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.     

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.     

三种类型汽车的能耗和使用成本的建模研究

本文对电动,传统,混合动力三种类型汽车的能耗和使用成本问题进行了建模、求解及分析．首先定义了电动汽车的能量利用率ηE。根据能量守恒将所有电量转换成汽油消耗量,而传统车型则直接反映到汽油的消耗上,混合动力汽车则综合电动汽车和传统汽车的能耗模型,从而统一能耗水平评价标准．这样,我们就得到了三种不同类型车的能耗模型再进行模型求解以此来分析比较三种类型车哪一种节能效果好．对电动汽车来说,使用成本主要包括驾驶维护成本、报废处理成本,而对传统汽车来说,使用成本主要包括驾驶维护成本、报废处理成本、环境成本和其他成本,混合动力汽车则结合二者使用成本．因此,根据不同车型使用成本类型建立相应的数学模型,按照建立的公式,可以得到电动汽车的使用成本LCC1、传统汽车的使用成本LCC2和混合动力汽车的使用成本LCC3,从而进行模型求解．     

Staggered solution of fluid-porous-media interaction using the method of local Lagrange multipliers

Surface interaction among non-overlapping bulk-fluid and porous-medium bodies occurs in different situations, e. g., the interaction of blood with a blood vessel wall, a body of water with an earth dam structure, or acoustic waves with acoustic panels used in soundproofing. These are multi-field phenomena, comprising various surface- and volume-coupling mechanisms that should be reflected in the corresponding mathematical models. These models, together with appropriate initial and boundary values, assemble a coupled problem, the solution of which reveals the behaviour of the system under external excitations. The solution is commonly done numerically, following a monolithic or a decoupled approach. Here, the focus is on the latter. To design an efficient decoupled scheme, different types of coupling within the problem are addressed. These are the volume coupling between the degrees of freedom (DOF) within each subdomain, and the surface coupling between the DOF on the common boundaries. In particular, the latter constrains the feasible space of the solution of the problem. In this regard, local Lagrange multipliers (LLM) are employed to reformulate the problem in an unconstrained form. Unlike other domain decomposition methods which are based on using global Lagrange multipliers, the LLM method yields a complete separation of the subdomains and, consequently, facilitates parallel solution of the sub-problems. Moreover, within the subdomains, the penalty method is used to decouple pressure from other DOF. This procedure, on the one hand, reduces the size of the problem that should be solved at the interface and, on the other hand, removes the burden of using mixed finite elements within the subsystems. In the next step, the stability behaviour of the resulting staggered approach is analysed, and the unconditional stability of the method is established. Finally, the method is employed to solve a benchmark example, and using the numerical results, the reliability of the outcomes of the stability analysis is investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Two-boundary problems for a Poisson process with exponentially distributed component

For a Poisson process with exponentially distributed negative component, we obtain integral transforms of the joint distribution of the time of the first exit from an interval and the value of the jump over the boundary at exit time and the joint distribution of the time of the first hit of the interval and the value of the process at this time. On the exponentially distributed time interval, we obtain distributions of the total sojourn time of the process in the interval, the joint distribution of the supremum, infimum, and value of the process, the joint distribution of the number of upward and downward crossings of the interval, and generators of the joint distribution of the number of hits of the interval and the number of jumps over the interval. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 7, pp. 922–953, July, 2006.     

Structural changes during torsion of polyethylene

X-ray structural studies on the changes in oriented polyethylene fibers during torsion at large and small angles showed that the crystallites undergo shear deformation, and the angle x between the axes of the macromolecules and the upper (lower) faces of the crystallites deviates appreciably from a right angle. As a result of torsion of the fibers, an axial texture of the fibrill is formed, inside which the crystallites are skewed, while the c axes of the crystallites are inclined to the texture axis. The nature of the more specific changes in the structure depends on the ratio between the temperatures of the preliminary orientational drawing of the samples, and the subsequent torsion.The V. I. Lenin Tadzhik State University, Dushanbe, Institute of Macromolecular Compounds, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 160–162, January–February, 1974.     

一维反应扩散方程中的行波波速及行波解

通过Painlev啨分析,详细研究了一类一维化学反应扩散方程中的行波解及波速。分别给出了当歼灭项的指数大于创造项的指数及创造项的指数大于歼灭项的指数时,这两种情形下的波速及行波解的显式表示。此外,还给出了一类常见激励介质中的波速及平面波解在薄的边界层内的公式。     

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.     

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).     

Multivariate Polynomials,Duality, and Structured Matrices

We first review the basic properties of the well known classes of Toeplitz, Hankel, Vandermonde, and other related structured matrices and reexamine their correlation to operations with univariate polynomials. Then we define some natural extensions of such classes of matrices based on their correlation to multivariate polynomials. We describe the correlation in terms of the associated operators of multiplication in the polynomial ring and its dual space, which allows us to generalize these structures to the multivariate case. Multivariate Toeplitz, Hankel, and Vandermonde matrices, Bezoutians, algebraic residues, and relations between them are studied. Finally, we show some applications of this study to rootfinding problems for a system of multivariate polynomial equations, where the dual space, algebraic residues, Bezoutians, and other structured matrices play an important role. The developed techniques enable us to obtain a better insight into the major problems of multivariate polynomial computations and to improve substantially the known techniques of the study of these problems. In particular, we simplify and/or generalize the known reduction of the multivariate polynomial systems to the matrix eigenproblem, the derivation of the Bézout and Bernshtein bounds on the number of the roots, and the construction of multiplication tables. From the algorithmic and computational complexity point, we yield acceleration by one order of magnitude of the known methods for some fundamental problems of solving multivariate polynomial systems of equations.     

基于模糊FNN-ELECTRE法的国有商业银行竞争力评价

随着金融业全方位开放,国有商业银行已成为国家经济命脉的核心,其竞争力强弱关系着国家经济的繁荣与衰退。本文基于模糊FNN-ELECTRE方法建立国有商业银行竞争力评价模型,以因素神经网络理论(FNN)与ELECTRE融合方法为基础,以现有商业银行竞争力评价指标为着眼,把国有商业银行竞争力的评价体系从现实竞争力和潜在竞争力两个因素抽取为一级指标,以规模、质量、业务结构、效率、成长性五个因素设为二级指标。从实证的角度对银行A、银行B、银行C、银行D、银行E五大国有银行进行分析验证,对其属性值进行和谐性与非和谐性检验得出,银行B竞争能力最强,银行E竞争能力最弱,五大国有银行均有改进空间。     

小麦蜡熟期茎杆抗倒伏数学模型的建立

以物理学力学理论为基础,在考虑小麦穗自重,风力大小、风力大小、方向及作用点的因素下,将茎杆状态分为无风情况下的静态过程和有风情况下的动态过程,分别建立小麦蜡熟期茎杆的静态和动态抗倒伏模型.提出合理假设,得到2008年和2011年数据中各品种的机械强度、茎杆鲜重和重心高度的计算公式,再结合已给的倒伏指数公式,计算得到各小麦品种的倒伏指数;接下来,通过斯皮尔曼相关系数分判断倒伏指数与外部特征因素的相关性大小;最后,在考虑穗自重,风力大小、方向及作用点,茎杆变形能的影响因素下,分别建立小麦抗倒伏静态模型和动态模型.其中静态模型以临界力为计算目标,动态模型同时考虑穗自重和风载因素,最终将静态模型和动态模型结合作为小麦抗倒伏模型.文章最后利用已知数据,计算得到抗倒伏模型各个参数,同时对动态模型进行仿真,得到在一定风速下茎杆摆动的运动轨迹.在此基础上,考虑到该模型为典型的非线性动力模型,利用相平面分析法发现存在明显混沌现象,并进一步找出可能导致混沌的相关特性参数.     

Electron diffraction investigation of the fracture surfaces of filled mixtures of SKS-85 butadiene-styrene copolymer

As the result of an electron microscope study of replicas from the fracture surface during the disintegration of samples of mixtures of SKS-85 butadiene-styrene copolymer with 20 vol.% DG-100 carbon black and chalk, in the temperature range from +60 to –60°C, it is shown that, in the region of vitrification of the copolymer and of the loss of the reinforcing effect of the carbon black, there is a sharp change in the character of the fracture micro-surface, and the particles of carbon black become the sites of additional fracture. In the region of the temperature transition of the copolymer, connected with the mobility of the phenyl groups in the same way as in the vitrification region, there is a sharp decrease in the number of particles of carbon black at the fracture surface, while the fracture surface of a mixture with chalk passes selectively along the contact boundary of a polymer with larger particles. The microstructure of the Wallner lines on the surface of a mixture with carbon black, at Tst, is made up of traces of secondary fracture, arising around the particles of carbon black.Moscow Institute of Technology for the Meat and Dairy Industry. M. V. Lomonosov Institute for the Technology of Fine Chemicals, Moscow. É. L. Ter-Gazaryan State Scientific-Research and Design Institute, Kirovakan. Translated from Mekhanika Polimerov, No. 3, pp. 437–444, May–June, 1970.     

The three-dimensional motion of optimalpyramidal bodies

The three-dimensional inertial motion of pyramidal bodies, optimal in their depth of penetration, formed from parts of planes tangential to a circular cone and having a base in the form of a rhombus or a star, consisting of four symmetrical cycles, is investigated using the numerical solution of the Cauchy problem of the complete system of equations of motion of a body. It is assumed that the force action of the medium on the body can be described within the framework of a local model, when the pressure on the body surface can be represented by a two-term formula, quadratic in the velocity, and the friction is constant. It is shown that the stability criterion, obtained previously for the rectilinear motion of a pyramidal body on the assumption that the perturbed motion of the body is planar, also enables one, in the case of an arbitrary specification of the small perturbations of the parameters leading to the tree-dimensional motion of the body, to determine the nature of development of these perturbations. It is shown that if the rectilinear motion of the body is stable, its perturbed three-dimensional motion can be represented in the form of the superposition of plane motions, and when investigating each of them, the analytical solution of the plane problem obtained earlier can be used.     

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.     

一类KdV-Burgers方程的奇摄动解与孤子解

讨论了一类具有大Reynolds数且弱频散性的KdV-Burgers方程, 在数学上表示为一类奇摄动KdV-Burgers方程.KdV-Burgers方程中含有的非线性项与频散项互补作用形成稳定向前传播的孤立子.通过数学分析, 描述了孤立子的传播途径和传播速度等物理量的发展变化规律.通过奇摄动展开方法, 构造了该问题的渐近解.首先,用Riemann-Earnshaw方法求得退化解, 得到了简单波, 该简单波波形中的任意一点与初始点都存在一个传播速度差, 这使得波在传播过程中波形不断畸变, 最终形成冲击波面, 即间断面, 在它的两侧质点的速度有一个跳跃, 且随时间不断变化;其次, 在退化解的间断曲面处做变量替换, 构造一种修正的行波变换, 得到了内解展开式的孤子解, 并证明了内外解的存在性与唯一性;最后,通过一致有界逆算子的存在性做了余项估计, 并得到渐近解的一致有效性.结果表明, KdV-Burgers方程在大Reynolds数且弱频散性的性质下,扰动集中在退化解的间断面附近,孤立子链接两侧质点,其传播途径不是时间与空间的线性形式,而是沿着退化解的间断面附近传播,形成稳定的波形.     

考虑双参照点和Choquet积分的新型研发机构绩效评估方法及应用

针对新型研发机构绩效评估值不确定、指标间存在关联、投资主体多元且有风险偏好、指标集权重未知等绩效问题,提出基于双参照点和Choquet积分的绩效评估方法。首先,结合新型研发机构的特点,构建绩效评估指标体系;其次,基于累积前景理论设计同行-期望双参照点;然后,构建指标间直接关联矩阵,依据K-可加模糊测度和平均边际贡献Banzhaf值优化求解指标集权重,代入Choquet积分方法和参照点权重公式计算各新型研发机构的综合绩效评估值,从而实现机构排序和问题分析。该方法考虑了新型研发机构的特点、数据不确定性、指标关联性、风险偏好性、权重未知性等因素,更加符合实际情况,案例验证了方法的有效性和实用性。     

Impressions of the early days of programming

The paper describes the author's experience of working with the Edsac, Cambridge, England, in 1951 and 1953. The author's background in astronomical calculations using hand methods and his plans for spending a year in Cambridge are first described. This is followed by impressions of the Mathematical Laboratory, Cambridge, its staff, the external characteristics of the Edsac, the library of subroutines, documentation for programmers, machine language, paper tape preparation equipment, and organization of the use of the Edsac. The second major part of the paper describes the steps leading to an Edsac-program for calculating the motion of a minor planet by step-by-step integration of the equations of motion, with special attention to the preparation and check of large amounts of input to the program.     

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.