非线性椭圆方程自由边值问题球对称解的存在性

给出了如下的非线性椭圆方程自由边值问题-Δu=λu+(1+ε)u+p,x∈B Rn,u|Ω=μ,∫Ωnu=-M(1)在C[0,1]中的球对称解的存在性.并得到比上述问题更一般的非线性椭圆方程自由边值问题-Δu=h(u),x∈B Rn,u|Ω=μ,∫Ωun=-M,在C[0,1]中的球对称解的存在性,其中B为Rn中的单位球,p>1,λ>0,μ<0,M>0,ε>0;λ,μ,M,ε均为常数,n为正整数.     

脉冲微分方程的上、下解及其在常微分方程上的应用

In this paper, we establish the existence of upper and lower solutions for a periodic boundary value problems (PBVP for short) of impulsive differential equations. which guarantees the existence of at least one solution for the problem. As an application, these results are applied to PBVP of ODE and some examples are given to illustrate our results.     

半连续格的性质

讨论了半连续格的一些基本性质。定义了一种新的元素——-素元,举例说明-素元与素元、伪素元是不同的,并给出了-素元与素元、伪素元相等的条件;同时,定义了半连续格上的拓扑和半连续格之间的映射,并证明了半连续格的收缩仍是半连续的。     

拟线性椭圆变分不等式的障碍最优控制问题

对拟线性椭圆变分不等式的障碍最优控制问题(即以障碍为控制变量)进行了研究．指标泛函为Lagrange型,其中含有控制变量二阶导数的p次幂,这使得最优性条件的推导颇为不易．对所考虑的问题给出了最优控制的存在性定理以及必要条件．     

三阶泛函微分方程的周期解的存在性

本文利用重合度理论研究了一类三阶泛函微分方程方程的2π-周期解的问题,获得了该方程存在2π-周期解的若干新结论,改进推广了有关文献中的已有结果．     

QUATERNION GENERALIZED SINGULAR VALUE DECOMPOSITION AND ITS APPLICATIONS

This paper derives a theorem of generalized singular value decomposition of quaternion matrices （QGSVD）,studies the solution of general quaternion matrix equation AXB -CYD= E,and obtains quaternionic Roth＇s theorem. This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.     

Mackey Theory for p-adic Lie Groups

This paper gives a p-adic analogue of the Mackey theory, which relates representations of a group of type G - H × t A to systems of imprimitivity.     

Gain Characteristics of Er^3＋-Doped Phosphate Glass Fibres

An erbium-doped phosphate glass fibre has been drawn by the rod-in-tube technique in our laboratory. The gain for the Er^3＋-doped phosphate glass fibre with different pump powers and with different input signal wavelengths is investigated. The 2.2-cm-long fibre, pumped by a single-mode 980-nm fibre-pigtailed laser diode, can provide a net gain per unit length greater than 1.SdB/cm. The pump threshold is about 50mW at the wavelength of 1534nm, and below 70roW at 1550nm. The gain linewidth of the Er^3＋-doped phosphate glass fibre is greater than 34 nm and can cover the C band in optical communication networks.     

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper,we will establish several strong convergence theorems for the approximation ofcommon fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banachspaces using the modiied implicit iteration sequence with errors,and prove the necessary and sufficient conditionsfor the convergence of the sequence.Our results generalize,extend and improve the recent work,in thistopic.     

一种“类耗散系统”中的“类Ⅴ型阵发”

一类不连续不可逆保面积映象可以展示类似耗散的行为,因此可称其为“类耗散系统”.在一种类耗散系统中观察到了椭圆周期轨道及其周围的椭圆岛与映象不连续边界碰撞而消失的现象.周期轨道消失后,经过一系列过渡椭圆周期轨道之后,系统的行为由一个混沌类吸引子主导.在混沌类吸引子刚刚出现时,混沌时间序列呈现层流相与湍流相的无规交替.这一切都与不连续耗散系统中发生的Ⅴ型阵发的相应性质十分相似,因此可称为“类Ⅴ型阵发”.然而,当混沌类吸引子刚刚出现时,仅可以找到最后一个过渡椭圆岛的“遗迹”,并不存在它的“鬼魂”,因此类Ⅴ型阵发不遵从Ⅴ型阵发的特征标度规律.反之,混沌类吸引子的鬼魂却存在于最后一个过渡椭圆周期轨道的类瞬态过程中,因此在类Ⅴ型阵发导致混沌运动的临界点之前,由此“类瞬态混沌奇异集”中逃逸的规律就成为标志这一种临界现象的标度律.这与Ⅴ型阵发又根本不同. 关键词： 类耗散性 类混沌吸引子 类Ⅴ型阵发