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1) Powerful inequatity
含幂不等式
2) power inequality
幂不等式
3) power exponent inequality
幂指不等式
1.
In 2002,Ni Renxing and Zhang Senguo put forward the following conjecture that power exponent inequality sum from k=1 to n akan-k+1≤sum from j=1 to n akjamj≤sum from k=1 to n akak is true when {ak} satisfies,0<a1≤a2≤…≤an,where {k1,k2,…,kn} and {m1,m2,…,mn} are the two arbitrary arrangements of{1,2,…,n}.
倪仁兴和张森国于2002年提出了下面一个幂指不等式猜想:对满足0
2.
By virture of some new techniques of analysis,a novel power exponent inequality was given(If a and b are arbitrary two posstive numbers,then a a+b b was no less than a b+b a),so was its extend.
幂指不等式在数学竞赛中时有出现 ,其证明往往是比较困难的 。
4) Double chord-power integrals inequalities
双弦幂积不等式
5) Power Mean Inequality
幂平均不等式
1.
With the application of Chebyshev inequality and power mean inequality,a series of new generalization of Shapiro inequality and its changes are shown,and some applications of the generalized conclusions are given.
利用Chebyshev不等式和幂平均不等式,研究了Shap iro不等式及其变形的一组新推广,给出了推广结果的一些应用。
2.
By using the Chebyshev inequality and the power mean inequality,a series of new generalizations of Klamkin inequality were studied.
利用Chebyshev不等式和幂平均不等式,研究了Klamkin不等式的一组新的推广,并给出了推广方法和结论的一组应用。
3.
By using Cauchy inequality and power mean inequality, a corrected power generalization of circular inequality and its dual generalization are studied, and the applications of the generalized conclusions are given.
利用Cauchy不等式和幂平均不等式,研究了循环不等式的校正加权推广及其对偶推广,给出了推广结果的应用。
6) mean value inequality of power
幂平均不等式
1.
This paper points out the incorrectness of the conclusion(2),and has obtained the mean value inequality of power about the concave function when α≤1,and also discusses the mean value inequality of power in other cases of α.
本文指出结论 (2 )是不正确的 ,并且得到了当α≤ 1时凹函数的幂平均不等式。
2.
This paper points out an error in paper \, It is in this paper that the author obtains the mean value inequality of power about the concave function when α≤1, corrects and enriches the theorem in paper \, and also discusses the mean value inequality of the power in other cases of α.
文 [1 ]获得了当 α≥ 1时的凸函数的幂平均不等式 (3)、(4 ) [1] 。
补充资料:Harnack不等式(对偶Harnack不等式)
Harnack不等式(对偶Harnack不等式) quality (dual Hatnack inequality) Harnack in- 【补注】一直到G的边界的H助nack不等式,见【AZI.l翻..‘不等式(对停H山丸朗k不等不)[ Har.改沁-勺函勺(d切红Hat’I犯‘k如为uaJ卿);rap.姗二p魄HcT助(月加湘oe)] 给出正调和函数的两个值之比u(x)/“(y)的上界和下界估计的一个不等式,由A.Hai,剐火(汇IJ)得到.令u)0是n维E议当d空间的区域G中的一个调和函数;令E。(y)是中心在点y处半径为;的球{x:}x一y!<;}.若闭包万了刃.CG,则对于所有的、“凡(,),o 0是常数,亡“(省:,…,氛)是任一。维实向量,叉‘G.不等式(2)中的常数M仅依赖于又,A,算子L的低阶项系数的某些范数以及G的边界与g的边界之间的距离. fy,1, …粤馨 对于形如u:+Lu“0的一致抛物型方程(算子L的系数可以依赖于t)的非负解:(x,t),类似于1压ar-恤比不等式的不等式也成立.在此情形下,对于顶点在点(y,动处开口向下的抛物面(图a) {(x,t川x一,I’<。,(T一t),:一v,簇t簇:}的内部的点(x,t),只能有单边的不等式(fs」): u(x,r)(M妇(y,T),这里,M依赖于y,T,又,A,料,,,算子L的低阶项系数的某些范数,以及抛物面的边界与在其中“(义,t))0的区域的边界之间的距离.例如,如果在柱形区域 Q二Gx(a,b],中“〕O,此外,歹CG,并且如果刁G与刁g之间的距离不小于d(>0),而d充分小,那么在gx(a一矛,bJ中不等式 。(、.t、___/,、一。1,.:一:.八 1。,二之二止,二止匕成几11止二一一丈‘.+一+11 u气y,T)\下一I“/成立(协J).特别地,如果在Q中u)0(图b),且如果对于位于Q中的紧集Q,和QZ有 占“们山n(t一:)>0, (义,t)‘Q- (y.下)〔QZ那么有 n知Lxu(x,t)簇M nunu(x,t), (x,‘)‘QZ(x,‘)‘Q-其中M“M(占,Q,QI,QZ,L).函数 ·、·,‘卜exn(‘睿,、‘一暮“:)—对于任意的k,,…,气,它是热方程u,一△拟“0的解—表明在抛物型情形下双边估计的不可能性,
说明:补充资料仅用于学习参考,请勿用于其它任何用途。
参考词条
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