AN EXTENSION OF THE HARDY-LITTLEWOOD-PóLYA INEQUALITY

The Hardy-Littlewood-Pólya (HLP) inequality [1] states that if a∈l~p,b∈l~q and p>1,q>1,1/p + 1/q>1, λ=2-(1/p+1/q),then Σ[(a_rb_s)/︱r-s︱~λ](r≠s)≤C‖a‖_P‖b‖_q.In this article, we prove the HLP inequality in the case where λ= 1, p = q = 2 with a logarithm correction, as conjectured by Ding [2]:Σ[(a_rb_s)/︱r-s︱~λ](r≠s,1≤r,s≤N)≤(2㏑N+1)‖a‖_2‖b‖_2.In addition, we derive an accurate estimate for the best constant for this inequality.     

一类修正Gross-Pitaevskii方程基态解的存在性

该文利用伸缩变换结合重排不等式等技巧得到了修正Gross-Pitaevskii方程对应极小化问题极小元的存在性与非线性项指数p的依赖关系.当2 p 2+4/N时,对任意c 0,极小化问题存在极小元.若p=2+4/N且c≤‖φ‖_2或者c(3/2)~(N/4)‖φ‖_2(‖φ‖_2的定义见第一节)或p 2+4/N,问题不存在极小解.而对于p=2+4/N且‖φ‖_2 c(3/2)~(N/4)‖φ‖_2,不知道是否存在极小解.     

逼近转化论与泛系逼近论

Domain D∈S_m(r,θ)means D(?)R~m, and contains certain cone with radius r and m solid angle θ issued from every point of D. Theorem Ⅰ If D∈S_m(r, θ), f∈C(D), ω(δ, f. W_∞~((0))(D))≤λδ~a, (λ~(-1)‖f‖_p)~a≤r, then for 1≤p≤q≤∞, we have ‖f‖_q≤cλ~b‖f‖_p~d, where a=p/(pa m),b=me/(ap m),d=pa p/q,c=(max[(m/θ)~(1/p),m/(m a)])~e,e=1-p/q.     

三维不可压霍尔磁流体方程组弱解的正则性准则(英文)

In this paper,we study the regularity criterion of weak solutions to the3 D incompressible Hall-magnetohydrodynamics,which is ifu and Bsatisfy the condition∫_0~T‖■_(x3)u(t)‖~q_(LP)+‖▽B‖~γ_(Lβ)dt∞ with 3/p+2/q≤1,3/β+2/γ≤1,p3,β3,then the weak solution(u,B) is a smooth one on(0,T].     

B值鞅的Davis型不等式与Banach空间的几何性质

下面两个结果被证明: 1.Banach空间X同构于p光滑空间(10使得每个X值鞅f=(f_n)满足‖f~*‖≤C‖S~((p))(f)‖_1。 2.Banach空间X同构于q凸空间(2≤q<∞)当且仅当存在C>0使得每个X值鞅f=(f_n)满足‖S~((q))(f)‖_1≤C‖f~*‖_1。 此外,应用f~*与S~((p))(f)的弱(1,1)型不等式以及集合{f~*<∞}{S~((p))(f)<∞}的相互包含关系刻划了B空间的p光滑性和q凸性。作为推论,给出了超自反空间以及与Hilbert空间同构的Banach空间的特征。     

Boussinesq方程组在Besov空间中局部解的存在性和延拓准则

本文研究二维无粘性Boussinesq方程组在超临界Besov空间B_(p,q)~s(R~2),s>1+2/p,1相似文献   

向量值树鞅及若干不等式

证明了向量值树鞅的若干不等式.主要结果是如下不等式若X同构于q一致凸空间(2≤q＜∞),则对每个X值的树鞅f=(ft,t∈T)α≥1和max(α,q)≤β＜∞成立‖(S(q)t(f),t∈T)‖ Mα∞≤Cαβ‖f‖ Pαβ‖(σ(p)t(f),t∈T)‖ Mα∞≤Cαβ‖f‖pαβ其中Cαβ是只依赖于α和β的常数.     

关于非线性微分方程渐近稳定的线性化原理

<正> 解的等渐近稳定性的条件.设 E 是 Banach 空间(范数为‖·‖_E),A(t)是几乎处处定义于[0,+∞)取值于 E 的有界线性算子空间(?)(范数为‖·‖)的局部一致(Bochner)可积函数,即 A(t)在每一紧区间[t_1,t_2)(?)[0,+∞)一致可测([2])和∫_(t_1)~(t_2)‖A(s)‖ds<+∞.这时(1)的几乎处处可微绝对连续解存在唯一.令 S_r={x∈E;‖x‖_E≤r},用 C(t_0,t_1,E)表定     

边界层的奇性分析

设 λ∈[λ_0,∞)(0<λ_0<<1),H_1=H_0~2(Ω)∩H~3(Ω),H_2=H_0~1(Ω)∩H~3(Ω),H_3=H~3(Ω),k_1=1/4,k_2=1/12,k_3=1/36,J_6(λ)=integral d(x,Γ)≥a~λlog(1+a~(-β) |△▽(u_e-u)|~2dx,α(ε)=1/6×log_ε1/C(C>1).我们考虑问题(?)定理.若 u=f∈H_i,对问题(1),有如下三种情形成立:i)正规区域 当 λ_0≤λ≤1/6-α(ε)时,有J_6(λ)≤C‖f‖_(H~3(Ω))~2;ii)奇性增长区域当1/6-α(ε)<λ<1/6+k_i/6时,有J_6(λ)≤Cε~(-6λ+2k_i)‖f‖_(H~3(Ω))~2;iii)奇性稳定区域当 λ≥1/6+(k_i)/6时,有J_6(λ)≤Cε~(-1+k_i)‖f‖_(H~3(Ω))~2;其中 i=1,2,3,β≥(45)/(32),C 为同 ε 无关的常数(见图1).     

混合幂的素变数丢番图逼近

证明了:如果λ_1,λ_2,λ_3,λ_4是正实数,λ_1/λ_2是无理数和代数数,V是well-spaced序列,δ0,那么对于v∈V,v≤X,ε0,使得|λ_(1p_1~2)+λ_(2p_2~2)+λ_(3p_3~3)+λ_(4p_4~3)-v|v~(-δ)没有素数解p1,p2,p3,p4的v的个数不超过O(X~(20/21+21δ+ε)).     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.