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《Discrete Mathematics》2022,345(12):113083
Let G be a graph, the order of G, the connectivity of G and k a positive integer such that . Then G is said to be k-extendable if it has a matching of size k and every matching of size k extends to a perfect matching of G. A Hamiltonian path of a graph G is a spanning path of G. A bipartite graph G with vertex sets and is defined to be Hamiltonian-laceable if such that and for every pair of vertices and , there exists a Hamiltonian path in G with endpoints p and q, or and for every pair of vertices , there exists a Hamiltonian path in G with endpoints p and q. Let G be a bipartite graph with bipartition . Define to be a maximum integer such that and (1) for each non-empty subset S of X, if , then , and if , then ; and (2) for each non-empty subset S of Y, if , then , and if , then ; and (3) if there is no non-negative integer satisfying (1) and (2).Let G be a bipartite graph with bipartition such that and . In this paper, we show that if , then G is Hamiltonian-laceable; or if , then for every pair of vertices and , there is an -path P in G with . We show some of its corollaries in k-extendable, bipartite graphs and a conjecture in k-extendable graphs. 相似文献
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本文采用分子动力学方法研究了FeCoCrCuNi高熵合金裂纹及孔洞模型结构在不同轴向拉伸应变速率下的力学与微观结构演化机理. 结果表明:应变速率越高FeCoCrCuNi裂纹结构对应更高的过冲应变和过冲应力,其主要原因是高拉伸速率会导致高强度的BCC结构及孪晶结构的生成,而BCC结构及孪晶结构的产生进而会抑制应力的下降,通过应力-应变曲线,可知FeCoCrCuNi裂纹模型在轴向应力作用下表现为塑性形变. 对于不同尺寸的孔洞FeCoCrCuNi裂纹模型的应力模拟与结构分析,可以得出:孔洞尺寸越大, FeCoCrCuNi裂纹结构对应的过冲应变和过冲应力越小,其主要原因是大尺寸的孔洞造成孔洞之间产生裂纹的,进而会影响这个材料的屈服应变和屈服强度. 相似文献
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Murad B. Khorsheed Qasim M. Zainel Oday A. Hassen Saad M. Darwish 《Entropy (Basel, Switzerland)》2020,22(12)
This paper applies the entropy-based fractal indexing scheme that enables the grid environment for fast indexing and querying. It addresses the issue of fault tolerance and load balancing-based fractal management to make computational grids more effective and reliable. A fractal dimension of a cloud of points gives an estimate of the intrinsic dimensionality of the data in that space. The main drawback of this technique is the long computing time. The main contribution of the suggested work is to investigate the effect of fractal transform by adding R-tree index structure-based entropy to existing grid computing models to obtain a balanced infrastructure with minimal fault. In this regard, the presented work is going to extend the commonly scheduling algorithms that are built based on the physical grid structure to a reduced logical network. The objective of this logical network is to reduce the searching in the grid paths according to arrival time rate and path’s bandwidth with respect to load balance and fault tolerance, respectively. Furthermore, an optimization searching technique is utilized to enhance the grid performance by investigating the optimum number of nodes extracted from the logical grid. The experimental results indicated that the proposed model has better execution time, throughput, makespan, latency, load balancing, and success rate. 相似文献
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Laurynas Dagys Vaidas Klimkevičius Vytautas Klimavicius Sergejus Balčiūnas Jūras Banys Vytautas Balevicius 《Journal of polymer science. Part A, Polymer chemistry》2020,58(23):3253-3263
The 1H–13C cross-polarization with magic-angle spinning (CP MAS) kinetics was studied in poly(methacrylic acid) (PMAA) having the purpose to track the links between the local order in the main chain and the proton dynamics in peripheral hydrogen bond networks. The experimental CP MAS kinetic curves were analyzed applying the models of isotropic and anisotropic spin-diffusion with thermal equilibration. The fractal dimension Dp ≈ 3 was deduced that indicates that PMAA behaves as an isotropic 3D-system. No proton conductivity in the neat PMAA was deduced from the impedance spectroscopy data analyzing the frequency dependences of the complex dielectric permittivity. The value of local order parameter S = 0.70 for CH2 in PMAA occupies an intermediate position between 0.63 and 0.85 deduced for CH2 sites in the main chains of poly(vinyl phosphonic acid) and poly(2-hydroxyethyl methacrylate), that is, the true proton conductor and the polymer that contains the H-bond network, however, no proton conductivity, respectively. 相似文献
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《Discrete Mathematics》2020,343(2):111679
A path in an edge-colored graph is called monochromatic if any two edges on the path have the same color. For , an edge-colored graph is said to be monochromatic -edge-connected if every two distinct vertices of are connected by at least edge-disjoint monochromatic paths, and is said to be uniformly monochromatic -edge-connected if every two distinct vertices are connected by at least edge-disjoint monochromatic paths such that all edges of these paths are colored with a same color. We use and to denote the maximum number of colors that ensures to be monochromatic -edge-connected and, respectively, to be uniformly monochromatic -edge-connected. In this paper, we first conjecture that for any -edge-connected graph , , where is a minimum -edge-connected spanning subgraph of . We verify the conjecture for . We also prove the conjecture for and with . When is a minimal -edge-connected graph, we give an upper bound of , i.e., . For the uniformly monochromatic -edge-connectivity, we prove that for all , , where is a minimum -edge-connected spanning subgraph of . 相似文献
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飞行器液压导管受接头和卡箍等约束,在使用的振动环境中,会因弯曲应力而导致破裂,影响到飞行安全.本文对飞行器液压系统通用的不锈钢导管的裂纹萌生寿命进行了试验研究.首先在对8 mm、12 mm 无缺陷导管和含U 型缺口8 mm 导管的疲劳试验和有限元分析的基础上,得到了导管的最大拉应变-裂纹萌生寿命数据.然后采用基于强度极限和弹性模量估算法的Manson-Coffin 公式来预测导管裂纹萌生寿命.最后引入加载类型修正系数、表面质量修正系数、试样尺寸修正系数、应力集中敏感系数和有效应力集中系数,使修正后的公式对三种类型的导管均有较好的裂纹萌生寿命预测精度. 相似文献
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