周期排列抛物形系列沟槽引起的线性水波Bragg共振及共振相位上移北大核心CSCD

该文解析研究了有限个周期排列的抛物形沟槽激发的水波Bragg共振.首先,利用变量替换,先将系数为隐函数的修正缓坡方程(MMSE)转化为系数为显函数的显式方程.然后,构造了修正缓坡方程的Frobenius级数解,并给出了级数解的收敛条件.最后,利用质量守恒的耦合条件,建立了反射系数的解析公式.根据反射系数的解析公式,分析了沟槽个数、沟槽深度与宽度对Bragg共振峰值、共振相位和共振带宽的影响.当沟槽深度和宽度固定而沟槽个数增加时,共振峰值逐渐增大并趋向于1,而共振带宽则逐渐变窄并趋于固定值.当沟槽个数和宽度固定时,Bragg共振峰值随沟槽深度增加而增加.当沟槽个数和深度固定时,Bragg共振反射峰值随沟槽宽度增加而先增后减,预示了沟槽存在某个宽度使得共振峰值达到最大,为Bragg共振反射针对沟槽宽度的优化奠定了理论基础.特别地,前不久在有限个周期排列旋轮线形沟槽上刚刚观察到的Bragg共振反射峰值相位的上移现象,再次在该文考虑的抛物形沟槽上得到确认,表明针对有限周期排列的沟槽地形,Bragg共振反射峰值的相位上移是一个普遍现象.也因此说明,凡是正弦沙纹和周期人工沙坝所激发的Bragg共振反射,其主振相位将会下移,而凡是周期系列沟槽所激发的Bragg共振反射,无论沟槽形状如何,其主振相位都将上移.另外,我们从Bragg共振的原始定义出发,定量地解释了相位上移发生的数学机理.     

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.     

物体垂直出入水的非定常空泡数学模型

研究了物体从水下向水面高速运动产生的非定常垂直空泡,建立了出水垂直空泡的数学模型,得到了匀速、空泡压力不变条件下的空泡外形、长度、体积随水深变化的解析解,给出了出水通气空泡发展为超空泡的条件．利用类似的方法建立了水平空泡和入水空泡的数学模型,并对3种空泡进行了比较研究．比较研究的结论是,随物体距水面的水深减小,出水空泡体积自身有增大趋势,空泡不容易发生泄气现象．且要保持出水空泡压力不变,空泡内的气体含量就应该增加（可通过人工通气方式）．入水空泡正好相反,随物体入水深度增加,空泡体积自身有收缩的趋势,并挤压空泡内的气体从环境压力较低的空泡尾部喷射而出,导致空泡内的气体含量减少,空泡压力降低．但是当空泡压力低于环境压力后,空泡尾部又将被环境高压所封闭,气体喷射不出来．随着入水深度继续增加,空泡尾部将重复上述过程,形成周期性的喷射 封闭 喷射 封闭的脉动过程,这个脉动喷射过程将在空泡尾部的流体中形成一连串小气泡,并由于空泡内的压力波动而导致空泡形状发生波动现象．     

不确定性军事冲突模式预测的数学方法

本文在模糊集上研究了不确定性军事冲突态势的变化模式 ,即 Nash协商对策模式、协调模式、谈判偏好模式、谈判让步模式和战争模式 ;探讨了不同模式下对应的 Nash均衡域、协商域、偏好域、代价域和冲突域的数学意义 ,给出了不同模式下解确定的数学方法 ,从定量的角度实现了对军事冲突模式的判断和预测 .     

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)     

A non-equilibrium model of a porous medium saturated with immiscible fluids

A model of a thermoelastic porous medium, saturated with two immiscible fluids, is considered. It is assumed that there are no phase transitions, the contribution of pulsations to the stress and kinetic energy is small, and that the components of the medium are in thermodynamic equilibrium. The non-equilibrium of the state, related to the finite time of redistribution of the fluids among the pores of the channels due to the presence of surface forces, is taken into account. A general form of the governing relations, necessary and sufficient to satisfy the principles of thermodynamic compatibility and independence of the choice of system of coordinates, is obtained. It is shown that the establishment of equilibrium is accompanied by dissipation due to capillary forces, which does not lead to seepage dissipation or thermal dissipation. For the case when the deformation of the skeleton and the deviation of the mean porous pressure and the temperature from the initial values are small, while the saturation and the non-equilibrium parameter undergo finite changes, an approximation of the potential of the skeleton is proposed in the form of a quadratic expansion in small parameters. A feature of the expansion is the presence of an initial value of the potential, which depends on the saturation and non-equilibrium. The relationship between the thermodynamic potential and the non-equilibrium kinetics, related to the requirement that the dissipation by the capillary forces should be non-negative, is determined. A generalized Darcy's law is formulated, which takes cross terms into account. It is shown that the proposed approximations enable key effects, which accompany the motion of immiscible fluids in a porous medium, to be described.     

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.     

Historical origins of the nine-point conic. The contribution of Eugenio Beltrami

In this paper, we examine the evolution of a specific mathematical problem, i.e. the nine-point conic, a generalisation of the nine-point circle due to Steiner. We will follow this evolution from Steiner to the Neapolitan school (Trudi and Battaglini) and finally to the contribution of Beltrami that closed this journey, at least from a mathematical point of view (scholars of elementary geometry, in fact, will continue to resume the problem from the second half of the 19th to the beginning of the 20th century). We believe that such evolution may indicate the steady development of the mathematical methods from Euclidean metric to projective, and finally, with Beltrami, with the use of quadratic transformations. In this sense, the work of Beltrami appears similar to the recent (after the anticipations of Magnus and Steiner) results of Schiaparelli and Cremona. Moreover, Beltrami's methods are closely related to the study of birational transformations, which in the same period were becoming one of the main topics of algebraic geometry. Finally, our work emphasises the role played by the nine-point conic problem in the studies of young Beltrami who, under Cremona's guidance, was then developing his mathematical skills. To this end, we make considerable use of the unedited correspondence Beltrami – Cremona, preserved in the Istituto Mazziniano, Genoa.     

上市公司财务绩效的改进集成评价研究——以26家运输公司为例

为解决以往上市公司集成评价模型中各方法评价结果不一致问题,本文构建了改进集成评价模型。该模型先采用层次分析法、灰色关联度法、因子分析法进行评价,并运用KENDALL-W协和系数法对各评价结果进行事前一致性检验;通过检验后,再分别运用算术平均组合评价模型、Borda组合评价模型和Copeland组合评价模型进行组合评价。为了衡量组合评价与各评价方法的评价结果是否吻合,应用Spearman等级相关系数进行组合评价方法的事后检验,并根据Spearman等级相关系数的大小,选出最优的组合评价方法。最后,对中国26家上市运输公司财务绩效进行了集成评价的实证研究,并以算术平均组合评价模型的标准得分为聚类指标,采用欧氏距离法对26家上市运输公司进行聚类。结果显示:铁路、水路、公路运输各存在一个典型绩优企业,分别是:铁龙物流、北京传媒、海峡股份,四类上市运输公司中铁路上市公司财务绩效最优。     

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.     

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。     

西安产业转型水平测度及其结构效应分析

以西安市的产业转型升级作为研究对象,首先从转型升级的高度、速度和方向等三个方面进行定量测度,然后采用偏离一份额分析方法对经济增长的结构效应进行分析,结果表明:1995-2015年期间,西安市产业结构非均衡化发展趋势明显,产业转型升级的水平越来越高,三次产业结构得到明显优化.2008年以来,西安市产业结构调整明显,劳动力在三次产业内部再分配的速度较快.第一产业和第二产业均发展滞后,第三产业超前发展,建筑业、金融业和房地产业结构素质较好,其增长率均高于全省平均水平,呈现明显的超前发展趋势.工业、住宿和餐饮业的结构素质较差,竞争能力相对较弱.技术进步效应是西安劳动生产率提高的重要原因.     

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.     

Studying the longitudinal flow of polymers with periodic deformation

Conclusions 1. At low rates of elongation the state of a polymer melt depends neither on the strain nor on the strain rate. The frequency dependence of the components of the complex longitudinal modulus, measured by superposition of a periodic deformation on a steady longitudinal flow, resemble, at low elongation rates, the frequency characteristics of the components of the complex shear modulus.2. Relaxation processes due to steady longitudinal flow affect the components of the complex longitudinal modulus measured by periodic deformation.3. A melt of a polydisperse polymer under conditions of longitudinal flow begins, at some definite strain rate, to respond to periodic deformation as a rubber-like body and continues to do so as the amount of elongation increases, which is manifested by the trend of the frequency dependence of the modulus component E', this trend becoming similar to that for a solid body.4. As the strain increases during elongation, the upper boundary of the flow range, which is determined by the periodic deformation, shifts toward low frequencies.5. The viscoelasticity characteristics of a material subject to elongation can be accurately enough described by nonlinear equations with the aid of the linear shear-relaxation spectrum.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 507–513, May–June, 1978.     

区域经济发展策略的数学模型及实证分析

区域经济的发展受许多不同因素的影响,结合江苏省如皋市的社会经济发展的特点,选取总产值指标、农业指标、工业指标、固定资产指标和科技交通指标为经济指标,基于灰色关联度分析方法建立数学模型,对如皋市的区域经济发展进行了简要优势分析,并通过MATLAB程序设计进行仿真计算,构建地方经济发展的投资决策系统,研究如皋市区域经济的发展状况,以期能为区域经济发展政策提供参考依据,从而提升政府的理性投资决策能力,促进地方经济和社会的全面发展.