关键词： Mathematical modeling   Cutting and packing   Optimization   Phi-function   No-Fit Polygon  

摘要： The article is devoted to mathematical models and practical algorithms for solving the cutting and packing (C&P) problem. We review and further enhance the main tool of our studies - phi-functions. Those are constructed here for 2D and 3D objects (unlike other standard tools, such as No-Fit Polygons, which are restricted to the 2D geometry). We also demonstrate that in many realistic cases the Phi-functions can be described by quite simple formulas without radicals and other complications. Lastly, a general Solution strategy using the phi-functions is Outlined and illustrated by several 2D and 3D examples. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Texture modeling   Color image decomposition   Projected gradient algorithm   Color texture modeling  

摘要： In this paper, we are interested in texture modeling with functional analysis spaces. We focus on the case of color image processing, and in particular color image decomposition. The problem of image decomposition consists in splitting an original image f into two components u and v. u should contain the geometric information of the original image, while v should be made of the oscillating patterns of f, such as textures. We propose here a scheme based on a projected gradient algorithm to compute the solution of various decomposition models for color images or vector-valued images. We provide a direct convergence proof of the scheme, and we give some analysis on color texture modeling.

关键词： Mathematical foundations of cryptography   Secret sharing protocols   Strategic information management   Mathematical linguistics   Design of cryptographic algorithms  

摘要： This publication discusses new opportunities for creating threshold schemes for secret sharing arising from the use of mathematical linguistic formalisms. Such methods are based on known threshold schemes of information splitting extended by adding an extra stage at which bit blocks of the shared information are coded using suitably defined context-free grammars, hi practice, this will help with developing new algorithms, which besides allowing information sharing will also make it possible to obtain protocols for the confidential exchange of this information with or without involving a trusted instance. Such protocols will contribute to the development of modern cryptographic techniques and future computer science. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： algorithmic algebras   program design   program synthesis   algorithm optimization   heuristics   artificial intelligence  

摘要： The paper proposes a new approach and a system to develop parallel algorithms based on the joint use of the algebraic-algorithmic methodology of specification and development of programs and non-algorithmic (heuristic) techniques for code generation. The algebraic part of the methodology provides the formalized process of parallel program design through high-level algebraic-algorithmic specifications and automating transformations up to program code in a standard programming language. The heuristic part of the system is the dynamic adjustment of program code to a target platform and its optimization using self-learning code generation and heuristic technologies.

关键词： 欧拉算符   高阶微商余项   三次插值函数   准拉格朗日法   欧拉法   时间积分方案   CFL判据  

摘要： 从预报方程组通式和欧拉算符出发,用泰勒级数展开,推导出时空间微商余项为二阶、四阶完全预报方程组。可以证明,同阶时空间微商余项的准拉格朗日法和向前差分欧拉法时间积分方案,具有相同的物理意义和数学一致性,相比之下,传统中央差欧拉法时间积分方案是"简单格式"与"增大不可预测计算误差"并存。进而讨论用"三次插值函数"实现二阶时空间微商余项准拉格朗日法、或同阶向前差分欧拉法(可"二选一"),它们应该分别替代"双线性插值"准拉格朗日法和传统时空间中央差欧拉法,因前二者时空间微商余项及计算精度高于后二者。所以,三次插值函数算法可将准拉格朗日法和欧拉法时间积分方案、以及CFL判据统一起来。由于三次插值函数具有对原函数"变量场"的数学定律"收敛性"和二阶可导"最优性",且一次"三次插值函数"运算,即具对网格变量场二阶可导拟合"等价性":不仅拟合变量场斜率、还拟合其曲率和挠率。并因周期"三次插值函数",可作全球变量场"三次插值函数"二阶可导拟合,实现全球"三次"数值模式,并且可按变量场曲率判断,作变量场局域或单点平滑,保持"三次"模式时间积分的稳定性。

关键词： 垃圾收运   路线优化   邻域搜索   车辆路径问题  

摘要： 给出了城市生活垃圾收运路线优化问题的一般描述,考虑时间窗、车容量等约束,以收运路线总行程最短为目标,建立了该优化问题的数学模型。设计了求解该问题的单一组合邻域搜索算法,随机邻域搜索算法和变邻域搜索算法三种类型的邻域搜索算法。通过对多组算例的求解实验,结果表明变邻域搜索算法的优化效果明显优于其余类型的邻域搜索算法。

关键词： 数学证明方法   算法实现   程序设计  

摘要： 从数学证明和程序设计的角度,分析比较了数学命题定理证明中常用的数学归纳法、递推算法、递归算法、反证法等数学方法.讨论了它们在理论证明、算法实现方面的联系和优缺点,提出教学中的一些建议.

关键词： 核径迹   自动计数   DM642   数学形态学   抗干扰  

摘要： 固体核径迹点的参数测量在核技术领域占有极其重要的地位,而传统的人工计数法局限性非常大.近年来,DSP和图像处理技术越来越多地应用在了核技术领域.本文介绍了一种基于DM642图像处理平台的核径迹点自动计数系统.该系统利用数学形态学算法,能有效地从背景中分离出径迹点并去除噪点,进行准确计数,有助于减小人工计数的目测误差.

关键词： 间谐波   数学形态学   TLS-ESPRIT算法   形态滤波器  

摘要： 在无干扰情况下,传统的间谐波检测方法能较好地检测出间谐波分量;而当有干扰存在时,就无法检测出间谐波。针对传统检测方法的局限性,提出一种新的间谐波检测方法,实现了在有干扰情况下对间谐波的准确检测,且检测结果具有较高的精度。该方法利用形态滤波器有效抑制噪声的特性对检测信号进行消噪处理,保留信号的主要特征分量;对消噪后的信号采用TLS-ESPRIT算法进行检测,通过特征值分解得到信号子空间,并对信号子空间进行奇异值分解确定出空间旋转矩阵,求解间谐波分量。算例仿真结果表明,所提出的方法是可行和有效的。

关键词： 小学数学   算法优化   学生  

摘要： 算法优化是学生不断反思,不断完善自身认知结构的过程;当学生呈现多种算法后,如果不及时地进行优化,就放任了学生低思维水平的算法。多样算法需要适时适法进行优化。优化的过程还需要教师的适时引导,学生主体的参与。