计算机代数系统Maple及其在机器人学上的应用

简要介绍计算机代数系统Maple功能 ,举例说明在机器人学中的应用 ,最后讨论了应用该系统应该注意的问题。利用其强大的符号计算功能使研究人员从推导公式的繁琐劳动中部分解脱 ,具有较强的现实意义     

On the Center of Generic Hecke Algebra

We knowthat the set of conjugancy class sumsof the group algebraR[W]forms a basisfor the cen-ter ofR[W]for any ringRand any finite WeylgroupW.It is knownthat thereis the Lusztig’siso-morphism between the group algebra ofWoverQ(q21)and the Hecke algebraH(W)overQ(q21),whereqis anindeterminate overQ[1].Therefore,itis natural to askif there is a“generic”analogue(or aq-analogue)of the above basis for the center ofR[W].Is there a canonical basis for the center ofthe Hecke algebraH(Sn)over…     

A 3D GIS spatial data model based on conformal geometric algebra

We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresponding basic elements (blades) in Clifford algebra, and the expressions of multi-dimensional objects are unified without losing their geometric meaning. Geometric and topologic computations are also processed in a clear and coordinates-free way. Under the CGA framework, basic geometrics are con...     

基于差分进化算法的手眼标定方法

针对眼在手机器人视觉系统的手眼标定问题，提出了一种基于差分进化算法的手眼标定方法。首先建立了眼在手机器人视觉系统手眼标定的数学模型，通过李群李代数理论，将手眼标定问题转化为误差函数的优化问题，同时保证了优化问题的最优解落在特殊欧氏群ＳＥ（３）上。通过差分进化算法对优化问题进行求解，避免了求解过程中的局部最优问题。最后在实物平台上进行了手眼标定实验，实验结果验证了算法的可行性和有效性。     

Multichannel image contrast enhancement based on linguistic rule-based intensificators

This study follows the direct approach to image contrast enhancement, which changes the image contrast at each its pixel and is more effective than the indirect approach that deals with image histograms. However, there are only few studies following the direct approach because, by its nature, it is very complex. Additionally, it is difficult to develop an effective method since it is required to keep a balance in maintaining local and global image features while changing the contrast at each individual pixel. Moreover, raw images obtained from many sources randomly influenced by many external factors can be considered as fuzzy uncertain data. In this context, we propose a novel method to apply and immediately handle expert fuzzy linguistic knowledge of image contrast enhancement to simulate human capability in using natural language. The formalism developed in the study is based on hedge algebras considered as a theory, which can immediately handle linguistic words of variables. This allows the proposed method to produce an image contrast intensificator from a given expert linguistic rule base. A technique to preserve global as well as local image features is proposed based on a fuzzy clustering method, which is applied for the first time in this field to reveal region image features of raw images. The projections of the obtained clusters on each channel are suitably aggregated to produce a new channel image considered as input of the pixelwise defined operators proposed in this study. Many experiments are performed to demonstrate the effect of the proposed method versus the counterparts considered.     

VEST: Abstract vector calculus simplification in Mathematica

We present a new package, VEST (Vector Einstein Summation Tools), that performs abstract vector calculus computations in Mathematica. Through the use of index notation, VEST is able to reduce three-dimensional scalar and vector expressions of a very general type to a well defined standard form. In addition, utilizing properties of the Levi-Civita symbol, the program can derive types of multi-term vector identities that are not recognized by reduction, subsequently applying these to simplify large expressions. In a companion paper Burby et al. (2013)  [12], we employ VEST in the automation of the calculation of high-order Lagrangians for the single particle guiding center system in plasma physics, a computation which illustrates its ability to handle very large expressions. VEST has been designed to be simple and intuitive to use, both for basic checking of work and more involved computations.     

区间集上的一元格蕴涵代数方程

把格蕴涵代数中滤子、素滤子、LI-理想、对偶原子和凸子格等概念拓展到区间集进行了重新定义,研究了三种基本的区间集上的一元格蕴涵代数方程,并给出了方程的可解性判断条件以及方程解集的若干性质.     

Boolean algebraic structure on [0,1]

In 1965 A. Renyi [1] demonstrated in his Landmark paper the mathematical model of random search. In this work we will study a generalized and modified model of Renyi. We will deduce the correspondence definitions of superimposed code for Renyi's model, and obtain lower and upper bounds for the optimal length of superimposed code     

RSA算法中的代数结构

本文首次应用二次剩余理论对RSA中的代数结构进行了研究.计算出了Zn中模n的二次剩余和二次非剩余的个数,对它们之间的关系进行了分析,并用所有二次剩余构成的群对Zn进行了分割,证明了所有陪集构成的商群是一个Klein四元群.对强RSA的结构进行了研究,证明了强RSA中存在阶为φ(n)/2的元素,并且强RSA中Zn可由三个...