Busy periods of discrete-time queues using the Lagrange implicit function theorem

In this paper, we study the busy-period distribution for discrete-time queues assuming a Bernoulli arrival process, with arbitrary service-time and batch-arrival distributions. We derive explicit analytic formulas for these distributions using the Lagrange Implicit Function Theorem applied to probability generating functions. The convenient coefficient operator notation used in these formulas leads to a computationally efficient method for obtaining the distributions in their entirety from these analytic formulas.     

Local Bifurcation of Critical Periods for a Class of Liénard Equations

In this paper,we study the local bifurcation of critical periods near the nondegenerate center(the origin) of a class of Liénard equations with degree 2n,and prove that at most 2n-2 critical periods(taken into account multiplicity) can be produced from a weak center of finite order.We also prove that it can have exactly2n-2 critical periods near the origin.     

Optimizing inventory decisions in a two-level supply chain with order quantity constraints

A fundamental assumption in traditional inventory models is that all of the ordered items are of perfect quality. A two-level supply chain is considered consists of one retailer and a collection of suppliers that operate within a finite planning horizon, including multiple periods, and a model is formulated that simultaneously determines both supplier selection and inventory allocation problems in the supply chain. It is supposed that the ordered products dependent on the suppliers include a certain percentage of imperfect quality products and have different prices. In this paper, we study the impact of the retailer’s financial constraint. On the other hand, suppliers have restricted capacities and set minimum order quantity (MOQ) policy for the retailer’s order amount happened in each period. So, the problem is modeled as a mixed integer nonlinear programming. The purpose of this model is to maximize the total profit. The nutrients, fishery and fruitage industries give good examples for the proposed model. A numerical example is presented to indicate the efficiency of the proposed model. Considering the complexity of the model, a genetic algorithm (GA) is presented to solve the model. We demonstrate analytically that the proposed genetic algorithm is suitable in the feasible situations.     

单水听器被动测距的脉冲周期最接近法

为了解决单水听器对运动目标的被动测距的问题,提出了一种基于最小二乘的脉冲周期最接近法。该方法适用于目标发射固定周期脉冲信号,推导了目标运动参数与单水听器接受信号脉冲周期的关系式,构建一个长方矩阵,在最小二乘意义下,计算目标最接近距离和速度。使用泰勒展开公式,分析了算法的误差特性。为单水听器被动测距提供了新方法。仿真结果表明了新方法的正确性。     

存在液膜的毛细蒸发过程研究

采用水浴恒温蒸发方法研究了液膜存在时的毛细蒸发过程. 研究结果表明：毛细蒸发过程中液/气界面符合黏性指延,且不受蒸发速度及液膜状态的影响;蒸发过程可分为剧烈减速、匀速蒸发、线性减速蒸发和边界效应四个阶段,分别对应不同的液膜状态;毛细蒸发的主要区域在毛细管端口液膜处,工质由液体区流向端口蒸发区的过程中液膜起到了通道桥梁作用. 关键词： 毛细蒸发 液/气界面 蒸发阶段 液膜     

聚乙二醇对振荡反应的影响

前文［1］曾指出，生物体系的化学振荡反应实际上是产生于水溶胶之中（包括高分子溶液及表面活性剂溶液）．作为反应介质，水溶胶对生物体系的周期现象有着不可忽略的重要作用．因此，要模拟生物体系的化学振荡就不能不考虑溶胶对振荡反应的影响．前文［2，3］报道了表面活性剂TritonX－100（简称TX－100），TritonX－305等对振荡反应的影响．为了解聚乙二醇类表面活性剂中EO链的作用及高分子溶液对振荡反应的特征影响，我们选用高分子聚乙二醇（PEG）作为添加剂，考虑由于它的加入而引起振荡反应的变化．为了减少PEG中自由羟基的还原…     

A note on: Optimal ordering policy for stock-dependent demand under progressive payment scheme

In a recent paper, Soni and Shah [Soni, H., Shah, N. H. (2008). Optimal ordering policy for stock-dependent demand under progressive payment scheme. European Journal of Operational Research 184(1), 91–100] developed a model to find the optimal ordering policy for a retailer with stock-dependent demand and a supplier offering a progressive payment scheme to the retailer. This note corrects some errors in the formulation of the model of Soni and Shah. It also extends their work by assuming that the credit interest rate of the retailer may exceed the interest rate charged by the supplier. Numerical examples illustrate the benefits of these modifications.     

HYPOELLIPTICITY OF NONSINGULAR CLOSED 1-FORMS ON COMPACT MANIFOLDS

ABSTRACT

Hypoellipticity of nonsingular closed 1-forms on compact manifolds is characterized by a diophantine condition on the generators of the group of periods of the form.     

Minimal periods of holomorphic maps on complex tori

We study the set of minimal periods of holomorphic self-maps of one- and two-dimensional complex tori. In particular, we characterize when the set of minimal periods of such maps is finite. In fact, we have an algorithm for doing this characterization for holomorphic self-maps of an arbitrary dimensional complex torus.