关键词： 计算机三维图形   平方根倒数   最优化  

摘要： 在计算机三维图形领域中存在一个仅使用位操作和减法运算的快速平方根倒数算法.作者利用代数分析结合Mathematica软件提供的数值方法,通过构造相对误差目标函数并最小化之,证明了此算法的有效性,指出了其适用条件并发现了算法中一个常数的较优替代值.此外如果按输入分两类分别进行计算能再提高精度.进一步利用C语言编程手段验证了优化后的算法.

关键词： Free left distributive algebra   Division algorithm   Normal form   Braid   Word  

摘要： The left distributive law is the law a center dot (b center dot c) = (a center dot b) center dot (a center dot c). Left distributive algebras have been classically used in the study of knots and braids, and more recently free left distributive algebras have been studied in connection with large cardinal axioms in set theory. We provide a survey of results on the free left distributive algebra on one generator, A, and a new, simplified proof of the existence of a normal form for terms in A. Topics included are: the confluence of A, the linearity of the iterated left division ordering <(L) of A, the connections of A to the braid groups, and an extension P of A obtained by freely adding a composition operation. This is followed by a simplified proof of the division algorithm for P, which produces a normal form for terms in A and is a powerful tool in the study of A.

关键词： Videolaryngoscope Image processing   Vocal cord dynamic images   Automatic vocal cord image selection  

摘要： The human larynx is an important organ for voice production and respiratory mechanisms. The vocal cord is approximated for voice production and open for breathing. The videolaryngoscope is widely used for vocal cord examination. At present, physicians usually diagnose vocal cord diseases by manually selecting the image of the vocal cord opening to the largest extent (abduction), thus maximally exposing the vocal cord lesion. On the other hand, the severity of diseases such as vocal palsy, atrophic vocal cord is largely dependent on the vocal cord closing to the smallest extent (adduction). Therefore, diseases can be assessed by the image of the vocal cord opening to the largest extent, and the seriousness of breathy voice is closely correlated to the gap between vocal cords when closing to the smallest extent. The aim of the study was to design an automatic vocal cord image selection system to improve the conventional selection process by physicians and enhance diagnosis efficiency. Also, due to the unwanted fuzzy images resulting from examination process caused by human factors as well as the non-vocal cord images, texture analysis is added in this study to measure image entropy to establish a screening and elimination system to effectively enhance the accuracy of selecting the image of the vocal cord closing to the smallest extent. (C) 2013 Elsevier Ireland Ltd. All rights reserved.

关键词： Cancer   Biomedical modeling   Signal generators   Therapeutics   Cell division  

摘要： We propose an algorithm based on cross-entropy to determine parameters of a piecewise linear model, which describes intermittent androgen suppression therapy for prostate cancer. By comparing with clinical data, the parameter estimation for the switched system shows good fitting accuracy and efficiency. We further optimize switching time points for the piecewise linear model to obtain a feasible therapeutic schedule. The simulation results of therapeutic effect are superior to those of previous strategy. (C) 2013 AIP Publishing LLC.

关键词： 机械制造专业   数学   遗传算法   eM   -Plant软件  

摘要： 将实用先进的数学工具"遗传算法"融合到课程的教学中,能使学生在众多解决未来实际问题的途径和方法中选取最优。遗传算法具有简单、通用和鲁棒性强等优点,因而迅速成为车间调度应用的重要而有效的手段。以引入遗传算法为手段,从应用现状、教学内容及过程、使用功能强大的寻优软件三个方面引入遗传算法的方法,引导机械制造专业学生对实际问题进行优化的能力,可有效提升高职机械制造专业高等数学的针对性和实用性,激发学生解决优化问题的兴趣。

关键词： 数学史   教学   进位制   算法   生成过程   设计背景   数学知识   历史  

摘要： 一、设计背景 数学是一种文化．数学的产生、发展是一部灿若星河的历史，记述着数学的过往与现在，蕴藏着鲜活的数学生成过程．在教学中，我们往往过于注重数学知识的本身的理解和灵活地运用，却忽视数学的生成过程，

关键词： 算法教学   高中数学   信息技术   计算机课程   教育工作者   系统结构   教学过程   数学教学  

摘要： 在计算机课程中，算法是课程开展的基础，有着非常丰富的内容，比如数据原理、系统结构、软件、算法原理等方面的内容．同时，在数学的教学过程中，算法是一个非常重要的组成部分，在整个数学的发展史中，算法都一直存在．随着教育的不断发展，教育工作者逐渐意识到信息技术和数学算法结合的重要性，它将成为未来数学教学的必然趋势．

关键词： Vehicle routing problem   Split load   Simultaneous delivery and pickup   Tabu search  

摘要： This paper aims to study the split load vehicle routing problem in order to find a solution which would decrease logistics' cost by implementing simultaneous delivery and pickup which is part of the multi-attribute vehicle routing problem. A model was established based on certain preconditions and assumptions considering some specific characteristics in this simultaneous delivery and pickup procedure. A tabu search algorithm was applied to obtain the satisfactory solution. In this algorithm, a good initial solution was acquired by using the nearest neighborhood insertion method with the nearest neighbor structured by four operation methods including relocation operation, exchange operation, 2-opt, and the split point reposition operation. A parameter of tabu length was determined by a randomly selecting method, and a penalty function was designed through an automatic adjustment parameter. Data derived from case studies from a subsidiary company of China Railway Express were used to testify to the effectiveness and feasibility of the model and algorithm studied in this paper by comparing characteristics of solution convergence, solution quality and computing time with those of present analogous studies.

关键词： automation   domain-specific languages   domain-specific compilers   numerical linear algebra   generation of algorithms   knowledge management  

摘要： In this paper, we tackle the problem of automatically generating algorithms for linear algebra operations by taking advantage of problem-specific knowledge. In most situations, users possess much more information about the problem at hand than what current libraries and computing environments accept;evidence shows that if properly exploited, such information leads to uncommon/unexpected speedups. We introduce a knowledge-aware linear algebra compiler that allows users to input matrix equations together with properties about the operands and the problem itself;for instance, they can specify that the equation is part of a sequence, and how successive instances are related to one another. The compiler exploits all of this information to guide the generation of algorithms, to limit the size of the search space, and to avoid redundant computations. We applied the compiler to equations arising as part of sensitivity and genome studies. For the first application, the algorithms produced by our compiler attained, when compared with ADIFOR, speedups of between 29x and 79x. In the case of genome studies, the produced algorithms outperformed the state-of-the-art libraries GenABEL and FaST-LMM by factors beyond 1000.

关键词： 数据挖掘   Apriori算法   关联规则   高等数学   考试  

摘要： 分析关联规则中的Apriori算法特点,适当加以改进,采集学生在高等数学考试中的相关数据,利用最小支持度和最小置信度,使用改进后的算法,挖掘出频繁项集,找出它们之间隐藏的信息,可以使教师对教学内容和教学方法加以改进,能更好地指导教师命题,从而提高教师教学质量。