关键词： Wind power prediction   Clustering algorithm   Dilation and erosion   Mathematical morphology   The number of clusters  

摘要： Wind power has the characteristic of daily similarity. Furthermore, days with wind power variation trends reflect similar meteorological phenomena. Therefore, wind power prediction accuracy can be improved and computational complexity during model simulation reduced by choosing the historical days whose numerical weather prediction information is similar to that of the predicted day as training samples. This paper proposes a new prediction model based on a novel dilation and erosion (DE) clustering algorithm for wind power generation. In the proposed model, the days with similar numerical weather prediction (NWP) information to the predicted day are selected via the proposed DE clustering algorithm, which is based on the basic operations in mathematical morphology. And the proposed DE clustering algorithm can cluster automatically without supervision. Case study conducted using data from Yilan wind farm in northeast China indicate that the performance of the new generalized regression neural network (GRNN) prediction model based on the proposed DE clustering algorithm (DE clustering-GRNN) is better than that of the DPK-medoids clustering-GRNN, the K-means clustering-GRNN, and the AM-GRNN in terms of day-ahead wind power prediction. Further, the proposed DE clustering-GRNN model is adaptive. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： block relocation and loading problem   container   heuristic algorithm   integer linear program  

摘要： This study considers the block relocation and loading problem in container terminals. The optimal loading sequence and relocation location are simultaneously decided on the basis of the desired ship-bay and initial yard space configuration. An integer linear programming model is developed to minimize the number of relocations in the yard space on the basis of no shifts in the ship bay. The accuracy of the model is tested on small-scale scenarios by using CPLEX. Considering the problem size in the real world, we present a rule-based heuristic method that is combined with a mathematical model for the removal, loading, and relocation operations. The influence of rules on algorithm performance is also analyzed, and the heuristic algorithm is compared with different types of algorithms in the literature. The extensive numerical experiments show the efficiency of the proposed heuristic algorithm.

关键词： Jarzynski's equality   Fluctuation theorem   Nonequilibrium dynamics   Free energy difference   Variance reduction   Reaction coordinate  

摘要： In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality.

关键词： 3SUM   Subquadratic algorithms   General position testing   Range searching   Dominance reporting   Algebraic geometry   Degeneracy testing  

摘要： The 3SUM problem asks if an input n-set of real numbers contains a triple whose sum is zero. We qualify such a triple of degenerate because the probability of finding one in a random input is zero. We consider the 3POL problem, an algebraic generalization of 3SUM where we replace the sum function by a constant-degree polynomial in three variables. The motivations are threefold. Raz et al. gave an O(n11/6) upper bound on the number of degenerate triples for the 3POL problem. We give algorithms for the corresponding problem of counting them. GrOnlund and Pettie designed subquadratic algorithms for 3SUM. We prove that 3POL admits bounded-degree algebraic decision trees of depth O(n12/7+epsilon), and we prove that 3POL can be solved in O(n2(loglogn)3/2/(logn)1/2) time in the real-RAM model, generalizing their results. Finally, we shed light on the General Position Testing(GPT) problem: Given n points in the plane, do three of them lie on a line?, a key problem in computational geometry: we show how to solve GPT in subquadratic time when the input points lie on a small number of constant-degree polynomial curves. Many other geometric degeneracy testing problems reduce to 3POL.

关键词： Beam search algorithm   carpooling   exact solution method   mathematical model   transportation  

摘要： Carpooling is an environmentally friendly transportation system. It can efficaciously help resolve a variety of societal concerns of the urban areas, ranging from traffic congestion to environmental pollution. In this paper, we propose a new mathematical model to solve the carpooling problem. The model simultaneously minimizes the costs of travel times, the vehicle use, and the vehicle delays. An exact solution method based on Branch-and-Bound (B&B) algorithm is proposed to efficiently obtain the optimal solution of the problem. In order to find the near-optimal solutions for large-scale problems, a heuristic beam search algorithm is introduced, which is based on the partial relaxation of some fathoming criteria applied in our proposed B&B. The computational experiments are conducted, based upon the transportation network of Isfahan city, Iran. The results demonstrate the great capability of the proposed exact solution method in terms of both computational solving time required and the number of the evaluated nodes, in comparison with CPLEX software package. The findings of this research can be applied to solve the carpooling problem compatible to the real-life situations.

关键词： 主成分分析法   模糊贴近度   数据融合  

摘要： 本文利用多元统计方法中的主成分分析法计算测量值与主成分的相关系数,得出各传感器的综合支持程度,剔除综合支持程度较低的数据,取得有效数据。对有效数据,利用多传感器数据模糊相关特性,提出了一种基于模糊贴近度的数据融合方法。该数据融合方法计算过程相对固定,计算量小,便于计算机实时实现。

关键词： 数学模型   网络拓扑结构   遗传算法  

摘要： 网络性能最优,成为网络拓扑结构热点问题。对网络拓扑结构的定义进行了分析,从常见的网络数学模型出发,阐述了遗传算法的发展史,并对遗传算法在网络性能优化方面的应用进行了分析,说明运用遗传算法解决网络拓扑结构问题具有很大的优势。

关键词： 算理算法   运算能力   数学素养  

摘要： 数学素养是现代社会每一个公民应该具备的基本素养,运算能力是数学学科的核心素养之一。提高学生的运算能力,关键是要科学地处理好算理和算法的关系,寻求算理与算法的最佳平衡点。重算理轻算法,只会纸上谈兵频出错;轻算理重算法,则使学生计算缺乏支撑,不利于学生思维发展,只有重算理明算法,才能提高学生运算能力,从而提升学生的数学素养。

关键词： 高中数学   算法思想   应用探究  

摘要： 在科学技术迅猛发展的今天,信息技术和互联网技术被广泛应用于高中数学教学的领域中。无论是信息技术还是互联网技术,从本质上来讲核心思想核心内容都是算法,因此教师可从算法的角度来深入剖析高中数学教学。

关键词： 小学数学   比较思想   算法教学   应用   研究  

摘要： 小学生处在生长发育期,不可能在一夜之间形成较高的抽象思维能力与逻辑思维能力,在数学学习上存在着一定的难度。因此,教师应当认真研究小学生的思维方式,选择适合学生知识结构、认知特点、心理特征的比较形式,引导学生掌握比较思想,最终提高学生的数学素质。本文将研究如何在小学数学算法教学中应用比较思想。