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1.
2.
This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent
uniformly [locally uniformly, strictly] convex norm if and only if there exists a continuous uniformly [locally uniformly,
strictly] convex function on some nonempty open convex subset of the space and presents some characterizations of super-reflexive
Banach spaces.
Supported by NSFC 相似文献
3.
Calculus has been witnessing fundamental changes in its curriculum, with an increased emphasis on visualization. This mode for representing mathematical concepts is gaining more strength due to the advances in computer technology and the development of dynamical mathematical software. This paper focuses on the understanding of the function and its derivative as viewed by students of a reformed Calculus 1 course offered in two experimental sections at the Lebanese American University in Beirut, Lebanon. Results have shown that the general approach adopted in the course proved to be unpopular for a great majority of the students, but rewarding for others. Interviews conducted with some students and a study of their performance on very specific exam questions reveal that for most students, the algebraic representation of a function still dominated their thinking; however, these students showed an almost complete understanding of the derivative, particularly the idea of the instantaneous rate of change and/or the slope of a curve at a given point. Furthermore, very few of these students referred to the mechanical methods for finding derivatives. 相似文献
4.
On the average complexity of 3D-Voronoi diagrams of random points on convex polytopes 总被引:1,自引:0,他引:1
It is well known that the complexity, i.e. the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as Θ(n2). It is also known that if the points are chosen Independently Identically Distributed uniformly from a 3-dimensional region such as a cube or sphere, then the expected complexity falls to O(n). In this paper we introduce the problem of analyzing what occurs if the points are chosen from a 2-dimensional region in 3-dimensional space. As an example, we examine the situation when the points are drawn from a Poisson distribution with rate n on the surface of a convex polytope. We prove that, in this case, the expected complexity of the resulting Voronoi diagram is O(n). 相似文献
5.
A locally convex space is said to be a Gateaux differentiability space (GDS)provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in D.This paper shows that the product of a GDS and a family of separable Frechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS. 相似文献
6.
关于Banach空间中凸泛函的广义次梯度不等式 总被引:2,自引:0,他引:2
本文在前人^[1,2]的基础之上,以凸泛函的次梯度不等式为工具,将Jensen不等式推广到Banach空间中的凸泛函,导出了Banach空间中的Bochner积分型的广义Jensen不等式,给出其在Banach空间概率论中某些应用,从而推广了文献[3—6]的工作. 相似文献
7.
Lahcne Mezrag 《Mathematische Nachrichten》2004,266(1):60-67
In [5], it is proved that a bounded linear operator u, from a Banach space Y into an Lp(S, ν) factors through Lp1 (S, ν) for some p1 > 1, if Y* is of finite cotype; (S, ν) is a probability space for p = 0, and any measure space for 0 < p < 1. In this paper, we generalize this result to uv, where u : Y → Lp(S, ν) and v : X → Y are linear operators such that v* is of finite Ka?in cotype. This result gives also a new proof of Grothendieck's theorem. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
Xu Tianzhou 《东北数学》1997,(1)
ModulesoverOperatorAlgebrasandItsModuleMapsXuTianzhou(许天周)(DepartmentofMathematics,NanjingUniersity,Nanjing,210093)AbstractLe... 相似文献
9.
Identification of nonlinear elliptic equations 总被引:1,自引:0,他引:1
An optimization theoretic approach and algorithm for the estimation of state-dependent coefficients in nonlinear elliptic equation is presented. It is based on a splitting method combined with convex analysis techniques. Convergence of the algorithm is established and numerical examples are included.The research of K. Kunisch was supported in part by a grant from the Bundesministerium für Wissenschaft und Forschung, Austria. 相似文献
10.
凸体的曲率映象与仿射表面积 总被引:4,自引:0,他引:4
本文研究了一些特殊凸体与其极体的曲率仿射表面积乘积的下界.对任意两个凸体,建立了它们的投影体的混合体积与其仿射表面积的一个不等式(见文[1-15]). 相似文献