共查询到20条相似文献,搜索用时 15 毫秒
1.
Nils Svanstedt 《Applications of Mathematics》2010,55(5):385-404
Stochastic homogenization (with multiple fine scales) is studied for a class of nonlinear monotone eigenvalue problems. More
specifically, we are interested in the asymptotic behaviour of a sequence of realizations of the form
$
- div\left( {a\left( {T_1 \left( {\frac{x}
{{\varepsilon _1 }}} \right)\omega _1 ,T_2 \left( {\frac{x}
{{\varepsilon _2 }}} \right)\omega _2 ,\nabla u_\varepsilon ^\omega } \right)} \right) = \lambda _\varepsilon ^\omega \mathcal{C}\left( {u_\varepsilon ^\omega } \right)
$
- div\left( {a\left( {T_1 \left( {\frac{x}
{{\varepsilon _1 }}} \right)\omega _1 ,T_2 \left( {\frac{x}
{{\varepsilon _2 }}} \right)\omega _2 ,\nabla u_\varepsilon ^\omega } \right)} \right) = \lambda _\varepsilon ^\omega \mathcal{C}\left( {u_\varepsilon ^\omega } \right)
相似文献
2.
In studying local harmonic analysis on the sphere Sn, R.S. Strichartz introduced certain zonal functions ϕ2(d(x, y)) which satisfy the equation
, where Δz is the Laplace operator and δ−y the Dirac measure. The explicit expression of the constant a (λ) is given by R.S. Strichartz in the case that n is odd. Appyling
the Apéry identity, we show in this paper that
for n even, where wn-1 is the surface area of Sn-1,
.
The author's research was supported by a grant from NSFC. 相似文献
3.
Qi Kang RAN 《数学学报(英文版)》2005,21(4):705-714
In this paper, we prove that the weak solutions u∈Wloc^1, p (Ω) (1 〈p〈∞) of the following equation with vanishing mean oscillation coefficients A(x): -div[(A(x)△↓u·△↓u)p-2/2 A(x)△↓u+│F(x)│^p-2 F(x)]=B(x, u, △↓u), belong to Wloc^1, q (Ω)(A↓q∈(p, ∞), provided F ∈ Lloc^q(Ω) and B(x, u, h) satisfies proper growth conditions where Ω ∪→R^N(N≥2) is a bounded open set, A(x)=(A^ij(x)) N×N is a symmetric matrix function. 相似文献
4.
Aleksandar Ivić 《Central European Journal of Mathematics》2004,2(4):494-508
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of
. If
with
, then we obtain
5.
Aleksandar Ivić 《Central European Journal of Mathematics》2005,3(2):203-214
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of
. If E
*(t)=E(t)-2πΔ*(t/2π) with
, then we obtain
6.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
7.
Giorgio Busetto 《Annali di Matematica Pura ed Applicata》1985,142(1):91-103
Sunto Siano G e
due gruppi, : GG una proiettività e N un sottogruppo normale di G. Vengono provati alcuni risultati sulle proprietà di immersions in
e G rispettivamente, del gruppi
, la chiusura normale di N in
modulo il nocciolo di N in
, e
.
Supported by a C.N.R. grant. 相似文献 8.
ShuJunDANG LiZhongPENG 《数学学报(英文版)》2004,20(2):255-260
This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators Tn:L^2(R)→L^2(C,e^-|z|^2/2dzd-↑z/4πi), s.t. TnL^2(R) lontain in L^2(C,e^-|z|^2/2dzd-↑z/4πi) are reproducing subspaces (n=0, Bargmann Space); and gives a reproducing kernel and an orthonormal basis (ONB) of TnL^2(R), Furthermore, it shows the orthogonal spaces decomposition of L^2(C,e^-|z|^2/2dzd-↑z/4πi). Finally, by using the preceding results, it shows the eigenvalues and eigenfunctions of a class of localization operators associated with WFT, which extends the result of Daubechies in [1] and [6]. 相似文献
9.
А. Й. Бастис 《Analysis Mathematica》1983,9(4):247-258
В работе рассматрива ется асимптотика в ме трике пространстваL p (T N ),T N ={x∈R N , 0<x i <2π} ядра Р исса-Бохнера $$\Theta ^s \left( {x, \lambda } \right) = \left( {2\pi } \right)^{ - N} \mathop \Sigma \limits_{\left| n \right|^2< \lambda } \left( {1 - \frac{{\left| n \right|^2 }}{\lambda }} \right)^s e^{inx} \left( {x \in T^N , s \geqq 0, \lambda \geqq 0} \right)$$ при λ→∞. Доказывается, что есл иN≧4,p≧2N/(N?1) иs>N((N?1)/2N?1/p), то для произвольной точкиx∈T N существует п остояннаяC=C p (x, s) такая, что выполняется неравен ство $$\parallel \Theta ^s \left( {x - y, \lambda } \right) - \left( {2\pi } \right)^{ - {N \mathord{\left/ {\vphantom {N 2}} \right. \kern-\nulldelimiterspace} 2}} 2^s \Gamma \left( {s + 1} \right)\lambda ^{{N \mathord{\left/ {\vphantom {N 2}} \right. \kern-\nulldelimiterspace} 2}} J_{{N \mathord{\left/ {\vphantom {N {2 + s}}} \right. \kern-\nulldelimiterspace} {2 + s}}} {{\left( {\left| {x - y} \right|\sqrt \lambda } \right)} \mathord{\left/ {\vphantom {{\left( {\left| {x - y} \right|\sqrt \lambda } \right)} {\left( {\left| {x - y} \right|\sqrt \lambda } \right)^{{N \mathord{\left/ {\vphantom {N {2 + s}}} \right. \kern-\nulldelimiterspace} {2 + s}}} \parallel _{L_p \left( {T^N } \right)} \leqq }}} \right. \kern-\nulldelimiterspace} {\left( {\left| {x - y} \right|\sqrt \lambda } \right)^{{N \mathord{\left/ {\vphantom {N {2 + s}}} \right. \kern-\nulldelimiterspace} {2 + s}}} \parallel _{L_p \left( {T^N } \right)} \leqq }}$$ где нормаL p (T N ) берется по пе ременнойy, а черезJ v обозначена функция Б есселя первого рода порядкаv. СлучаиN=2 иN=3 рассматриваются отдельно. 相似文献
10.
Kenji Nishihara 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(4):604-614
We consider the Cauchy problem for the nonlinear dissipative evolution system with ellipticity on one dimensional space
11.
This paper deals with the solvability of the boundary value problem
12.
D. V. Goryashin 《Moscow University Mathematics Bulletin》2011,66(3):125-128
For the number N(x) of solutions to the equation aq − bc = 1 in positive integers a, b, c and square-free numbers q satisfying the condition aq ≤ x the asymptotic formula
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