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31.
Xiaochun Fang 《Proceedings of the American Mathematical Society》2006,134(10):3015-3024
Let be a unital -algebra, and let be a -dynamical system with abelian and discrete. In this paper, we introduce the continuous affine map from the trace state space of the crossed product to the -invariant trace state space of . If is of real rank zero and is connected, we have proved that is homeomorphic. Conversely, if is homeomorphic, we also get some properties and real rank zero characterization of . In particular, in that case, is of real rank zero if and only if each unitary element in with the form can be approximated by the unitary elements in with finite spectrum, where , , and if moreover is a unital inductive limit of the direct sums of non-elementary simple -algebras of real rank zero, then the above can be cancelled.
32.
33.
In this paper, a successive supersymmetric rank‐1 decomposition of a real higher‐order supersymmetric tensor is considered. To obtain such a decomposition, we design a greedy method based on iteratively computing the best supersymmetric rank‐1 approximation of the residual tensors. We further show that a supersymmetric canonical decomposition could be obtained when the method is applied to an orthogonally diagonalizable supersymmetric tensor, and in particular, when the order is 2, this method generates the eigenvalue decomposition for symmetric matrices. Details of the algorithm designed and the numerical results are reported in this paper. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
34.
We study finite rank semicommutators and commutators of Toeplitz operators on the Bergman space with quasihomogeneous symbols.
We show that in this context, the situation is different from the case of harmonic Toeplitz operators.
Submitted: July 23, 2007. Accepted: December 4, 2007. 相似文献
35.
In this paper, we study lower bounds on the size of a maximum independent set and a maximum matching in a hypergraph of rank three. The rank in a hypergraph is the size of a maximum edge in the hypergraph. A hypergraph is simple if no two edges contain exactly the same vertices. Let H be a hypergraph and let and be the size of a maximum independent set and a maximum matching, respectively, in H, where a set of vertices in H is independent (also called strongly independent in the literature) if no two vertices in the set belong to a common edge. Let H be a hypergraph of rank at most three and maximum degree at most three. We show that with equality if and only if H is the Fano plane. In fact, we show that if H is connected and different from the Fano plane, then and we characterize the hypergraphs achieving equality in this bound. Using this result, we show that that if H is a simple connected 3‐uniform hypergraph of order at least 8 and with maximum degree at most three, then and there is a connected 3‐uniform hypergraph H of order 19 achieving this lower bound. Finally, we show that if H is a connected hypergraph of rank at most three that is not a complete hypergraph on vertices, where denotes the maximum degree in H, then and this bound is asymptotically best possible. © 2012 Wiley Periodicals, Inc. J. Graph Theory 相似文献
36.
Moufang sets were introduced by Jacques Tits in order to understand isotropic linear algebraic groups of relative rank one, but the notion is more general. We describe a new class of Moufang sets, arising from so‐called mixed groups of type in characteristic 2, obtained as the fixed point set under a suitable involution. 相似文献
37.
We study the complexity of automatic structures via well-established concepts from both logic and model theory, including ordinal heights (of well-founded relations), Scott ranks of structures, and Cantor–Bendixson ranks (of trees). We prove the following results: (1) The ordinal height of any automatic well-founded partial order is bounded by ωω. (2) The ordinal heights of automatic well-founded relations are unbounded below , the first non-computable ordinal. (3) For any computable ordinal α, there is an automatic structure of Scott rank at least α. Moreover, there are automatic structures of Scott rank . (4) For any computable ordinal α, there is an automatic successor tree of Cantor–Bendixson rank α. 相似文献
38.
带号图是每条边带有符号(正或负)的简单图.探讨了带号图的秩,刻画了秩为2与3的带号图,以及秩为4的带号二部图. 相似文献
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40.
岩相因子对煤的燃烧特性的预测 总被引:2,自引:0,他引:2
为了研究显微组分对煤及焦的燃烧特性的影响,从显微组分和煤阶的角度描述反应性能的变化。本文提出考虑显微组分和煤阶的岩相因子,较好的表示煤的类型和煤化程度对燃烧特性的影响,较前人孤立地看待显微组分和煤阶的影响量大进步。用岩相因子一煤的着火关,取得比较满意的结果。 相似文献