利用杨辉三角形对称性推导高阶运动微分方程

利用Mathematica数学软件计算函数r=r(q(t),t)各变量之间偏导和高阶导数的关系，发现具有杨辉三角形对称性.结合杨辉三角形的对称性规律和牛顿第二定律推导出了高阶运动微分方程，并讨论了理想约束系统下的高阶运动微分方程. 关键词： 杨辉三角形 牛顿第二定律 高阶运动微分方程 高阶力变率 高阶速度能量 理想约束     

Pump–probe second harmonic generation study of ultrafast spin dynamics in semiconductor multilayers

We report the first application of pump–probe second harmonic generation (SHG) measurements to characterize optically induced magnetization in non‐magnetic multilayer semiconductors. In the experiment, spin‐polarized electrons are excited selectively by a pump beam in the GaAs layer of GaAs/GaSb/InAs structures. However, the resulting net magnetization manifests itself through the induced SHG probe signal from the GaSb/InAs interface, thus indicating a spin‐polarized electron transport across the heterostructure. We find that the magnetization dynamics are governed by an interplay between the spin density evolution at the interfaces and the spin relaxation. Copyright © 2003 John Wiley & Sons, Ltd.     

OSCILLATION RESULTS FOR A SECOND ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.     

强流四脉冲电子束源实验研究

 为了进行强流多电子束源研究，对现有2MeV LIA 注入器进行了四脉冲改造，二极管脉冲电压约500kV。实验研究了天鹅绒阴极在四脉冲条件下的发射能力、传导电流负载效应以及阴极等离子体运动对阴极电子发射和束能量的影响。利用空间电荷限制流模型推算出阴极等离子体膨胀速率在1 ~4cm/μs之间。     

Low‐gain adaptive stabilization of semilinear second‐order hyperbolic systems

In this paper low‐gain adaptive stabilization of undamped semilinear second‐order hyperbolic systems is considered in the case where the input and output operators are collocated. The linearized systems have an infinite number of poles and zeros on the imaginary axis. The adaptive stabilizer is constructed by a low‐gain adaptive velocity feedback. The closed‐loop system is governed by a non‐linear evolution equation. First, the well‐posedness of the closed‐loop system is shown. Next, an energy‐like function and a multiplier function are introduced and the exponential stability of the closed‐loop system is analysed. Some examples are given to illustrate the theory. Copyright © 2004 John Wiley & Sons, Ltd.     

一类二阶椭圆型微分方程振动性的判定

利用积分平均和完全平方技巧，给出了一类二阶椭圆型微分方程所有解在R^n的一个外区域Ω上均振动的新的充分条件。     

LB膜混合聚集体中极性基团相互作用对光学非线性的影响

通过紫外－可见吸收光谱、压力－面积等温线、二次谐波的测量，研究了不同活性分子混合聚集体的形成对ＬＢ膜光学性质的影响。分子极性基团间的相互作用，使激发态能量及平均偶极矩发生变化，导致ＬＢ膜的光学非线性明显地增强或减弱。     

1.5μm波段基于级联二阶非线性的铌酸锂光波导全光波长变换的理论分析

研究了基于级联二阶非线性的铌酸锂波导全光波长变换器的特性.首先从耦合模方程出发,比较了数值分析结果与小信号近似分析的结果.其次在数值分析基础上,分析了铌酸锂晶体的温度变化导致相应基频光波波长与极化反转光栅周期的变化关系.最后分析了在不同相互作用长度下,转换的光波功率与有效基频光波波长带宽、温度调谐带宽、极化反转光栅周期带宽等关系,以对全光波长变换器件进行优化设计 关键词： 级联二阶非线性 波长变换 准位相匹配 铌酸锂光波导     

用三个关系式与Mathematica软件求第二类自然数幂和公式

首先介绍三个第二类自然数幂和关系式并对其中的两式给出证明,接着利用这些关系式与数学软件M athem atica4.0,给出求解第二类自然数幂和公式的若干机械计算方法.     

Second order parabolic equations in Banach spaces with dynamic boundary conditions

In this paper, we exhibit a unified treatment of the mixed initial boundary value problem for second order (in time) parabolic linear differential equations in Banach spaces, whose boundary conditions are of a dynamical nature. Results regarding existence, uniqueness, continuous dependence (on initial data) and regularity of classical and strict solutions are established. Moreover, several examples are given as samples for possible applications.