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Characterization of sign patterns that allow diagonalizability has been a long-standing open problem. In this article, necessary and sufficient conditions for a sign pattern to allow diagonalizability are obtained, in terms of allowing related properties. Some properties of normal sign patterns are considered. In particular, it is shown that normal sign patterns of order up to 3 allow diagonalizability. Two combinatorial necessary conditions for a sign pattern to allow diagonalizability are also presented. 相似文献
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V. M. Manuilov 《Mathematical Notes》1997,62(6):726-730
The classical Hilbert-Schmidt theorem can be extended to compact operators on HilbertA-modules overW
*-algebras of finite type; i.e., with minor restrictions, compact operators onH*
A
can be diagonalized overA. We show that ifB is a weakly denseC
*-subalgebra ofA with real rank zero and if some additional condition holds, then the natural extension fromH
B
toH*
A
⊃H
B
of a compact operator can be diagonalized so that the diagonal elements belong to the originalC
*-algebraB.
Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 865–870, December, 1997.
Translated by O. V. Sipacheva 相似文献
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刻画符号模式矩阵允许对角化一直是一个长期的开问题.在本文中,我们获得了一些符号模式矩阵允许对角化的充分和(或)必要条件.另外,我们还给出了从一个秩为${\rm mr}(A)$的实矩阵$B\in Q(A)$出发需要改变多少个元素能够获得一个秩为${\rm MR}(A)$的实矩阵$B''\in Q(A)$ 的一些结论.最后,我们还获得了一些用Frobenius标准形表示的符号模式矩阵的允许对角化的结论. 相似文献
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Friderik Klampfer 《Acta Analytica》2004,19(33):119-161
That we are morally responsible for what we do willingly and knowingly is a commonplace. That our moral responsibility extends as far as to cover at least the intended consequences of our voluntary actions and perhaps also the ones we did not intend, but could or did foresee, is equally beyond dispute. But what about omissions? Are we, or can we be, (equally) morally responsible for the harm that has occured because we did not prevent it, even though we could have done so? Say, for all the enormous suffering, caused daily by famine, deprivation and curable diseases in the Third World countries?Moral intuitions and practices that one could consult in this matter seem to leave us in the dark. We regularly ascribe responsibility to people for harms resulting from their negligence or failure to fulfill professional duties. On the other hand, we tend to think that unless there is some evidence of the causal contribution that agents made to a harmful event and/or state, it is not really fair to blame it on them. And finally, to complicate things even more, most of us deny that omissions could effect anything (any change) in the world and consequently regard them as causally impotent (as well as possibly harmless).Most of the proposed solutions to this perplexing issue simply take negative moral responsibility for granted and then either try to revise our ordinary notion of causation accordingly or, alternatively, weaken the conditions for holding someone morally responsible. In the paper I present and defend the relative merits of the third approach, one sceptical of the notion of moral responsibility for the ‘outcomes’ of omissions. I try to show that for some identifiable core notion of moral responsibility and paradigmatic cases of omissions, the prospects for a happy marriage are rather slim. 相似文献
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具有库存损耗且允许缺货的EOQ模型 总被引:2,自引:0,他引:2
提出了一种库存损耗量随时间和库存量变化,且允许缺货的EOQ模型,证明了该模型的平均总费用函数在给定条件下为凸函数,并讨论了模型的最优策略及近似解. 相似文献
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Stefan Weigert 《Czechoslovak Journal of Physics》2005,55(9):1183-1186
Given a non-Hermitian matrix M, the structure of its minimal polynomial encodes whether M is diagonalizable or not. This note explains how to determine the minimal polynomial of a matrix without going through its
characteristic polynomial. The approach is applied to a quantum mechanical particle moving in a square well under the influence of a piece-wise
constant PT-symmetric potential. Upon discretizing the configuration space, the system is described by a matrix of dimension three which
turns out not to be diagonalizable for a critical strength of the interaction. The systems develops a three-fold degenerate eigenvalue, and two of the three eigenfunctions disappear at this exceptional point, giving a difference between the algebraic and geometric multiplicity of the eigenvalue equal to two.
Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22,
2005. 相似文献
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We present three new algorithms for on‐line multiple string matching allowing errors. These are extensions of previous algorithms that search for a single pattern. The average running time achieved is in all cases linear in the text size for moderate error level, pattern length, and number of patterns. They adapt (with higher costs) to the other cases. However, the algorithms differ in speed and thresholds of usefulness. We theoretically analyze when each algorithm should be used, and show their performance experimentally. The only previous solution for this problem allows only one error. Our algorithms are the first to allow more errors, and are faster than previous work for a moderate number of patterns (e.g. less than 50–100 on English text, depending on the pattern length). © 2002 John Wiley & Sons, Inc. Random Struct. Alg., 20, 23–49, 2002 相似文献
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