条件期望的两种定义及其等价性探讨

讨论随机变最在给定子σ代数下条件期望的定义,利用投影定理这一数学工具给出条件期望的几何定义,并通过对它与现今各种概率论基础或随机过程教材中常见的公理化定义相互等价性的证明,揭示了条件期望这一概念的内涵.     

Hybrid Mann-Halpern iteration methods for nonexpansive mappings and semigroups

In this paper, we introduce some new iteration methods based on the hybrid method in mathematical programming, the Mann’s iterative method and the Halpern’s method for finding a fixed point of a nonexpansive mapping and a common fixed point of a nonexpansive semigroup Hilbert spaces.     

Spectral sequences in combinatorial geometry: Cheeses, inscribed sets, and Borsuk-Ulam type theorems

Algebraic topological methods are especially well suited for determining the non-existence of continuous mappings satisfying certain properties. In combinatorial problems it is sometimes possible to define a mapping from a space X of configurations to a Euclidean space Rm in which a subspace, a discriminant, often an arrangement of linear subspaces A, expresses a target condition on the configurations. Add symmetries of all these data under a group G for which the mapping is equivariant. If we remove the discriminant from Rm, we can pose the problem of the existence of an equivariant mapping from X to the complement of the discriminant in Rm. Algebraic topology may sometimes be applied to show that no such mapping exists, and hence the image of the original equivariant mapping must meet the discriminant.We introduce a general framework, based on a comparison of Leray-Serre spectral sequences. This comparison can be related to the theory of the Fadell-Husseini index. We apply the framework to:

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solve a mass partition problem (antipodal cheeses) in Rd,

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determine the existence of a class of inscribed 5-element sets on a deformed 2-sphere,

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obtain two different generalizations of the theorem of Dold for the non-existence of equivariant maps which generalizes the Borsuk-Ulam theorem.

     

凸可行问题的一种强收敛算法

无限维Hilbert空间中,解凸可行问题的平行投影算法通常是弱收敛的.本文对一般的平行投影算法进行改进,设计了一种解凸可行问题的具有强收敛性的新算法.该算法主要是在原有算法基础上引入了一个参数序列,在参数序列满足一定的控制条件下保证了算法的强收敛性.为了简单证明算法的强收敛性,我们构建了一个新的积空间,然后把原空间的这种改进平行投影算法转换为积空间中的交替投影算法.这样,改进的平行投影算法的强收敛性就可以通过交替投影算法的收敛性证明得到.     

互补约束规划问题的一个广义梯度投影算法

本文研究了一类均衡约束最优化问题.利用广义梯度投影法,结合罚函数思想,得到了一个初始点可以任意的广义梯度投影算法.在较弱的条件下,证明了算法的全局收敛性.     

Pointwise supercloseness of quadratic serendipity block finite elements for a variable coefficient elliptic equation

For a variable coefficient elliptic boundary value problem in three dimensions, using the properties of the interpolation operator of projection type, we derive the weak estimate of the first type for the quadratic serendipity block finite element. In addition, the estimate for the W^1,1 ‐seminorm of the discrete derivative Green's function is given. Finally, we prove that the derivatives of the finite element approximation and the corresponding interpolant of projection type are superclose in the pointwise sense of the L^∞ ‐norm. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1253‐1261, 2011     

Strong Convergence Theorems for a Family of Quasi-φ-Asymptotically Nonexpansive Mappings

The purpose of this article is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-φ-asymptotically nonexpansive mappings.Its results hold in reflexive,strictly convex,smooth Banach spaces with the property(K).The results of this paper improve and extend recent some relative results.     

Analysis on 3D object measurement based on fringe projection

A coordinate measuring method is presented, which is specially devised to perform the measurement of coordinates with projected fringe techniques of projectors in three dimensions. The system is composed of two parts: one is a target which can move freely in three dimensions, and the other is a stationary two-dimensional array of photodetectors. The mini-projector is tied to the target, and the projected fringe is monitored by the photodetectors. The phase of the photodetectors can be precisely measured with the phase-shifting algorithm, so that, the xyz location of the target can be determined with the geometric model of multilateration using the method of optimization. In this paper, the measuring principle, iterative method, computer simulation and preliminary results are given. The phase-shifting technique has the advantages of high accuracy and noise endurance. The method will provide the basis for follow-up iterative optimization calculation. The experimental results prove that the proposed coordinate measuring method is of high precision.     

基于经验模式分解的三频彩色条纹投影轮廓术

为实现动态物体的实时三维测量,提出了一种基于经验模式分解的三频彩色条纹投影轮廓术。将低、中、高三种频率的正弦条纹分别经投影仪红(R),绿(G),蓝(B)通道同时投影至被测物面,CCD在另一角度拍摄变形条纹图。将变形条纹图R、G、B三分量互减消减背景干扰,用经验模式分解进行颜色解耦,分离各载频项,进而以傅里叶变换解调相位。以变精度去包裹算法按低、中、高频依次完成包裹相位展开,得到高频载频项的展开相位。计算机模拟时相位解调的标准差小于0.0417rad,具有较高的测量精度;对比实验和面部表情变化实验进一步说明了方法的可靠性。该方法在单次拍摄下实现了相位的解调及高精度相位的精确展开,为动态物体的高精度轮廓测量提供了有效的手段。     

均质椭圆柱面刚体转动惯量的计算

根据转动惯量的定义,运用计算转动惯量的质量投影法,计算了均质椭圆柱面刚体对转轴的转动惯量.