Well-Posedness by Perturbations of Variational Problems

In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented.     

The Hahn–Banach Theorem for Partially Ordered Totally Convex, Positively Convex and Superconvex Modules

The Hahn–Banach Theorem for partially ordered totally convex modules [3] and a necessary and sufficient condition for the existence of an extension of a morphism from a submodule C ₀ of a partially ordered totally convex module C (with the ordered unit ball of the reals as codomain) to C, are proved. Moreover, the categories of partially ordered positively convex and superconvex modules are introduced and for both categories the Hahn–Banach Theorem is proved.     

线性分式规划最优解集的求法

本文使用多面集的表示定理，导出了线性分式规划最优解集的结构，并给出确定全部最优解的计算步骤。     

Stochastic signal analysis: Numerical representation and applications to system theory

Alternative procedures for representing a stochastic signal as a denumerable series with uncorrelated terms are developed. The study includes considerations about parametric rescaling and its repercussions on the orthogonal expansion, as well as numerical techniques for approaching such an expansion. In addition, applications to the Gaussian characterization of stochastic signals, filtering and stochastic modelling are treated.     

Orthogonal double covers by super‐extendable cycles

An Orthogonal Double Cover (ODC) of the complete graph K_n by an almost‐hamiltonian cycle is a decomposition of 2K_n into cycles of length n?1 such that the intersection of any two of them is exactly one edge. We introduce a new class of such decompositions. If n is a prime, the special structure of such a decomposition allows to expand it to an ODC of K_n+1 by an almost‐hamiltonian cycle. This yields the existence of an ODC of K_p+1 by an almost‐hamiltonian cycle for primes p of order 3 mod 4 and its eventual existence for arbitrary primes p. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 283–293, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10011     

Global and uniform convergence of subspace correction methods for some convex optimization problems

This paper gives some global and uniform convergence estimates for a class of subspace correction (based on space decomposition) iterative methods applied to some unconstrained convex optimization problems. Some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems.

     

基于旋转描述的三维几何造型方法

提出了一种能用凸四边形表示并可作平面展开的三维实体造型的设计方法。该方法用旋转描述表把二维平面展开图和三维实体联系起来，模拟人工折叠过程，由二维平面展开图逐次旋转变换完成三维造型重建。造型重建后，再通过纹理映射将平面设计图案映射到实体的各个面上，完成对实体着色渲染，生成具有真实感的三维实体。     

弱(L_1,L_2)-BLD映射的正则性

本文首先将文［１］中的ＢＬＤ映射推广为弱（Ｌ１，Ｌ２）－ＢＬＤ映射，并证明了如下正则性结果：存在两个可积指数 Ｐ１＝Ｐ１（ｎ，Ｌ１，Ｌ２）＜ｎ＜ｑ１＝ｑ１（ｎ，Ｌ１，Ｌ２），使得对任意弱（Ｌ１，Ｌ２）－ＢＬＤ映射ｆ∈（Ω，Ｒｎ），都有ｆ∈（Ω，Ｒｎ），即ｆ为（Ｌ１，Ｌ２）－ＢＬＤ映射．     

一致Banach空间中非扩张映象的弱收敛定理

设犈是一致凸Ｂａｎａｃｈ空间，满足Ｏｐｉａｌ条件或具有Ｆｒｅｃｈｅｔ可微范数，犆是犈的非空闭凸子集，且犜：犆→犆是非扩张映象．又设对任何初始数据狓１ ∈犆，序列｛狓狀｝由下列修改了的Ｉｓｈｉｋａｗａ迭代程序生成：狓狀＋１ ＝狋狀犜狀（狊狀犜狀狓狀＋ （１－狊狀）狓狀）＋ （１－狋狀）狓狀，　狀≥１， （Ｉ）其中，数列｛狋狀｝与｛狊狀｝满足下列条件（ｉ）和（ｉｉ）之一：（ｉ）狋狀∈ ［犪，犫］且狊狀∈ ［０，犫］；（ｉｉ）狋狀∈ ［犪，１］且狊狀∈ ［犪，犫］，这里，常数犪，犫满足０＜犪≤犫＜１．作者证明了，犜有不动点的充要条件是，｛狓狀｝ 弱收敛且｛‖狓狀－犜狓狀‖｝收敛到０．而且，由此即知，若犜有不动点，则｛狓狀｝弱收敛到犜的一个不动点．     

凸序列不等式的控制证明

利用控制不等式理论简洁地证明了一类凸序列不等式 (包括著名的 Nanson不等式的几个推广 ) ,并给出若干应用 .