Maximizing H‐Colorings of Connected Graphs with Fixed Minimum Degree

For graphs G and H , an H‐coloring of G is a map from the vertices of G to the vertices of H that preserves edge adjacency. We consider the following extremal enumerative question: for a given H , which connected n‐vertex graph with minimum degree δ maximizes the number of H‐colorings? We show that for nonregular H and sufficiently large n , the complete bipartite graph is the unique maximizer. As a corollary, for nonregular H and sufficiently large n the graph is the unique k‐connected graph that maximizes the number of H‐colorings among all k‐connected graphs. Finally, we show that this conclusion does not hold for all regular H by exhibiting a connected n‐vertex graph with minimum degree δ that has more ‐colorings (for sufficiently large q and n ) than .     

Matching Extension Missing Vertices and Edges in Triangulations of Surfaces

Let G be a 5‐connected triangulation of a surface Σ different from the sphere, and let be the Euler characteristic of Σ. Suppose that with even and M and N are two matchings in of sizes m and n respectively such that . It is shown that if the pairwise distance between any two elements of is at least five and the face‐width of the embedding of G in Σ is at least , then there is a perfect matching M₀ in containing M such that .     

Bolzano's Theorems for Holomorphic Mappings

The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions.A more complicated proof,using Cauchy's argument principle,provides uniqueness of the zero,when the sign conditions on the boundary are strict.Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions.Extensions to holomorphic mappings from Cn to Cn are obtained using Brouwer degree.     

不确定需求与产出供应链回购契约决策

针对市场需求的不确定性和供应商产出产品合格率的不确定性,提出供应商产出量小于销售商订购量时需再生产满足销售商的订购,以及供应商生产过量和回购的产品通过折扣市场出售,建立以供应链期望利润为目标函数,以回购单价为决策变量的供应链回购契约决策模型.通过模型的分析,证明了模型存在最优的期望利润,给出了最优回购单价满足的方程;同时,也证明了最优订购量,最优生产量和销售商最优期望利润是回购单价的增函数.最后,通过算例验证了模型的有效性.     

ITS示范工程对城市交通畅通性的贡献率研究

通过分析城市交通畅通性的影响因素及其与ITS(智能交通系统)的关系,挖掘ITS对城市交通畅通性的贡献率指标.搜集实证研究对象数据,采用灰色预测模型预测贡献率指标的数值,将ITS示范工程实施前后的数值进行对比,计算得到ITS示范工程对城市交通畅通性的贡献率.由贡献率结果判断ITS示范工程对城市交通畅通性的作用及ITS示范工程的实施效果如何,为未来ITS的发展提供相应的参考建议.     

一类具有收获率的脉冲Lotka-Volterra竞争合作系统的八个正概周期解

研究了一类具有收获率的脉冲Lotka-Volterra竞争合作系统的正概周期解.通过利用重合度理论延拓定理、概周期理论和不等式分析技巧,获得了系统至少存在8个正概周期解的充分条件,推广和改进了早期文献的相关结果.     

基于可拓和组合赋权的矿井通风系统优化评价

矿井通风系统具有随机性、模糊性和不确定性等特征,一般单一的赋权评价法难以对其进行准确的优化评价.采用模糊层次分析法和熵权法的组合赋权法不仅可以提升对目标评价的准确性还能避免单一赋权的偶然性和局限性,结合可拓学的优度评价法,依据优度排序,得到最优方案.事实证明,基于组合赋权的可拓评价模型较其他评价方法更为客观,评价结果更加符合实际,可为解决类似优化方案问题提供一种新思路和方法.     

基于改进的模糊综合评价法的低渗油藏CO_2驱筛选体系的建立及应用

以某低渗透油藏为对象,首先在数据挖掘的基础上制定了低渗透油藏注CO_2驱筛选标准.基于模糊综合评价法,建立了适用于低渗透油藏CO_2驱适宜度评价的模糊综合评价模型,并运用该模型对目标油藏注CO_2的适宜度进行了评价.计算结果表明目标油藏注气驱开发适应性较好.评价过程有效地降低了直接进行注气开发的风险,为之后低渗透油藏注气开发提供了技术和经济上的指导.     

内部算子生成的直觉I-Fuzzy拓扑空间

在直觉I-fuzzy拓扑空间中定义了内部度,并研究了它的一些性质,接着给出了直觉I-fuzzy拓扑空间内部算子的概念,最后得到了从拓扑的直觉I-Fuzzy内部算子I出发,得到一个直觉I-fuzzy拓扑r,再利用r定义的内部算子恰好回到了I等结论.