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.     

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.     

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.     

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.     

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.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Stable cohomologies of the complements of the discriminants of deformations of singularities of smooth functions

Complements to discriminants of singularities of smooth functions are far generalizations of the classifying spaces of Artin and Brieskorn braid groups. A group of stable cohomologies (i.e., cohomologies preserved under adjacency of singularities) is described for these spaces. A relationship between these cohomologies and Gauss-Manin connectivity of singularities is indicated. A cellular realization of cohomologies of symmetric groups with coefficients in Z₂ is described.Translated from Itogi Nauki i Tekhniki, Seriya Sovermennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 33, pp. 3–29, 1988.     

Tracing of pseudotrajectories of dynamical systems and stability of prolongations of orbits

We investigate properties of dynamical systems associated with the approximation of pseudotrajectories of a dynamical system by its trajectories. According to modern terminology, a property of this sort is called the “property of tracing pseudotrajectories” (also known in the English literature as the “shadowing property”). We prove that dynamical systems given by mappings of a compact set into itself and possessing this property are systems with stable prolongation of orbits. We construct examples of mappings of an interval into itself that prove that the inverse statement is not true, i.e., that dynamical systems with stable prolongation of orbits may not possess the property of tracing pseudotrajectories. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 8, pp. 1016–1024, August, 1997.     

Preservation of equivalence of derivations under reduction of depth of formulas

In this paper we consider derivations in the (&, )-fragment of the intuitionistic propositional calculus. As is known, replacement of any occurrence of a formula [F] in a sequent S by an occurrence of the formula [p], where p is a new propositional variable, with the simultaneous addition to the antecedent of the formula F p or p F depending on the sign of the occurrence of F in S, leaves the derivability unchanged. We give a proof of the fact that the natural extension of this transformation to derivations preserves the relation of equivalence of derivations, i.e., transformed derivations are equivalent if and only if the originals are equivalent. (Derivations are considered equivalent if certain of their normal forms coincide, or, what is the same, if their deductive terms coincide.) It is proved that by the iteration of this transformation, each derivation of an arbitrary sequent S can be transformed into a derivation of a sequent S, depending only on S, whose succedent is a variable, and in the antecedent there occur only formulas of the form a,a & b, a b,,(a b) c, a & b c, a (b & c), wherea, b, c are variables. Here if S is balanced, then S is also balanced. (A sequent is called balanced if each variable occurs in it no more than twice.) The familiar correspondence between certain concepts of the theory of categories and concepts of the theory of proofs allows one to assert that there has been constructed a univalent functor, mapping a free Cartesian closed category into itself.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 197–207, 1979.     

Finiteness of basis of identities of finite-dimensional representations of solvable lie algebras

Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 3, pp. 78–86, May–June, 1988.     

Estimates of orders of groups of projective transformations of Riemannian spaces

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

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.     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

关于整数和集的定理的推广

本文主要利用加性数论的理论考察整数和集,稚广了Vscvolod F．Lev的关于整数和的定理：设n≥1,B增包含[1,n],｜B｜〉n/4,k=｜B｜＋1,则 （1）当1≤n≤2k-3时,有ia^s能写成两个不同B中元之和。 （2）当2k-2≤,1〈3k-3时,有ia^s能写成最多四个B中元之和。 （3）当3k-3≤n〈4k-4时,有ia^s能写成最多2h个B中元之和。 其中h=max[2k/4k-4-n],i=1,2,3,4,6     

Religion of positivity of solutions of elliptic equations

The class of elliptic equations is identified whose solutions which are nonnegative in a sphere of a certain radius vanish identically. A generalization is indicated to the case of equations with complex coefficients and solutions whose values lie in a sector of the complex plane determined by the equation.Translated from Matematicheskie Zametki, Vol. 9, No. 1, pp. 83–87, January, 1971.     

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.     

Stepanov method of the estimation of the number of roots of some equations

Translated from Matematicheskie Zametki, Vol. 51, No. 6, pp. 52–58, June, 1992.     

Stability estimates of solutions of systems of functional-differential equations of neutral type

A system of linear functional-differential equations of neutral type is considered. Investigation of stability is carried out by the method of Lyapunov functions of quadratic form. Sufficient conditions for the asymptotic stability and estimates of the exponential decay of solutions for an arbitrary and a small deviation of the argument are obtained.Candidate of the Physicomathematical Sciences.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43. No. 9, pp. 1123–1135, September, 1991.     

Birational aspects of the geometry of Varieties of Sums of Powers

Varieties of Sums of Powers describe the additive decompositions of a homogeneous polynomial into powers of linear forms. The study of these varieties dates back to Sylvester and Hilbert, but only few of them, for special degrees and number of variables, are concretely identified. In this paper we aim to understand a general birational behavior of VSP. To do this we birationally embed these varieties into Grassmannians and prove the rational connectedness of many VSP in arbitrary degrees and number of variables.