共查询到20条相似文献,搜索用时 93 毫秒
1.
设E=■或■,■(x)∈L~2(R~2)且■_(jk)(x)=2■(E~jx-k),其中j∈Z,k∈Z~2.若{■_(jk)|jJ∈Z,k∈Z~2}构成L~2(R~2)的紧框架,则称■(x)为E-紧框架小波.本文给出E-紧框架小波是MRA E-紧框架小波的一个充要条件,即E紧框架小波■来自多尺度分析当且仅当线性空间F_■(ξ)的维数为0或1,其中F_■(ξ)=■(ξ)|j■1},■_j(ξ)={■((E~T)~j(ξ+2kπ))}_(k∈EZ~2,j■1。 相似文献
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多尺度分析生成元的刻画 总被引:1,自引:0,他引:1
本文将给出多尺度分析生成元的一种完全刻画.将证明:函数φ∈L~2(R)是二进多尺度分析生成元的充要条件是(1)存在{a_k}∈l~2,φ(x)=∑_(k∈Z)a_kφ(2x-k);(2)存在正数A相似文献
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研究了L2(R)中小波框架{ψj,k}j,k={sjψ(sj·-kb)}j,k∈Z的膨胀列{sj}j的性质.如果{ψj,k}j,k是L2(R)的一个小波框架,那么膨胀列是无界的,在某些条件下{sj}j∈Z一定能够被重排为指标集Z上的一个非减数列,而且存在常数λ,μ∈(0,1)和p∈Z ,使得对j∈Z有λ相似文献
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Wang Junyu 《数学年刊B辑(英文版)》1991,12(1):106-121
This paper studies the boundary value problem involving a small parameter
$$((k(V(t))+s)|V'(s)|^{N-1}V'(s))'+(sg(V(s))+f(V(s)))V'(s)=0 for s\in R$$,
$$V(-\infty)=A,V(+\infty)=B;A0$$,
$$U(x,0)=A for x<0,U(x,0)=B for x>0$$
under the hypotheses H1—H4 . The author's aim is not only to determine explicitly the discontinuous solution ,to the reduced problem;and the form and the number of its curves of discontinuity, but also to present, in an extremely natural way, the jump conditions which it must satisfy on each of its curves of diseontinuity. It is proved that the problem has a unique solution $U_{\varepsilon}(x,t)=V_{\varepsilon}(s),s=x/p(t),s\geq0,V_{\varepsilon}$pointwise converges to $V_{0}(s)$ as $s\downarrow0,V_{0}(s)$ has at least one jump point if and only if k(y) possesses at least one interval of degeneracy in [A-B], and there exists a one-to-one correspondence between the collection of all intervals of degeneracy of k(y) in [A-B] and the set of all jump points of $V_{0}(s)$ 相似文献
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记Ore2=min{d(y) d(x)|x,y∈V(G),d(x,y)=2},本得到:若n阶图G的Ore2≥n 1,则G是[5;n]泛连通图。此是比Faudree等人的定理进一步的结果。 相似文献
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为了从采样值稳定和惟一地重建信号f(x),函数在采样集{xj,j=∈Z}上的采样值{f(xj),j∈Z}要满足A||f||L^p^p≤∑j∈Z|f(xj)|^p≤B||f||L^p^p.本文研究在平移不变空间V^p[φ]中使上式成立的条件,在几种情况下,得到了使上式成立的采样条件,并建立了由采样值重建f(x)的重建算法,该算法比一般的迭代重建算法收敛更快. 相似文献
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紧支撑正交插值的多小波和多尺度函数 总被引:10,自引:0,他引:10
本文给出一类伸缩因子为α的紧支撑正交插值多尺度函数和多小波的构造方法.设{Vj}是尺度函数Φ(x)=[φ1(x),φ2(x),…,φa(x)]T生成的多分辨分析,Vj(?)L2(R)是{a-j/2φ(?)(ajx-k),k∈Z,(?)=1,2,…,a)线性扩张构成的子空间,其插值性是指φ1(x),φ2(x),…,φa(x)满足φj(k+(?)/a)=δk,0δj,e,j,(?)∈{1,2,…,a).当Φ(x)是正交插值的,则多分辨分析的分解或重构系数能用采样点表示而不需要用计算内积的方法产生.基于此,我们建立多小波采样定理,即如果一个连续信号f(x)∈VN,则f(x)=∑i=0a-1∑k∈Zf(k/aN+i/aN+1)φi+1(aNx-k),并给出对应多小波的显式构造公式.更进一步,证明了本文构造的多小波也有插值性.最后,还给出一个构造算例. 相似文献
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An L(d1,d2,...,dt)-labeling of a graph G is a function f from its vertex set V(G) to the set {0, 1,..., k} for some positive integer k such that {f(x) - f(y)| ≥ di, if the distance between vertices x and y in G is equal to i for i = 1,2,...,t. The L(d1,d2,...,dt)-number λ(G;d1,d2,... ,dt) of G is the smallest integer number k such that G has an L(d1,d2,... ,dt)labeling with max{f(x)|x ∈ V(G)} = k. In this paper, we obtain the exact values for λ(Cn; 2, 2,1) and λ(Cn; 3, 2, 1), and present lower and upper bounds for λ(Cn; 2,..., 2,1,..., 1) 相似文献
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引入部分双曲集的概念,证明了紧黎曼流形上的微分同胚在其部分双曲集的小邻域内具有如下形式的拟跟踪性:设f为紧黎曼流形M上的一个微分同胚,Λ为f的部分双曲集.则存在Λ的邻域O(Λ),使得对于任意ε>0,存在δ>0,使得f在O(Λ)中的任意δ-伪轨{x_k}k∈Z,存在点列{y_k}k∈Z,和中心向量列{u_k∈E_(xk)~c}k∈Z满足d(x_k,y_k)<ε,其中y_k=exp_(x_k)(exp_(x_k)^(-1)(f(y_(k-1)))+u_k).作为一个应用,给出任意微分同胚在C^0扰动下,如果在双曲集邻域内存在不变集,则其是拓扑拟稳定的. 相似文献
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Pm×Kn的邻点可区别全色数 总被引:6,自引:0,他引:6
设G是简单图.设f是一个从V(G)∪E(G)到{1,2,…,k}的映射.对每个v∈V(G),令C_f(v)={f(v)}∪{f(vw)|w∈V(G),vw∈E(G)}.如果f是k-正常全染色,且对任意u,v∈V(G),uv∈E(G),有C_f(u)≠C_f(v),那么称f为图G的邻点可区别全染色(简称为k-AVDTC).数x_(at)(G)=min{k|G有k-AVDTC}称为图G的邻点可区别全色数.本文给出路P_m和完全图K_n的Cartesion积的邻点可区别全色数. 相似文献
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Fusion-Riesz frame (Riesz frame of subspace) whose all subsets are fusion frame sequences with the same bounds is a special fusion frame. It is also considered a generalization of Riesz frame since it shares some important properties of Riesz frame. In this paper, we show a part of these properties of fusion-Riesz frame and the new results about the stabilities of fusion-Riesz frames under operator perturbation (simple named operator perturbation of fusion-Riesz frames). Moreover, we also compare the operator perturbation of fusion-Riesz frame with that of fusion frame, fusion-Riesz basis (also called Riesz decomposition or Riesz fusion basis) and exact fusion frame. 相似文献
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Jorge Picado 《Applied Categorical Structures》2002,10(6):593-602
This note characterizes gauge structures for frames, i.e., families of metric diameters which completely describe frame uniformities. Some applications are presented. 相似文献
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在Hilbert空间中框架扰动的基础上,运用算子论的方法,给出对偶框架扰动性的一些结果及证明. 相似文献
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In this paper we show that there exist wavelet frames that have nice dual wavelet frames, but for which the canonical dual frame does not consist of wavelets, i.e., cannot be generated by the translates and dilates of a single function. 相似文献
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In this paper, we give a method which allows us to construct a class of Parseval frames for L2 (R) from Fourier frame for L2 (I). The result shows that the function which generates a Gabor frame by translations and modulations has "good" properties, i.e., it is sufficiently smooth and compactly supported. 相似文献
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This paper addresses the theory of multi-window subspace Gabor frame with rational time-frequency parameter products.With the help of a suitable Zak transform matrix,we characterize multi-window subspace Gabor frames,Riesz bases,orthonormal bases and the uniqueness of Gabor duals of type I and type II.Using these characterizations we obtain a class of multi-window subspace Gabor frames,Riesz bases,orthonormal bases,and at the same time we derive an explicit expression of their Gabor duals of type I and type II.As an application of the above results,we obtain characterizations of multi-window Gabor frames,Riesz bases and orthonormal bases for L2(R),and derive a parametric expression of Gabor duals for multi-window Gabor frames in L2(R). 相似文献
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对于给定冗余的仿射框架X(Ф)={Ф1,…,ФL),存在对偶Y(ψ)={ψ1,…,ψL),这个对偶可能不是仿射框架,因为它不满足Bessel条件.这样的对偶我们称为伪仿射对偶,并给出伪仿射对偶框架的一种构造公式. 相似文献