负系数差分方程的振动性质

研究了一类负系数差分方程的振动性质,得到了这类差分方程振动的判据.     

一类二阶非线性中立型差分方程的振动性

研究了二阶非线性中立型差分方程Δ2(xn+pxn-l)+qnf(xn-k)=0的振动性,获得了该类方程振动的三个充分性定理.所得结果将一阶非线性中立型差分方程已有振动性的相应结论推广到了二阶非线性中立型差分方程.     

二阶中立型差分方程的振动性

研究了一类变系数的二阶中立型时滞差分方程的振动性,得到了该类方程振动及解的一阶差分振动的充分条件。     

一类具多滞量的二阶中立型差分方程的振动定理

研究了一类具有多个滞量的变系数的二阶中立型差分方程的振动性,给出了该类方程振动及差分算子振动的充分条件。     

二阶中立型变时滞差分方程解的振动性

研究了二阶中立型变时滞差分方程Δ2(xn+pxn-l)+qnf(xσ(n))=0解的振动性,获得了该类方程全部非平凡解振动的三个定理.所得结果将二阶中立型差分方程已有的振动性的相应结论推广到了二阶中立型变时滞差分方程.     

一阶中立型时滞差分方程的线性化振动性定理

本文考虑一类非线性中立型时滞差分方程,证明了在一定条件下,若与此方程相关的一个线性差分方程的每个解振动,则该非线性差分方程的每个解也振动。     

带有多个变滞量的二阶中立型差分方程振动性判据

研究了一类较广泛的带有多个变滞量的变系数的二阶中立型差分方程的振动性 ,给出了该类方程振动及差分算子△振动的判据 .     

一类非线性延迟微分方程数值解的振动性分析

本文考虑一类非线性延迟微分方程-带有单峰造血率的造血模型数值解的振动性及非振动性。运用线性化理论,把非线性差分方程的振动性转化为其对应的线性差分方程的振动性,通过判断线性方程的特征方程根的情况,得到了非线性差分方程振动和存在非振动解的充分条件。对于非振动的数值解,证明了非振动的数值解最终都趋于方程的平衡解。为了更有力的说明我们的结果给出了相应的算例.     

具有可变时滞的非线性非自治差分方程的振动性及其应用

本文获得了一类具有可变时滞的非线性非自治差分方程的振动准则,建立了这类差分方程的几个线性化振动性定理,并得到了具有可变时滞的离散型非自治广义Logistic方程关于其正平衡点振动的一系列充分条件.     

具有连续变量的差分方程振动性的判据

本文借助研究离散变量的差分方程振动性的一般方法，建立了具有连续变量、变系数的差分方程振动性判据，并给出了具体例子。     

Diophantine representation of enumerable predicates

This paper is the author's abstract of dissertation in partial fulfillment of the requirements for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended on February 24, 1972 at a session of the faculty council of the V. A. Steklov Mathematics Institute, Academy of Sciences of the SSSR. The official opponents were: Doctor of Physicomathematical Sciences S. I. Adyan; Corresponding Member of the Academy of Sciences of the USSR Yu. L. Ershov; and Corresponding Member of the Academy of Sciences of the USSR D. K. Faddeev.Translated from Matematicheskie Zametki, Vol. 12, No. 1, pp. 115–120, July, 1972.     

Studies in the matrix representability of abstract groups and in matrix groups

The author presents a summary of his dissertation in competition for the academic degree Doctor of Physicomathematical Sciences. The dissertation was defended on April 26, 1972, before the Academic Council of the Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR. The official opponents were Prof. D. M. Smirnov (Doctor of Physicomathematical Sciences), Prof. A. I. Starostin (Doctor of Physicomathematical Sciences of the Belorussian SSR and Doctor of Physicomathematical Sciences), and Prof. A. I. Shirshov (Corresponding Member of the Academy of Sciences of the USSR and Doctor of Physicomathematical Sciences).Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 597–606, October, 1973.     

Certain problems of the theory of difference boundary value problems

This is an author's abstract of a dissertation for the degree of doctor of physicomathematical sciences. The dissertation was defended on December 2,1969,at a session of the Scientific Council of the Institute of Applied Mathematics, Academy of Sciences of the USSR. The official opponents were: Doctor of Physicomathematical Sciences Prof. K. I. Babenko, Doctor of Physicomathematical Sciences Prof. N. S. Bakhvalov, and Doctor of Physicomathematical Sciences E. A. Volkov.Translated from Matematicheskie Zametki, Vol. 7, No. 5, pp. 655–663, May, 1970.     

Prime extensions and categoricity in power

This paper deals with the notion of prime extension defined by Morley. A connection is established between the categoricity of a theory in a cardinal greater than the power of its language and the existence of prime extensions. For such theories we prove a minimality property of the prime extensions and we conclude by a property of the group of automorphisms of their models. Author working on Ph. D. thesis under supervision of Prof. M. O. Rabin. Author working at the CNRS under the supervision of Prof. D. Lacombe.     

Lyapunov first method for nonholonomic systems with circulatory forces

We consider the problem of instability of equilibrium states of scleronomic nonholonomic systems moving in a stationary field of conservative and circulatory forces. The applied methodology is based on the existence of solutions of differential equations of motion which asymptotically tend to the equilibrium state of the system. It is assumed that the forces in the neighbourhood of the equilibrium position can be presented in the form of the sum of two components, the first one being a homogeneous function of the position with the positive degree of homogeneity; the second one being infinitely small in comparison to the first one. The results obtained, which partially generalize results from [S.D. Taliaferro, Instability of an equilibrium in a potential field, Arch. Ration. Mech. Anal. 109 (2) (1990) 183–194; V.A. Vujičić, V.V. Kozlov, Lyapunov’s stability with respect to given state functions, J. Appl. Math. Mech. 55 (4) 9 (1991) 442–445; D.R. Merkin, Introduction to the Theory of the Stability of Motion, Nauka, Moscow, 1987 (in Russian); A.V. Karapetyan, On stability of equilibrium of nonholonomic systems, Prikl. Mat. Mekh. 39 (6) (1975) 1135–1140 (in Russian)], are illustrated by an example.     

Baryon string model. II. Special solutions of classical three-string equations of motion

Conclusions We have considered the simplest solutions of the three-string equations of motion; these are solutions with a finite number of excited degrees of freedom. It is of interest to construct the quantum theory of such motions of the relativistic three-string. Quantum theory of a meson string with finite number of degrees of freedom was constructed in [4]. Quantization of finite-mode solutions of the baryon string model will be considered in the third paper of the present work.Institute of High Energy Physics, Serpukhov. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 64, No. 2, pp. 245–258, August, 1985.     

A family of extension operators

The definition of the degree of a family of extension operators is given. The connection of lower estimates with general properties is established. The problem of approximation of the segment [0, 1] by finite subsets is studied. In the class of homogeneous operators the independence of norms of operators from the degree of the family of extension operators is proved.Translated from Matematicheskie Zametki, Vol. 22, No. 2, pp. 215–219, August, 1977.     

A solution of the problem of oscillations of a die on a two-phase base under a seismic impact

A method of studying nonstationary seismic oscillations of a cylindrical die on a two-phase base is developed, which is modeled with an application of the theory of M. Bio-Ya. I. Frenkel'—V.N. Nikolaevskii. In the solution of the problem integral transforms are used in combination with the method of orthogonal polynomials for a representation of required contact stresses. Numerical results are given, which characterize a change of coefficients of expansion of the series of contact stresses with respect to time, including their resultant, under different masses of the die. Transformations of the projection diagram of normal contact stresses are shown as time passes.Translated from Dinamicheskie Sistemy, No. 7, pp. 32–41, 1988.     

The multidimensional plateau problem in Riemannian varieties

This paper is the author's abstract of his dissertation for the degree of Doctor of Physico-Mathematical Sciences. The dissertation was defended on September 29, 1972 at a session of the Council of the Mechanico-Mathematical Faculty of M. V. Lomonosov Moscow University. The official opponents were Prof. V. M. Alekseev, Doctor of Phys.-Mat. Sci.; Prof. D. V. Anosov, Doctor of Phys.-Mat. Sci.; and Prof. M. M. Postnikov, Doctor of Phys.-Mat. Sci.Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 159–167, January, 1973.     

Approximations relative to Hausdorff distance

The present paper is an abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Physical and Mathematical Sciences. The dissertation was defended on November 30, 1967 before the faculty of the V. A. Steklov Mathematical Institute of the Academy of Sciences of the USSR. The official opponents were Professors N. P. Korneichuk, P. P. Korovkin, and S. B. Stechkin, Doctors of Physical and Mathematical Sciences.