THE EXISTENCE OF A FINITE-DIMENSIONAL SOLUTION NONLINEAR INTEGRAL FREDHOLM EQUATION OF THE FIRST KIND

In this paper, the existence of a finite-dimensional solution of a nonlinear integral equation is proved when the right-hand side and the kernel are given approximately. A finite-dimensional regularizing operator is constructed, and it is proved that for n → ∞ and for a special choice of the parameter n from δ, the solution of the finite-dimensional problem converges to the exact solution of the original equation. It is shown by an example that using the Green's function it is possible to approximate a differential operator by an integral operator.

Degenerate C-distribution cosine functions and degenerate C-ultradistribution cosine functions in locally convex spaces

The main purpose of this paper is to investigate degenerate C-(ultra)distribution cosine functions in the setting of barreled sequentially complete locally convex spaces. In our approach, the infinitesimal generator of a degenerate C-(ultra)distribution cosine function is a multivalued linear operator and the regularizing operator C is not necessarily injective. We provide a few important theoretical novelties, considering also exponential subclasses of degenerate C-(ultra)distribution cosine functions.

On one Approach for Stable Estimate of Technical System Efficiency

<p class="R-AbstractKeywords"><span lang="EN-US">In present paper the problem of efficiency evaluation of technical system by measurable structural design parameters is investigated. To accomplish the purpose of considered problem it is constructed the mathematical model in the form of a finite-dimensional operator equation, where desired elements are both influence weights of the calculated structural design parameters and technical effectiveness indicator of the system. First, the constructed model is reduced to the normal system, and then the apparatus of the ill-posed inverse problem theory is used for the reduced problem: a regularizing operator is constructed and an algorithm for finding the regularization parameter is developed</span><span lang="EN-US">. </span></p>