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(辶回)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．     

形式实模的核心

通过含单位元的交换环的实素理想构造出对应的模的实素子模,得到模的序存在的一个充要条件,并对模的所有序的支集的交集(文中称作"模的核心")作出一定的刻划,找到了判断模中的元素属于模的核心的充要条件.     

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     

几何学概论(三)

(四)罗氏几何的光辉照亮了科学前进的道路我们来分析他的学说的哲学意义.在罗氏的时代,哲学中占统治地位的思想是康德的"不可知论",按照这批人的说法,客观世界是存在的,但是不可知的,时间空间是人心的创造,是人心给经验安排的秩序,我们所确实知道的世界的规律性是人心按先天的原则所创造出来的,先天就是与经验无关的,这样,我们的空间观念就完全是人心的创造,     

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...     

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.     

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.     

两类带有确定潜伏期的SEIS传染病模型的分析

通过研究两类带有确定潜伏期的SEIS传染病模型,发现对种群的常数输入和指数输入会使疾病的传播过程产生本质的差异．对于带有常数输入的情形,找到了地方病平衡点存在及局部渐近稳定的阈值,证明了地方病平衡点存在时一定局部渐近稳定,并且疾病一致持续存在．对于带有指数输入的情形,发现地方病平衡点当潜伏期充分小时是局部渐近稳定的,当潜伏期充分大时是不稳定的．     

Chaotic synchronization with filter based on wavelet transformation

A kind of chaotic synchronization method is presented in the paper. In the transmitter, part signals are transformed by wavelet and the detail information is removed. In the receiver, the component with low frequency is reconstructed and discrete feedback is used, we show that synchronization of two identical structure chaotic systems is attained. The effect of feedback on chaotic synchronization is discussed. Using the synchronous method, the transmitting signal is transported in compressible way, system resource is saved, the component with high frequency is filtered and the effect of disturbance on synchronization is reduced. The synchronization method is illustrated by numerical simulation experiment.     

Backward bifurcation of an epidemic model with standard incidence rate and treatment rate

An epidemic model with standard incidence rate and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infectives on the disease spread. It is assumed that treatment rate is proportional to the numbers of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infectives. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.     

Banach空间有界线性算子强连续双半群

本文在Ｂａｎａｃｈ空间上研究单参数有界线性算子族－强连续双半群。     

Stability and bifurcation of an SIS epidemic model with treatment

An SIS epidemic model with a limited resource for treatment is introduced and analyzed. It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.     

Detection of multivariate outliers with location slippage or scale inflation in left orthogonally invariant or elliptically contoured distributions

This paper is concerned with two kinds of multiple outlier problems in multivariate regression. One is a multiple location-slippage problem and the other is a multiple scale-inflation problem. A multi-decision rule is proposed. Its optimality is shown for the first problem in a class of left orthogonally invariant distributions and is also shown for the second problem in a class of elliptically contoured distributions. Thus the decision rule is robust against departures from normality. Further the null robustness of the decision statistic which the rule is based on is pointed out in each problem.     

The Toroidal Embedding Arising From an Irrational Fan

A toroidal embedding is defined which does not assume the fan consists of rational cones. For a rational fan, the toroidal embedding is the usual toric variety. If the fan is not rational, the toroidal embedding is in general a quasi-compact noetherian locally ringed space which is not a scheme. A divisor theory exists and a class group is defined. A second construction is also carried out which mimics the gluing construction of the usual toric variety, but which makes no reference to a lattice. The resulting scheme is separated but infinite dimensional. The Picard group is described in terms of the group of real valued locally linear support functions on the fan and the Brauer group is shown to be trivial. Many examples are given throughout the paper; in particular, it is shown that there is associated to a real hyperplane arrangement of full rank a toroidal embedding.     

Traveling waves in a nonlocal dispersal population model with age-structure

This paper is concerned with the traveling waves in a single species population model which is derived by considering the nonlocal dispersal and age-structure. If the birth function is monotone, then the existence of traveling wavefront is reduced to the existence of a pair of super and subsolutions without the requirement of smoothness. It is proved that the traveling wavefront is strictly increasing and unique up to a translation. The asymptotic behavior of traveling wavefronts is also obtained. If the birth function is not monotone, the existence of traveling wave solution is affirmed by introducing two auxiliary nonlocal dispersal equations with quasi-monotonicity.     

Invariance and asymptotic stability

The stability of the zero solution of an autonomous non-linear system is considered. The problem of finding the variables in relation to which the solution is asymptotically stable if the Lyapunov function with a sign-definite derivative is known, is formulated and solved. The maximality of the set in relation to which the solution is asymptotically stable is established. The investigation is based on the method of auxiliary functions and clarifies the relation between the properties of invariance and the asymptotic stability of dynamical systems. The constructiveness of the results obtained is demonstrated by an example.     

On the oil-whipping of a rotor-bearing system by a continuum model

The nonlinear dynamic behavior of a rotor-bearing system is analyzed based on a continuum model. The finite element method is adopted in the analysis. Emphasis is placed on the so-called “oil-whip phenomena” which might lead to the failure of the rotor system. The dynamic response of the system in unbalanced conditions is approached by a direct integration method. It is found that a typical “oil-whip phenomenon” is successfully simulated, and the effect of the refinement of the finite element mesh is also checked. Furthermore, the bifurcation behavior of the oil-whip phenomenon that is of much concern in recent nonlinear dynamics research is analyzed. The rotor-bearing system is also examined by a simple discrete model. Significant differences are found between these two models. It is suggested that a careful examination should be made in modeling the nonlinear dynamic behavior of a rotor system.