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991.
Ádám Besenyei 《Linear algebra and its applications》2011,435(5):984-997
Some functions f:R+→R+ induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define a linear mapping on matrices (which is basic in the constructions of monotone metrics). The present subject is to check the complete positivity of in the case of a few concrete functions f. This problem has been motivated by applications in quantum information. 相似文献
992.
Aljoša Peperko 《Linear algebra and its applications》2011,435(4):902-907
Given a bounded set Ψ of n×n non-negative matrices, let ρ(Ψ) and μ(Ψ) denote the generalized spectral radius of Ψ and its max version, respectively. We show that
993.
For a pair of n×n Hermitian matrices H and K, a real ternary homogeneous polynomial defined by F(t,x,y)=det(tIn+xH+yK) is hyperbolic with respect to (1,0,0). The Fiedler conjecture (or Lax conjecture) is recently affirmed, namely, for any real ternary hyperbolic polynomial F(t,x,y), there exist real symmetric matrices S1 and S2 such that F(t,x,y)=det(tIn+xS1+yS2). In this paper, we give a constructive proof of the existence of symmetric matrices for the ternary forms associated with trigonometric polynomials. 相似文献
994.
Bounds for a multivariate extension of range over standard deviation based on the Mahalanobis distance 总被引:1,自引:0,他引:1
E.G. Gath 《Linear algebra and its applications》2011,435(6):1267-1276
The range over standard deviation of a set of univariate data points is given a natural multivariate extension through the Mahalanobis distance. The problem of finding extrema of this multivariate extension of “range over standard deviation” is investigated. The supremum (maximum) is found using Lagrangian methods and an interval is given for the infinimum. The independence of optimizing the Mahalanobis distance and the multivariate extension of range is demonstrated and connections are explored in several examples using an analogue of the “hat” matrix of linear regression. 相似文献
995.
The rank-k-numerical range of an n×n matrix A is defined as
996.
We consider the robust estimation of regression parameters in linear models with long memory and heavy-tailed errors. Asymptotic Bahadur-type representations of robust estimates are developed and their limiting distributions are obtained. It is shown that the limiting distributions are very different from those obtained under short memory. A simulation study is carried out to compare the performance of various asymptotic representations. 相似文献
997.
Classification of a screened data into one of two normal populations perturbed by a screening scheme
Hea-Jung Kim 《Journal of multivariate analysis》2011,102(10):1361-1373
In normal classification analysis, there may be cases where the population distributions are perturbed by a screening scheme. This paper considers a new classification method for screened data that is obtained from the perturbed normal distributions. Properties of each population distribution is considered and the best region for classifying the screened data is obtained. These developments yield yet another optimal rule for the classification. The rule is studied from several aspects such as a linear approximation, error rates, and estimation of the rule using the EM algorithm. Relationships among these aspects as well as investigation of the rule’s performance are also considered. The screened classification ideas are illustrated in detail using numerical examples. 相似文献
998.
M.R. Koushesh 《Topology and its Applications》2011,158(16):2191-2197
For a locally pseudocompact space X let
ζX=X∪clβX(βX\υX). 相似文献
999.
In Bani?, ?repnjak, Merhar and Milutinovi? (2010) [2] the authors proved that if a sequence of graphs of surjective upper semi-continuous set-valued functions fn:X→X2 converges to the graph of a continuous single-valued function f:X→X, then the sequence of corresponding inverse limits obtained from fn converges to the inverse limit obtained from f. In this paper a more general result is presented in which surjectivity of fn is not required. The result is also generalized to the case of inverse sequences with non-constant sequences of bonding maps. Finally, these new theorems are applied to inverse limits with tent maps. Among other applications, it is shown that the inverse limits appearing in the Ingram conjecture (with a point added) form an arc. 相似文献
1000.
E. Michael 《Topology and its Applications》2011,158(13):1526-1528
Principal result: Suppose Y is metrizable. Then: (a) if X is metrizable and A⊂X is closed, then every continuous g:A→Y extends to an l.s.c. ψ:X→K(Y); (b) Y satisfies (a) for all paracompact X if and only if Y is completely metrizable. 相似文献