关键词： 应用程序   递归算法   程序设计  

摘要： 随着计算机技术的快速发展,数学知识在计算机技术发展中,尤其是在计算机应用程序设计中处于及其重要的地位.同时,用数学的思维解决各种程序设计方面的难题也是十分重要的.在程序设计当中所解决的相当一部分问题都会涉及到各种各样的科学计算,这需要程序员将实际问题转换为程序,要经过对问题抽象的过程,建立起完善的数学模型,才能设计出好的软件.文章将介绍递归算法在程序设计中的应用并探讨数学知识在程序设计中应用及其重要性.

关键词： 配电网   电压暂降   数学形态滤波   求导  

摘要： 配电网出现单相接地故障时,故障相会出现大短路电流.智能电器要求在出现大短路电流情况下尽快启动瞬动保护,清除故障.但目前瞬动保护算法难以保证在各种短路情况下都能快速清除故障,保护重要负荷.本文对智能电器的瞬动保护算法进行了研究,提出了基于数学形态学(MM)滤波的瞬动保护算法,该算法先用级联数学形态滤波器对短路电流信号进行滤波,有效滤除了故障信号中的非周期分量和高频分量,滤波后用快速求导算法计算短路电流的有效值.算法简洁快速,兼顾瞬动保护的快速性和可靠性、不但有效地保护了线路和负荷,而且能缩短短路引起的电压暂降的持续时间,减少了短路造成的经济损失.

关键词： MOBILE communication systems   RADIO networks   RADIO transmitters & transmission   MATHEMATICAL optimization   MATHEMATICAL models  

摘要： Radio networks of universal mobile telecommunication system (UMTS) need accurate planning and optimisation, and many factors not seen in second generation (2G) networks must be considered. However, planning and optimisation of UMTS radio networks are often carried out with static simulations, for efficiency and to save time. To obtain a good trade-off between accuracy and computational load, link-level performance factors need to be taken into account. The authors propose a mathematical model for UMTS radio network planning taking into consideration fast power control, soft handover and pilot signal power in both uplink and downlink. Optimisation strategies are investigated based on three meta-heuristics: genetic algorithm, simulated annealing (SA) and evolutionary-SA. The base station location problem is modelled as a simplified p-median problem, and parameter tuning of these meta-heuristics are presented. Extensive experimental results are used to compare the performance of different algorithms in terms of statistical measurements. [ABSTRACT FROM AUTHOR]

关键词： 算法多样化   数学   教学片段   算理  

摘要： 《数学课程标准(实验稿)》从尊重每个学生的个性差异出发,在教学建议的第一、二学段分别都提到了"提倡算法多样化"和"鼓励算法多样化"的主张,这一建议不仅帮助教师了解不同学生的学习特点,而且有利于学生的个性发展,是培养学生创新精神和创新能力的一个崭新平台;同时也是实现"不同的人在数学上得到不同的发展"的一个新举措。随着课程改革的逐步深入,在落实"算法多样化"的过程中。

关键词： 数学建模   算法   优化   预测  

摘要： 本文讨论了在数学建模中的两类常用算法,对优化类算法中的先进算法包括遗传算法、神经网络、模拟退火法以及预测类的先进算法包括灰色预测、时间序列预测的算法思想和算法实现过程进行了说明.

关键词： 数学形态学   正电子发射计算机体层显像图像   背景噪声   医学图像配准   互信息  

摘要： 基于数学形态学的背景噪声处理算法通过图像二值化、二值形态学处理及背景替换消除背景噪声。其减小了互信息配准测度的局部极值,改善了配准测度。

关键词： real-time simulation   vehicle dynamics   vehicle-trailer coupling   commercial vehicles   differential-algebraic equations  

摘要： The real-time simulation of vehicle trains requires an accurate and numerically feasible representation of the vehicle-trailer coupling. Although the equations of motion for the chassis instances can be reduced to systems of ordinary differential equations, additional constraints on the relative motion of vehicle and trailer are introduced when considering the hitch. In this article, we present a strategy for the simulation of vehicle-trailer combinations, where the algebraic constraints of the coupling are treated explicitly. Although this approach allows exact modeling of the respective joint geometry and realistic calculation of the coupling forces, a suitable numerical algorithm is required in order to solve the resulting differential-algebraic system of index 3 in real-time. The implementation in a commercial vehicle dynamics program is discussed and real-time simulation results are shown, which prove its feasibility for different coupling joints and demanding driving maneuvers.

关键词： local optimization   complementarity   mathematical programming problem with equilibrium constraints   active-set algorithm  

摘要： In this paper, an algorithm for solving a mathematical programming problem with complementarity (or equilibrium) constraints (MPEC) is introduced, which uses the active-set methodology while maintaining the complementarity restrictions throughout the procedure. Finite convergence of the algorithm to a strongly stationary point of the MPEC is established under reasonable hypotheses. The algorithm can be easily implemented by adopting any active-set code for nonlinear programming. Computational experience is included to highlight the efficacy of the proposed method in practice.

关键词： symmetric generalized eigenvalue problem   preconditioned eigensolver   algebraic multigrid  

摘要： This paper presents a new algebraic extension of the Rayleigh quotient multigrid (RQMG) minimization algorithm to compute the smallest eigenpairs of a symmetric positive definite pencil (A, M). Earlier versions of RQMG minimize the Rayleigh quotient over a hierarchy of geometric grids. We replace the geometric mesh information with the algebraic information defined by an algebraic multigrid preconditioner. At each level, we minimize the Rayleigh quotient with a block preconditioned algorithm. Numerical experiments illustrate the efficiency of this new algorithm to compute several eigenpairs. Copyright (c) 2007 John Wiley & Sons, Ltd.

关键词： 数学选择题   算法   运算能力   估算   科学   估值   数学能力   能力要求  

摘要： 运算能力是一种重要的数学能力，也是新课标对学生的能力要求之一．运算能力主要是指明确算理和根据法则、公式、运算律对数与式的组合或分解变形的能力．数学对运算能力的要求可概括为“熟练、迅速、合理、准确”八个字，重在算理和算法，对运算的灵活性和实用性也有一定的要求．