电子监控探测人物身高的分析

依据重庆市公安局刑警大队提供的监控数据,分析监控器摄象时影响身高的因素,利用多元回归的原理建立了三个预测身高的回归模型,并对其作出了优劣评价,最终确定出犯罪嫌疑人实际身高与其在照片上的像高、电子监控器距地面的高度、人与监控器的垂直和偏离距离四个因素的最优回归模型.该最优模型的可决系数R2=0.9931,预测身高与实际身高有97.89%的误差点在±0.02m范围内,73.09%在±0.01m范围内.并对最优模型中的预测身高与实际身高进行配对样本的t检验,两者间无显著性差异.     

利用人的手部数据推断身高的研究

利用男性(52例)成人人体手部的有关数据(手长、手宽、掌长、掌宽、拇指长、食指长、中指长、环指长、小指长)与身高数据应用多元线性回归统计数值计算软件系统,得出上述9个指标值推断身高的回归方法,经过结果分析,有其应用价值。     

(二)所有人的身高一样

命题:所有人的身高一样。用数学归纳法证明如下。 n=1时,命题显然成立. 设n=k时命题真,即对任何k个人,其身高一样。那么n=k+1时,即有k+1个人时,先将这k十1个人编号,记为A_1 A_2…,A_3,A_k+1,由归纳假设可知,A_1,A_2,…A_k-1,A_k+1这k个人身高相等,记作m,又A_2,A_3,…,A_k,A_(k+1)这k个人的身高也相等,记作m_1,显然m=m_1,即这k+1个人的身高都相等。综上所述,所有人的身高都相等。     

身高与体重的数学建模案例设计

本文首先根据生物学知识,结合马尔萨斯模型建立未成年人身高与平均体重之间关系的数学模型;接着借助Matlab软件拟合数据得到函数解析式并检验模型;最后根据拟合结果与未成年人青春发育期特征将模型进行分段优化.     

青年男女体质形态度量标准

文章检验了青年男女的体重（ｋｇ）／身高（ｍ）这一连续型随机变量服从正态分布，首次制定了综合测量男女青年体质形态的标准。同时对非正常青年男女的体质形态作了路径分析，指出先天影响尤其是父亲的体重（ｋｇ）／身高（ｍ）对子女的体重（ｋｇ）／身高影响巨大     

实践性作业：推动学生思维向更深处漫溯——以“大树身高是多少”为例

数学实践性作业作为一种独特的作业形式,既为学生提供了将数学知识转化为数学能力的新路径,又为学生创造了小组参与、探究实践、动手操作的学习环境.“大树身高是多少”是九年级数学实践性作业,通过组织学生测量大树的身高,引导学生观察、思考、判断、实践,在探索中归纳相关数学知识,发展学生数学思维和数学素养.     

三角函数的两个黄金分割比

众所周知,((5～(1/2))-1)/2≈0.618…叫做黄金分割比.它在生活生产中大量存在,就人体中亦有黄金分割比的美学之称,即人的肚脐将身高分成的下半部分与上半部分为黄金分割比的称为体态美.数学中的黄金分割比更是枚不胜举了,可中学数学所介绍的黄金分割比大多数都是几何学科,介绍三角函数的黄金分割比并不     

影响农民工随迁子女学业成绩的潜变量因素及回归分析

采用调查研究与统计分析相结合的方法,描述并研究了影响农民工随迂子女学业成绩的潜变量因素.潜变量因素包括四个方面:外部环境因素(包括:父母期望、亲子关系和师生关系以及家庭流动性)、行为因素(包括:家庭支持和课余学习时间)、内部心理因素(包括:学习兴趣和自我认知)和学习经验(包括:学习焦虑、学习动机和学习态度).以Spss软件为工具,得到了以下结论:亲子关系和师生关系、家庭支持、课余学习时间、学习兴趣、自我认知、学习态度和学习动机都与学业成绩呈正相关关系,家庭流动性和学习焦虑都与学业成绩呈负相关关系,父母期望对学业成绩的影响很小.外部环境因素、行为因素、内部心理因素和学习经验对学业成绩均有预测作用.     

以身高测树高

乡下外公家的院子里,有一棵高高的水杉树特别引人注目,尤其是炎热的夏天,那郁郁葱葱、密密层层的枝叶,就像一把绿色的大伞.暑假里我们每次去外公家,都会在树下乘凉、玩耍. 一个晴朗的中午,外公指着水杉树,神秘地问我:“你知道这棵树有多高吗?”我一下子愣住了,心想:这树这么高,我爬不上去,尺子也伸不上去,该怎么办呢?正当我着急得直跺脚时,我忽然想到了数学课上学过的知识,于是有了办法.我胸有成竹地对外公说:“外公,你给我一把卷尺,我能量出树高,不过你要配合我.”     

我国运筹学的创始者——著名数学家越民义

<正>1.苦学勤练,乐于进取越民义1921年6月22出生于贵州省贵阳市花溪镇.他的父亲越国祥是一个识字不多的朴实农民,母亲越熊氏不但不识字,甚至没有自己的名字.越民义的父母都非常勤劳,靠耕种几亩薄田养活着一群儿女.虽然贫困,一家人敬老爱幼、互相关怀,生活也还是很有人情味儿的.不幸的是,在旧社会动荡岁月里,这样的日子也不能长久,在越民义还不到4岁时,他的父亲被土匪打死了.他的母亲倔强地把养育子女     

Collatz猜想中的同高连续数对族

在Collatz猜想中 ,有些连续整数具有相同的高 ,本文特别研究了同高连续数对 ,发现自然数中有无限多同高连续数对族且以各种不同的形式出现 .     

On the Fitting Height of a Group with Two Sylow Numbers

We show that there is no absolute bound on the Fitting height of a group with two Sylow numbers.     

Height Preserving Minimal Interval Extensions

We consider minimal interval extensions of a partial order which preserve the height of each vertex. We show that minimal interval extensions having this property bijectively correspond to the maximal chains of a sublattice of the lattice of maximal antichains of the given order. We show that they also correspond to the set of minimal interval extensions of a certain extension of this order.     

The ABC Conjecture Implies Vojta's Height Inequality for Curves

Following Elkies (Internat. Math. Res. Notices7 (1991) 99-109) and Bombieri (Roth's theorem and the abc-conjecture, preprint, ETH Zürich, 1994), we show that the ABC conjecture implies the one-dimensional case of Vojta's height inequality. The main geometric tool is the construction of a Belyǐ function. We take care to make explicit the effectivity of the result: we show that an effective version of the ABC conjecture would imply an effective version of Roth's theorem, as well as giving an (in principle) explicit bound on the height of rational points on an algebraic curve of genus at least two.     

The Height of Increasing Trees

Increasing trees have been introduced by Bergeron, Flajolet, and Salvy [1]. This kind of notion covers several well-know classes of random trees like binary search trees, recursive trees, and plane oriented (or heap ordered) trees. We consider the height of increasing trees and prove for several classes of trees (including the above mentioned ones) that the height satisfies EH _n ~ γlogn (for some constant γ > 0) and Var H _n =  O(1) as n → ∞. The methods used are based on generating functions. This research was supported by the Austrian Science Foundation FWF, project S9604, that is part of the Austrian National Research Network "Analytic Combinatorics and Probabilistic Number Theory".     

Fitting Height and Character Degree Graphs

Given a group G, Γ(G) is the graph whose vertices are the primes that divide the degree of some irreducible character and two vertices p and q are joined by an edge if pq divides the degree of some irreducible character of G. By a definition of Lewis, a graph Γ has bounded Fitting height if the Fitting height of any solvable group G with Γ(G)=Γ is bounded (in terms of Γ). In this note, we prove that there exists a universal constant C such that if Γ has bounded Fitting height and Γ(G)=Γ then h(G)≤C. This solves a problem raised by Lewis. Research supported by the Spanish Ministerio de Educación y Ciencia, MTM2004-06067-C02-01 and MTM2004-04665, the FEDER and Programa Ramón y Cajal.     

逐段单调函数的高度与拓扑共轭

迭代运算下,函数值可以交叉于不同的子区间,使得逐段单调函数的高度异常复杂.本文考虑一个非单调点的连续函数类.首先给出高度的充分必要条件,以此获得此类函数的一种划分.其次针对函数类的一个非空子集,给出判定拓扑共轭的充分必要条件和构造拓扑共轭的新方法.进一步地,我们阐明这样的事实:两个逐段单调函数拓扑共轭是其高度相等的充分不必要条件,最后举例说明.     

Height uniformity for integral points on elliptic curves

We recall the result of D. Abramovich and its generalization by P. Pacelli on the uniformity for stably integral points on elliptic curves. It says that the Lang-Vojta conjecture on the distribution of integral points on a variety of logarithmic general type implies the uniformity for the numbers of stably integral points on elliptic curves. In this paper we will investigate its analogue for their heights under the assumption of the Vojta conjecture. Basically, we will show that the Vojta conjecture gives a naturally expected simple uniformity for their heights.

     

Height Uniformity for Algebraic Points on Curves

We recall the main result of L. Caporaso, J. Harris, and B. Mazur's 1997 paper of Uniformity of rational points. It says that the Lang conjecture on the distribution of rational points on varieties of general type implies the uniformity for the numbers of rational points on curves of genus at least 2. In this paper we will investigate its analogue for their heights under the assumption of the Vojta conjecture. Basically, we will show that the Vojta conjecture gives a naturally expected simple uniformity for their heights.     

Asymptotic Density of Surds with Stable Height

We investigate the asymptotic density of surds, namely, the numbers of the form m ^1/d with positive integers m and d such that their height is equal to their metric height among all surds. It is shown that, given an integer d2, this density is equal to 6/². Moreover, similar results for some fixed m are also obtained.