关键词： linear algebraic method   minimal reaction   direct mechanism   simplexes  

摘要： We discuss here a new general linear algebraic method (both model and algorithm) for describing and generating (among others) minimal reactions and also minimal mechanisms in stoichiometry, or dimensionless groups in physics as well. (Further applications in process network syntheses will be discussed in [1].) With some minor modifications of the input this method can be extended for several related questions: for generating direct and overall reactions, direct (steady state) mechanisms, for finding the possible resulting (overall) reactions among all possible mechanisms, etc. Computational results in section 4 show the speed of our algorithm. We give also mathematical background and results in sections 3, 5 and 6. However, we do not restrict ourselves to mathematics only, we also talk on the language of chemistry, too. The theoretical results in sections 3.2, 3.3, 5 and the computational examples in section 4 are completely new, further theoretical results will appear in [1,2] and in [3].

关键词： 序列号   软件加密   飞天诚信   数学算法  

摘要： 数学算法一向都是密码加密的核心,但在一般的软件加密中,它似乎并不太为人们所关心,因为大多数时候软件加密本身实现的都是一种编程上的技巧。但近几年来随着序列号加密程序的普及,数学算法在软件加密中的比重似乎是越来越大了。我们先来看看在互联网络上大行其道的序列号加密的工作原理。当用户从网络上下载某个Shareware——共享软件后,

关键词： 遗传算法   数学基础   数理哲学  

摘要： Tutte introduced a V by V skew-symmetric matrix T = (t(ij)), called the Tutte matrix, associated with a simple graph G=(V,E). He associates an indeterminate z(e) with each e is an element of E, then defines t(ij) = +/-z(e) when ij = e is an element of E, and t(ij) = 0 otherwise. The rank of the Tutte matrix is exactly twice the size of a, maximum matching of G. Using linear algebra and ideas from the Gallai-Edmonds decomposition, we describe a very simple yet efficient algorithm that replaces the indeterminates with constants without losing rank. Hence, by computing the rank of the resulting matrix, we can efficiently compute the size of a. maximum matching of a graph.

摘要： This thesis explores the application of symbolic mathematics to nonlinear constrained mathematical optimization. Nonlinear programming (NLP) has been applied to a wide variety of business and scientific problems in such areas a chemical process engineering, electrical circuit design, inventory planning, financial portfolio optimization, parameter estimation, airline reservation planning, optimal control optimization, and many other areas. Symbolic mathematics is the application of computing technology to the manipulation of mathematical expressions and mathematical concepts. In recent years the techniques of symbolic mathematics have been popularized by the availability of software packages such as Mathematica and Maple. In contrast, numeric computing is the application of computing technology to the manipulation of numeric quantities (floating point representations) and has been used extensively for mathematical programming implementations. Symbolic mathematics extends the applicability of computing to such problems as: (1) Finding a mathematical expression for the gradient or Hessian of an expression. (2) Finding an expression or quantity for the limit of an expression as a variable approaches a given value from one or more directions. (3) Finding the greatest common denominator (GCD) expression of two polynomials which may be used to simplify the quotient of two polynomials. (4) Performing exact arithmetic in the rational polynomial domain [special characters omitted] to avoid numeric loss of accuracy from repeated computations. (5) Finding all solutions to a given system of nonlinear equations. As part of this thesis the author has developed a specialized object-oriented symbolic optimization system called SyOpt which has the ability to do symbolic computations over both rational and real fields and is highly extensible to future symbolic optimization research efforts. The SyOpt implementation is focused on taro particular algorithms for symbolic optimization; (

关键词： 数学竞赛   估算法   整数部分  

摘要： “估算法”是解有关竞赛问题的一种基本方法,举例如下: 一、范围估计范围估计就是根据题意,把所求数的大小范围估计出来,再在这一范围内探求。

关键词： 过值问题   初值问题   数学模型  

摘要： 利用求解初值问题的方法数值计算边值问题，建立了将边值问题转化为形式上的初值问题的数学模型，给出了相应的计算步骤．实例计算表明，本文方法的计算量小，精确度高．

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.