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。     

BOOK REVIEWS

Book reviewed in this article: Beloved Scientist , by David O. Woodbury. Physics , A Textbook for Colleges , by Oscar M. Stewart. Modern Physics , by Charles E. Dull. Experiments in Organic Chemistry , by E. Wertheim. Dynamical Analogies , by Harry F. Olson, E.E., Ph.D. A Peimer of Electronics , by Don P. Caverly. Applied Mechanics and Heat , by L. Raymond Smith. An Elementary Course in Qualitative Analysis , by William Lloyd Evans, Jesse Erwin Day, and Alfred Benjamin Garrett. Fundamentals of Machines , by John A. Clark. Fundamentals of Machines , by Charles E. Dull. Algebra (Mathematics for Technical Training ), by Paul L. Evans. Geometry with Military and Naval Applications , by Willis F. Kern and James R. Bland. Plane Trigonometry with Tables , by Paul L. Evans. Elementary Applied Electricity , by L. Raymond Smith. Fundamentals of Electricity , Based on Material Developed for the Teaching of Learners and Apprentices of the Carnegie -Illinois Steel Corporation . Rewritten to Conform to the Preinduction Training Course in Fundamentals of Electricity as Prepared by the War Department . Fundamental Jobs in Electricity , by Edgar C. Perry, A. M. and Harry V. Schafebook.     

Quasi-planar graphs have a linear number of edges

A graph is calledquasi-planar if it can be drawn in the plane so that no three of its edges are pairwise crossing. It is shown that the maximum number of edges of a quasi-planar graph withn vertices isO(n).Work on this paper by Pankaj K. Agarwal, Boris Aronov and Micha Sharir has been supported by a grant from the U.S.-Israeli Binational Science Foundation. Work on this paper by Pankaj K. Agarwal has also been supported by NSF Grant CCR-93-01259, by an Army Research Office MURI grant DAAH04-96-1-0013, by an NYI award, and by matching funds from Xerox Corporation. Work on this paper by Boris Aronov has also been supported by NSF Grant CCR-92-11541 and by a Sloan Research Fellowship. Work on this paper by János Pach, Richard Pollack, and Micha Sharir has been supported by NSF Grants CCR-91-22103 and CCR-94-24398. Work by János Pach was also supported by Grant OTKA-4269 and by a CUNY Research Award. Work by Richard Pollack was also supported by NSF Grants CCR-94-02640 and DMS-94-00293. Work by Micha Sharir was also supported by NSF Grant CCR-93-11127, by a Max-Planck Research Award, and by grants from the Israel Science Fund administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development. Part of the work on this paper was done during the participation of the first four authors in the Special Semester on Computational and Combinatorial Geometry organized by the Mathematical Research Institute of Tel Aviv University, Spring 1995.     

带干扰的Erlang(2)过程

本篇论文主要讨论带干扰的E rlang(2)过程,首先通过指数分布的可加性来推得生存概率所满足的积分微分方程,进而得到破产概率(由干扰引起和由索赔引起)所满足的积分微分方程,最后得到破产概率的拉氏变换所满足的方程.     

On Solvability of Lie Rings with an Automorphism of Finite Order

A new criterion for a Lie ring with a semisimple automorphism of finite order to be solvable is proved. It generalizes the effective version of Winter's criterion obtained earlier by Khukhro and Shumyatsky and by Bergen and Grzeszczuk in replacing the ideal generated by a certain set by the subring generated by this set. The proof is inspired by the original theorem of Kreknin on solvability of Lie rings with regular automorphisms of finite order and is conducted mostly in terms of Lie rings graded by a finite cyclic group.     

Symmetry Reductions of the Combined KdV—mKdV Equation

ＳｙｍｍｅｔｒｙＲｅｄｕｃｔｉｏｎｓｏｆｔｈｅＣｏｍｂｉｎｅｄＫｄＶ－ｍＫｄＶＥｑｕａｔｉｏｎＺｈａｎｇＪｉｅｆａｎｇ（张解放）；ＸｕＸｕｅｊｕｎ（许学军）；ＣｈｅｎｇＤｅｓｈｅｎｇ（程德声）（ＤｅｐａｒｔｍｅｎｔｏｆＰｈｙｓｉｃｓ，Ｚｈｅｊｉａｎｇ...     

Dynamic instability of a non-uniform beam modeled in a two-degree-of-freedom system

The behaviour of a non-uniform beam loaded by a parallel or tangential compressive force respectively is analyzed by exploiting a two-degree-of-freedom dynamic model. The same system has been analyzed previously by Lee and Reissner from a static point of view and by Neer and Baruch by a dynamic approach using a one-degree-of-freedom model. The previous analyses revealed only part of the phenomena by the present approach.Here, for the tangential force a classical flutter instability is obtained and for the parallel force only static instability is possible.     

An elementary approach to lower bounds in geometric discrepancy

For eachd≥2, it is possible to placen points ind-space so that, given any two-coloring of the points, a half-space exists within which one color outnumbers the other by as much ascn ^1/2−1/2d , for some constantc>0 depending ond. This result was proven in a slightly weaker form by Beck and the bound was later tightened by Alexander. It was recently shown to be asymptotically optimal by Matoušek. We present a proof of the lower bound, which is based on Alexander's technique but is technically simpler and more accessible. We present three variants of the proof, for three diffrent cases, to provide more intuitive insight into the “large-discrepancy” phenomenon. We also give geometric and probabilistic interpretations of the technique. Work by Bernard Chazelle has been supported in part by NSF Grant CCR-90-02352 and The Geometry Center, University of Minnesota, an STC funded by NSF, DOE, and Minnesota Technology, Inc. Work by Jiří Matoušek has been supported by Charles University Grant No. 351, by Czech Republic Grant GAČR 201/93/2167 and in part by DIMACS. Work by Micha Sharir has been supported by NSF Grant CCR-91-22103, by a Max-Planck Research Award, and by grants from the U.S.-Israeli Binational Science Foundation, the Fund for Basic Research administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development.     

Intrinsic regular submanifolds in Heisenberg groups are differentiable graphs

We characterize intrinsic regular submanifolds in the Heisenberg group as intrinsic differentiable graphs. G. Arena is supported by MIUR (Italy), by INDAM and by University of Trento. R. Serapioni is supported by MIUR (Italy), by GALA project of the Sixth Framework Programme of European Community and by University of Trento.     

A five facets frame for the design of heuristics

The author suggested to distinguish between the ‘engineering approach’ and the ‘mathematical approach’ in connection with the design of heuristics. Stainton and Papoulias extended the scope by suggesting the ‘relational approach’. Based upon this extension, a five facets frame is presented here which is suggested to precede and accompany the ‘technical’ design of the heuristic. The facets are: coverage by participation, experience by doing, abstraction by structuring, extension by comparison, exploration by creativity.     

Asymptotic expansions for Markov processes with lévy generators

This paper considers a deterministic flow inn-dimensional space, perturbed by a Markov jump process with small variance. Asymptotic expansions are obtained for certain functionals of Feynman—Kac type, in powers of a small parameter representing a noise intensity. The methods are analytical rather than probabilistic.The research of the first author was partly supported by AFOSR under Contract No. 91-0116-0, by ONR under Contract No. N0014-83-K-0542, and by the Institute for Mathematics and Its Applications with funds provided by the NSF and ONR. The second author's research was partly supported by NSF under Contract No. DMS-8702537, and by the Institute for Mathematics and Its Applications with funds provided by the NSF and ONR.