关键词： 国际计算机   程序设计   思维方式   数学思维   ACM/ICPC   艺术   算法   感受  

摘要： ACM／ICPC是国际计算机协（Association for Computing Machinery）组织的国际大学生程序设计竞赛（International Collegiate Programming Contest），这项每年一届的计算机学科竞赛始于1976年，是大学生智力与计算机解题能力的竞赛，是世界公认的、目前全球高校之间规模最大且最具影响力的国际顶级赛事。

关键词： 图像识别   数字水印   三维模型   图像处理  

摘要： 随着数字媒体信息处理技术的发展和应用领域的拓展，作者的版权保护问题变得越来越重要。数字水印技术是解决这个问题的一个很好的方法。由于三维模型数据日益成为流行的多媒体数据类型，用于互联网上数据的交换和可视化，三维模型数字水印技术将用于解决随之而来增长的版权问题。\n 本文首先介绍了研究三维模型数字水印技术的目的，及对版权保护的重要意义，并且概述了目前国内外对三维模型数字水印的研究状况。接着介绍了三维模型的建模方法和数据表示，三维模型数字水印技术的基本框架，基本特性，在研究过程中遇到的难题，三维模型数字水印技术的性能评估和攻击方法，最后对三维模型数字水印算法的分类进行了介绍。在以国内外先进的三维模型数字水印技术的参考背景下，本文提出一种基于块矢量的三维网格模型数字水印改进算法。对三维网格模型进行分块，用块质心集替代原模型质心，构造模型块曲面的基本几何单元，视觉系统产生最小代价的基础上，调整块质心来嵌入单位水印信息，从而改变顶点位置使水印信息遍布整个模型。该算法对噪声、简化、仿射变换等不同的攻击特别是剪切攻击具有较好的鲁棒性。此外还提出一种基于拉普拉斯矩阵的三维模型数字水印改进算法，根据三维模型顶点的链接关系，构造拉普拉斯矩阵，然后进行频谱分析，在此基础上调整频谱系数，从而将水印信息嵌入到三维模犁中，水印信息在嵌入模型之前利用扩频原理进行了预处理，从而增加了水印对随机噪声攻击的鲁棒性。最后，用图像水印信息替代简单的水印信号量信息，基于位分解原理对灰度图像进行了预处理。实验结果表明该算法可抵抗如仿射变换、顶点坐标的随机噪声、网络平滑（网格的低通滤波）等不同的攻击，但对剪切攻击抵抗能力差。因此，结合两种算法的原理，提出一种基于块矢量拉普拉斯矩阵的算法，对灰度水印图像进行置换预处理，从而在原有的对网格攻击的基础上又互补了彼此没有的抵抗性，较大地提高了算法的鲁棒性。

关键词： 高中数学   教学   算法  

摘要： 作为基础教育的数学新课程改革已把算法列为高中数学课程新的双基内容之一。的确，算法学习的现实意义不容忽视，它不但能够培养学生有条理地思考与表达的能力，而且能发展学生解决实际问题的能力，并为今后学习程序设计打下基础。

关键词： 小波变换   数学形态学   图像去噪  

摘要： 针对文本图像存在的噪声,提出了小波变换和数学形态学相结合的文本图像去噪算法。通过小波变换对原始图像进行多尺度分解,对小波近似系数进行线性拉伸处理,细节系数进行域值化处理后重建图像,对重建图像进行直方图均衡化,然后再进行数学形态学运算去除剩余噪声。结果显示本文方法对于存在大量噪声的文本图像可以起到很好的去噪效果。

关键词： “改革障碍”报告   数理教学   算法教学   教育隐喻  

摘要： 美国的"从国际视角评价美国数学改革障碍"报告(以下简称"改革障碍"报告)针对"数理"和"算法"教学的选择争议,评析了美国数学教育改革的五大障碍,从中提炼了关于美国数学教育乃至整个教育的诊断性建议。本文将其与我国数学教学的特色和长处相对比,提出了三个教育隐喻,一是跨国教学的一致性趋势;二是教育的学科发展问题和什么是"好"的教学标准问题;三是教师培训的学科方向性问题。

关键词： 蚁群算法   配电网   信息素  

摘要： 介绍了蚁群算法在配电网中数学模型的建立。在搜索算法中首先确定的是权值,在配电网中权值是由无功消耗、线路重要性、线路长度和线路成本来确定的。通过权值分析了蚂蚁从原点到终点的搜索模型,蚂蚁在游程中会释放信息素,权值大的说明支路最短,蚂蚁释放的信息素也会增多,最后通过蚂蚁在反复游程中释放信息素的多少会寻找到最优解或者次优解的最优路径。把蚁群算法应用在配电网中能够有效地搜索出最优解或次优解,大大地减少了最优解的搜索时间。

关键词： parametric optimization   assignment problem   max-algebra   characteristic max-polynomial   essential terms  

摘要： This article presents a fast algorithm for a class of parametric assignment problems. Moreover, it is shown how this algorithm can be applied to a problem arising in the so-called max-algebra which results as an analogue of classical linear algebra by replacing the classical addition and multiplication by a circle plus b = max(a, b) and a circle times b = a + b, respectively. An instance of the linear parametric assignment problem is given by a bipartite graph G = (U, V, E) with 2n vertices, m edges and affine-linear parametric edge weights c(lambda)(i, j) = c(i, j) - b(i, j)lambda for (i, j) is an element of E. The task is to find an assignment with minimum weight with respect to the parametric weights c(lambda) for all values of lambda. We develop an algorithm which solves the special case for which b(i, j) is an element of {0,1} for all (i, j) e E in O(mn + n(2) log n) time. Our algorithm can be extended to solve the special parametric assignment problem which arises in connection with computing the essential terms of the so-called characteristic max-polynomial. The resulting algorithm runs in O(n(3)) time and thus improves upon the best-known algorithm for computing the characteristic max-polynomial due to Burkard and Butkovic (Appl Math 130 (2003), 367-380) by a factor of n. (C) 2009 Wiley Periodicals, Inc. NETWORKS, Vol. 55(2), 61-77 2010

关键词： EUCLIDEAN algorithm   POLYNOMIALS   NUMBER theory   PLANE curves  

摘要： Finding the intersection point of two lines in the plane is easy. But doing the same for a pair of algebraic plane curves is more difficult, not least because each point on both curves may be a multiple intersection point. However, we show that, with the help of the Euclidean algorithm for polynomials, this general problem can be reduced to the case of intersecting lines, giving an algorithm for finding these intersection points, with multiplicities. It also yields a simple proof of Bézout’s theorem, giving the total number of such points.

关键词： BCI-algebra   Fuzzy point   p-ideals   (m, n)-fold p-ideal   Fuzzy (m, n)-fold p-ideal  

摘要： In [C. Lele, S. Moutari, M.L.N. Mbah, Algorithms and computations for foldedness of p-ideals in BCI-algebras, J. Appl. Logic 6 (4) (2008) 580-588], the notion of the n-fold p-ideals in BCI-algebras as a generalization of p-ideals in BCI-algebras, is introduced, but we show that an ideal is an n-fold p-ideal if and only if it is a p-ideal. and that the results of the mentioned paper is the same as those in [Y.B. Jun, J. Meng, Fuzzy P-ideals of a BCI-algebra, Math. Japon. 2 (1994) 271-282, X.H. Zhang, J. Hao, S.A. Bhatti, On p-ideals of a BCI-algebra, Punjab Univ. J. Math. 27 (1994) 121-128]. In this paper we the notions of (m.n)-fold p-ideals and fuzzy (m.n)-fold p-ideals, for each observe that, positive integers m, n, are indeed the natural generalization of p-ideals and fuzzy p-ideals, respectively. A characterization of (m, n)-fold p-ideals and fuzzy (m, n)-fold p-ideals is given, and conditions for which an ideal (respectively fuzzy ideal) is an (m, n)-fold p-ideal (respectively fuzzy (m, n)-fold p-ideal) are studied. We also establish extension properties for (m, n)-fold p-ideals and fuzzy (m, n)-fold p-ideals. Furthermore, we construct some algorithms to determine whether certain finite sets provided with a well defined operation, are BCI-algebras, (m, n)-fold p-ideals, fuzzy subsets or fuzzy (m, n)-fold p-ideals. (C) 2009 Elsevier B.V. All rights reserved.

关键词： algebraic path problem   orbital systolic algorithms   array processors   data manipulation  

摘要： The algebraic path problem (APP) is a general framework which unifies several solution procedures for a number of well-known matrix and graph problems. In this paper, we present a new 3-dimensional (3D) orbital algebraic path algorithm and corresponding 2-D toroidal array processors which solve the n x n APP in the theoretically minimal number of 3n time-steps. The coordinated time-space scheduling of the computing and data movement in this 3-D algorithm is based on the modular function which preserves the main technological advantages of systolic processing: simplicity, regularity, locality of communications, pipelining, etc. Our design of the 2-D systolic array processors is based on a classical 3-D -> 2-D space transformation. We have also shown how a data manipulation (copying and alignment) can be effectively implemented in these array processors in a massively-parallel fashion by using a matrix-matrix multiply-add operation.