一个数学问题的研究性学习

1　问题《数学通报》2 0 0 2年第 8期“数学问题解答”栏中的第 1 3 88题为 :已知x >0 ,y>0 ,且x +y =1 ,求证(x +y) ( 11 +x+11 +y)≤ 43 .①本题由黑龙江的刑进喜提供 ,证明发表在该刊第9期上 .证明 :由已知得①式 ( 1 +2xy) ( 32 +xy+22 +xy)≤1 63 ( 1 +u) ( 38+u2 +18+u2 )≤ 43(其中u =2xy) 3 ( 1 +u) 8+u2 ≤ 4u2 -9u +2 3 94( 1 +u) 2 +( 8+u2 )≤ 4u2 -9u +2 3 u2 -1 8u +1 7≥ 0 (u -1 ) (u -1 7)≥ 0 u≤ 1 2xy≤x +y .2　转化在①式 ,令x =aa +b,y =ba +b,可得等价不等式 :已知　a >0 ,b >0 ,求证(a +b)·( 1a +2b+12a +b)≤ …     

具有p—Laplace的非线性特征值问题的多重解

利用变分方法和B．Ricceri三临界点定理,获得了具有p-Laplace的非线性特征值问题 {-（｜u′（t）｜^p-2u′（t））′＋｜u（t）｜^p-2u（t）=λf（u（t））,0〈t〈1, u（0）=u（1）=0 至少存在3个弱解的充分条件．推广了现有文献的结果．     

关于四阶微分方程周期边值问题

本文用上下解方法与单调迭代法相结合 ,证明了四阶微分方程周期边值问题 ,u( 4 ) - 2mu″=f(t,u ,u″ -mu) (m >0 )u( 0 ) =u( 2π) ,u′( 0 ) =u′( 2π) ,u″( 0 ) =u″( 2π) .u ( 0 ) =u ( 2π)的解的存在性 ,推广和改进了文〔1〕的结果。     

一类二阶微分方程正解的存在性

本文借助锥不动点定理证明了带混合两点边值条件的二阶微分方程u‘ m^2u f(t,u)=0,αu(0)-βu‘(0)=0,γu(1) δu‘(1)=0正解的存在性．     

介绍两道新编题

[题1](1)当k取何值时,二次曲线Ck:x29-k+y24-k=1表示椭圆?表示双曲线?(2)任取平面上一点P(u,v)(u·v≠0),上述曲线中是否总有一个椭圆和一条双曲线通过P点?有则证明;没有,则找出点P(u,v)的一个反例.解:(1)当40.∴f(k)=0的根一个在(-∞,4)内,另一个根在(4,9)内.∴对于平面上任一点P(u,v)(u·v≠0),总有Ck中一条双曲线和一个椭圆…     

素环上的广义(θ,θ)-导子

R是2-扭自由素环，Z(R)是R的中心，J是R的非零Jordan理想，F是R的广义(θ,θ)-导子，d是F的伴随(θ,θ)-导子.若对任意的u,v∈J,F满足以下条件之一：(ⅰ)F(u°v)=0,(ⅱ)F(u°v)=θ(u°v),(ⅲ)F(u°v)=θ([u,v]),则d=0或J?Z(R).     

奇异(n-1,1)共轭边值问题的多重正解

利用锥映射不动点指数定理证明了 (n - 1,1)共轭边值问题un+a(t)f(u) =O ,u(j) (0 ) =u(1) =0 ,0≤j≤n - 2 ,至少存在两个正解 ,本文允许a(t)d在 [0 ,1]两端点处具有奇性 ,并允许a(t)在 [0 ,1]某些子区间上恒为零。     

一类临界指标椭圆方程解的存在性

运用变分方法及Hardy不等式讨论了下列椭圆方程: -Δu-μu/x2==u2*-1+u,x∈Ω其中该方程满足条件u>0,x∈Ω和u=0,x∈Ω,并且、μ<-μN-2/2,2*=2N/N-2.N≥3,Ω(∈ )RN是包含0的有界光滑区域;并且获得该方程解的存在性.     

一类二阶微分方程正解的存在性

文章借助锥不动点定理证明了带混合两点边值条件的二阶微分方程（u^n＋m^2u＋f（t,u）=0, 0〈t〈1 au（0）-βu′（0）=0,γu（1）＋ δu′（1）=0） 正解的存在性。     

X(u,λ,N)=intergral from n=0 to ∞λ~(-Nt){1/4〔(lim2·-1(n to ∞)~2-1)}~t dt 的存在性和特性

设u,λ,N是三个参变量,其中u,λ∈R,N∈Z .本文所构造的一个积分函数X(u,λ,N)如下:X(u,λ,N)=∫ ∞0λ-Nt14(limn→∞2·u u u …-1)2-1tdt　　　　　　　　　　　n重根号()·极·限·存·在·性考虑极限limn→∞u u u …,显然给定u=0时极限存在且等于0.　　　　　　　　　　　n重根号(1)给定u≥1时,令Wn=u u u …,因W1=u<2u,而Wn 1=u Wn,　　　　　　　　　　　n重根号故Wn<2uWn 1<2u,所以根据数学归纳法知,Wn有上界:Wn<2u(一切n).另一方面,由Wn 1=u Wn知Wn单调递增.(2)给定0相似文献   

用EXCEL处理物理实验数据

许多物理实验是探索性实验,这类实验的特征就是依靠一定的实验装置进行测量,获得多组测量数据,然后对这些数据进行分析、处理,得到实验结论。Excel是一个功能强大、使用方便的电子表格软件,主要用于管理、组织和处理各种各样的数据,并能将数据生成表格、各式各样的图表、统计图形,而且可以对数据进行回     

Playing with computers,playing with ideas

In this article I react to the thoughts of Hennessey, addressing mainly the student, and Esquivel, addressing mainly the teacher. These authors present complementary, interesting, and consistent pictures of creativity education. Here I comment on a few issues that are less clear and discuss implications of these authors' work for computers in education. I conclude that teachers need to play with ideas about how they might use computers to build a culture that promotes deep, meaningful, and creative learning.Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.     

Choices with clients with profound hearing impairments

Kurt L. Johnson, Ph.D., and E. Jane Burkhead, Ph.D., are Assistant Professors with the Program in Counseling Psychology and Human Systems, Department of Human Services and Studies, at the Florida State University. D. Anthony Clark, M.S. is a Doctoral Candidate at the Florida State University.     

有理论的实验和有实验的理论

科学实验是科学认识的基础,没有科学实验就没有真正意义上的科学。近年来,发展心理学家对传统的研究方法作了创造性的改进,使研究对象有所扩大,研究内容有所拓展,从而对早期教育产生了更加丰富的实用价值。在儿童发展心理学中,实验法与其他方法的综合运用有着广阔的发展空间,但主流的方法依然是实验法。无论是哪一种研究方法,都必须坚持客观性原则。沉浸于后现代主义的相对主义和无政府主义思潮对科学发展和社会实践活动,包括对幼儿教育的发展是有害的。     

从容面对慢生

"没有天生的差生,只有有差异的学生"。差生一定程度上是教育本身制造的。"慢生"变为"差生"与教师有极大的关系。使"慢生"的成长速度加快,最关键的是想方设法激发慢生的内在积极性,使他们为自己的"大器晚成"保持自信和勇气。     

Parental sensitivity and attachment in children with autism spectrum disorder: comparison with children with mental retardation, with language delays, and with typical development

This study on sensitivity and attachment included 55 toddlers and their parents. Samples included children with autism spectrum disorder (ASD), mental retardation, language delay, and typical development. Children were diagnosed at 4 years of age. Two years before diagnosis, attachment was assessed with the Strange Situation procedure, and parental sensitivity and child involvement during free play were assessed with the Emotional Availability Scale. Parents of children with ASD were equally sensitive as parents of children without ASD, but their children showed more attachment disorganization and less child involvement. More sensitive parents had more secure children, but only in the group without ASD. Less severe autistic symptoms in the social domain predicted more attachment security. Autism challenges the validity of attachment theory.     

Using Assistive Technology with Individuals with Severe Disabilities

No abstract available for this article.     

Preschoolers' Relational Aggression with Siblings and with Friends

As part of a longitudinal study examining sibling and friend relationships in early and middle childhood, relational aggression by 4-year-olds and their interaction partners in semi-structured free play sessions with siblings and friends was examined during sibling sessions involving both same-gender and mixed-gender sibling pairs. Identifiable acts of relational aggression occurred during many of the interactions observed, but there was also a wide range in the amount of relational aggression produced. Both boys and girls used relational aggression with their siblings much more than they did with their friends. Although boys' and girls' relationally aggressive behaviors occurred at similar rates, the form and function of their relational aggression varied depending on the age and gender of their sibling.     

CASS工艺处理油漆生产废水

采用隔油——气浮——CASS——过滤工艺处理高浓度油漆生产废水，工程运行稳定，出水水质达到国家一级排放标准。     

浅析信托与代理、行纪的异同

在对信托与代理、信托与行纪进行比较的基础上,析出信托制度在财产管理方面灵活、安全、高效的优势.