Scheduling networks of queues: Heavy traffic analysis of a simple open network

We consider a queueing network with two single-server stations and two types of customers. Customers of type A require service only at station 1 and customers of type B require service first at station 1 and then at station 2. Each server has a different general service time distribution, and each customer type has a different general interarrival time distribution. The problem is to find a dynamic sequencing policy at station 1 that minimizes the long-run average expected number of customers in the system.The scheduling problem is approximated by a dynamic control problem involving Brownian motion. A reformulation of this control problem is solved, and the solution is interpreted in terms of the queueing system in order to obtain an effective sequencing policy. Also, a pathwise lower bound (for any sequencing policy) is obtained for the total number of customers in the network. We show via simulation that the relative difference between the performance of the proposed policy and the pathwise lower bound becomes small as the load on the network is increased toward the heavy traffic limit.     

GM(1,1)建模方法的改进及其应用

应用微分方程的两种数值解法估计GM(1,1)模型中的待辩参数a、u,并对模型的边界条件做了改进,建立了灰微分方程的时间响应表达式,讨论了由此建立的GM(1,1)模型的适用范围和预测精度.通过实例的分析计算,证明改进的模型具有良好的预测精度,满足工程实际需要,拓广了GM(1,1)模型的适用范围.     

Global stability and asymptotics of some classes of rational difference equations

In this note we prove that the positive solutions of some classes of rational difference equations are globally asymptotically stable. Using a Berg's result, we also find asymptotics of some solutions of these equations.     

Control of the temperature responsiveness of poly(N-isopropylacrylamide-co-2-hydroxyethyl methacrylate) copolymer using ultrasonic irradiation

Poly(N-isopropylacrylamide-co-2-hydroxyethyl methacrylate) (poly(NIPAM-co-HEMA)) is a temperature-responsive copolymer that is expected to be applicable as an advanced functional polymeric material in various fields. In this study, a novel method was developed to control the responsive temperature of poly(NIPAM-co-HEMA) using an ultrasonic polymerization technique. Initially, the behavior of the reaction was investigated using NIPAM and HEMA monomers under ultrasonic irradiation. A high ultrasonic power was found to produce a high reaction rate and low number average molecular weight of the copolymer. The polydispersity of the synthesized copolymer was approximately 1.5 for all ultrasonic powers examined. In the early stage of the reaction, the molar fraction of NIPAM in the copolymer was lower than the initial molar fraction of the monomers. It was concluded that ultrasonic irradiation affected the initiation reaction and polymer degradation, but did not affect the propagation reaction. Furthermore, the effect of the ultrasonic irradiation conditions on the temperature responsiveness of the copolymer was investigated. The lower critical solution temperature (LCST) of the copolymer was found to increase with increasing ultrasonic irradiation time. In addition, in the early stages of the reaction, the measured values of the LCST were higher than the estimated values using copolymer composition. This can be attributed to some parts of the copolymer chain possessing a higher NIPAM fraction than the overall fraction due to different reactivities of the monomers and terminated radicals. This hypothesis was indirectly verified by the synthesis of a block copolymer from the PNIPAM homopolymer and HEMA monomer.     

A new approach for modelling the damped Helmholtz oscillator:applications to plasma physics and electronic circuits

In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.     

Padé approximations of quantized-vortex solutions of the Gross–Pitaevskii equation

Quantized vortices are important topological excitations in Bose–Einstein condensates. The Gross–Pitaevskii equation is a widely accepted theoretical tool. High accuracy quantized-vortex solutions are desirable in many numerical and analytical studies. We successfully derive the Padéapproximate solutions for quantized vortices with winding numbers ω = 1, 2, 3, 4, 5, 6 in the context of the Gross–Pitaevskii equation for a uniform condensate. Compared with the numerical solutions, we find that(1) they approximate the entire solutions quite well from the core to infinity;(2) higher-order Padé approximate solutions have higher accuracy;(3) Padé approximate solutions for larger winding numbers have lower accuracy. The healing lengths of the quantized vortices are calculated and found to increase almost linearly with the winding number. Based on experiments performed with ~(87)Rb cold atoms, the healing lengths of quantized vortices and the number of particles within the healing lengths are calculated, and they may be checked by experiment. Our results show that the Gross–Pitaevskii equation is capable of describing the structure of quantized vortices and physics at length scales smaller than the healing length.     

Linear superposition of Wronskian rational solutions to the KdV equation

A linear superposition is studied for Wronskian rational solutions to the Kd V equation, which include rogue wave solutions. It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear Kd V equation. It is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.     

Antisolvent crystallization of aqueous ammonium dihydrogen phosphate solutions by addition of acetone at different rates

Results of an investigation of in situ measurements of laser‐beam intensity I_s and I_m transmitted through aqueous ammonium dihydrogen phosphate (ADP) solutions saturated at 30 °C and water, respectively, and temperature T_s of solution and T_m of water during feeding of antisolvent acetone at different rates R_A, using an indigenously designed experimental setup, are presented and discussed. It was found that: (1) for the measurement of MSZW, defined as the maximum volume fraction of acetone content Δx_max in the solution, obtained from temperature measurements are more reliable than transmitted laser‐beam intensity measurements for solutions, (2) two minima ΔT_min1 and ΔT_min2 associated with endothermic reactions, separated by a maximum ΔT_max due to exothermic reactions appear in the plots of temperature difference ΔT = T_s−T_m against acetone feeding time t, and (3) in the ΔT(t) plots there are time intervals Δt of constant rates R_T of increase in ΔT of aqueous ADP solutions, and these values of R_T increase linearly with acetone feeding time rate R_A. The experimental data on the observed dependence of MSZW on antisolvent feeding rate R_A, the appearance of minima ΔT_min1 and ΔT_min2 and maximum ΔT_max and their dependence on R_A, and the relationship between R_T and R_A are discussed from consideration of processes of nucleation and growth of crystallites.     

Green and mild laccase-catalyzed aerobic oxidative coupling of benzenediol derivatives with various sodium benzenesulfinates

The oxidative coupling reaction between hydroquinone or catechols and various sodium benzenesulfinates was investigated using the laccase from Trametes versicolor, in the presence of O₂ in a phosphate buffer solution at room temperature to afford sulfonyl benzenediols in 75–95% yield.