一类二阶三点边值问题单调正解的存在性

利用范数形式的锥上不动点定理,研究了一类二阶微分方程三点边值问题单调正解的存在性．分别给出了齐次和非齐次边界条件下的三点边值问题单调正解存在的充分条件,确定了解曲线的凹凸性,并且给出了一个应用实例．     

方程f(x)=P-x与f-1(x)=P-x的两根之和一定为P吗

常见题目:①设方程10x=p-x的根为x1,方程lgx=p-x的根为x2,则x1 x2=p;②设方程x3=p-x的根为x1,方程3x=p-x的根为x2,则x1 x2=p.可以用数形结合法或函数的单调性证明,此略.我们类比猜想:方程f(x)=p-x与f-1(x)=p-x的两根之和一定为p(p为实常数)吗?经过探究发现,此结论不一定成立.一     

一类两点边值问题的多重非负解

该文考虑两点边值问题[1/q(t)][q(t)y′(t)]′+p(t)f(y(t))= 0,λ_1 y(α)-λ_2y′(α)=0 and y(β)=B非负解的存在性, 其中p(t)可能在t=α或t=β附近具有奇异性, f(0)≥0, lim_(y→+∞)f(y)/y=+∞, 并且存在y>0, 使得f(y)<0.      

Quantum State Transfer between Two Distant Atoms by Connecting Two Cavities via Optical Fibres

A scheme is proposed to unconditionally implement state transfer between two distant atoms by sending the atoms across two distant cavities connected via an optical fibre, respectively. The field state, which preserves the information about the first atom, is transmitted from one cavity to the other along the fibre. A Faraday rotator integrated in the fibre can be designed to completely stop the fields reflected from the second cavity, thus after the field interacts with the second atom for a defined time, the state transfer can be accomplished with unit efficiency.     

色彩校正方法及应用

介绍了色彩校正的几种基本方法、不同模式之间转换的计算方法及色彩管理的应用.将这些方法运用到计算机的输入、输出及显示器的色彩校正中,使色彩通过三种物理设备之间的转换后还原再现,达到色彩保真的效果.     

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.     

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．     

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.