一类复超球上的Riemann边值问题及其应用

本文将推广一维的 Riemann 边值问题(可参考路见可教授[2])提出复超球上的内外值函数的定义和 Riemann 边值问题,我们将先讨论内外值函数的性质,给出一类Riemmann 问题的解,最后给出一类复超球上一类奇异积分方程的解的具体形式:     

棱锥底面上一特殊点的一个有趣性质

近日，笔者在研究棱锥内切球球心的性质时，得到了一个由棱锥内切球球心带来的棱锥底面上的一特殊点的一个有趣性质．     

对两个猜想的否定及改进

文[1]对一道高考试题进行了推广和引申，并在文末时提出了以下两个猜想． 猜想1若几何体存在内切球，过内切球球心的任意戴面，将几何体分成两个几何体．若这两个几何体的体积分别为V1，V2表面积分别为S1，S2，截面面积为S，则V1/V2=S1-S/S2-S。     

关于超圆,超球等几何图形面,体积的计算

关于超圆、超球等几何图形面、体积的计算张正印（内蒙民族师院数学系０２８０４３）圆与球在理论研究与实际应用上都十分常见，它们的简单变形是椭圆与椭球．有关计算问题在数学分析【叩］中均已解决，本文将试用微积分的方法进一步解央圆与球的另外两种变形，即超圆与超...     

R~n中超球帽面积公式及其应用

n维超球帽在几何分析中扮演着重要的角色,为进一步研究其性质,本文给出了Rn中超球帽的面积公式,给出了它在计算Rn中超球扇和超球冠的体积公式中的应用.     

一类对偶平坦的球对称的芬斯勒度量

本文研究了对偶平坦的芬斯勒度量的构造问题.通过分析球对称的对偶平坦的芬斯勒度量的方程的解,我们构造了一类新的对偶平坦的芬斯勒度量,并得到了球对称的芬斯勒度量成为对偶平坦的充分必要条件.     

一类射影平坦的球对称的芬斯勒度量

本文研究了射影平坦芬斯勒度量的构造问题.通过分析射影平坦的球对称的芬斯勒度量的方程的解,构造了一类新的射影平坦的芬斯勒度量,并得到了射影平坦的球对称的芬斯勒度量的射影因子和旗曲率.     

利用多面体解多球相切问题

多球相切问题在各类竞赛中经常出现 ,但由于作图复杂 ,给分析解决问题带来困难 .如果能透过现象 ,抓住问题的本质 ,将其转化为多面体问题 ,常能顺利解决 ,请看以下几例 .例 1　 (2 0 0 2年“希望杯”试题 )将 3个半径为 1的球和一个半径为 2 -1的球叠为两层放在桌面上 ,上层只放一个较小的球 ,四个球两两相切 ,那么上层小球的最高点到桌面的距离是 (　　 ) .(Ａ) 3 2 + 63 　　 (Ｂ) 3 + 2 63(Ｃ) 2 + 2 63 　　 (Ｄ) 2 2 + 63分析　两球相外切时 ,球心连线通过切点 ,球心距等于两球半径之和 .不妨设下层三个大球球心分别为Ｏ1 、Ｏ2 、Ｏ3,…     

一些球对称射影平坦的Finsler度量的构造

研究刻画球对称Finsler度量的射影平坦性质的偏微分方程,通过对射影平坦Finsler度量PDE的研究,构造了两类球对称射影平坦Finsler度量,得到了一些球对称的射影平坦Finsler度量,并进一步给出这些Finsler度量的射影因子和旗曲率.     

关于一个单形不等式的简单证明

苏化明先生在文[1]建立如下与n维单形外接超球心有关的一个不等式。     

广义度量方程的改进及其应用(I)

众所周知, 度量方程作为距离几何的基本内容和工具之一,在几何约束求解中扮演着主要的角色.改进了杨定华关于$n$维欧氏空间中两个等数量有限基本元素构成集合的广义度量方程, 建立了更为一般意义的、应用方便的广义度量方程,作为其初步应用,导出了两个单形之间的一些有趣的矩阵恒等式关系.特别地,将其两边取行列式,可以简洁得到关于联系两个单形的几何恒等式.     

有关度量加的几个几何不等式

本文利用代数的方法建立了一个与距离几何中度量加单形的体积和外接超球半径有关的几何不等式,作为其应用,由此可以导出一系列重要的几何不等式.在文末还给出了“广义度量加”的概念,并提出若干猜想供进一步研究.     

Metric regularity of a positive order for generalized equations

This paper focuses on the metric regularity of a positive order for generalized equations. More concretely, we establish verifiable sufficient conditions for a generalized equation to achieve the metric regularity of a positive order at its a given solution. The provided conditions are expressed in terms of the Fréchet coderivative/or the Mordukhovich coderivative/or the Clarke one of the corresponding multifunction formulated the generalized equation. In addition, we show that such sufficient conditions turn out to be also necessary for the metric regularity of a positive order of the generalized equation in the case where the multifunction established the generalized equation is closed and convex.     

Metric nonlinear connections

For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection, we can find the whole family of metric nonlinear connections that can be associated with a system of SODE and a generalized Lagrange metric. For the particular case when the system of SODE and the metric structure are Lagrangian, we prove that the canonical nonlinear connection of the Lagrange space is the only nonlinear connection which is metric and compatible with the symplectic structure of the Lagrange space. For this particular case, the metric tensor determines the symmetric part of the canonical nonlinear connection, while the symplectic structure determines the skew-symmetric part of the nonlinear connection.     

非欧空间中的广义度量方程及其应用

本文改进了杨世国关于非欧空间中基本图形的度量方程,建立一个一般意义下的、应用更为方便的广义度量方程,作为其初步应用,导出了非欧空间中两个单形之间的一些有趣的几何关系．     

A generalization of the coupled integrable dispersionless equations

The paper investigates an extension of the coupled integrable dispersionless equations, which describe the current‐fed string within an external magnetic field. By using the relation among the coupled integrable dispersionless equations, the sine‐Gordon equation and the two‐dimensional Toda lattice equation, we propose a generalized coupled integrable dispersionless system. N‐soliton solutions to the generalized system are presented in the Casorati determinant form with arbitrary parameters. By choosing real or complex parameters in the Casorati determinant, the properties of one‐soliton and two‐soliton solutions are investigated. It is shown that we can obtain solutions in soliton profile and breather profile. Copyright © 2016 John Wiley & Sons, Ltd.     

有限组两个完全同向单形的广义加权度量加

利用广义Menger度量嵌入定理,推广了关于两组两个完全同向n维单形"广义度量加"的概念,提出了关于有限组两个完全同向n维单形的"广义加权度量加"的概念,并运用距离几何理论同矩阵不等式结合的方法,证明了几个涉及"广义加权度量加"的几何不等式,它们进一步推广了杨路和张景中关于Alexander猜想的结果,这些结论蕴含近期诸多文献的主要结果.     

Lipschitzian stability of fully parameterized generalized equations

This paper concerns the study of Lipschitzian stability of fully parameterized generalized equations in which both single-valued and set-valued functions depend on parameters. Various relationships between the Lipschitz-like and metric regularity properties of the solution mapping, the base mapping, or field mapping in the fully perturbed generalized equations are established by using the Dontchev–Hager Fixed Point Theorem. The implicit mapping theorem for metric regularity is also extended to fully parameterized generalized equations.     

构造辅助函数计算准Vandermonde行列式

通过构造线性方程组和一元高次方程,利用线性方程组的解与一元高次方程根与系数的关系推导出第一类准Vandermonde行列式的值.通过构造辅助函数计算一个特殊的第一类准Vandermonde行列式,并把这种方法推广于两类特殊第二类准Vandermonde行列式的计算.     

On Lipschitz Semicontinuity Properties of Variational Systems with Application to Parametric Optimization

In this paper, two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to parameterized generalized equations. In the consideration of the metric nature of such properties, some related sufficient conditions are established, which are expressed via nondegeneracy conditions on derivative-like objects appropriate for a metric space analysis. For certain classes of generalized equations in Asplund spaces, it is shown how such conditions can be formulated by using the Fréchet coderivative of the field and the derivative of the base. Applications to the stability analysis of parametric constrained optimization problems are proposed.