Exponential boundedness of solutions for impulsive delay differential equations

For an impulsive delay differential equation

exponent estimates of solutions have been obtained.     

Some generalizations of the classical moment problem

The article is devoted to two generalizations of the classical power moment problem, namely: 1) instead of representing the moment sequence by ⁿ , a representation by polynomialsP _n (), ¹, connected with a Jacobi matrix, appears; 2) in the representation, instead of ⁿ , the expression ⁿ figures, where is a real generalized function (i.e., we investigate some infinite-dimensional moment problem).The work is partially supported by the DFG, Project 436 UKR 113/39/0 and by the CRDF, Project UM1-2090.     

Conductivity of electrolytes and their mixtures: The aqueous HCl-MgCl2 system at low concentrations

The Onsager-Fuoss-Chen theory of conductance for mixtures has been explored and compared with experimental results for the system HCl−MgCl₂−H₂O from 5×10⁻⁵ to 0.02 mol-kg⁻¹ of water. In the theory, the higher order term O(ka) which involves the ion size parameter has been replaced by a linear term with an empirical constant. The theory including the additional linear term agrees well with the experimental results. The mixture effect on the equivalent conductance is small, but on the individual ionic mobilities is substantial.     

Image of the Spectral Measure of a Jacobi Field and the Corresponding Operators

By definition, a Jacobi field is a family of commuting selfadjoint three-diagonal operators in the Fock space The operators J(ϕ) are indexed by the vectors of a real Hilbert space H₊. The spectral measure ρ of the field J is defined on the space H₋ of functionals over H₊. The image of the measure ρ under a mapping is a probability measure ρ_K on T₋. We obtain a family J_K of operators whose spectral measure is equal to ρ_K. We also obtain the chaotic decomposition for the space L²(T₋, d_{ρ K}).     

On stability of some linear and nonlinear delay differential equations

New explicit conditions of exponential stability are obtained for the nonautonomous equation with several delays

     

Commutative Jacobi fields in Fock space

A jacobi field is understood to be a family (Ã()) of commuting selfadjoint operatorsÃ() acting in a Fock space, having a Jacobi structure, and depending linearly on the test functions . In this article, we give a spectral representation of such a family and outline its applications to the theory of distributions on an infinite dimensional space.This article is dedicated to the memory of my dear teacher Mark G. KreinThe work is partially supported by Fundamental Research Foundation of Ukraine, grant 1.4/62.     

Nicholson’s blowflies differential equations revisited: Main results and open problems

This review covers permanence, oscillation, local and global stability of solutions for Nicholson’s blowflies differential equation. Some generalizations, including the most recent results for equations with a distributed delay and models with periodic coefficients, are considered.     

Positive solutions for a scalar differential equation with several delays

For a scalar delay differential equation , we obtain new explicit conditions for the existence of a positive solution.