Investigations in the theory of Stochastic equations

This is the author-review of a dissertation presented in the competition of the degree of the Doctor of Physicomathematical Sciences. The dissertation was defended on February 27, 1975 at a meeting of the Scientific Council of V. A. Steklov Mathematics Institute of the Academy of Sciences of the USSR. The official opponents were: A. A. Borovkov, Corresponding Member of the Academy of Sciences of the USSR; A. V. Skorokhod, Corresponding Member of the Academy of Science of the Ukrain. SSR, and V. N. Sudakov, Doctor of Physicomathematical Sciences.Translated from Matematicheskie Zametki, Vol. 20, No. 1, pp. 147–159, July, 1976.     

Solvable subgroups of finite simple groups

This article is the author's abstract of his dissertation for the degree Doctor of Physico-mathematical Sciences. The dissertation was defended on September 17, 1973, at the session of the Academic Council on the conferring of academic degrees in the mathematical sciences of the Uralian Order of the Red Banner of Labor of the A. M. Gor'kii State University. The official opponents were: Professor A. I. Shirshov, Corresponding Member of the Academy of Sciences of the USSR and Doctor of Physicomathematical Sciences; Professor A. I. Kostrikin, Doctor of Physicomathematical Sciences; Professor A. I. Starostin, Doctor of Physicomathematical Sciences; Professor L. A. Shemetkov, Doctor of Physico-mathematical Sciences. The chief institution was the Institute of Mathematics, Academy of Sciences of the Ukrainian SSR.Translated from Matematicheskie Zametki, Vol. 16, No. 5, pp. 833–842, November, 1974.     

Investigation of boundary value problems for elliptic systems of first order

This paper is the author's abstract of a dissertation submitted for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended November 2, 1972 at a session of the Scientific Council of the V. A. Steklov Mathematical Institute of the Academy of Sciences, USSR. Official referees: Corresponding Member of the Academy of Sciences of the USSR Professor A. V. Bitsadze, Corresponding Member of the Academy of Sciences of the USSR Professor M. M. Lavrent'ev, and Doctor of Physicomathematical Sciences, Professor P. I. Lizorkin.Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 291–304, August, 1973.     

Isometric imbedding in E3 of noncompact domains of nonpositive curvature

Author's abstract of a dissertation for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended on Oct. 21, 1977, at a session of the Specialized Council D 002.38.02 at the V. A. Steklov Mathematics Institute of the Academy of Sciences of the USSR. Official opponents: Academician of the Academy of Sciences of the USSR, Doctor of Physicomathematical Sciences A. V. Pogorelov; Professor, Doctor of Physicomathematical Sciences É. G. Poznyak; Professor, Doctor of Physicomathematical Sciences A. S. Fedenko.Translated from Matematicheskie Zametki, Vol. 25, No. 5, pp. 785–797, May, 1979.     

饱和粘土非线性渗流规律与径向固结

以多孔介质等效渗流概念得出粘土平均孔隙微尺度数量级范围在0.01 μm至0.1μm,与测试结果一致．实验结果表明饱和粘土微尺度孔隙渗流为非线性流．理论推导表明固液界面作用与渗透率平方根或孔隙半径成反比,固液界面相互作用是导致饱和粘土非线性渗流的重要原因．提出了精确描述饱和粘土微尺度孔隙非线性渗流基本规律的数学模型,其参数量纲明确,物理意义清楚．建立了饱和粘土非线性渗流新定律,统一描述了从较低到较高水力梯度全过程渗流曲线特征,达西定律是其特例．基于新定律,建立了饱和粘土非线性渗流定流量径向固结数学模型．以粘性边界层思想与稳态依序替换法及积分方程法,导出了粘土非线性渗流平均质量守恒方程及活动边界运动方程,给出了饱和粘土非线性渗流超孔隙水压力分布公式与平均固结度计算公式,获得了粘土层压力分布规律和平均固结度随时间变化规律．结果表明:饱和粘土非线性渗流使活动边界运动速度减小．研究结果为粘土地质工程与岩土工程应用提供了新的科学依据．达西渗流径向固结计算是新的非线性渗流固结计算的特例．     

Free alternative algebras

The author's abstract of a dissertation submitted as a requirement for the advanced degree of Doctor of Physicomathematical Sciences. The dissertation was defended on Feb. 2, 1978, at a session of the Specialized Council D 002.23.01 of the Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR. The official examiners were: Corresponding Member of the Academy of Sciences of the USSR, Doctor of Physicomathematical Sciences A. I. Kostrikin; Doctor of Physicomathematical Sciences V. D. Mazurov; Doctor of Physicomathematical Sciences Yu. M. Ryabukhin.Translated from Matematicheskie Zametki, Vol. 25, No. 5, pp. 775–783, May, 1979.The author would llke to express his sincere gratitude to A. I. Shirshov for his unfailing interest and total support. The author is particularly indebted to his teacher, K. A. Zhevlakov, who greatly influenced his scientific interests.     

Finite-dimensional perturbations of Volterra operators

This paper is a review by the author of his dissertation, presented in competition for the academic degree of Doctor of Physicomathematical Sciences. This dissertation was defended on December 20, 1973 at the Scientific Council of the Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR. The examining committee consisted of Professor A. G. Kostyuchenko, Doctor of Physicomathematical Sciences; Professor A. F. Leont'ev, Corresponding Member of the Academy of Sciences of the USSR; and Professor M. K. Fage, Doctor of Physicomathematical Sciences.Translated from Matematicheskie Zametki, Vol. 16, No. 4, pp. 669–680, October, 1974.     

Numerical inversion of Laplace transform by the method of asymptotic extension of the interval in dynamic viscoelasticity problems

Conclusions 1. A numerical investigation into the process of wave propagation in infinite and finite viscoelastic rods has been carried out by means of the method of asymptotic extension of the interval.2. It is established that use, in the calculations, of kernels of relaxation with weak singularity does not give rise to a stress jump at the wave front.3. The effect of parameters of the Rzhanitsyn kernel on the "erosion" of the wave front has been investigated. It is discovered that the instant of occurrence of a stress that is appreciably different from zero, at points far away from the beginning of the rod, is determined by the long-term modulus of elasticity of the material of the rod.4. The solution of the problem concerned with the propagation of a load impulse of finite duration shows a decrease of the maximum value of the stress in the rod, when the duration of the applied impulse decreases, and an intense change in the shape of the impulse while it propagates along the rod, as a consequence of wave dispersion.P. Stuchka Latvian State University, Riga. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 864–870, September–October, 1976.     

The concept of the cg-genus of quadratic forms

The concept of cg-genus of quadratic forms is introduced, intermediate between the concepts of genus and spinor genus. This gives the possibility to identify properties of quadratic forms, dependent first of all on the structure of the group of the classes of the ground field. The fundamental properties of cg-genera, analogous in many respects with the properties of spinor genera, are considered. Applications of this concept to various aspects of the problem of the classification of quadratic forms are given. Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 160, pp. 170–181, 1987.     

Partitions and centralizers in the theory of finite groups

This paper is the author's abstract of a dissertation for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended on February 10, 1969 at a united council for adjudicating academic degrees in mathematical sciences at the A. M. Gor'kii Urals State University. Official opponents: Corresponding Member of the Academy of Sciences of the USSR M. I. Kargapolov, Corresponding Member of the Academy of Sciences of the Ukrainian SSR S. N. Chernikov, Doctor of Physicomathematical Sciences Professor B. I. Plotkin, and Doctor of Physicomathematical Sciences V. S. Charin.Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 499–511, October, 1969.     

On extension of continuous mappings,topological products and retracts

One of the fundamental concepts of the extension theory developed in the works of A. N. Dranishnikov and E. V. Shchepin is the concept of relation of extensiveness, which was introduced by K. Kuratowski. We describe the behavior of the relation of extensiveness with respect to certain types of subspaces of topological products and spaces, which are the Stone–Cech compactifications of the discrete sums of the Hilbert cube.     

M-curves of degree 10

The known restrictions on the disposition of ovals of a nonsingular projective real algebraic curve leave possible for M-curves of degree 10 about 70,000 real schemes. These schemes divide naturally into 18 families. Basic result: in each of these families there exist representatives realizing M-curves of degree 10. Using the method of O. Ya. Viro, based on perturbations of curves with involved singularities, there are constructed more than 500 M-curves of degree 10. Incidentally there are obtained a large number of perturbations of points of tangency of five branches.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 122, pp. 146–161, 1982.In conclusion, I want to thank O. Ya. Viro for constant interest in my work and a series of important comments.     

中国科大数学系是怎样办学的

中国科学技术大学原副校长、数学系教授龚昇先生2011年1月10日不幸病逝.本刊编委会、编辑部于2011年1月第1期发表《沉痛悼念著名数学家龚？教授》一文,简短介绍了他的生平和学术成就.本期特转载他为《中国科学技术大学数学五十年》一书所作的序,以纪念这位杰出的数学家和数学教育家.本文标题为编者所加.1958年,经中共中央...     

Information aspects in the theory of approximation and recovery of operators

We present a brief review of new directions in the theory of approximation which are associated with the information approach to the problems of optimum recovery of mathematical objects on the basis of discrete information. Within the framework of this approach, we formulate three problems of recovery of operators and their values. In the case of integral operator, we obtain some estimates of the error. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal. Vol. 51, No. 3, pp. 314–327, March, 1999.     

基于计划行为理论的个人网上银行使用研究

首先介绍了网上银行发展的现状,以及计划行为理论和其他学者对网上银行使用的研究,然后以计划行为理论为基础,建立了个人网上银行的使用模型.通过问卷调查收集数据,运用统计软件对数据的信度和效度进行检验,在此基础上,对测量模型和结构方程模型的拟合优度,各系数的显著性水平,运用Lisrel8.7进行检验,并对初始模型进行了修正,根据计算出的路径系数,提出促进个人网上银行业务发展的建议,最后指出研究的不足和今后的研究方向.     

Involutive divisions for effective involutive algorithms

Properties of involutive divisions on monomials are studied. A new method of involutive graphs is developed. The concept of complete global involutive division is introduced. A criterion of Noetherianity of involutive divisions, a property of graphs of global involutive division, a test for completeness of global involutive division, and a criterion of global involutive division are considered. A new series of involutive divisions is obtained by the process of completion. The properties of the divisions contained in the constructed series are studied. It is shown that the divisions from the series are better than the classical involutive divisions for involutive algorithms. A problem stated by Gao is solved: another series of involutive divisions is obtained. It is proved that all divisions of this series are continuous. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 237–253, 2003.     

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.     

Current state and prospects for development of the physical theory of brittle strength of polymers

Various mechanisms of brittle fracture and theories of the time dependence of the strength of rigid polymers are examined. The effect of various types of mechanical losses (deformation, dynamical, surface) on polymer strength and life is analyzed. The principal shortcomings of Griffith's theory of strength are pointed out. From an examination of the two basic mechanisms of brittle fracture of polymers-nonthermal and thermal (thermal fluctuation)-it is concluded that the latter is the more important. A comparison is made of the fluctuation theory of polymer strength with new experimental data on polymethyl methacrylate, and the causes of the transition from brittle to nonbrittle fracture are discussed. The effect of molecular orientation on the strength of polymers is examined on the basis of the fluctuation theory of strength.Mekhanika Polimerov, Vol. 2, No. 5, pp. 700–721, 1966     

The Combinatorics of Polynomial Sequences

We present a combinatorial model for the several kinds of polynomial sequences of binomial type and develop many of the theorems about them from this model. In the first section, we present a prefab model for the binomial formula and the generating-function theorem. In Sec. 2, we introduce the notion of U-graph and give examples of binomial prefabs of U-graphs. The umbral composition of U-graphs provides an interpretation of umbral composition of polynomial sequences in Sees. 3 and 5. Rota's interpretation of the Stirling numbers of the first kind as sums of the Mobius function in the partition lattice inspired our model for inverse sequences of binomial type in Sec. 4. Section 6 contains combinatorial proofs of several operator-theoretic results. The actions of shift operators and delta operators are explained in set-theoretic terms. Finally, in Sec. 6 we give a model for cross sequences and Sheffer sequences which is consistent with their decomposition into sequences of binomial type. This provides an interpretation of shift-invariant operators. Of course, all of these interpretations require that the coefficients involved be integer and usually non-negative as well.     

Optimization of a cylindrical shell of reinforced plastic with a filler under dynamic loading

Conclusions 1. The numerical investigation of profiles of functions of the physical constraints carried out in this work allows us to assume that problems of optimal design of shells of reinforced plastics, strengthened by an elastic filler, for purposes of stability (static and dynamic) under axial compression, in the given formulation, are problems of convex programming. This guarantees uniqueness of their solution and allows us to use gradient methods for a numerical realization.2. Optimal shells of a composite material have a smaller mass than equivalent shells of high-strength metal alloys. The gain in the expenditure of the material is ensured not only as a result of higher specific characteristics of the composite, but basically as a result of optimizing the reinforcement structure of the pack of orthotropic layers of the shell.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 879–885, September–October, 1977.