在度量空间中几个点集的一点注记

将实线段上连续自映射的w-极限点集和几个周期点集推广到度量空间中,得出两个结果：（1）设X是序列紧度量空间,f：X→X是连续的一一映射,如果y∈X是f的w-极限点,则n∈N＋,都存在f的w-极限点x0∈X,使得fn（x0）=y;（2）在度量空间中,周期点集与终于周期点集的并集等于准周期点集.即P（f）∪E′P（f）=EP（f）.     

关于ω-极限集的一点注记

讨论了[0，1）区间上连续映射的ω-极限集，指出对于[0，1）上的连续映射f而言。如果f的周期点的周期都是2的方幂，任意x∈[0，1），ω（xf）都是肾致的．     

利用导数解题应注意的几个问题

一、利用导数求函数的单调区间应注意单调区间的写法 例1 求函数f（x）=x^4-2x^2＋3的单调区间. 解f′（x）=4x^3-4x=4x（x＋1）（x-1）． 由f′（x）〉0,可得x〉1或-1〈x〈0; 由f′（x）〈0,可得x〈-1或0〈x〈1． ∴f（x）的增区间为[-1,0],[1,＋∞）;减区间为（-∞,-1],[0,1]．     

一道数学高考错题的深度分析

以下是2005年福建省高考试卷理科12题： 题目：f（x）是定义在R上的以3为周期的奇函数，且f（2）=0，则方程f（x）=0在区间（0，6）内的解的个数的最小值是（ ）．[第一段]     

运用特殊值法解题应注意的问题

一、“问题”的展示 例1（2006年高考陕西卷）已知函数．f（x）=ax^2＋2ax＋4（0〈a〈3），若x1〈x2,x1＋x2=1-a，则………（ ） （A）f（x1）〉f（x2）； （B）f（x1）〈f（x2）； （C）f（x1）=f（x2）； （D）f（x1）与f（x2）的大小不能确定． 何老师在《数学教学》2007年第4期《高考中二次函数问题的命题特点与教学建议》一文中给出的答案如下：     

N维单体上的连续自映射有素周期点的条件

设f为N维单体到自身的连续映射，F是f的下降．中给出了这种映射有素周期点的一个必要条件——存在x∈Ω(f)，使x是准周期点，但不是周期点．     

2006《数学教学通讯·高考数学》（3）解答与提示

函数与方程的思想方法 1.此问题由于常见的思维定势。易把它看成关于x的不等式进行分类讨论。然而，若变换一个角度以m为主元。记f（m）－（x^2－1）m－（2x－1）。则问题转化为求一次函数（或常数函数）f（m）的值在区间[-2，2]内恒负时参数x应该满足的条件。要使f（m）＜0，只要使{f（-2）＜0， f（2）＜0，即{-2（x^2－1）－（2x－1）＜0， 2（x^2－1）－（2x－1）＜0，从而解得x∈（（√7-1）/2，（√3＋1）/2）。     

巧解一类直线斜率题

我们知道：若点P（x1,y1）,Q（x2,y2）在直线l：f（x,y）=0的两侧,则f（x1,y1）·f（x2,y2）〈0,反之也成立．利用这个性质可巧妙解决一类直线斜率的范围问题．现举例说明之．[第一段]     

一道函数的n-周期点问题的证明

<正>2009年复旦大学自主招生的一道试题如下:对函数f:[0,1]→[0,1],定义f1(x)=f(x),…,fn+1(x)=f(fn(x)).n=1,2,3,…,满足fn(x)=x的点x∈[0,1]称为f的n-周期点,现设f(x)=2x,0≤x≤12,2-2x,12≤x≤1,烅烄烆     

一类三阶泛函微分方程的周期解

利用重合度理论,研究了一类三阶泛涵微分方程x＇＇＇（t）＋a1[x”（t）]^k＋a2[x＇（t）]^k＋a3[x（t）]^k＋f（t,x（t）,x（t—τ））=p（t）的周期解的存在性,得到了周期解存在的充分条件。     

卡思卡特城堡

It is worthy of noting that, whilst Crookston Castle witnessed the earlier and happier portion of Mary's variegated life,     

Western and Eastern culture differences in commercial field

The communication of people partially is the communication of cultures. Culture has a direct effect on international commercial activities in all aspects. Different conceptions about time, space, equality, law and the like, lead people to deal with things in different ways. So to know cultures of the counterpart is to facil-itate our enterprises so as to have a smooth and successful communication in commercial activity.     

不同的吃喝玩乐

一、吃和喝吃苹果 eat an apple, 吃药 take medicine,吃糖 have some sweets,吃饭 have one's meals,吃馆子 dine out,吃惊 be surprised/     

漏洞百出的教育

Many college freshmen arrive woefully unprepared to do college work, and as disadvantaged populations continue to grow, the share of the American work force that has made it through college is expected to plummet. Many experts blame that educational failure not just on high schools but also on colleges. School & College, a special report by The Chronicle, looks at efforts to fix the system. What reforms would better prepare students for college? What should schools and colleges be doing differently? How should state and federal officials help?     

只要努力,不要后悔

There are numbers of crossroads on our long and unpredictable life journey where we totally have no idea about which direction to choose. No matter what our decision is, we should not turn back, but face the music and go ahead instead. I am this kind of girl who always does try without regretting, one example is how I dealt with my love.     

浅谈移民问题

Migration occurs behind a variety of reasons and has a great effect on the whole world. People may migrate in order to improve their economic situation, or in order to escape civil strife, persecution, and environmental disasters. The impact of migration is complex, bringing both benefits anddisadvantages. This paper briefly talks about the causes of migration, the allocation of benefits, and the ways in which individual countries and the international community deal with this important subject.     

Sister Carrie, an Adherent of Desires

Sister Carrie is one of the most controversial characters in American literature.Thought as a "fallen woman" firstly,she was defined as a "new woman" by some critics later. However, by digging into the motivaton behind the whole process of Carrie's "success", the relationship between Carrie and her creator (the author), the social conditions of then American, it can be found that Carrie has never been free-standing on her thought and she has never found her real-sdf even after becoming a famous actress. In a society dominated by mass consumerism Carrie is only an adherent of her own desires. She also is a representative of all those country girls flooded into cities, a symbol and a sacrifice of the urbanization of America in a time countryside was overcome by cities.     

Improvement of one-cycle controller by use of proportional integral differential controller

1.IntroductionOne-cyclecontrolmethod,whichwasproposedaboutonedecadeago[1],hasbecomeanattractivemethodinspecialfieldssuchaspowerfactorcorrection[2-6],switchingamplifiers[7,8],etc.Themainideaofthiscontrollerisbasedonintegrationofdiodevoltageinone-cycleandforcesittobeexactlyequaltothereferencevalue.Themainadvantageofthiscontrollerisitsrealtimeabilitytorejectthevariationofinputvoltage[1].Despitethisgreatability,ithasnogoodperformancesinrejectingofloaddisturbanceandfollowingreferencecommands.Espec…     

风的曲线

Rosco and I wait for the fishermen to return.I sit at a wooden bench near the store at Mt.Baker Resort and watch the clouds change shape. Rosco has my belt around his neck and an eight foot tow chain hooked to a tree. Dogs must be on a leash. Ducks and rabbits are loose.