Mathematics |
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2008, No. 3
A.D. Baev
ON GENERAL BOUNDARY PROBLEM IN BAR FOR DEGENERATING HIGH ORDER ELLIPTIC EQUATION
In this paper unique existence theorem is proved for solution of boundary problem, like Dirichlet problem, in bar for one class of degenerating high order elliptic equations. The solution of this problem a priori estimation is proved in specially selected spaces like Sobolev spaces.
A.D. Baev
A new method to prove the solutions a priori estimations and solutions existence theorem of general boundary problem in half-space for degenerating high order elliptic equations is suggested.
N.A. Vavilov, A.V. Stepanov
OVERGROUPS OF SEMISIMPLE GROUPS
The paper is a systematic survey of results on overgroups of elementary subgroups of semisimple groups over a commutative ring in the group of points of another semisimple group (generally speaking, over different commutative ring). As a general context we use the framework of Aschbacher’s subgroup structure theorem. We specially concentrate on the recent results obtained in Saint-Petersburg. In particular we expound the description of overgroups of classical groups, obtained by Viktor Petrov, the first author and Hong You, as well as further related results by Alexander Luzgarev on overgroups of exceptional groups Aschbacher class C8), and the description of overgroups of subring subgroups, obtained by the second author (Aschbacher class C5). Furthermore, we outline in some detail description of overgroups of tensored subgroups obtained by Alexei Ananievski, the first author and Sergei Sinchuk (Aschbacher classes C4+C7) and recent results on ovegroups of subsystem subgroups in exceptional groups (Aschbacher classes C1+C2). We state 50 further unsolved problems in this field.
V.A. Goloveshkin, M.V. Ulyanov
In the paper analytical solution for special class of recurrence relations is proposed. Analysed recurrence relations are characterized for the of labour-intensiveness recurrence relations functions processed by decomposition method and has linear labour-intensiveness of union obtained solutions. Analytical solution for two subclasses arising at theoretical examination of investigated class recurrence relations is obtained. The results can be used to receive explicit functions of labourintensiveness recurrence algorithms decompising the task with linear labour-intensiveness of results union.
I.A. Zorina, V.G. Tkachev
ON ENTIRE SOLUTIONS OF A QUASILINEAR PDE WITH A QUADRIC PRINCIPAL PART
In the present paper, we prove the existence of a countable family of entire solutions for a wide class of quasilinear equations. In particular, we show that all obtained solutions have a polynomial growth and their topological structure is similar to that of harmonic polynomials.
M.V. Ignatev
BASIC SUBSYSTEMS OF ROOT SYSTEMS OF TYPES Bn AND Dn AND ASSOCIATED COADJOINT ORBITS
To each basic subsystem of root system of type Bn or Dn one can assign the set of coadjoint orbits of maximal unipotent subgroup of corresponding classical group over a finite field. We construct polarizations of the canonical forms on these orbits (Theorem 2.7) and describe the dimensions of these orbits in terms of the Weil group (Theorem 4.5).
A.G. Lozhkin
DIRECT ANALYTICAL METHOD OF LINEAR TRANSFORMATIONS OF FIGURES IN PLANE
The task of arbitrary linear transformations of figures was considered. A category of figures was limited as figures is describe by parametric piecewise continuous functions equations set. The method’s formulas may be find in non orthogonal basis only was proof.
D. E.Klepnev
VITALI–ARESHKIN THEOREM FOR DIAGONAL SEQUENCE OF MEASURES
In theorem of G.Ya. Areshkin, which is a generalization of classical Vitali’s theorem on the case of sequence of measures, the pointwise convergence of integrated functions is required. In this work we consider the case when the sequence of integrating measures is weakly diagonal. In this case the pointwise convergence may be substituted on the weaker convergence about the sequence of integrated measures.
A.I. Kozhanov
ON SOLVABILITY OF CERTAIN SPATIALLY NONLOCAL BOUNDARY PROBLEMS FOR LINEAR PARABOLIC EQUATIONS
In this work, the solvability of certain problems for parabolic equation
with nonlocal conditions
α1(t)u(a, t) + α2(t)u(b, t) +
α3(t)ux(a, t) + α4(t)ux(b, t) = 0,
β1(t)u(a, t) + β2(t)u(b, t) +
β3(t)ux(a, t) + β4(t)ux(b, t) = 0.
is proved. The proof is mainly based on the regularization method and
the method of continuation with respect to a parameter.
S.A. Korolkov, A.G. Losev, E.A. Mazepa
ON HARMONIC FUNCTIONS ON RIEMANNIAN MANIFOLDS WITH QUASIMODEL ENDS
In the paper harmonic functions on Riemannian manifolds with quasimodel ends are considered. Conditions of existence and uniqueness some boundary problems based on spectral properties of these manifolds and also conditions of Liuville type theorems are obtained.
M.G. Svistula
A SIGNED QUASI-MEASURE DECOMPOSITION
The concept of a proper signed quasi-measure is considered. The theorem about expansion of space of signed quasi-measures in a direct sum of the space of signed measures and the space of proper signed quasi- measures is proved. Finally, we apply our results to the quasi-linear functionals.
A.I. Shashkin, M.M. Shiryaev
JOB SCHEDULING BASED ON FUZZY INPUT DATA
This article describes mathematical model of project job scheduling that represented as oriented fuzzy graph. Possibility of fuzzy sets using to increase quality of authors developed genetic algorithms working results is investigated. The article source is most applicable for automation solutions in firms where primary resources are manpower resources and duties are complex.