Some remarks on distance in natural sciences
J. Tabor (1973)
Applicationes Mathematicae
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Displaying similar documents to “The Kantorovič-Rubinstein distance”
Some remarks on distance in natural sciences
On Marczewski-Steinhaus type distance between hypergraphs
M. Karoński, Z. Palka (1977)
Applicationes Mathematicae
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On Maps which Preserve Equality of Distance in F*-spaces
Dongni Tan (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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We prove that every map T between two F*-spaces which preserves equality of distance and satisfies T(0) = 0 is linear.
Graphs with equal domination and 2-distance domination numbers
Joanna Raczek (2011)
Discussiones Mathematicae Graph Theory
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Let G = (V,E) be a graph. The distance between two vertices u and v in a connected graph G is the length of the shortest (u-v) path in G. A set D ⊆ V(G) is a dominating set if every vertex of G is at distance at most 1 from an element of D. The domination number of G is the minimum cardinality of a dominating set of G. A set D ⊆ V(G) is a 2-distance dominating set if every vertex of G is at distance at most 2 from an element of D. The 2-distance domination number of G is the minimum...
On -distance in three dimensional space.
Gelişgen, Özcan, Kaya, Rüstem (2006)
APPS. Applied Sciences
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The maximum number of unit distances among points in dimension four.
van Wamelen, Paul (1999)
Beiträge zur Algebra und Geometrie
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The Gromov-Hausdorff distance: a brief tutorial on some of its quantitative aspects
Facundo Mémoli (2013)
Actes des rencontres du CIRM
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We recall the construction of the Gromov-Hausdorff distance. We concentrate on quantitative aspects of the definition and on quantitative properties of the distance .
On the distribution of the distances of multiples of an irrational number to the nearest integer
Henk Don (2009)
Acta Arithmetica
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Bilipschitz embeddings of metric spaces into euclidean spaces.
Stephen Semmes (1999)
Publicacions Matemàtiques
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When does a metric space admit a bilipschitz embedding into some finite-dimensional Euclidean space? There does not seem to be a simple answer to this question. Results of Assouad [A1], [A2], [A3] do provide a simple answer if one permits some small ("snowflake") deformations of the metric, but unfortunately these deformations immediately disrupt some basic aspects of geometry and analysis, like rectifiability, differentiability, and curves of finite length. Here we discuss a (somewhat...
Fixed point theorem by altering distance between the points.
El Amrani, M., Mbarki, A.B. (2000)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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On the adjacent eccentric distance sum of graphs
Halina Bielak, Katarzyna Wolska (2015)
Annales UMCS, Mathematica
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In this paper we show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree and minimum degree. We extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum. Vol. 7 (2O02) no. 26. 1280-1294]. The adjaceni eccentric distance sum index of the graph G is defined as [...] where ε(υ) is the eccentricity of the vertex υ, deg(υ) is the degree of the vertex υ and D(υ) = ∑u∊v(G) d (u,υ)is...
Closed k-stop distance in graphs
Grady Bullington, Linda Eroh, Ralucca Gera, Steven J. Winters (2011)
Discussiones Mathematicae Graph Theory
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The Traveling Salesman Problem (TSP) is still one of the most researched topics in computational mathematics, and we introduce a variant of it, namely the study of the closed k-walks in graphs. We search for a shortest closed route visiting k cities in a non complete graph without weights. This motivates the following definition. Given a set of k distinct vertices = x₁, x₂, ...,xₖ in a simple graph G, the closed k-stop-distance of set is defined to be , where () is the set of all permutations...
The Path-Distance-Width of Hypercubes
Yota Otachi (2013)
Discussiones Mathematicae Graph Theory
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The path-distance-width of a connected graph G is the minimum integer w satisfying that there is a nonempty subset of S ⊆ V (G) such that the number of the vertices with distance i from S is at most w for any nonnegative integer i. In this note, we determine the path-distance-width of hypercubes.
Codes that attain minimum distance in every possible direction
Gyula Katona, Attila Sali, Klaus-Dieter Schewe (2008)
Open Mathematics
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The following problem motivated by investigation of databases is studied. Let be a q-ary code of length n with the properties that has minimum distance at least n − k + 1, and for any set of k − 1 coordinates there exist two codewords that agree exactly there. Let f(q, k)be the maximum n for which such a code exists. f(q, k)is bounded by linear functions of k and q, and the exact values for special k and qare determined.
On the nonexistence of bilipschitz parametrizations and geometric problems about A-weights.
Stephen Semmes (1996)
Revista Matemática Iberoamericana
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How can one recognize when a metric space is bilipschitz equivalent to an Euclidean space? One should not take the abstraction of metric spaces too seriously here; subsets of R are already quite interesting. It is easy to generate geometric conditions which are necessary for bilipschitz equivalence, but it is not clear that such conditions should ever be sufficient. The main point of this paper is that the optimistic conjectures about the existence of bilipschitz parametrizations are...