关于warped乘积S^1（A）×fS^n（b）的迷向曲率

在本文中，我们研究了warped乘积S^1（A）×fS^n（b）（a^2＋b^2=1,a〉0，b〉0，n≥3），给出了这类黎曼流形具有正述向曲率的充分必要条件．     

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初一年级1.已知方程（2a＋1）x＝1995无解，则a＝2．已知|a|＝2，|b|＝5，则a＋b＝（A）7；（B）－3；（C）3；（D）±7或±3；3．如果单项式－1995a2b2n＋1和1996am＋1b7是同类项，则（2m－n）1997＝4．求证：3＋32＋33＋…＋31996．初二年级1．已知2a－3b－12c＝0，a—2b－4c＝0（c≠0），则2．若x2－3x＝－9，则x3＝3已知a为整数，试求的最大整数值和最小整数值．4．三个人单独做某一件工作分别需a、b、c天，如果他们一起做，则完成工作所需要的天数是初一年级1.当2a＋1＝0,即时原方程无解2．因为|a|＝2，|b|＝5，故a＝±2，b＝±5，选…     

一道竞赛题的多角度审视

1992年沈阳市“育才环”初中数学邀请赛有这样一道试题：在四边形ABCD中，着∠B＝∠＝90°，∠＝120°，则这是一道四边形问题，解此题的指导思想是：通过作适当的辅助线，把四边形问题转化为三角形问题，辅助线的作法有如下10种：1．作DE⊥AB于E，CF⊥DE于F（如图1），则FEBC为矩形，∠ADE＝30°，∠DCF＝30°．若没AE＝a，HF＝b，则AH＝2a，DE＝，CD＝2b，所以AB＝2．作CE∥BA交AD于E，EF⊥AB于F（如图2），则EFBC为矩形，∠AEF＝30°，∠DCE＝30°．若设AF＝a，DE＝b，则AE＝2a，CE＝BF＝2b，CD＝所以AB＝…     

解集合问题中的几种常见错解剖析

有关集合问题，涉及的范围广，内容多，难度大，题目灵活多变，解法花样繁多，往往产生错解，是教学中的一个难点．现将常见的几类错误分类、整理，以期引起重视．一、忽视空集是任何集合的子集导致出错．例1设A={x-x~2 3x-2≥0}，B＝{xx~2-mx 1≤0}．且有BA，求实数m的取值范围．错解易知A＝［1，2］．设x_1，x_2是方程x~2-mx l≤0的两个根（x_1≤x_2），则由BA得x_1≥1，x_2≤2．因此，m所满足的条件由下列不等式组确定解得m=2，∴所求实数m＝2．错解剖析取m＝0，得方程x~2-mx 1＝0无实数解，即B＝φ，也满足BA，所以原解答漏解，出错…     

能力小题训练6——不等式

一、选择题(每小题5分,共60分)1.不等式|x-2|≥|x|的解集是().A.{x|x≤1}B.{x|x≥1}C.{x|x≤0或x≥2}D.{x|0≤x≤2}2.设a,b∈R,则“a>b”是“a>|b|”的().A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分条件也不必要条件3.不等式axx-1>a的解集为M,且2M,则实数a的取值范     

《解直角三角形》测试题

一、填空题1．在Rt△ABC中,若AB＝5,BC＝3,则cosA＝________2在Rt△ABC中,若,则cosB＝_________3．已知sina＝,则锐角a＝________4．已知sin35°＝0．5736,则cos55°＝_________5．比较大小：Sin48°37°______cos41°22′6．7．若则8．若是方程的一个根,且a是锐角,则a＝＿．9．若则10．等腰梯形一底角为,面积为,中位线长6cm,则此梯形的周长为_______二、单项选择题1．若,则锐角a的度数是（）（A）20°;（B）30°;（C）40°;（D）50°．2在Rt△ABC中,则斜边C的长为（）（A）62（B）42（C）：（D）．3．若A是锐…     

2006年高考数学模拟试题（一）

第一卷(选择题共50分) 一、选择题：本大题共10小题，每小题5分，共50分．在每小题给出的四个选项中，只有一项符合题目要求． 1．不等式|2-x|>1的解集是 ( ) A．{x|x<3} B．{x|13} 2．设从集合R到R的映射f：x→y=x~2-1，那么3在f下的原象构成的集合是 ( ) A．{2} B．{-2} C．{2，-2} D．{8} 3．若a，b，c成等比数列，m是a，b的等差中项，n是b，c的等差中项，则(a/m)+(c/n)= ( ) A．1 B．2 C．3 D．4 4．若a=(-3，(1/3)~2)，b=((1/3)~2，1)，则a与b的夹角是 ( ) A．30° B．60° C．90° D．120° 5．如果直线l，m与平面α，β，γ，满足：l=β∩γ，l∥α，m(?)α，m⊥γ，那么必有 ( ) A．α⊥γ，l⊥m B．α⊥γ，m⊥β C．m∥β，l⊥m D．α∥β，α⊥β 6．在△ABC中，“sin(A+B-C)=sin(A-B+C)”是“△ABC是等腰三角形”的 ( ) A．充分而不必要条件 B．必要而不充分条件 C．充分必要条件 D．既不充分也不必要条件     

关于warped乘积S^1（a）×fS^n（b）的迷向曲率

在本文中,我们研究了warped乘积S^1（a）fS^n（b）（a^2＋b^2=1,a〉0,b〉0．n≥3）,给出了这类黎曼流形具有正迷向曲率的充分必要条件．     

一类竞赛题的设计方法初探

在初中数学竞赛中，常见到如下类型的题目：①方程|x-2|＋|x-3|＝1的实根个数有()个.（第四届初中《祖冲之杯》数学邀请赛试题）则x的范围是（广州、武汉、福州联合数学竞赛试题）③方程有解，求④求函数（选自《中学数学竞赛题精选》）若能了解这类问题的设计原理，则对编拟、解答此类问题是有益的，为此本文作如下探讨.a2，b1，b2为实数，b1，b2均不为0，且al＜a2），则有：∵b1与b2均不为零，则bl≠b2，∴M≠m.y＝f（x）的图象如（A）（B）定性所示，∴对于直线y＝A来说当A＜m或A＞M时，无交点．当A＝m或A＝M时，有无穷多个交点.当m…     

关于一元一次不等式组解集的确定

一元一次不等式组的解集是指一元一次不等式组中各个不等式解集的公共部分，除教材中通过数轴，直观地表示出解集的公共部分外，还可用四句口快来揭示一元一次不等式组解集的确定规律，即：“同大于取大的，同小于取小的，两界之间要连写，两界之外是空集．”一、同大于型设a＜b，不等式组例1解不等式组解由不等式（1）得x≥1；由不等式（2）得x≥3．所以原不等式组的解集为x≥3．二、同小于型设a＜b，则不等式解由（1）得x≤－1；由（2）得x≤－3；由（3）得x＜0．所以原不等式组的解集为x≤－3．三、在大小两级之间型设。a＜b，则不等式组…     

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,     

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?     

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.     

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.