一类常微分方程组周期解构造的耦合方法

本文通过建立一类常微分方程组的耦合泛函微分方程组，解决其周期解的构造问题．     

关于区间上的Lorenz映射

本文引进了变换ζ．首先，用比文［４］简捷的方法证明了Ｌｏｒｅｎｚ映射的Ｓａｒｋｏｖｓｋｉ定理并更正了文［４］中的一个错误，还得到了扩张的Ｌｏｒｅｎｚ映射中周期点的存在性与其扩张常数之间的关系．其次，证明了Ｌｏｒｅｎｚ映射与其在变换ζ的像具有相等的捏制行列式．此外，给出了广义的Ｌｏｒｅｎｚ映射的周期点的存在性适合Ｓａｒｋｏｖｓｋｉ序关系的一个充分条件     

The first report on the catalytic oxidation of urazoles to their corresponding triazolinediones via in situ catalytic generation of Br using periodic acid or oxone/KBr system

A combination of periodic acid or oxone^® and a catalytic amount of KBr in the presence of few drops of water, were used for the catalytic oxidation of urazoles and bis-urazoles to their corresponding triazolinediones under mild and heterogeneous conditions with moderate to excellent yields.     

Existence of nontrivial nonnegative periodic solutions for a class of doubly degenerate parabolic equation with nonlocal terms

In this paper, the authors establish the existence of nontrivial nonnegative periodic solutions for a class of doubly degenerate parabolic equation with nonlocal terms by using the theory of Leray-Schauder's degree.     

弱Silnikov现象中的全局分支问题

本文考虑在一条同宿于具一对纯虚特征值的鞍－焦点的轨道邻域内的分支问题，证明了在同宿分支值的邻域内，存在着可数无穷多个鞍结点分支值，倍周期分支值和２－脉冲同宿分支值，并且两相邻鞍结点分支值的比趋于常数１。     

Vector sampling expansions in shift invariant subspaces

Multi-input multi-output (MIMO) sampling scheme which is motivated by applications in multi-channel deconvolution and multi-source separation has been investigated in many aspects. Common for most of results on MIMO systems is that the input signals are supposed to be band-limited. In this paper, we study vector sampling expansions on general finitely generated shift-invariant subspaces. Necessary and sufficient conditions for a vector sampling theorem to hold are given. We also give several examples to illustrate the main result.     

Asymptotic stability of continuum sets of periodic solutions to systems with hysteresis

We consider hysteresis perturbations of a system of ODEs which possesses an asymptotically stable periodic solution z_∗. Where the oscillation of an appropriate projection of this periodic solution is smaller than some threshold number defined by the hysteresis nonlinearity, it is shown that the perturbed system has a continuum of periodic solutions with a rather simple structure in a vicinity of z_∗. The main result is a theorem on the stability of this continuum.     

一类非自治系统的周期解

利用矩阵测度的性质，通过对线性系统解的估计形式，得到了关于一类非自治系统周期解的存在唯一性定理．     

Analysis of a statistical multiplexer with generalized periodic sources

We provide solution techniques for the analysis of multiplexers with periodic arrival streams, which accurately account for the effects of active and idle periods and of gradual arrival. In the models considered in this paper, it is assumed that each source alternates (periodically) between active and idle periods of fixed durations. Incoming packets are transmitted on the network link and excess information is stored in the multiplexing buffer when the aggregate input rate exceeds the capacity of the link. We are interested in the probability distribution of the buffer content for a given network link speed as a function of the number of sources and their characteristics, i.e., rate and duration of idle and active periods. We derive this distribution from two models: discrete time and continuous time systems. Discrete time systems operate in a slotted fashion, with a slot defining the base unit for data generation and transmission. In particular, in each slot the link is capable of transmitting one data unit and conversely an active source generates one data unit in that time. The continuous time model of the paper falls in the category of fluid models. Compared to previous works we allow a more general model for the periodic packet arrival process of each source. In discrete time, this means that the active period of a source can now extend over several consecutive slots instead of a single slot as in previous models. In continuous time, packet arrivals are not required to be instantaneous, but rather the data generation process can now take place over the entire duration of the active period. In both cases, these generalizations allow us to account for the progressive arrival of source data as a function of both the source speed and the amount of data it generates in an active period.This work was done while at the IBM T.J. Watson Research Center.This work was done while at the IBM T.J. Watson Research Center.Part of the work was done while visiting the IBM T.J. Watson Research Center.     

快变量空间中的同宿轨道分支

本文考虑奇摄动问题的位于快变量空间中的奇异同宿轨道的保存和周期轨道分支问题.文中关于奇异同宿轨道保存的结论推广了一些已知的结果,而周期轨道产生于奇异同宿轨道的分支则提供了一种新的分支类型.