Confluence of cycles for hypergeometric functions on

The hypergeometric function of general type, which is a generalization of the classical confluent hypergeometric functions, admits an integral representation derived from a character of a linear abelian group. For the hypergeometric function on the space of matrices, a basis of cycles for the integral is constructed by a limit process, which is called a process of confluence. The determinant of the period matrix is explicitly evaluated to show the independence of the cycles.

     

葡萄糖B-Z体系中酸度变化诱导的复杂振荡反应

本文首次报导了葡萄糖-KBrO_3-丙酮-MnSO_4-H_2SO_4体系的化学振荡反应,在这一体系中改变酸度可产生一系列复杂的振荡现象,当[H_2SO_4]_0>0.36mol·l~(-1)或[H_2SO_4]_0<0.074mol·l~(-1)时,体系分别出现二种不同类型的振荡波形OA和OB,OA振荡存在一诱导期,OB振荡无锈导期;OA的振幅较小,但振荡频率比OB快得多;OB的振荡周期逐渐缩短,但OA.却相反变化.当0.074mol·l~(-1)<[H_2SO_4]_0<0.36mol·l~(-1)时,体系同时出现上述二种类型的振荡波形,中间存在一过渡区域,即产生连续振荡波形.文章讨论了诱导期及过渡时间与[H_2SO_4]_0的关系,对酸度的影响机理作了说明.     

MD simulation of nanoindentation on (001) and (111) surfaces of Ag–Ni multilayers

We perform MD simulations of the nanoindentation on (001) and (111) surfaces of Ag–Ni multilayers with different modulation periods, and find that both the hardness and maximum force increase with the increase of modulation period, in agreement with the inverse Hall–Petch relation. A prismatic partial dislocation loop is observed in the Ni(111)/Ag(111) sample when the modulation period is relatively large. We also find that misfit dislocation network shows a square shape for the Ni(111)/Ag(111) interface, while a triangle shape for the Ni(001)/Ag(001) interface. The pyramidal defect zones are also observed in Ni(001)/Ag(001) sample, while the intersecting stacking faults are observed in Ni(111)/Ag(111) sample after dislocation traversing interface. The results offer insights into the nanoindentation behaviors in metallic multilayers, which should be important for clarifying strengthening mechanism in many other multilayers.     

Asymptotical synchronization for chaotic Lur’e systems using sampled-data control

This paper presents a new method for the asymptotical synchronization of two identical chaotic Lur’e systems using sampling control. The method is based on a new Lyapunov–Krasovskii functional (LKF) in the framework of an input delay method. Compared with existing works, the new LKF makes full use of the information on the nonlinear part of the system and introduces a novel term, which waives the common positive requirement of each LKF term to guarantee the positive of the whole LKF. A typical Chua’s circuit is given to verify the effectiveness of the proposed method.     

1-Butene isomerization and metathesis over Mo/mordenite-alumina: Factors influencing product distribution and induction period

Effects of space velocity, reaction temperature and support acidity on product distribution and induction period in 1-butene isomerization and metathesis over Mo/mordenite-alumina were investigated. As revealed by the catalytic performance results, induction period and objective product were closely related to the reaction conditions. Lower space velocity led to longer induction period and higher propene yield. The optimal reaction temperature for propene production is around 150 °C and it shifted to 100 °C for ethene production. 1-Butene auto-metathesis predominated in the reaction network if the support with lower degree of sodium exchanged. And propene gradually became the dominant product upon increasing the support sodium exchange degree. 6Mo/H₁₀₀Na₀M-30Al catalyst with a support of full sodium exchange degree exhibited the highest propene yield.     

单摆作谐振动的最大摆角的分析

本文根据实验上的微小偏差准则和试验中的最小可分辨时间来确定单摆作谐振动时的最大摆角     

三线摆周期的旋转矢量求法

由能量方程出发，引入新变量，用旋转矢量法讨论了三线摆大角度摆动时的周期。     

A discrete-time retrial queueing model with one server

This paper presents a one-server queueing model with retrials in discrete-time. The number of primary jobs arriving in a time slot follows a general probability distribution and the different numbers of primary arrivals in consecutive time slots are mutually independent. Each job requires from the server a generally distributed number of slots for its service, and the service times of the different jobs are independent. Jobs arriving in a slot can start their service only at the beginning of the next slot. When upon arrival jobs find the server busy all incoming jobs are sent into orbit. When upon arrival in a slot jobs find the server idle, then one of the incoming jobs (randomly chosen) in that slot starts its service at the beginning of the next slot, whereas the other incoming jobs in that slot, if any, are sent into orbit. During each slot jobs in the orbit try to re-enter the system individually, independent of each other, with a given retrial probability.     

Busy period analysis for <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">PH</Emphasis>/1 queues with workload dependent balking

We consider an M/PH/1 queue with workload-dependent balking. An arriving customer joins the queue and stays until served if and only if the system workload is no more than a fixed level at the time of his arrival. We begin by considering a fluid model where the buffer content changes at a rate determined by an external stochastic process with finite state space. We derive systems of first-order linear differential equations for the mean and LST (Laplace-Stieltjes Transform) of the busy period in this model and solve them explicitly. We obtain the mean and LST of the busy period in the M/PH/1 queue with workload-dependent balking as a special limiting case of this fluid model. We illustrate the results with numerical examples.      

Analysis of period and visibility of dual phase grating interferometer

Dual phase grating interferometer may simultaneously achieve large field of view and high x-ray dose efficiency. Here, we develop a simple theoretical method to better understand the imaging process of the dual phase grating interferometer. The derivation process of fringe period and the optimal visibility conditions of the dual phase grating interferometer are given in detail. Then, we theoretically prove that the fringe period and optimal visibility conditions of the dual phase grating interferometer include that of the Talbot interferometer. By comparing our experimental results with those of other researchers, we find that when the positions of phase gratings are far away from the positions where the fringe visibility is optimal, the fringe period of the dual π -phase grating interferometer is twice the theoretical results under the illumination of polychromatic x-ray. This conclusion may explain the contradictory research results of dual phase grating interferometer among different researchers.