Internal fundamental sequences and approximative retracts

We introduce the notion of internal fundamental sequence and prove that any shape morphism from an arbitrary compactum X to an internally movable compactum Y is induced by an internal fundamental sequence. We use this special kind of fundamental sequences to give characterizations and some properties of AANR_C-sets and AANR_N-sets. The paper ends with a section devoted to internal FANR's.     

棱镜-漏波导耦合器的理论分析

根据多光束干涉原理,理论上分析了棱镜-漏波导耦合器,且与棱镜-波导耦合器作了比较,给出正确使用这两种耦合器的判据.分析结果表明,在强耦合条件下,棱镜-漏波导耦合器可用于薄膜参数测量和光波导输入-输出耦合;对于弱耦合,本文的结果与Tien和Ulrich的理论一致.     

静态偏振风成像干涉仪中光在四面角锥棱镜中的传播规律研究

简述了自行设计的新型静态偏振风成像干涉仪的原理和四面角锥棱镜的分光机理;应用光线追迹法,推导出了主截面内任意光线在棱镜中的传播方向及出射点坐标,建立了平行光束经角锥棱镜后的偏向角和透过率的理论表达式;采用计算机模拟给出了偏向角和透过率随入射角的变化关系曲线;根据静态偏振风成像干涉仪的具体参数确定了四面角锥棱镜的侧面和底面夹角以及底边长度.该研究为静态偏振风成像干涉仪的研制提供了理论依据.     

球面角锥棱镜非稳腔钕玻璃激光器

为了将虚共焦非稳腔输出光束质量高和角锥棱镜谐振腔具有免调试的优点结合到一起,提出了用球面角锥棱镜构成虚共焦非稳腔的方案。利用已有虚共焦非稳腔钕玻璃激光器,设计加工了一球面角锥棱镜非稳腔钕玻璃激光器。模拟计算了两谐振腔输出光束的模式分布,然后对两钕玻璃激光器进行了实验对比研究。结果表明:实验得到的模式分布与模拟计算结果相吻合,球面角锥棱镜非稳腔钕玻璃激光器与虚共焦非稳腔钕玻璃激光器分别获得了最大2176.9J和2340.6J的能量输出,二者的电光效率与束散基本相同,分别为4.3%,0.30mrad和4.6%,0.26mrad。     

五角棱镜补偿法加工工艺研究

由于五角棱镜两B棱的投影夹角对第二光学平行差影响倍率较大且加工过程中无法测量该夹角,从而导致棱镜加工合格率较低。通过分析侧面垂直度误差及Δ45°对五角棱镜光学平行差的影响,提出一种新的五角棱镜加工工艺方法:利用最后一个加工面对前3个已加工面存在的角度误差进行一次性补偿,从而降低了对各加工面的加工误差要求。实践证明:该方法能够有效地提高五角棱镜加工的合格率和生产效率,减小加工难度,并能显著降低对加工和检测设备的精度要求。     

On the stability of a compressible Rivlin's cube made of transversely isotropic material

^** Email: kostas.soldatos{at}nottingham.ac.uk This paper considers a unit cube made of a compressible, transverselyisotropic elastic material, with the direction of transverseisotropy being aligned normal to one pair of the cube's faces,and investigates the stability of a dilatation equilibrium stateof that cube, with respect to superposed pure homogeneous deformationswith principal directions parallel to the cube edges. This dilatation,intermediate equilibrium state (state I) of the cube is assumedattainable in two different ways. Accordingly, in what is termedas the ‘principal stability problem’ under investigation,state I is considered to be that of uniform dilatation, whichis attained upon loading normally and uniformly the oppositefaces of the unit cube with certain pairs of equal and oppositelydirected forces having appropriately selected magnitudes. Inwhat is termed as the ‘modified stability problem’under investigation, the same compressible, transversely isotropicunit cube is loaded uniformly by three identical pairs of equaland oppositely directed forces acting normally to its faces,and, hence, it attains in state I the shape of a certain rectangularparallelepiped. The necessary and sufficient conditions forstability of state I of the cube deformation are obtained inthe form of three inequalities, which are found to hold regardlessof whether the intermediate equilibrium state I is that of uniformdilatation or that of the aforementioned rectangular parallelepiped(non-uniform dilatation). These, however, lead to quite differentspecific results and conclusions when applied in connectionwith, first, the principal and, then, the modified stabilityproblem of a unit cube made of a particular type of a transverselyisotropic extension of the Blatz–Ko (isotropic) material.     

Universal quadratures for boundary integral equations on two-dimensional domains with corners

We describe the construction of a collection of quadrature formulae suitable for the efficient discretization of certain boundary integral equations on a very general class of two-dimensional domains with corner points. The resulting quadrature rules allow for the rapid high-accuracy solution of Dirichlet boundary value problems for Laplace’s equation and the Helmholtz equation on such domains under a mild assumption on the boundary data. Our approach can be adapted to other boundary value problems and certain aspects of our scheme generalize to the case of surfaces with singularities in three dimensions. The performance of the quadrature rules is illustrated with several numerical examples.     

Counting spanning trees in prism and anti-prism graphs

In this paper, we calculate the number of spanning trees in prism and antiprism graphs corresponding to the skeleton of a prism and an antiprism. By the electrically equivalent transformations and rules of weighted generating function, we obtain a relationship for the weighted number of spanning trees at the successive two generations. Using the knowledge of difference equations, we derive the analytical expressions for enumeration of spanning trees. In addition, we again calculate the number of spanning trees in Apollonian networks, which shows that this method is simple and effective. Finally we compare the entropy of our networks with other studied networks and find that the entropy of the antiprism graph is larger.     

基于斯托克斯矢量的偏振成像仪器及其进展

偏振成像技术将景物的偏振信息转化为二维图像信息,从而可以和灰度图像一样对目标景物进行场景特征分析。介绍了基于斯托克斯矢量的偏振成像原理。按照获取斯托克斯矢量方法的不同,分别介绍了偏振片起偏、偏振棱镜分光和可变延迟波片调制三类分时偏振成像方式,分振幅、分孔径、分焦平面三种同时偏振成像方式。结合我国的制造水平,设计了双CCD渥拉斯顿棱镜同时偏振成像实验系统,并采集了实验图像。分析了各种偏振成像方式的优缺点。指出了偏振激光照明主动偏振成像、光谱偏振成像是偏振成像仪器进一步的发展方向。     

光热偏转光谱法的研究

为了建立棱镜型光热偏转光谱法的理论框架,采用棱镜的光色散特性研究了激励光源对待测样品表面周期性照射情况下的探测光偏转角与光热信号之间的解析关系。得到了棱镜型样品表面周期性变化的偏转角表达式。实现结果表明,该方法比传统型光谱法具有理论模型简单、实验容易实现、分辨率高、灵敏度高等优点。