基于NSCT和泰勒级数的图像超分辨率重建

结合非下采样Contourlet变换(NSCT)的多尺度、方向特性、各向异性、平移不变性以及泰勒级数高效逼近的优点,提出一种利用泰勒级数插值代替双线性插值的超分辨率图像重建算法.实验结果显示,该算法可以较好地恢复图像的细节信息和纹理特征,有效抵抗高斯噪声的干扰.     

The Laplace transform in discrete fractional calculus

We develop properties of the Laplace Transform in a discrete, fractional calculus setting, giving a precise treatment to convergence along the way. The end goal is to apply the Laplace Transform Method to solve a fractional initial value problem.     

非线性控制系统状态方程直接积分解法

鉴于非线性系统分析的核心归结为系统状态方程的求解,针对一般非线性控制系统,引入由状态量、控制量与自变量时间t为坐标构成的＂广义时态空间＂.为了求解非线性状态方程,在广义时态空间（tk,x（k）,u（k））处将方程的右端展开为（t？tk）的Taylor级数,通过直接积分获得了非线性控制系统状态方程关于自变量时间（τ=t？tk）的级数解,并证明了解的收敛性.     

Application of the modified Taylor approximation

In this paper we introduce and describe a new scheme for the numerical integration of smooth functions. The scheme is based on the modified Taylor expansion and is suitable for functions that exhibit near-sinusoidal or repetitive behaviour. We discuss the method and its rate of convergence, then implement it for the approximation of certain integrals. Examples include integrands involving Airy wave, Bessel, Gamma, and elliptic functions. The results, from the data in the tables, demonstrate that the method converges rapidly and approximates the integral as well as some well-known numerical integration methods used with sufficiently small step sizes.     

Taylor collocation method for solution of systems of high-order linear Fredholm–Volterra integro-differential equations

A Taylor collocation method is presented for numerically solving the system of high-order linear Fredholm–Volterra integro-differential equations in terms of Taylor polynomials. Using the Taylor collocations points, the method transforms the system of linear integro-differential equations (IDEs) and the given conditions into a matrix equation in the unknown Taylor coefficients. The Taylor coefficients can be found easily, and hence the Taylor polynomial approach can be applied. This method is also valid for the systems of differential and integral equations. Numerical examples are presented to illusturate the accuracy of the method. The symbolic algebra program Maple is used to prove the results.     

A new homotopy perturbation method for system of nonlinear integro-differential equations

In this paper, a new homotopy perturbation method (NHPM) is introduced to obtain exact solutions of system of nonlinear integro-differential equations. Theoretical considerations are discussed. Two examples are given to demonstrate the efficiency of NHPM to the classical HPM and variational iteration methods.     

On the reinitialization procedure in a narrow‐band locally refined level set method for interfacial flows

A local level set algorithm for simulating interfacial flows described by the two‐dimensional incompressible Navier–Stokes equations is presented. The governing equations are solved using a finite‐difference discretization on a Cartesian grid and a second‐order approximate projection method. The level set transport and reinitialization equations are solved in a narrow band around the interface using an adaptive refined grid, which is reconstructed every time step and refined using a simple uniform cell‐splitting operation within the band. Instabilities at the border of the narrow band are avoided by smoothing the level set function in the outer part of the band. The influence of different PDE‐based reinitialization strategies on the accuracy of the results is investigated. The ability of the proposed method to accurately compute interfacial flows is discussed using different tests, namely the advection of a circle of fluid in two different time‐reversed vortex flows, the advection of Zalesak's rotating disk, the propagation of small‐amplitude gravity and capillary waves at the interface between two superposed viscous fluids in deep water, and a classical test of Rayleigh–Taylor instability with and without surface tension effects. The interface location error and area loss for some of the results obtained are compared with those of a recent particle level set method. Copyright © 2005 John Wiley & Sons, Ltd.     

基于离散泰勒级数的新型联想记忆系统

基于离散泰勒级数提出一种对任意阶多维函数可实现无差逼近的新型联想记忆系统，详细讨论了该系统的插值算法、训练规则及寻址机制，新型联想记忆系统相对于CMAC具有逼近精度更高、占用存储单元较少、学习速度较快等优点，该系统在信号处理、模式识别、过程建模及高精度实时智能控制等领域具有广泛的应用价值，仿真实例表明了系统的可行性与有效性。     

双线性系统参数估计中的泰勒级数方法

本文给出了一种利用泰勒级数估计双线性系统参数的方法。通过将输入输出进行泰勒级数展开,把原微分方程模型转化成一个代数方程,进而利用最小二乘原理得到参数的估值。