共查询到19条相似文献,搜索用时 93 毫秒
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在实Schur分解的基础上,构造一新特征量表示正规矩阵特征值的虚部最大值,同时表示了所有实部. 相似文献
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给出二元Copula为弱Schur凹的充分必要条件.引入弱Schur几何凹的概念,讨论了一类Copula的弱Schur凹及其弱Schur几何凹.综合考虑了左边块对称与右边块对称,回答了王沁提出的几个问题,提出几个进一步讨论的问题. 相似文献
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本文用一种新方法研究两类对称函数的Schur凸性.首先,对x=(x1,...,xn)∈(-∞,1)n∪(1,+∞)n和r∈{1,2,...,n},讨论Guan(2007)定义的对称函数Fn(x,r)=Fn(x1,x2,...,xn;r)=∑1≤i1≤i2≤···≤ir≤n r∏j=1xij/(1-xij)的Schur凸性,其中i1,i2,...,in为正整数;推广褚玉明等人(2009)的主要结果,因而用新方法推广并解决Guan(2007)提出的一个公开问题.然后,对x=(x1,...,xn)∈(-∞,1)n∪(1,+∞)n和r∈{1,2,...,n},研究本文定义的对称函数Gn(x,r)=Gn(x1,x2,...,xn;r)=∑1≤i1≤i2≤···≤ir≤n(r∏j=1xij/(1-xij))1/r的Schur凸性、Schur乘性凸性和Schur调和凸性,其中i1,i2,...,in为正整数.作为应用,用Schur凸函数自变量的双射变换得到其他几类对称函数的Schur凸性,用控制理论建立一些不等式,特别地,由此给出Sharpiro不等式和Ky Fan不等式一个共同的推广,导出Safta猜想在高维空间的推广. 相似文献
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对x=(x_1,…,x_n)∈[0,1)~n∪(1,+∞o)~n,定义对称函数■其中r∈N,i_1,i_2,…,i_n为非负整数.研究了F_n(x,r)的Schur凸性、Schur乘性凸性和Schur调和凸性.作为应用,用控制理论建立了一些不等式,特别地,给出了高维空间的一些新的几何不等式. 相似文献
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讨论了两个初等对称函数的商的Schur调和凸性.作为应用,得到了两个新的分析不等式.最后提出了一个有研究价值的公开问题. 相似文献
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《数学的实践与认识》2013,(19)
利用Schur凸函数、Schur几何凸函数和Schur调和凸函数的有关性质简化证明了一类与对数凸函数有关的对称函数的Schur凸性、Schur几何凸性和Schur调和凸性. 相似文献
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Zhi‐Hua Zhang Hari M. Srivastava 《Mathematical Methods in the Applied Sciences》2019,42(18):6459-6474
This paper provides some characteristic properties of the weighted particular Schur polynomial mean of several variables. In addition, an elementary proof of an important inequality involving the weighted particular Schur polynomial mean is given. Various related results involving a family of the Schur polynomials, symmetric polynomials, and other associated polynomials, together with the potential for their applications, are also considered. 相似文献
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用Schur分拆证明一类含参数的不等式 总被引:2,自引:0,他引:2
利用对称多项式的Schur分拆方法,以及单变元多项式实根隔离算法,证明了一个不等式猜想.并将这一方法用于处理一类含有参数的有理对称不等式. 相似文献
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The double Schur function is a natural generalization of the factorial Schur function introduced by Biedenharn and Louck. It also arises as the symmetric double Schubert polynomial corresponding to a class of permutations called Grassmannian permutations introduced by A. Lascoux. We present a lattice path interpretation of the double Schur function based on a flagged determinantal definition, which readily leads to a tableau interpretation similar to the original tableau definition of the factorial Schur function. The main result of this paper is a combinatorial treatment of the flagged double Schur function in terms of the lattice path interpretations of divided difference operators. Finally, we find lattice path representations of formulas for the symplectic and orthogonal characters for sp(2n) and so(2n + 1) based on the tableau representations due to King and El-Shakaway, and Sundaram. Based on the lattice path interpretations, we obtain flagged determinantal formulas for these characters. 相似文献
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J. H. Brandts 《Numerical Linear Algebra with Applications》2002,9(3):249-261
In Matlab 6, there exists a command to generate a real Schur form, wheras another transforms a real Schur form into a complex one. There do not exist commands to prescribe the order in which the eigenvalues appear on the diagonal of the upper (quasi‐) triangular factor T. For the complex case, a routine is sketched in Golub and Van Loan (Matrix Computations (3rd edn). The John Hopkins University Press: Baltimore and London, 1996), that orders the diagonal of T according to their distance to a target value τ. In this technical note, we give a Matlab routine to sort real Schur forms in Matlab. It is based on a block‐swapping procedure by Bai and Demmel (Linear Algebra and Its Applications 1993; 186 : 73) We also describe how to compute a partial real Schur form (see Saad (Numerical methods for large eigenvalue problems. Manchester University Press: Manchester, 1992.)) in case the matrix A is very large. Sorting real Schur forms, both partially and completely, has important applications in the computation of real invariant subspaces. Copyright © 2002 by John Wiley & Sons, Ltd. 相似文献
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Schur convexity, Schur geometrical convexity and Schur harmonic convex-ity of a class of symmetric functions are investigated. As consequences some known inequalities are generalized. In addition, a cl... 相似文献
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Symmetric and Exterior Powers, Linear Source Modules and Representations of Schur Superalgebras 总被引:3,自引:0,他引:3
We study modules for the general linear group (over an infinitefield of arbitrary characteristic) which are direct summandsof tensor products of exterior powers and symmetric powers ofthe natural module. These modules, which we call listing modules,include the tilting modules and the injective modules for Schuralgebras. The modules are studied via their relationship tolinear source modules for symmetric groups on the one hand,and simple modules for Schur superalgebras on the other. Listingmodules are parametrized by certain pairs of partitions. Theyare used to describe, by generators and relations, the Grothendieckring of polynomial functors generated by the symmetric and exteriorpowers. We also (continuing work of J. Grabmeier) describe thevertices and sources of linear source modules for symmetricgroups. 2000 Mathematical Subject Classification: 20G05, 20C30. 相似文献
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In this article,we prove that the symmetric function F_n~*(x,r)=i_1+i_ 2_++i_n =r(x_1~(i~1)x_2~(i~2)... x_n~(i~n)1/r is Schur harmonic convex for x∈R~n_+and r∈N={1,2,3,...}.As its applications,some analytic inequalities are established. 相似文献
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Cristian Lenart 《Journal of Algebraic Combinatorics》2000,11(1):69-78
Macdonald defined an involution on symmetric functions by considering the Lagrange inverse of the generating function of the complete homogeneous symmetric functions. The main result we prove in this note is that the images of skew Schur functions under this involution are either Schur positive or Schur negative symmetric functions. The proof relies on the combinatorics of Lagrange inversion. We also present a q-analogue of this result, which is related to the q-Lagrange inversion formula of Andrews, Garsia, and Gessel, as well as the operator of Bergeron and Garsia. 相似文献
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CHU YuMing XIA WeiFeng & ZHAO TieHong Department of Mathematics Huzhou Teachers College Huzhou China Institut de Mathmatiques Universit Pierre et Marie Curie Paris F- France 《中国科学 数学(英文版)》2010,(2)
The Schur convexity and concavity of a class of symmetric functions are discussed, and an open problem proposed by Guan in Some properties of a class of symmetric functions is answered. As consequences, some inequalities are established by use of the theory of majorization. 相似文献