Estimates of orders of groups of projective transformations of Riemannian spaces

Translated from Matematicheskie Zametki, Vol. 43, No. 2, pp. 256–262, February, 1988.     

Construction of normal bases of rings of integral elements of certain fields of algebraic functions

This article is devoted to the construction of normal bases of rings of integral elements of certain fields of algebraic functions. These fields are algebraic extensions of the initial fields, given by appropriate algebraic equations. The extensions are given only by the monodromy group. The device of the matrix Riemann boundary-value problem on a Riemann surface is used.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 1004–1007, July, 1990.     

Bases of the identities of products of certain varieties of groups

The following theorem is proved: The product of any variety of two-step solvable groups and a variety having a finite basis of identity relations has a finite basis of identity relations.Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 137–144, January, 1969.     

Axiomatizability of reducts of algebras of relations

In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based. We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras. Received October 7, 1998; accepted in final form September 10, 1999.     

A problem of control of bundles of trajectories

Odessa. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 2, pp. 196–199, March–April, 1992.     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Determination of asymptotic solutions of problems of nonlinear theories of thermoviscoelasticity

It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 3, pp. 395–400, May–June, 1976.     

Properties of operators of extension and contraction of ideals of algebras of invariants of reductive groups in positive characteristic

V. I. Lenin Tashkent State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 4, pp. 53–61, October–December, 1991.     

Structure of genera of representations of nonsemisimple rings

The investigation of integral representations of arbitrary rings is shown to be equivalent to the case of orders in semisimple algebras. An example is constructed showing that, for an order in a nonsemisimple algebra, the number of representations in the genus may increase without limit with varying genera.Translated from Matematicheskie Zametki, Vol. 10, No. 1, pp. 63–87, July, 1971.     

Variant of statistical interpretation of the formation of viscoelastic deformations of polymers

A variant of a statistical probability interpretation of elementary micromechanisms of formation of viscoelastic deformations of polymers is examined with the aid of the concept of dissymmetric media and the dissymmetry coefficient. A new rheological relationship is obtained, a particular case of which is the known equation of a typical linear viscoelastic body. A method is given for determining the relaxation spectrum for different intensity functions figuring in the rheological relationships. The results of the calculation are compared with the experimental data, exemplified by the creep of polyamide P-68.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 392–396, May–June, 1973.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Orders of the torsion of points of curves of genus 1

Let K be an algebraic number field of degree n; let be the number of divisor classes of the field K; y: v²=u⁴+au²+B is the Jacobian curve over where C is an integral divisor, q₁, ..., q_N are distinct prime divisors. One proves that there exists an effectively computable constant c=c(n, h(K), N), such that the order m of the torsion of any primitive K-point on is bounded by it: mC.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, AN SSSR, Vol. 82, pp. 5–28, 1979.     

Separation of zeros of entire functions of exponential type and completeness of characters

Translated from Matematicheskie Zametki, Vol. 52, No. 2, pp. 83–91, August, 1992.     

Approximation of sobolev classes of functions by sums of products of functions of fewer variables

Translated from Matematicheskie Zametki, Vol. 48, No. 6, pp. 10–21, December, 1990.     

Problem of the theory of functions and essential self-adjointness of powers of operators

A connection is established between the essential self-adjointness of powers of a symmetric operator and a generalization of a problem of the theory of functions which was studied by Levitan, Vul, and other authors.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1492–1500, November, 1990.     

Approximate methods of solution of problems of mechanics application of B-splines to bending of rectangular panels

A method is proposed to analytical solution of boundary-value problems for fourth-order differential equations describing the bending of rectangular panels of variable stiffness. Fifth-order B-splines are used to satisfy the rigid clamping boundary conditions.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 47–51, 1988.     

Estimate of growth of Lebesgue functions of linear methods of summation

Sufficient conditions are obtained in terms of matrix elements for the boundedness of Lebesgue functions of linear methods of summation of expansions in orthogonal systems of polynomial type.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 277–286, September, 1969.     

Method of elastic solutions of problems of thermoviscoelasticity

The quasi-static mixed boundary value problem is considered for a viscoelastic body with time-dependent properties and a singular nondegenerate relaxation kernel. The existence of a time-temperature (or similar) analogy is not assumed. A method of reducing the viscoelastic problem to the solution of a series of uniform elastic problems is proposed and its convergence proved. The method is illustrated with reference to examples of solutions of specific viscoelastic problems.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 4, pp. 603–614, July–August, 1970.     

Estimates of the widths of classes of analytic functions

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 4, pp. 567–570, April, 1989.