منابع مشابه
Packing Dimension, Hausdorff Dimension and Cartesian Product Sets
We show that the dimension adim introduced by R. Kaufman (1987) coincides with the packing dimension Dim, but the dimension aDim introduced by Hu and Taylor (1994) is different from the Hausdorff dimension. These results answer questions raised by Hu and Taylor. AMS Classification numbers: Primary 28A78, 28A80.
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The combinatorial dimension relative to an arbitrary fractional Cartesian product is defined. Relations between dimensions in certain archetypal instances are derived. Random sets with arbitrarily prescribed dimensions are produced; in particular, scales of combinatorial dimension are shown to be continuously and independently calibrated. A combinatorial concept of cylindricity is key. © 2004 W...
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A method for the construction of open approximate models from vector time series Preface PhD research is a largely open proces in which a stimulating environment plays a crucial role. I am indebted to several people and institutions that shaped such an environment for me during the years since April 1990. First and for all, I would like to thank my supervisor, Christiaan Heij. He set me on the ...
متن کاملOn the metric dimension of Cartesian powers of a graph
A set of vertices S resolves a graph if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of a graph is the minimum cardinality of a resolving set of the graph. Fix a connected graph G on q ≥ 2 vertices, and let M be the distance matrix of G. We prove that if there exists w ∈ Z such that ∑ i wi = 0 and the vector Mw, after sorting its coor...
متن کاملOn the Metric Dimension of Cartesian Products of Graphs
A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. This paper studies the metric dimension of cartesian products G H. We prove that the metric dimension of G G is tied in a strong sense to the minimum order of a so-called doubly resolving set ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1974
ISSN: 0021-8693
DOI: 10.1016/0021-8693(74)90169-0