随机变量的差的分布函数的积分表达式

本文利用Lebesgue-Stieltjes积分，把连续型随机变量差的密度函数的积分表选式推广为一般随机变量的分布函数的积分表达式。     

(0,1)-矩阵的积和式的图表示及其相关性质

将(0，1)．矩阵的积和式的记数问题转化为它的伴随图或伴随有向图上相关元素的记数问题，能使复杂的计数问题变得相对直观化和简单化．本文给出了(0，1)-矩阵的积和式的图论表达式，并以该表达式为基础，主要解决了2．正则图类的邻接矩阵的最大积和式的记数问题以及它的反问题，即确定了零积和式临界图的极大边数及其图类．     

关于方程标准解的积分表示

构造方程标准解的积分表达式是人们关心的问题。到目前为止。只有R.M.Range等人用欧氏度量在单位球上。Stanton在强拟凸Siegal域■上给出了方程标准解的积分表达式。注意到欧氏度量在双全纯映照下是可变的。本文首先给出关于(0,q)形式的积分公式,然后构造出在全纯等价于球的光滑区域上方程标准解的积分表达式。并给出了相应的-Neumann算子。     

y＂十py＇＋qy＝f（x）通解的一种直接求法

对二阶常系数线性非齐次微分方程．本文给出了其通解的一种积分表达式，所用方法不同于常数交易法。     

随机变量的差的分布函数的积分表达式

本文利用Ｌｅｂｅｓｇｕｅ－Ｓｔｉｅｌｔｊｅｓ积分，把连续型随机变量差的密度函数的积分表达式推广为一般随机变量的分布函数的积分表达式     

亚纯多叶函数的子类

本文引进研究一类新的亚纯多叶函数，建立了包含关系，讨论了类中函数的积分表达式，并得到了类中函数准确的系数估计。     

论平面上的可求长曲线

本文利用Hausdorff分数型导数与积分理论给出平面上可求长曲线的积分表 达式.     

一类时滞偏微分方程的不变集和吸引性

讨论了一类时滞偏微分方程的Cauchy问题，利用该问题解的积分表达式和适当的分析技巧，得到了其不变集，吸引集和吸引盆一些新的充分条件．     

广义双正则函数向量的非线性边值问题

利用Schauder不动点定理和积分方程的方法，讨论了实Clifford分析中广义双正则函数向量的非线性边值问题解的存在性及其解的积分表达式。     

高阶原函数及其应用

给出高阶原函数的概念，借助分部积分法和数学归纳法对其进行研究，可利用积分表达式获得关于高阶原函数的统一表示，即连续函数f（x）的n阶原函数可以表为Fn（x）=1/n-1∫0^x t^n-1f（x-t）dt.根据此表示式能简捷地解决一些应用问题．     

A resource for introducing students to the integral concept

Many students do not have a deep understanding of the integral concept. This article defines what a deep understanding of the integral is in respect to integration involving one independent variable; briefly discusses factors which may inhibit such an understanding; and then describes the design of a mathematical resource for introducing students to the integral concept. The resource addresses a number of challenges when introducing the integral: (1) choosing an appropriate, intuitive context which gives meaning to the symbols in the integral expression; (2) aiding the transfer of the integral expression to different contexts via using the Riemann sum in an informal way so that students can see and interpret the rectangles which are inherent in this sum; and (3) the gradual formalizing of the Riemann sum and its linkage with the Fundamental Theorem of Calculus. The resource has been used over a number of years at this university amongst first-year undergraduate science and engineering students. Anecdotal evidence would suggest that the resource is beneficial.     

Levinson定理证明的一些简化

<正> (一)1974年,Levinson N.证明了他的关于Riemann ζ-函数在直线σ=1/2上的零点个数的著名定理:对充分大的T有     

Solution of the 2D ising model on a triangular lattice by the method of auxiliaryq-deformed Grassmann fields

A representation in the form of a functional integral is obtained for the partition function of the inhomogeneous 2D Ising model on a triangular lattice where the coupling parameters are arbitrary functions of coordinates. The method for transforming the partition function into an integral uses an auxiliary six-component Grassmann field in which the Grassmann fields corresponding to one of the components commute with the others. Thus, one pair of components realizes a representation of the q-deformed group SL_q(2, R) with q=–1 and the other two pairs correspond to the usual Grassmann spinors (q=1). An explicit expression in terms of the modified Pfaffian is found for the Gaussian integral over these fields and its relation to the ordinary Grassmann functional integral is established.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 441–463, December, 1996.     

三维体积计算中的等参变换法

利用散度定理将体积计算转化为闭曲面上的积分,对曲面进行三角形网格剖分.构造等参变换,建立任一空间三角形与标准三角形的1-1对应关系,推导出空间三角形上的曲面积分表达式.引入了简单四面体的有向体积概念,最后得多面体体积计算公式.     

On mean curvatures in submanifolds geometry

By using moving frame theory,first we introduce 2p-th mean curvatures and(2p 1)-th mean curvature vector fields for a submanifold.We then give an integral expression of them that characterizes them as mean values of symmetric functions of principle curvatures.Next we apply it to derive directly the celebrated Weyl-Gray tube formula in terms of integrals of the 2p-th mean curvatures and some Minkowski-type integral formulas.     

On a Multiple Stratonovich-type Integral for Some Gaussian Processes

We construct a multiple Stratonovich-type integral with respect to Gaussian processes with covariance function of bounded variation. This construction is based on the previous definition of the multiple Itô-type integral given by Huang and Cambanis [Ann. Propab. 6(4), 585–614] and on a Hu–Meyer formula (that is, an expression of the multiple Stratonovich integral as a sum of Itô-type integrals of inferior or equal order) for the elementary functions. We also apply our results to the fractional Brownian motion with Hurst parameter $H > \frac{1}{2}We construct a multiple Stratonovich-type integral with respect to Gaussian processes with covariance function of bounded variation. This construction is based on the previous definition of the multiple It?-type integral given by Huang and Cambanis [Ann. Propab. 6(4), 585–614] and on a Hu–Meyer formula (that is, an expression of the multiple Stratonovich integral as a sum of It?-type integrals of inferior or equal order) for the elementary functions. We also apply our results to the fractional Brownian motion with Hurst parameter .     

关于C~n中凸域上解析函数的积分表示

<正> 本文目的是建立C~n中凸域D={z|Φ(z)<0}上解析函数f(z)的一类积分表示     

Feynman principle for fermions with odd covariant symbol of the Hamiltonian

An expression is obtained for the Feynman path integral in the case of Fermi systems with covariant symbol of the Hamiltonian of arbitrary Grassmann parity.Leningrad State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 155–160, January, 1992.     

Existence of discontinuous solutions for simplest semidefinite problems of variational calculus

An existence theorem is proved for discontinuous solutions of a semidefinite quasiregular variational problem concerned with determining inf J [y], in which the expression under the integral sign is of a special form.Translated from Matematicheskie Zametki, Vol. 7, No. 1, pp. 69–78, January, 1970.     

A topological classification of integrable geodesic flows on the two-dimensional sphere with an additional integral quadratic in the momenta

Summary The analytic expression for a Riemannian metric on a 2-sphere, having integrable geodesic flow with an additional integral quadratic in momenta, is given in [Ko1]. We give the topological classification, up to topological equivalence of Liouville foliations, of all such metrics. The classification is computable, and the formula for calculating the complexity of the flow is straightforward. We prove Fomenko's conjecture that, from the point of view of complexity, the integrable geodesic flows with an additional integral linear or quadratic in momenta exhaust “almost all” integrable geodesic flows on the 2-dimensional sphere.