数列求和公式教学优化及其拓展

数列求和是高中数学的重要知识点,特别是要求学生掌握等差与等比数列的求和公式。现行的人教版新教材在初高中数学教学衔接上不尽如人意;对数列求和中蕴含的数学思想方法,没有充分的利用与挖掘;对有关素材的处理也不是很到位。本文力图对数列求和公式教学进行再思考,通过优化知识呈现过程,开阔学生的思路,拓展公式的应用,使初高中内容更好的衔接,使学生学习起来更容易理解,更好地掌握其重要的数学思想与方法。本文对高中数列求和教学有一定的借鉴与指导意义。     

广义Lucas数列的一些求和公式

由二次线性递推公式所定义的Lucas数列ΣLnΣ在数学的理论研究中有重要的作用.本文在已有的有关广义Lucas数列相关定理的基础上进一步推广,给出了更为广泛的广义Lucas数列的求和公式,采用了递推归纳的方法证明。     

双差数列的几个性质

讨论了双差数列与周期双差数列的通项公式以及求和公式。     

无穷级数求和方法研究

任何一个级数要么收敛要么发散,收敛的级数都是应该有和或和函数的。无穷级数求和方法很多,有很强的技巧性,文章就通过例子介绍无穷级数求和的若干方法,如裂项相消法、逐项微分或积分法、转化为函数项级数求解法、利用子列的极限等等,其目的是让学习者更加熟练地掌握无穷级数求和方法及技巧,从而进一步促进其对该知识的学习和理解。     

浅谈高等数学中极限定义的研究和应用

极限概念是微积分学中最重要,最基本的概念。掌握好利用定义证明函数极限是学好高等数学的基础。极限有数列极限,函数极限,多元函数极限等几类,本文直接或间接地用极限定义来证明一些我们经常见到高等数学问题。     

灰色多层次综合评判模型在建设项目监理评标中的应用

将层次分析法和灰色关联分析的方法有机地结合起来，建立灰色多层次综合评判模型，利用层次分析法计算影响施工监理评标的各个因素的权重，然后构造各项因素的比较数列和参考数列，计算各个投标方案的关联度，确定参与投标的监理公司的排序。     

从函数观点解数列问题

数列是一类定义在正整数集或它的有限子集上的特殊函数，可见，任何数列问题都蕴含着函数的本质及意义，具有函数的一些固有特征。另外，数列与函数的综合也是当今高考命题的重点与热点，因此我们在解决数列问题时，应充分利用函数有关知识，以它的概念、图象、性质为纽带，架起函数与数列间的桥梁，揭示了它们间的内在联系，从而有效地分解数列问题。     

总量指标动态数列平均发展水平计算方法的优化

总量指标动态数列平均发展水平的计算方法是最基本的,它是计算相对数或平均数动态数列平均发展水平的基础。现行总量指标动态数列序时平均数的计算公式有四个,正确的使用公式需要学生有一定的数学基础和较强的逻辑推理能力才能很好的应用,针对中职学校学生学习的困难,对计算方法进行了优化。     

巧用不动点求数列通项公式

确定数列的通项公式,对于研究数列的性质起着至关重要的作用。不动点求通项就是其中之一,运用不动点求数列通项既是竞赛数学的内容之一,也是近年来高考命题的热点。文章着重介绍两种运用不动点求数列通项的方法。     

“四纬度网格化数列法”成本调控模式

分析数列“0.1，0.2，0.3，0.4”不难发现，它有两个特性：一是该数列是等差数列；二是该数列的所有项加起来正好为1。文章将该数列这两个特性应用于企业的成本管理，以同煤集团铁峰煤业有限公司为研究对象，摸索出一套“四纬度网格化数列法”成本管控的管理模式；引入了“不可控成本”、“可控成本”、“期望降低成本”“期望增长成本”等概念，将责任划分为纵向四个纬度和横向四个纬度。根据数列的性质确定了责任系数与绩效系数，从而建立起横到边纵到底的成本考评体系。     

幂级数的求和方法

本文应用高等数学的知识,介绍了幂级数的几种常见的求和方法及技巧。     

Sensitivity of the weighting summation decision method to incorrect application

The weighting summation decision method is commonly used and misused for multiobjective decisions. The formal requirements of this method are outlined and some of the kinds of errors that are commonly made in applying it are discussed. Monte Carlo simulation is used to assess the potential that five classes of errors have for causing incorrect decisions. An index is developed which quantifies the complexity of decision problems. The simulations demonstrate that complexity can be about twice as important to quality of decisions as are errors in applying the weighting summation.     

TRUE VERSUS MEASURED THEIL INEQUALITY

This article deals with several problems that arise when the Theil coefficient of income inequality is computed in practice.
Aggregation of income data into brackets leads to an underestimation of the true Theil inequality, which is defined as the value of the coefficient as computed from individual income data. The assumption that the individual incomes are distributed according to a linear density function within the income brackets is suggested as a method to estimate this aggregation error. Calculations show that this method approximates the true aggregation error reasonably well.
Several methods are discussed concerning the treatment of negative incomes. In particular one can construct an income bracket that contains both negative and positive incomes and which in the summation formula is weighted with zero weight. Of all methods this procedure using the assumption of a linear density function within brackets, yields the highest value of the Theil coefficient and is thus preferred to the other alternatives.     

基于序号总和理论的御河大桥交通量预测研究

为了评价公路网设计的可靠性,提高交通量预测的精确度,以交通工程的基本理论为指导,在大量调查数据的基础上,运用时间序列法的线性、二项式、指数等方法进行交通量预测,得到了相应的预测模型,通过序号总和理论得到了精确度较高的预测模型,并通过预测模型计算出未来特征年的交通量,为交通量的预测研究提供了一种新的研究思路。     

W.F. Sheppard's Smoothing Method: A Precursor to Local Polynomial Regression

W.F. Sheppard has been much overlooked in the history of statistics although his work produced significant contributions. He developed a polynomial smoothing method and corrections of moment estimates for grouped data as well as extensive normal probability tables that have been widely used since the 20th century. Sheppard presented his smoothing method for actuaries in a series of publications during the early 20th century. Population data consist of irregularities, and some adjustment or smoothing of the data is often necessary. Simple techniques, such as Spencer's summation formulae involving arithmetic operations and moving averages, were commonly practised by actuaries to smooth out equally spaced data. Sheppard's method, however, is a polynomial smoothing method based on central differences. We will show how Sheppard's smoothing method was a significant milestone in the development of smoothing techniques and a precursor to local polynomial regression.     

城市物流基地选址问题研究

本文将物流基地纳入城市交通网络中，以体现交通状况对物流基地选址的影响。在进行选址时，以运输费用和基地的投资、管理费用总和最小为规划者的主要目标，建立目标函数。选址的上层模型体现了运输费用和基地投资费用、管理费用最小的原则，下层模型体现了入选点的不同对交通流量分配的影响，下层模型是求解上层模型的基础。     

注浆对地基沉降量的影响关系

对于软粘土型路基,在车辆行驶时会产出不均匀沉降,沉降量可以通过分层总和法进行计算,地面接触压力、土体的自重应力、土层的压缩模量均是影响沉降的重要因素。地面的接触压力是外界影响因素,由于外界条件的限制而无法改变,而土体的自重应力、土层的压缩模量均可以通过注浆来改变,注浆后,土体自重和压缩模量将会提高,通过力学分析,得出一个注浆对地基沉降量的影响关系,可供设计与施工参考。     

An integrated fuzzy mathematical model and principal component analysis algorithm for forecasting uncertain trends of electricity consumption

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.     

Forecasting monthly and quarterly time series using STL decomposition

This paper is a re-examination of the benefits and limitations of decomposition and combination techniques in the area of forecasting, and also a contribution to the field, offering a new forecasting method. The new method is based on the disaggregation of time series components through the STL decomposition procedure, the extrapolation of linear combinations of the disaggregated sub-series, and the reaggregation of the extrapolations to obtain estimates for the global series. Applying the forecasting method to data from the NN3 and M1 Competition series, the results suggest that it can perform well relative to four other standard statistical techniques from the literature, namely the ARIMA, Theta, Holt-Winters’ and Holt’s Damped Trend methods. The relative advantages of the new method are then investigated further relative to a simple combination of the four statistical methods and a Classical Decomposition forecasting method. The strength of the method lies in its ability to predict long lead times with relatively high levels of accuracy, and to perform consistently well for a wide range of time series, irrespective of the characteristics, underlying structure and level of noise of the data.