Highly Accurate Pseudospectral Approximations of the Prolate Spheroidal Wave Equation for Any Bandwidth Parameter and Zonal Wavenumber

The prolate spheroidal wave equation (PSWE) is transformed, using suitable mappings, into three different canonical forms which resemble the Jacobi, Laguerre and the Hermite differential equations. The eigenpairs of the PSWE are approximated with the corresponding classical orthogonal polynomial as a basis set. It is observed that for any zonal wavenumber m the Jacobi type pseudospectral methods are well suited for small bandwidth parameters c whereas the Hermite and Laguerre pseudospectral methods are appropriate for very large c values. Moreover, Jacobi pseudospectral methods work well for any parameter values such that \(m\ge c\). Our numerical results confirm that for any values of m, the Jacobi \(\left[ (\alpha ,\beta )=(\pm 1/2,m)\right] \) and the Laguerre \(({\upgamma }=\pm 1/2)\) pseudospectral methods formulated in this article for the numerical solution of the PSWE with small and very large bandwidth parameters, respectively, are highly efficient both from the accuracy and fastness point of view.     

High Order Weighted Essentially Non-oscillation Schemes for Two-Dimensional Detonation Wave Simulations

In this paper, we demonstrate the detailed numerical studies of three classical two dimensional detonation waves by solving the two dimensional reactive Euler equations with species with the fifth order WENO-Z finite difference scheme (Borges et al. in J. Comput. Phys. 227:3101?C3211, 2008) with various grid resolutions. To reduce the computational cost and to avoid wave reflection from the artificial computational boundary of a truncated physical domain, we derive an efficient and easily implemented one dimensional Perfectly Matched Layer (PML) absorbing boundary condition (ABC) for the two dimensional unsteady reactive Euler equation when one of the directions of domain is periodical and inflow/outflow in the other direction. The numerical comparison among characteristic, free stream, extrapolation and PML boundary conditions are conducted for the detonation wave simulations. The accuracy and efficiency of four mentioned boundary conditions are verified against the reference solutions which are obtained from using a large computational domain. Numerical schemes for solving the system of hyperbolic conversation laws with a single-mode sinusoidal perturbed ZND analytical solution as initial conditions are presented. Regular rectangular combustion cell, pockets of unburned gas and bubbles and spikes are generated and resolved in the simulations. It is shown that large amplitude of perturbation wave generates more fine scale structures within the detonation waves and the number of cell structures depends on the wave number of sinusoidal perturbation.     

基于海浪谱估计的减摇鳍浪级调节器设计

由于减摇鳍的最大工作鳍角是有一定限制的,所以当减摇鳍工作的环境高于设计海情时减摇鳍的鳍角饱和率就会增加,从而使减摇鳍长时间工作于非线性状态,这不仅使减摇效果下降,而且会使机械装置加剧磨损。为了在海情增高时控制住减摇鳍的鳍角饱和率,设计浪级调节器是很有必要的。根据船舶横摇时历数据,采取现代谱分析技术,由船舶横摇时历反推海浪功率谱,然后由海浪功率谱来获取海浪信息从而进行浪级调节,以保证鳍角饱和率不超过设计的要求。通过仿真证明此方法不仅很好地控制了鳍角的饱和率而且使减摇鳍的减摇效果有了明显的提高。     

Deformable Image Registration Based on Functions of Bounded Generalized Deformation

International Journal of Computer Vision - Functions of bounded deformation (BD) are widely used in the theory of elastoplasticity to describe the possibly discontinuous displacement fields inside...     

High Order Fluctuation Schemes on Triangular Meshes

We develop a new class of schemes for the numerical solution of first-order steady conservation laws. The schemes are of the residual distribution, or fluctuation-splitting type. These schemes have mostly been developed in the context of triangular or tetrahedral elements whose degrees of freedom are their nodal values. We work here with more general elements that allow high-order accuracy. We introduce, for an arbitrary number of degrees of freedom, a simple mapping from a low-order monotone scheme to a monotone scheme that is as accurate as the degrees of freedom will allow. Proofs of consistency, convergence and accuracy are presented, and numerical examples from second, third and fourth-order schemes.     

Mixed Fourier-Laguerre Spectral and Pseudospectral Methods for Exterior Problems Using Generalized Laguerre Functions

In this paper, we develop the mixed spectral and pseudospectral methods for two-dimensional exterior problems, by using the scaled generalized Laguerre functions. Some basic results on the mixed Fourier-Laguerre orthogonal approximation and Gauss-type interpolation are established, which play important roles in the related spectral and pseudospectral methods. As an example, we propose the mixed spectral and pseudospectral schemes for a model problem. The convergence of proposed schemes are proved. Numerical results demonstrate the spectral accuracy efficiency of this new approach. This work is supported in part by NSF of China, N.10771142, the National Basic Research Project N.2005CB321701, SF of Shanghai N.075105118, The Shanghai Leading Academic Discipline Project N.T0401 and The Fund for E-institute of Shanghai Universities N.E03004.     

一种优化FP-growth的支持度相同项的排序算法

Han等人提出了频繁模式增长FP-growth算法,该算法在第一次扫描数据库后,得到频繁项集合和每个频繁项的支持度,并按支持度降序排列,但没有对支持度相同项的排列做进一步说明。本文依据"越是频繁出现,越可能被共享"的建树原则,提出了通过比较该项与前后项项集的支持度,较大者先排列的方法,使后续构建的FP-tree比任意排序构建的FP-tree更优。     

基于广义高斯函数的二阶非线性系统滑模控制

为了减小被控对象跟踪参考信号在边界的跟踪误差,针对不确定二阶非线性系统,并考虑到模糊控制中控制灵敏度对隶属度函数形状的要求,利用广义T-S模糊模型中广义高斯隶属函数本身对控制灵敏度的自适应性和广义T-S模糊系统,设计了自适应参数调节律和自适应模糊滑模控制器。克服和补偿了系统的建模误差,在不加监督控制和有界控制的情况下,有效地改善了控制系统在参考信号边界的跟踪性能。比较采用高斯隶属函数的T-S模糊模型,基于广义T-S模糊模型的控制系统在闭环稳定的前提下使跟踪误差收敛到了一个更小的邻域。对倒立摆二阶子系统的仿真,实验表明跟踪性能改善的效果是明显的,证明控制器的设计是合理和有效的。     

大规模RC网络的优化消去模型降阶算法

针对电路后仿中大规模、多端口RC矩阵在降阶时非零元会显著增加,导致降阶系统处理时间大幅上升的问题,提出了寻找最优剩余节点数,使降阶后的网络求解速度达到最优的算法.首先采用统计建模的方法得到RC网络求解时间与节点数、非零元数的近似关系;然后在对实际电路进行模型降阶时用节点消去法快速得到剩余节点数与非零元的关系,从中选出最优的剩余网络节点数并根据它实施模型降阶,实验结果表明,采用该策略得到的降阶网络不造成精度损失,且使电路求解速度比已有方法快2～5倍.     

Optimal Control Based on Neuro Estimator for Fractional Order Uncertain Non-linear Continuous-Time Systems

Neural Processing Letters - In this paper, a novel method is presented for optimal control of fractional order systems in the presence of an unknown term in system dynamic where fractional order...     

基于扰动方法的广义最佳鉴别矢量集求解的一种迭代算法

本文对广义最佳鉴别矢量的求解方法进行研究，根据矩阵的扰动理论，改进了郭提出的求解广义最佳鉴别矢量的一种迭代算法，提出了求解广义最佳鉴别矢量的一种新的迭代算法，本文算法的一个突出优点是随着类别数目的增加，计算时间反而缩短；而老算法随着类别数目的增加计算时间随着增加，不仅如此，新算法的识别率不劣于老算法，在ORL人脸数据库的数值实验，验证了上述论断的正确性。     

基于孤立电流脉冲群的电磁导波激励源优化设计

目前,电磁导波检测系统的激励源大都采用重复电流脉冲群+高频大功率放大器输出大电流脉冲的方式,由于这种电流脉冲是连续的,平均功耗较大,成本高,不利于系统的简单化和实用化;通过电路分析和电路参数的优化选取,给出了电容储能放电产生孤立电流脉冲群作为电磁导波激励信号的新方法,整个系统设计简单,无需功率放大器放大,成本大为降低;实际放电波形表明:这种激励信号瞬时电流很高,能达到重复脉冲群激励信号的3倍以上,完全满足实际电磁导波检测要求.     

Bounded Error Schemes for the Wave Equation on Complex Domains

This paper considers the application of the method of boundary penalty terms (SAT) to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell’s equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g., the staggered Yee scheme)—we achieve a decrease of two orders of magnitude in the level of the L₂-error.     

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.      

A Family of Finite Volume Schemes of Arbitrary Order on Rectangular Meshes

In this paper, we analyze vertex-centered finite volume method (FVM) of any order for elliptic equations on rectangular meshes. The novelty is a unified proof of the inf-sup condition, based on which, we show that the FVM approximation converges to the exact solution with the optimal rate in the energy norm. Furthermore, we discuss superconvergence property of the FVM solution. With the help of this superconvergence result, we find that the FVM solution also converges to the exact solution with the optimal rate in the $L^2$ -norm. Finally, we validate our theory with numerical experiments.     

基于口令的盲签名方案

利用Ｃｈａｎｇ－Ｌｉａｏ口令认证方案建立了两个盲签名方案。利用这些方案，网络中的用户使用口令不但可以访问计算机系统，而且可以用口令计算有关信息的签名，这使得签名收方在验证签名有效性的同时，还可以确认签名者是否具有签名的合法资格。作者对这些方案的安全性和实际应用还做了详细的讨论和分析。     

Optimal Communication Primitives on the Generalized Hypercube Network

Efficient interprocessor communication is crucial to increasing the performance of parallel computers. In this paper, a special framework is developed on thegeneralized hypercube, a network that is currently receiving considerable attention. Using this framework as the basic tool, a number of spanning subgraphs with special properties to fit various communication needs are constructed on the network. The importance of these spanning subgraphs is demonstrated with the development of optimal algorithms for four fundamental communication problems, namely, theone-to-allandall-to-all broadcastingand theone-to-allandall-to-all scattering. Broadcastingis the distribution of the same group of messages from a source processor to all other processors, andscatteringis the distribution of distinct groups of messages from a source processor to each other processor. We consider broadcasting and scattering from a single processor of the network (one-to-all broadcasting and scattering) and simultaneously from all processors of the network (all-to-all broadcasting and scattering). For the all-to-all broadcasting and scattering algorithms, a special technique is developed on the generalized hypercube so that messages originating at individual nodes are interleaved in such a manner that no two messages contend for the same edge at any given time. The communication problems are studied under thestore-and-forward, all-portcommunication model. Lower bounds are derived for the above problems under the stated assumptions, in terms of time and number of message transmissions, and optimal algorithms are designed.