连续渐变周期的一维光子带隙结构全能反射器

采用转移矩阵法设计了一种具有连续渐变周期的一维光子带隙结构全能反射器,它在一般材料选取情况下(如TiO2/SiO2),在可见光区能达到几十甚至几百纳米量级的带隙宽度全向反射.研究表明,其带隙宽度随着周期数和渐变周期的大小改变而改变.当周期数不断增大时,带隙宽度不断增大;当渐变周期的大小在一定范围内不断增大时,带隙宽度同样不断增大.这主要是光波在各层之间的传播随着周期和渐变周期的大小不断增大而产生的相干散射和干涉效应不断增强所导致的.     

渐变周期弯曲光栅的衍射和成像特性

阐述了渐变周期弯曲光栅的原理,对其衍射特性和成像特性进行了分析,结果表明:渐变周期弯曲光栅具有分束和聚焦的双重作用;其对称衍射级起到焦距相等的正透镜和负透镜的作用;它可把不同景深的的物体聚焦成像于空间分离的同一焦面上.     

Nekrasov prepotential with fundamental matter from the quantum spin chain

Nekrasov functions were conjectured in Mironov and Morozov (2009) [1] to be related to exact Bohr-Sommerfeld periods of quantum integrable systems. This statement was thoroughly checked for the case of the pure SU(Nc) gauge theory in Mironov and Morozov (2009) [2] and Popolitov (2010) [3]. Here we successfully perform a set of checks in the case of gauge group SU(Nc) with additional Nf fundamental hypermultiplets. We show that the Baxter equation for the spin chain gives the same quantum periods as the one for the Gaudin system in this case.     

非线性接触率SIR模型脉冲接种策略研究

建立了具有非线性接触率脉冲预防接种的SIR传染病模型,利用脉冲微分方程理论,对模型的动力学性态进行了分析,给出了模型的阀值,证明了无病周期解的存在性及全局渐近稳定性.     

A theoretical study of the long-range-disorder mixed-spin antiferromagnet L2BaNiO5

In this paper, we introduce a quasi-one-dimensional S = 1 antiferromagnet Heisenberg model, and some physical properties of antiferromagnet L₂BaNiO₅ without antiferromagnet long-range-order above the Néel temperature are analyzed based on the frame of two-time Green’s function theory. In a high temperature region, we calculate the correlation functions, and obtain excitation spectrum along Ni chains and the Haldane gap in this spectrum versus temperature. We find that the short-range correlation still exists at high temperature, which leads to the existence of Haldane gap in excitation spectrum. The increment of excitation energy in the spectrum along the Ni chain is found to be induced by the AF interaction between spins of rare-earth and Ni ions. Additionally, we also find that Haldane gap goes up with temperature increasing.     

Queues with hysteretic control by vacation and post-vacation periods

The paper investigates the queueing process in stochastic systems with bulk input, batch state dependent service, server vacations, and three post-vacation disciplines. The policy of leaving and entering busy periods is hysteretic, meaning that, initially, the server leaves the system on multiple vacation trips whenever the queue falls below r (⩾1), and resumes service when during his absence the system replenishes to N or more customers upon one of his returns. During his vacation trips, the server can be called off on emergency, limiting his trips by a specified random variable (thereby encompassing several classes of vacation queues, such as ones with multiple and single vacations). If by then the queue has not reached another fixed threshold M (⩽ N), the server enters a so-called “post-vacation period” characterized by three different disciplines: waiting, or leaving on multiple vacation trips with or without emergency. For all three disciplines, the probability generating functions of the discrete and continuous time parameter queueing processes in the steady state are obtained in a closed analytic form. The author uses a semi-regenerative approach and enhances fluctuation techniques (from his previous studies) preceding the analysis of queueing systems. Various examples demonstrate and discuss the results obtained. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cusp Forms on GL(2n) with GL(n) × GL (n) Periods,and Simple Algebras

The notion of a period of a cusp form on GL(2,D(??)), with respect to the diagonal subgroup D(??)^X × D(??)^X, is defined. Here D is a simple algebra over a global field F with a ring ?? of adeles. For D^x = GL(1), the period is the value at 1/2 of the L-function of the cusp form on GL(2, ??). A cuspidal representation is called cyclic if it contains a cusp form with a non zero period. It is investigated whether the notion of cyclicity is preserved under the Deligne - Kazhdan correspondence, relating cuspidal representations on the group and its split form, where D is a matrix algebra. A local analogue is studied too, using the global technique. The method is based on a new bi-period summation formula. Local multiplicity one statements for spherical distributions, and non - vanishing properties of bi - characters, known only in a few cases, play a key role.     

Second-Order Tail Behavior of the Busy Period Distribution of Certain GI/G/1 Queues

We consider the stable GI/G/1 queue in which the service time distribution has a dominated-varying tail. Under simple assumptions, we obtain the first- and second-order tail behavior of the busy period distribution in this queue.     

A nonparametric procedure to detect periods in time series

Suppose that for a given time series the experimenter knows that it has a certain periodic property and that he wishes to find out the length of the period. For this problem a nonparametric procedure is proposed. It consists of a new smoothing technique based on Kendall's Tau and a specific counting method. The procedure is studied under a simple model of periodic time series which are composed of periodic (deterministic) functions, a linear trend and exchangeable (stochastic) sequences. The performance of the procedure is illustrated by a simple example.