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.     

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.     

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。     

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,     

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     

映射与函数、指数函数

1　重、难点分析关于映射与函数的概念 ,重点是映射、函数的概念的理解与掌握 ,难点是对映射、函数概念 ,对函数符号 ｙ =ｆ(ｘ) ,以及对函数是一种特殊的映射的理解 ,对函数的定义域、值域的理解与掌握 .对于函数的单调性和奇偶性 ,重点是对函数的单调性、奇偶性的概念的理解 ,难点是对函数的单调性、奇偶性的判断与应用 .关于反函数 ,重点是反函数的概念的理解 ,难点是对求反函数的方法的掌握 .关于指数、指数函数 ,重点是分数指数幂的概念和分数指数幂的运算性质、指数函数的图象和性质的理解与掌握 ,难点是根式的概念和分数指数幂的概念…     

任意角的三角函数

1本单元重点、难点分析三角函数是中学数学的重要内容之一,也是高等数学的重要基础。本单元首先将角的概念进行推广,并引入弧度制的表示方式,再定义六种三角函数,然后探讨同角三角函数间的一些基本关系式及三角函数的诱导公式。角的概念的推广和角的度量单位的更新(引入弧度制)是本单元的第一个重点,它拓宽了三角函数的应用范围,简化了三角函数的研究,是进一步学习三角函数的基础,起到了承上启下的作用.任意角的三角函数的定义是进一步学习三角函数的根基,由此导出的三角函数的符号、同角三角函数间的基本关系式及三角函数的诱导公式是本单…     

微分差分方程解之稳定性

最近20—30年来在调节过程的研究中微分差分方程得到很多的应用.在调节理论和在很多其他具有时滞的过程的理论中所发生的基本问题中的一个问题是关于过程的稳定性的问题,一般化为关于微分差分方程解的稳定性的问题.这具问题吸引了非常多的工作者的注意(参考交末的目录),但据我们所知,这些零散的研究从未被有系统地综述过.这篇文章的目的是用简要的形式综述关于微分差分方程解的稳定性的工作的结果,也包括本文作者的若干研究在内.     

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.     

Limit theorems for path-functionals of regenerative processes

Regenerative processes were defined and investigated by Smith [12]. These processes have limiting distributions under very mild regularity conditions. In certain applications, such as shot-noise processes and some queueing problems, it is of interest to consider path-functionals of regenerative processes. We seek to extend the nice asymptotic properties of regenerative processes to path-functionals of regenerative processes. We show that these more general processes converge to a “steady-state” process in a certain weak sense. This is applied to show convergence of shot-noise processes. We also present a Blackwell theorem for path-functionals of regenerative processes.     

Large Deviation Probabilities for Square-Gaussian Stochastic Processes

We investigate properties of square-Gaussian stochastic processes. These processes are formed by quadratic forms of Gaussian processes or by limits in the mean square of quadratic forms of Gaussian processes. Special classes of these processes are determined and investigated. For processes from these classes estimates of large deviation probability are obtained. These estimates we use to estimate the probability that Gaussian vector-valued process leave some region on some interval of time. We construct asymptotic confidence regions for estimates of covariance functions of vector-valued Gaussian processes. Criterion of hypothesis testing on covariance functions of these processes is constructed.     

Sampling and reconstruction for shift-invariant stochastic processes

In this paper, combining stochastic processes with shift-invariant spaces, we introduce shift-invariant stochastic processes. It is a general case of the classical band-limited stochastic processes and a kind of non-band-limited stochastic processes. Two sampling theorems are obtained for the shift-invariant stochastic processes. The results for band-limited stochastic processes and shift-invariant spaces are generalized by our new results.     

Infinite Divisibility for Stochastic Processes and Time Change

General results concerning infinite divisibility, selfdecomposability, and the class L _m property as properties of stochastic processes are presented. A new concept called temporal selfdecomposability of stochastic processes is introduced. Lévy processes, additive processes, selfsimilar processes, and stationary processes of Ornstein–Uhlenbeck type are studied in relation to these concepts. Further, time change of stochastic processes is studied, where chronometers (stochastic processes that serve to change time) and base processes (processes to be time-changed) are independent but do not, in general, have independent increments. Conditions for inheritance of infinite divisibility and selfdecomposability under time change are given.     

Measuring deviations from stationarity

Various parameters for measuring the deviation from stationarity for processes belonging to two classes of nonstationarity processes are proposed. Several new results for the two types of processes are obtained. Points of contact are established with the class of oscillatory processes and with the Hamiltonian equation of motion in quantum mechanics. The relation to processes of normal type and to innovations stable processes is also discussed.     

Semi-Selfsimilar Processes

A notion of semi-selfsimilarity of R ^d -valued stochastic processes is introduced as a natural extension of the selfsimilarity. Several topics on semi-selfsimilar processes are studied: the existence of the exponent for semi-selfsimilar processes; characterization of semi-selfsimilar processes as scaling limits; relationship between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions, and examples; construction of semi-selfsimilar processes with stationary increments; and extension of the Lamperti transformation. Semi-stable processes where all joint distributions are multivariate semi-stable are also discussed in connection with semi-selfsimilar processes. A wide-sense semi-selfsimilarity is defined and shown to be reducible to semi-selfsimilarity.     

Stochastic order for alpha-permanental point processes

We establish relations of stochastic comparison among point processes elements of the set of alpha-permanental point processes. This set contains in particular, the determinantal point processes, the Poisson point processes and the permanental point processes. We show that these three classes of point processes can be ordered according to the increasing stochastic order. Elementary particles provide illustrations of some of the obtained relations of stochastic comparison.     

What is a multi-parameter renewal process?

The concept of the renewal property is extended to processes indexed by a multidimensional time parameter. The definition given includes not only partial sum processes, but also Poisson processes and many other point processes whose jump points are not totally ordered. A new version of the waiting time paradox is proven for multidimensional Poisson processes, and is shown to imply the renewal property. Finally, martingale properties of renewal processes are studied.     

THE STATIONARY DIFFUSION PROCESSES GENERATED BY SECOND ORDER DIFFERENTIAL OPERATIONS AND THEIR PROBABILITY CURRENTS

In this paper,we are concerned with the stationary Markov processes generated by second order differential operators under the local boundary conditions, It is proved that all those processes have constnt probability currents, known as circulations of the processes, and hence the processes are called single circulation processes. The invariant measures and the circulation values of those processes are calculated in all cases of boundary classification. It is shown that thr circulation value is an elementary characteristic of irreversible stationary Markov processes and that all the reversible Markov processes in the same problem are just the special ones of the single circulation processes whose circulation values are equal to zero and whose ergodic limits in the sense of weak convergence are not trivial.     

Ruin Probabilities in Cox Risk Models with Two Dependent Classes of Business

In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes.