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141.
Charles R. Johnson 《Linear algebra and its applications》2008,429(4):875-886
There is remarkable and distinctive structure among Hermitian matrices, whose graph is a given tree T and that have an eigenvalue of multiplicity that is a maximum for T. Among such structure, we give several new results: (1) no vertex of T may be “neutral”; (2) neutral vertices may occur if the largest multiplicity is less than the maximum; (3) every Parter vertex has at least two downer branches; (4) removal of a Parter vertex changes the status of no other vertex; and (5) every set of Parter vertices forms a Parter set. Statements (3), (4) and (5) are also not generally true when the multiplicity is less than the maximum. Some of our results are used to give further insights into prior results, and both the review of necessary background and the development of new structural lemmas may be of independent interest. 相似文献
142.
Karl Gustafson 《Linear algebra and its applications》2009,430(10):2705-907
A brief account of the conceptual formulation of the two entities in this paper’s title, plus an initial preliminary investigation of some of their mathematical properties, is given. 相似文献
143.
C. M. Da Fonseca 《Annali di Matematica Pura ed Applicata》2008,187(2):251-261
A different approach is given to recent results due mainly to R. C. Johnson and A. Leal Duarte on the multiplicities of eigenvalues
of a Hermitian matrix whose graph is a tree. The techniques developed are based on some results of matching polynomials and
used a work by O. L. Heilmann and E. H. Lieb on an apparently unrelated topic.
相似文献
144.
Natalia Osipova 《Operations Research Letters》2008,36(3):372-376
We study the Processor Sharing queueing model with a hyper-exponential service time distribution and Poisson batch arrival process. In the case of the hyper-exponential service time distribution we find an analytical expression for the expected conditional response time function and obtain an alternative proof of its concavity with respect to the service time. 相似文献
145.
Sidney W. Graham 《Discrete Applied Mathematics》2008,156(16):3150-3154
We show that using character sum estimates due to H. Iwaniec leads to an improvement of recent results about the distribution and finding RSA moduli M=pl, where p and l are primes, with prescribed bit patterns. We are now able to specify about n bits instead of about n/2 bits as in the previous work. We also show that the same result of H. Iwaniec can be used to obtain an unconditional version of a combinatorial result of W. de Launey and D. Gordon that was originally derived under the Extended Riemann Hypothesis. 相似文献
146.
Let M(A) denote the comparison matrix of a square H-matrix A, that is, M(A) is an M-matrix. H-matrices such that their comparison matrices are nonsingular are well studied in the literature. In this paper, we study characterizations of H-matrices with either singular or nonsingular comparison matrices. The spectral radius of the Jacobi matrix of M(A) and the generalized diagonal dominance property are used in the characterizations. Finally, a classification of the set of general H-matrices is obtained. 相似文献
147.
We consider a class of graphs subject to certain restrictions, including the finiteness of diameters. Any surjective mapping φ:Γ→Γ′ between graphs from this class is shown to be an isomorphism provided that the following holds: Any two points of Γ are at a distance equal to the diameter of Γ if, and only if, their images are at a distance equal to the diameter of Γ′. This result is then applied to the graphs arising from the adjacency relations of spaces of rectangular matrices, spaces of Hermitian matrices, and Grassmann spaces (projective spaces of rectangular matrices). 相似文献
148.
L.Yu. Kolotilina 《Linear algebra and its applications》2008,429(10):2521-2539
The paper considers the sharpness problem for certain two-sided bounds for the Perron root of an irreducible nonnegative matrix. The results obtained are applied to prove the sharpness of the related eigenvalue inclusion sets in classes of matrices with fixed diagonal entries, bounded above deleted absolute row sums, and a partly specified irreducible sparsity pattern. 相似文献
149.
A. G. D’yakonov 《Computational Mathematics and Mathematical Physics》2008,48(5):866-876
It is shown that, in the pattern recognition problem with two nonoverlapping classes, the matrices of estimates of the object closeness are described by a metric. The transition to the algebraic closure of the model of recognizing operators of finite degree corresponds to the application of a special transformation of this metric. It is proved that the minimal degree correct algorithm can be found as a polynomial of a special form. A simple criterion for testing classification implementations is obtained. 相似文献
150.
Costa et al. (Oper. Res. Lett. 31:21–27, 2003) presented a quadratic O(min (Kn,n
2)) greedy algorithm to solve the integer multicut and multiflow problems in a rooted tree. (n is the number of nodes of the tree, and K is the number of commodities). Their algorithm is a special case of the greedy type algorithm of Kolen (Location problems
on trees and in the rectilinear plane. Ph.D. dissertation, 1982) to solve weighted covering and packing problems defined by general totally balanced (greedy) matrices. In this communication
we improve the complexity bound in Costa et al. (Oper. Res. Lett. 31:21–27, 2003) and show that in the case of the integer multicut and multiflow problems in a rooted tree the greedy algorithm of Kolen
can be implemented in subquadratic O(K+n+min (K,n)log n) time. The improvement is obtained by identifying additional properties of this model which lead to a subquadratic transformation
to greedy form and using more sophisticated data structures.
相似文献