ISBN: (纸本)9787111427711

关键词： MATHEMATICAL models   NEURAL networks (Computer science)   COMPUTER algorithms   MATHEMATICAL optimization   PERFORMANCE evaluation  

摘要： The tank capacity chart calibration problem of two oil tanks with deflection was studied, one of which is an elliptical cylinder storage tank with two truncated ends and another is a cylinder storage tank with two spherical crowns. Firstly, the function relation between oil reserve and oil height based on the integral method was precisely deduced, when the storage tank has longitudinal inclination but has no deflection. Secondly, the nonlinear optimization model which has both longitudinal inclination parameter.. and lateral deflection parameter.. was constructed, using cut-complement method and approximate treatment method. Then the deflection tank capacity chart calibration with a 10 cm oil level height interval was worked out. Lastly, the tank capacity chart was corrected by BP neural network algorithm and got proportional error of theoretical and experimental measurements ranges from 0% to 0.00015%. Experimental results demonstrated that the proposed method has better performance in terms of tank capacity chart calibration accuracy compared with other existing approaches and has a strongly practical significance.

关键词： 高中数学   算法教学   信息技术   整合分析  

摘要： 算法为算理的实际体现,是数学思维的关键载体,同时也是数学知识体系的重要组成。将算法纳入现代高中数学教学中,良性反映了高中数学课程同信息时代的协调发展,同时也彰显了我国基础教育范畴内数学课程教育的与时俱进。在课堂实际教学中所作出的高中数学算法同信息技术整合过程及教学心得,旨在为广大教育同仁提供借鉴思考。

关键词： 算法   算法教学   案例分析   教学建议  

摘要： 21世纪信息技术已应用到社会的各个领域,与人们的生活紧密联系。计算机发挥作用依赖于严格的程序控制,而算法是程序设计的基础,现代世界各国的中学课程中一般都加入有关算法的内容,我国也受到这种发展趋势的影响,在2003年4月教育部出台了《普通高中数学课程标准(实验)》,首次将算法列入高中数学必修教材之中,既然算法的引入已成为数学教育改革发展的必然结果,那么我们如何进行有效的算法教学,这是数学教育研究者以及从事高中数学教学的一线教师们值得深入思考和探讨的问题。 本论文主要分为以下三个部分： 第一部分包括第一章绪论和第二章文献综述,主要介绍了选题的缘由、研究的理论价值和实践意义,以及国内外关于算法的研究现状。 第二部分是第三章核心概念界定及研究的理论基础,主要阐述了算法及其相关概念的定义范畴,以及相应的理论基础。 第三部分包括第四至六章是本论文的核心部分,旨在研究算法教学应遵循的目标、原则和方法。在此基础上,将理论构想的案例教学设计放入实践中检验,得到及时的课堂教学反馈,并对今后的算法教学提出了相应的建议。 本文力图从理论基础的研究到教学过程的实践等多个方面对算法教学做出详细的探讨,理论联系实践,希望能对一线教师的教学有所帮助。

关键词： Fractal dimension  

摘要： Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.

ISBN: (纸本)9787118085433

关键词： 算法思想   数学思想   渗透方法   初中数学教学  

摘要： 算法是数学内容及数学思想方法的重要组成部分,反映了数学思想在实际问题中的灵活应用.掌握算法是现代社会人才的必备素质之一.因此,中学数学教学过程中,有必要渗透算法思想的介绍.本文通过两个实例介绍如何渗透算法,克服学生只懂数学,不知如何转化为算法,进而解决不了实际问题的困难.

关键词： 高中数学   “算法初步”   教学策略  

摘要： 算法是一个由来已久的概念,它是计算科学的基础,也是高中数学教学的重要内容。随着新课程的不断深入,"算法初步"教学也受到广大师生的重视。如何在高中数学课堂教学中有效地实施"算法初步"也就成为数学教师所关注的重点。本文在分析高中数学"算法初步"的教学设计原则的基础上,对高中数学"算法初步"的教学策略进行了主要的探讨。

关键词： Tomography  

摘要： Radio-frequency tomography was originally proposed to image underground cavities. Its flexible forward model can be used in free-space by choosing an appropriate dyadic Green's function and can be translated in the microwave domain. Experimental data are used to validate a novel inversion scheme, based on the algebraic reconstruction technique. The proposed method is improved by introducing physical bounds on the solution returned. As a result, the images of the dielectric permittivity profiles obtained are superior in quality to the ones obtained using classical regularization approaches such as the truncated singular value decomposition. The results from three experimental case studies are presented and discussed.

关键词： 数字图像   数学形态学   图像分割   去噪算法  

摘要： 随着信息时代计算机的日益普及,人们对数字图像的质量要求越来越高。但是数字图像在采集和传输的过程中,难免受到噪声污染,噪声恶化了图像质量,使图像变得模糊,甚至淹没图像特征,这对图像后续更高层次的处理是十分不利的,因此,在图像的预处理阶段,很有必要对图像进行降噪,这样可以提高图像的信噪比,消除混杂在图像中的干扰,改善图像质量,强化图像表现特征。 本文以数字图像去噪方法为研究对象,以数学形态学去噪算法为研究方向,首先综合分析了图像噪声,并对海藻图像及其噪声的特点进行了初步分析。然后综述了数学形态学处理和图像增强、图像分割的基本理论。最后,提出了一种新颖的滤波方法——将图像分割和形态学处理相结合对海藻图像进行滤波,经实验仿真验证,此算法简单有效,对海藻图像实现了较好的滤波效果。