关键词： 数学课程标准   技术课程标准   算法   课程难度   问题解决  

摘要： 本文首先比较了数学课和技术课中算法的内容及其难度,然后在假设授课时数不变的情况下,为降低数学课中算法的难度,通过对算法形成过程的分析,得到了对算法教学内容进行适当调整的结论:数学课程中的算法应当加强程序框图设计的教学,减少算法语句的教学,与技术课程紧密协调,将算法语句在技术课程中进行强化学习。

关键词： blind identification   digital modulations   parametric normal forms   matrix of traces  

摘要： We introduce in this paper a new algebraic approach to some problems arising in signal processing and communications that can be described as or reduced to systems of multivariate quadratic polynomial equations. Based on methods from computational algebraic geometry, the approach achieves a full description of the solution space and thus avoids the usual local minima issue of adaptive algorithms. Furthermore, unlike most symbolic methods, the computational cost is kept low by a subtle split of the problem into two stages. First, a symbolic pre-computation of normal forms is done offline once for all sets of parameters, to get a more convenient parametric trace-matrix representation of the problem. The solutions of the problem are then easily obtained for any set of parameters from this representation by solving a single univariate polynomial equation. This approach is quite general and can be applied to a wide variety of problems: SISO channel identification of PSK modulations but also filter design and MIMO blind source separation by deflation.

关键词： ophthalmology   photokeratoscope   videokeratoscope   corneal   modeling   topography   algorithm   Sobolev   steepest   descent   numerical   differential   geometry  

摘要： Due to the resolution of current laser technology, the accuracy of corneal topography as measured by the videokeratoscope is no longer adequate to provide precise enough data for refractive surgery or for the fitting of customized contact lenses. We present an algorithm for recovering corneal topography that makes use of modern differential geometric techniques and numerical descent in Sobolev spaces. We believe this algorithm may be used with the photo- and videokeratoscope to increase the accuracy of the recovered corneal topography. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： 数学形态学   计算机围棋   地域  

摘要： 地域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。本研究在数学形态学的形式化基础上探讨了划分我领土、我领空、我领海、敌领土、敌领海、敌领空、公海、公空及未定区等9种地域的过程,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。

关键词： 供水管网   蚂蚁算法   节点方程   数学模型  

摘要： 管网水力计算的问题可归结为联立求解连续性方程、能量方程和压降方程.牛顿法是求解非线性方程组的一个经典方法,但当初值选择不好时,有可能不收敛.将新型的仿生算法———蚂蚁算法引入到求解管网数学模型中.利用拟牛顿法与蚂蚁算法相互之间较强的互补性,提出了求解供水管网微观数学模型的新算法———嫁接法.计算表明,嫁接法结合了蚂蚁算法与拟牛顿法各自的优点,计算速度快,效果良好.

关键词： 数字识别   数字仪表   数学形态学   击中击不中变换  

摘要： 结合水信息数字仪表检测系统的开发,对数字仪表数码的识别算法进行了研究,为满足仪表数字识别刷新速率快、数码位数多的特点,提出了一种基于数学形态学的识别方法;利用击中击不中原理,根据数码的特征,重新设计结构元素对,克服了HTM中一字一模的缺点,通过关键点的比较,利用结构元素对一次侦测得出数码的编码,然后通过编码确定数字值;由于每个数码只对应一个相应的编码,所以这种方法不会造成误判,在保证系统要求的识别的准确性的同时,提高了识别速度;同时本算法能够更加方便地提取结构元素对;实验表明能完全适应大型水信息数码识别的实时采集。

关键词： First order optics   Image reconstruction   Moire deflectometry   Optical computed tomography   Ray tracing   Reconstruction algorithms  

摘要： A novel algebraic iterative algorithm based on deflection tomography is presented. This algorithm is derived from the essentials of deflection tomography with a linear expansion of the local basis functions. By use of this algorithm the tomographic problem is finally reduced to the solution of a set of linear equations. The algorithm is demonstrated by mapping a three-peak Gaussian simulative temperature field. Compared with reconstruction results obtained by other traditional deflection algorithms, its reconstruction results provide a significant improvement in reconstruction accuracy, especially in cases with noisy data added. In the density diagnosis of a hypersonic wind tunnel, this algorithm is adopted to reconstruct density distributions of an axial symmetry flow field. One cross section of the reconstruction results is selected to be compared with the inverse Abel transform algorithm. Results show that the novel algorithm can achieve an accuracy equivalent to the inverse Abel transform algorithm. However, the novel algorithm is more versatile because it is applicable to arbitrary kinds of distribution. (c) 2006 Optical Society of America.

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.