包含—受扭迴转轴的半空间的性质*

本文研究包含有一根部份嵌入的迴转轴的半空间的性质.不用知道一给定的嵌入的轴的扭转问题的精确解,这些性质能指出此半空间的位移或应力场的某些特点并且有时可以用来检查数值解.文中给出嵌入半空间的受扭的刚性圆柱的轴的表面上的正确的应力分布的检查的例子.     

平面图形的形心在旋转体体积计算中的应用

本文讨论平面图形绕平面内的直线旋转的旋转体体积与被旋转的平面图形的形心的关系.当被旋转的平面图形的内部与旋转轴没有交点时,得到了用被旋转的平面图形的面积以及被旋转的平面图形的形心到旋转轴的距离表示的旋转体体积公式.     

维数不同的相关量之间的微积分关系

维数不同的相关量之间的微积分关系王金贵（北京电力高等专科学校１０００４４）我们可能都留意过，圆的面积的导数等于圆的周长，即，球的体积的导数等于球的表面积，即．反过来，当然有圆的周长的积分等于圆的面积，即．球的表面积的积分等于球的体积，即．事实上，不仅...     

多元化与公司风险研究

文章研究了公司的系统风险、债务风险和经营风险与公司的多元化程度的相关性。本文的实证结果表明,公司的系统风险与公司的多元化程度是正相关的;公司的债务风险与公司的多元化程度是正相关的;公司的经营风险与公司的多元化程度是负相关的。随着公司多元化程度加深,公司的经营风险会变小,但是公司面临的宏观的资本市场的系统风险和企业自身的债务风险,会随着变大。     

方程a~x=loga~x的解

一个方程的解可以看作两个函数的图象的交点的横坐标。反过来,方程的解又可以反映两个函数之间的某种关系,即它们的图象相交的情况。因此,可以利用函数的性质对方程的解,特别是直接求解很困难的某些超越方程的解的情况作出定性的讨论。也可以利用方程的解对函数的图象间的交点个数作出定量的研究,本文主要通过对函数y=x~(1/x)和y=x~x的性质的分析,就方程a~x=x和a~x=loga~x等的解的情况进行讨论。     

赋权图的圆染色与区间染色

赋权图的区间染色的定义与赋权图的圆染色的定义非常类型,唯一的区别就是将Ｇ的顶点对应圆周上的孤换为Ｇ的顶点对应区间上的子区间,讨论了赋权的圆染色与区染色的关系。     

一个命题的中间点的渐近性

关于中值定理的中间点的渐近性的讨论已得到大量有趣的结果,对于某些经典命题的中间点的渐近性的讨论也是十分有趣的课题,本文给出了数学分析中的一个经典命题的中间点的一个渐近性的刻画.     

李群表示论和Schubert条件

本文将Grassmann流形上的Schubert子簇所满足的经典的Schubert条件推广到一般的复半单李群G的广义旗流形.利用复半单李群的表示理论,我们首先在李群的权空间上引入自然的Ehresman偏序.这一偏序可以导出李群的最高权表示的权系、Weyl群及其陪集空间上的Ehresman偏序.然后我们对一般的复表示定义了相应的射影空间,Grassmann流形和旗流形.这使得能够像经典的情形一样来分析广义旗流形的Schubert子簇满足的Schubert条件.在讨论中,我们还给出了李群G的Weyl群及其陪集空间中的Bruhat-Chevalley偏序的简单判别条件.我们的结果应用到例外群,给出了Fulton提出的关于例外群的Schubert分析的问题的部分回答.     

可引进群运算的两类平面图

在某些文献中,我们常常看到图论与代数的概念及方法的密切联系和交错应用。例如,不久前,Babai等人即考虑了有敏锐的边可迁置换群的有向图,得到了关于这种图的最大外度数的估计的一些定理。而Bertram则反过来借助于图论的概念及方法,给出了关于有限群的某些数值(如非交换群中两两可换的一组元素的最大个数,等等)的大小的估计。 本文也将讨论群与图之间的联系。我们将使某些平面图的顶点与某些置换群的元素相对应,使顶点的序列与群元素的乘积相对应,然后通过对群的性质的研究,发现相应的平面图的顶点度数的一些规律,并据此解决     

关于线性偏微分方程的Cauchy问题的唯一性

<正> Cauchy问题的唯一性是偏微分方程的基本问题之一.经典的Cauchy-Kowalewski定理断言,解析方程或方程组的解析解是唯一的.1901年,Holmgren证明了,线性的解析方程或方程组的光滑解的唯一性.在取消关于系数的解析性的假设这个方向上的第一个结果是由Carleman在1939年给出的,他证明了两个自变量的相应结果,其中假设方程的主部的系数是实的,以及特征根是单重的,因而特征根的虚部如果不恒为零则总不为零.     

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 .     

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)     

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.