Reproducing kernel enhanced local radial basis collocation method

Standard radial basis functions (RBFs) offer exponential convergence, however, the method is suffered from the large condition numbers due to their ‘nonlocal’ approximation. The nonlocality of RBFs also limits their applications to small‐scale problems. The reproducing kernel functions, on the other hand, provide polynomial reproducibility in a ‘local’ approximation, and the corresponding discrete systems exhibit relatively small condition numbers. Nonetheless, reproducing kernel functions produce only algebraic convergence. This work intends to combine the advantages of RBFs and reproducing kernel functions to yield a local approximation that is better conditioned than that of the RBFs, while at the same time offers a higher rate of convergence than that of reproducing kernel functions. Further, the locality in the proposed approximation allows its application to large‐scale problems. Error analysis of the proposed method is also provided. Numerical examples are given to demonstrate the improved conditioning and accuracy of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

三元搭配视角下的汉语动词语义角色知识库构建

动词语义角色一直是国内外语言学界研究的重点和难点。在自然语言处理领域,相关的语言资源也在逐步构建。对于汉语而言,国内大部分工作集中在语义角色标注上。该文创造性地提出了一种三元搭配的动词语义角色知识表征形式,并在前人研究的基础上,提出了一套语义角色分类体系。在该体系指导下,对汉语动词进行了穷尽式的语义角色认定及相关知识加工,以构建汉语动词语义角色知识库。截至目前,该工程考察了5 260个动词,加工了语义角色及引导词的动词数量为2 685个,加工认定语义角色4 307个。     

基于区间拟shannon小波配点法的供水系统水锤计算技术方法研究

文中将区间拟shannon小波配点法应用于水锤方程求解,通过将水锤方程中的待求函数用一系列拟shannon小波基函数逼近,对空间域进行离散,从而建立起关于时间的常微分方程组,构造出了水锤方程在小波空间的计算方法,并推演了管道中水锤波的传播。最后通过仿真实例计算出水锤方程的数值解,说明该方法对水锤计算具有较好的数值模拟性,从而为确保供水系统的安全和稳定运行提供技术支持。     

Selection and refinement of finite elements for optimal design and control: A Hamiltonian function approach

In this work, we propose a /methodology for the selection and refinement of finite elements for the integration of process design and control. The proposed methodology is based on the selection criteria of the Hamiltonian function through the implementation of the Pontryagin's minimum principle. The Hamiltonian function features to be continuous and constant over time for autonomous systems; nevertheless, the Hamiltonian function shows a nonconstant profile for underestimated discretization meshes, which is exploited in this work for the refinement of the discretization. Furthermore, the residuals at noncollocation points are evaluated to estimate the collocation error, this is used as a second refinement criterion in the proposed framework. The methodology is illustrated using two case studies featuring a reaction system with two CSTRs in series and the Williams–Otto reactor, respectively. The results showed that an accurate selection of the finite elements return economically attractive designs with fewer elements than those obtained with equidistributed finite element strategies.     

浅谈我国女性大学生体育舞蹈训练服装的选择与搭配

文章以四季色彩理论、基于外观的体型分类为依据,结合体育舞蹈训练服装的特色,分析我国女性大学生体育舞蹈训练服装色彩、款式等的选择和搭配方法,以期给此群体提供参考与指导。     

Least-energy path planning and oscillation analysis of robotic manipulator using direct collocation with nonlinear programming

ABSTRACT

Direct collocation is a method that converts a two-point boundary-value problem into a nonlinear programming problem by approximating the state variables and controls into parameters. It has been broadly used in studies of space and orbital mechanics yet has been rarely applied in the fields of robotics. This study builds up a mathematical model of a five-linked manipulator arm. Gradually reducing the upper and lower bounds of the five joint actuator outputs, this paper explores the variations in the least-energy cost function and the final time. Special attention has been focused on whether restrictions would ever arouse any un-anticipated oscillation in the joints. The numerical results show some irony. Excessively restricting the upper and lower output bounds of actuators does not actually gain traction in minimizing the cost index. On the contrary, the value of the cost index is increased by 41.77% from 924.87 to 1310.44 for a tunnel case whose radius is 1.5 m. The simulation cautions that unwanted frequency of oscillation begins to surface due to this wishful restricting. This paper demonstrates how Direct Collocation with Nonlinear Programming can be successfully applied to solve robotic path planning problems. It also cautions the users and designers of the manipulator about the unwanted frequency drift so that the users and designers can amend it before the oscillation builds up.     

A UNIFIED COLLOCATION ALGORITHM FOR PACKED-BED CHEMICAL REACTOR SIMULATION

Mathematical models of packed-bed catalytic reactors are aimed to predict the conversions and temperature profiles in both fluid and solid phases within the reactor. Although very general models can be mathematically formulated, usually several simplifying hypothesis are introduced for the fluid phase and/or the solid phase, in order to overcome computational difficulties

We describe in this paper a computational algorithm based on Orthogonal Collocation Method on finite elements, with elimination of the knot unknown functions, coupled with an integration method for stiff ordinary differential equations. This has been used in the development of a computer code, which allows us to find the transient behavior of the reactor by solving the equation relative to the external field, coupled with those describing the transient behavior in the catalyst particles, for a wide class of reactor models. The most general examined model includes axial dispersion in the external fluid phase, interphase mass and heat transfer resistances, intraphase mass resistance and any given kinetic scheme with complex reaction rate expressions.     

HOMOTOPY ANALYSIS OF FREE CONVECTION BOUNDARY LAYER FLOW WITH HEAT AND MASS TRANSFER

A steady two-dimensional laminar boundary layer flow of an incompressible viscous fluid over a semi-infinite surface is considered to investigate the accuracy of the homotopy analysis method. The governing coupled nonlinear system of differential equations is solved by means of the HAM approach. Explicit analytical series solutions are obtained and compared with numerical solutions. Good agreement is observed between the numerical results and HAM analytical solutions.     

Inverse heat conduction problems by using particular solutions

Based on the method of fundamental solutions, we develop in this paper a new computational method to solve two‐dimensional transient heat conduction inverse problems. The main idea is to use particular solutions as radial basis functions (PSRBF) for approximation of the solutions to the inverse heat conduction problems. The heat conduction equations are first analyzed in the Laplace transformed domain and the Durbin inversion method is then used to determine the solutions in the time domain. Least‐square and singular value decomposition (SVD) techniques are adopted to solve the ill‐conditioned linear system of algebraic equations obtained from the proposed PSRBF method. To demonstrate the effectiveness and simplicity of this approach, several numerical examples are given with satisfactory accuracy and stability. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20335