关键词： C语言   最大公因数   Euclid辗转相除法  

摘要： 通过数学理论证明给出计算机C语言编程中求两个正整数的最大公因数的算法的数学解释。

关键词： Electricity consumption   Fuzzy regression   Principal component analysis   Preprocessing   Time series   Uncertainty  

摘要： This paper introduces an integrated algorithm for forecasting electricity consumption (EL) based on fuzzy regression, time series and principal component analysis (PCA) in uncertain markets such as Iran. The algorithm is examined by mean absolute percentage error, analysis of variance (ANOVA) and Duncan Multiple Range Test. PCA is used to identify the input variables for the fuzzy regression and time series models. Monthly EL in Iran is used to show the superiority of the algorithm. Moreover, it is shown that the selected fuzzy regression model has better estimated values for total EL than time series. The algorithm provides as good results as intelligent methods. However, it is shown that the algorithm does not require utilization of preprocessing methods but genetic algorithm, artificial neural network and fuzzy inference system require preprocessing which could be a cumbersome task to deal with ambiguous data. The unique features of the proposed algorithm are three fold. First, two type of fuzzy regressions with and without preprocessed data are prescribed by the algorithm in order to minimize the bias. Second, it uses PCA approach instead of trial and error method for selecting the most important input variables. Third, ANOVA is used to statistically compare fuzzy regression and time series with actual data.

关键词： short term synaptic dynamics   short term depression   facilitation   stochastic simulation   stochastic synapse   vesicle site model   synaptic plasticity models   short term plasticity  

摘要： The release of neurotransmitter vesicles after arrival of a pre-synaptic action potential (AP) at cortical synapses is known to be a stochastic process, as is the availability of vesicles for release. These processes are known to also depend on the recent history of AP arrivals, and this can be described in terms of time-varying probabilities of vesicle release. Mathematical models of such synaptic dynamics frequently are based only on the mean number of vesicles released by each pre-synaptic AP, since if it is assumed there are sufficiently many vesicle sites, then variance is small. However, it has been shown recently that variance across sites can be significant for neuron and network dynamics, and this suggests the potential importance of studying short-term plasticity using simulations that do generate trial-to-trial variability. Therefore, in this paper we study several well-known conceptual models for stochastic availability and release. We state explicitly the random variables that these models describe and propose efficient algorithms for accurately implementing stochastic simulations of these random variables in software or hardware. Our results are complemented by mathematical analysis and statement of pseudo-code algorithms.

关键词： 数学思维训练   教学   算法   解读   素数   测试题   数学题   微软  

摘要： 这是一道微软的招聘测试题：中间只隔一个数字的两个素数被称为素数对，如5和7，17和19，证明素数对之间的数字总能被6整除（假设这两个素数都大于6），现在证明没有由三个素数组成的素数对。这是一道显而易见的数学题，微软为何要出这样一道题？

关键词： 小学数学   算法   多样化  

摘要： 新课程理念下的小学数学教学,越来越关注算法的获得,探讨新的数学课堂教学的模式,调动不同层次学生学习数学的积极性,充分发挥学生的思维,培养学生分析问题、解决问题的能力,以及学生在课堂中学习的互补性。但在具体的教学中需要教师重新去认识,正确去解决。

关键词： 数学公式   二叉树   归一化   相似度  

摘要： 提出了一种基于二叉树结构的LaTeX格式数学公式匹配算法。首先根据数学公式的LaTeX格式生成其二叉树表示,并对树形结构作归一化处理,然后先序遍历二叉树得到公式元素序列,并对序列中的变量名称作归一化处理。对于待匹配的两个数学公式,根据两个公式元素序列对应位相同的公式元素数计算两个公式的相似度。实验结果表明,该算法实现了数学公式的准确匹配,是一种较实用的算法。

关键词： 高中数学教学   算法思想   数学概念  

摘要： 算法思想在高中数学中有着广泛的运用,如一元二次不等式的求解、线性规划、二分法求方程的解等都渗透了算法思想.在高中数学教学中渗透算法思想,既助于优化学生的认知结构,培养学生的思维品质,又有助于增强学生解决问题的能力以及发展学生的应用意识.

关键词： 华南师范大学   最优控制问题   混合有限元   数学科学   高效算法   学院   成果展   计算问题  

摘要： 解决大规模科学计算问题有赖于两方面的努力，一方面是大大提高计算机的性能，另一方面是创造出更高效的计算方法。在某种意义上来说，高效算法的研究对提高计算速度比提高计算机的计算能力更为重要。华南师范大学数学科学学院陈艳萍教授团队完成的“最优控制问题混合有限元高效算法研究”项目系统深入地为有关自适应算法提供理论的根据和指导，引领和推动高效算法理论研究，具有重要的科学意义与应用前景。