共查询到20条相似文献,搜索用时 93 毫秒
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本文证明了格的极小生成元集一定是最小生成元集且只能是非零完全并既约元全体,证明了分配格具有最小生成元集的必要条件是它满足并无限分配律.本文还证明了完全Heyting代数具有最小生成元集当且仅当它是强代数格,证明了完备格是强代数格当且仅当它和它的对偶格均是具有最小生成元集的分配格. 相似文献
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矩阵频域乘子是由本质有界可测函数组成的矩阵,它能将多重小波紧框架映射成多重小波紧框架.引入二元多重小波紧框架的矩阵频域乘子的概念,给出了一个矩阵值函数成为二元多重小波紧框架的矩阵乘子的充要条件,并给出了构造例子. 相似文献
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实值二维信号可以用四元数来表示,因此,四元数的尺度函数和小波的构造就成为分析二维信号的关键.引入了四元数小波包的概念,并且借助于四元数多分辨分析和四元数尺度函数和四元数小波函数的概念和若干公式,给出并构造了一类四元数正交小波包的构造方法,得到了四元数正交小波包的3个正交性公式,最后,利用四元数正交小波包给出了L^2(R... 相似文献
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陈赐平 《数学年刊A辑(中文版)》1990,(5)
图G的恰饱和|V(G)|-d个顶点的对集称为G的d-亏数对集。本文给出若干有关d-亏数对集的结果,其中推广或充实了Bernstein定理,Lov(?)sz的定理及Las Vergnas的定理。 相似文献
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〈I〉型三角剖分下非张量积连续小波基的构造 总被引:1,自引:0,他引:1
多维非张量积小波是近年小波研究领域中的热点问题之一 ,它们与多维张量积小波相比具有更多的优势 .关于高维张量积、非张量积小波 ,目前已有一些很好的工作 (见文[2 ] [3 ] [4 ] ) ,但关于样条小波 ,还有许多问题有待于研究 .本文针对〈I〉型三角剖分下的二维线性元空间 ,讨论其具有紧支集和对称性的半正交样条小波基 .给定 x1 x2 平面上的〈I〉型三角剖分 (图 1 ( a)所示 ) ,记 j=( j1 ,j2 ) ,| j| =j1 + j2 ,πm= { 0≤ |j|≤ mCj1j2 xj11 xj22 ,Cj1,j2 是任意实数 }为次数不超过 m的代数多项式全体 .引入剖分尺度为 1的线性元空间 V0… 相似文献
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Starting from any two compactly supported refinable functions in L2(R)
with dilation factor d,we show that it is always possible to construct 2d wavelet functions
with compact support such that they generate a pair of dual d-wavelet frames in L2(R).
Moreover, the number of vanishing moments of each of these wavelet frames is equal
to the approximation order of the dual MRA; this is the highest possible. In particular,
when we consider symmetric refinable functions, the constructed dual wavelets are also
symmetric or antisymmetric. As a consequence, for any compactly supported refinable
function in L2(R), it is possible to construct, explicitly and easily, wavelets that are
finite linear combinations of translates (d · – k), and that generate a wavelet frame with
an arbitrarily preassigned number of vanishing moments.We illustrate the general theory
by examples of such pairs of dual wavelet frames derived from B-spline functions. 相似文献
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A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set,
while a paired-dominating set of a graph is a dominating set such that the subgraph induced by the dominating set contains
a perfect matching. In this paper, we show that no minimum degree is sufficient to guarantee the existence of a disjoint dominating
set and a paired-dominating set. However, we prove that the vertex set of every cubic graph can be partitioned into a dominating
set and a paired-dominating set. 相似文献
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We consider a mixed integer set that results from the intersection of a simple mixed integer set with a vertex packing set from a conflict graph. This set arises as a relaxation of the feasible set of mixed integer problems such as inventory routing problems. We derive families of strong valid inequalities that consider the structures of the simple mixed integer set and the vertex packing set simultaneously. 相似文献
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Norbert Patzschke 《Proceedings of the American Mathematical Society》1997,125(7):2119-2125
To describe some fractal properties of a self-similar set or measure, such as the Hausdorff dimension and the multifractal spectrum, it is useful that it satisfy the strong open set condition, which means there is an open set satisfying the open set condition and, additionally, a part of the self-similar set must meet the open set. It is known that in the non-random case the strong open set condition and the open set condition are equivalent. This paper treats the random case. If the open set condition is assumed, we show that there is a random open set satisfying the strong open set condition. Further, we give an application to multifractal analysis of the random self-similar fractal.
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在粗糙直觉模糊集的基础上,从新的角度提出了不确定目标概念的近似表示和处理的方法(通过近似模糊集和近似精确集刻画).首先将已有的直觉模糊集相似概念和均值直觉模糊集概念引入到该模型,定义了Pawlak近似空间U/R下的阶梯直觉模糊集、0.5-精确集的概念,然后得到了均值直觉模糊集(0.5-精确集)是所有直觉模糊集中与目标直觉模糊集最接近的直觉模糊集(近似精确集),接着分析了均值直觉模糊集、0.5-精确集分别与目标直觉模糊集的相似度随着知识粒度变化的变化规律. 相似文献
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This paper addresses Gabor analysis on a discrete periodic set. Such a scenario can potentially find its applications in signal processing where signals may present on a union of disconnected discrete index sets. We focus on the Gabor systems generated by characteristic functions. A sufficient and necessary condition for a set to be a tight Gabor set in discrete periodic sets is obtained; discrete periodic sets admitting a tight Gabor set are also characterized; the perturbation of tight Gabor sets is investigated; an algorithm to determine whether a set is a tight Gabor set is presented. Furthermore, we prove that an arbitrary Gabor frame set can be represented as the union of a tight Gabor set and a Gabor Bessel set. 相似文献
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The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. Since its appearance, there has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. The intuitionistic fuzzy soft set is a combination of an intuitionistic fuzzy set and a soft set. The rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. Using rough set theory, this paper proposes a novel approach to intuitionistic fuzzy soft set based decision making problems. Firstly, by employing an intuitionistic fuzzy relation and a threshold value pair, we define a new rough set model and examine some fundamental properties of this rough set model. Then the concepts of approximate precision and rough degree are given and some basic properties are discussed. Furthermore, we investigate the relationship between intuitionistic fuzzy soft sets and intuitionistic fuzzy relations and present a rough set approach to intuitionistic fuzzy soft set based decision making. Finally, an illustrative example is employed to show the validity of this rough set approach in intuitionistic fuzzy soft set based decision making problems. 相似文献
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Vague集上模糊熵的几点注记 总被引:5,自引:0,他引:5
V ague集上的不确定性度量有两种途径,一种是度量V ague集是模糊集的程度,一种是度量V ague集具有的模糊性的程度。后者将模糊集的模糊熵作为特例。本文基于“投票模型”分析了V ague集的熵应具有的特征,对国内作者提出的V ague集上的模糊熵进行了评述。 相似文献
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For a convex closed bounded set in a Banach space, we study the existence and uniqueness problem for a point of this set that is the farthest point from a given point in space. In terms of the existence and uniqueness of the farthest point, as well as the Lipschitzian dependence of this point on a point in space, we obtain necessary and su.cient conditions for the strong convexity of a set in several infinite-dimensional spaces, in particular, in a Hilbert space. A set representable as the intersection of closed balls of a fixed radius is called a strongly convex set. We show that the condition “for each point in space that is sufficiently far from a set, there exists a unique farthest point of the set” is a criterion for the strong convexity of a set in a finite-dimensional normed space, where the norm ball is a strongly convex set and a generating set. 相似文献
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《Optimization》2012,61(2-3):161-178
We consider a linear semi-infinite programming problem where the index set of the constraints is compact and the constraint functions are continuous on it. The set of all continuous functions on this index set as right hand sides are the parameter set. We investigate how large various unicity sets are.We state a condition on the objective function vector and the “matrix” of the problem which characterizes when the set of a parameters with a non-unique optimal point is a set of the first Baire category in the solvability set. This is the case if and only if the unicity set is a dense subset of the solvability set. Under the same assumptions it is even true that the interior of the strong unicity set is I also dense. If the index set of the constraints contains a dense subset with the property that each point1 is a G 8-set, then the parameters of the strong unicity set, such that the optimal point satisfies the linear independence constraint qualification, are also dense. We apply our results to a characterization of a unique continuous selection for the optimal set I mapping and to a one-sided L 1-approximation problem 相似文献