共查询到20条相似文献,搜索用时 31 毫秒
1.
Bin Heng SONG Huai Yu JIAN 《数学学报(英文版)》2005,21(5):1183-1190
We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1(u^mi)xixi in R^n × (O,∞), where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n(2 + ∑i^n=1 mi). 相似文献
2.
Positive Solutions for Semipositone
<Emphasis Type="Italic">m</Emphasis>-point Boundary-value
Problems 总被引:7,自引:0,他引:7
Abstract
Let ξ
i
∈ (0, 1) with 0 <
ξ1 < ξ2 <
··· < ξ
m−2 < 1,
a
i
, b
i
∈ [0,∞) with
and
. We consider the
m-point boundary-value
problem
where f(x, y) ≥ −M, and M is a positive constant. We show the
existence and multiplicity of positive solutions by applying the
fixed point theorem in cones.
*Supported by the NSFC (10271095).
GG-110-10736-1003, NWNU-KJCXGC-212 and the Foundation of Major
Project of Science and Technology of Chinese Education
Ministry 相似文献
3.
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
4.
E.M.E.ZAYED 《数学学报(英文版)》2004,20(2):209-222
The asymptotic expansion for small |t| of the trace of the wave kernel ∧↑μ(t) =∑v=1^∞exp(-it μv^1/2), where i= √-1 and {μv}v=1^∞ are the eigenvalues of the negative Laplacian -△=-∑β=1^2(δ/δx^β)^2 in the (x^1, x^2)-plane, is studied for a multi-connected vibrating membrane Ω in R^2 surrounded by simply connected bounded domains Ωj with smooth boundaries δΩj(j=1,...,n), where a finite number of piecewise smooth Robin boundary conditions on the piecewise smooth components Гi(i=1 κj-1,...,κj) of the boundaries δΩj are considered, such that δΩj=∪i=1 κj-1^κj Гi and κ0=0. The basic problem is to extract information on the geometry of Ω using the wave equation approach. Some geometric quantities of Ω (e.g. the area of Ω, the total lengths of its boundary, the curvature of its boundary, the number of the holes of Ω, etc.) are determined from the asymptotic expansion of the trace of the wave kernel ∧↑μ(t) for small |t|. 相似文献
5.
Let {εt;t ∈ Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {a3;j ∈ Z} is a sequence of real numbers satisfying ∑j=-∞^∞|aj| 〈 ∞. Define a moving average process Xt = ∑j=-∞^∞aj+tEj,t ≥ 1, and Sn = ∑t=1^n Xt,n ≥ 1. In this article, by using the weak convergence theorem of { Sn/√ n _〉 1}, we study the precise asymptotics of the complete convergence for the sequence {Xt; t ∈ N}. 相似文献
6.
E. M. E. ZAYED 《数学学报(英文版)》2005,21(4):733-752
The trace of the wave kernel μ(t) =∑ω=1^∞ exp(-itEω^1/2), where {Eω}ω^∞=1 are the eigenvalues of the negative Laplacian -△↓2 = -∑k^3=1 (δ/δxk)^2 in the (x^1, x^2, x^3)-space, is studied for a variety of bounded domains, where -∞ 〈 t 〈 ∞ and i= √-1. The dependence of μ (t) on the connectivity of bounded domains and the Dirichlet, Neumann and Robin boundary conditions are analyzed. Particular attention is given for a multi-connected vibrating membrane Ω in Ra surrounded by simply connected bounded domains Ω j with smooth bounding surfaces S j (j = 1,……, n), where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components Si^* (i = 1 + kj-1,……, kj) of the bounding surfaces S j are considered, such that S j = Ui-1+kj-1^kj Si^*, where k0=0. The basic problem is to extract information on the geometry Ω by using the wave equation approach from a complete knowledge of its eigenvalues. Some geometrical quantities of Ω (e.g. the volume, the surface area, the mean curvuture and the Gaussian curvature) are determined from the asymptotic expansion ofexpansion of μ(t) for small │t│. 相似文献
7.
E.M.E.ZAYED 《数学学报(英文版)》2003,19(4):679-694
The asymptotic expansions of the trace of the heat kernel θ(t)=∑^∞v=1^exp(-tλv) for small positive t,where {λv} are the eigenvalues of the negative Laplacian -△n=-∑^ni=1(D/Dx^1)^2 in R^2(n=2 or 3),are studied for a general annular bounded domain Ω with a smooth inner boundary DΩ1 and a smooth outer boundary DΩ2,where a finite number of piecewise smooth Robin boundary conditions(D/Dnj γh)Ф=0 on the components Гj(j= 1,...,m) of (DΩ1 and on the components Гj (j=k 1,…,m) of of DΩ2 are considered such that DΩl=U^kj=lГj and DΩ2= U^m=k 1Гj and where the coefficients γj(j=1,...,m) are piecewise smooth positive functions. Some applications of θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are given. Further results are also obtained. 相似文献
8.
E. M. E. Zayed 《数学学报(英文版)》2000,16(4):627-636
Abstract
Small-time asymptotics of the trace of the heat semigroup
where {μ
ν
} are the eigenvalues of the negative Laplacian
in the (x
1, x
2)-plane, is studied for a general bunded domain Ω with a smooth boundary ∂Ω, where a finite number of Dirichlet, Neumann and
Robin boundary conditions, on the piecewise smooth parts Γ
i
(i = 1, ..., n) of ∂Ω such that
, are considered. Some geometrical properties associated with Ω are determined. 相似文献
9.
Michel WEBER 《数学学报(英文版)》2006,22(2):377-382
Let D be an increasing sequence of positive integers, and consider the divisor functions:
d(n, D) =∑d|n,d∈D,d≤√n1, d2(n,D)=∑[d,δ]|n,d,δ∈D,[d,δ]≤√n1,
where [d,δ]=1.c.m.(d,δ). A probabilistic argument is introduced to evaluate the series ∑n=1^∞and(n,D) and ∑n=1^∞and2(n,D). 相似文献
10.
De-xiang Ma Wei-gao Ge Xue-gang Chen 《应用数学学报(英文版)》2005,21(4):661-670
In this paper, we obtain positive solution to the following multi-point singular boundary value problem with p-Laplacian operator,{( φp(u'))'+q(t)f(t,u,u')=0,0〈t〈1,u(0)=∑i=1^nαiu(ξi),u'(1)=∑i=1^nβiu'(ξi),whereφp(s)=|s|^p-2s,p≥2;ξi∈(0,1)(i=1,2,…,n),0≤αi,βi〈1(i=1,2,…n),0≤∑i=1^nαi,∑i=1^nβi〈1,and q(t) may be singular at t=0,1,f(t,u,u')may be singular at u'=0 相似文献
11.
Zheng Yan LIN Sung Chul LEE 《数学学报(英文版)》2006,22(2):535-544
Let {Xn,n ≥ 0} be an AR(1) process. Let Q(n) be the rescaled range statistic, or the R/S statistic for {Xn} which is given by (max1≤k≤n(∑j=1^k(Xj - ^-Xn)) - min 1≤k≤n(∑j=1^k( Xj - ^Xn ))) /(n ^-1∑j=1^n(Xj -^-Xn)^2)^1/2 where ^-Xn = n^-1 ∑j=1^nXj. In this paper we show a law of iterated logarithm for rescaled range statistics Q(n) for AR(1) model. 相似文献
12.
Multilinear Singular Integrals with Rough Kernel 总被引:9,自引:0,他引:9
ShanZhenLU HuoXiongWU PuZHANG 《数学学报(英文版)》2003,19(1):51-62
For a class of multilinear singular integral operators T
A
,
where R
m
(A; x, y) denotes the m-th Taylor series remainder of A at x expanded about y, A has derivatives of order m − 1 in
is homogeneous of degree zero, the authors prove that T
A
is bounded from L
p
(ℝ
n
) to
and from L
1(ℝ
n
) to L
n/(n−β),∞(ℝ
n
) with the bound
And if Ω has vanishing moments of order m − 1 and satisfies some kinds of Dini regularity otherwise, then T
A
is also bounded from L
p
(ℝ
n
) to
with the bound
Supported by the National 973 Project (G1990751) and SEDF of China (20010027002) 相似文献
13.
Characterization of Compact Support of Fourier Transform for Orthonormal Wavelets of L^2(R^d) 总被引:1,自引:0,他引:1
Zhi Hua Zhang 《数学学报(英文版)》2005,21(4):855-864
Let{ψμ} be an orthonormal wavelet of L^2(R^d) and the support of a whole of its Fourier transform be Uμsupp{ψμ}=Пi=1^d[Ai, Di]-Пi=1^d(Bi, Ci), Ai≤Bi≤Ci≤Di. Under the weakest condition that each │ψμ│, is continuous for ω ∈ δ(Пi=1^d[Ai, Di]), a characterization of the above support of a whole is given. 相似文献
14.
Shi Ping LU Wei Gao GE 《数学学报(英文版)》2005,21(6):1309-1314
Thc main aim of this paper is to use the continuation theorem of coincidence degree theory for studying the existence of periodic solutions to a kind of neutral functional differential equation as follows:(x(t)-^n∑i=1cix(t-ri))″=f(x(t))x′+g(x(t-τ))+p(t).In order to do so, we analyze the structure of the linear difference operator A : C2π→C2π, [Ax](t) =x(t)-∑^ni=1cix(t-ri)to determine some flmdamental properties first, which we are going to use throughout this paper. Meanwhile, we also prove some new inequalities which are useful for estimating a priori bounds of periodie solutions. 相似文献
15.
Yah SUN Gen Xiang CHAI 《数学学报(英文版)》2007,23(4):685-696
In this article the following random intercept mixed effects model will be considered: yij = vi =v^τijβ+ εij,i=1,…,m;j=1,2,…,ni, where {vi} are i.i.d, random effects with mean α 2. 2 and finite variance σ^2 v, {εij} are i.i.d, random errors with finite variance ε^2 ε. Here we will estimate α,σ^2 v,σ^2 ε,β and study their large sample properties, such as strong consistency, strong convergence rates and asymptotic normality. 相似文献
16.
Let T = T(p, q, α) be the number of solutions of the congruence xα ≡ 1 (mod pηqθ). Let A
and B be sets of primes satisfying x1 < p ≤ x2 and y1 < q ≤ y2, respectively. A mean value estimation
of
is given.
Supported by National Natural Science Foundation of China (No. 19971024) and Zhejiang Provincial Natural
Science Foundation of China (No. 199047) 相似文献
17.
Precise asymptotics in the Baum-Katz and davis law of large numbers for positively associated sequences 总被引:6,自引:1,他引:5
§ 1 Introduction and resultsL et { X,Xi;i≥ 1} be a sequence of i.i.d.random variables,and set Sn= ni=1 Xi,n≥1.Hsu and Robbins[1 ] introduced the conceptof complete convergence.They together withErdos[2 ] proved n≥ 1 P(|Sn|≥εn) <∞ ,ε>0 (1)if and only if EX=0 and EX2 <∞ .L ater,Spitzer[3] proved n≥ 11n P(|Sn|≥εn) <∞ ,ε>0if and only if EX =0 and E|X|<∞ .More generally,it was shown by Baum and Katz[4 ]that,for 0
0 (… 相似文献
18.
Qi Keng LU Ke WU 《数学学报(英文版)》2007,23(4):577-598
For an integer m ≥ 4, we define a set of 2[m/2] × 2[m/2] matrices γj (m), (j = 0, 1,..., m - 1) which satisfy γj (m)γk (m) +γk (m)γj (m) = 2ηjk (m)I[m/2], where (ηjk (m)) 0≤j,k≤m-1 is a diagonal matrix, the first diagonal element of which is 1 and the others are -1, I[m/2] is a 2[m/1] × 2[m/2] identity matrix with [m/2] being the integer part of m/2. For m = 4 and 5, the representation (m) of the Lorentz Spin group is known. For m≥ 6, we prove that (i) when m = 2n, (n ≥ 3), (m) is the group generated by the set of matrices {T|T=1/√ξ((I+k) 0 + 0 I-K) ( U 0 0 U), (ii) when m = 2n + 1 (n≥ 3), (m) is generated by the set of matrices {T|T=1/√ξ(I -k^- k I)U,U∈ (m-1),ξ=1-m-2 ∑k,j=0 ηkja^k a^j〉0, K=i[m-3 ∑j=0 a^j γj(m-2)+a^(m-2) In],K^-=i[m-3∑j=0 a^j γj(m-2)-a^(m-2) In]} 相似文献
19.
Piotr Niemiec 《Rendiconti del Circolo Matematico di Palermo》2008,57(3):391-399
The aim of the paper is to prove that every f ∈ L
1([0,1]) is of the form f = , where j
n,k
is the characteristic function of the interval [k- 1 / 2
n
, k / 2
n
) and Σ
n=0∞Σ
k=12n
|a
n,k
| is arbitrarily close to ||f|| (Theorem 2). It is also shown that if μ is any probabilistic Borel measure on [0,1], then for any ɛ > 0 there exists a sequence (b
n,k
)
n≧0
k=1,...,2n
of real numbers such that and for each Lipschitz function g: [0,1] → ℝ (Theorem 3).
相似文献
20.
De Li LI Fu Xing ZHANG Andrew ROSALSKY 《数学学报(英文版)》2007,23(3):557-562
Let {X, Xn; n≥ 1} be a sequence of i.i.d. Banach space valued random variables and let {an; n ≥ 1} be a sequence of positive constants such that
an↑∞ and 1〈 lim inf n→∞ a2n/an≤lim sup n→∞ a2n/an〈∞
Set Sn=∑i=1^n Xi,n≥1.In this paper we prove that
∑n≥1 1/n P(||Sn||≥εan)〈∞ for all ε〉0
if and only if
lim n→∞ Sn/an=0 a.s.
This result generalizes the Baum-Katz-Spitzer complete convergence theorem. Combining our result and a corollary of Einmahl and Li, we solve a conjecture posed by Gut. 相似文献