Siberian Mathematical Journal最新文献

Abstract

We study unification and admissibility for an infinite class of modal logics. Conditions superimposed to these logics are to be decidable, Kripke complete, and generated by the classes of rooted frames possessing the greatest clusters of states (in particular, these logics extend modal logic S4.2). Given such logic ( L ) and each formula ( alpha ) unifiable in ( L ) , we construct a unifier  ( sigma ) for  ( alpha ) in  ( L ) , where ( sigma ) verifies admissibility in ( L ) of arbitrary inference rules ( alpha/beta ) with a switched-modality conclusions  ( beta ) (i.e.,  ( sigma ) solves the admissibility problem for such rules).

We consider the Dirichlet problem for the ( p )-Laplace equationin presence of a gradient not satisfying the Bernstein–Nagumo type condition.We define some class of gradient nonlinearities,for which we prove the existence of a radially symmetric solution with a Hölder continuous derivative.

We consider the asymptotic properties of solutions to the mixed problemsfor the quasilinear nonautonomous first-order hyperbolic systems withtwo variables in the case of smoothing boundary conditions.We prove that all smooth solutions to the problem for a decoupled hyperbolic systemstabilize to zero in finite time independently of the initial data.If the hyperbolic system is coupled then we show thatthe zero solution to the quasilinear problem is exponentially stable.

We give sufficient conditions for regularizing a distribution of the form( a(sigma,lambda)f(lambda) ),where( f(lambda) )is a distribution holomorphic in the parameter ( lambda ),while ( a(sigma,lambda) )is an infinitely differentiable function of ( sigma )outside some closed set ( N )with power singularities of derivatives on ( N )and holomorphic in ( lambda ).

Let ( G ) be the group of all limited permutations of the naturals ( N ).We prove that every countable locally finite group is isomorphic to a subgroup in ( G ).

We obtain some sufficient conditions for potency and virtual potency for automorphismgroups and the split extensions of some groups. In particular, consideringa finitely generated group ( G ) residually ( p )-finite for every prime ( p ),we prove that each split extension of ( G ) by a torsion-free potent group is a potent group,and if the abelianization rank of ( G ) is at most 2 then the automorphism group of ( G ) is virtuallypotent. As a corollary, we derive the necessary and sufficient conditions of virtual potencyfor certain generalized free products and HNN-extensions.

We present the inverse problem of successive determinationof the two unknowns that are a coefficient characterizingthe properties of a medium with weakly horizontal inhomogeneityand the kernel of an integral operator describing the memory of the medium.The direct initial-boundary value problem involves the zero dataand the Neumann boundary condition.The trace of the Fourier image of a solution to the direct problemon the boundary of the medium serves as additional information.Studying inverse problems, we assume that the unknown coefficient is expandedinto an asymptotic series in powers of a small parameter.Also, we construct some method for findingthe coefficient that accounts for the memory of the environmentto within an error of order ( O(varepsilon^{2}) ).At the first stage, we determinea solution to the direct problem in the zero approximationand the kernel of the integral operator,while the inverse problem reduces to an equivalent problem ofsolving the system of nonlinear Volterra integral equations of the second kind.At the second stage, we consider the kernel given and recovera solution to the direct problem in the first approximationand the unknown coefficient.In this case, the solution to the equivalent inverse problem agreeswith a solution to the linear system of Volterra integral equations of the second kind.We prove some theorems on the unique local solvability of the inverse problemsand present the results of numerical calculations of the kernel and the coefficient.

We study 0-1-sequences and establish the connectionbetween the values of the upper and lower Sucheston functionalon such sequence and the set of all possible divisorsof the elements in the sequence support.If the union of the sets of all simple divisorsof the elements in a 0-1-sequence support is finite then thesequence is almost convergent to zero. We study the 0-1-sequenceswhose support consists exactly of the multiples ofthe elements in a given set, and establish somenecessary and sufficient conditions for the upper Suchestonfunctional to be equal to 1 on such sequence. We prove that there areinfinitely many sequences at which the lower Sucheston functionalis 1, and the lower Sucheston functional never vanishes at any ofsuch sequences.

Considering the groups ( PSL_{3}(2^{m}) ) and ( PSU_{3}(q^{2}) ), we find the minimal number of generatinginvolutions whose product is 1. This number is 7 for ( PSU_{3}(3^{2}) ) and 5 or 6in the remaining cases.

Under study are the relations between ( E )-rings and quotient divisible abelian groups.We obtain a criterion for the quotient divisibility of the additive groupof an ( E )-ring and give a negative solution to the Bowshell and Schultz problemabout the quasidecompositions of ( E )-rings.