共查询到20条相似文献,搜索用时 31 毫秒
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Let (M^2m+4n+k-2, T) be a smooth closed manifold with a smooth involution T whose fixed point set is RP(2^m) ∪ P(2^m, 2n - 1) (m 〉 3, n 〉 0). For 2n ≥ 2^m, (M^2m+4n+k-2, T) is bordant to (P(2^m, RP(2n)), To). 相似文献
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《数学教学》2012年第12期的数学问题874为:题目 已知 m,n∈N+,m,n≥2,xi∈R+(i=1,2,…,m),(^m∑i=1)xi=S,n∈N+,求证:(^m∑i=1)^n√xi/S-xi≥.看完此题,笔者不禁想起了文[1]中的不等式:题源1已知a,b,c为正数,求证:√a/(b+c)+√b/(c+a)+√c/(a+b)〉2。 相似文献
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POKORNY Milan 《偏微分方程(英文版)》2011,(4):334-350
We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain with the pressure law p(e,θ) - qθ+eln^α(1+e). For the heat flux q ~ -(1+θ^m) △θwe show the existence of a weak solution provided α〉max{1,1/m}, m 〉0. This improves the recent result from [1]. 相似文献
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定理 设数列{αn}是等差数列,sn=α1^m+α2^m+…+αn^m,m∈N^*,则存在λi∈R(i=2,3,…,m+1),有g(n)=λm+1αn^m+1+λmαn^m+…+λ3αn^3+λ2αn^2,使{sn-g(n)}为等差数列. 相似文献
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In this paper, we study an important class of (α,β)-metrics in the form F = (α+β)^m+1/α^m on an n-dimensional manifold and get the conditions for such metrics to be weakly- Berwald metrics, where α = √aij(x)y^iy^j is a Riemannian metric and β = bi(x)y^i is a 1-form and m is a real number with m ≠ -1,0,-1/n. Furthermore, we also prove that this kind of (α,β)-metrics is of isotropic mean Berwald curvature if and only if it is of isotropic S-curvature. In this case, S-curvature vanishes and the metric is weakly-Berwald metric. 相似文献
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文[1]对问题:“已知a,b∈R+,a+b=2,求1/1+a^n+1/1+b^n的最小值”,运用先猜后证的数学思想, 相似文献
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Yandong Jiao Guidong Dai Quandong Feng Yifa Tang 《计算数学(英文版)》2007,25(6):690-696
We prove that any linear multi-step method G1^T of the form
∑k=0^mαkZk = T∑k=0^mβkJ^-1↓ΔH(Zk)
with odd order u (u≥ 3) cannot be conjugate to a symplectic method G2^T of order w (w 〉 u) via any generalized linear multi-step method G3^T of the form
∑k=0^mαkZk = T∑k=0^mβkJ^-1↓ΔH(∑l=0^mγklZl).
We also give a necessary condition for this kind of generalized linear multi-step methods to be conjugate-symplectic. We also demonstrate that these results can be easily extended to the case when G3^T is a more general operator. 相似文献
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题目(第二十一届“希望杯”高二第2试)已知a,b∈R+,且ab=2,则b/2+a2+a/2+b2的最小值是.本文从两个角度对问题进行研究,先对问题作一题多解,然后对问题作多方面变式,供大家参考.1.一题多解解法1∵a,b∈R+,且ab=2,∴b=2/a,∴b/2+a2+a/2+b2=2/a2+a2+a/2+4/a2=2/a(2+a2)+a3/2(2+a2)=4+a4/2a(2+a2), 相似文献
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柯西不等式的一般形式为(a1^2+a2^2+…+an^2)(b1^2;+b2^2…+bn^2)≥(a1-b1+a2b2+…+dnbn)^2(n∈N+),它的结构特征可用对联“‘方、和、积’不小于‘积、和、方’”来帮助记忆.“方、和、积”是指不等式的一边先为“平方”,再进行“求和”,最后才是两组矩个数平方和的“乘积”;而“积、和、方”则指不等式的另一边应先为“乘积”,再进行“求和”, 相似文献
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人教版高二数学课本习题6.5第4题是:求证
|a|+|b|/1+|a|+|b|≥|a+b|/1+|a+b|
这是一道看似极其平凡的习题,下面拟从“多证”与“多变”两个不同角度进行一些不平凡的探究,希望能给同学们的学习带来启发. 相似文献
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《数学通报》1999,(10)
1999年9月号问题解答(解答由问题提供人给出)12if.求ig勺O”+ig‘SO”+tgc7o“的值.解设A—ig1o”一ig5o”+ig7o“,B—tglo“ig7o“-tglootg500-ig5o”ig7o”,C—tglo”ig5o”ig700.首先,求出A、B、C的值.由ig3a的公式得,ig“a-3ig3atg“a-3tga+ig3a—O,易见,a—-SO”、IOo、7O”是方程ig‘a-/3ig‘a-3tga+H’-j—’、—-·—-”一”3一O的在正切函数tga的单调区间(-goo,gO肝内的三个不同的根,由韦达定理得:A一人,B—一A3,卜———”~3其次,令D,;一ig”Ic“+(-ig5o“)’‘+ig”7O(n… 相似文献
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设数列{an}的前n项和为Sn则Sm+n=Sn+(am+1+…+an+n).(1)若数列如{an}是公差为d的等差数列,则Sm+n=Sm+Sn+mnd(1)特别地,sn+1=a1+Sn+nd.推论等差数列的前n项和为A,次n项和为B,后n项和为C,则(2)若数列{an}是公比为q的等比数列,则am+1+…+am+n特别地,Sn 1=a1+qSn(2)推论对等比数列有SS+Sg。一战(SZ。+Ss。).在处理某些等差(或等比)数列的“和”问题时,运用上述公式可简捷求解.例1已知k。)是等比数列,若。1+。2+a。218,a;+a3+a。—一人且入一al+a。+…+a。,那么tims"的值… 相似文献
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The Cauchy problem for a linear 2mth-order Schrōdinger equation ut=-i(-△)^mu, in R^N×R+,u|t=0=u0;m≥1 is an integer,is studied, for initial data uo in the weighted space L^2ρ(R^N),withρ^*(x)=e|x|^a and a=2m/2m-1∈(1,2].The following five problems are studied: (I) A sharp asymptotic behaviour of solutions as t → +∞ is governed by a discrete spectrum and a countable set Ф of the eigenfunctions of the linear rescaled operator B=-i(-△)^m+1/2my·↓△+N/2mI,with the spectrum σ(B)={λβ=-|β|≥0}. (Ⅱ) Finite-time blow-up local structures of nodal sets of solutions as t → 0^- and a formation of "multiple zeros" are described by the eigenfunctions, being generalized Hermite polynomials, of the "adjoint" operator B=-i(-△)^m-1/2my·↓△,with the same spectrum σ(B^*)=σ(B).Applications of these spectral results also include: (Ⅲ) a unique continuation theorem, and (IV) boundary characteristic point regularity issues. Some applications are discussed for more general linear PDEs and for the nonlinear Schr6dinger equations in the focusing ("+") and defocusing ("-") cases ut=-(-△)^mu±i|u|^p-1u,in R^N×R+,where P〉1,as well as for: (V) the quasilinear Schr6dinger equation of a "porous medium type" ut=-(-△)^m(|u|^nu),in R^N×R+,where n〉0.For the latter one, the main idea towards countable families of nonlinear eigenfunctions is to perform a homotopic path n → 0^+ and to use spectral theory of the pair {B,B^*}. 相似文献
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问题1第十七届“希望杯”全国数学邀请赛高二第2试的第3题为:设直角三角形两直角边的长分别为a和b,斜边长为c,斜边上的高为h,则a+6和c+h的大小关系是 相似文献
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(a1,a2,…,an是正数,n∈且≥2)解证有关不等式问题,常常无法直接解决,而是先将解证的不等式进行适当的变形,凑出均值不等式的条件,再用均值不等式解决.这时,恰当的变形便成为解题的关键.下面介绍七种常用的变形技巧.1补项例1已知X>-1,且x≠0,n∈N,求证:(1+x)n>1+nx.证明例2设x1,x2,…,xn。都是正数,证明:2拆项例3已知a、b∈R ,且a≠b,求证:证明a5+b5例5已知a、b、c∈R ,且a+b+c=1,求证:证明例8已知a+b+c—1,$证:rt‘+b‘+C‘MM.证明”.”1一(a+b+c)‘一a‘+b’+c’+Zab+Zbc+… 相似文献