Mathematics

On Numerical Approximation of Differential Polynomials

A numerical approximation formula was devised for differential operators of a special form. An absolute approximation error value was indicated. It was shown that the mentioned approximation is accurate for polynomials.

On Solvability of Certain Classes of Irregular the Second Order Variation Problems

In the work the irregular model of the Stiltjes string on segment [0, ℓ] with boundary conditions u(0) = u(ℓ) = 0 is discussed. The solvability conditions of the mentioned problem are described.

Research of Stability for Extremal Rotation Surfaces

In this work we obtain the first and second variations of area type functional for rotation surfaces formulas. We proof the feature of stability and instability in the terms of the local coordinates and special integrals. We consider some examples by application our results for research if stability for rotation surfaces.

On Riesz Basises of the Eigen and Associated Functions of the Functional-Differential Operator with a Variable Structure

For a functional-differential operator of a variable structure with integral boundary conditions the Riesz basisness of its eigen and associated functions in the space L32[0, 1] is proved.

Recovering of a Mapping Via Jacobi Matrix, Normalized Homogeneous Function

Consider system of the differential equations f′(x) = Φ(f′(x))×M(x) with generalized partial derivatives, where f′(x) is a matrix Jacobi of sought mapping, M is a given n×n matrix-value function with integrable elements, Φ is a given function of matrices.

Expansions in Eigenfunctions of the n-th Order Differential Operator with Non-Regular Boundary Conditions

The paper deals with the expansions in eigenfunctions of the n-th order differential operator with non-regular boundary conditions of special type. Necessary and sufficient conditions for existing of such expansions either on the interval [0, 1] or inside it are derived.

Equiconvergence Theorem for Expansions in Eigenfunctions of Integral Operators with Discontinuous Involution

In the paper we consider the equiconvergence of expansions in trigonometric Fourier series and in eigen- and associated functions of integral operators with involution having discontinuities of the first type.

About Nonsingularity of One Boundary Value Problem of Forth Order with Derivatives by Measure

In the work sufficient conditions for nonsingularity of boundary value problem of forth order with derivatives by measure are obtained.