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.     

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．     

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.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Regularity of minimizers of non-isotropic integrals of the calculus of variations

The regularity of the minimizers of a special type of non-isotropic variational minimization problem is studied. The particularity of the potential of energy is that it has different growth rate with respect to different parts of the derivatives of the function. In particular, the model treated in this paper can be described as $$\Phi (Du) = |\partial _1 u|^2 + |\partial _2 u|^2 + |\partial _3 u|^2 + |\partial _3 u - |^p .$$ By using a result of P.Marcellini (cf. [4]) and perturbation method, it is proved that the minimizer of the Dirichlet boundary value problem is a function of W _loc ^{1, ∞} .     

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.     

Doubly-Exponential Growth of the Number of Vectors of Multipilicities for Solutions of Systems of Polynomial

Earlier, D. Yu. Grigoriev and N. N. Vorob'yov obtained an upper bound for the number of vectors of multiplicities for solutions of systems of the form (assuming that the system has a finite number of solutions). In the system above, are polynomials of degrees . In the present paper, we show that the order of growth of this bound is close to the exact one. In particular, in the case d=n, the construction provides a doubly-exponential (in n) number of vectors of multiplicities. Bibliography: 4 titles.     

Robustness of a class of problems of characterization of distributions and a lemma of Gabovich

The robustness of characterization problems of mathematical statistics is considered, and some results of Gabovich are extended.Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei — Trudy Seminara, pp. 46–51, 1980.     

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.     

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.     

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.     

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.     

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.     

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.     

Cohomology of compactified manifolds of modules of Ϝ -sheaves of rank 2

The present paper is one of a series of papers of the author devoted to the proof of Langlands' conjecture for GL(2). The preceding parts were published in Funktsional'nyi Analiz i ego Prilozheniya,21, Nos. 2 and 4, 1987.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 162, pp. 107–158, 1987.     

Estimates of orders of groups of projective transformations of Riemannian spaces

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

On a method of constructing the solutions of boundary-value problems of the theory of bendings of surfaces of positive curvature

A new method is proposed for constructing the solutions of boundary-value problems of Riemann-Hilbert type for noncanonical linear and quasilinear first-order elliptic systems in a simply connected bounded region of the plane. For a linear boundary condition we obtain complete results; for a nonlinear boundary condition we study the solvability in a neighborhood of zero. Applications are given to the problem of isometric transformations of a surface diffeomorphic to the disk and having positive curvature all the way to the boundary under prescribed boundary conditions.Translated from Ukrainskií Geometricheskií Sbornik, Issue 29, 1986, pp. 56–82.     

Decidability of elementary theories of lattices of subsemigroups

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 1, pp. 27–33, January–February, 1990.     

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.