Siberian Mathematical Journal最新文献

We find the conditions for a compact Hardy operator in Lorentz spacesto belong to the operator ideals generated by sequences of ( s )-numbers.We obtain some estimates of the norms of the Hardy operator in these ideals in terms of integralexpressions depending on the weight functions of the operator.

We prove the existence of a family of computably enumerable sets that,up to equivalence,has a unique computable minimal but not least numbering.

All pretabular extensions of the minimal logic were described andthe tabularity problem was solved earlier. As turned out, in total, there are sevenpretabular logics over the minimal logic. It was proved that four of them haveCraig’s interpolation property (CIP) and two do not. In the present article,we solve the problem of CIP in the seventh logic. We prove thatit has Craig’s interpolation property.

We find explicit expressions for optimal recovery methods in the problemof recovering the values of continuous linear operators on a Sobolev function classfrom the following information: The Fourier transform of functions is known approximatelyon some measurable subset of the finite-dimensional space on which the functions aredefined. As corollaries, we obtain optimal methods for recovering the solution to the heatequation and solving the Dirichlet problem for a half-space.

We show thatchanging the level curve of a harmonic functionwith the classical Hadamard variation with a small parameterentails a change in the Dirichlet integral of the functionwhich is quadratic in the parameter.As a corollary,we supplement the well-known theorem of Teichmüllerabout the sum of moduli of doubly connected domainsinto which an annulus is subdividedby a continuum that differs little from a concentric circle.

In 1974 Kharchenko proved that if a ( 0 )-component of an ( n )-graded associative algebra is PI then this algebra is PI.In the Novikov algebras of characteristic 0 the existence of a polynomial identity is equivalent to the solvability of the commutator ideal.We study a ( 𝕑_{2} )-graded Novikov algebra ( N=A+M ) and prove that if the characteristic of the basic field is not 2 or 3and its 0-component ( A ) is associative or Lie-nilpotent of index 3 thenthe commutator ideal ( [N,N] ) is solvable.

We study the structure of self-homeomorphism groups of fibered manifolds.A fibered topological spaceis a Birman–Hilden spacewhenever in each isotopic pair of its fiber-preserving(taking each fiber to a fiber)self-homeomorphismsthe homeomorphisms are also fiber-isotopic(isotopic through fiber-preserving homeomorphisms).We prove in particular thatthe Birman–Hilden class containsall compact connected locally trivial surface bundles over the circle,including nonorientable ones and those with nonempty boundary,as well as all closed orientable Haken 3-manifold bundles over the circle,including nonorientable ones.

We study and solve some class of infinite systems ofalgebraic equations with monotone nonlinearity and Toeplitz-type matrices.Such systemsfor the specific representations of nonlinearities arise in the discrete problems ofdynamic theory of clopen ( p )-adic strings for a scalar field of tachyons,the mathematical theory of spatio-temporal spread of an epidemic, radiation transfer theoryin inhomogeneous media, and the kinetic theory of gases in the framework of the modified Bhatnagar–Gross–Krookmodel. The noncompactness of the corresponding operator in the bounded sequence spaceand the criticality property (the presence of trivial nonphysicalsolutions) is a distinctive feature of these systems.For these reasons, the use of the well-known classical principles of existenceof fixed points for such equations do not lead to the desired results.Constructing some invariant cone segments for the correspondingnonlinear operator, we prove the existence and uniqueness of a nontrivialnonnegative solution in the bounded sequence space.Also, we study the asymptotic behavior of the solution at ( pminfty ).In particular, we prove that the limit at ( pminfty ) of a solution is finite.Also, we show that the difference betweenthis limit and a solution belongs to ( l_{1} ).By way of illustration, we provide some special applied examples.

Homogenization of the Neumann problem for a differential equationin a periodically broken multidimensional cylinderleads to a second-order ordinary differential equation.We study asymptotics for the coefficient of the averaged operatorin the case of small transverse cross-sections.The main asymptotic term depends onthe “area” of cross-sections of the links,their lengths,and the coefficient matrix of the original operator.We find the characteristics of kink zones which affect correction terms,while the asymptotic remainder becomes exponentially small.The justification of the asymptoticsis based on Friedrichs’s inequalitywith a coefficient independent of both small parameters:the period of fractures and the relative diameter of cross-sections.

We describe the algebras of binary formulas forcountably categorical weakly circularly minimal theories with 1-transitive nonprimitiveautomorphism group and trivial definable closurehaving convexity rank 1. We find some criterion for commutativity of the algebras.