共查询到20条相似文献,搜索用时 515 毫秒
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在粗糙集理论研究中,覆盖方法的应用越来越受到重视,其中拓扑空间的子集关于子基的内部和闭包两个概念尤为重要.本文在由它们导人的关于子基的开集,闭集的基础上,给出了拓扑空间关于子基的分离性概念,并研究它们的性质,得到分离性公理定义的一般拓扑空间的进一步分类. 相似文献
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向量到子空间的距离及其应用 总被引:1,自引:0,他引:1
给出了向量到有限维子空间距离的定义及求法 ,并推广到向量到可数无限维子空间距离 .采用两种方法求距离并比较了它们的运算量 .揭示了 Cholesky分解法与 Schmidt正交化方法的内在联系 .最后利用向量到子空间距离给出了矛盾方程组最小二乘解的求法 相似文献
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给出了直觉I-fuzzy拓扑空间的基与子基,并利用它研究了模糊连续和模糊开函数.我们还给出了直觉I-fuzzy拓扑空间的乘积空间的定义,并研究了乘积空间与因子空间的关系. 相似文献
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求解TSP的子空间遗传算法 总被引:17,自引:0,他引:17
为避免遗传算法在计算过程中搜索冗余空间而耗费不必要的资源及时间,本提出了一种以经费遗传算法为基础,通过分析问题的特殊解集,以找出原问题解空间的区域特征从而构造出缩小算法搜索空间的子空间遗传算法,并用它求解TSP。结果表明,该算法实施起来非常有效。 相似文献
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In this article, a new characterization of the closedness of the sum of two closed subspaces of a Hilbert space is established. 相似文献
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Wavelet frames for (not necessarily reducing) affine subspaces II: The structure of affine subspaces
This is a continuation of the investigation into the theory of wavelet frames for general affine subspaces. The main focus of this paper is on the structural properties of affine subspaces. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces, while every reducing subspace (with respect to the dilation and translation operators) is the orthogonal direct sum of two purely non-reducing ones. This result is obtained through considering the basic question as to when the orthogonal complement of an affine subspace in another one is still affine. Motivated by the fundamental question as to whether every affine subspace is singly-generated, and by a recent result that every singly generated purely non-reducing subspace admits a singly generated wavelet frame, we prove that every affine subspace can be decomposed into the direct sum of a singly generated affine subspace and some space of “small size”. As a consequence we establish a connection between the above mentioned two questions. 相似文献
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本文运用算子理论方法,讨论了Hilbert空间H中的子空间框架和子空间框架算子的性质,研究了子空间框架的摄动,给出了一些有意义的结果. 相似文献
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We present an alternative proof of a characterization, due to M. Lauzon and S. Treil, of subspaces with a common complement
in a separable Hilbert space. Our approach is motivated by known results concerning the relative position of two subspaces
in a Hilbert space. As byproducts we obtain a simple example of a double triangle subspace lattice which is not similar to
an operator double triangle and a characterization of pairs of subspaces in generic position which are not completely asymptotic
to one another.
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讨论了一维不可约强局部Dirichlet,型的正则子空间的Mosco收敛性.如果正则子空间的特征集是收敛的,那么相应的正则子空间在Mosco意义下也是收敛的.最后,用一些具体的例子说明了Mosco收敛不能保持Dirichlet型整体特性的稳定. 相似文献
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关于多个子空间的交空间与维数公式的推广 总被引:1,自引:1,他引:0
通过讨论,得到了关于多个子空间的交空间的进一步的结果.并利用这些结果,给出了维数公式的一个新的推广形式,从而完善了维数公式的理论. 相似文献
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Qingyue Zhang 《Numerical Functional Analysis & Optimization》2013,34(3):349-364
We study the structure of finitely generated shift-invariant subspaces with generators from the super Hilbert space L 2(? d )(N). We give a characterization for these subspaces. Moreover, we show that every finitely generated shift-invariant subspace possesses a tight frame. We also give a necessary and sufficient condition for such a space to be principal. Our results generalize similar ones for which generators are from L 2(? d ). 相似文献
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Wojciech Czaja Gitta Kutyniok Darrin Speegle 《Journal of Fourier Analysis and Applications》2008,14(4):514-537
Pseudoframes for subspaces have been recently introduced by Li and Ogawa as a tool to analyze lower dimensional data with
arbitrary flexibility of both the analyzing and the dual sequence.
In this paper we study Gabor pseudoframes for affine subspaces by focusing on geometrical properties of their associated sets
of parameters. We first introduce a new notion of Beurling dimension for discrete subsets of ℝ
d
by employing a certain generalized Beurling density. We present several properties of Beurling dimension including a comparison
with other notions of dimension showing, for instance, that our notion includes the mass dimension as a special case. Then
we prove that Gabor pseudoframes for affine subspaces satisfy a certain Homogeneous Approximation Property, which implies
invariance under time–frequency shifts of an approximation by elements from the pseudoframe.
The main result of this paper is a classification of Gabor pseudoframes for affine subspaces by means of the Beurling dimension
of their sets of parameters. This provides us, in particular, with a Nyquist dimension which separates sets of parameters
of pseudoframes from those of non-pseudoframes and which links a fixed value to sets of parameters of pseudo-Riesz sequences.
These results are even new for the special case of Gabor frames for an affine subspace.
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本文讨论了线性子空间Pl cker的线性表示,给出了Pl cker关系式的矩阵形式,并由之导出了子空间关联关系、零化子空间、和子空间与交子空间Pl cker坐标的矩阵表达式. 相似文献