摘要： This paper describes three algorithms for q-hypergeometric summation: it multibasic analogue of Gosper's algorithm, the q-Zeilberger algorithm, and an algorithm for finding q-hypergeometric solutions of linear recurrences together with their MAPLE implementations, which is relevant both to people being interested in symbolic computation and in q-series. For all these algorithms, the theoretical background is already known and has been described, so we give only short descriptions, and concentrate ourselves on introducing our corresponding MAPLE implementations by examples. Each section is closed with a description of the input/output specifications of the corresponding MAPLE command. We present applications to q-analogues of classical orthogonal polynomials. In particular, the connection coefficients between families of q-Askey-Wilson polynomials are computed. MATHEMATICA implementations have been developed for most of these algorithms, whereas to our knowledge only Zeilberger's algorithm has been implemented in MAPLE so far (Koornwinder, 1993 or Zeilberger, cf. Petkovsek et al., 1996). We made an effort to implement the algorithms as efficient as possible which in the q-Petkovsek case led us to an approach with equivalence classes. Hence, our implementation is considerably faster than other ones. Furthermore the q-Gosper algorithm has been generalized to also find formal power series solutions. (C) 1999 Academic Press.

关键词： mathematical computer knowledge   computer simulation of complicated intellectual processes   computer-aided theorem proving   problem solving   logical inference search   evidence algorithm   verification of mathematical texts  

摘要： A series of research works on the realization of the "evidence algorithm" program initiated by V. M. Glushkov in the sixties is described. The works are planned in the context of a new understanding of the theorem-proving problem and according to modern trends in information technologies and computer science.

关键词： Digital signal processing   Algorithms   Mathematical transformations   Algebra   Computational methods   Signal encoding   Pipeline processing systems   Computational complexity   Inverse problems   Discrete Hartley transform   Algebraic integer   Pipelined systolic architecture   computational methods   Algebra   Algebraic integer   Dihydrotestosterone   Pipeline processing systems   algorithms   Inverse method   complexity classes   discrete Hartley transforms   Signal encoding  

摘要： A novel algorithm for computing the discrete Hartley transform (DHT) is presented. The proposed algorithm is based on the algebraic integer encoding scheme. With the aid of this scheme, an error-free representation of the cas function becomes possible. Furthermore, for the implementation of the algorithm, a fully pipelined systolic architecture with O(N) throughput is proposed. (Author abstract) 6 Refs.

关键词： Camera calibration   Cameras   Surfaces   Vision  

摘要： An algebraic derivation of the Kruppa equations is presented. This derivation is much simpler and thus easier to understand than the conventional derivation based on projective geometry. Using the newly derived Kruppa equations, we further propose a new algorithm for determining a camera's intrinsic parameters. Experimental results and discussions are given for both synthetic and real images. (C) 1999 Optical Society of America [S0740-3232(99)02310-8].

关键词： Genetic algorithms  

摘要： We present and apply a new simulation/optimization approach for single- and multiple-planning period problems in groundwater remediation. Instead of the traditional control locations for contaminant concentrations, we use an L-infinity norm as a global measure of aquifer contamination (CMAX). We use response-surface constraints to represent CMAX within the optimization model. We compare the performance of formal mixed integer nonlinear programming and a genetic algorithm for several optimization scenarios.

关键词： image processing sequence   learning   mathematical morphology   genetic algorithms  

摘要： This paper presents a method to obtain an image processing procedure by showing an original image and a goal image. There has been previous work concerning automatic acquisition of image processing procedures by combining subroutine packages. In our approach, we do not use any image processing subroutine packages, but use only hierarchical mathematical morphology procedures, i.e. erosion and dilation operators. We use genetic algorithms to search procedures, i.e. erosion and dilation operators. Utilizing a parallel searching function of genetic algorithms and introducing a concept of era, we construct hierarchical procedures of mathematical morphology. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： max-plus algebra   linear optimization   eigenvalue   duality  

摘要： We consider the eigenvalue problem in the max-plus algebra for matrices in {-infinity boolean OR R}(nxn) but with eigenvectors in R-n. The problem is relaxed to a linear optimization (LO) problem of which the dual problem is solved by finding a maximal average weight circuit in the graph of the matrix. The Floyd-Warshall procedure is used to find such a circuit. This procedure also provides an efficient algorithm for finding an eigenvector. (C) 1999 Elsevier Science Inc. All rights reserved.

关键词： 13D05   13D45   14B15   13P10   16S32  

摘要： In this paper we present algorithms that compute certain local cohomology modules associated to ideals in a ring of polynomials containing the rational numbers. In particular, we are able to compute the local cohomological dimension of algebraic varieties in characteristic zero. Our approach is based on the theory of D-modules. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： 试题库   模型   高等数学   组卷  

摘要： 本文讨论了高等数学试卷生成模型及其实现算法问题.针对该问题,试研究出一种生成算法,尽管该算法不尽完善,但能很好地解决试卷生成中所遇到的问题.

关键词： 数学模型   遗传算法   优化   自动控制系统  

摘要： 采用遗传算法对控制系统的数学模型进行优化，由实验数据可以得出遗传算法是适合于控制系统模型寻优的。