例谈α≤f(x)≤b■(f(x)-α)(f(x)-b)≤0的应用

众所周知在二次不等式解的法则中有(x-a)(x-b)≤0(?)≤x≤b，(a相似文献   

“分”得巧妙 解得精彩——一类函数不等式证明策略的剖析

<正>数学是自然的，这不仅体现在数学概念的形成上、数学原理的归纳上，还体现在数学方法的使用上，以及数学解题的过程中．函数不等式的证明中有这样一类问题:要证明f(x)>0，通过等价变形可以将证明f(x)>0转化为证明g(x)>h(x)，而此时g(x)_min>h(x)_max恰好成立，从而原命题得证．这种“一分为二”处理策略的难点在于:如何合理的拆分，使得拆分后的两个函数“恰好”出现满足“g(x)的最小值大于h(x)最大值”这种理想状况?     

相对论热力学中温度的Lorentz变换

本文在简要介绍温度的Lorentz变换现状的基础上,给出了温度Lorentz变换的一种推导方法,结果和H．Ott的结果一致。     

洛仑兹变换的推广及超光速“佯谬”的解决

在本文中,笔者通过恰当地推广Lorentz变换,使其既能缓解超光速(υ＞c)下的某些矛盾,同时在亚光速(υ＜c)下又能自然地回到原Lorentz变换,使之成为一组兼容超--亚光速的变换,并预示超光速的可能性.     

时空代数的若干性质及应用

由Clifford代数引入时空代数，时空球，时空单位球，时空单位球面等概念．利用时空单位球面的性质导出四维时空的一般Lorentz变换．     

三角函数的图象变换及应用

三角函数图象的变换是三角函数的重点内容，也是高考考查的热点之一，函数y=sinx与函数y=Asin(ωx ψ)的图象间的关系实质上就是函数y=f(x)与函数y=Af(ax b)图象之间关系的具体反映，研究三角函数图象变换，可以在掌握函数图象变换的基础上，再结合三角函数本身的具体特点进行。     

温度是Lorentz不变量

相对论热力学中关于温度的变换关系一直是物理学界学论的热点,本文从不同物理量的变换关系和温度的不同定义得出温度是 Lorentz 不变量。     

导数江湖行,证题有神功

在新课标中,应用导数研究函数的单调性进而证明不等式是近些年来高考中出现的新热点．导数为证明提供了“金钥匙”,解题如行云流水,简捷明快．现举几例,予以说明．例1若x＞-1,证明：In(x+1)≤x．证明：令f(x)=In(x+1)-x,则f(x)=1/(x+1)-1．令f′(x)=0,解得x=0．当-1＜x＜0时,f(x)＞0,所以f(x)在区间(-1,0)上单调递增．当x＞0时,f(x)＜0,所以f(x)在区间(0,+∞)上单调递减．所以,当x＞-1时,f(x)=In(x+1)-x≤f(0)=0,即In(x+1)≤x．方法步骤：(1)移项,使不等式一边为0,构造辅助函数；     

用根变换解一类竞赛题

对一元代数方程（多项式）的根x作一个变换：是处理与其根有关的一类问题的有效手段，特别是解证一些竞赛题简捷、明快例1证明，对任意非零的a、β，多项式ax~3-ax~2 βx β的根x_1,x_2,x_3满足（民主德国1977年竞赛题）证对多项式：作根变换：x→1/x,得多项式：∵多项式(1)的根为x_1，x_2，x_3,∴多项式(2)的根为对多项式(1),(2)分别用韦达定理，得例2设多项式：恰有n个正根，证明，它们都相等.(保加利亚1983年竞赛题)证设多项式(1)的n个正根为x_1，x_2,据韦达定理，现对多项式(1)作根变换:x→1/x,得多项式：其根为由韦达定理，由Canchy不…     

B-型双曲运动与Lorentz群

在双曲平面H~2的Beltrami模型下,双曲运动群同构于Lorentz群L~(3.2),设A(?)是本原(非本原)Lorentz矩阵,那么(?):X’=Ax(或x’=Ax)表示一个双曲运动,我们有如下的     

日本民间力量对中日邦交正常化的作用探析

20世纪550年代针对中日官方外交难以启动的情况,中国政府基于两国人民之间的传统友谊,从民间外交入手实现了中日关系的正常化。对于这段历史过去多从中国的角度研究,然而不容忽视的是日本民间力量对两国邦交正常化同样起到了积极的促进作用。对该问题作进一步探析,以期再次唤起人们对民间交流的关注,进一步拓宽两国民间团体和个人的交流与合作。     

关于K极光滑空间

2001年冼军引入了k极光滑空间的概念,作为与其对偶的想法苏雅拉图和李广利引入了k极凸空间,并充分地研究了这一类凸性空间.虽然k极光滑空间概念较早被提出来,但是这一类光滑性空间尚未得到深入的研究,甚至这一类光滑性与其它光滑性之间的关系尚未弄清楚,本文深入研究了这一类光滑性空间,得到了它的一些性质以及与其它光滑性质之间的关系.另外,证明了:若X是弱局部k一致凸空间,则对每个x∈S(X),f∈Sx是X*的k光滑点。     

拟阵的导算子与内部算子的完备格同构

定义了拟阵的导算子、内部算子,证明了对每个给定的有限集X,可以给D（X）（即X上拟阵导算子的全体）,I（X）（即X上拟阵内部算子的全体）上赋予适当的序≤使得（D（X）,≤）与（I（X）,≤）（即X上拟阵导算子的全体）之间是完备格同构的。     

Leadership situations in academic departments: Relations among measures of situational favorableness and control

Measures of attributes of leadership situations faced by chairmen in academic divisions and departments were theoretically and empirically related. Measures of task structure and member relations were derived from Fiedler's (1967) Contingency Model of Leadership, and measures of total control and relative control were derived from Tannenbaum's (1967) Control Graph Theory. Two correlational studies using samples of community college divisions and university departments indicated that hypotheses derived from research undertaken in business and military settings were not generally supported in higher educational settings. Consistent findings across both studies indicated that high task structure (faculty homogeneity and academic task structure) is associated with better member relations and greater cooperation on administrative matters. Implications for administrators are briefly discussed.     

关于杨辉三角错位变体和克隆变体的猜想

从杨辉三角的两种基本变体即错位变体和克隆变体的概念,提出两个猜想,并证明两种变体的各行和与形如a_(n k l)=a_(n k) a_n的线性递归数列的对应关系,同时给出这类递归数列的两种通项公式1)。借助杨辉三角及其变体研究线性递归数列的性质将会是一种新颖而且有效的方法。     

社会资本：提高地方政府绩效的基础

地方公共事务的管理应看成是一种治理的过程,这个过程是一个比地方政府范围更大的对话空间,实践证明,丰富的社会资本有助于减少社会的等级关系,增强公民社会的自治能力,降低社会的治理成本。     

The derived generalization of thought suppression

Thought suppression appears to be a relatively ineffective and even counterproductive strategy for dealing with unwanted thoughts. However, the psychological processes responsible for unsuccessful suppression are still underspecified. One process that may be implicated is derived stimulus relations, which may underlie the formation of unintentional relations that act to hamper suppression attempts. To test this prediction, participants were trained and tested for the formation of three derived equivalence relations using a match-to-sample procedure. Subsequently, they were instructed to suppress all thoughts of a particular target word that was a member of one of the three relations and were also allowed to selectively remove words that appeared on a computer screen in front of them by pressing the space bar. Results showed, as predicted, that participants not only removed the to-be-suppressed stimulus, but also removed words in derived relations with that stimulus, thus showing transformation of suppression/interference functions via derived equivalence. The theoretical implications of this demonstration, including its potential as a model for a key psychological process involved in unsuccessful thought suppression, are discussed.     

Adolescents' perceptions of chronic self-concept,peer relations,and learning conditions

Based on Lewin's Field Theory, Bronfenbrenner's Bioecological Systems Theory and social network analysis, the authors collected data from 405 Chinese adolescents about their peer relations, chronic self-concept levels and learning condition variables through questionnaire distributing, and from their teachers about their annual average academic achievement. It is proposed that the impacts of peer relations should be studied from a psycho-ecological perspective by considering the direct and joint effects of peer relations and student bio-psychological environment (as for instance chronic self-concept) on student outcomes. With hierarchical multiple regression analysis, hypothesis formulated on the research purpose was tested to be almost true. Finally, theoretical and practical implications were discussed.     

关于Diophantine方程x~4-py~4=2z~2

设素数p≡1(mod8),(2/p)4≠1,证明了不定方程x4-py4=2z2无正整数解(x,y)．     

微积分基本定理的一种推广

本文利用微积分学的理论证明了如下结论:设f(x)在[a,b]上黎曼可积,函数g(x)在[a,b]上满足李普希兹条件,且几乎处处有g(x)=f(x),则integral from n=1 to ∞(f(x)dx)=g(b)-g(a)。