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1.
The following reaction-diffusion system in spatially non-homogeneous almost-periodic media is considered in a bounded domain : (1)tu=Auf(u)+g, u|∂Ω=0. Here u=(u1,…,uk) is an unknown vector-valued function, f is a given nonlinear interaction function and the second order elliptic operator A has the following structure: where aijl(y) are given almost-periodic functions. We prove that, under natural assumptions on the nonlinear term f(u), the longtime behavior of solutions of (1) can be described in terms of the global attractor of the associated dynamical system and that the attractors  , 0<<01, converge to the attractor of the homogenized problem (1) as →0. Moreover, in the particular case of periodic media, we give explicit estimates for the distance between the non-homogenized and the homogenized attractors in terms of the parameter .  相似文献   

2.
For fLp( n), with 1p<∞, >0 and x n we denote by T(f)(x) the set of every best constant approximant to f in the ball B(x). In this paper we extend the operators Tp to the space Lp−1( n)+L( n), where L0 is the set of every measurable functions finite almost everywhere. Moreover we consider the maximal operators associated to the operators Tp and we prove maximal inequalities for them. As a consequence of these inequalities we obtain a generalization of Lebesgue's Differentiation Theorem.  相似文献   

3.
The main result of this paper is a (2 + )-approximation scheme for the minimum dominating set problem on circle graphs. We first present an O(n2) time 8-approximation algorithm for this problem and then extend it to an time (2 + )-approximation scheme for this problem. Here n and m are the number of vertices and the number of edges of the circle graph. We then present simple modifications to this algorithm that yield (3 + )-approximation schemes for the minimum connected and the minimum total dominating set problems on circle graphs. Keil (1993, Discrete Appl. Math.42, 51–63) shows that these problems are NP-complete for circle graphs and leaves open the problem of devising approximation algorithms for them. These are the first O(1)-approximation algorithms for domination problems on circle graphs.  相似文献   

4.
This paper discusses the incompressible non-Newtonian fluid with rapidly oscillating external forces g(x,t)=g(x,t,t/) possessing the average g0(x,t) as →0+, where 0<0<1. Firstly, with assumptions (A1)–(A5) on the functions g(x,t,ξ) and g0(x,t), we prove that the Hausdorff distance between the uniform attractors and in space H, corresponding to the oscillating equations and the averaged equation, respectively, is less than O() as →0+. Then we establish that the Hausdorff distance between the uniform attractors and in space V is also less than O() as →0+. Finally, we show for each [0,0].  相似文献   

5.
We show how any BSP tree for the endpoints of a set of n disjoint segments in the plane can be used to obtain a BSP tree of size for the segments themselves, such that the range-searching efficiency remains almost the same. We apply this technique to obtain a BSP tree of size O(nlogn) such that -approximate range searching queries with any constant-complexity convex query range can be answered in O(min>0{(1/)+k}logn) time, where k is the number of segments intersecting the -extended range. The same result can be obtained for disjoint constant-complexity curves, if we allow the BSP to use splitting curves along the given curves.We also describe how to construct a linear-size BSP tree for low-density scenes consisting of n objects in such that -approximate range searching with any constant-complexity convex query range can be done in O(logn+min>0{(1/d−1)+k}) time.  相似文献   

6.
The set of all probability measures σ on the unit circle splits into three disjoint subsets depending on properties of the derived set of {|n|2}n0, denoted by Lim(σ). Here {n}n0 are orthogonal polynomials in L2(). The first subset is the set of Rakhmanov measures, i.e., of σ with {m}=Lim(σ), m being the normalized (m( )=1) Lebesgue measure on . The second subset Mar( ) consists of Markoff measures, i.e., of σ with mLim(σ), and is in fact the subject of study for the present paper. A measure σ, belongs to Mar( ) iff there are >0 and l>0 such that sup{|an+j|:0jl}>, n=0,1,2,…,{an} is the Geronimus parameters (=reflectioncoefficients) of σ. We use this equivalence to describe the asymptotic behavior of the zeros of the corresponding orthogonal polynomials (see Theorem G). The third subset consists of σ with {m}Lim(σ). We show that σ is ratio asymptotic iff either σ is a Rakhmanov measure or σ satisfies the López condition (which implies σMar( )). Measures σ satisfying Lim(σ)={ν} (i.e., weakly asymptotic measures) are also classified. Either ν is the sum of equal point masses placed at the roots of zn=λ, λ , n=1,2,…, or ν is the equilibrium measure (with respect to the logarithmic kernel) for the inverse image under an m-preserving endomorphism zzn, n=1,2,…, of a closed arc J (including J= ) with removed open concentric arc J0 (including J0=). Next, weakly asymptotic measures are completely described in terms of their Geronimus parameters. Finally, we obtain explicit formulae for the parameters of the equilibrium measures ν and show that these measures satisfy {ν}=Lim(ν).  相似文献   

7.
Orthogonal polynomials on the unit circle are completely determined by their reflection coefficients through the Szeg recurrences. We assume that the reflection coefficients tend to some complex number a with 0<a<1. The orthogonality measure μ then lives essentially on the arc {eit :αt2πα} where sin with α(0,π). Under the certain rate of convergence it was proved in (Golinskii et al. (J. Approx. Theory96 (1999), 1–32)) that μ has no mass points inside this arc. We show that this result is sharp in a sense. We also examine the case of the whole unit circle and some examples of singular continuous measures given by their reflection coefficients.  相似文献   

8.
This article discusses the perturbation of a non-symmetric Dirichlet form,(ε, D(ε)), by a signed smooth measure μ, whereμ=μ1 -μ2 with μ1 and μ2 being smooth measures. It gives a sufficient condition for the perturbed form (εμ, D(εμ)) (for some αo ≥ 0) to be a coercive closed form.  相似文献   

9.
Given a planar convex set C, we give sublinear approximation algorithms to determine approximations of the largest axially symmetric convex set S contained in C, and the smallest such set S that contains C. More precisely, for any >0, we find an axially symmetric convex polygon QC with area |Q|>(1−)|S| and we find an axially symmetric convex polygon Q containing C with area |Q|<(1+)|S|. We assume that C is given in a data structure that allows to answer the following two types of query in time TC: given a direction u, find an extreme point of C in direction u, and given a line , find C. For instance, if C is a convex n-gon and its vertices are given in a sorted array, then TC=O(logn). Then we can find Q and Q in time O(−1/2TC+−3/2). Using these techniques, we can also find approximations to the perimeter, area, diameter, width, smallest enclosing rectangle and smallest enclosing circle of C in time O(−1/2TC).  相似文献   

10.
In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process Xn =-μ ∞∑j=-∞ψn-jεj, where {ε, εn; -∞< n < ∞}is a sequence of independent, identically distributed random variables with zero mean, μ>0 is a constant and the coefficients {ψi;-∞< i <∞} satisfy 0 <∞∑j=-∞|jψj| <∞. Under the conditions that the distribution function of |ε| has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{supn≥0(-nμ ∞∑j=-∞εjβnj) > x}is discussed. Then the result is applied to ultimate ruin probability.  相似文献   

11.
In 1929, Birkhoff proved the existence of an entire function F on with the property that for any entire function f there exists a sequence {ak} of complex numbers such that {F(ζ+ak)} converges to f (ζ) uniformly on compact sets. Luh proved a variant of Birkhoff's theorem and the second author proved a theorem analogous to that of Luh for the multiplicative group *. In this paper extensions of the above results to the multi-dimensional case are proved. Let M(n,  ) be the set of all square matrices of degree n with complex coefficients, and let G=GL(n,  ) be the general linear group of degree n over . We denote by (G) the set of all holomorphic functions on G. Similarly, we define ( ). Let K be the (G)-hull of a compact set K in G. Finally we denote by B(G) the set of all compact subsets K of G with K=K such that there exists a holomorphic function f on M(n,  ) with f(0)(f(K)), where (f(K)) is the ( )-hull of f(K). Our main result is the following. There exists a holomorphic function F on G such that for any KB(G), for any function f holomorphic in some neighbourhood of K, and for any >0, there exists CG with maxZK |F(CZ)−f(Z)|<.  相似文献   

12.
This paper continues the study started in [12]. In the upper half-plane, consider the elliptic equation
, submitted to the nonlinear oblique derivative boundary condition Ux = UUz on the axis x = 0. The solution of this problem appears to be the self-similar solution of the heat equation with the same boundary condition. As goes to 0, the function U converges to the non trivial solution U of the corresponding degenerate problem. Moreover there exists z0 > 0 such that U vanishes for zz0, is C on ]0, z0+, is continuous on the boundary x = 0 and is discontinuous on the half-axis {z = 0, x> 0}.  相似文献   

13.
Let be a sequence of polynomials with real coefficients such that uniformly for [α-δ,β+δ] with G(ei)≠0 on [α,β], where 0α<βπ and δ>0. First it is shown that the zeros of are dense in [α,β], have spacing of precise order π/n and are interlacing with the zeros of pn+1(cos) on [α,β] for every nn0. Let be another sequence of real polynomials with uniformly on [α-δ,β+δ] and on [α,β]. It is demonstrated that for all sufficiently large n the zeros of pn(cos) and strictly interlace on [α,β] if on [α,β]. If the last expression is zero then a weaker kind of interlacing holds. These interlacing properties of the zeros are new for orthogonal polynomials also. For instance, for large n a simple criteria for interlacing of zeros of Jacobi polynomials on [-1+,1-], >0, is obtained. Finally it is shown that the results hold for wide classes of weighted Lq-minimal polynomials, q[1,∞], linear combinations and products of orthogonal polynomials, etc.  相似文献   

14.
In this paper we show that for a given set of l real disjoint intervals El=lj=1 [a2j−1a2j] and given >0 there exists a real polynomial and a set of l disjoint intervals El=lj=1 [ã2j−1ã2j] with ElEl and (ã1, …, ã2l)−(a1, …, a2l)max<, such that −1([−1, 1])=El. The statement follows by showing how to get in a constructive way by a continuous deformation procedure from a minimal polynomial on El with respect to the maximum norm a polynomial mapping of El.  相似文献   

15.
Let G be an undirected graph with nonnegative edge lengths. Given two vertices as sources and all vertices as destinations, we investigated the problem how to construct a spanning tree of G such that the sum of distances from sources to destinations is minimum. In the paper, we show the NP-hardness of the problem and present a polynomial time approximation scheme. For any >0, the approximation scheme finds a (1+)-approximation solution in O(n1/+1) time. We also generalize the approximation algorithm to the weighted case for distances that form a metric space.  相似文献   

16.
Let be a nontrivial involution, i.e., R=R−1≠±In. We say that is R-symmetric if RGR=G. The set of all -symmetric matrices is denoted by . In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors in and a set of complex numbers , find a matrix such that and are, respectively, the eigenvalues and eigenvectors of A. We then consider the following approximation problem: Given an n×n matrix , find such that , where is the solution set of IEP and is the Frobenius norm. We provide an explicit formula for the best approximation solution by means of the canonical correlation decomposition.  相似文献   

17.
The maximum asymptotic bias of an S-estimate for regression in the linear model is evaluated over the neighborhoods (called (c,γ)-neighborhoods) defined by certain special capacities, and its lower and upper bounds are derived. As special cases, the (c,γ)-neighborhoods include those in terms of -contamination, total variation distance and Rieder's (,δ)-contamination. It is shown that when the model distribution is normal and the (,δ)-contamination neighborhood is adopted, the lower and upper bounds of an S-estimate (including the LMS-estimate) based on a jump function coincide with the maximum asymptotic bias. The tables of the maximum asymptotic bias of the LMS-estimate are given. These results are an extension of the corresponding ones due to Martin et al. (Ann. Statist. 17 (1989) 1608), who used -contamination neighborhoods.  相似文献   

18.
Galerkin methods are used to approximate the singular integral equation
with solution φ having weak singularity at the endpoint −1, where a, b≠0 are constants. In this case φ is decomposed as φ(x)=(1−x)α(1+x)βu(x), where β=−α, 0<α<1. Jacobi polynomials are used in the discussions. Under the conditions fHμ[−1,1] and k(t,x)Hμ,μ[−1,1]×[−1,1], 0<μ<1, the error estimate under a weighted L2 norm is O(nμ). Under the strengthened conditions fHμ[−1,1] and , 2α<μ<1, the error estimate under maximum norm is proved to be O(n2αμ+), where , >0 is a small enough constant.  相似文献   

19.
For n1, let {xjn}j=1n be n distinct points and let Ln[·] denote the corresponding Lagrange Interpolation operator. Let W : →[0,∞). What conditions on the array {xjn}1jn, n1 ensure the existence of p>0 such
for every continuous f : → with suitably restricted growth, and some “weighting factor” φb? We obtain a necessary and sufficient condition for such a p to exist. The result is the weighted analogue of our earlier work for interpolation arrays contained in a compact set.  相似文献   

20.
This paper is devoted to a study of interpolatory refinable functions. If a refinable function φ on sis continuous and fundamental, i.e., φ(0)=1 and φ(α)=0 for α s\{0}, then its corresponding mask bsatisfies b(0)=1 and b(2α)=0 for all α s\{0}. Such a refinement mask is called an interpolatory mask. We establish the existence and uniqueness of interpolatory masks which are induced by masks of box splines whose shifts are linearly independent.  相似文献   

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