Spectral-luminescent properties of silver molecular clusters and nanoparticles formed by ion exchange in antimony-doped photo-thermo-refractive glasses

Optics and Spectroscopy - The formation of silver molecular clusters and nanoparticles in photo-thermo-refractive (PTR) glasses with different antimony contents has been investigated using ion...     

Asymptotic expansion of the solution of a differential-difference equation of general form

We obtain an asymptotic expansion of the solution of an mth-order inhomogeneous differential-difference equation of general form. We establish an integral estimate with a submultiplicative weight for the remainder of the expansion depending on the existence of the corresponding submultiplicative moment of the right-hand side of the equation.     

Asymptotic expansion of the solution of a matrix differential-difference equation of the general form

We obtain the asymptotic expansion of the solution of an inhomogeneous matrix differential-difference equation that belongs to the retarded or neutral type. The case of unbounded delays is considered. We take into account the influence of roots of the characteristic equation. An integral estimate of the remainder with a semimultiplicative weight is obtained depending on the semimultiplicative moment of the free matrix term in the equation.     

Exact Asymptotic Behavior of the Solution of a Matrix Difference Equation

An asymptotic expansion of the solution of a nonhomogeneous matrix difference equation of general form is obtained. The case when there is no bound on the differences of the arguments is considered. The effect of the roots of the characteristic equation is taken into account. The asymptotic behavior of the remainder is established depending on the asymptotics of the free term of the equation.

     

On invertibility conditions for elements of Banach algebras of measures

Classical theorems concerning invertibility conditions for elements of Banach algebras of measures are generalized.     

Exponential estimates of the rate of convergence for the higher renewal moments

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 4, pp. 143–152, July–August, 1991.     

On the singularities of the gradient of the solution to the Dirichlet-Neumann problem outside a plane cut

The problem considered in this paper deals with the Laplace equation outside a cut of sufficiently arbitrary form. The Dirichlet condition is given on one side of the cut and the Neumann condition on the other. Using the integral representation for the solution, we obtain explicit asymptotic formulas describing the singularity of the gradient of the solution at the edges of the cut. We discuss the effect of the disappearance of the singularity.Translated from Matematicheskie Zametki, vol. 77, no. 3, 2005, pp. 364–377Original Russian Text Copyright © 2005 by P. A. Krutitskii, A. I. Sgibnev.This revised version was published online in April 2005 with a corrected issue number.     

Wiener–Hopf equation whose kernel is a probability distribution

We prove the existence of a solution of an inhomogeneous generalized Wiener–Hopf equation whose kernel is a probability distribution on R generating a random walk drifting to +∞, while the inhomogeneous term f of the equation belongs to the space L ₁(0,∞) or L _∞(0,∞). We establish the asymptotic properties of the solution of this equation under various assumptions about the inhomogeneity f.