关键词： 数学形态学   边缘   图像处理  

摘要： 研究图像边缘优化提取问题。由于图像在进行边缘提取过程中,容易受到外界信息的干扰,特别是当受到噪声等因素影响时,造成图像边缘提取困难。为此提出了一种新的采用两层数学形态学增强操作提取图像边缘的技术。首先将利用形态学对灰度图像进行增强,并以为基础利用形态学的膨胀操作单独对边缘进行增强,然后将图像切分成小块,针对不同的小块来区分边缘与非边缘;最终经过模板滤波,获得清晰的边缘结果图像。仿真结果表明,改进的算法快速有效,在提取完整的边缘的同时,能够有效的抑制噪声和背景因素对边缘的干扰,并优于其他传统边缘提取方法。

关键词： Google   PageRank   导向量   阻尼因子  

摘要： 提出了求解PageRank高阶导向量的两种新算法.讨论了PageRank问题系数矩阵的一些数学性质,并从理论上分析了两个公式求解PageRank高阶导向量的优劣.数值实验表明了新算法的数值性态.

关键词： 算法思想   经典数学问题  

摘要： 算法思想的渗透帮助学生体会中国古代数学的思想与方法，进而理解中国古代的数学文化算法在中国古代早已有之．其中所蕴涵的丰富的算法思想对今天的数学学习与数学研究都有很大的影响．本文主要是列举算法思想在一些中国古代经典数学问题中的渗透．从而进一步体会算法思想在古代数学中的贡献的同时也认识到中国古代数学的博大精深．

关键词： Oil price   Uncertainty and complexity   Forecasting   Fuzzy regression   Artificial neural network  

摘要： This paper presents a flexible algorithm based on artificial neural network (ANN) and fuzzy regression (FR) to cope with optimum long-term oil price forecasting in noisy, uncertain, and complex environments. The oil supply, crude oil distillation capacity, oil consumption of non-OECD. USA refinery capacity, and surplus capacity are incorporated as the economic indicators. Analysis of variance (ANOVA) and Duncan's multiple range test (DMRT) are then applied to test the significance of the forecasts obtained from ANN and FR models. It is concluded that the selected ANN models considerably outperform the FR models in terms of mean absolute percentage error (MAPE). Moreover, Spearman correlation test is applied for verification and validation of the results. The proposed flexible ANN-FR algorithm may be easily modified to be applied to other complex, non-linear and uncertain datasets. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： computer model   algebra of algorithms   data   algorithmic construction   operation of algebra of algorithms   D-operator  

摘要： A system of algorithmic algebras is formed on the basis a modified Glushkov computer model. Data are formalized and specified at inputs and outputs of D-operators and, hence, the formal apparatus constructed is based on data. Some properties of D-operators and operations that form the signature of the algebras are proved and the possibility of construction of derived D-operators is shown.

关键词： Flexible manufacturing systems   Machine loading problem   Genetic algorithm   Process planning  

摘要： Machine loading problem in a flexible manufacturing system (FMS) encompasses various types of flexibility aspects pertaining to part selection and operation assignments. The evolution of flexible manufacturing systems offers great potential for increasing flexibility by ensuring both cost-effectiveness and customized manufacturing at the same time. This paper proposes a linear mathematical programming model with both continuous and zero-one variables for job selection and operation allocation problems in an FMS to maximize profitability and utilization of system. The proposed model assigns operations to different machines considering capacity of machines, batch-sizes, processing time of operations, machine costs, tool requirements, and capacity of tool magazine. A genetic algorithm (GA) is then proposed to solve the formulated problem. Performance of the proposed GA is evaluated based on some benchmark problems adopted from the literature. A statistical test is conducted which implies that the proposed algorithm is robust in finding near-optimal solutions. Comparison of the results with those published in the literature indicates supremacy of the solutions obtained by the proposed algorithm for attempted model. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Immersion and Invariance   differential algebraic systems   transient stability   electrical power systems  

摘要： A stability result based on the Immersion and Invariance control strategy is derived for a class of systems described by differential equations with algebraic constraints. The result is then applied to synthesize a stabilizing control law for a two machine electrical power system with a controllable series capacitor (CSC). The dynamics of the two-machine system. is given by differential equations and the active power balance at the load buses is given by algebraic equations. The CSC dynamics is described by a first order differential equation.

关键词： Nonstandard analysis   Skolem paradox   Lowenheim-Skolem theorem   computability   Takagi function  

摘要： Non-standard analysis can be harnessed by the recursion theorist. But as a computable economist, the conundrums of the Lowenheim-Skolem theorem and the associated Skolem paradox, seem to pose insurmountable epistemological difficulties against the use of algorithmic nonstandard analysis. Discontinuities can be tamed by recursive analysis. This particular kind of taming may be a way out of the formidable obstacles created by the difficulties of Diophantine Decision Problems. Methods of existence proofs, used by the "classical" mathematician - even if not invoking the axiom of choice - cannot be shown to be equivalent to the exhibition of an instance in the sense of a constructive proof. These issues were prompted by the fertile and critical contributions to this special issue.

关键词： MATHEMATICAL analysis   ASYMPTOTIC expansions   NUMERICAL analysis   ALGEBRA   POLYNOMIALS   MATHEMATICS   ALGORITHMS  

摘要： A polynomial in three variables is considered near a singular point where the polynomial itself and its partial derivatives vanish. A method for calculating asymptotic expansions in parameters for all branches of the set of roots of the polynomial near the singular point is proposed. The method is based on spatial power geometry and uses modern computer algebra algorithms: for calculating Grobner bases and for work with algebraic curves. The implementation of the method is demonstrated on the example of a sixth-degree polynomial in three variables considered near infinity and near a degenerate singular point.