关键词： Finite termination   Convex programming   Variational inequality  

摘要： Two well-known results on the unified treatment of finite termination of a class of algorithms for solving convex programming problems and for solving variational inequality problems are reconsidered. In particular, some of the underlying assumptions employed in the existing literature are shown to be redundant. (C) 2008 Elsevier B.V. All rights reserved.

关键词： system of algorithmic algebras   regular scheme   data formalization   algorithm design   algorithm transformation  

摘要： A system of algorithmic algebras is considered whose basic concepts are newly interpreted to formalize the interrelation between operators and data of such a system. A modified formal instrument is constructed that extends the possibilities of design and transformation of regular schemes of algorithms.

关键词： Induction motors  

摘要： A technique of using design calculations that minimize the number of varied parameters, to drastically decrease the variation range, to protect the optimization algorithm from entering an inadmissible region, and to speedup the calculation process is described. The mathematical model proposed can be used both within optimization software and independently. Experience gained from the stand-alone use of design-calculation software when developing a lineup of energy-efficient IEMs shows that the time of searching for an optimal version is reduced by a factor of two to three compared to the calculations performed using classical confirmatory analysis technique. © 2008 Allerton Press, Inc.

关键词： Max-plus algebra   Reducible matrices   Eigenmode   Recurrent equations   Algorithm   Metro-bus  

摘要： In this paper, an algorithm for computing a generalized eigenmode of reducible regular matrices over the max-plus algebra is applied to the Metro-bus public transport system in Mexico city. A timed event Petri net model is constructed from the data table that characterizes the transport system. A max-plus recurrence equation, with a reducible and regular matrix, is associated with the transport system timed event Petri net. Next, given the reducible and regular matrix, the problem consists of giving an algorithm which will tell us how to compute its generalized eigenmode over the max plus algebra. The solution to the problem is achieved by studying some type of recurrence equations. In fact, by transforming the reducible regular matrix into its normal form, and considering a very specific recurrence equation, an explicit mathematical characterization is obtained, upon which the algorithm is constructed. The generalized eigenmode obtained sets a timetable for the transport system. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： 17世纪   算法倾向   机械化  

摘要： 目的揭示17世纪数学发展的倾向。方法对原始文献进行综合分析,从总体和概括的角度着眼。结果17世纪数学形成四大分支———解析几何、微积分、代数和综合几何。结论17世纪的数学思维活动侧重于计算而非证明,强调算法的获得而不注重命题的逻辑推理,即这个阶段的数学发展具有算法倾向。

关键词： 边缘检测   形态学梯度   梯度方向   非极大值抑制  

摘要： 针对传统数学形态学边缘检测算法存在的边缘分辨率较低、低强度边缘保护能力较差等问题,提出一种改进的数学形态学边缘检测算法。该算法在保持传统形态学方法优点的基础上引入边缘方向信息,采用非极大值抑制方法对形态学梯度图像进行细化处理,利用新的基于方向的检测和连接方法从中提取边缘,既提高了检测出的边缘的分辨率,又实现了低强度边缘的保护,同时还获得了更强的抗噪声能力。与应用较为广泛的传统形态学方法及Canny边缘检测方法的比较研究也证明了该算法的有效性。

关键词： 离散型随机变量   数学期望  

摘要： 利用定义求解离散型随机变量的数学期望有时显得非常复杂,本文给出了三种巧妙计算离散型随机变量数学期望的方法:对称性法、随机变量分解法、公式演变法.计算过程非常简洁,达到了简化计算的目的.

关键词： 贝叶斯网   自适应遗传算法   K2算法  

摘要： 基于某高校统计学院自1984-2005年间学生所学10门课程的成绩，利用K2算法并结合自适应遗传算法构建了课程贝叶斯网。用学生成绩样本的信息将有向无环图与概率理论有机地结合，直观地揭示了各门课程之间的依赖关系，通过条件概率表体现了依赖关系的强弱程度，不仅对学院不同学期课程的设置有一定的参考价值，而且对学生进一步学习而选择适合自己的研究方向提供权衡依据。

关键词： 教师   数学教学   阅读   算法  

摘要： 顺应潮流，算法第一次引入到了高中数学课程中．本文将着重举例说明计算机算法体现的数学基本思想方法．

关键词： stochastic programming   mathematical decomposition   Lagrangian relaxation   L-shaped decomposition   algebraic modelling language   open-source software  

摘要： An algebraic modelling language (AML) is a domain-specific computer programming language for describing and solving mathematical programming models. We propose extending AMLs so that solution algorithms that are based on iteratively manipulating, modifying and solving a model are supported at a high abstraction level. We specifically focus on stochastic programming models with random parameters formulated as discrete scenarios and mathematical decomposition algorithms, which are commonly applied to solve such models. We identify the necessary language constructs and develop a design based on the open-source modelling software APLEpy. The proposed design, although specifically addressing decomposition algorithms, proves useful for implementing heuristic solution algorithms as well. The object-oriented nature of the design enables the algorithms that are coded with the proposed extensions to work with any other model that satisfies the assumptions of the initial model. This flexible and robust design helps inexperienced modellers to easily apply an advanced solution algorithm, and experienced modellers to build sophisticated algorithms quickly within the same development environment that is used to describe the model under consideration.