共查询到20条相似文献,搜索用时 328 毫秒
1.
John Villavert 《数学物理学报(B辑英文版)》2011,31(6):2285-2288
The Hardy-Littlewood-Pólya (HLP) inequality [1] states that if a∈lp,b∈lq and p>1,q>1,1/p + 1/q>1, λ=2-(1/p+1/q),then Σ[(arbs)/︱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[(arbs)/︱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. 相似文献
2.
本文研究一类弹性梁方程边值问题y(1)-α1y+β1y"+g(x,y,y")=e,02(0.1),而g:[0,1]×R×R→R为连续有界函数,特征对(α1,β1)满足α1+(0+0.5)2π2β1=(0+0.5)4π4及α1+(k+0.5)2π2β1≠(k+0.5)4π4,?k∈N 相似文献
3.
研究了一类特殊循环环即循环准整环的构造,得到的主要结论有:1)所有的无限循环准整环就是M~0和 1)的标准分解式为n=p1α1p2α2…psαs,ⅰ)若s=1,则n阶循环准整环共有α1+1个,它们是dZ/ndZ,其中d=p1β1,0≤β1≤α1;ⅱ)若s>1,则n阶循环准整环共有α1α2…αs个,它们是dZ/ndZ,其中d=p1β1p2β2…psβs,... 相似文献
4.
We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem {D(α0) + u(x) = f(x, u(x)), 0 < x < 1, 3 < α≤ 4 u(0) = α0 , u’’ (0) = α2 u(1) = β0 , u’’(1) = β2} (1) where D(0α)+u is Caputo fractional derivative and α0,α2,β0,β2 is not zero at all,and f:[0,1]×R→ R is continuous.The calculated numerical results show reliability and efficiency of the algorithm given.The numerical procedure is tested on linear and nonlinear problems. 相似文献
5.
In this paper, we consider the following quadratic pencil of Schr?dinger operators L(λ)generated in L2(R+) by the equation ■ with the boundary condition ■ where p(x) and q(x) are complex valued functions and α0, α1, β0, β1 are complex numbers with α0β1-α1β0≠0. It is proved that L(λ) has a finite number of eigenvalues and spectral singularities,and each of them is of a finite multiplicity... 相似文献
6.
令R=Fq+vFq是一个有限非链环,其中q是一个奇素数的方幂,v2=v.文章利用二元斜多项式环R[x,y;ρ,θ]来研究环R上的2维斜常循环码的代数结构和相关性质,其中ρ和θ是环R上的两个自同构映射.基于中国剩余定理,文章确定了环R上2维(α1+β1v,α2+β2v)-斜常循环码的生成元结构并且考虑了它们的Gray象,其中α1+β1v和α2+β2v都是环R上的可逆元.此外,文章研究了环R上2维(α1+β1v,α2+β2v)-斜常循环码的对偶码并且确定了对偶码子码的生成元结构. 相似文献
7.
本文研究具有二次等式约束的最小二乘问题(LSS): min‖Ax-b‖2 s.t. ‖x‖2=1, 其中A∈Rm×n, b∈Rm, 并假定‖A+b‖2<1.重点关注一个极端情形: ‖A+b‖2≈0. 敏度分析表明,这是一种病态问题. 基于Padé逼近给出了一种迭代解法. 数值算例表明,新方法在速度上较已有方法有优势. 相似文献
8.
本文研究带有非线性阻尼项的广义Hartree方程的整体适定性:■其中d≥3,a>0,0<α0‖L2≤‖Q‖L2时,我们证明了解是整体存在的;当p=1+2+α/d且q=2+4/d时,我们发现阻尼项可以阻止解的爆破,并进一步研究了解的散射问题. 相似文献
9.
Let m, t, r and ki(1 ≤ i ≤ m) be positive integers with ki ≥((t+3)r)/2, and G be a digraph with vertex set V(G) and arc set E(G). Let H1, H2, · · ·, Ht be t vertex-disjoint subdigraphs of G with mr arcs. In this article, it is verified that every [0, k1 + k2 + · · · + km-(m-1)r]-digraph G has a [0, ki]1~m-factorization r-orthogonal to every Hi for 1 ≤ i ≤ t. 相似文献
10.
We find the exact forms of meromorphic solutions of the nonlinear differential equations ■,n≥ 3,k≥1,where q,Q are nonzero polynomials,Q■ Const.,and p1,p2,α1,α2 are nonzero constants with α1≠α2.Compared with previous results on the equation p(z)f3+q(z)f"=-sinα(z) with polynomial coefficients,our results show that the coefficient of the term f~((k)) perturbed by multiplying an exponential function will affect the structur... 相似文献
11.
K是Banach空间E的一个非空闭凸子集,T:K→K是一个广义Lipschitz伪压缩映射.对Lipschitz强伪压缩映射f:K→K和x_1∈K,序列{x_n}由下式定义:x_n+1=(1-α_n-β_n)x_n+α_nf(x_n)+β_nTx_n.在{α_n}与{β_n}满足合适条件的情况下,每当{z∈K;μ_n‖x_n-z‖~2=inf_(y∈K)μ_n‖x_n-y‖~2}∩F(T)≠φ时,{x_n}强收敛到T的某个不动点x~*. 相似文献
12.
设E是实的一致凸Banach空间,K是E的一个非空闭凸集,P是E到K上的非扩张的保核收缩映射.设T1,T2,T3:K→E分别是具有数列{hn},{ln},{kn}[1,∞)的渐近非扩张非自映射,使得sum (hn-1) from n=1 to ∞<∞,sum ((ln-1)) from n=1 to ∞<∞及sum (n=1(kn-1) from n=1 to ∞<∞,且F=F(T1)∩F(T2)∩F(T3)={x∈K:T1x=T2x=T3x}≠Ф.定义迭代序列{xn}:x1∈K,xn+1=P((1-αn)xn+αnT1(PT1)n-1yn),yn=P((1-βn)xn+βnT2(PT2)n-1zn),zn=P((1-γn)xn+γnT3(PT3)n-1xn),其中{αn},{βn},{γn}[ε,1-ε],ε是大于零的实数.(i)如果T1,T2,T3中有一个是全连续的或者半紧的,则{xn}强收敛于某一点q∈F;(ii)如果E具有Frechet可微范数或者满足Opial’s条件或者E的对偶空间E~*具有Kadec-Klee性质,则{xn}弱收敛于某一点q∈F. 相似文献
13.
<正>考虑下列混合型议程的唯一性问题 K(y)u_(xx)+u_(yy)=0 (K(0)=0;当y≠0时,■(1) 所考慮的區域D由三條曲綾圍成.其一是雙曲區域(y<0)中由原點引出的特徵线Γ_1,它滿足下面條件 相似文献
14.
A Logarithmically Improved Blow-up Criterion for a Simplified Ericksen-Leslie System Modeling the Liquid Crystal Flows 下载免费PDF全文
In this paper, we prove a logarithmically improved blow-up criterion in terms of the homogeneous Besov spaces for a simplified 3D Ericksen-Leslie system modeling the hydrodynamic flow of nematic liquid crystal. The result shows that if a local smooth solution (u,d) satisfies $$∫^T_0\frac{||u||^{\frac{2}{1-r}}_{\dot{B}^{-r}{∞,∞}}+||∇ d||²_{L^∞}}{1+1n(e+||u||_H^S+||∇ d||_H^S)}dt‹∞$$ with 0 ≤ r ‹ 1 and s ≥ 3, then the solution (u,d) can be smoothly extended beyond the time T. 相似文献
15.
Ning Zhu 《偏微分方程(英文版)》1996,9(2):129-138
In this paper, we consider the Cauchy problem \frac{∂u}{∂t} = Δφ(u) in R^N × (0, T] u(x,0} = u_0(x) in R^N where φ ∈ C[0,∞) ∩ C¹(0,∞), φ(0 ) = 0 and (1 - \frac{2}{N})^+ < a ≤ \frac{φ'(s)s}{φ(s)} ≤ m for some a ∈ ((1 - \frac{2}{n})^+, 1), s > 0. The initial value u_0 (z) satisfies u_0(x) ≥ 0 and u_0(x) ∈ L¹_{loc}(R^N). We prove that, under some further conditions, there exists a weak solution u for the above problem, and moreover u ∈ C^{α, \frac{α}{2}}_{x,t_{loc}} (R^N × (0, T]) for some α > 0. 相似文献
16.
设OI_n是[n]上的保序严格部分一一变换半群.对任意1≤k≤n-1,研究半群OI_n(k)={α∈OI_n:(■x∈dom(α))x≤k■xα≤k}的秩,证明了半群OI_n(k)的秩为n+1. 相似文献
17.
<正> 考虑拟线性微分方程系 dX/dt=A(t)X十f(t)十μF(X,t,μ),(1)其中A(t)是t的n阶连续方阵,x是n向量,f(t),F(X,t,μ)是各变量的n连续向量,μ真是小参数. 当A(t)是常数方阵,f(t),F(X,t,μ)是t的一致概周期向量函数,Coddington,Levinson,等人建立了(1)的周期解的存在定理.此可参考[1]和[2].对A(t)为常数方阵,f(t),F(X,t,μ)是t的一致概周期向量函数,更进一步建立了(1)的概周期解的存在定理. 相似文献
18.
In this paper, we study the perturbation bounds for the polar decomposition A= QH where Q is unitary and H is Hermitian. The optimal (asymptotic) bounds obtained in previous works for the unitary factor, the Hermitian factor and singular values of A are σ2r||△Q||2F ≤ ||△A||2F,1/2||△H||2F ≤ ||△A||2F and ||△∑||2F ≤ ||△A||2F, respectively, where ∑ = diag(σ1, σ2,..., σr, 0,..., 0) is the singular value matrix of A and σr denotes the smallest nonzero singular value. Here we present some new combined (asymptotic)perturbation bounds σ2r ||△Q||2F+1/2||△H||2F≤ ||△A||2F and σ2r||△Q||2F+||△∑ ||2F ≤||△A||2F which are optimal for each factor. Some corresponding absolute perturbation bounds are also given. 相似文献
19.
Ping ZHANG 《数学年刊B辑(英文版)》2008,29(3)
Motivated by the results of J.Y.Chemin in "J.Anal.Math.,77,1999,27-50" and G.Furioli et al in "Revista Mat.Iberoamer.,16,2002,605-667",the author considers further regularities of the mild solutions to Navier-Stokes equation with initial data u0∈Ld(Rd).In particular,it is proved that if u∈C([0,T*); Ld(Rd)) is a mild solution of (NSv),then u(t,x) -evt△u0∈(L)∞ ((0,T); (B)1/d/2,∞)∩(L)1((0,T);(B)3/d/2,∞) for any T<T*. 相似文献
20.
给出了最佳参数α_1,α_2,α_3,β_1,β_2,β_3∈R,使得双向不等式α_1Q(a,b)+(1-α_1)G(a,b)0且a≠b成立.其中A(a,b)=(a+b)/2,H(a,b)=2ab/(a+b),G(a,b)=(ab)~(1/2),Q(a,b)=((a~2+b~2)/2)~(1/2),C(a,b)=(a~2+b~2)/(a+b),T(a,b)=2/π∫_0~(π/2)(a~2cos~2t+b~2sin~2)~(1/2)tdt分别是两个正数a和b的算术平均,调和平均,几何平均,二次平均,反调和平均和Toader平均. 相似文献