关键词： 航空发动机   非线性数学模型   混合粒子群算法   计算效率   收敛性  

摘要： 以双转子混合排气涡扇发动机为研究对象,研究了粒子群算法(PSO)应用于航空发动机性能仿真时,控制参数对模型收敛性的影响,并结合N+1点残量法的优点,提出了在模型不收敛点采用粒子群算法与N+1点残量法交替计算的混合算法。理论分析与数值仿真结果表明,该算法既保持了N+1点残量法的高效率、高精度计算,又继承了粒子群算法大范围收敛的优点,可实现模型大范围、高效率、高精度收敛。

关键词： 数字签名   离数对数问题   大整数分解问题   二次剩余   公钥密码  

摘要： 为在同等计算复杂度的前提下提高算法的安全性,提出一个新的数字签名方案。在不扩大有限域zq*的基础上,通过增加本原根的维数,并且引入HAsh函数和二次剩余,基于多个数学难题对经典的Neberg-Rueppel[1]签名体制进行改进。通过比较发现新算法的安全性大大增强,但是其复杂度却没有相应增加。

关键词： 精度控制   浮点运算   数学函数   算法实现  

摘要： 文章在分析函数常用的级数法和迭代法算法的基础上,提出一种基于归约、逼近、重建的函数改进算法,满足浮点运算要求。通过测试证明了优化算法精度的优越性。同时,对基础数学库实现方法的研究,能够更有效满足高性能计算的精度要求和性能要求。

关键词： 高中数学   新教科书   算法初步   教科书比较   教学建议  

摘要： 教科书是新课程目标以及教学改革的物质载体．《标准》颁布后，新教科书中加入了算法的内容．为更好地为高中数学教育提供素材，通过以人教A版教科书和人教B版教科书的必修3中“算法初步”内容为研究对象，主要对教科书的章节结构、内容的组织和例题、习题配置等方面进行详细的比较研究．

关键词： 服装排料   数学表达   排放策略   计算机算法  

摘要： 服装排料问题是在一定的二维面料上排出尽可能多的服装样片,使面料的利用率高,以达到节省面料的目的。现研究用计算机智能化对服装面料排料的问题的策略进行数学分析和计算。

关键词： REPRESENTATIONS of algebras   ALGEBRAIC varieties   POLYNOMIALS   ALGORITHMS   MATHEMATICAL models   ALGEBRA   MATHEMATICAL analysis  

摘要： We suggest a model of representation of algebraic varieties based on representative systems of points of their irreducible components. Deterministic polynomial-time algorithms that substantiate this model are described in characteristic zero. The main result here is a construction of the intersection of algebraic varieties. As applications, we obtain efficient algorithms for constructing a smooth stratification and a smooth cover of an algebraic variety, which were introduced by the author earlier. Bibliography: 16 titles. © 2011 Springer Science+Business Media, Inc.

关键词： Constructive homological algebra   Abelian category   localization  

摘要： In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian category, which for the sake of computability need to be turned into constructive ones. We do this explicitly for the often-studied example Abelian category of finitely presented modules over a so-called computable ring R, i.e. a ring with an explicit algorithm to solve one-sided (in) homogeneous linear systems over R. For a finitely generated maximal ideal m in a commutative ring R, we show how solving (in) homogeneous linear systems over R-m can be reduced to solving associated systems over R. Hence, the computability of R implies that of R-m. As a corollary, we obtain the computability of the category of finitely presented R-m-modules as an Abelian category, without the need of a Mora-like algorithm. The reduction also yields, as a byproduct, a complexity estimation for the ideal membership problem over local polynomial rings. Finally, in the case of localized polynomial rings, we demonstrate the computational advantage of our homologically motivated alternative approach in comparison to an existing implementation of Mora's algorithm.

关键词： MODULES (Algebra)   ALGEBRA   WEYL groups   ALGORITHMS   CHARACTERISTIC functions   DIFFERENTIAL equations  

摘要： Let K be a field of characteristic zero n >= 1 an integer and A(n+1) = K[X, Y(1) Y(n)] the (n+1)th Weyl algebra over K Let S is an element of A(n+1) be an order-1 differential operator of the type S = partial derivative(X) + Sigma(n)(i=1) (a(1)Y(1) + b(1))partial derivative(Y1) + Sigma(n)(i=1) g(1) with a(1) b(1) is an element of K[X] and g(1) is an element of K[X Y(1)] for every i = 1 n We construct an algorithm that allows one to recognize whether S generates a maximal left Ideal of A(n+1) hence also whether A(n+1)/A(n+1)S is an irreducible non-holonomic A(n+1)-module The algorithm which is a powerful instrument for producing concrete examples of cyclic maximal left Ideals of A(n) is easy to implement and quite useful we use it to solve several open questions The algorithm also allows one to recognize whether certain families of algebraic differential equations have a solution in K[X Y(1) Y(n)] and when they have one to compute It (C) 2010 Elsevier B V All rights reserved

关键词： Ancient Chinese mathematics   He's amplitude-frequency formulation   Nonlinear oscillator  

摘要： An ancient Chinese mathematical method is briefly introduced, and its application to nonlinear oscillators is elucidated where He's amplitude-frequency formulation is outlined. Three examples are given to show the extremely simple solution procedure and remarkably accurate solutions. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： 数学形态学   计算机围棋   形势判断  

摘要： 形势判断是人类棋手必不可少的抽象概念,计算机围棋可以建立此概念以提高搜索效率.该文在数学形态学的形式化基础上探讨了对围棋实地和外势进行估算的过程,并结合实战对局评价了此算法的性能,指出了此算法的应用价值.