首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 46 毫秒
1.
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   

2.
李林 《数学季刊》1992,7(4):20-25
We discuss the existence and the number of periodic solutions of differential equation dx/dt=A1(t)x A2(t)x^2 A3(t)x^3/α0(t) α1(t)x α2(t)x^2 (1)where Ai(t),αj(t)(i=1,2,3;j=0,1,2) are continuous periodic functions.The results of this paper ex-tend the work of paper[1].  相似文献   

3.
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   

4.
§1. IntroductionThispaperisconcernedwiththeasymptoticbehavioroftheoscillatorysolutionsofnonlin-earforcedneutraldelaydifferentialequationsoftheform[x(t)-∑mi=1pi(t)x(t-τi)]′ ∑nj=1qj(t)f(x(t-σj))=r(t), t≥t0,(1)wherepi,qj,r∈C([t0,∞),R),τi,σj≥0,i=1,2,…,m;j=1,2,…,n,f∈C(R,R),xf(x)>0forx≠0.Whenpi(t)≡0,i=1,2,…,m,Eq.(1)reducestox(t) ∑nj=1qj(t)f(x(t-σj))=r(t), t≥t0,(2)whoseasymptoticbehaviorofallsolutionshasbeenstudiedinJ.R.Yan[5].Whenr(t)≡0,f(x)≡xandm=n=1,Eq.(1)reducesto[…  相似文献   

5.
Let L^2([0, 1], x) be the space of the real valued, measurable, square summable functions on [0, 1] with weight x, and let n be the subspace of L2([0, 1], x) defined by a linear combination of Jo(μkX), where Jo is the Bessel function of order 0 and {μk} is the strictly increasing sequence of all positive zeros of Jo. For f ∈ L^2([0, 1], x), let E(f, n) be the error of the best L2([0, 1], x), i.e., approximation of f by elements of n. The shift operator off at point x ∈[0, 1] with step t ∈[0, 1] is defined by T(t)f(x)=1/π∫0^π f(√x^2 +t^2-2xtcosO)dθ The differences (I- T(t))^r/2f = ∑j=0^∞(-1)^j(j^r/2)T^j(t)f of order r ∈ (0, ∞) and the L^2([0, 1],x)- modulus of continuity ωr(f,τ) = sup{||(I- T(t))^r/2f||:0≤ t ≤τ] of order r are defined in the standard way, where T^0(t) = I is the identity operator. In this paper, we establish the sharp Jackson inequality between E(f, n) and ωr(f, τ) for some cases of r and τ. More precisely, we will find the smallest constant n(τ, r) which depends only on n, r, and % such that the inequality E(f, n)≤ n(τ, r)ωr(f, τ) is valid.  相似文献   

6.
The aim of this paper is to prove the a.e.convergence of sequences of the Cesa`ro and Riesz means of the Walsh–Fourier series of d variable integrable functions.That is,let a=(a1,...,ad):N→Nd(d∈P)such that aj(n+1)≥δsupk≤n aj(k)(j=1,...,d,n∈N)for someδ0 and a1(+∞)=···=ad(+∞)=+∞.Then,for each integrable function f∈L1(Id),we have the a.e.relation for the Ces`aro means limn→∞σαa(n)f=f and for the Riesz means limn→∞σα,γa(n)f=f for any 0αj≤1≤γj(j=1,...,d).A straightforward consequence of our result is the so-called cone restricted a.e.convergence of the multidimensional Ces`aro and Riesz means of integrable functions,which was proved earlier by Weisz.  相似文献   

7.
Let μ denote the set of all n×n nonsingular M-matrices. If A∈μ, then there exists a permutation matrix p such that where B_ⅱ(1≤i≤m) is an irreducble nonsingular M-matrix, B_(ij)≤0 (ij). Let V=B~(-1). Then V is a block upper triangular matrix of the form  相似文献   

8.
Let {εt; t ∈ Z^+} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2+1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^+} is a sequence of real numbers satisfying ∑j=0^∞|aj|〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E|ε1|^2+δ′〈 for some δ′〉0 and μ(n)=O(n^-ρ) for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.  相似文献   

9.
By means of an abstract continuation theory for κ-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following neutral functional differential equation dN/dt=N(t)[α(t)-β(t)N(t)-∑j=1^n bj(t)N(t-σj(t))-∑i=1^mci(t)N‘(t-γi(t)0].  相似文献   

10.
51. IntroductionThe boundedness problem of solutions of the following nonlinear scalar differelltial equa-nons of second order..x f(x, t)ic g(x, t) = 0 (1'1)has been widely investigated by many authors since the 1940's, where f(x, t 1) = j(x, t),g(x, t 1) = g(x, t).When j(x, t) = 0, Equation (1.1) is a conservative system and takes the following form..x g(x, t) ~ 0. (1'2)The first contribution of the boundedness of all the solutions of Equation (1.2) is due toMorrislll, whO proved …  相似文献   

11.
利用Grassmann代数的理论与方法,给出了n维欧氏空间En中n维单形第二余弦定理一种简单的证明.然后利用第二余弦定理给出了n维单形正弦定理一种新的简单证明.  相似文献   

12.
知识规律与规律的属性扰动   总被引:1,自引:0,他引:1  
By employing the knowledge(R-element equivalence class)in one direction Srough sets and dual of one direction S-rough sets,the concept of knowledge law is given;the generation theorem of knowledge law,the excursion theorem of knowledge law,and the attribute disturbance discernible theorem of knowledge law are proposed.Knowledge law is a new characteristic of S-rough sets.  相似文献   

13.
For the multivariate ℓ1-norm symmetric distributions, which are generalizations of the n-dimensional exponential distribution with independent marginals, a geometric representation formula is given, together with some of its basic properties. This formula can especially be applied to a new developed and statistically well motivated system of sets. From that the distribution of a t-statistic adapted for the two-parameter exponential distribution and its generalizations is determined. Asymptotic normality of this adapted t-statistic is shown under certain conditions.  相似文献   

14.
骆舒心  凌晓亮  张蓓 《大学数学》2011,27(2):181-183
指出[2]中一道习题的错解,并分析出现错误的原因.  相似文献   

15.
Consider Ginibres ensemble of N×N non-Hermitian random matrices in which all entries are independent complex Gaussians of mean zero and variance As N the normalized counting measure of the eigenvalues converges to the uniform measure on the unit disk in the complex plane. In this note we describe fluctuations about this Circular Law. First we obtain finite N formulas for the covariance of certain linear statistics of the eigenvalues. Asymptotics of these objects coupled with a theorem of Costin and Lebowitz then result in central limit theorems for a variety of these statistics.This work was supported in part by the grant NSF-9983320.Revised version: 13 February 2004  相似文献   

16.
We consider the almost sure asymptotic behavior of the periodogram of stationary and ergodic sequences. Under mild conditions we establish that the limsup of the periodogram properly normalized identifies almost surely the spectral density function associated with the stationary process. Results for a specified frequency are also given. Our results also lead to the law of the iterated logarithm for the real and imaginary parts of the discrete Fourier transform. The proofs rely on martingale approximations combined with results from harmonic analysis and techniques from ergodic theory. Several applications to linear processes and their functionals, iterated random functions, mixing structures and Markov chains are also presented.  相似文献   

17.
本文详细了研究了种群纯死定律的概率结构,给出了求解转移概率显式的三种方法及一个定理,最后拟合了一个实例。  相似文献   

18.
Let X 1,X 2,… be a sequence of random variables. Let S k =X 1+???+X k and assume that S k /b k converges in distribution for some numerical sequence (b k ). We study the weak convergence of the random processes {Λ n (z), z∈?}, where
$\Lambda_{n}(z)=\frac{1}{n}\sum_{k=1}^{n}I\left\{\frac{S_{k}}{b_{k}}\leq z\right\}.$
We consider the same problem when the normalized partial sums S k /b k are replaced by other functionals of the sequence (X n ). In particular, we investigate the case of sample extremes in detail.
  相似文献   

19.
《大学数学》2016,(4):123-126
讨论结合律在无穷级数中的运用,并对2015年浙江省高等数学竞赛中一道竞赛题进行了分析和探讨.  相似文献   

20.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 1, pp. 97–100, January, 1989.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号