Symmetric Surface Momentum and Centripetal Force for a Particle on a Curved Surface

The Hermitian surface momentum operator for a particle confined to a 2D curved surface spanned by orthogonal coordinates and embedded in 3D space is expressed as a symmetric expression in derivatives with respect to the surface coordinates and so is manifestly along the surface. This is an alternative form to the one reported in the literature and usually named geometric momentum, which has a term proportional to the mean curvature along the direction normal to the surface, and so "apparently" not along the surface. The symmetric form of the momentum is the sum of two symmetric Hermitian operators along the two orthogonal directions defined by the surface coordinates. The centripetal force operator for a particle on the surface of a cylinder and a sphere is calculated by taking the time derivative of the momentum and is seen to be a symmetrization of the well-known classical expressions.     

Lagrangian Grassmann manifold Λ(2)

Based on the relationship between symplectic group Sp(2) and Λ(2), we provide an intuitive explanation (model) of the 3-dimensional Lagrangian Grassmann manifold Λ(2), the singular cycles of Λ(2), and the special Lagrangian Grassmann manifold SΛ(2). Under this model, we give a formula of the rotation paths dened by Arnold.     

Geometric Potential and Dirac Quantization

A fundamental problem regarding the Dirac quantization of a free particle on an () curved hypersurface embedded in N flat space is the impossibility to give the same form of the curvature‐induced quantum potential, the geometric potential as commonly called, as that given by the Schrödinger equation method where the particle moves in a region confined by a thin‐layer sandwiching the surface. This problem is resolved by means of a previously proposed scheme that hypothesizes a simultaneous quantization of positions, momenta, and Hamiltonian, among which the operator‐ordering‐free section is identified and is then found sufficient to lead to the expected form of geometric potential.     

SINS/GPS组合导航系统选星算法

选星算法是SINS/GPS组合导航定位系统中一个重要的步骤。在最佳选星算法的基础上,提出了一种适用于基于伪距、伪距率的SINS/GPS紧耦合组合系统的选星算法。该算法通过ENU（东北天）坐标系中几何矩阵及几何精度因子的定义,利用星历给出的卫星在ENU坐标系中的高度角和方位角解算出最佳四颗导航定位卫星,即基于G矩阵的选星算法。通过与两种常规选星算法的对比,验证了本算法具有较强的工程实用性。此外又推导了基于G矩阵的伪距、伪距率的SINS/GPS组合系统量测方程。该算法避免了求解卫星的位置,从而有效减少了计算量。     

Experimental verification of Foreman dislocation model

We present a strain analysis of an edge dislocation core, and a detailed discussion of the Foreman dislocation model. In order to examine the model, the quantitative measurement of strain field around an edge dislocation in aluminum is performed, and high-resolution transmission electron microscopy and geometric phase analysis are employed to map the strain field of the edge dislocation core in aluminum. The strain measurements are compared with the Foreman dislocation model, showing that they are in good agreement with each other when 0.7 ≤ a ≤ 1.5.     

基于瞳孔几何特征的驾驶疲劳检测嵌入式系统的设计

驾驶员疲劳驾驶是引发交通事故的一个重要原因。针对驾驶疲劳检测算法运算复杂、视频图像数据量大的特点,设计了基于瞳孔几何特征的疲劳驾驶检测嵌入式系统。系统以TI公司的DSPTMS320DM642为核心,采用瞳孔图像的几何特征约束定位人眼,识别疲劳帧。在此基础上,提出了疲劳状况测评的判定方法,从而达到检测驾驶员疲劳程度的效果。实验结果表明,该系统算法简单、快速,是一种行之有效的、实时的非接触式疲劳驾驶检测系统。     

波前编码景深延拓与几何光学景深的关系

波前编码成像系统将模拟编码方法与数字解码技术相结合解决景深延拓问题,可以用信息光学的方法进行分析,得到波前编码系统的景深延拓扩展率。但是这种方法使用的景深概念和几何光学的景深概念有所不同。从几何光学角度研究了信息光学导出的波前编码系统的景深延拓扩展率与几何光学景深延拓的关系。最后得出结论,在F数一定的情况下,随着探测器分辨率的提高,几何光学景深延拓扩展率与信息光学给出的波前编码光学系统的景深延拓扩展率趋于一致。     

简谐载荷下嵌入式单壁碳纳米管动态响应的Magnus方法

基于两端固支的弹性梁模型,研究嵌入式单壁碳纳米管在横向简谐载荷作用下的非线性振动问题。利用Galerkin方法对运动微分方程进行近似处理,将原方程从非线性动力学系统转化到二阶动力学系统,对于二阶动力学方程采用Magnus级数方法进行求解。通过数值实验,分析了嵌入式单壁碳纳米管非线性振动幅频特性,根据非线性动力学理论分析了碳纳米管动态响应,结果表明倍周期分岔产生混沌。     

Geometric characterizations for variational minimizing solutions of charged 3-body problems

We study the charged 3-body problem with the potential function being (-α)-homogeneous on the mutual distances of any two particles via the variational method and try to find the geometric characterizations of the minimizers. We prove that if the charged 3-body problem admits a triangular central configuration, then the variational minimizing solutions of the problem in the π2-antiperiodic function space are exactly defined by the circular motions of this triangular central configuration.     

工件带简单线性恶化函数和共同交货期单机排序问题

本文研究单机排序问题,其中工件加工时间具有简单线性恶化函数.同时,所有工件均具有一个给定共同交货期.目标函数为最小化提前有奖延误受罚之和.在逆一致性条件下,给出了求解该排序问题的一个伪多项式时间动态规划算法.同时借助于几何舍入技巧,对求解这类排序问题给出了一个充分多项式时间的近似算法(FPTAS)。