Results 151 to 160 of about 3,484,215 (187)
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2006
We investigate notions of randomness in the space ${\mathcal {C}}[2^{\mathbb {N}}]$ of nonempty closed subsets of {0,1}ℕ. A probability measure is given and a version of the Martin-Lof Test for randomness is defined. Π02 random closed sets exist but there are no random Π01 closed sets. It is shown that a random closed set is perfect, has measure 0, and
Paul Brodhead +2 more
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We investigate notions of randomness in the space ${\mathcal {C}}[2^{\mathbb {N}}]$ of nonempty closed subsets of {0,1}ℕ. A probability measure is given and a version of the Martin-Lof Test for randomness is defined. Π02 random closed sets exist but there are no random Π01 closed sets. It is shown that a random closed set is perfect, has measure 0, and
Paul Brodhead +2 more
+4 more sources
Journal of Combinatorial Designs, 2011
Summary: A concept called P3BD-closed set is introduced to describe a set of positive integers which is both PBD-closed and 3BD-closed. The theory of P3BD-closure is developed and a few examples of P3BD-closed sets are exhibited. In the process, the existence spectrum of OLIQ \(^{\diamond }\)s (overlarge sets of idempotent quasigroups with their own ...
Zhou, Junling, Chang, Yanxun
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Summary: A concept called P3BD-closed set is introduced to describe a set of positive integers which is both PBD-closed and 3BD-closed. The theory of P3BD-closure is developed and a few examples of P3BD-closed sets are exhibited. In the process, the existence spectrum of OLIQ \(^{\diamond }\)s (overlarge sets of idempotent quasigroups with their own ...
Zhou, Junling, Chang, Yanxun
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Combinatorica, 2005
A smallest separator in a finite, simple, undirected graph G is a set S ⊆ V (G) such that G–S is disconnected and |S|=κ(G), where κ(G) denotes the connectivity of G.A set S of smallest separators in G is defined to be closed if for every pair S,T ∈ S, every component C of G–S, and every component S of G–T intersecting C either X(C,D) := (V (C) ∩ T ...
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A smallest separator in a finite, simple, undirected graph G is a set S ⊆ V (G) such that G–S is disconnected and |S|=κ(G), where κ(G) denotes the connectivity of G.A set S of smallest separators in G is defined to be closed if for every pair S,T ∈ S, every component C of G–S, and every component S of G–T intersecting C either X(C,D) := (V (C) ∩ T ...
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Combinatorica, 1984
A subset T of the node set V of a digraph \(G=(V,E)\) is called path-closed if for each v,v'\(\in T\) all nodes lying on directed paths from v to v' also belong to T. The author characterizes the convex hull of the incidence vectors of all path-closed sets by a set of linear inequalities thus turning the problem of finding a maximum path-closed set (in
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A subset T of the node set V of a digraph \(G=(V,E)\) is called path-closed if for each v,v'\(\in T\) all nodes lying on directed paths from v to v' also belong to T. The author characterizes the convex hull of the incidence vectors of all path-closed sets by a set of linear inequalities thus turning the problem of finding a maximum path-closed set (in
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Extremal Union-Closed Set Families
Graphs and Combinatorics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Guantao +3 more
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On Closed, Totally Bounded Sets
Canadian Mathematical Bulletin, 1966C. Goffman asserts that "… in a metric space X a set S is compact if and only if it is closed and totally bounded." [1] and "… every totally bounded sequence in a metric space has convergent subsequence." [2].The statements (incidentally, equivalent to each other) are both wrong, as the following counter-example shows.
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Size–biased random closed sets
Pattern Recognition, 1999We indicate how granulometries may be useful in the analysis of random sets. We define a suitable size distribution function as a tool in exploratory data analysis and give a new Hanisch style estimator for it. New Markov random sets are constructed which favour certain sizes above others.
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Trial of Hybrid Closed-Loop Control in Young Children with Type 1 Diabetes
New England Journal of Medicine, 2023R Paul Wadwa
exaly
Between Closed Sets And -Closed Sets
Educational Administration Theory and PracticesSathishkumar R +3 more
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