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Marek Niezgoda 《Linear algebra and its applications》2007,420(1):163-174
In this paper, we extend a majorization result of Hwang and Pyo [LAA 332-334 (2001) pp. 15-21] from the ordinary majorization ordering to the class of group induced cone orderings induced by non-effective groups. The case of effective groups is also investigated. A particular attention is paid to positive operators. 相似文献
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David D. Yao 《Operations Research Letters》1985,3(6):313-317
The throughput function of a closed network of queues is shown to be Schur concave and arrangement increasing. As a consequence of these properties, loading and server-assignment policies can be compared based on the majorization and the arrangement orderings. Implications of the results are discussed. 相似文献
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D. D. Yao 《Annals of Operations Research》1987,9(1):531-543
Consider an open Jackson network of queues. Majorization and arrangement orderings are studied to order, respectively, various loading and server-assignment policies. It is shown that under these order relations, stochastic and likelihood ratio orderings can be established for the maximum and the minimum queue lengths and for the total number of jobs in the network. Stochastic majorization and stochastic orderings are also established, respectively, for the queue-length vector and the associated order-statistic vector. Implications of the results on loading and assignment decisions are discussed. 相似文献
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Marek Niezgoda 《Linear algebra and its applications》2012,436(3):579-594
We generalize some results on majorization in papers by Wu and Debnath [S. Wu, L. Debnath, Inequalities for convex sequences and their applications, Comput. Math. Appl. 54 (2007) 525–534] and Marshall et al. [A.W. Marshall, I. Olkin, F. Proschan, Monotonicity of ratios of means and other applications of majorization, in: O. Shisha (Ed.), Inequalities, Academic Press, New York, 1967, pp. 177–190]. We present sufficient conditions for some vector inequalities to hold in the case of cone orderings and group-induced cone orderings. The framework used is based on results for similarly separable vectors given in paper [M. Niezgoda, Bifractional inequalities and convex cones, Discrete Math. 306 (2006) 231–243]. 相似文献
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This paper shows that some characterizations of the harmonic majorization of the Martin function for domains having smooth
boundaries also hold for cones. 相似文献
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Marek Niezgoda 《Linear algebra and its applications》2011,434(8):1968-594
In this paper, some results established in [H.-N. Shi, Refinement and generalization of a class of inequalities for symmetric functions, Math. Practice Theory 29 (4) (1999) pp. 81-84] are extended from the classical majorization preordering to group-induced cone orderings. To this end the notion of relative concavity introduced in [C.P. Niculescu, F. Popovici, The extension of majorization inequalities within the framework of relative convexity, J. Inequal. Pure Appl. Math. 7 (1) (2005) (Article 27)] is used. In addition, some Ky Fan’s inequalities are discussed. 相似文献
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In this paper, we are concerned with mathematical programs which construct nonmajorizing vectors for several specific majorization applications. In particular, we develop a linear integer program and two integer goal programs which solve the assignment majorization problem. We also develop a quadratic program for solving majorization problems which arise in probability and statistics. In the appendix, we present a general goal-programming algorithm for these, as well as others, goal programs.The authors would like to thank Professor Y. Tong for introducing them to majorization and its applications. They would also like to thank Professors Y. Tong and D. Mesner for helpful discussions. 相似文献
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Leonard J. Schulman 《Positivity》2009,13(3):559-574
Muirhead’s majorization inequality was extended by Rado to the case of arbitrary permutation groups. We further generalize
this inequality to compact groups and their linear representations over the reals. We characterize saturation of the inequality,
and describe the saturation condition in detail for the case of actions on Hermitian operators.
Supported in part by the National Science Foundation and the Center for the Mathematics of Information. 相似文献
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This paper investigates some properties of Euclidean distance matrices (EDMs) with focus on their ordering structure. The ordering treated here is the group majorization ordering induced by the group of permutation matrices. By using this notion, we establish two monotonicity results for EDMs: (i) The radius of a spherical Euclidean distance matrix (spherical EDM) is increasing with respect to the group majorization ordering. (ii) The larger an EDM is in terms of the group majorization ordering, the more spread out its eigenvalues are. Minimal elements with respect to this ordering are also described. 相似文献
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Majorization is a basic concept in matrix theory that has found applications in numerous settings over the past century. Power majorization is a more specialized notion that has been studied in the theory of inequalities. On the other hand, the trumping relation has recently been considered in quantum information, specifically in entanglement theory. We explore the connections between trumping and power majorization. We prove an analogue of Rado’s theorem for power majorization and consider a number of examples. 相似文献
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In this article, by means of the theory of majorization, Adamovic's inequality is extended to the cases of the general elementary symmetric functions and its duals, and the refined and reversed forms are also given. As applications, some new inequalities for simplex are established. 相似文献
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In this paper, we study the stochastic comparisons of order statistics from generalized normal distributions. We obtain some sufficient conditions for ordering results based on parameter matrix and vector majorization comparisons. These conditions are necessary in some cases. 相似文献
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一类对称函数的Schur凸性及其应用 总被引:1,自引:0,他引:1
吴善和 《数学的实践与认识》2004,34(12):162-172
给出一类对称函数 Schur凸性的推广 ,运用该结果并结合控制不等式理论建立若干对称函数不等式及 n维欧氏空间 En中的单形不等式 ,所得结果是以往某些结果的推广或补充 . 相似文献
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DingHua Yang 《中国科学A辑(英文版)》2009,52(10):2287-2308
Using the axiomatic method,abstract concepts such as abstract mean, abstract convex function and abstract majorization are proposed. They are the generalizations of concepts of mean, convex function and majorization, respectively. Through the logical deduction, the fundamental theorems about abstract majorization inequalities are established as follows: for arbitrary abstract mean Σ and Σ , and abstract Σ → Σ strict convex function f(x) on the interval I, if xi, yi ∈ I (i = 1, 2, . . . , n) satisfy that (x1... 相似文献
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关于Gamma分布的秩序统计量的随机比较 总被引:2,自引:0,他引:2
对于独立不同分布的两个Gamma样本,当它们相同的形状参数大于或等于1时,最近Korwar(2002)证明了,当它们的尺度参数满足优化序时,样本的卷积就满足似然比序.本文我们证明了,当Gamma分布的形状参数小于1时,样本的对应秩序统计量之间存在一致的一般随机序;然而当形状参数大于1时,样本对应的极大值和极小值统计量有着相反的一般随机序。 相似文献
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Manabu Iwasa 《Journal of multivariate analysis》1996,59(2):249-271
A variety of convolution inequalities have been obtained since Anderson's theorem. ?In this paper, we extend a convolution theorem forG-monotone functions by weakening the symmetry condition ofG-monotone functions. Our inequalities are described in terms of several orderings obtained from a cone. It is noteworthy that the orderings detect differences in directions. A special case of the orderings induces a majorization-like relation on spheres. Applying our inequality, Bartholomew's conjectures, which concern directions yielding the maximum power and the minimum power of likelihood ratio tests for order-restricted alternatives, are partly settled. 相似文献