ON DIFFERENCE EQUATIONS RELATING TO GAMMA FUNCTION

We consider the existence, the growth, poles, zeros, fixed points and the Borel exceptional value of solutions for the following difference equations relating to Gamma function y(z + 1) -y(z) = R(z) and y(z + 1) = P (z)y(z).     

(渐近)非扩张映象的不动点的迭代逼近

Let E be a uniformly convex Banach space which satisfies Opial‘s condition or has aFrechet differentiable norm,and C be a bounded closed convex subset of E. If T： C→C is(asymptotically)nonexpansive,then the modified Ishikawa iteration process defined by     

Three-Step Iterative Sequences with Errors for Uniformly Quasi-Lipschitzian Mappings

The purpose of this paper is to investigate some sufficient and necessary conditions for three-step Ishikawa iterative sequences with error terms for uniformly quasi-Lipschitzian mappings to converge to fixed points. Our results extend and improve the recent ones announced by Liu [3,4], Xu and Noor [5], and many others.     

Limit Cycles near Stationary Points in the Lorenz System

The limit cycles in the Lorenz system near the stationary points are analysed numerically. A plane in phase space of the linear Lorenz system is used to locate suitable initial points of trajectories near the limit cycles. The numerical results show a stable and an unstable limit cycle near the stationary point. The stable limit cycle is smaller than the unstable one and has not been previously reported in the literature. In addition, all the limit cycles in the Lorenz system are theoreticallv Proven not to be planar.     

基于大口径高温固定点黑体的光谱辐射照度国家基准量值复现新方法

采用国际前沿的大口径高温固定点黑体新技术,中国计量科学研究院NIM(National Institute of Metrology)组建了大口径钨碳-碳WC-C高温固定点黑体辐射源,在3 020.11 K的融化点温度,实现了250～2 500 nm光谱辐射照度、相关色温和分布温度基准的量值复现。这是国际上首次将大口径高温固定点黑体技术成功应用于光谱辐射度基准复现领域。针对大口径固定点黑体熔化温坪曲线的特点、以及测量期间温坪曲线中间部分缺失的问题,提出了固定点熔化温坪拐点温度计算新方法,重构了缺失的熔化温坪曲线。采用光谱比较法,通过双光栅光谱比较测量系统将黑体的量值传递至光谱辐射照度副基准灯组,完成光谱辐射照度基准量值的复现和保存。新的量值复现方法将黑体温度的测量不确定度减小为0.36 K,缩短了量传链,实现光谱辐射照度最佳测量不确定度0.25%(k=2)。在250～2 500 nm,基于固定点新方法和传统变温黑体法进行量值复现的平均偏差为0.42%,将两种方法相结合,最终实现我国光谱辐射照度基准的测量不确定度(k=2)为：250～400 nm,U_rel=1.9%～...     

一种含放大机构的负刚度动力吸振器的参数优化

在大多数情况下机械振动是有害的,它不仅产生噪声还会降低设备的工作精度和使用寿命.采用正刚度特性的吸振、隔振系统往往难以达到满意效果,这种情况在低频振动控制系统中尤其明显.放大机构与负刚度元件在振动控制领域均表现出良好性能,但是较少有对同时含有放大机构与负刚度装置的动力吸振系统的研究.以Voigt型动力吸振器为基础提出了一种将放大机构应用于含负刚度弹簧元件的动力吸振器模型,对该模型的最优参数进行了研究.首先建立了系统的运动微分方程并得到了其解析解,发现该系统存在两个固定点,利用固定点理论得到了动力吸振器的最优频率比.根据负刚度的特性,在保证系统稳定的前提下得到了最优负刚度比,并推导了系统的近似最优阻尼比.通过数值仿真验证了解析解的正确性.与多种动力吸振器在简谐激励与随机激励下进行了对比,说明了本文模型相比于已有的动力吸振器,能够大幅降低共振振幅、拓宽减振频带并且降低系统的谐振频率,为设计新型动力吸振器模型提供了理论依据.      

Travelling Wave Solutions in Delayed Reaction Diffusion Systems with Partial Monotonicity

This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of ＂desirable pair of upper-lower solutions＂, through which a subset can be constructed. We then apply the Schauder＇s fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.     

MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.