关键词： Linear   Hypoderma   algorithms   Linear system   error distribution   Algebra   Laplace\'s equation  

摘要： In this article, the QMC method is applied to solving linear algebraic equations. In particular a finite difference analogue of the five-dimensional Laplace equation is examined. The error distribution is studied for linear systems and some high-dimensional integrals. A modification of the QMC method for linear systems is suggested which allows to considerably reduce the constructive dimension of the algorithm.

关键词： Comment on "A Unified Mathematical Framework for Strapdown Algorithm Design"   Artículo  

摘要： In the above-mentioned paper [1], Savage described a unied mathematical framework forstrapdown inertial navigation algorithm design. Quite recently, the present author also proposed a dual- quaternion representation of the principle of strapdown inertial navigation [2]. This Comment makes signicant simplications to the differential equation of the velocity translation vector (VTV) and shows the underlying connections between them.

关键词： quasi-steady states   reaction kinetics   generalized algorithm   mathematical modeling  

摘要： A generalized algorithm for mathematical models of chemical kinetics in quasi-equilibrium and quasi-steady-state approximations is proposed.

关键词： 形式化推导   PAR方法   算法程序  

摘要： 计算机科学的核心内容是使用算法处理离散数据,组合数学的重要性日渐凸显.使用形式化方法PAR开发了两个组合数学问题的算法,形式化推导过程为问题求解提供了思路,自然地引进了算法程序中用到的变量,清晰地展示了算法程序的设计过程,最终可得到简洁、易理解、可靠性高的算法程序.对形式化方法开发组合算法做了积极的探索,有利于促进组合算法设计自动化的研究及形式化开发方法的推广应用.

关键词： 算法思想   数学故事   现代信息技术   逻辑思维能力   组成部分   计算科学   科学技术   社会发展  

关键词： 自适应遗传算法   试题库   组卷   约束  

摘要： 针对传统组卷算法组卷速度慢,成功率较低,组卷质量不高等缺点,利用自适应遗传算法,设计出一种智能抽题算法的数学模型,能有效地解决试题库中的智能组卷问题.

关键词： 数学文化   《算法统宗》   程大位   珠算   中国传统数学  

关键词： Protein structure alignment   improved complete information set method   double dynamic programming   integer programming  

摘要： Protein structure alignment is one of the most important computational problems in molecular biology. From the viewpoint of computational complexity, a pairwise structure alignment is a NP-hard problem. In this paper, based on the discrepancy of two proteins, we define the structure alignment as a mixed integer-programming (MIP) problem with the simpler form and prove the existence of optimal solution. The optimal alignment is achieved by incorporating improved complete information set method used to modify the score matrix into iterative double dynamic programming algorithm. Convergence of algorithm is proved. A number of benchmark examples are tested. The results show that our model and approach are general and improve computational efficiency as well as quality of the structure alignment.

关键词： semi-algebraic sets   Euler-Poincare characteristic  

摘要： We present an algorithm which takes as input a closed semi-algebraic set, S subset of R-k, defined by P-1 <= 0,..., P-l <= 0, P-i is an element of R[X-1,..., X-k], deg(P-i) <= 2, and computes the Euler-Poincare characteristic of S. The complexity of the algorithm is k(O(l)).

关键词： COMPUTER algorithms   MATHEMATICAL models   ALGORITHMS   MATHEMATICAL analysis  

摘要： In this paper we present a tool to carry out the multifractal analysis of binary, two-dimensional images through the calculation of the Renyi D(q) dimensions and associated statistical regressions. The estimation of a (mono)fractal dimension corresponds to the special case where the moment order is q=0. (c) 2006 Elsevier B.V. All rights reserved.