浅谈数列之求和方法

数列求和问题是高考中的重要内容之一,如何掌握数列求和方法至关重要。一般数列求和是对通项变形,将其转化成熟悉的数列求和问题,或利用代数式的对称性,采用消元等方法求和。依据对数列求和的认识和理解,通过不断积累,结合具体实例,本文主要对四种方法进行了分析研究。将这些方法恰到好处地运用在教学过程中,能帮助学生较快地吸收知识,掌握求解方法及技巧。     

关于Fibonacci数列通项的探讨

本文给出了Fibonacci数列通项公式的几种不同证法,体现了Fibonacci数列蕴含的数学思想。     

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。     

利用不动点理论研究分式递推数列

利用不动点理论,给出分式递推数列:an+1=αan+β/γan+δ,n=1,2,…的等比数列和等差数列形式。     

Stolz定理在求极限中的应用

本文阐述了Stolz定理及其推广,给出了Stolz定理及其推广在求数列和函数不定式极限中的应用。     

运用直线外推法预测现金流量简介

线外推法是根据实际的时间数列资料,利用几何平均法算出平均发展速度,然后再利用数列的最末一项指标与平均发展速度相乘,从而得出下一期的预测值。直线外推法适合乡镇企业预测未来现金流量,现将此法之运用简介如下:例:某企业1994年至1998年经营活动产生现金流量分别为70万...     

EXCEL的描述统计功能及应用（二）

Excel的“描述统计”工具虽能一次给出十几项数值,但要计算其中的某一项数值,还需使用统计函数。用于描述统计的函数是按未分组资料设计的,如遇分组资料则可使用公式直接计算。下面分别按数列的集中趋势和离散程度说明其操作方法。一、集中趋势的描述1. 描述数列集中趋势最常用的数值是均值,求均值的统计函数是AVERAGE。前举100户餐饮业年营业额要计算均值,首先需将数据输入 A1～A101单元格,然后选择“插入”菜单中的“fx函数”,或单击“常用”工具栏中的“fx”按钮,从弹出的对话框左侧“函数分类”列表中选择“统计”,从右侧“函数名”…     

简约为美

如果你仔细地观察一下雏菊,你会发现雏菊的小花呈螺旋形,并按顺时针和逆时针两个方向蔓生。无论你按两个方向中随便哪个方向计算螺旋数,你都会发现这些数构成一个“斐波那契数列”:1,2,3,5,8,13,21,34,55……它的特点是从第三项开始每一项都是数列中前两项之和。该数列由欧洲数论学家斐波那契最先提出,故名“斐波那契数列”。这种现象,不禁令人生疑:难道植物也懂得数学吗?这样排列又有何价值呢?植物当然不懂数学,它们只是按照自然的法则才进化成这样的。这是自然的一个简约法则:雏菊花冠排列的螺旋花序中,小花互以137度30分的夹角排列,这个…     

中通快递欲借IT弯道超车

一年前,中通快递引入了红杉资本,当时,被问及＂红杉给予中通的建议中,哪一项让他印象最深＂时,中通副总裁金任群直言是＂花钱买IT＂。一年后,中通内部的管理模式、运营体系都开始发生了变化。＂自从去年投资人进来后,中通内部最大的变化是开始将信息技术视为核心竞争力之一,通过技术应用,在内部深刻变革原来的运营体系,并对外改善上下游客户的服务和体验。＂中通快递信息中心总监朱晶熙坦言。     

基于结构元理论的复Fuzzy数

在文献[2—6]的基础上,给出了基于结构元理论的复Fuzzy数,定义了两个复模糊数的距离、大小关系、上下界及四则运算等,并探讨了复Fuzzy数项数列的收敛性,给出了数列收敛的充要条件及收敛的唯一性、有界性、保号性等结论。     

VARIATIONS ON THE THEME OF CONNINGa IN MATHEMATICAL ECONOMICS

Abstract The mathematization of economics is almost exclusively in terms of the mathematics of real analysis which, in turn, is founded on set theory (and the axiom of choice) and orthodox mathematical logic. In this paper I try to point out that this kind of mathematization is replete with economic infelicities. The attempt to extract these infelicities is in terms of three main examples and one general discussion: dynamics, policy and rational expectations and learning are the examples; a game theory without ‘subjectivism’, based on the axiom of determinateness, is discussed in general terms. The focus is on the role and reliance of standard fixed‐point theorems in orthodox mathematical economics.     

Fixed effects demeaning in the presence of interactive effects in treatment effects regressions and elsewhere

The present paper shows that cross-section demeaning with respect to time fixed effects is more useful than commonly appreciated, in that it enables consistent and asymptotically normal estimation of interactive effects models with heterogeneous slope coefficients when the number of time periods, T, is small and only the number of cross-sectional units, N, is large. This is important when using OLS but also when using more sophisticated estimators of interactive effects models whose validity does not require demeaning, a point that to the best of our knowledge has not been made before in the literature. As an illustration, we consider the problem of estimating the average treatment effect in the presence of unobserved time-varying heterogeneity. Gobillon and Magnac (2016) recently considered this problem. They employed a principal components-based approach designed to deal with general unobserved heterogeneity, which does not require fixed effects demeaning. The approach does, however, require that T is large, which is typically not the case in practice, and the results reported here confirm that the performance can be extremely poor in small-T samples. The exception is when the approach is applied to data that have been demeaned with respect to fixed effects.     

用几何画板软件描述平面区域上的动点

利用几何画板软件描述平面区域上的动点,动态地展现出几何对象的位置关系,对发现解题思路有很大的帮助。     

Comparative statics in dynamic programming models with an application to job search

This paper presents a technique for qualitative comparative statics analysis in dynamic programming models. Let the value function υ be the fixed point of a contraction mapping which depends differentiably on some exogenous parameter θ. Ten the derivative of υ with respect to θ exists and is also the fixed point of a contraction mapping. Since this derivative is the fixed point of a contraction mapping, its qualitative properties can be investigated using mathematical induction. This comparative statics methodology is illustrated with an application to a model of job search.     

基于智能调度的散点货源动态集散点设置研究

动态集散点是系统应对客户随机需求,为了降低企业成本以及方便客户及时送件而设置的临时、随机的物流集散点。与城市的客源相比,城市货源的分布更加分散,需求随机性更强,因而一般的固定集散点往往不能满足需求。针对此问题,文章对城市散点货源的动态集散点设置进行研究。依托智能车辆自动化取件为背景,运用层次聚类分析思想,并通过Matlab进行仿真,对集散点的设置进行分析及优化。通过算例分析文章得出合理地设置动态集散点能够有效地提高企业取件效率,且能够满足客户的特殊需求。文章研究可以为物流企业在智能取件模式下的货物集散点设置提供方法参考。     

Discrete fixed point theorem reconsidered

The aim of this note is to indicate an example that demonstrates the incorrectness of Iimura’s discrete fixed point theorem [Iimura, T., 2003. A discrete fixed point theorem and its applications. Journal of Mathematical Economics 39, 725–742] and to present a corrected statement using the concept of integrally convex sets.     

Discrete fixed point theorem reconsidered

The aim of this note is to indicate an example that demonstrates the incorrectness of Iimura’s discrete fixed point theorem [Iimura, T., 2003. A discrete fixed point theorem and its applications. Journal of Mathematical Economics 39, 725–742] and to present a corrected statement using the concept of integrally convex sets.     

Smooth estimation of a monotone hazard and a monotone density under random censoring

We consider kernel smoothed Grenander‐type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate n^2/5 and that the limit distribution at a fixed point is Gaussian with explicitly given mean and variance. It is well known that standard kernel smoothing leads to inconsistency problems at the boundary points. It turns out that, also by using a boundary correction, we can only establish uniform consistency on intervals that stay away from the end point of the support (although we can go arbitrarily close to the right boundary).     

CASIO-4800p计算器在城市立交桥施工测量中的具体应用

文章通过对城市曲线立交桥上放样点位坐标计算的通用数学模型的研究，结合CASIO-4800p可编程计算器的优点，提出一种简易实用的计算方法，并编写了曲线上放样点坐标计算程序。