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.     

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。     

关于二次曲线的切线及奇异点的探讨

利用二次曲线的切线的定义,分别讨论过二次曲线上的一点的切线的求法及过二次曲线外的一点的切线的两种求法,并且得到了存在奇异点的二次曲线的具体类型.     

关于直接揭露本貭特征对于学生掌握几何基本概念的作用的問題

一、研究的任务和方法概念乃是一种反映对象和現象的一般的并且是本质的特征的思维形式。概念的形成是在人类历史发展过程中进行的,概念的掌握是掌握現成的、社会上形成的概念。所以概念的掌握就不需要通过概念形成时人类所走过的复杂的、漫长的道路。虽然如此,但是概念的掌握仍然是一种复杂的过程,它取决于过去的經驗、已有的知识、掌握过程中实现的活动(如教学活动、生活活动等)、掌握借以实現的智力过程的系统。概念的教学方法是多种多样的,主要可分为两种:一种是直接揭露本质特征的方法,另一种是間接揭露本质特征的方法(如变式、对比等)。在平面几何的概念的教学中应該采用直接揭露本质特征的方法还是采     

横看成岭侧成峰善于联想思路清——一类三角问题的解法分析

匈牙利数学家乔治·波利亚致力于解题的研究,为了回答"一个好的解法是如何想出来的"这个令人困惑的问题,他专门研究了解题的思维过程,并把研究所得写成<怎样解题>一书.在波利亚的解题表中,拟定计划是解题的关键环节,拟定计划的过程是在"过去的经验和已有的知识"基础上,探索解题思路的发现过程,是不断变换问题,把复杂的问题向简单的问题转化,陌生的问题向熟悉的问题转化,最终把待解决的问题化归为已解决的或易解决的问题的过程,其中善于联想又是转化的关键.下面通过一道习题的分析,体验这种联想转化的思维过程.     

大学校长为何很多是数学家

1 大学校长多是数学家 经常关注数学教育的人可能会发现一个有趣的现象：国内许多大学的校长（包括现任的、离任的，以及正职、副职），都是数学专业出身，一些还是大名鼎鼎的数学家．比如：老一代的，1890-1920年间出生的就有云南大学的熊庆来、重庆大学（安徽大学）的何鲁、中国科大的华罗庚、复旦大学的苏步青、四川大学的柯召、南开大学的吴大任、上海大学的钱伟长等；     

条件中位数的最近邻估计和它的Bootstrap统计量的渐近性质

本文讨论条件中位数的估计问题,证明了条件中位数的最近邻估计序列的渐近正态性。在讨论估计的误差的分布特性时,作者引用了Efron的Bootstrap方法。证明了在一定条件下,最近邻估计的误差的Bootstrap分布在渐近意义下是可用的。即估计量的误差的渐近分布与它的Bootstrsp统计量的渐近分布是相同的。     

斜三角形的面积向量式及其应用

文[1]介绍了余弦定理的向量式：以同一点为起点的任意两向量的数量积等于这个向量的模的平方和与这两个向量终点的连线段所表示的向量的模的平方的差的一半．如△ABC中，     

非定常的热传导-对流问题的非线性Galerkin混合元法(Ⅱ):向后一步的Euler全离散化格式

1．引言本文的工作主要是讨论非定常的热传导一对流问题的向后一步的Euler全离散化的非线性Galerkin混合元解的存在性及其误差估计．该工作是对山中的同一问题研究的第二部分．在第一部分［1］，我们已经讨论了此问题的半离散化的情形．由于所研究的目标都是非定常的热传导一对流问题，其背景是相同的，在此将不重复了，请参考［1］．本文的安排如下，52先回顾非定常的热传导一对流问题的混合元解的经典性质．53回顾半离散化的非线性Galerkin混合元解的性质，并导出后续讨论需要的一些关于时间导数的估计．54讨论向后一步的Euler全离散化…     

L-模糊正规子群之间的对应定理

群G的一个L-模糊正规子群A的陪集做成的群G／A与群G的一个商群是自然同构的。如果f：G→G’是群的满同态，则G’的L-模糊正规子群做成的群与G的在f的核上取定值的L-模糊正规子群做成的群之间存在一个保序的双射。     

Inspection and maintenance optimization methods

Three methods of the optimal planning of the inspection and maintenance of offshore structures are described. The models are based on respectively: the maximization of the effect of inspections, measured by the total importance value of the errors detected, subject to a given total economical budget; the minimization of the total costs of obtaining respectively: a given importance value of errors detected or given numbers of inspections of various types. Special selections of the importance values of structural elements give problems of the maximization of the reliability of the structural system, or the minimization of the economical consequences of failures, or the minimization of the sum of the costs of inspections and failure-consequences, subject to a given total failure probability of the system.Different failure types of elements and time schedules of inspections can be included in the model.An extension of the incremental method of Fox is applied, and an evaluation measure is given for the calculation of bounds of the optimal objective value, or given numbers of inspections are planned by application of continuous linear programming with integral solutions.     

The stability of the equilibrium of two-phase elastic solids

The distinctive features of the loss of stability of elastic solids which undergo phase transitions are investigated for the case of small deformations. The non-uniqueness of the solution of the boundary-value problem for the describing of the thermodynamic equilibrium of a two-phase body is caused by the non-linearity associated with the unknown interface. The solution can be chosen by comparing the potential energies of the body in the two-phase and single phase states and by analysing of the local stability of the two-phase states. A linearized boundary-value problem is formulated which describes infinitesimal small perturbations of an initial two-phase state which is in thermodynamic equilibrium. Analysis of the stability of the two-phase state reduces to an investigation of the bifurcation points and the behaviour of the small solutions of the system of integrodifferential equations in terms of functions describing the perturbations of the interface. The problem of the non-uniqueness and loss of stability of centrisymmetric equilibrium two-phase deformations is investigated as an example. A theorem concerning the number of centrisymmetric solutions is proved. The energy changes accompanying the formation and development of two-phase states and the stability of the solutions obtained are investigated. The concept of topological instability as a bifurcation is introduced, as a result of which the type of geometry of a solution of the boundary-value problem changes and surfaces of separation of the phases actually appear and disappear. Macrodiagrams of the deformational are constructed which demonstrate the effect of deformation softening in the path of a phase transition.     

播挪运算及其性质

在现有的播挪定义基础上,引入了对偶播挪的概念和任意论域子集族的内并、内交两种新运算,提出了十个定理.它们是：平凡播挪空间定理,最小播挪定理,播挪内运算封闭性定理,播挪任意交定理,播挪上确界定理,播挪运算分配性定理,播挪基判定定理,播挪基闭包定理,播挪基约简定理,播挪基内运算封闭性定理.这些定理对于播挪空间的研究具有一定的理论价值.     

中国科大数学系是怎样办学的

中国科学技术大学原副校长、数学系教授龚昇先生2011年1月10日不幸病逝.本刊编委会、编辑部于2011年1月第1期发表《沉痛悼念著名数学家龚？教授》一文,简短介绍了他的生平和学术成就.本期特转载他为《中国科学技术大学数学五十年》一书所作的序,以纪念这位杰出的数学家和数学教育家.本文标题为编者所加.1958年,经中共中央...     

Some qualitative effects in the exact solutions of the Lamé problem for large deformations

Qualitative effects in the solution of a number of radially symmetric and plane axisymmetric problems for bodies made of non-linearly elastic incompressible materials are analysed for large deformations. In the case of problems of the axisymmetric plane deformation of cylindrical bodies, the lack of uniqueness of the solution for a given follower load in the case of a Bartenev–Khazanovich material and the existence of a limiting load in the case of a Treloar (neo-Hookian) material have been studied in detail and the dependences of the limiting load on the ratio of the external and internal radii of a hollow cylinder in the undeformed state have been presented. A similar study has been carried out for constitutive relations of a special form that well describe the properties of rubber. For this material, the lack of uniqueness of the solution is revealed for fairly high loads. The axisymmetric problem of the plane stress state of a circular ring made of a Bartenev–Khazanovich material has been solved and a lack of uniqueness of the solution for a given follower load was discovered in the case when the dimensions of the ring are given in the undeformed state. Similar studies have been carried out for Chernykh and Treloar materials in the case of the problem of the radially symmetric deformation of a spherical shell. It was established that, in the case of a Chernykh material, the lack of uniqueness of the solution depends considerably on the constant characterizing the physical non-linearity. The limit case of the deformation of a spherical cavity in an infinitely extended body has been investigated. The effect of an unbounded increase in the boundary stresses is observed for finite external loads, that appears in the case of the problem of the plane axisymmetric deformation of a cylindrical cavity in an infinitely extended body made of a Bartenev–Khazanovich material and in the case of the problem of the radially symmetric deformation of an infinitely extended body made of a Chernykh material with a spherical cavity.     

Price and incomes policy: a ‘Sraffian’ perspective

A Sraffa-type model of price determination is proposed that will serve as a characterization of the consequences of some of the activities of a prices board that has been charged with attempting to control the rate of increase of the absolute level of commodity prices by controlling rates of increase of factor incomes (wages and profits). Specifically, the board chooses new elements for the diagonal matrix of rates of profit and for the vector of labor incomes of a set of (Sraffa-type) equations of production that have been cast into matrix form. The unknowns of these equations are the commodity prices, and with a new set of factor incomes, a new solution set of commodity prices will be generated. The problem of fulfilment of a strict positivity condition for the price solution and that of ensuring the viability of the input-output structure are examined. A possible solution to these problems derives from exclusive concentration by the board on the ‘basic’ (in Sraffa's sense) sector of the economy. A switch from attempting to control rates of increase of factor incomes to attempting to control, directly, the rate of increase in the absolute level of commodity prices is also considered.     

饱和粘土非线性渗流规律与径向固结

以多孔介质等效渗流概念得出粘土平均孔隙微尺度数量级范围在0.01 μm至0.1μm,与测试结果一致．实验结果表明饱和粘土微尺度孔隙渗流为非线性流．理论推导表明固液界面作用与渗透率平方根或孔隙半径成反比,固液界面相互作用是导致饱和粘土非线性渗流的重要原因．提出了精确描述饱和粘土微尺度孔隙非线性渗流基本规律的数学模型,其参数量纲明确,物理意义清楚．建立了饱和粘土非线性渗流新定律,统一描述了从较低到较高水力梯度全过程渗流曲线特征,达西定律是其特例．基于新定律,建立了饱和粘土非线性渗流定流量径向固结数学模型．以粘性边界层思想与稳态依序替换法及积分方程法,导出了粘土非线性渗流平均质量守恒方程及活动边界运动方程,给出了饱和粘土非线性渗流超孔隙水压力分布公式与平均固结度计算公式,获得了粘土层压力分布规律和平均固结度随时间变化规律．结果表明:饱和粘土非线性渗流使活动边界运动速度减小．研究结果为粘土地质工程与岩土工程应用提供了新的科学依据．达西渗流径向固结计算是新的非线性渗流固结计算的特例．     

On Discrete Limits of Sequences of Approximately Continuous Functions and tae-Continuous Functions

We show that the classes of all discrete limits of sequences of ap- proximately continuous functions, of all discrete limits of sequences of derivatives and of all discrete limits of sequences of Baire 1 functions are the same. We describe also the discrete limits of sequences of quasicontinuous functions, and of sequences of almost everywhere continuous functions, and we present anec- essary condition which must be satisfied by the discrete limits of sequences of T_ae -continuous functions.     

Contact interaction of cylindrical shells of different lengths

We solve a problem of determination of the contact rigidity of a structural joint of a steel thin-walled pipe under the action of internal pressure with a shroud made of a composite material using a special technology. A mathematical model of the contact interaction of the pipe and shroud modeled by cylindrical shells of different length was constructed using the classical Kirchhoff–Love theory of shells. We obtain an analytic solution of the contact problem under conditions of ideal contact of the elements of the structural joint by the conjugation method. A numerical analysis of the influence of geometric and physicomechanical characteristics of the shroud on the contact pressure and rigidity of the shrouded pipe is presented.     

Good lattice points,discrepancy, and numerical integration

Summary Methods based on Diophantine approximations lead to a simple and easy construction of rational vectors the multiple of which, reduced modulo 1, form finite sequences of points with certain properties of equipartition over the unit square. Given a function of bounded variation over this square, it is suggested that computing the average of its values at the points of such a sequence can be a practical method of numerical integration. Precise bounds for the error ore obtained. In the general case, these are of the order of the product of the reciprocal and of the logarithm of the number of points; in the case of a function satisfying stated conditions of regularity and periodicity, they are of the order of the logarithm of the number of points divided by an appropriately high power of this number. A slight sharpening of some well-known results on equipartiton is obtained incidentally. A part of this paper was read at a meeting of the Accademia Nazionale di Scienze Lettere e Arti in Modena on April 7th. 1965.