An M/G/1 queue with second optional service

We study an M/G/1 queue with second optional service. Poisson arrivals with mean arrival rate (>0) all demand the first essential service, whereas only some of them demand the second optional service. The service times of the first essential service are assumed to follow a general (arbitrary) distribution with distribution function B(v) and that of the second optional service are exponential with mean service time 1/₂ (₂>0). The time-dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been derived explicitly. Also the mean queue length and the mean waiting time have been found explicitly. The well-known Pollaczec–Khinchine formula and some other known results including M/D/1, M/E_k/1 and M/M/1 have been derived as particular cases.     

变质量任意阶非完整系统的相对论性广义Appell型方程

本文构造了一个新型的相对论性动力学函数——广义加速度能 S~■,建立变质量系统的相对论性万有 D'Alembert 原理,由此导出任意阶非完整约束系统多种形式的相对论性广义 Appell 型方程.     

一类递推关系式的解的计算公式

文献[1]给出了一个三项单指标的常系数齐次递推式的一般解公式。本文一类带双指标的变系数非齐次递推关系的解的结构。其结果，对双指标的相应递推关系式的解的求出，亦或在其有关理论的研究方面，皆有其作用。     

A stochastic theory for clustering of quenched-in vacancies—III. A continuum model

In continuation of our earlier investigation on the problem of clustering of quenched-in vacancies reported earlier, starting from the discrete model, we derive a second order partial differential equation for the growth of the clusters. The solution of this equation is shown to be in reasonable agreement with the solution of the discrete model proposed earlier. However, the total number of vacancies is not conserved under slightly less stringent conditions than the conditions dictated by the solution of the discrete model, suggesting a slightly modified differential equation for the concentration of the clusters. The solution of this modified differential equation has the required properties. The leading part of the distribution when transferred into the space designating the linear dimension of the cluster has a Gaussian form. This feature is shown to be consistent with writing a Langevin equation with the linear dimension of the cluster taking the role of the random variable. This permits the identification of the smallness of parameter. An alternate formulation is also given where the concentration of the vacancies stored in a cluster of a certain size is considered as the dynamical variable. The solution obtained in this alternate formulation is shown to be consistent with the other formulation.     

Variable Neighborhood Decomposition Search

The recent Variable Neighborhood Search (VNS) metaheuristic combines local search with systematic changes of neighborhood in the descent and escape from local optimum phases. When solving large instances of various problems, its efficiency may be enhanced through decomposition. The resulting two level VNS, called Variable Neighborhood Decomposition Search (VNDS), is presented and illustrated on the p-median problem. Results on 1400, 3038 and 5934 node instances from the TSP library show VNDS improves notably upon VNS in less computing time, and gives much better results than Fast Interchange (FI), in the same time that FI takes for a single descent. Moreover, Reduced VNS (RVNS), which does not use a descent phase, gives results similar to those of FI in much less computing time.     

Rewritable Broad-Band Color Filters for Spectral Image Analysis

We propose an optical system to implement rewritable transparent broad-band color filters. The filter consists of a linear variable filter and a liquid crystal spatial light modulator in which an expected filter function is written. A time-integrated intensity image was taken while the filter was passing the lens aperture of a CCD camera. The averaged norm error between the implemented and the expected filter functions was about 5.4#x0025;. The system was applied to spectral estimation in a two-dimensional color image.     

二乙烯基苯为交联剂COPNA树脂的研究

以煤沥青为单体、二乙烯基苯（DVB）为交联剂,在对甲苯磺酸的催化作用下合成了缩合多环芳烃（COPNA）树脂。研究了工艺条件对COPNA树脂的收率、溶解性能、软化点和焦化率的影响;此外,采用扫描电镜（SEM）和微分扫描量热法（DSC）研究了COPNA树脂的形成及相转变行为。结果表明：煤沥青含有“惰性”组分,导致COPNA树脂的收率偏低,其收率偏低,其收率最高为42.6%;与煤沥青比较,COPNA树脂的溶解性能较差;COPNA树脂具有良好的工艺性和耐热性;COPNA树指的形成是以球晶方式来进行的,因此不同反应时间树脂的相转变行为有很大的差异。     

Adaptive nodeless variable finite elements with flux-based formulation for thermal–structural analysis

A nodeless variable element method with the fluxbased formulation is developed to analyze two-dimensional thermal-structural problems. The nodeless variable formula- tion provides accurate temperature distributions to yield more accurate thermal stress solutions. The flux-based formulation is used to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element meshes that can adapt and move along with the transient solution behavior. A version of a nearly optimal element size determination is proposed to provide high convergence rate of the predicted solutions. The combined procedure is evaluated by solving several thermal, structural, and thermal stress problems.     

Extension of Variable Separable Solutions for Nonlinear Evolution Equations

We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.     

Periodic Semifolded Solitary Waves for （2＋1）-Dimensional Variable Coefficient Broer-Kaup System

Applying the extended mapping method via Riccati equation, many exact variable separation solutions for the （2＆1 ）-dimensional variable coefficient Broer-Kaup equation are obtained. Introducing multiple valued function and Jacobi elliptic function in the seed solution, special types of periodic semifolded solitary waves are derived. In the long wave limit these periodic semifolded solitary wave excitations may degenerate into single semifolded localized soliton structures. The interactions of the periodic semifolded solitary waves and their degenerated single semifolded soliton structures are investigated graphically and found to be completely elastic.