Theoretical and applied problems of Physics and Mathematics

The study of integral operators properties with generalized hypergeometric function in the kernel

We consider the integral operators with generalized functions of hypergeometric type in the kernel, notably (τ,β) - and τ - generalized hypergeometric Gaussian functions and (τ,β)-generalized Kummer function. We also obtain compositional relations for these operators with Liouville fractional integral and fractional derivative.

Convergence of elements sums of autoregressive sequences with random coefficients

This paper deals with autoregressive sequences with random coefficients. More precisely, we study necessary and sufficient conditions for convergence of almost surely the sums of elements of such sequences.

Linear differential equations with essentially infinite-dimensional operators

The present paper investigates the equations for functions on a Hilbert space with essentially infinitedimensional differential operators (Laplace–Levy type) Аnu+а1Аn-1u+...+аn-1Аu+аnu=f Furthermore, the existence and unity of solution of these equations are proved, and the explicit formula for the first-order equation is obtained

On the common extension of measures

In this paper, we describe the conditions, providing the existence of splicing of the measures λ, μ and υ – finite, finitely additive and integral functions of sets, defined on the algebras of subsets B and C of some set Ω and the algebra A, , based on the algebras B and C.

Preparation of Sensitive Substrates for Surface-Enhanced Raman Spectroscopy on the Basis of Ag/Si Nanoisland Films

The paper aims to examine nanostructured silver films prepared by a thermal deposition on silicon and to investigate their properties as substrates for surface-enhanced Raman spectroscopy (SERS). To that end, we establish the optimal conditions of the post-growth annealing of the substrates. The study of dispersion by atomic force microscopy reveals that the silver films with relatively dense and homogeneous arrays of 60–80 nm high pyramidal nanoislands are the most efficient for SERS of both organic dye and inorganic nanoparticles analytes

The study of the biomorphic silicon carbide structure by raman spectroscopy

Our paper studies biomorphic silicon carbide (bioSiC) prepared by forced infiltration with liquid silicon of carbon matrixes derived from hardwood precursors. The Raman spectroscopy shows that 3Cpolytype is formed at synthesis temperatures of about ~1550 °C, but both 3C and 6H SiC are formed at the increase of temperatures. By employing the film of silver nanoparticles deposited by immersion plating, we propose to use the surface enhancement effect for analysis of bio–SiC composition. This method allows detecting residual carbon clusters in bio-SiC.