关键词： 面积计算   格点   定理   圆面积   算法  

摘要： 本文通过毕克定理,即通过格点面积法,用圆内正方格的面积去逼近圆面积,从而近似计算圆的面积,提出来一种新思路,是一个有趣的探索。

关键词： two-dimensional integrable lattice   x-integral   integrable reduction   cutoff condition   open lattice   Darboux-integrable system   characteristic Lie algebra  

摘要： We study the problem of the integrable classification of nonlinear lattices depending on one discrete and two continuous variables. By integrability, we mean the presence of reductions of a chain to a system of hyperbolic equations of an arbitrarily high order that are integrable in the Darboux sense. Darboux integrability admits a remarkable algebraic interpretation: the Lie-Rinehart algebras related to both characteristic directions corresponding to the reduced system of hyperbolic equations must have a finite dimension. We discuss a classification algorithm based on the properties of the characteristic algebra and present some classification results. We find new examples of integrable equations.

关键词： logistics   milk-run   routing   mixed integer linear formulation   first   best-fit strategy   grouping evolution strategy  

摘要： The operational planning of distribution network for automotive industry is complex with many conditions to consider, including heterogeneous fleet, enforcing the feasibility of 3D-packing of pallets into vehicles to address the vehicle's capacity in terms of weight and volume, compatibility of orders in a vehicle, returning empty pallets from assembly-plants backwards to suppliers, and delivery time windows. A mathematical model (MILP) is proposed that takes account of these conditions to minimise total transportation costs. The network structure can be a combination of direct shipment and milk-run for both forward and reverse flow of pallets. The model is solved optimally for small-size problems. For solving larger problems, a heuristic algorithm (in two versions) is proposed that uses a similarity measure to generate a reasonable list of orders. Best/first-fit strategies are employed to generate a feasible solution with the aid of a relaxed version of the proposed MILP. Improvement heuristics are also designed. Unlike most of existing constructive heuristics, our aim for developing the heuristic approach is to force routing decision, with all of its considerations, being made optimal. We also use the proposed best-fit strategy in the body of grouping evolution strategy (GES) algorithm to attain an effective meta-heuristic approach. The effectiveness of heuristics is tested on generated instances which demonstrates they are optimal for small-size problems. They are also tested on the data of daily auto-parts shipments gathered from the largest Iranian automobile company. Results demonstrate there exists a significant potential for cost saving through milk-run strategy compared with the direct shipping strategy.

关键词： Optimization   genetic algorithm   solar energy   Jarghoyeh power plant   solar technology type  

摘要： With growing proliferation of environmental pollution and reduction of energy sources, human being has been always looking for a solution to reduce pollution. One of these solutions is to use solar energy. In this research, a mathematical model is developed for optimization location decision of solar cells to minimize the operational and investment costs. The location of placement and the type of solar technology is planned and optimized by Genetic Algorithm (GA). To show the validity of the model, an accurate solving method is applied for small dimensions. Then, the GA efficiency is shown by comparing GAMS and GA results in large dimensions using the optimum values of the GA parameters. Finally, the applicability of the proposed model is presented for Jarghoyeh power plant in Iran. The results indicate that GA with spending less time could find better answers in comparison with GAMS. The results show the effectiveness of the proposed model.

关键词： 算法多样化   数学思维   策略方法  

摘要： 算法多样化可以让学生在掌握基本运算方法时,获得解决问题、创新思维、发展思维的能力。运用算法多样化,可以活跃课堂学习氛围,学生积极参与,实现师生互动,提高学生数学素养。

关键词： 算法思想   高中数学   教学应用  

摘要： 高中数学教学顺应新课程改革提出的教学理念,正不断地丰富和发展着教学内容和积极的转变教学模式、更新教育理念等。算法在当前的教育背景下,越来越成为高中数学教学的重要部分,算法思想是数学学科核心素养的组成部分,是贯穿于数学发展始终,能够很好的应用于数学实践。因此,在高中数学教学中有效地应用算法思想有助于学生核心素养的培养和推进学生综合素质的有效提升。

关键词： 小学数学课堂教学   引导学生   学科核心素养   数学思维   方格图   乘法分配律  

摘要： 义务教育数学课程标准(2011版)提出了10个关键词,运算能力赫然在列。普通高中数学课程标准(2017版)明确提出数学学科核心素养包括:数学抽象、逻辑推理、数学建模、直观想象、数学运算和数据分析。数学运算再次名列其中,由此可见,数学运算及其能力作为后续学习和将来生活所必需的能力基础是何其重要。

关键词： S曲线加减速   数控机床   加减速控制   数学模型   数学算法  

摘要： 在数控机床使用中,机床初始启动所引起的惯性加速度会严重影响机床的稳定性,且容易产生磨损。采用S曲线加减速控制方法能够有效地解决数控机床出现的加速度突兀问题,从而使机床运行平稳,增大其工作效率。总结了数控机床的发展状况,介绍当前数控机床的控制方法以及S曲线加减速控制的主要特点。针对S曲线加减速控制的特点,分别分析了加减速控制特征对比、S曲线算法以及S曲线的数学模型。

关键词： 智能算法   数学建模教学   建模竞赛  

摘要： 文章首先介绍了常用智能算法并阐述了解决范畴分类,然后从现有情况、数学建模教学模式的提出、智能算法在数学建模教学中的实施办法、实施成效四个方面对智能算法在数学建模教学中的实施进行了探究。

关键词： 托槽   焊膏   数学形态学   主动轮廓模型  

摘要： 针对牙齿矫正托槽加工中的焊膏残留问题,提出一种数学形态学和主动轮廓模型的托槽焊膏图像检测算法。首先对三原色(RGB)彩图进行R-B灰度化处理,并进行灰度图阈值分割;然后对二值图进行数学形态学操作,去除噪声并提取托槽区域彩图。对托槽彩图进行色度,饱和度,纯度(HSV)转换,用主动轮廓模型对H分量进行分割。将托槽作为初始分割范围,再利用循环伏安(CV)模型分割出焊膏。试验结果表明:提出的算法目标定位能力强,能很好地提取焊膏目标,Jaccard相似度(SD)指数、正确率、错分率、漏分率分别为83.41%,90.96%,16.97%,2.43%。