Algebraic dynamics algorithm:Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

Based on the exact analytical solution of ordinary differential equations, a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm. A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models. The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision, and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.     

A note on the efficient implementation of Hamiltonian BVMs

We discuss the efficient implementation of Hamiltonian BVMs (HBVMs), a recently introduced class of energy preserving methods for canonical Hamiltonian systems (see Brugnano et al. [8] and references therein), also sketching their blended formulation. We also discuss the case of separable problems, for which the structure of the problem can be exploited to gain efficiency.     

High‐order asymptotic‐preserving schemes for linear systems: Application to the Goldstein–Taylor equations

In this work, we address the numerical approximation of linear systems with possibly stiff source terms which induce an asymptotic diffusion limit. More precisely, we are interested in the design of high‐order asymptotic‐preserving schemes. Our approach is based on a very simple modification of the numerical flux associated with the usual HLL scheme. This alteration can be understood as a numerical diffusion reduction technique and allows to capture the correct asymptotic behavior in the diffusion limit and to consider uniformly high‐order extensions. We more specifically consider the case of the Goldstein–Taylor model but the overall approach is shown to be easily adapted to more general systems.     

颗粒线度和非谐效应对传感器电极材料导电性能及其热稳定性的影响

本文考虑到原子的非简谐振动,应用固体物理理论和方法,研究了氧传感器多孔电极材料导电性能及热稳定性随温度和颗粒线度的变化规律,探讨原子非简谐振动和材料颗粒线度的影响.结果表明:(1)多孔Pt电极材料的电导率随温度的升高而非线性减小;电导率随颗粒半径的增大而非线性增大;电导率随时间增长而减小,但变化极小;(2)多孔Pt电极材料的电导率远小于Pt纳米材料的电导率,也小于块状Pt电极材料的电导率,且颗粒越小,颗粒线度效应越显著;(3)电导率的温度稳定性系数随温度的升高和颗粒线度的减小以及表面层参数的增大而非线性减小,即温度越高、颗粒线度越小、表面层参数越大,电极材料导电性的热稳定性越好;(4)表面层的存在使电导率降低,且降低情况与温度和颗粒线度有关,即颗粒越小,温度越低,电导率下降越明显;非简谐效应对电极材料的电导率几乎没有影响.     

基于局部保持投影的掌纹识别

为了保持掌纹空间的局部结构,运用局部保持投影(LPP)方法进行掌纹识别.在小样本图像识别中,特征方程矩阵存在奇异性.传统的解决方法是运用主元分析(PCA)获得原样本的低维特征子空间,在该空间中运用LPP进行特征提取.由于PCA和LPP的投影标准本质上是不同的,PCA降维时丢失许多重要的判别信息.为了解决这个问题,提出运用三级小波变换、图像下抽样、图像分块求平均值三种方法降低掌纹空间的维数,在低维图像上应用LPP提取局部特征.计算特征矢量间的余弦距离进行掌纹匹配.运用PolyU掌纹图像库进行测试,结果表明,该算法的识别性能均优于PCA和PCA LPP.特征提取和匹配总时间小于0.1 S,具有快速、有效、易于实现等优点.     

STRONG STABILITY PRESERVING PROPERTY OF THE DEFERRED CORRECTION TIME DISCRETIZATION

In this paper, we study the strong stability preserving （SSP） property of a class of deferred correction time discretization methods, for solving the method-of-lines schemes approximating hyperbolic partial differential equations.     

Approximation by α$$ \alpha $$-Bernstein–Schurer operators and shape preserving properties via q$$ q $$-analogue

Our work in this article is to construct the $\alpha$- Bernstein–Schurer operators which includes the $q$-integers. For these new operators, we discuss the shape preserving properties, namely, monotonicity and convexity. Next, we study the uniformly global approximation in terms of the Ditzian–Totik modulus of continuity and calculate the local direct estimate by Lipschitz-maximal functions. In the last Voronovskaja-type approximation theorems are also presented.     

Optical characterization of thermally evaporated thin CdO films

Cadmium Oxide films have been prepared by vacuum evaporation method on a glass substrate at room temperature. Detailed structural, optical, and electrical properties of the films are presented at different annealing temperatures. The crystal structure of the samples was studied by X‐ ray diffraction. The spectral absorption coefficient of the CdO film at the fundamental absorption region (450‐650nm) was determined using the spectral data of transmittance. The direct and indirect band gap energies were determined and found to be 2.33 eV and 1.95 eV respectively. The third order optical nonlinearities χ(3) of CdO films has been measured used the z‐can technique. The real and imaginary parts of χ(3) have been measured at 514 nm and found to be 1.7x10^‐3 esu and 3.0x10^‐3 esu, respectively. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals

To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations. In this paper, we propose and analyze a class of iteration schemes for the discretized Kohn-Sham Density Functional Theory model, with which the iterative approximations are guaranteed to converge to the Kohn-Sham orbitals without any orthogonalization as long as the initial orbitals are orthogonal and the time step sizes are given properly. In addition, we present a feasible and efficient approach to get suitable time step sizes and report some numerical experiments to validate our theory.