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Vol. 24 (63), No. 1. 2011
Physics and Mathematics Sciences.

Belan E.P., Shiyan O.V.
Stable - Oscillating Regimes Combustion on the Strip
We consider the auto-oscillating system of connected diffusionally Van-der Pole oscillators. This system describe the front movement of the combustion on the segment with isolated edges. We constructed and investigate the stability of periodic spatially inhomogeneous solutions that bifurcate from the losing stability of spatially homogeneous periodic solution. We investigate problems of the form and the stability of this periodic solution in the deeply supercritical domain.

Akhramovich M.V.
A Similarity of Pairs of q-Commuting Nilpotent Matrices
We prove that the problem of classification (up to a similarity transformation)
the pair of matrixes (A, B) satisfying next conditions:

is a "wild" problem.

Veksler A.S., Muratov M.A., Rubshteyin B.A.
Convergence with a Regulator in Ergodic Theorems

Voytitsky V.I.
On the Normal Motions of a Heavy Superfluid in an Open Vessel
We consider the spectral properties of linear initial boundary value problem, generated by process of small motions of a heavy superfluid in an open vessel. In considering model capillary forces are neglected. We proved that properties of this problem is analogous to properties of the problem on normal motions of a viscous fluid in an open vessel. We find localization of the spectrum, asymptotics of two branches of eigenvalues with p-basis property of corresponding eigenfunctions in some Hilbert spaces.

Gorokhova I.V.
An Eigenvalue Asymptotic of the Rod with the Loaded Ends under the Viscous Friction
A spectral problem describing small transversal vibrations of an elastic stretched rod under viscous friction is considered. There are massive rings at the ends of the rod with a hinge joint. The rings can move orthogonally to equilibrium position of the rod with viscous friction. Location of the spectrum of such a problem is described and asymptotic formula for the eigenvalues is provided.

Krivoruchko A.I.
On Some Infinite Reflection Groups
Let G be an infinite reflection group and each proper subset of the set of all linear spans of G-orbits of symmetry directions is independent. In the paper all basic invariants of G are calculated and the conditions of completeness of G are obtained.

Kudryashov Yu.L.
Minimality σ — Symmetrical Dilation of Knot of Unbounded Operator
In the paper minimality σ — symmetrical dilation of knot of unbounded operator with unempty set of regular points is prove.

Kuzmenko E.M.
Conditions of Well-Posedness and Compact Continuity of Variational Functionals in Sobolev Spaces W1,p(Ω)
The concept of pseudoquadratic integrand of variational functional is generalized to the case of an arbitrary Banach spaces. The known statements on cell-posedness and compact continuity of the variational functionals having pseudoquadratic integrand in the Hilbert-Sobolev space W1,2 over an interval are extended to the case of an arbitrary compact domain in ℝn . The obtained results are generalised to the case of the variational functionals having a K-pseudopolynomial integrand in the corresponding Sobolev space W1,p for an arbitrary p ∈ ℕ.

Muminov K.K., Gafforov R.A.
The Equivalence of Finite Systems of Pathes Respect to Action of the Special Pseudoorthogonal Group

Proskurin D.P.
On *- Representations of Wick Analogues of CCR
In this paper we study *-representations of Wick analogue of algebra of canonical commutation relations, annihilating certain homogenenous Wick ideals of degrees 3 and 4. The construction of descending chain of homogeneous Wick ideals of growing degrees is presented.

Anashkin O.V., Mitko O.V.
Instability in Systems with Impulse Effect
The problem of stability of the zero solution of a nonlinear system of ordinary differential equations with impulse effect at fixed times is considered. Sufficient conditions for instability of the zero solution are obtained by Lyapunov’s direct method.