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11.
Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a finite union
of convex sets (i.e., the set, described by reverse-convex inequalities) are given. These characterizations provide ways of
verifying the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated
systems. The convex sets considered in this paper are the solution sets of an arbitrary number of convex inequalities, which
can be either weak or strict inequalities. Particular cases of dual characterizations of set containments have played key
roles in solving large scale knowledge-based data classification problems where they are used to describe the containments
as inequality constraints in optimization problems. The idea of evenly convex set (intersection of open half spaces), which
was introduced by W. Fenchel in 1952, is used to derive the dual conditions, characterizing the set containments. 相似文献
12.
Yuanqiu Huang 《Discrete Applied Mathematics》2007,155(3):405-409
A stable set of a graph is a vertex set in which any two vertices are not adjacent. It was proven in [A. Brandstädt, V.B. Le, T. Szymczak, The complexity of some problems related to graph 3-colorability, Discrete Appl. Math. 89 (1998) 59-73] that the following problem is NP-complete: Given a bipartite graph G, check whether G has a stable set S such thatG-Sis a tree. In this paper we prove the following problem is polynomially solvable: Given a graph G with maximum degree 3 and containing no vertices of degree 2, check whether G has a stable set S such thatG-Sis a tree. Thus we partly answer a question posed by the authors in the above paper. Moreover, we give some structural characterizations for a graph G with maximum degree 3 that has a stable set S such that G-S is a tree. 相似文献
13.
Marion SCHEEPERS 《数学学报(英文版)》2007,23(7):1153-1162
We show that a set of real numbers is a Sierpinski set if, and only if, it satisfies a selection property similar to the familiar Menger property. 相似文献
14.
Marco Dall'Aglio Theodore P. Hill 《Journal of Mathematical Analysis and Applications》2003,281(1):346-361
For fair-division or cake-cutting problems with value functions which are normalized positive measures (i.e., the values are probability measures) maximin-share and minimax-envy inequalities are derived for both continuous and discrete measures. The tools used include classical and recent basic convexity results, as well as ad hoc constructions. Examples are given to show that the envy-minimizing criterion is not Pareto optimal, even if the values are mutually absolutely continuous. In the discrete measure case, sufficient conditions are obtained to guarantee the existence of envy-free partitions. 相似文献
15.
单循环赛赛程安排的一个图论方法 总被引:2,自引:0,他引:2
唐保祥 《数学的实践与认识》2004,34(5):120-125
利用图论的边着色理论建立了一个赛程安排的数学模型 .首先建立 n支球队与完全图 Kn的 n个顶点间的一一对应 ,把球队 Ai和 Aj间的比赛关系抽象成 Kn的顶点 i和 j间的边 ( i,j) .然后分别构造出了图K2 m- 1和 K2 m的正常 2 m-1边着色 .从而给出了各球队每两场比赛间得到的休整时间最均等 ,休整的间隔场次数达到上限值 n2 的一个赛程安排方案 相似文献
16.
E. Hernández L. Rodríguez-Marín 《Journal of Optimization Theory and Applications》2007,134(1):119-134
In this paper, we study optimization problems where the objective function and the binding constraints are set-valued maps
and the solutions are defined by means of set-relations among all the images sets (Kuroiwa, D. in Takahashi, W., Tanaka, T.
(eds.) Nonlinear analysis and convex analysis, pp. 221–228, 1999). We introduce a new dual problem, establish some duality theorems and obtain a Lagrangian multiplier rule of nonlinear type
under convexity assumptions. A necessary condition and a sufficient condition for the existence of saddle points are given.
The authors thank the two referees for valuable comments and suggestions on early versions of the paper. The research of the
first author was partially supported by Ministerio de Educación y Ciencia (Spain) Project MTM2006-02629 and by Junta de Castilla
y León (Spain) Project VA027B06. 相似文献
17.
The generalized Mycielskians (also known as cones over graphs) are the natural generalization of the Mycielski graphs (which were first introduced by Mycielski in 1955). Given a graph G and any integer m?0, one can transform G into a new graph μm(G), the generalized Mycielskian of G. This paper investigates circular clique number, total domination number, open packing number, fractional open packing number, vertex cover number, determinant, spectrum, and biclique partition number of μm(G). 相似文献
18.
图的划分问题曾引起图论界的广泛关注,在文献[4]中讨论了k-单圈划分,本文进一步研究基于k-单圈划分的优化问题,即在一个赋权图中求一个最小权可k-单圈划分的支撑子图,以及对一个不存在k-单圈划分支撑子图的图,如何添最少的边使得它有k-单圈划分的支撑子图。 相似文献
19.
Lenglart不等式与特殊半鞅的收敛集 总被引:3,自引:1,他引:2
本文讨论局部鞅和特殊半鞅的收敛集。我们给出Lenglart不等式的一个推广形式,利用这一不等式对一些定理给出了简单证明,对一些结果作了改进和推广。 相似文献
20.
K. Popov-Pergal L. Cuckovic M. Rancic M. Pergal D. Djokovic 《Chemistry of Heterocyclic Compounds》2003,39(8):1090-1093
A series of methyl 2-(arylidene-2,4-dioxotetrahydrothiazol-3-yl)propionates were prepared. A study of the 3D structure was performed. The log P values are given for all the synthesized compounds. 相似文献