共查询到20条相似文献,搜索用时 140 毫秒
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积分型Hilbert定理的改进与应用 总被引:9,自引:1,他引:8
本文建立如下权函数的不等式w (x) = ∫∞01x + y + 1(x + 1y + 1)1/2dy ≤π[1 - 1 - 2/π(x + 1)1/2] (x ∈[0,∞)),这里,常数1- 2/π是最佳值,从而改进了积分型Hilbert定理,作为应用,建立一个Hilbert类积分不等式及其加强式;并改进推广了Hardy-Littew ood 积分不等式. 相似文献
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关于Hardy-Hilbert积分不等式的推广 总被引:19,自引:1,他引:18
本文通过引入适当的参数,及如下形式的权系数(x+β)1-tkt(r)-ln2α+βx+β1-1/r,x∈[α,∞)(α-β,r>1,1-1/r<t1).而使Hardy-Hilbert积分不等式得到有意义的推广.这里kt(r)=∫∞01(1+u)t1u1/rdu,常数ln2=0.69314718+. 相似文献
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高中课本《平面解析几何》第131页例4是“化圆锥曲线的极坐标方程ρ=ep1-ecosθ为直角坐标方程”,解题时涉及到方程x2+y2=e(x+p)(1)与两边平方后所得方程(1-e2)x2+y2-2e2px-e2p2=0(2)的等价性问题.课本中有这样... 相似文献
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若a∈R,则a2≥2a-1①当且仅当a=1时等号成立.将此不等式推广到一般,有定理若a∈R+,n∈N且n≥2,则a2≥na-(n-1)②当且仅当a=1时等号成立.证由均值不等式,有a2+(n-1)=an+1+1+…+1n-1个≥na,∴an≥na-(... 相似文献
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我在教学中发现:对有些不等式的证明,可根据不等式的特点,用构造二次函数的方法加以解决;本文结合具体例子,谈谈怎样构造二次函数证明不等式;1 确定主元构造例1 设a、b都是实数,求证:a2+b2≥a+b+ab-1.分析 求证结论是二元二次对称不等式,可以a(或b)为主元构造二次函数;证明 设f(a)=a2-(b+1)a+b2-b+1.因二次项系数大于零,且Δ=〔-(b+1)〕2-4(b2-b+1)=-3(b-1)2≤0故f(a)≥0,即a2+b2≥a+b+ab-1.2 根据判别式构造例2 设实数a… 相似文献
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一个素变数的Diophantine不等式 总被引:3,自引:3,他引:0
设1<C<13/12.本文证明了存在N(C)>0使得对任意实数N>N(C),下面的不等式|++ -N|<N- )logsN有素数解p1,p2,p3,其中s=2(15). 相似文献
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THE VARIATION OF INVARIANT LINES AND LIMIT CYCLES FOR A QUADRATIC DIFFERENTIAL SYSTEM 总被引:1,自引:0,他引:1
1IntroductionConsidertherealquadraticdiferentialsystemx=-y+δx-4x2+3xy+13y2y=x(1-13x-y).(1)First,forconvenience,wedenotethetwo... 相似文献
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某些含有等号的不等式的证明题,若从等号成立的条件出发,利用基本不等式,则可迅速获证.下面举例说明.例1已知a+b+c=1,求证a2+b2+c2≥13.分析:考虑到当且仅当a=b=c=13时,不等式取等号,此时,a2=19,于是有下面的证法.证a2+1... 相似文献
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改进了Hlder不等式,并利用加强的Hlder的不等式对联系β函数的带参数的Hardy-Hilbert型不等式进行了改进,建立一个新的形如sum from n=1 to ∞ sum from m=1 to ∞(ambn/(m+n)λ)/相似文献
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对Yang Bicheng不等式进行了再加强,获得了如下不等式:e 1-2n+(4-1 e)/(e-2)1+n1n相似文献
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HARDY-HILBERT不等式一个新的推广与改进 总被引:2,自引:0,他引:2
吕中学 《数学的实践与认识》2005,35(5):141-145
给出了如下形式的权系数ω(q,n)∶=∑1m +nnm1/ q<πsin(π/ p) -1abn1/ q +n -1 / qq >1 ,1P +1q =1 ,n∈N ,a >0 ,b >0 ,0 相似文献
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幂平均不等式的最优值 总被引:20,自引:0,他引:20
设Mn[r](a)为a的r阶幂平均,0<α<θ<β,那么满足不等式[Mn[α](a)]1-λ.[Mn[β](a)]λ≤Mn[θ](a)的最大实数λ是λ≥{1+(β-θ)/[m(θ-α)]}-1.这里m=min{[2+(n-2)tβ]/[2+(n-2)tα],t∈R++};满足反向不等式的最小实数λ是λ=[β(θ-α)]/[θ(β-α)].本文的方法基于优势理论与解析技巧,对于建立不等式的最优化思想作了尽可能多的展示.作为应用,得到了一些涉及和、积分与矩阵的新不等式(含Hardy不等式的推广与加强). 相似文献
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Vesselin Vatchev 《分析论及其应用》2011,27(2):187-200
For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln(ψ) = n ∑ k=0 akψ(k), where the constant coefficients ak ∈ R may be adapted to f . We prove that for each f ∈ C(n)(I), there is a selection of coefficients {a1, ,an} and a corresponding linear combination Sn( f ,t) = n ∑ k=1 bkeλkt of functions ψk(t) = eλkt in the nullity of L which satisfies the following Jackson’s type inequality: f (m) Sn(m )( f ,t) ∞≤ |an|2n|Im|1/1q/ep|λ|λn|n|I||nm1 Ln( f ) p, where |λn| = mka x|λk|, 0 ≤ m ≤ n 1, p,q ≥ 1, and 1p + q1 = 1. For the particular operator Mn(f) = f + 1/(2n) f(2n) the rate of approximation by the eigenvalues of Mn for non-periodic analytic functions on intervals of restricted length is established to be exponential. Applications in algorithms and numerical examples are discussed. 相似文献
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Let (sn) be an s-number sequence. We show for each k = 1, 2, . . . and n ≥ k + 1 the inequality between the eigenvalues and s-numbers of a compact operator T in a Banach space. Furthermore, the constant (k + 1)1/2 is optimal for n = k + 1 and k = 1, 2, . . .. This inequality seems to be an appropriate tool for estimating the first single eigenvalues. On the other
hand we prove that the Weyl numbers form a minimal multiplicative s-number sequence and by a well-known inequality between eigenvalues and Weyl numbers due to A. Pietsch they are very good
quantities for investigating the optimal asymptotic behavior of eigenvalues.
Research of the second author was supported by the DFG Emmy-Noether grant Hi 584/2-3. 相似文献
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In this work, we present a new sharpened version of the classical Neuberg–Pedoe inequality. As an application, the following improved Neuberg–Pedoe inequality is derived: 相似文献
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Masatoshi Fujii Eizaburo Kamei 《Proceedings of the American Mathematical Society》1996,124(9):2751-2756
Very recently, Furuta obtained the grand Furuta inequality which is a parameteric formula interpolating the Furuta inequality and the Ando-Hiai inequality as follows : If and is invertible, then for each ,
is a decreasing function of both and for all and . In this note, we employ a mean theoretic approach to the grand Furuta inequality. Consequently we propose a basic inequality, by which we present a simple proof of the grand Furuta inequality.
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Bai zhengguo 《数学年刊B辑(英文版)》1988,9(1):32-37
A Riemannian manifold V~m which admits isometric imbedding into two spaces V~(m+p)ofdifferent constant curvatures is called a manifold of quasi constant curvature.TheRiemannian curvature of V~m is expressible in the formand conversely.In this paper it is proved that if M~n is any compact minimal submanifoldwithout boundary in a Riemannian manifold V~(n+p)of quasi constant curvature,then∫_(M~u)(2-1/p)σ~2-[na+1/2(b-丨b丨)(n+1)]σ+n(n-1)b~2*丨≥0,where σ is the square of the norm of the second fundamental form of M~n When V~(n+p)is amanifold of constant curvature,b=0,the above inequality reduces to that of Simons. 相似文献