共查询到20条相似文献，搜索用时 500 毫秒
1.
2.
薛观林 《中学数学研究(江西师大)》2011,(2):24-24
文[1]给出柯西不等式的一个有趣推广,本文将其作进一步的推广,得到：
定理设Pi∈R^＋,贝4（p1a1^m＋P2a2^m＋…＋pnan^m）（p1b1^m＋p2b2^m＋…＋pnbn^m）≥1/n^m-2（p12/m·a1b1＋p2^2/ma2b2＋…＋pn^2/manbn）^m,其中m,n∈N^＋,当m为奇数时,ai〉0,bi〉0,i=1,2,…,n;当m为偶数时,ai,b;可为任意实数,i=1,2,…,n． 相似文献
3.
完整的柯西不等式通常是在进入大学后才具体见识和应用的，是解决相关数学问题最常用的定理之一．它的一般形式为：对于任意实数ai，bi（i=1，2，…，n），有（a1b1＋a2b2＋…＋anbn）^2≤（a^2＋a2^2＋…＋an^2）（b1^2＋b2^2＋…＋bn^2），其中当且仅当ai=kbi，即ai与bi（i=1，2，…，n）成比例时取到等号． 相似文献
4.
戴志祥 《数理天地(高中版)》2010,(4):23-24
柯西不等式
设a1,a2,…,an,b1,b2,…,bn∈R,则（a1^2;＋a2^2＋…＋an^2）（b1^2＋b2^2＋…＋bn^2）≥（a1b1＋a2b2＋…＋anbn）,当且仅当bi=0（i=1,2,…,n）或存在一个数k,使得ai=kbi（i=1,2,…,n）时,等号成立． 相似文献
5.
刘爱农 《中学数学教学参考》2004,(5)
琴生不等式是:若f(x)是区间L上的凸函数,ai∈L ,i=1 ,…,n ,则 ni=1f(ai)≤nf( 1n ni=1ai) .我们还有(以下把 ni=1记作 )定理 设f(x)是闭区间[a ,b]上的凸函数,ai∈[a ,b],i=1 ,…,n ,则f(ai)≥kf(b) (n -k -1 ) f(a) f(c) .①其中 k = ai-nab-a ,c= ai-kb -(n -k -1 )a .证明:任取x1、x2 ,使a 相似文献
6.
数论部分1.求所有正整数n≥2,满足对所有与n互素的整数a和b,a≡b（mod n）当且仅当ab≡1（mod n）.解:所给条件等价于满足（a,n）=1的每个整数a,a2≡1（mod n）.事实上,若a≡b（mod n）等价于ab≡1（mod n）,则由ab≡1（mod n）,当b=a时,即有a2≡1（mod n）. 相似文献
7.
乐茂华 《海南师范学院学报》2004,17(4):303-304
设p是奇素数，文章证明了：当p=3时，方程x^2=p^a p^2 p^c?BD鲇蟹歉赫?x，a，b,c)=(3^n，2n-1，2n-1，2n-1)，其中n是正整数；当p＞3且p≠7(mod8)时，该方程无非负整数解(x，a，b，c)． 相似文献
8.
设a、b,c,d、r是适合a^2＋db^2=c^r，gcd（a，db）=1，a恒等于-3（mod4），b恒等于2（mod4），d恒等于1（mod2），r恒等于1（mod2）。r〉1．（b／a）=-1，（d／a）=1的正整数，其中（＊／＊）是Jacobi符号，本文证明了：当c是奇素数时，方程a^x＋db^y=c^z仅有正整数解（x，y，z）=（2，2，r） 相似文献
9.
黄崇智 《内江师范学院学报》2009,24(12):9-12
对群论定理“设a,b为群（G,·）之二元．如 1）a·b=b·a,2）（o（a）,o（b））=1,则o（a·6）=o（a）×o（6）″进行推广．首先,仅变更2）为2′）（o（a）,o（b））=d,得到定理1：设a,b为群（G,·）之二元,如 1）n·6=b·a．2′）（o（a）,o（6））=d,则o（a·6）=o（a）/d×o（b）/d×q,q∈N且1≤q≤d;其次,不仅变更2）为2″）（o（ai）,a（aj））=1,i≠j,i,j=1,2,…,n,且变更1）为1′）ai·aj=aj·ai,i≠j,i,j=1,2,…,n,得到定理2：设a1,a2,…,an为群（G,·）之n（≥2）元, 相似文献
10.
韦兴洲 《中学生数理化(高中版)》2013,(6)
本文讨论了n个正整数的和与积相等的一个必要条件,并证明了两个与素数、合数有关的结论.
结论1:若n(n≥2)个正整数a1,a2,…,an满足条件n∑i=1ai=n∏i=1ai,则ai≤n(i=1,2,…,n).
证明:(1)当n=2时,a1·a2-(a1+a2)=(a1-1)·(a2-1)-1≥0,当且仅当a1=a2=2时等号成立,故a1·a2=(a1+a2)时a1≤2,a2≤2,符合结论1.
(2)当n≥3时,设a1≤a2≤…≤an.令a1=a2=…=an-2=1,an-1=2,an=n,则n∑i=1ai=n∏i=1ai=2n.此时ai≤n(i=1,2,…,n).
又设存在n(n≥2)个正整数b1,b2,…,bn满足条件1≤b1≤b2≤…≤bn-1≤bn,bn＞n,且n∑i=1bi=n∏i=1bi.不妨令bi=1+ti(i=1,2,…,n-1,ti∈N),bn=n+tn(n∈N+). 相似文献
11.
邱崇丙 《唐山师范学院学报》2014,(1):21-23
汉字的六书,《说文》对“转注”一类,语焉不详。后世学者提及转注,也仅限于许慎所举出的例字。《汉字例说》一文,作者从转注的角度综合考虑,对部分现代常用字作了分析,跟传统的解释有所不同。希望能抛砖引玉,互相切磋,以推进学术研究。 相似文献
12.
13.
Rachel Zupek 《海外英语》2007,(11):40-41
我们绝大部分人都同意一件事情——我们喜欢金钱。但是你对金钱的喜欢之情足够到让你创立一份事业么?.财富通常被人忽视,主要在于人们不能真正了 相似文献
14.
《海外英语》2007,(4):36
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. 相似文献
15.
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. 相似文献
16.
YANGShiguo 《重庆大学学报(英文版)》2004,3(1):86-88
The problem on the geometrc inequalities involving an n-dimensional simplex and its inscribed simplex is studied. Aninequality is established, which reveals that the difference between the squared circumradius of the n-dimensional simplex andthe squared distance between its circumcenter and barycenter times the squared circumradius of its inscribed simplex is not lessthan the 2(n-1)th power of n times its squared inradius, and is equal to when the simplex is regular and its inscribed siplex is atangent point one. Deduction from this inequality reaches a generalization of n-dimensional Euler inequality indicating that thecircumradius of the simplex is not less than the n-fold inradius. Another inequality is derived to present the relationship betweenthe circumradius of the n-dimensional simplex and the circumradius and inradius of its pedal simplex. 相似文献
17.
18.
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. 相似文献
19.
20.
RUZBEHANI Mohsen 《重庆大学学报(英文版)》2004,3(1):20-25
1.IntroductionOne-cyclecontrolmethod,whichwasproposedaboutonedecadeago[1],hasbecomeanattractivemethodinspecialfieldssuchaspowerfactorcorrection[2-6],switchingamplifiers[7,8],etc.Themainideaofthiscontrollerisbasedonintegrationofdiodevoltageinone-cycleandforcesittobeexactlyequaltothereferencevalue.Themainadvantageofthiscontrollerisitsrealtimeabilitytorejectthevariationofinputvoltage[1].Despitethisgreatability,ithasnogoodperformancesinrejectingofloaddisturbanceandfollowingreferencecommands.Espec… 相似文献