Anna Tarasenko

Mathematical Models for the Study of Resource Systems Based on Functional Operators with Shift

In previous works we proposed a method for the study of systems with one renewable resource. The separation of the individual and the group parameters and the discretization of time led us to scalar linear functional equations with shift. Cyclic models, in which the initial state of the system coincides with the final state, were considered. In this work, we present models for systems with two renewable resources. In modelling, the interactions and the reciprocal influences between these two resources are taken into account. Analysis of the models is carried out in weighted Holder spaces. For cyclic models a method for the solution of the balance equations is proposed. The equilibrium state of the system is found. Some problems for the optimal exploitation of resources of open systems are formulated.

The Multiplicative and Spectral Structure of Analytic Operator-Valued Functions

We study the limiting values of multiplicative integrals under the following assumptions: operator functions belong to the Holder class H μ , 0 < μ ≤ 1, and the derivative of operator functions belongs to the Hardy class ℍ1. We obtain the description of the typical multiplicative and spectral structure of analytic families of weak contractions.