A scaling limit for the length of the longest cycle in a sparse random digraph

We discuss the length of the longest directed cycle in the sparse random digraph , constant. We show that for large there exists a function such that a.s. The function where is a polynomial in . We are only able to explicitly give the values , although we could in principle compute any .     

Polytopal estimate of Mirkovi?–Vilonen polytopes lying in a Demazure crystal

In this paper, we give a polytopal estimate of Mirkovi?–Vilonen polytopes lying in a Demazure crystal in terms of Minkowski sums of extremal Mirkovi?–Vilonen polytopes. As an immediate consequence of this result, we provide a necessary (but not sufficient) polytopal condition for a Mirkovi?–Vilonen polytope to lie in a Demazure crystal.     

环状硅酸盐图的友好指数集

Let G be a graph with vertex set V(G) and edge set E(G). A labeling f : V(G) →Z2 induces an edge labeling f*: E(G) → Z2 defined by f*(xy) = f(x) + f(y), for each edge xy ∈ E(G). For i ∈ Z2, let vf(i) = |{v ∈ V(G) : f(v) = i}| and ef(i) = |{e ∈ E(G) : f*(e) =i}|. A labeling f of a graph G is said to be friendly if |vf(0)- vf(1)| ≤ 1. The friendly index set of the graph G, denoted FI(G), is defined as {|ef(0)- ef(1)|: the vertex labeling f is friendly}. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS(n, m).     

用于梳状结构光学测速系统的周期优化方法

为了提高梳状结构光学测速系统的测速精度,采用数学原理研究了梳状结构的间距大小对输出光强信号周期性的影响,通过优化输出光强信号的周期性来提高测速精度,并采用一种结合图像处理选择最佳间距的实验方法,进行了相关的理论分析,对两种不同路面进行了实验仿真验证,得到不同间距下不同的输出光强信号的周期性情况。结果表明,当栅状结构的间距大小与地面特征点大小一致时,得到的输出光强周期性最优,对于普通的柏油和水泥路面,对应到地面的最佳栅状结构间距大小为1.0mm ~1.5mm。     

脉冲反应磁控溅射氧化钒薄膜的电学性能研究

室温下,采用脉冲直流反应磁控溅射技术在玻璃衬底上制备了氧化钒薄膜.研究了脉冲调制功率占空比对薄膜物相、表面形貌、组分和热敏电学性能的影响.X射线衍射测试结果表明在室温及不同占空比下生长的氧化钒薄膜均为非晶结构;原子力显微镜表面形貌测试表明降低占空比可以得到更加光滑的薄膜表面;X射线光电子能谱测试表明降低占空比能够在反应溅射气氛不变的情况下促进钒的氧化;对薄膜的热敏电学特性测试发现,在293～368 K,小极化子跳跃是脉冲反应磁控溅射氧化钒薄膜中主要的导电机制.     

双极型电压比较器的强电磁脉冲效应

基于大电流注入法(BCI),利用瞬态脉冲产生器模拟强电磁脉冲在双极型电压比较器中产生的耦合电流,观测到输出信号在注入瞬态大电流后的波形变化,包括占空比变化及脉冲衍生等。从基本电路原理方面分析了实验现象的产生机理,以及注入电流幅值、电路偏置等因素对双极型电压比较器强电磁脉冲效应的影响。     

蒸汽压缩式制冷循环教学实验台的研制

为改进机械式实验仪器,即蒸汽压缩式制冷循环实验台的性能缺陷,设计了基于STM32F103的数据采集板卡,提高数据采集的精度和稳定性;采用基于C#语言的实验软件并结合ASP.NET技术实现实验过程自动化和远程实验教学功能。在此对上述功能的实现过程进行必要的阐述并对实验台的重要性能指标不确定度进行了详细的分析。结果表明实验台能满足现有教学实验要求,并对同类实验装置的研发具有一定的参考价值。     

A cloud model-based method for the analysis of accelerated life test data

Various curve fitting models, including the Arrhenius stress model, inverse power law model, and Eyring model have been used to model the load (stress) – life relationship to aid in planning accelerated life tests; that is, the relationship between the mean of the sample lifetimes and the testing stress level. The load-life relationship is a one-to-one relationship: one mean of the sample lifetimes corresponds to one testing stress level. However, due to the random uncertainties existing in the testing stress, the relationship should be a many-to-many relationship rather than one testing stress corresponding one mean lifetime of the tested product. Based on the one-to-one relationship of the mean of the sample lifetimes to the testing stress level, a many-to-many relationship can be derived using the reasoning method presented in this paper. The reasoning method is constructed as ‘If X, then Y.’ X is termed the rule antecedent, and Y is called the rule consequent. They are constructed with the stress values and the sample lifetimes, respectively, based on the cloud model, which represents random uncertainty and fuzzy uncertainty. The reasoning method presented is called the multi-rule-based cloud reasoner, which can refine the one-to-one relationship established by models such as the Arrhenius stress model to a many-to-many relationship. In the case study, the multi-rule-based cloud reasoner was applied to a thermal stress accelerated life test of ammunition fuses. The results from the multi-rule-based cloud reasoner were compared with the estimation results from a normal cloud generator under a stress level of 20 °C. The results showed that the many-to-many relationship between the uncertain stress level and the means of the sample lifetimes was derived by the multi-rule-based cloud reasoner.     

具有固定时滞的经济周期模型的动态分析

在经济活动中,投资行为和资本存量存在一定的时滞效应,这会影响经济周期模型的动态行为,进而使得投资政策对经济的稳定调整复杂化.考虑到资本存量的预期时间以及投资时滞对经济活动的影响,采用Hopf分岔理论,研究具有固定时滞的经济周期模型的均衡点的稳定性以及形成经济周期的条件.研究发现,投资过程中的投资时滞,以及投资决策中对于资本存量的预测时间构成经济周期产生的诱因;同时可通过政府投资政策调整达到预期均衡目标,这对保持经济周期稳定及经济政策制定有一定的指导作用.     

关于具有二次相关性收获率的捕食与被捕食系统极限环的存在性分析

讨论了一类两种群具有二次相关性收获率的捕食与被捕食系统,利用常微分定性方法和分支理论,得到了系统平衡点处的性态和极限环的存在性条件,并用Matlab软件对其进行数值模拟,推广了相关文献中两种群捕食模型定性分析的相应结论.