On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Operation of the quasi-optical gyrotron at harmonics of the gyrofrequency

This paper investigates the performance of a quasioptical gyrotron, when the electron beam interacts with the radiation fields at harmonics of the gyrofrequency. The nonlinear equations of motion are obtained in the slow-timescale. The expression for the linear gain is derived and the conditions for excitation are given (frequency threshold, optimal operating point, bean current and resonator quality thresholds). In the nonlinear regime, it is shown that maximum efficiencies comparable to those at the fundemental (50%) are possible, albeit at a prohitively high radiation field amplitude, while realistically feasible field amplitudes can give somewhat smaller, but nevertheless still high efficiencies (15%). Finally, the results are suplemented by empirical scaling laws, useful for experimental designs.     

关于污染线性回归模型参数估计的注记

文[1] 、[2] 研究了简单回归模型中响应变量受到另一随机变量序列污染时，模型参数和污染系数的估计方法，但在 利用误差的不同阶矩估计给出污染系数的估计时发生了错误。我们证明了这种方法是行不通的。     

纳米磁性颗粒小点阵体系的动力学响应

通过数值解Landau Lifshitz Gilbert(LLG)方程,来研究一个具有垂直各向异性的N×N平方点阵结构的单畴铁磁颗粒体系的动力学响应.由于磁性颗粒间的偶极相互作用,我们发现存在三种不同的典型磁矩构形分布.这些构形由磁晶各向异性和磁偶相互作用之间的竞争所决定.磁性粒子的点阵几何构形是影响磁矩翻转的重要因素,偶极相互作用的增强,引起不同位置的颗粒磁矩发生先后顺序的翻转.当初态所有颗粒磁矩都平行于 z方向,且颗粒间的偶极相互作用不足以使磁矩发生耦合翻转,反转某个磁矩所需的最小翻转场将比反转单个(即无偶极相互作用)磁矩时所需的最小翻转场小得多.该种效应随着颗粒间距的增加,将明显地减弱,最小翻转场很快地增加且趋于反转单个磁矩时所需的最小翻转场.当所有颗粒磁矩处于各种不同初态时,弱偶极相互作用加宽了翻转场的取值范围.     

低频弯张换能器指向性数值计算及实验测试

应用亥姆霍兹积分方程与有限元方法，建立了换能器在水中的振动方程，导出了换能器辐射声场指向性公式．实验结果表明，在谐振频率1．16kHz处，换能器水平面上的辐射指向性呈现各向均匀分布的特点，这与理论计算结果一致．     

筏形基础一地基共同作用非线性数值分析

结合大型有限元软件ANSYS，建立了筏形基础一地基相互作用体系的全三维有限元模型．考虑土体的弹塑性性质，模拟基础和地基交界面上的状态非线性，采用中厚板理论分析筏板，对筏形基础的受力进行了非线性数值分析．结果表明，考虑地基非线性特性时，地基反力及基础沉降的计算结果更接近实际．     

基于OEM的网站用户访问历史模型

基于适合半结构Web数据分析的OEM模型 ,对用户和网站交互进行了形式化定义 ,在此基础上提出基于OEM模型的网站用户访问历史模型 ,同时给出分析用户访问行为的指标定义 ,为进一步分析用户访问行为模式、优化网站结构以及展开个性化服务提供较强的支持     

C_0-半群的脉冲扰动与一类半线性脉冲发展方程(英文)

研究无限维Banach空间中一半群的脉冲扰动及一类非线性脉冲系统的温和解的存在性、唯一性、正则性和连续依赖性,最后给出例子加以说明。     

基于网络的多媒体课件的交互设计与实现

基于网络的多媒体课件必须具备交互性的特点，以实现学生与计算机、教师与学生的交互功能，探讨了课件人机交互、教学交互的几种交互方式的设计思路和制作方法，并阐述了基于WEB的B／S模式体系结构的课件设计技术。