Vol 61, No (2016)

Full Issue


Morse-Smale Systems and Topological Structure of Supporting Manifolds

Grines V.Z., Zhuzhoma Y.V., Pochinka O.V.


In this paper, we review the results describing the connection between the global dynamics of Morse-Smale systems on closed manifolds and the topology of supporting manifolds. Also we consider the results related to topological classification of Morse-Smale systems.
Contemporary Mathematics. Fundamental Directions. 2016;61:5-40
pages 5-40 views

Model of the Oldroyd Compressible Fluid

Zakora D.A.


In this paper, mathematical models of compressible viscoelastic Maxwell, Oldroyd, and Kelvin- Voigt uids are derived. A model of rotating viscoelastic barotropic Oldroyd uid is studied. A theorem on strong unique solvability of the corresponding initial-boundary value problem is proved. The spectral problem associated with such a system is studied. Results on the spectrum localization, essential and discrete spectra, and spectrum asymptotics are obtained. In the case where the system is in the weightlessness state and does not rotate, results on multiple completeness and basisness of a special system of elements are proved. In such a case, under condition of su ciently large viscosity, expansion of the solution of the evolution problem with respect to a special system of elements is obtained.
Contemporary Mathematics. Fundamental Directions. 2016;61:41-66
pages 41-66 views

Abstract Mixed Boundary-Value and Spectral Conjugation Problems and Their Applications

Kopachevskii N.D., Radomirskaya K.A.


Basing on the abstract Green formula, we study general approach to abstract boundary-value conjugation problems. We consider examples of some con gurations of docked domains for conjugation problems using generalized Green formula for the Laplace operator. Also we consider spectral problems with two complex parameters: one of them can be treated as xed and the other one as spectral. By means of the proposed general approach, we reduce these problems to the spectral problem for operator pencil with self-adjoint operator coe cients acting in Hilbert space and depending on two parameters.
Contemporary Mathematics. Fundamental Directions. 2016;61:67-102
pages 67-102 views

On the volume formula for a hyperbolic octahedron with mm2-symmetry

Krasnov V.A., Khisyametdinova E.S.


In this paper, explicit integral volume formulas for arbitrary compact hyperbolic octahedra with mm2-symmetry are obtained in terms of dihedral angles. Also we give an algorithm for calculation of volume of such octahedra in spherical space.
Contemporary Mathematics. Fundamental Directions. 2016;61:103-114
pages 103-114 views

Topological Algebras of Measurable and Locally Measurable Operators

Muratov M.A., Chilin V.I.


In this paper, we review the results on topological ∗-algebras S(M), S(M,τ), and LS(M) of measurable, τ -measurable, and locally measurable operators a liated with the von Neumann algebra M. Also we consider relations between these algebras for di erent classes of von Neumann algebras and establish the continuity of operator-valued functions with respect to local convergence in measure. We describe maximal commutative ∗-subalgebras of the algebra LS(M) as well.
Contemporary Mathematics. Fundamental Directions. 2016;61:115-163
pages 115-163 views

On Coercive Solvability of Parabolic Equations with Variable Operator

Hanalyev A.R.


In a Banach space E, the Cauchy problem vt(t)+ A(t)v(t)= f (t) (0 >t > 1), v(0) = v0 is considered for a di erential equation with linear strongly positive operator A(t) such that its domain D = D(A(t)) is everywhere dense in E independently o t and A(t) generates an analytic semigroup exp{-sA(t)} (s < 0). Under some natural assumptions on A(t), we establish coercive solvability of the Cauchy problem in the Banach space C0β,γ (E). We prove a stronger estimate of the solution compared to estimates known earlier, using weaker restrictions on f(t) and v0.
Contemporary Mathematics. Fundamental Directions. 2016;61:164-181
pages 164-181 views

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