离散几何的两个铺砌问题

利用图论和代数的方法研究离散几何中的两个铺砌问题:1)给出1×2长方形铺砌多米诺骨牌的充分必要条件;2)对高维空间盒子的情形,给出m_1×m_2×…×m_n砖能够铺砌a_1×a_2×…×a_n盒子的一些必要条件和充要条件.     

An optimal rigidity theorem for complete submanifolds in a sphere

It is proved that if M^n is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in S^n＋p（1）, and if supM S 〈 α（n, H）, where α（n,H）=n＋n^3/2（n-1）H^2-n（n-2）/n（n-1）√n^2H^4＋4（n-1）H^2,then M^n must be the totally urnbilical sphere S^n（1/√1＋H^2）.An example to show that the pinching constant α（n, H） appears optimal is given.     

变分原理分析开裂简支箱梁剪力滞效应

变分原理通常应用于箱形截面梁剪力滞效应弹性分析,本文基于换算截面法,运用变分原理推导了预应力混凝土简支箱梁均布荷载作用、钢筋混凝土简支箱梁集中荷载作用的剪力滞系数计算公式,考虑了混凝土开裂对箱梁剪力滞效应的影响,并与试验结果和规范方法进行了对比分析。变分原理分析开裂混凝土箱梁剪力滞效应方法力学概念明确,是其弹性分析适用范围的拓展,亦可推广应用到混凝土连续箱梁开裂后的剪力滞效应分析,具有广阔的应用前景。     

共形平坦的Randers度量

本文研究共形平坦的Randers 度量的性质. 证明了具有数量旗曲率的共形平坦的Randers 度量都是局部射影平坦的, 并且给出了这类度量的分类结果. 本文还证明了不存在非平凡的共形平坦且具有近迷向S 曲率的Randers 度量.     

聚合物发光二极管面光源的光热特性

运用传输矩阵法及MATLAB软件模拟计算了以MEH-PPV为发光材料的PLED面光源出光率,分析了发光层、PEDOT层、ITO层对器件出光率的影响.模拟分析了玻璃表面半球形、圆台形、圆锥形3种微形貌对器件出光率的影响.仿真结果表明,玻璃表面为圆锥形微散射层对提高器件出光率最有利,且出光均匀性最好.最后分析了PLED面光...     

组合曲线回归法计算螺旋扁管管内对流传热系数

针对螺旋扁管壁面温度难于准确测试的特点,提出采用线性曲线回归与非线性曲线回归相结合的方法进行管内传热系数计算.进行了光管与螺旋扁管管内对流传热实验,并用该方法计算管内对流传热系数.光管传热系数计算值与经典公式的大偏差小于6%.螺旋扁管管内传热系数的计算值略大于通过测量壁温获得的传热系数值,分析了二者存在差异的原因.组合...     

瑞奇-康芒两角度检测法的一种波像差解读方法

瑞奇-康芒法是大口径平面元件面形检测的有效方法.通过分析检测光瞳到被检平面的位置转换关系以及波像差到面形误差的幅值转换关系,分别对检测得到的波像差以及干涉仪离焦产生的Power进行转换处理,利用最小二乘法计算出瑞奇-康芒两角度检测时的干涉仪离焦量,从而获得被检平面的面形误差分布.实验部分给出了第4项到第37项泽尼克多项...     

On the generalized Weyl problem for flat metrics in the hyperbolic 3-space

The paper deals with the study of complete embedded flat surfaces in H³${\mathbb{H}}^3$ with a finite number of isolated singularities. We give a detailed information about its topology, conformal type and metric properties. We show how to solve the generalized Weyl?s problem of realizing isometrically any complete flat metric with Euclidean singularities in H³${\mathbb{H}}^3$ which gives the existence of complete embedded flat surfaces with a finite arbitrary number of isolated singularities.     

Imposing symmetry in augmented linear systems

This paper discusses the methods of imposing symmetry in the augmented system formulation (ASF) for least‐squares (LS) problems. A particular emphasis is on upper Hessenberg problems, where the challenge lies in leaving all zero‐by‐definition elements of the LS matrix unperturbed. Analytical solutions for optimal perturbation matrices are given, including upper Hessenberg matrices. Finally, the upper Hessenberg LS problems represented by unsymmetric ASF that indicate a normwise backward stability of the problem (which is not the case in general) are identified. It is observed that such problems normally arise from Arnoldi factorization (for example, in the generalized minimal residual (GMRES) algorithm). The problem is illustrated with a number of practical (arising in the GMRES algorithm) and some ‘purpose‐built’ examples. Copyright © 2014 John Wiley & Sons, Ltd.     

A note on static spaces and related problems

In this paper we study static spaces introduced in Hawking and Ellis (1975)  [1], Fischer and Marsden (1975) [3] and Riemannian manifolds possessing solutions to the critical point equation introduced in Besse (1987)  [11], Hwang (2000)  [12]. In both cases, on the manifolds there is a function satisfying a particular Ricci–Hessian type equation (1.6). With an idea similar to that used in Cao et al. (2012)  [15], [16], we have made progress in solving the problem raised in Fischer and Marsden (1975)  [3] of classifying vacuum static spaces and in proving the conjecture proposed in Besse (1987)  [11] concerning manifolds admitting solutions to the critical point equation in general dimensions. We obtain even stronger results in dimension 3.