共查询到20条相似文献,搜索用时 203 毫秒
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设{αk}∞k=-∞为正数缺项序列,满足infkαk+1/dk=α>1,Ω(y′)为Besov空间B0,11(Sn-1)上的函数,其中Sn-1为Rn(n2)上的单位球面.本文证明:若∫Sn-1Ω(y′)dσ(y′)=0,则离散型奇异积分TΩ(f)(x)=∑∞k=-∞∫Sn-1f(x-αky′)Ω(y′)dσ(y′)和相关的极大算子TΩ(f)(x)=supN∑∞k=N∫Sn-1f(x-αky′)Ω(y′)dσ(y′)均在L2(Rn)上有界.上述结果推广了Duoandikoetxea和RubiodeFrancia[1]在L2情形下的一个结果 相似文献
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函数f(x)在区间[a,b]上单调增加(或单调减少),又c、d∈[a,b]上,若f(c)=f(a),则有c=d.1 求代数式的值例1 已知x、y∈[-π4,π4],a∈R,且 x3+sinx-2a=04y3+sinycosy+a=0则cos(x+2y)= .(1994年全国高中数学竞赛题)解 由已知条件,可得 x3+sinx=2a(-2y)3+sin(-2y)=2a故可设函数f(t)=t3+sint,则有f(x)=f(-2y)=2a.由于函数f(t)=t3+sint,在[-π2,π2]上是单… 相似文献
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1.引言方程是在国内外引起广泛关注的一类重要的非线性发展方程.文[1]在函数f(s)满足局部 Lip-schitz条件及单调性条件(f(s2)-f(s1))(s2-s1)> 0的假设下得到了(1.1)初边值问题整体弱解的存在与唯一性;文[2]用 Galerkin方法,研究了(1.1)的初边值问题,周期边值问题和初值问题,并在函数f’(s)下方有界的假设下得到了整体强解的存在与唯一性. 本文在有限区域 QT=[0,1]×[0,T](T> 0)上讨论方程(1.1)带有初值条件和边值条件(u(x,t)为未知… 相似文献
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脉冲中立型时滞微分方程解的振动性 总被引:18,自引:0,他引:18
本文讨论一阶脉冲中立型时滞微分方程[y(t)+Py(t-σ)]′+Q(t)y(t-σ)=0,t0,t≠tk,k=1,2,…,y(t+k)-y(t-k)=bky(tk),k=1,2,…,{(E)这里τ,σ,P均为常数,τ>0,σ>0,Q(t)∈C([0,∞),R+),bk>-1,k=1,2,….分三种情况,P-1;-1<P<0;P>0给出了方程(E)所有解振动的充分条件. 相似文献
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Riccati微分方程的可积条件 总被引:6,自引:1,他引:5
In1998,ZhaoLinlong[1]obtainedtheintegrablecondition:R=1αγPe2∫(Q-βD)dx (α,β,γisconst).(1)ForRiccatiequation:y′=p(x)y2+Q(x)y+R(x) (PR≠0).(2) Herethenewintegrableconditionsisgiven:L[y0]=1αγPe2∫(Q+2y0p-βD)dx.(3)L[AB+y0]=1αγ(AB)2L[y0]e2∫(2BAL[y0]+Q+2y… 相似文献
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向开理 《高校应用数学学报(A辑)》1995,(4)
本文提出了两类数值积分二阶周期性初值问题y″=f(x,y),y(x0)=y0,y'(x0)=y'0具有极小相位延迟的显式两步法。这些方法推广和改进了文献[1]-[7]中的某些方法。数值试验表明本文中的某些方法优于[1]-[7]中的某些方法。 相似文献
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本文建立多线性算子TA1,A2,…Akf(x)=p.v∫RneiP(x,y)Ω(x-y)|x-y|n+M-kkj=1Rmj(Aj;x,y)f(y)dy,n2,的一个变形的sharp估计,其中P(x,y)是Rn×Rn上的实值多项式,Ω是零阶齐性函数且满足某种消失性条件,M=∑kj=1mj,Rmj(Aj;x,y)表示Aj在x点关于y的mj阶Taylor级数余项,对所有满足|α|=mj-1(j=1,2,…,k)的指标α,DαAj∈BMO(Rn).作为sharp估计的推论,得到了算子TA1,A2…Ak在Lp(1<p<∞)上的有界性. 相似文献
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题目 已知当x∈[0,1]时,不等式x2cosθ-x(1-x)+(1-x)2sinθ>0恒成立,试求θ的取值范围.这是1999年全国高中数学联合竞赛试题第三题,下面给出一种有别于“标准答案”的简单解法.解 若对一切x∈[0,1],恒有f(x)=x2cosθ-x(1-x)+(1-x)2sinθ>0,则 sinθ=f(0)>0,cosθ=f(1)>0,∴ 2kπ<θ<2kπ+π2,k∈Z.(1)又 f(x)=(1+sinθ+cosθ)x2-(1+2sinθ)x+sinθ=(1+sinθ+cosθ)[… 相似文献
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圆锥曲线弦的中点问题的一种简捷解法 总被引:3,自引:0,他引:3
求直线被圆锥曲线截得弦的中点问题,是解析几何教学中的一类重要问题;常规解法计算量较大,如何简化其解法一直为人们所关注;文[1]、[2]、[3]等都作过很好的研究;本文介绍一种利用两曲线公共弦方程求解的简捷方法;如图,设P(m,n)是圆锥曲线c的一条弦AB的中点,c′是c关于点P对称的曲线;容易证明,c′的方程为f(2m-x,2n-y)=0;(见注1)而弦AB就是曲线c与c′的公共弦;且公共弦AB所在的直线方程为f(x,y)-f(2m-x,2n-y)=0(见注2),从而使问题得到解决;这一方法既适… 相似文献
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Calibration and identification of the exchange effect between the karst aquifers and the underlying conduit network are important issues in order to gain a better understanding of these hydraulic systems. Based on a coupled continuum pipe-flow (CCPF for short) model describing flows in karst aquifers, this paper is devoted to the identification of an exchange rate function, which models the hydraulic interaction between the fissured volume (matrix) and the conduit, from the Neumann boundary data, i.e., matrix/conduit seepage velocity. The authors formulate this parameter identification problem as a nonlinear operator equation and prove the compactness of the forward mapping. The stable approximate solution is obtained by two classic iterative regularization methods, namely, the Landweber iteration and Levenberg-Marquardt method. Numerical examples on noisefree and noisy data shed light on the appropriateness of the proposed approaches. 相似文献
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何吉欢 《数学物理学报(A辑)》2001,21(Z1):577-583
该文以Schrodinger方程为例,分析变分迭代法的一些基本特点.在该方法中引进了一广义拉氏乘子构造了一迭代格式,拉氏乘子可由变分理论最佳识别.由于在识别拉氏乘子是应用了限制变分的概念,所以只能通过迭代才能得到收敛解.为了加快收敛速度,可以在初始近似引入待定常数,而待定常数又可用各种方式最佳识别.文中初步分析了该方法的收敛性,对于Schrodinger方程,其一阶近似即可得到Jost解. 相似文献
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In this paper, the existence of solutions to a class of fractional differential equations $D_{0+}^{\alpha}u(t)=h(t)f(t, u(t), D_{0+}^{\theta}u(t))$ is obtained by an efficient and simple monotone iteration method. At first, the existence of a solution to the problem above is guaranteed by finding a bounded domain $D_M$ on functions $f$ and $g$.
Then, sufficient conditions for the existence of monotone solution to the problem are established by applying monotone iteration method. Moreover, two efficient iterative schemes are proposed, and the convergence of the iterative process is proved by using the monotonicity assumption on $f$ and $g$. In particular, a new algorithm which combines Gauss-Kronrod quadrature method with cubic spline interpolation method is adopted to achieve the monotone iteration method in Matlab environment, and the high-precision approximate solution is obtained. Finally, the main results of the paper are illustrated by some numerical simulations, and the approximate solutions graphs are provided by using the iterative method. 相似文献
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本文研究退化椭圆型方程-Δxu-(α+1)2|x|~(2α)Δyu=|u|~(p-1)u,(x,y)∈Rm×Rk和方程-Δxu-(α+1)2|x|~(2α)Δyu=|u|~(p-1)u,(x,y)∈Π的Liouville型定理,其中-Δx-(α+1)2|x|~(2α)Δy是Grushin算子,Π={(x,y)∈Rm×Rk:x10}或{(x,y)∈Rm×Rk:y10}.本文将证明,当1p(Q+2)/(Q-2)时,上述方程Morse指数有限的有界解只有零解,其中Q=m+(α+1)k为齐次空间的维数,因此,本文将Laplace方程的结果推广到含Grushin算子的方程. 相似文献
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Luchuan Zeng 《高等学校计算数学学报(英文版)》2006,15(1):31-39
Let 1<ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the equation Tx=f by the Ishikawa iteration procedure with errors (?) where x_0 ∈ E,{u_n},{υ_n}are bounded sequences in E and{α_n},{b_n},{c_n},{a_n~'},{b_n~'},{c_n~'} are real sequences in[0,1].Under the assumption of the condition 0<α≤b_n c_n,An≥0, it is shown that the iterative sequence{x_n}converges strongly to the unique solution of the equation Tx=f.Furthermore,under no assumption of the condition(?)(b_n~' c_n~')=0,it is also shown that{x_n}converges strongly to the unique solution of Tx=f. 相似文献
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在任意的Banach空间的条件下,具误差的Ishikawa迭代程序强收敛到非线性方程x+Tx=f的唯一解并且是几乎稳定的.其结果推广、改进和统一了Zeng和Liu的相关结果. 相似文献
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Houde Han Zhongyi Huang Shangyou Zhang 《Numerical Methods for Partial Differential Equations》2013,29(3):961-978
In this article, we propose an iterative method based on the equation decomposition technique ( 1 ) for the numerical solution of a singular perturbation problem of fourth‐order elliptic equation. At each step of the given method, we only need to solve a boundary value problem of second‐order elliptic equation and a second‐order singular perturbation problem. We prove that our approximate solution converges to the exact solution when the domain is a disc. Our numerical examples show the efficiency and accuracy of our method. Our iterative method works very well for singular perturbation problems, that is, the case of 0 < ε ? 1, and the convergence rate is very fast. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
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We consider linear systems of equations and solution approximations derived by projection on a low-dimensional subspace. We propose stochastic iterative algorithms, based on simulation, which converge to the approximate solution and are suitable for very large-dimensional problems. The algorithms are extensions of recent approximate dynamic programming methods, known as temporal difference methods, which solve a projected form of Bellman’s equation by using simulation-based approximations to this equation, or by using a projected value iteration method. 相似文献