-HSP65) displayed prophylactic and therapeutic effect in a mice model for tuberculosis. This protection was attributed to induction of a strong cellular immunity against HSP65. As specific immunity to HSP60 family has been detected in arthritis, multiple sclerosis and diabetes, the vaccination procedure with DNA-HSP65 could induce a cross-reactive immune response that could trigger or worsen these autoimmune diseases.