Hardy-Hilbert型不等式的一个加强

改进了Hlder不等式,并利用加强的Hlder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   

一个二元丢番图不等式

本文证明了如果1相似文献   

关于Euler常数的一个不等式

利用Γ函数的对数微商的渐近公式,我们建立了下面双边不等式:12n+∑2p+1k=1(-1)kBk2kn2k<∑nk=11k-lnn-γ<12n+∑2pk=1(-1)kBk2kn2k,这里γ=0.57721566…是Euler常数,Bk(k=1,2,…)是Bernoulli数,p0和n1是整数.     

关于Hardy不等式的加强改进

对 Hardy不等式 ,建立如下结构的加强不等式 :∑∞n=11n∑nk=1akp 1 ,an≥ 0 (n∈ N) ,0 <∑∞n=1apn<∞ ,Cp=1 -(1 -p- 1) p- 1,p≥ 2 ;1 -p- 1,1 相似文献   

Heisenberg's critical mass calculations for an explosive nuclear reaction

Based on the declassified records of Heisenberg's Farm-Hall “lecture”, we are attempting in the present work to follow Heisenberg's thoughts and results and show in a more transparent way how he arrived at his surprisingly quite accurate estimation of the critical mass of a reflected U235 sphere undergoing explosive neutrons fission. We conclude with a discussion regarding the contraversy concerning the so-called German Uranium bomb and the role played by Heisenberg and C.F. von Weizsäcker in this connection during and after the war.     

一个关于非负矩阵的不等式

证明:若(xij)是一个元素不全为零的m×n非负矩阵,则当0相似文献   

An Improved Hardy's Inequality

In this paper we shall extend Hardy's inequality associated with Fourier transform to the strip n(2-p) ≤ σ < n+p(N +1) where N = [n(1/p-1)], the greatest integer not exceeding n(1/p−1).     

On Bohr's Inequality

Bohr's inequality says that if is a bounded analytic function on the closed unit disc, then for 0 leq r 1/3 and that1/3 is sharp. In this paper we give an operator-theoretic proofof Bohr's inequality that is based on von Neumann's inequality.Since our proof is operator-theoretic, our methods extend toseveral complex variables and to non-commutative situations. We obtain Bohr type inequalities for the algebras of boundedanalytic functions and the multiplier algebras of reproducingkernel Hilbert spaces on various higher-dimensional domains,for the non-commutative disc algebra A_n, and for the reduced(respectively full) group C*-algebra of the free group on ngenerators. We also include an application to Banach algebras. We provethat every Banach algebra has an equivalent norm in which itsatisfies a non-unital version of von Neumann's inequality. 2000 Mathematical Subject Classification: 47A20, 47A56.     

Stability of Linear Inequality Systems in a Parametric Setting

In this paper, we propose a parametric approach to the stability theory for the solution set of a semi-infinite linear inequality system in the n-dimensional Euclidean space . The main feature of this approach is that the coefficient perturbations are modeled through the so-called mapping of parametrized systems, which assigns to each parameter, ranging in a metric space, a subset of . Each vector of this image set provides the coefficients of an inequality in and the whole image set defines the inequality system associated with the parameter. Thus, systems associated with different parameters are not required to have the same number (cardinality) of inequalities. The paper is focused mainly on the structural stability of the feasible set mapping, providing a characterization of the Berge lower-semicontinuity property. The role played by the strong Slater qualification is analyzed in detail.This research has been partially supported by Grant PB98-0975 from DGES (Spain), Grant BFM2002-04114-C02 (01–02) from MCYT (Spain), FEDER (European Union), and Bancaja-UMH (Spain).     

一个加强的Carleman不等式

建立如下权系数的不等式：１＋１ｍｍ≤ｅ１－１－２／ｅｍ（ｍ＝１，２，…），这里，１－２／ｅ＝０．２６４２４１１＋为最佳值．从而得到一个加强的Ｃａｒｌｅｍａｎ不等式．     

Remarks to Heisenberg's Farm-Hall lecture on the critical mass of fast neutron fission

Heisenberg's estimate of the critical mass of an explosive nuclear chain reaction is discussed with a view to the future of world peace and a real effective treaty on non-proliferation.     

关于Yang Bicheng不等式的另一个最佳常数

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   

一个素变数丢番图不等式

本文证明了如果1相似文献   

Hardy-Sobolev类上的Bohr型不等式

Let β 〉 0 and Sβ ：= {z ∈ C ： ｜Imz｜ 〈β} be a strip in the complex plane. For an integer r ≥ 0, let H∞^Г,β denote those real-valued functions f on R, which are analytic in Sβ and satisfy the restriction ｜f^（r）（z）｜ ≤ 1, z ∈ Sβ. For σ 〉 0, denote by Bσ the class of functions f which have spectra in （-2πσ, 2πσ）. And let Bσ^⊥ be the class of functions f which have no spectrum in （-2πσ, 2πσ）. We prove an inequality of Bohr type
‖f‖∞≤π/√λ∧σ^r∑k=0^∞（-1）^k（r＋1）/（2k＋1）^rsinh（（2k＋1）2σβ）,f∈H∞^r,β∩B1/σ,
where λ∈（0,1）,∧and ∧′are the complete elliptic integrals of the first kind for the moduli λ and λ′=√1- λ^2,respectively,and λ satisfies
4∧β/π∧′=1/σ.
The constant in the above inequality is exact.     

关于算子迹的Bellman不等式

本文将矩阵中关于半正定 Hermite矩阵的 Bellman不等tr(AB) k tr(Ak Bk) ,k =1 ,2 ,…推广到 Hilbert空间 ,得到关于正的迹算子的相应不等式     

Remarks on the Extremal Functions for the Moser-Trudinger Inequality

We will show in this paper that if A is very close to 1, then I（M,λ,m） =supu∈H0^1,n（m）,∫m｜△↓u｜^ndV=1∫Ω（e^αn｜u｜^n/（n-1）-λm∑k=1｜αnun/（n-1）｜k/k!）dV can be attained, where M is a compact-manifold with boundary. This result gives a counter-example to the conjecture of de Figueiredo and Ruf in their paper titled ＂On an inequality by Trudinger and Moser and related elliptic equations＂ （Comm. Pure. Appl. Math., 55, 135-152, 2002）.     

Radon不等式的新推广

利用Ho。lder不等式、Young不等式、Chebyshev不等式、幂平均不等式建立Radon不等式的指数推广形式,得到一个具有广泛应用价值的不等式.指出文[7]中给出的关于Radon不等式的推广结果是错误的,并在本文中作了修正.     

基于Legendre函数的Landau′s型不等式

首先研究了L2ω(-1,1)上关于L egendre多项式Xn(x)的L andau′s型不等式.利用Xn(x)的正交性,建立了代数多项式pn(x)的L andau′s型不等式,并且指出其不等式的系数在某种意义上是最好可能的.     

一类组合不等式的简证与推广

利用概率方法给出了形如sum from k=1 to n(1/k)>π/4(sum from k=1 to n((-1)k-1Cnk)1/(k～1/2))与sum from k=1 to n(1/k)<2～(1/2)(sum from k=1 to n((-1)k-1Cnk)1/k2)1/2的组合不等式.