从一道高考题谈对高中数学教材的一点看法

2004年普通高等学校春季招生考试(安徽卷)数学(理工农医类)试题第7题: 若二面角α-l-β为120°,直线m上α,则β所在平面内的直线与m所成角的取值范围是( ).     

^95Zr核的高自旋态研究

利用102MeV的^28Si束流，通过^60Ni(^28Si，2pn)熔合蒸发反应布居了^85Zr核的高自旋态，测量了γ-γ符合及DCO比值，建立了一个有43条能级，75条γ跃迁的能级纲图，新增加了36条γ跃迁，25条能级。将能级自旋推高到（49/2^ ），首次观察到了转边带的第二回弯。并确认了一条建立在17/2^-负字称带上的磁转动带。     

Puzzle and Solution:Diagonal String

“Suppose there were one nail in each of thefour walls of this room and in addition one nail onthe ceiling and one in the floor,Suppose furtherthat we had to tie strings between these nails.Ihave tWO colors of strings which I use—red andblue.Each connection between any two nails iseither with a red string or with a blue string. “All these strings make up many triangles,that is,any three nails can be considered apexesof a triangle formed by the strings connecting these three nails.My problem is to see if I could distribute the colors so that no triangle has all three sides the same color.”Said young Nicho—las. “This is rather complicated,”mused the mathematician. “It must involve calculations of permutations and combinations,and the like.I didn't think you knew that much algebra,Nick.”“I don’t,”replied young Nick。“but I can still do the problem.”“Well,all right,tell us how。”said the eld—er. “It is really very simple.”said young Nicho—las,“You only have to know enough to start rea-soning, “The answer is that there will be at least onetriangle all sides of which are the same color.Iwill show that it is impossible to avoid this. “Consider any one nail. Out from it theremust stretch five strings,one to each of the otherfive nails。No matter how you distribute the col—ors in these five strings,at least three of themmust be the same,since you have only two colors.For the sake of argument let assume that three ofthe strings are red. “Consider now the triangle formed betweenthree nails at which the three red strings haveterminated. “If we are to try to avoid a triangle with all three sides the same color,it follows thatthese three nails cannot all be joined to each other with one color.Putting this more simply,thetriangle formed by the three terminal nailsshould not be all blue.At least one of the stringsbetween the three nails must be red.But if so,we have completed a red triangle from the origi—nal nail.”     

最大似然方法和Bayes方法在结构方程模型分析中的讨论(英文)

本文通过模拟研究,讨论了最大似然方法和Bayes方法在分析结构方程模型中的相似点和不同之处。     

漫画趣题

选自《超时空数学之旅》编著:李毓佩绘画:林航王皓第一题 5根相同颜色的绝缘电线拧成一束,电线的一端在河的左岸,另一端在河的右岸.用一只万用表怎样把这5根电线的两端分别标上1、2、3、4、5,使相同的电线标上同一个号,并且要求过河的次数越少越好,如何测法宁遴继携戮豁参第四题一位年近古稀的老人指着一张照片说:“这是我和表哥在1943年的合影,表哥比我大7岁,我们都是20年代出生的.那年表哥参军,当时他的岁数正好等于我出生年份的数字和,而我当时的岁数也恰好等于他出生年份的数字和,”请问,这位老人在1998年的岁厂落数是多少? ...‘「漫画…     

一竞赛求值题的多种解法

在数学竞赛中,常有一元二次方程的根的代数式求值问题.这类问题,有直接的方法,就是先解此一元二次方程,然后把根代入就能求出结果;其实不解方程,也可以把值求出来.下面以一竞赛题为例,学会用多种解法解这类题目.     

TiO2∶Mo体系的光子雪崩上转换

在 978nm激光二极管的激发下 ,Mo掺杂的TiO2 材料表现出很强的宽带上转换发光 ,该发光来源于 [MoO4]2 - 基团的激发态3T1 ,3T2 能级到基态1 A1 能级的电子跃迁 .通过研究发光强度与抽运功率的关系及上转换发光的上升时间曲线 ,发现TiO2 ∶Mo体系的上转换发光中存在着雪崩机制 ,应用转换函数理论分析了光子雪崩的产生条件和主要特征 ,理论结果和实验数据很好地符合     

等温平台石墨炉原子吸收光谱法测定高纯镍中痕量杂质锑

利用石墨炉原子吸收法，在等温平台条件下直接测定高纯镍中的痕量杂质锑，对石墨炉加热程序中的干燥时间、灰化温度及原子化温度进行了优化，同时考察了介质酸度的影响。试验表明，基体镍对锑的测定有显著的影响，为此进行了标准系列基体匹配。该法的特征质量为6．6pg；相对标准偏差为6．5％；加标回收率为100％-103％。     

模糊数序列的收敛性

探讨L-R型模糊数序列的S-和问题，定义关于模糊数的模糊小于的概念，在此基础上探讨模糊数的有序性，模糊数的截集函数的连续性，模糊数的格结构以及模糊数序列的收敛性等重要性质。     

字母代数 简捷直观

代数,代数,字母代数,也就是用字母表示数.代数是初中数学的重要课程,代数对于算术来说.是人类又一大进步,字母代数往往比算术更加简单明了,更加通俗易懂.