关键词： 数学形态学   结构元素   骨架抽取  

摘要： 本文首先介绍了三种骨架抽取算法,并选取了最大圆盘的形态学骨架抽取算法作为研究对象,并对传统算法进行改进,不是选取单一的结构元素,而是选取两组(共8个)结构元素同时在各个方向对图像进行处理,得到了很好的效果。

关键词： Helmholtz   multigrid   eigenvalue   wave-ray  

摘要： Helmholtz equations with variable coefficients are known to be hard to solve both analytically and numerically. In this paper, we introduce a numerical multigrid solver for one-dimensional Helmholtz eigenvalue problems with periodic potentials and solutions. The solvers employ wave-ray methodology suggested by Brandt, Livshits for Helmholtz equations with constant coefficients. The paper concludes with numerical experiments and the discussion of future efforts for solving two-dimensional problems. Copyright (C) 2004 John Wiley Sons, Ltd.

关键词： computational biology   protein identification   weighted strings  

摘要： We investigate a problem which arises in computational biology: Given a constant-size alphabet A with a weight function mu : A --> N, find an efficient data structure and query algorithm solving the following problem: For a string sigma over A and a weight M is an element of N, decide whether sigma contains a substring with weight M, where the weight of a string is the sum of the weights of its letters (ONE-STRING MASS FINDING PROBLEM). If the answer is yes, then we may in addition require a witness, i.e., indices i less than or equal to j such that the substring beginning at position i and ending at position j has weight M. We allow preprocessing of the string and measure efficiency in two parameters: storage space required for the preprocessed data and running time of the query algorithm for given M. We are interested in data structures and algorithms requiring subquadratic storage space and sublinear query time, where we measure the input size as the length n of the input string a. Among others, we present two non-trivial efficient algorithms: LOOKUP solves the problem with O(n) storage space and O(n/log n) time;INTERVAL solves the problem for binary alphabets with O(n) storage space in O(log n) query time. We introduce other variants of the problem and sketch how our algorithms may be extended for these variants. Finally, we discuss combinatorial properties of weighted strings. (C) 2003 Elsevier B.V. All rights reserved.

关键词： 食品蒸煮机械   BP算法   双螺杆挤压机   数学模型   建模   操作参数  

摘要： 本文以玉米、小麦的混合物料为原料,进行了双螺杆挤压机的螺杆转速、进料速度、供水速度、机筒温度四种操作参数对双螺杆挤压机的挤压膨化效果(以膨化度来衡量)的影响的研究。依据要因实验设计及实验数据建立了系统的BP神经网络模型,实现对过程参数控制和目标输出的预测,结果用于指导生产实践。

关键词： 小学   数学教学   课程改革   课程标准   算法多样化   思维训练   探索精神  

摘要： 走进课改的数学课堂,经常可以看见这样的现象:一道计算题出来后,老师们常常要鼓励、引导学生思考采用不同的算法.有的教师会对学生说:'可以用你自己喜欢的方法计算.'于是问题就出现了,学生用的方法往往不是老师事先估计的'基本方法'(即老教材推崇的),也不一定是老师认为比较好的方法.教师的疑问也由此产生:为什么要提倡算法多样化?如何体现算法多样化?要不要对多样的算法进行优化?算法是不是越多越好?一堂课里如何处理'体现算法多样化'与'巩固计算方法'在时间分配上的矛盾?

关键词： Reconstruction   Polycrystals   Boundaries   Powders   Image  

摘要： A reconstruction method is presented for generation of three-dimensional maps of the grain boundaries within powders or polycrystals. The grains are assumed to have a mosaic spread below 1degrees. They are mapped by diffraction with a wide beam of hard X-rays, using a setup similar to that of parallel-beam absorption contrast tomography. First the diffraction spots are sorted with respect to grain of origin. Next, for each grain the reconstruction is performed by an algebraic algorithm known as three-dimensional ART. From simulations it is found that reconstructions with a spatial accuracy better than the pixel size of the detector can be obtained from as few as five diffraction spots. The results are superior to three-dimensional reconstructions based on the same data using a variant of the filtered back-projection algorithm. In comparison with layer-by-layer type reconstructions based on the two-dimensional ART algorithm, as introduced by Poulsen & Fu [J. Appl. Cryst. (2003), 36, 1062-1068], the quality of the maps is found to be similar, provided that five to ten spots are available for analysis, while data acquisition with the three-dimensional method is much faster. The three-dimensional ART methodology is validated on experimental data. With state-of-the-art detectors, the spatial accuracy is estimated to be 5 mum.

关键词： 编译原理   递归下降算法   数学表达式   LL算法   程序文件   编译程序  

摘要： 本文介绍使用编译原理理论中的LL(1)算法中最简单的种形式-递归下降算法来解决数学表达式的解析问题。同时．也介绍手工构造EBNF文法的分析器代码的方法．本文能对开发自己的语法分析器带来帮助。

关键词： Boolean algebra  

摘要： Neural networks have been applied in various domain including science, commerce, medicine, and industry. However, The knowledge learned by a trained neural network is difficult to understand. This paper proposes a Boolean algebra based algorithm to extract comprehensible Boolean rules from supervised feed-forward neural networks to uncover the black-boxed knowledge. This algorithm is called the BAB-BB rule extraction algorithm, which stands for a Boolean algebra based rule extraction algorithm for neural networks with binary and bipolar inputs. Decomposition techniques and interval arithmetic are used in the algorithm. First, each neuron associated with its inputs is analyzed and a Boolean function, describing the activation rule from its inputs to the neuron, is derived. These Boolean functions are merged into an aggregated Boolean rule according to the network topology. The Boolean rule is then further simplified by Boolean algebra operations. During the rule extraction procedure, redundant hidden neurons can be detected and removed without affecting the original function of the neural network. Examples of unipolar and bipolar inputs are presented to demonstrate the use of our algorithm. Finally, the Exclusive OR problem is presented and solved by our algorithm. Results show that our BAB-BB algorithm is practicable and of high efficiency.

关键词： Jacobians   Polynomials   Vector spaces   Curves   Embeddings   Geometric planes   Coordinate systems  

摘要： We use an embedding of the symmetric dth power of any algebraic curve C of genus g into a Grassmannian space to give algorithms for working with divisors on C, using only linear algebra in vector spaces of dimension O(g), and matrices of size O(g(2)) x O(g). When the base field k is finite, or if C has a rational point over k, these give algorithms for working on the Jacobian of C that require O(g(4)) field operations, arising from the Gaussian elimination. Our point of view is strongly geometric, and our representation of points on the Jacobian is fairly simple to deal with;in particular, none of our algorithms involves arithmetic with polynomials. We note that our algorithms have the same asymptotic complexity for general curves as the more algebraic algorithms in Florian Hess' 1999 Ph. D. thesis, which works with function fields as extensions of k[x]. However, for special classes of curves, Hess' algorithms are asymptotically more efficient than ours, generalizing other known efficient algorithms for special classes of curves, such as hyperelliptic curves (Cantor 1987), superelliptic curves (Galbraith, Paulus, and Smart 2002), and C-ab curves (Harasawa and Suzuki 2000);in all those cases, one can attain a complexity of O(g(2)).

关键词： 算法   数学教育   “算法”教与学   数学文化传统  

摘要： 算法是一种强有力的通用智慧工具，非常有助于人们学习和理解其他学科的知识。然而从笔者设计的问卷调查和师生访谈结果来看，我国当前中学数学教育中“算法”教学的现状不容乐观。从文化视角深入探究数学教育中的算法不仅有利于数学教育的现代化，而且有利于继承和发扬我国的数学文化传统，有利于促进开发和提高我国国民智力与民族素质。 在对各种“算法”概念综合的基础上，论文界定了数学教育中的“算法”概念，即一种人人都明白的清楚的(无歧义的)规定(规则、程序、严格的运算顺序)，准确地执行这些规定，任何一类建立了这种规定的问题都可以得到解决。就其本质而言，包括以下几个主要特征：确定性、序列性、有限性和一般性。“算法”所蕴涵的是一种特殊的“寓理于算”的机械化思想。借助现代数学教育理论，认知科学和建构主义理论，具体分析了“算法”的教育价值：培养良好的思维习惯；提高数学思维能力；发展数学应用意识与科技意识；形成积极的、良好的情感因素。根据现代数学课程理论、现代课程理论和现代教学理论，考察国外发达国家“算法”教学的概况，结合我国数学文化传统，探讨了算法教学内容在中学数学教育中的组织与实施。指出算法内容的选择要注重基础性、民族性和时代性，具体选择中可以将现行教材进一步挖掘，实现算法化；增加中国古代数学中的“术”、与计算机相结合的算法初步。算法内容的编排要遵循整体性原则、面向全体学生的原则、应用性原则和统一化与区别化相结合的原则，编排形式体现多样化、突出问题解决、呈现螺旋式上升。并分别选择初中和高中的一节数学教材进行改编，作为示范。具体到算法内容的教学，论文结合具体教学案例，从实践层面提出了四条建议：讲算法、重算理；进行算法化教学；鼓励算法多样化；强调动手“做”，用机“算”，这其中包括借助直观性学具进行实践操作、借助计算机等现代信息技术探索数学规律、通过书面记录反思算法活动。最后从理论和实践两个层面分别提出了中学数学教育中算法研究有待进一步研究的问题：算法在中学数学课程中与其在中学信息技术课程中如何取得平衡与协调?与中学数学课程中其他内容相比，算法有其特殊的学习机制吗?它是简单的概念学习或命题学习吗?算法的内容纷繁复杂，算法教学的原则及策略更是丰富多样，我们能从中提炼出算法教学的一般模式吗?等等。为促进后续研究的深入开展，论文还附上了“算法”教与学现状调查的所有问卷。