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Vol. 27 (66), No. 1. 2014
Physics and Mathematics Sciences.

II.V. Baran
Mean value theorem and Taylor formula for symmetric derivatives and symmetric K-subdifferentials

Y.V. Bogdanski, Ya.Yu. Sanzharevskiy
Laplacian on measure and the Dirichlet problem
It was proposedLaplace operator version on functions on a separable real Hilbert space H(dimH 6 ∞) that is generated by the (non-negative finite Borel) measure μdefined on H. It was studied both of existence and uniqueness of solutions(including "weak" ones) of the Dirichlet peoblem for the elliptic equation ina region G that is agreed with an initial measure μ. It was given an example ofagreeing of a measure μ with a region G.

E.V. Bozhonok, E.M. Kuz'menko
Classes of variational functionals having nonlocal K–extremum in W1,p(D) on multi-dimensional domain
In this paper the investigation scheme of nonlocal compact extremum at zero forvariational functional in Sobolev space W1,p(D), p N, on multi-dimensionalcompact domain D RN, N N, is derived. Some examples of variationalfunctionals having nonlocal K–extremum are considered.

E.L. Haziyev
Spectral problem with transmission conditions on curvilinear interface
This paper deals with a spectral problem arising in a problem of small motions ofa system "ideal capillary fluid–gas" in a rectangular vessel with the solid walls.We suppose that a gas density is exponentially stratified opposite to the directionof gravitational forces and conjugation conditions for potential displacement areformulated on the fluid surface which is not horizontal at rest. A projectionmethod for finding a generalized solution is offered.

N.D. Kopachevskii, K.A. Radomirskaya
Abstract mixed boundary and spectral transmission problems
On the basis of the abstract Green’s formula for the triple of Hilbert spacesand the generalized Green’s formula for the Laplace operator we consider a newclass of mixed boundary value and spectral transmission problems.

I.V. Melnikova, O.S. Starkov
Weak and generalized solutions of the abstract cauchy problem
Weconsider three types of solutions (weak, generalized with respect to t and withrespect to a random variable) for the infinite dimensional stochastic Cauchyproblem X(t) = AX(t) + BW(t), t 0,X(0) = ζ, with A being the generatorof a regularized semigroup in a Hilbert space H and a white noise W in anotherHilbert space H, B ∈ L(H,H). It is proved coincidence of the solutions underthe conditions they exist.

E.V. Siomkinа
Spectral problem associated with a Cauchy problem on small motions of a dissipative dynamical system

N.G. Soldatovа
On the solution of three-criteria problem under uncertainty
In this paper the definition of guaranteed solution for three-criteria problemunder uncertainty is introduced. New solution is based on the method ofdecision-making in hierarchical two-level game. The conditions of existence areformulated. The example is given.

F.S. Stonyakin
Sequential version of Uhl Theorem on convexity and compactness for vector measure range.

F.S. Stonyakin, R.O. Shpilev
Analog Lyapunov convexity theorm for e-quasimeasures and its application to fair division problem.

Z.I. Khalilovа
Extreme variational problems with subsmooth integrand

A.V. Tsygankova
Elimination of Jacobi equation in variational problems with non-smooth integrand

V. Zhukovsky, P.K. Ahrameev
Guaranteed on risk solution in problem of sum distribution into three deposits (in rubles, dollars and euros)
We are looking at problemsof sum distribution (in rubles) into three deposits (in rubles, dollars and euros)in order to obtain the maximum annual income (in terms of rubles). Thedecision maker (investor) does not know the real dollar and the euro rates atthe end of the year, and has to look at some possible rate boundaries or limitsfor them. The solution of this problem depends on the readiness of the decisionmakerto take risks. The contents of this article are the ways to construct thedecisions of guaranteed risks onto account. This paper is actually devoted toconstructing of a guaranteed on risk solution.

V. Zhukovsky, M.I. Vysokos
Guaranteed in outcomes and risks solution for single-criterion problem
Concept of Pareto-guaranteed in outcomes and risks solution for singlecriterionproblem under uncertainty is proposed. It is based on a modificationof the maximin. Explicit solution for the problem of a single contribution to thediversification of ruble and foreign currency deposit is found.

A. V. Dereza
Definition     of Time Component Petri net  for Different ways of  it  Construction  

A. S. Gorbatov, V. I. Zhukovskiy
About Deposit Diversification Problem

О. S. Kisel, J. S. Pashkova
Comparison      of  Orlicz, Lorentz and Orlicz- Lorentz Spaces

V. I. Voytitsky, D. A. Zakora
On the Spectral Properties of Some Auxiliary Boundary Value  Problems from Theory of Metamaterials

V. I. Zhukovskiy, S. N. Sachkov, L. V. Smirnova
Existence of  Berge  Equilibrium in  Mixed Strategies