Universal algebras

A survey of the development of the theory of universal algebras in the years 1976–1988. Such basic directions of development of this theory as classes of universal algebras (varieties, quasivarieties, etc.), Mal'tsev conditions, congruences, sheaves, homomorphisms, subalgebras, products of algebras, clones of operations, completeness, systems of equations in algeberas, and connections with computer mathematics show up in it. Considerable attention is given to concrete classes of algebras (p-algebras, BCK-algebras, unary algebras, etc.).Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 27, pp. 45–124, 1989.     

基于DEA-博弈论模型的铁路电子车票实名制查验评价分析

将基于数据包络分析(DEA)模型和纳什讨价还价博弈论结合, 作为一种合作博弈方法, 对铁路电子车票实名制的查验进行了综合评价, 为准确评估铁路电子车票实名制查验的效率, 加强铁路客运服务水平提供决策判断。本文以20个不同等级的铁路车站为研究对象, 分人工和机器两大类, 选取身份证购票比例、通勤员工购票比例、临时身份证购票比例, 以及人工查验旅客数/小时/通道、机器查验的通过人数/闸机/小时、闸机人脸自动识别比例和延误比例等7个指标作为投入指标, 选取人、证、票三证合一的实名制查验比例作为产出指标, 基于数据包络分析(DEA)和纳什讨价还价博弈论结合的合作博弈模型, 从人工查验和机器查验两个角度对铁路电子车票实名制查验进行统一综合评价。案例结果表明, 铁路电子车票实名制查验效率呈现出人工查验和机器查验效率不均衡的态势; 车站人脸识别闸机的数量投入与所需闸机数量的不匹配是造成实名制查验效率下降的主要原因。根据评价结果, 从人工和机器查验两个角度提出了可行建议, 促进了铁路电子车票实名制查验效率的进一步提升。     

统计在生命科学中的实践与认识(Ⅵ) 临床试验(上)

本文回顾了临床试验发展的简史、随机临床试验的主要特征、临床试验实践中所面临的问题和困难，介绍了有关临床试验研究和应用的近展     

区域资源禀赋、成本约束与农业生产效率测度

农业是我国基础产业,是保障粮食安全和经济发展的根本。根据经济发展战略要求和区域资源禀赋,合理发展区域农业,提升农业对区域资源使用效率和区域资源产业配置效益,形成区域农业高效发展和资源最优配置,是区域经济发展战略的重要内容。在柯布道格拉斯生产函数的基础上,利用随机前沿技术效率测度、产业投入产出分析、偏离-份额分析,构建农业产业生产效率的测度模型,探索地区农业产出的技术效率、资源利用效率和使用效率,为农业生产和区域资源配置提供参考。结果表明,大部分区域农业产出与资源禀赋未形成最佳匹配,应在大力提高农业对区域内资本资源、政府服务资源和劳动力资源使用效率的同时,鼓励过剩的资源在产业间和区域间进行适度转移,从低使用效益产业转移到高使用效益产业,从低产出弹性区域转移到高产出弹性效益区域。     

In Defense of Logical Universalism: Taking Issue with Jean van Heijenoort

Van Heijenoort??s main contribution to history and philosophy of modern logic was his distinction between two basic views of logic, first, the absolutist, or universalist, view of the founding fathers, Frege, Peano, and Russell, which dominated the first, classical period of history of modern logic, and, second, the relativist, or model-theoretic, view, inherited from Boole, Schr?der, and L?wenheim, which has dominated the second, contemporary period of that history. In my paper, I present the man Jean van Heijenoort (Sect. 1); then I describe his way of arguing for the second view (Sect. 2); and finally I come down in favor of the first view (Sect. 3). There, I specify the version of universalism for which I am prepared to argue (Sect. 3, introduction). Choosing ZFC to play the part of universal, logical (in a nowadays forgotten sense) system, I show, through an example, how the usual model theory can be naturally given its proper place, from the universalist point of view, in the logical framework of ZFC; I outline another, not rival but complementary, semantics for admissible extensions of ZFC in the very same logical framework; I propose a way to get universalism out of the predicaments in which universalists themselves believed it to be (Sect. 3.1). Thus, if universalists of the classical period did not, in fact, construct these semantics, it was not that their universalism forbade them, in principle, to do so. The historical defeat of universalism was not technical in character. Neither was it philosophical. Indeed, it was hardly more than the victory of technicism over the very possibility of a philosophical dispute (Sect. 3.2).     

Quality rating of a metal matrix-diamondcomposite from its thermal conductivity and electric resistance

The efficiency of hot-pressed diamond-containing composite materials (DCM) for various tool applications is greatly affected by microdefects, namely, the residual porosity of the metal matrix, damaged diamond grains, and imperfect diamond-matrix interfaces. An instrumental evaluation of these microdefects, predetermining the quality of a tool equipped with DCM, is rather difficult due to the small size, the nonstandard shape, and the strong heterogeneity of specimens. Proposed here is an alternative, nondestructive technique of DCM quality rating, which includes the measurement of electric resistance and thermal conductivity of diamond-containing composites and processing the obtained data by the methods of composite mechanics. It exploits the fact that diamond, being a dielectric, possesses an extremely high thermal conductivity, which allows estimating the residual porosity of a sintered metal matrix from the ratio of specific electric resistances, one being measured and another predicted by a theory. These data, in turn, are utilized to predict the thermal conductivity ofDCMwith an imperfect matrix. Matching with experiments, after solving the inverse problem gives the thermal resistance of diamond-matrix interface, which, within the frame work of the given model, simulates the damage of both the diamond grains and their bonds with the matrix. Thus, the numerical rating of quality is given in terms of two dimensionless parameters. The first one, 0 < K < 1, reflects the quality of the sintered metal matrix, whereas the second one, 0 < R <1, is an aggregate measure of the integrity of diamond grains and the perfection degree of composite interfaces. The quite satisfactory agreement observed between the theory and experiment confirms the efficiency of the technique and the reliability of the data obtained. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 361–374, May–June, 2006.     

城市老旧居住小区交通环境评价指标与评价方法

定量的评判城市老旧居住小区整体交通环境质量并进而科学有效的提出老旧小区交通环境更新与改善措施,对城市老旧居住小区交通环境进行了调查,明确了老旧居住小区存在的突出交通问题,并提出了城市老旧居住小区交通环境评价的指标体系,包括行人跨路出行指数、无人行道路段长度占比、停车泊位供需比、路内非法停车占比、平均停车步行距离、泊位数量户数比、人均步行空间、无障碍通道、盲道设置比例、非机动车泊位供需比、地面停放车辆数小区面积比、外部穿行交通周转量小区面积比等。并给出了具体指标的计算方法与获得办法。以长沙市四个典型老旧居住小区为例,对评价方法进行了论证,并得到城市老旧居住小区存在的一般问题,包括人车混杂、人车交织现象严重,停车泊位短缺、车辆乱停乱放,交通设施、特别是弱势群体交通设施缺乏。给出的评价指标、评价方法与结论可为城市老旧小区改造更新,特别是其中很重要的交通环境更新提供决策依据。     

On free products in varieties of associative algebras

Varieties of associative algebras over a field of characteristic zero are considered. Belov recently proved that, in any variety of this kind, the Hilbert series of a relatively free algebra of finite rank is rational. At the same time, for three important varieties, namely, those of algebras with zero multiplication, of commutative algebras, and of all associative algebras, a stronger assertion holds: for these varieties, formulas that rationally express the Hilbert series of the free product algebra via the Hilbert series of the factors are well known. In the paper, a system of counterexamples is presented which shows that there is no formula of this kind in any other variety, even in the case of two factors one of which is a free algebra. However, if we restrict ourselves to the class of graded PI-algebras generated by their components of degree one, then there exist infinitely many varieties for each of which a similar formula is valid. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 693–702, May, 1999.     

Algebraic analysis of offsets to hypersurfaces

In this paper, we present a complete algebraic analysis of degeneration and existence of simple and special components of generalized offsets to irreducible hypersurfaces over algebraically closed fields of characteristic zero. More precisely, we analyze the degeneration situations when offseting, and we state that there exist, at most, a finite set of distances for which the offset of a hypersurface may degenerate. As a consequence of this analysis, an algorithmic method to determine such distances is derived. Furthermore, as an application of these results, a complete degeneration analysis of the generalized offset to the sphere is developed. In addition, we study the existence of simple and special components of the offset. In this context we prove that, in the case of classical offsets, there always exists at least one simple component and, in the case of generalized offsets, we prove that for almost every distance and for almost every isometry, all components of the offset are simple. Received November 9, 1998; in final form March 5, 1999 / Published online May 8, 2000     

Sturm comparison and separation theorems for linear,second order,self-adjoint,ordinary, differential equations and for first order systems

Sturm comparison and separation theorems, for first order linear combinations of solutions of linear, second order, self-adjoint, ordinary, differential equations, are obtained as consequences of Sturm comparison and separation theorems for linear combinations of components of solutions of linear, first order systems of ordinary, differential equations.     

一個多元函數的內插公式

本文介绍一个新型多元函数结构.它在一定条件下: 1)可根据一定的已知数值决定函数的其他近似值, 2)可作为构成经验公式的骨架.     

Convolution equations in multidimensional spaces

Author's abstract of a dissertation for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended on Nov. 10, 1977, at the session of the Specialized Council D 002.38.03 at the V. A. Steklov Mathematics Institute of the Academy of Sciences of the USSR. Official opponents: Corresponding Member of the Academy of Sciences of the USSR, Doctor of Physicomathematical Sciences, Professor A. G. Vitushkin; Corresponding Member of the Academy of Sciences of the USSR, Doctor of Physicomathematical Sciences, Professor V. K. Ivanov; Doctor of Physicomathematical Sciences, Professor Yu. F. Korobeinik.Translated from Matematicheskie Zametki, Vol. 25, No. 5, pp. 761–774, May, 1979.     

Instability of solitary waves in non-linear composite media

A problem on the dynamic instability of soliton solutions (solitary waves) of Hamilton's equations, describing plane waves in non-linear elastic composite media with or without anisotropy, is considered. In the anisotropic case, there are two two-parameter families of solitary waves: fast and slow and, when there is no anisotropy, there is one three-parameter family. A classification of the instability of solitary waves of the fast family in the anisotropic case and of representatives of families of solitary waves, the velocities of which lie outside of the range of stability when there is anisotropy and when there is no anisotropy, is given on the basis of a numerical solution of a Cauchy problem for the model equations. In this paper, the fundamental equations describing plane waves in non-linear, anisotropic, elastic composites are derived, the Hamilton form of the basic equations is presented, the symmetries in the anisotropic and isotropic cases are considered, the conserved quantities and the soliton solutions, that is, the solitary waves are presented, the nature of the instability of representatives of all three families is investigated, brief formulation of the results is presented and problems of the instability of the fast family in the anisotropic case and of representatives of the families, the velocities of which lie outside of the range of stability in the presence and absence of anisotropy (explosive instability), are discussed.     

BOOK REVIEWS

Book reviewed in this article: Textbook of Quantitative Inorganic Analysis, by I. M. Kolthoff, Ph.D., Professor of Analytical Chemistry, University of Minnesota, and E. B. Sandell, Ph.D., Assistant Professor of Analytical Chemistry, University of Minnesota. A Chemical-Technical Dictionary (German-English-French-Russian), by A. W. Mayer. (Translation under direction of B. N. Menschutkin and M. A. Bloch.) Preservice Course in Automotive Mechanics, by James V. Frost, Instructor in Automotive Trades, Brooklyn High School of Automotive Trades, Brooklyn, New York. Automotive Mechanics, in two volumes by Clarence G. Barger Elements of Food Biochemistry, by William H. Peterson, Ph.D., Professor of Biochemistry, University of Wisconsin, Madison, Wisconsin; John T. Skinner, Ph.D., Assistant Chemist, Kentucky Agricultural Experiment Station, Lexington, Kentucky; and Frank M. Strong, Ph.D., Associate Professor of Biochemistry, University of Wisconsin, Madison, Wisconsin. The Chemical Formulary. A Collection of Valuable, Timely, Practical Commercial Formulae and Recipes for Making Thousands of Products in Many Fields of Industry. Volume VI. Editor-in-Chief, H. Bennett. Air Navigation. Flight Preparation Series. Published under the Supervision of the Training Division, Bureau of Aeronautics, U. S. Navy, Part One, Introduction to Earth. Radio—I, Written to Conform to the Pre-induction Training Course in Fundamentals of Radio as Prepared by the War Department, by R. E. Williams, Manager, School Service, Westinghouse Electric and Manufacturing Company, Pittsburgh, Pennsylvania, and Charles A. Scarlott, Editor, Westinghouse Engineer. Minerals, Their Identification, Uses, and How to Collect Them, by Herbert S. Zim, and Elizabeth K. Cooper. Basic Radio Principles, by Maurice Grayle Suffern, Captain, Signal Corps, Army of the United States.     

Moduli of elasticity of crystal lattices of polyamides and crystallike elements of amorphous poly(amido acids)

From the displacement of meridional reflections on large angle x-ray diffractograms of fibers from polyimides PM, PFG, DFOFG and the corresponding poly(amido acids) during their elastic deformation along the axis, determinations were made of the elasticity moduli of crystalline lattices of polyamides and of the crystallike elements of amorphous poly(amido acids).Collaborator in the Structural-Chemical Laboratory of the Academy of Sciences of Hungary; participated in this study during probation in the Laboratory of Physical Chemistry of Polymers, Institute of High-Molecular-Weight Compounds, Academy of Sciences of the USSR, in 1971.Institute of High-Molecular-Weight Compounds, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, Vol. 6, pp. 1014–1020, November–December, 1972.     

Srinivasa Ramanujan (1887‐1920) A centennial tribute

This centennial tribute commemorates Ramanujan the man and Ramanujan the mathematician. A brief account of his remarkable mathematical contributions is presented to describe the great talent of Srinivasa Ramanujan. Considerable discussion is made of his new and important ideas, results and theorems in various subjects including definite integrals, hypergeometric series, Bernoulli and Euler numbers, the Riemann zeta function, distribution of prime numbers, theory of partitions and statistical mechanics, continued fractions, hypergeometric functions, Rogers‐Ramanujan identities, theory of representation of numbers as sums of squares, Ramanujan's τ‐function, q‐series, elliptic and modular functions.     

Numerical identification of properties of particle-reinforced composite materials

The paper deals with numerical identification of the average elastic properties of particle-reinforced composite materials. The finite element method for the determination of deformation energy of the characteristic volume element was used. In earlier analytical investigations, an approximation function of the averaged elastic properties of the composite was derived. An identification procedure allows the estimation of the unknown approximation parameters from numerical experiments. The obtained functions describe precisely the numerical data for any relationships between constituents of the material.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Institute of Computer Analysis of Structures, Riga Technical University, Riga PDP-1658, Latvia. Institute of Materials Science, Department of Materials Science, Martin-Luther-University Halle-Wittenberg, D-06099 Halle, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 383–390, May–June, 1998.     

Investigations of multidimensional,infinite-dimensional and limit theorems of the theory of probabilities

Author's abstract of a dissertation in competition for the scientific degree of Doctor of Physical-Mathematical Sciences. The dissertation was defended on May 30, 1968 at a meeting of the Scientific Council of the V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR. The official opponents were: V. S. Korolyuk, Corresponding Member, Academy of Sciences of the Ukrainian SSR, A. V. Skorokhod, Corresponding Member, Academy of Sciences of the Ukrainian SSR, and V. A. Statulyavichus, Doctor of Physical-Mathematical Sciences.Translated from Matematicheskie Zametki, Vol. 4, No. 5, pp. 611–619, November, 1968.