Mathematics

The Solution of the Inverse Boundary Value Problem for a Wing Profile, Located Close to Rectilinear Screen, in a New Setting

The paper shows the inve r se boundar y value problem for the airfoil located near the solid rectilinear boundary and streamlined by a potential flow of the incom pressible inviscid fluid with speed parallel to the boundary,

Inverse Problem for Sturm – Liouville Operators in the Com plex Plane

The inverse problem for the standard Sturm – Liouville equation with a spectral parameter ρ and a potential function, piecewise-entire on a rectifiable curve γ ⊂ C, on which only the starting point is given, is studied for the first time. A function Q that is bounded on a curve γ is piecewise-entire on it if γ can be splitted by a finite number of points into parts on which Q coincides with entire functions, different in neighboring parts. The split points, the initial and final points of the curve are called critical points. The problem is to find all the critical

To Chang Theorem. III

Various multilinear polynomials of Capelli type belonging to a free associative algebra F {X ∪ Y } over an arbitrary field F generated by a countable set X ∪ Y are considered. The formulas expressing coefficients of polynomial Chang R(¯x, ¯y|¯w) are found. It is proved that if the characteristic of field F is not equal two
then polynomial R(¯x, ¯y| ¯w) may be represented by different ways in the form of sum of two consequencesof standard polynomial S

On Application of Elliptic Curves in Some Electronic Voting Protocols

Electronic voting protocols allow us to carry out voting procedure in which ballots exist only electronically. These protocols provide the secret nature of vote. The main property of electronic voting protocols is the universal checkability, i.e. provision of an opportunity to any person interested, including detached onlookers to check correctness of counting of votes at any moment. In operation cryptography protocols of electronic vote of Shauma - Pederson and Kramera - Franklin - Shoyenmeykersa - Yunga are considered.

On the Representation of Functions by Absolutely Convergent Series by H -system

The paper deals with the representation of absolutely convergent series of functions in spaces of homogeneous type. The definition of a system of Haar type (H-system) associated to a dyadic family on a space of homogeneous type X is given in the Introduction. It is proved that for almost everywhere (a.e.) finite and measurable on a set  X  function f there exists an absolutely convergent series by the system H, which converges to  f  a.e. on  X .

Asymptotic Formulae for Weight Numbers of the Sturm–Liouville Boundary Problem on a Star-shaped Graph

In this article the Sturm-Liouville boundary value problem on the graph Γof a special structure is considered. The graph Γhas m edges, joined at one common vertex, and m vertices of degree 1. The boundary value problem is set by the Sturm-Liouville differential expression with real-valued potentials, the Dirichlet boundary conditions, and the standard matching conditions. This problem has a countable set of eigenvalues. We consider the so-called weight numbers, being the residues of the diagonal elements of the Weyl matrix in the eigenvalues.

Stability of Periodic Billiard Trajectories in Triangle

The problem of stability of periodic billiard trajectories in triangles is considered. The notion of stability means the preservation of a period and qualitative structure of a trajectory (its combinatorial type) for sufficiently small variations of a triangle. The geometric, algebraic and fan unfoldings are introduced for stable trajectories description. The new method of fan coding, using these unfoldings, is proposed. This method permits to simplify the stability analysis.

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