A method for exact calculation of the discrepancy of low-dimensional finite point sets (II)

1995 ◽  
Vol 11 (4) ◽  
pp. 422-434 ◽  
Author(s):  
Yaochen Zhu
Keyword(s):  
Exact Calculation ◽  
Point Sets ◽  
Finite Point ◽  
Low Dimensional

Approximation by Exponential-Polynomial Products on Finite Point Sets

1972 ◽  
Vol 10 (1) ◽  
pp. 125-127 ◽  
Author(s):  
CHARLES B. DUNHAM
Keyword(s):  
Exponential Polynomial ◽  
Point Sets ◽  
Finite Point

scholarly journals Discrepancy bounds for low-dimensional point sets

2014 ◽  
pp. 58-90 ◽  
Author(s):  
Henri Faure ◽  
Peter Kritzer
Keyword(s):  
Point Sets ◽  
Low Dimensional

Borsuk’s partition problem and finite point sets

2018 ◽  
Vol 59 (4) ◽  
pp. 709-716
Author(s):  
Theo Grundhöfer
Keyword(s):  
Partition Problem ◽  
Point Sets ◽  
Finite Point

scholarly journals Finite point-sets on S2 with minimum distance as large as possible

1986 ◽  
Vol 60 ◽  
pp. 3-66 ◽  
Author(s):  
L. Danzer
Keyword(s):  
Minimum Distance ◽  
Point Sets ◽  
Finite Point

Most Finite Point Sets in the Plane have Dilation $$>1$$ > 1

2014 ◽  
Vol 53 (1) ◽  
pp. 80-106 ◽  
Author(s):  
Rolf Klein ◽  
Martin Kutz ◽  
Rainer Penninger
Keyword(s):  
Point Sets ◽  
Finite Point

Matching algorithms for finite point sets in plane

2002 ◽  
Author(s):  
N.S.V. Rao ◽  
W. Wu ◽  
C.W. Glover
Keyword(s):  
Point Sets ◽  
Finite Point

Point Sets and Dynamical Systems In the Autocorrelation Topology

2004 ◽  
Vol 47 (1) ◽  
pp. 82-99 ◽  
Author(s):  
Robert V. Moody ◽  
Nicolae Strungaru
Keyword(s):  
Dynamical System ◽  
Point Sets ◽  
Finite Point ◽  
Locally Finite ◽  
Uniform Topology ◽  
Regular Model ◽  
Model Sets ◽  
Project Scheme ◽  
Compact Abelian Groups ◽  
Delone Sets

AbstractThis paper is about the topologies arising from statistical coincidence on locally finite point sets in locally compact Abelian groupsG. The first part defines a uniform topology (autocorrelation topology) and proves that, in effect, the set of all locally finite subsets ofGis complete in this topology. Notions of statistical relative denseness, statistical uniform discreteness, and statistical Delone sets are introduced.The second part looks at the consequences of mixing the original and autocorrelation topologies, which together produce a new Abelian group, the autocorrelation group. In particular the relation between its compactness (which leads then to aG-dynamical system) and pure point diffractivity is considered. Finally for generic regular model sets it is shown that the autocorrelation group can be identified with the associated compact group of the cut and project scheme that defines it. For such a set the autocorrelation group, as aG-dynamical system, is a factor of the dynamical local hull.

On the Geometric Dilation of Finite Point Sets

2003 ◽  
pp. 250-259 ◽  
Author(s):  
Annette Ebbers-Baumann ◽  
Ansgar Grüne ◽  
Rolf Klein
Keyword(s):  
Point Sets ◽  
Finite Point
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