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981.
982.
J. -P. Penot 《Journal of Optimization Theory and Applications》1993,79(3):551-561
The stability of the image of a moving convex set by a multifunction is considered. This study completes the persistence results obtained in Part 1 of this paper (Ref. 1). The results can be applied to epigraphs, hence to the convergence of convex functions. 相似文献
983.
984.
This paper investigates the closedness and convexity of the range sets of the variational inequality (VI) problem defined by an affine mappingM and a nonempty closed convex setK. It is proved that the range set is closed ifK is the union of a polyhedron and a compact convex set. Counterexamples are given such that the range set is not closed even ifK is a simple geometrical figure such as a circular cone or a circular cylinder in a three-dimensional space. Several sufficient conditions for closedness and convexity of the range set are presented. Characterization for the convex hull of the range set is established in the case whereK is a cone, while characterization for the closure of the convex hull of the range set is established in general. Finally, some applications to stability of VI problems are derived.This work was supported by the Australian Research Council.We are grateful to Professors M. Seetharama Gowda, Olvi Mangasarian, Jong-Shi Pang, and Steve Robinson for references. We are thankful to Professor Jim Burke for discussions on Theorem 2.1 and Counterexample 3.5. 相似文献
985.
As is well known, the stability of a dynamical system in two dimensions may be demonstrated in a very intuitive fashion from the existence of a suitable positive-definite Liapunov function, providing the contours of this function in a neighborhood of the stable point are Jordan curves. It is shown that the Liapunov function will certainly have this property if the stable point is an isolated stationary point in the sense of the Clarke calculus, but a counterexample is given if this assumption is weakened to the stable point being an isolated local extremum.This work was carried out with the support of the Natural Sciences and Engineering Council of Canada, which is gratefully acknowledged. 相似文献
986.
Giuseppe Mingione 《Journal of Global Optimization》2008,40(1-3):209-223
I will report on some recent developments concerning the problem of estimating the Hausdorff dimension of the singular sets
of solutions to elliptic and variational problems. Emphasis will be given on some open issues. Connections with measure data
problems will be outlined. 相似文献
987.
雷达船目标的模糊智能识别 总被引:2,自引:0,他引:2
模糊集理论和技术给复杂的模糊背景下的模式识别问题提供了一种简易有效的处理手段。基于模糊集理论,定量地分析和处理识别过程中的各种不确定性信息,以提高识别系统的可靠性和智能度,便是我们研究舰船雷达目标识别系统中识别算法的一重要内容。本文通过舰船雷达目标识别这一典型的模糊模式识别问题,系统地论述了模糊模式识别系统的一般性框架、模糊特征抽取和隶属函数的建立、模糊特征选择和匹配分类、层次化模糊分类系统构造等一系列关键性问题。本文提出的各种方法具有通用性,已建立的识别系统在试验中具有良好的目标识别能力。 相似文献
988.
The aim of this paper is to establish both necessary and sufficient conditions for the existence of viable solutions of a higher-order differential inclusion. Higher-order tangent sets are introduced and studied to get such conditions. These tangent sets are analysed in the case of the viable set defined by equality or inequality constraints and viability conditions are rewritten in terms of these constraints. 相似文献
989.
Ignacio Garcia Ursula Molter Roberto Scotto 《Proceedings of the American Mathematical Society》2007,135(10):3151-3161
We estimate the packing measure of Cantor sets associated to non-increasing sequences through their decay. This result, dual to one obtained by Besicovitch and Taylor, allows us to characterize the dimension functions recently found by Cabrelli et al for these sets.
990.
This article extends a paper of Abraham and Bonnet which generalised the famous Hausdorff characterisation of the class of
scattered linear orders. They gave an inductively defined hierarchy that characterised the class of scattered posets which
do not have infinite incomparability antichains (i.e. have the FAC). We define a larger inductive hierarchy κℌ* which characterises the closure of the class of all κ-well-founded linear orders under inversions, lexicographic sums and FAC weakenings. This includes a broader class of “scattered”
posets that we call κ-scattered. These posets cannot embed any order such that for every two subsets of size < κ, one being strictly less than the other, there is an element in between. If a linear order has this property and has size
κ it is unique and called ℚ(κ). Partial orders such that for every a < b the set {x: a < x < b} has size ≥ κ are called weakly κ-dense, and posets that do not have a weakly κ-dense subset are called strongly κ-scattered. We prove that κℌ* includes all strongly κ-scattered FAC posets and is included in the class of all FAC κ-scattered posets. For κ = ℵ0 the notions of scattered and strongly scattered coincide and our hierarchy is exactly aug(ℌ) from the Abraham-Bonnet theorem.
The authors warmly thank Uri Abraham for his many useful suggestions and comments. Mirna Džamonja thanks EPSRC for their support
on an EPSRC Advanced Fellowship. 相似文献