Mathematics

Finite Closed 5-Loops of Extended Hyperbolic Plane

Authors: Romakina L. N.

There are four types of finite closed 5-loops which are invariant by the fundamental group G and singled out on the extended hyperbolic plane H2. It is proved that convex 5-loops belong to two types. The interior of the first type 5-loop coincides with the plane H2 . The 5-loop of the second type allows the partition into two simple loops of three and four dimension. Its interior coincides with the interior of the component of the simple 4-loop. The topological 5-loop properties are researched.

Solvability of Boundary Value Problems for the Schrodinger Equation with Purely Imaginary Coefficient

Authors: Mahmudov N. M.

The paper examines regional problems for nonlinear Schrodinger equation when factor of the equation is the square-summable function that has a square-summable derivative. In this process, theorems of existence and uniqueness of the solution of the boundary value problems under consideration have been proved.

Leray – Serra Spectral Sequence for Tolerant Quasifibering of Tolerant Ways

Authors: Korobchenko E. V., Nebaluev S. I.

The article constructs Leray – Serra homological spectral sequence for tolerant quasifibering of tolerant ways and computes the two first members of this sequence.

On Transformation Operator for the System of Dirac Equations with Summable Potentials

Authors: Guseinov I. M., Lyatifova A. R.

The paper proves the existence of the transformation operator for summable functions and finds the analogy of the formula for the potential with the transformation operator in the given case.

Asymptotics Around the Degeneration Spot of Heat Equation Solution with Strong Degeneration

Authors: Glushko A. V., Baev A. D., Shumeeva D. S.

The paper deals with heat equation with strong degeneration. It is known that for such problems initial conditions are not stated at t = 0 as there exists the only smooth solution of such equation. The paper investigates a class of uniqueness of the solution and studies solvability of the problem in spaces of continuous functions. An asymptotic representation of solution around the degeneration spot is built, i.e. the main part of the solution is defined at t → +0 and residuals are estimated.

An Inverse Problem for Quasilinear Elliptic Equations

Authors: Aliev R. A.

The article examines incorrect return problems in the defining unknown factors in the quasilinear elliptic equation. Theorems of existence, uniqueness and stability have been proved. The consecutive approach method is used for the construction of the regulating algorithm for defining several factors.