共查询到20条相似文献,搜索用时 46 毫秒
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《Journal of Parallel and Distributed Computing》2004,64(11):1286-1296
In this paper, we investigate the star graph with faulty vertices and/or edges from the graph theoretic point of view. We show that between every pair of vertices with different colors in a bicoloring of , , there is a fault-free path of length at least , and there is a path of length at least joining a pair of vertices with the same color, when the number of faulty elements is or less. Here, is the number of faulty vertices. , , with at most faulty elements has a fault-free cycle of length at least unless the number of faulty elements are and all the faulty elements are edges incident to a common vertex. It is also shown that , , is strongly hamiltonian-laceable if the number of faulty elements is or less and the number of faulty vertices is one or less. 相似文献
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Yongge Tian 《Computers & Mathematics with Applications》2011,61(6):1493-1501
Let and be two linear matrix expressions, and denote by and the collections of the two matrix expressions when and run over the corresponding matrix spaces. In this paper, we study relationships between the two matrix sets and , as well as the two sets and , by using some rank formulas for matrices. In particular, we give necessary and sufficient conditions for the two matrix set inclusions and to hold. We also use the results obtained to characterize relations of solutions of some linear matrix equations. 相似文献
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A well-known lemma of Suslin says that for a commutative ring if is unimodular where is monic and , then there exist such that the ideal generated by equals . This lemma played a central role in the resolution of Serre’s Conjecture. In the case where contains a set of cardinality greater than such that is invertible for each in , we prove that the can simply correspond to the elementary operations , , where . These efficient elementary operations enable us to give new and simple algorithms for reducing unimodular rows with entries in to using elementary operations in the case where is an infinite field. Another feature of this paper is that it shows that the concrete local–global principles can produce competitive complexity bounds. 相似文献
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Francisco J. Solis Fausto Ongay Silvia Jerez Marcos Capistran 《Computers & Mathematics with Applications》2010,59(1):499-505
We define a family of discrete Advection–reaction operators, denoted by , which associate to a given scalar sequence the sequence given by , where for . For we explicitly find their iterates and study their convergence properties. Finally, we show the relationship between the family of discrete operators with the continuous one dimensional advection–reaction equation. 相似文献
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Ahmed M.E. Bayoumi Mohamed A. Ramadan 《Computers & Mathematics with Applications》2018,75(9):3367-3378
In this paper, an iterative algorithm for solving a generalized coupled Sylvester-conjugate matrix equations over Hermitian -conjugate matrices given by and is presented. When these two matrix equations are consistent, the convergence theorem shows that a solution can be obtained within finite iterative steps in the absence of round-off error for any initial arbitrary Hermitian -conjugate solution matrices , . Some lemmas and theorems are stated and proved where the iterative solutions are obtained. A numerical example is given to demonstrate the behavior of the proposed method and to support the theoretical results. 相似文献
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This paper aims at providing an alternative approach to study global dynamic properties for a two-species chemotaxis model, with the main novelty being that both populations mutually compete with the other on account of the Lotka–Volterra dynamics. More precisely, we consider the following Neumann initial–boundary value problem in a bounded domain , with smooth boundary, where are positive constants.When and , it is shown that under some explicit largeness assumptions on the logistic growth coefficients and , the corresponding Neumann initial–boundary value problem possesses a unique global bounded solution which moreover approaches a unique positive homogeneous steady state of above system in the large time limit. The respective decay rate of this convergence is shown to be exponential.When and , if is suitable large, for all sufficiently regular nonnegative initial data and with and , the globally bounded solution of above system will stabilize toward as in algebraic. 相似文献
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Josef Cibulka 《Theoretical computer science》2011,412(8-10):822-834
We are given a stack of pancakes of different sizes and the only allowed operation is to take several pancakes from the top and flip them. The unburnt version requires the pancakes to be sorted by their sizes at the end, while in the burnt version they additionally need to be oriented burnt-side down. We are interested in the largest value of the number of flips needed to sort a stack of pancakes, both in the unburnt version () and in the burnt version ().We present exact values of up to and of up to and disprove a conjecture of Cohen and Blum by showing that the burnt stack is not the hardest to sort for .We also show that sorting a random stack of unburnt pancakes can be done with at most flips on average. The average number of flips of the optimal algorithm for sorting stacks of burnt pancakes is shown to be between and and we conjecture that it is .Finally we show that sorting the stack needs at least flips, which slightly increases the lower bound on . This bound together with the upper bound for sorting found by Heydari and Sudborough in 1997 [10] gives the exact number of flips to sort it for and . 相似文献
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Aleksandar Ilić 《Computers & Mathematics with Applications》2010,59(8):2776-2783
Let be a simple undirected graph with the characteristic polynomial of its Laplacian matrix , . It is well known that for trees the Laplacian coefficient is equal to the Wiener index of , while is equal to the modified hyper-Wiener index of the graph. In this paper, we characterize -vertex trees with given matching number which simultaneously minimize all Laplacian coefficients. The extremal tree is a spur, obtained from the star graph with vertices by attaching a pendant edge to each of certain non-central vertices of . In particular, minimizes the Wiener index, the modified hyper-Wiener index and the recently introduced Incidence energy of trees, defined as , where are the eigenvalues of signless Laplacian matrix . We introduced a general transformation which decreases all Laplacian coefficients simultaneously. In conclusion, we illustrate on examples of Wiener index and Incidence energy that the opposite problem of simultaneously maximizing all Laplacian coefficients has no solution. 相似文献
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Mingqing Zhai Guanglong Yu Jinlong Shu 《Computers & Mathematics with Applications》2010,59(1):376-381
Let be the class of bicyclic graphs on vertices with girth . Let be the subclass of consisting of all bicyclic graphs with two edge-disjoint cycles and . This paper determines the unique graph with the maximal Laplacian spectral radius among all graphs in and , respectively. Furthermore, the upper bound of the Laplacian spectral radius and the extremal graph for are also obtained. 相似文献