任意阶显式精细积分多步法的常用形式及其高阶次数值计算

基于任意阶显式精细积分多步法的一般公式，给出其几种常用形式，并实现了高阶次数值计算，将新算法应用于射线方程和双原子系统经典轨迹数值计算中．数值计算结果表明任意阶显式精细积分多步法是一种高精度、高效率、稳定性较好的方法，并且可方便地进行高阶次的运算．     

卷积积分与三要素法在电路分析中的应用

一阶电路在任意激励下的零状态响应，既可以用卷积积分法，也可以用三要素法进行分析与计算，本文通过对具体电路的计算，以阐明这两种方法的特点。     

卷积积分与三要素法在电路分析中的应用

一阶电路在任意激励下的零状态响应，既可以用卷积积分法，也可以用三要素法进行分析与计算．本文通过对具体电路的计算，以阐明这两种方法的特点．     

任意四边形网格上解辐射输运方程的一种数值方法

解二维辐射输运问题时，对于矩形网格，用Sn菱形(diamond)格式处理十分简单有效，但该格式不能直接用于非矩形网格，而辐射流体力学计算往往要求在非矩形网格上进行．本文讨论任意四边形网格的辐射输运数值方法，给出一种全正的子网格平衡计算格式，并进行数值计算，与矩形网格Sn菱形格式结果比较，得出本方法可行性结论。     

非线性系统的任意项精细积分外插多步法及其在混沌数值分析中的应用

对非线性系统提出了高精度的精细积分任意项外插多步法的计算公式.本方法只需增加插值 项数即可提高计算精度，同时不会增加过大的计算量，发展完善了精细积分法.将本方法应 用于混沌方程中，取得了较好的效果.数值计算结果表明，该方法是一种高精度、高效率的 方法，在求解混沌系统上比传统方法有很大的优势. 关键词： 非线性系统 任意项精细积分多步法 混沌系统     

矩形槽光栅矢量模式理论的数值计算

本文根据矩形槽光栅的矢量模式理论进行了数值计算。对于任意入射方向及任意偏振态的入射场，计算了其衍射效率和偏振特性变化，并详细研究了光栅结构参数（周期、槽宽、槽深等）对衍射场的影响。     

正,负电子被原子散射的光学势方法—e^±—Na散射总截面的计算

将原子核散射理论中的光学势方法应用于正、负电子被原子散射的计算，提出了不含任意参数的光学势以及由此确定散射矩阵元的方法，计算了低能（≤５０ｅＶ）正、负电子被Ｎａ散射的总截面并与实验结果进行了比较。     

正、负电子被原子散射的光学势方法──e~±－Na散射总截面的计算

将原子核散射理论中的光学势方法应用于正、负电子被原子散射的计算，提出了不含任意参数的光学势以及由此确定散射矩阵元的方法，计算了低能（≤５０ｅＶ）正、负电子被Ｎａ散射的总截面并与实验结果进行了比较。     

小尺度阻尼边界封闭空间声传递函数的有限元素法计算

如何求解阻尼边界封闭空间中声源点到接收点的低频声传递函数已成为目前小尺度封闭空间可听化技术研究的关键技术，能处理任意形状及复杂边界条件的有限元素法可作为求解该问题的适合方法，以室内声声有源Helmholtz方程及其相应边界方程为基础，本文推导出了用于小尺度阻尼边界封闭空间声传递函数的有限元素求解方法，并编制了相应的计算机程序，在算例中，首先通过与模态叠加法计算结果进行比较，验证了该方法的正确性。最后计算了某型车体内腔中任意两点间声传递函数。     

变焦距镜头高斯光学设计的新方法

突破了对像面漂移量的有理函数计算传统，考虑到组元运动曲线的间断性，给出了变焦距镜头高斯光学全新的最优化设计方法，供助于切比雪夫多项式，做到了任意组元联合直线运行的光学补偿，以及实现了简便的和有效的任意组元任意变焦方式的机械补偿。     

Bargmann–Wigner方程与高自旋场方程

在坐标表象中由Bargmann-Wigner方程导出了便于求解的高自旋场方程,并给出了相应的拉氏函数.     

Scattering Characteristics of Dielectric Periodic Structure Composed of Left-handed Materials with Arbitrary Oblique Incidence

Scattering characteristics of monolayer and multilayer dielectric periodic structure composed of left-handed materials (LH-DPS) with plane wave arbitrary oblique incidence are carefully analyzed using a method which combines multimode network theory with the rigorous mode matching method. Our analysis results reveal that the arbitrary oblique incident angles and relative position between different LH-DPS have great effects to the scattering characteristics of LH-DPS which different from the situation of dielectric periodic structure composed of right-handed materials (RH-DPS). The reasons why the reflection characteristics of the LH-DPS are totally different from those of the RH-DPS with arbitrary oblique incidence are also given. The present quantitive investigation provides guidelines for the design of the monolayer and multilayer dielectric frequency selective surfaces for millimeter wave applications.     

Torsional vibration of multi-step non-uniform rods with various concentrated elements

An analytical approach and exact solutions for the torsional vibration of a multi-step non-uniform rod carrying an arbitrary number of concentrated elements such as rigid disks and with classical or non-classical boundary conditions is presented. The exact solutions for the free torsional vibration of non-uniform rods whose variations of cross-section are described by exponential functions and power functions are obtained. Then, the exact solutions for more general cases, non-uniform rods with arbitrary cross-section, are derived for the first time. In order to simplify the analysis for the title problem, the fundamental solutions and recurrence formulas are developed. The advantage of the proposed method is that the resulting frequency equation for torsional vibration of multi-step non-uniform rods with arbitrary number of concentrated elements can be conveniently determined from a homogeneous algebraic equation. As a consequence, the computational time required by the proposed method can be reduced significantly as compared with previously developed analytical procedures. A numerical example shows that the results obtained from the proposed method are in good agreement with those determined from the finite element method (FEM), but the proposed method takes less computational time than FEM, illustrating the present methods are efficient, convenient and accurate.     

基于光学全息的任意矢量光的生成方法

基于光学全息的角度复用特性, 根据空间光调制器对光场的相位和振幅调制原理, 通过加载产生任意矢量光所需要的相位分布, 设计了一种生成任意矢量光的方法. 该方法首先利用光学全息技术记录空间光调制器加载的相位, 从而制作一个全息光栅; 再现过程中, 两束具有相同入射角度的参考光照射全息光栅, 使得两束再现光相干叠加, 进而获得可调控的任意矢量光. 该方法能够避免复杂偏振态的出现, 并且具有生成光路简单、方便操作、生成矢量光的偏振纯度高等优势. 通过计算机模拟生成了任意矢量光, 获得了很好的效果.     

变系数KdV方程和变系数MKdV方程的无穷多守恒律

本文利用Miura方法研究具有三个任意函数的变系数KdV方程和变系数MKdV方程的无穷多守恒律,结果表明:守恒密度仅与一个任意函数有关,并且与常系数KdV(和MKdV)方程的守恒密度有完全类似的结构,另两个任意函数仅包含于相应的流密度中。 关键词：     

Exact calculations and a fermion pair description of the s-bosons used in the interacting boson approximation

A convenient method is proposed for exact calculations using wave functions that are products of correlated fermion pairs coupled to zero angular momentum. The method is valid for arbitrary forces and arbitrary single-particle energies. The exact results are compared to various approximations and are used to generate an equivalent s-boson Hamiltonian.     

Vibration analysis of plates of arbitrary shape—A new approach

The so-called finite strip method combined with the deflection contour method has proved highly successful in the analysis of bending of thin elastic plates of arbitrary shape. Here the same technique is used to obtain the fundamental frequency of plates of arbitrary shape. The method of approach is much simpler than the conventional finite element method since it requires less programming effort and a reduction in both memory space and time on the computer. Several representative plate problems of irregular boundaries are treated by the proposed method. For all cases, comparison of the results are made with other known solutions and the agreement appears to be excellent.     

Designing and fabricating diffractive optical elements with a complex profile by interference

We demonstrate a novel (to our knowledge) method for the design and the fabrication of diffractive optical elements (DOEs) with an arbitrary complex phase profile based on interference. The DOEs are designed to modulate the complex light wave by the analytical formulas, and an asymmetric holographic DOE with cubic phase modulation is fabricated by a two-step exposure technique. The desired Airy beams are produced experimentally, which demonstrates the validity of this method. It is a simple approach with a low cost for the design and the fabrication of DOEs with a large area and arbitrary phase distribution.     

Arbitrary laser beam propagation in free space

The propagation of arbitrary laser beams in free space is examined. For this purpose, starting with an incident field of arbitrary field distribution, the intensity at the receiver plane is formulated via Huygens Fresnel diffraction integral. Arbitrary source field profile is produced by decomposing the source into incremental areas (pixels). The received field through the propagation in free space is found by superposing the contributions from all source incremental areas. The proposed method enables us to evaluate the received intensity originating from any type of source field. Using the arbitrary beam excitation, intensity of various laser beams such as cos-Gaussian, cosh-Gaussian, general type beams are checked to be consistent with the already existing results in literature, and the received intensity distributions are obtained for some original arbitrary beam field profiles. Our received intensity formulation for the arbitrary source field profiles presented in this paper can find application in optics communication links, reflection from rough surfaces, optical cryptography and optical imaging systems.     

Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps

A new approach to reconstructing the object wave front in phase-shifting interferometry with arbitrary unknown phase steps is proposed. With this method the actual phase steps are first determined from measured intensities with an algorithm based on the statistic property of the object phase distribution in the recording plane. Then the original object field is calculated digitally with a derived formula. This method is simple, accurate, and capable of retrieving the original object field, including its amplitude and phase distributions simultaneously, with arbitrary and unequal phase steps in a three- or four-frame method. The effectiveness and correctness of this approach are verified by a series of computer simulations for both smooth and diffusing surfaces.