球面空间单形的两个几何不等式（英文）

In this paper, by using the theory and method of distance geometry, we study the geometric inequality of a n-dimensional simplex in the spherical space and establish two geometric inequalities involving the edge-length and volume of one simplex and the volume,height and(n-1)-dimensional volume of the side of another simplex in the n-dimensional spherical space. They are the extensions of the results [10] in the n-dimensional Euclidean geometry to the n-dimensional spherical space.     

高维情形的Routh定理

本文研究了n维欧氏空间En中n维单形的体积有关问题.利用距离几何的理论与解析方法,建立了n维情形的Routh定理,作为其特例建立了n维情形的Ceva定理.     

A numerical solution of nonlinear Volterra-Fredholm integral equations

In this paper, a numerical procedure for solving a class ofnonlinear Volterra-Fredholm integral equations is presented. Themethod is based upon the globally defined sinc basis functions.Properties of the sinc procedure are utilized to reduce thecomputation of the nonlinear integral equations to some algebraicequations. Illustrative examples are included to demonstrate thevalidity and applicability of the method.     

A Class of Schur Convex Functions and Several Geometric Inequalities

Schur convexity, Schur geometrical convexity and Schur harmonic convex-ity of a class of symmetric functions are investigated. As consequences some known inequalities are generalized. In addition, a cl...     

关于单形一个对偶式的商榷与两个新的对偶式

讨论了n维欧氏空间E^n中n维单形不等式的对偶式．利用距离几何理论与解析方法，建立了n维单形两个不等式的对偶式，指出了最近所建立的单形Finsler-Hadwiger不等式的A维对偶式是错误的．     

n维特殊伸缩矩阵的构造与n维广义插值细分函数向量

本文构造了一种特殊的n维特殊伸缩矩阵,且定义了n维正交广义插值多小波.基于这种特殊的伸缩矩阵,讨论n维正交广义插值多小波的构造算法. 并且最后给出了算例.     

关于双曲空间中n维Pedoe不等式及应用

本文应用距离几何的理论与方法,研究了双曲空间中n维单形的几何不等式问题,建立了双曲空间中涉及两个单形棱长的n维Pedoe不等式和彭-常不等式,由此获得双曲空间n维单形的一些新的不等式.     

欧氏空间E~n中Euler不等式的加强推广(英文)

The relation between the circum-radius and the in-radius of an n-dimensional simplex in E~n is studied.Two new generalizations of Euler inequality for the n-dimensional simplex are established.Besides,we obtain some stronger generalizations of Euler inequality for the n-dimensional simplex than previously known results.     

多元FFT与FST的直接方法

一、多元变换矩阵与矩阵的张量积 矩阵的张量积(Kronecker乘积)是导出多元直接变换的主要工具,因此,这里首先列出张量积的定义及其简单性质. 定义.设A_n,B_m分别是n×n,m×m方阵,则A_n与B_m的张量积是一个(n·m)×(n·m)方阵:A_nB_m=[A_nb_(ij)],其中B_m=[b_(ij)].并记A~(k)=?.     

关于n维单形的两个轨迹定理

在n维欧氏空间En中,应用向量方法,给出了关于n维单形的两个优美的轨迹定理.     

A Lp Brunn-Minkowski Theory for Logarithmic Capacity

Potential Analysis - In the present paper, we first introduce the concepts of the Lp n-dimensional Logarithmic-Capacity measure and Lp mixed n-dimensional Logarithmic-Capacity and then prove some...     

模糊环境下的最优装载问题

将动态规划中的一维背包问题推广到了n维,并利用模糊数为工具,在模糊环境下给出了n维背包问题的最优解,最后通过实例说明该方法的简便、有效和实用性.     

关于高维单形的两个性质

应用度量几何理论与解析方法,研究了n维欧氏空间En中n维单形的性质,将三角形内心与中线两个性质推广到n维单形,获得n维单形内心与中位面的两个性质.     

(∈,∈∨q)-n维凸模糊集

利用n维模糊集截集理论和模糊点与n维模糊集的邻属关系,并利用n+1-值Lukasiewicz蕴涵,首先给出(α,β)-n维凸模糊集的定义,然后对(∈,∈)-n维凸模糊集和(∈,∈∨q)-n维凸模糊集这两种非常有意义的n维凸模糊集进行了讨论,最后得到了一些有意义的结果。这将为n维凸模糊分析理论研究打下基础。     

Generalization and sharpening of Safta's Conjeture in the n-dimensional space

In this paper, a generalization and an improvement of Safta's conjecture in the n-dimensional space are given.     

BANDED TOEPLITZ PRECONDITIONERS FOR TOEPLITZ MATRICES FROM SINC METHODS

We give general expressions, analyze algebraic properties and derive eigenvalue bounds for a sequence of Toeplitz matrices associated with the sinc discretizations of various orders of differential operators. We demonstrate that these Toeplitz matrices can be satisfactorily preconditioned by certain banded Toeplitz matrices through showing that the spectra of the preconditioned matrices are uniformly bounded. In particular, we also derive eigenvalue bounds for the banded Toeplitz preconditioners. These results are elementary in constructing high-quality structured preconditioners for the systems of linear equations arising from the sinc discretizations of ordinary and partial differential equations, and are useful in analyzing algebraic properties and deriving eigenvalue bounds for the corresponding preconditioned matrices. Numerical examples are given to show effectiveness of the banded Toeplitz preconditioners.     

涉及两个单形的几何不等式及应用

建立了涉及两个n维单形的几个不等式,推广了一些重要几何不等式.     

Rigidity and stability of submanifolds with entropy close to one

Geometriae Dedicata - We show that an n-dimensional surface whose entropy is close to that of an n-dimensional plane is close in Hausdorff distance to some n-dimensional plane at every scale....     

有限点集的m级连心线及其性质(英文)

In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formula in finite points set. As its application,we extend the Leibniz formula and length of medians formula in n-dimensional simplex to polytope.     

关于可三角剖分的紧致流形的模2示嵌类

<正> 引言 关于复合形或更一般的空間在欧氏空間中的实現問題,Whitney和Thom分別有下面的結果: 定理.(Whitney)n維紧致微分流形M~n可微分实現于R~N中的必要条件为 W~k(M~n)=0,k≥N-n.(1) 定理.(Thom)一个有可数基而局部可縮的紧致Hausdorff空間X可以拓扑实現