图形显示中的几何变换

本文主要获得了以下结果：（ｉ）透视仿射映射的矩阵表示；（２）透视仿射变换的矩阵表示；（３）一般仿射映射的几何中实现及矩阵表示；（４）一般仿射变换的几何实现及矩阵表示。     

光学元件兆声辅助化学刻蚀工艺参数优化

对传统的静态刻蚀方法进行了改进,提出了一种光学元件兆声辅助化学刻蚀新方法,并对传统静态刻蚀与兆声辅助化学刻蚀效果进行了对比分析,综合考虑刻蚀液的配比、刻蚀时间、添加活性剂种类和功率对光学元件激光损伤阈值的影响,通过正交设计实验优选出最佳的兆声辅助化学刻蚀工艺参数。结果表明：兆声清洗对各类杂质的去除效果要明显好于手工擦洗,兆声辅助化学刻蚀比传统的静态刻蚀有更高的刻蚀速率,在兆声的作用下刻蚀液能够进入到传统静态刻蚀难以进入的微裂纹中,对微裂纹等缺陷的刻蚀效果更为明显,能够将熔石英元件激光损伤阈值进一步提高。     

二阶线性矩阵微分系统的振动性

本文研究了矩阵微分系统（P（t）Y′）′＋Q（t）Y＝0，t∈［t0，∞）．其中P，Q和Y是n×n实连续矩阵函数，且P（t）和Q（t）是对称的．P（t）是正定矩阵（P（t）＞0，t∈［t0，∞））．利用推广的Riccati变换，得到了系统（1）振动的若干新判据．所得结果改进了Erbe，Kong和Ruan的相应结果．     

A deflation method for regular matrix pencils

A generalization of the concept of eigenvalue is introduced for a matrix pencil and it is called eigenpencil; an eigenpencil is a pencil itself and it contains part of the spectral information of the matrix pencil. A Wielandt type deflation procedure for regular matrix pencils is developed, using eigenpencils and supposing that they can have both finite and infinite eigenvalues. A numerical example illustrates the proposed method.     

Matrix-Based Analytical Model of Critical Coupling Length of Titanium In-Diffused Integrated-Optic Directional Coupler on Lithium Niobate Substrate

The critical coupling length Lc is the most important design parameter of an integrated-optic directional coupler, which is the basic building block of a variety of optical integrated circuits. The existing methods of estimating Lc of a Ti in-diffused waveguide directional coupler on LiNbO3 substrate are based on the beam propaga tion method (BPM), which requires huge computing time. A considerably simpler and computationally faster analytical method involving only multiplication of 2 x 2 matrices with no iterations is described in this article. A staircase type step-index profile is generated from the one-dimensional effective index profile in the lateral direction by partitioning the latter into a large number of thin sections of different refractive indices. The overall transfer matrix of the step-index layered structure so obtained may be computed by the progressive multiplication of individual transfer matrices (2 x 2) relating the field components in adjacent layers. Hence the wave amplitude in any layer may be computed as a function of the input wave amplitude for different angles of incidence. This method has been successfully employed to compute the propagation constants for symmetric and asymmetric guided modes in the coupled region of the directional coupler and hence compute the coupling length. The values of Lc computed for a variety of devices agree closely with the published experimental results reported by several research groups. The computer program implementing the model runs reasonably fast in an ordinary PC and is versatile enough to consider arbitrary waveguide dimensions. Ti film thickness, and diffusion parameters for any wavelength of input light and for both transverse electric and transverse magnetic polarizations.     

最弱受约束电子势模型中束缚-自由非相对论跃迁矩阵元的计算公式

研究最弱受约束电子势模型的散射态，获得了精确的按“ｋ／２π标度”归一化的散射态波函数以及相移表达式，给出了束缚—自由非相对论跃迁矩阵元的解析计算公式。这些结果可广泛应用于处理原子的散射问题之中。     

采用激光诱导击穿光谱技术测定合金钢中锰和硅的含量

基于激光诱导击穿光谱(LIBS)技术定量分析多品种合金钢中锰(Mn)和硅(Si)的浓度,采用的校正方法为多元二次非线性函数定标方法。分析的钢种有普通合金钢、不锈钢、碳素工具钢等。由于不同钢种在基体组成上存在较大差异,而且钢的光谱还存在复杂的谱线重叠干扰,所以受基体效应影响严重。因此,对钢这类复杂化学体系物质的定量分析,若采用单谱线信息的校正方法会造成很多有用信息的丢失,而采用多变量的定标法会更充分利用光谱中的信息,更有效校正多基体组分的基体效应,进而提高LIBS定量分析的重复性和准确性。相比线性标准定标曲线法,测量结果的相对标准差从20%以上降低到10%以下,Mn元素测量结果的准确度提高了5倍多,Si元素提高了6倍多。     

Chaos‐related Localization in Modulated Lattice Array

This paper will discuss the chaos‐related localization in a lattice array with an external periodical field acted on a boundary site that allows us to realize the controllable chaotic dynamics with a tunable driving frequency. Two types of chaos‐related localization, short‐term and long‐term localization, which are closely related to the degree of chaos are reported and may provide a way to realize switching from chaos‐related localization to chaos‐assisted tunneling. Interestingly, with the increase of nonlinearity, driving frequency or even second‐order coupling, there always exists a parameter window with sharp edges for long‐term localization which facilitates us to find the thresholds to control the system into or out of localization region. In addition, the numerical results further demonstrate that the initial phase of the driving field may greatly influence the degree of the chaos. These results can be extended to finite driven N‐site system and may deepen our understanding of chaos‐related localization in nonlinear driving system.     

Morphology and magnetic properties of CeCo5 submicron flakes prepared by surfactant-assisted high-energy ball milling

CeCo₅ permanent magnetic alloy has been processed by surfactant assisted high energy ball milling. Heptane and oleic acid were used as the solvent and surfactant, respectively. The amount of surfactant used was 50% by weight of the starting powder. The produced particles were deposited on a piece of copper (4 mm in length and width) under a magnetic field of 27 kOe applied along the copper surface and immobilized by ethyl α-cyanoacrylate. Scanning electron microscope pictures show that the particles are flakes, several μm in length and width and tens of nm in thickness. X-ray diffraction patterns and magnetic measurements prove that the flakes are crystalline with c-axes magnetic anisotropy. The easy magnetization axis is oriented perpendicular to the surface of the flake. A maximum coercivity of 3.3 kOe was obtained for the sample milled for 40 min.