Evaluation of the pliability and rigidity of nonbalanced monoclinic composites

Conclusions As the result of a change in the deformation characteristics of the elementary layers, which is asymmetric with respect to the middle plane of the composite, and caused by imperfections of technical character, aging, the effect of temperature, moisture content, corrosive media, and other factors, the balancing of the laminated polymeric composites is disturbed. Formulas were obtained for determining all the pliability and rigidity matrix components of a nonbalanced monoclinic composite from known deformation characteristics, volume, and order of packing of the elementary layers.Institute of Wood Cellulose Chemistry, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1030–1035, November–December, 1976.     

A. N. Kolmogorov: Historian and philosopher of mathematics on the occasion of his 80th birthday

The contributions to the philosophy and history of mathematics of one of the most eminent contemporary mathematicians, A. N. Kolmogorov, are analyzed. Although these contributions are not numerous, they contain discussions of the gradual generalization of the subject of mathematics, a partition of the development of mathematics—in particular, of the theory of probability—into periods, and, also, an evaluation of the works of a number of great savants, such as Newton, Lobatchevsky, etc.     

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     

Personae at play. ‘Men of Mathematics’ in commentary

Mathematical writers, above all, Euclid, tend to present their theorems as decontextualized, abstract propositions, which has become the standard modus of textual presentation in theoretical mathematics. Mathematical commentators, however, provide their readers with personal names and historical facts in order to elucidate problems, provide contexts of discovery, or construct doxographies, among other things. Modern readers have used such information for the construction of histories of science. When we look at these passages, however, we see that personal names and information about mathematicians of the past can serve quite a range of different objectives, such as the strategic self-positioning of the commentator vis-à-vis the past or present of mathematics, the education of the reader, mathematical or moral, the construction of the history of the field, etc. Not only does the commentator present a persona of himself to the reader, he can also turn colleagues and predecessors into personae. This paper attempts to elucidate the practice, by offering four examples of such plays of and with personae, in Pappus, Eutocius, al-Nayrīzī, and Proclus.     

From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions

In this paper, the authors review origins, motivations, and generalizations of a series of inequalities involving finitely many exponential functions and sums. They establish three new inequalities involving finitely many exponential functions and sums by finding convexity of a function related to the generating function of the Bernoulli numbers. They also survey the history, backgrounds, generalizations, logarithmically complete monotonicity, and applications of a series of ratios of finitely many gamma functions, present complete monotonicity of a linear combination of finitely many trigamma functions, construct a new ratio of finitely many gamma functions, derive monotonicity, logarithmic convexity, concavity, complete monotonicity, and the Bernstein function property of the newly constructed ratio of finitely many gamma functions. Finally, they suggest two linear combinations of finitely many trigamma functions and two ratios of finitely many gamma functions to be investigated.     

The mechanism of fatigue failure of plastics

Based on the study of the kinetics of deformation or rigidity, of the rise in temperature, and of the fracture surfaces, the article describes the mechanism of failure of plastics. It as found that in a cyclically loaded solid there occur two processes: strengthening and loss of strength. The main factors affecting strengthening in fatigue were discovered. Among them are the structure of the material, the degree of crystallinity, the load level, conditions of deformation, etc. The kinetics of rigidity can yield the most accurate information providing an idea of the process of fatigue failure of plastics.Paper read at the 9th International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Kaunas Technological University, Lithuania. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 2, pp. 279–285, March–April, 1996.     

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     

单形的心距向量公式及其几何特征

给出了判断单形五"心"的一组向量形式的充要条件,并以单形ΣA={A0,A1,…,An}的重心为坐标起点,以此单形的n个顶点A0,A1,…,Ak-1,Ak+1,…,An(k=0,1,…,n)为终点的向量为基底,给出了单形中关于超球的心距向量公式,同时进一步研究了这些特征向量的有趣的几何性质.     

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.     

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.     

High-temperature rheology of SHS composite materials

Specific features of SHS materials as the objects of rheology are discussed, various types of viscosimetric flows and the choice of rheological variables are delineated, a technique of constructing isochoric rheological curves for porous bodies is illustrated, and their possible types are reported. Such factors as nonuniformity of the porosity distribution external friction, and nonisothermality of the process are considered. A compression rheometer intended for studying the compaction kinetics and rheological properties of the SHS materials is described.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Institute of Structural Macrokinetics, Russian Academy of Sciences, Moscow Region. Institute of Chemical Physics. Russian Academy of Sciences. Moscow Region. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 2, pp. 265–269, March–April, 1996.     

环的(k,l,m,n)一根

Brown和McCoy在文[1]中建立了(F,Ω)-群的根理论,并由此考察了环的BrownMcCoy-根及其它一些根,根据这一方法,Szsz在文[2]中引进了环的(k,l,m,n)-根,其中k,l,m,n是任意的非负整数,并证明了环的Brown-McCoy根与(1,1,1,1)-根,(1,1     

与多值随机微分方程相关马氏半群的无穷小生成元（英文）

当多值随机微分方程的扩散及漂移系数满足利普希兹连续性条件时,我们考虑其解的无穷小生成元问题.为了找出该无穷小生成元的核,我们研究了对应的多值椭圆方程及其粘性解.     

geometry of differential equations

This paper contains a survey of papers on the geometry of differential equations, which appeared no earlier than 1972, continuing the general survey (RZhMat, 1974, 11A800), and considers in more detail a special cycle of investigations of the geometry of systems of partial differential equations, distinguished by the presence of practical applications. Then we continue the survey of new results on the geometry of an ordinary differential equation of arbitrary order, started in (RZhMat, 1978, 1A645). There is constructed a general theory of invariants of equations, and classes of equations admitting a simplified coordinate representation are invariantly distinguished.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 12, pp. 127–164, 1981.     

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.     

岭回归估计的向量参数方法

本文提出岭回归估计的向量参数方法,选择均方误差函数的负梯度方向作为参数向量方向,根据均方误差与拟合误差的预期约束条件选择确定参数向量模长.文中获得了两个单调性结论,向量参数岭回归估计的均方误差是参数向量模长的单调减函数,而拟合误差是参数向量模长的单调增函数.基于两类误差的单调性结论,本文创建了关于两类误差的预期约束条件,预期条件约束下的向量参数岭回归方法有望成为兼备均方误差次优与拟合误差适度的双赢估计.文章最后是一个应用实例.