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Smallest enclosing ball multidistance

2012
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Communications in Information and Systems
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Metric space, Fermat

doi:10.4310/cis.2012.v12.n3.a1
fatcat:2yetjgyrqvhixmuwfa5psmbzlq
*multidistance*,*smallest**enclosing**ball*, midpoint property, Fermat property, m-dimensional Euclidian space. 1. Introduction. ... By using the diameter of the*smallest**enclosing**ball*of a set of points, we find conditions in order to ensure that the mentioned measure is a*multidistance*. Keywords. ... The*Multidistance*based on the*Smallest**Enclosing**Ball*. 3.1. The*Smallest**Enclosing**Ball*. Let (X, d) be a non trivial (|X| 2) proper metric space. Proposition 1. ...##
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Functionally Expressible Multidistances

2011
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Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011)
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An example of non functionally expressible

doi:10.2991/eusflat.2011.24
dblp:conf/eusflat/MartinMV11
fatcat:23za7m6fkfbsrgocejz2twfpgu
*multidistance*is exhibited. ... After introducing the concept of functionally expressible*multidistance*, several essential types of multidimensional aggregation functions are considered to construct such kind of*multidistances*. ... Figure 3 : 3 A*smallest**enclosing**ball*in the d ∞ -plane. D 1 (Figure 4 : 14 P 1 , . . . , P n ) A*smallest**enclosing**ball*in the d 1 -plane. ...##
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On the best constants associated with n-distances
[article]

2019
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arXiv
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pre-print

Finally, we discuss an interesting link between the concepts of n-distance and

arXiv:1907.06586v1
fatcat:zjafb35knzf75euieopwjnkbge
*multidistance*. ... It is easy to see that this is also the case for the diameter of the*smallest**enclosing*Chebyshev*ball*in R q for any integer q ≥ 2, that is, d(x 1 , . . . , x n ) = max {i,j}⊆{1,... ... circle*enclosing*n points in R 2 (X = R 2 ). • Area of the*smallest*circle*enclosing*n points in R 2 (X = R 2 and n ≥ 3). ...##
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A generalization of the concept of distance based on the simplex inequality

2018
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Contributions to Algebra and Geometry
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Properties of

doi:10.1007/s13366-018-0379-5
fatcat:kyumkwdymfhzfmuxo6o5zyrumi
*multidistances*as well as instances including the Fermat*multidistance*and*smallest**enclosing**ball**multidistances*have been investigated for example in [2, [18] [19] [20] . ... In Section 4 we consider some geometric constructions (*smallest**enclosing*sphere and number of directions) to define n-distances and study their corresponding best constants. ...##
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Data Fusion: Theory, Methods, and Applications
[article]

2022
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arXiv
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pre-print

and A. 3 , 3 which relies on the CGAL library.Figure A.10 gives an exemplary Rcpp implementation of a routine to compute the

arXiv:2208.01644v1
fatcat:3bien2qm6zd3pbtvmrtchfb6kq
*smallest**enclosing**ball*. ... The Euclidean 1-center (*smallest**enclosing**ball*radius) is given by: 1center d2 (x (1) , . . . , x (n) ) = arg min y∈R d n i=1 d 2 (x (i) , y), (2.8) where d 2 is the Euclidean metric. Example 2.9. ...##
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Data Fusion: Theory, Methods, and Applications
[article]

2015
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Zenodo
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and A. 3 , 3 which relies on the CGAL library.Figure A.10 gives an exemplary Rcpp implementation of a routine to compute the

doi:10.5281/zenodo.6960327
fatcat:ohur72os4nddfan2tz7jqbske4
*smallest**enclosing**ball*. ... The Euclidean 1-center (*smallest**enclosing**ball*radius) is given by: 1center d2 (x (1) , . . . , x (n) ) = arg min y∈R d n i=1 d 2 (x (i) , y), (2.8) where d 2 is the Euclidean metric. Example 2.9. ...##
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Medial/skeletal linking structures for multi-region configurations
[article]

2015
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arXiv
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pre-print

Convex Hull: The

arXiv:1402.5517v3
fatcat:7gedeero2jhjxd3fmbcfvvpq7e
*smallest*convex region which contains a configuration is the convex hull of the configuration. ... We view Ω as the region*enclosed*by the boundary B = ϕ(X), for ϕ : X → R n+1 a smooth embedding and X a smooth compact n-manifold. ... Then for the perturbation, we are considering the partial multijet of the*multidistance*functionρ i about the points (x There are two cases involving x (0) (= x (jp) 1 ), u (0) , and u (1) . ...