On the enumeration of certain weighted graphs

We enumerate weighted simple graphs with a natural upper bound condition on the sum of the weight of adjacent vertices. We also compute the generating function of the numbers of these graphs, and prove that it is a rational function. In particular, we show that the generating function for connected bipartite simple graphs is of the form p₁(x)/(1-x)^m+1. For nonbipartite simple graphs, we get a generating function of the form p₂(x)/(1-x)^m+1(1+x)^l. Here m is the number of vertices of the graph, p₁(x) is a symmetric polynomial of degree at most m, p₂(x) is a polynomial of degree at most m+l, and l is a nonnegative integer. In addition, we give computational results for various graphs.     

供应链中的MQ(t)/Gj/∞排队群

本文研究由一个非时齐Poisson到达过程驱动的多个MQ(t)／Gj／∞型排队系统．当一个K型到达发生时(K(?){1,…,m}),对每一个j∈K,顾客按批量QjK进入排队系统j,(Q1K,…,QmK)是相依的随机向量．我们导出了联合队长过程和联合输出过程的多变量母函数,并给出各排队系统之间的相关性分析．这些结果为非时齐供应链分析提供了理论依据     

一个温度自动精密测控实验的设计与分析

本文给出一个温度自动精密测控实验的设计方案，并详细说明该实验系统应用于生产实际所遇到的主要技术问题的解决措施。     

有两个服务阶段、反馈、强占型的M/G/1重试排队

在假定重试区域中只有队首的顾客允许重试的条件下,重试时间是一般分布时,考虑具有两个服务阶段、反馈、强占型的M／G／1重试排队系统．得到了系统稳态的充要条件．求得稳态时系统队长和重试区域中队长分布及相关指标,并且得到了系统的随机分解性质．     

Hypergeometric Solutions of Some Algebraic Equations

We give the hypergeometric solutions of some algebraic equations including the general fifth-degree equation.     

一类强极限定理与矩母函数方法

本文利用似然比的概念，研究离散随机变量序列的极限性质，得到了一类用不等式表示的强极限定理．证明中结合区间剖分法，提出了将矩母函数的工具应用于强极限定理的研究的一种途径．     

Gompertz模型在高龄阶段的修正及模拟

近年来我国人口老龄化呈加快之势 ,精确估计高龄老人的年龄别死亡概率对人寿保险公司计算年金显得尤为重要 .本文针对观察年龄别死亡概率在高龄阶段不再呈现指数增长的事实 ,对 Gompertz模型进行了修正 ,以使模型更好地拟合观察年龄别死亡概率 .     

Random walk with persistence

The exact analytic result is obtained for the Fourier transform of the generating functionF(R,s)= _n=0 s ⁿ P(R,n), whereP(R,n) is the probability density for the end-to-end distanceR inn steps of a random walk with persistence. The moments R ²(n), R ⁴(n), and R ⁶(n) are calculated and approximate results forP(R,n) and R ^–1(n) are given.     

Base‐amplifying silicone resins with photobase‐generating side chains and their application to negative‐working photoresists

To accomplish high photosensitivity of resist systems including photobase generators, we have proposed the concept of base‐proliferation reactions that generate base molecules in a nonlinear manner by the action of a catalytic amount of base; however, excessive diffusion of generated base molecules is still a problem. We have designed novel functional silicone resins bearing both base‐amplifying units and photobase‐generating units, and synthesized resins with various composition ratios. The synthesized resins are decomposed autocatalytically after UV irradiation and subsequent heating at 100 °C, which indicates progression of base‐proliferation reactions. High photosensitivity (8.1 mJ cm^?2) was recorded, and it was found that the photosensitivity is about 490 times enhanced by replacing a base‐catalytic reaction system with the base‐proliferation reaction system. Furthermore, a 4 × 10 µm line‐and‐space pattern has been successfully fabricated using the silicone resin. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1205–1212     

New generating function formulae of even- and odd-Hermite polynomials obtained and applied in the context of quantum optics

By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.