For an ordered set W = {w1, w2, . . . , wk} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W ) := (d(v,w1), d(v,w2), . . . , d(v,wk)) is called the (metric) representation of v with respect to W , where d(x, y) is the distance between the vertices x and y. The set W is called a resolving set for G if distinct vertices of G have distinct representations with respect ...

Works on ontology versioning pay special attention to the logical analysis of ontology evolution. The paper considers extensible declarative approach to ontology change description. Metric temporal description logic with metric temporal modalities “future n” and “past n” and hybrid satisfaction operator @ is proposed as the logical basis for declarative ontology evolution analysis. Underlying t...

Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vectorspace. Ralf Koetter and Frank R. Kschischang [?] introduced a metric on the set af vector-spaces and showed that a minimal distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and re...

For an ordered set W = {w1, w2, · · · , wk} of vertices and a vertex v in a connected graph G, the representation of v with respect to W is the ordered k-tuple r(v|W ) = (d(v, w1), d(v, w2), · · · , d(v, wk)) where d(x, y) represents the distance between the vertices x and y. The set W is called a resolving set for G if every vertex of G has a distinct representation. A resolving set containing...

This paper,  applies the concept  of KM-fuzzy metric spaces and  introduces a novel concept of KM-fuzzy metric  graphs based on KM-fuzzy metric spaces.  This study, investigates the finite KM-fuzzy metric spaces with respect to metrics and KM-fuzzy metrics and constructs KM-fuzzy metric spaces on any given non-empty sets. It tries to  extend   the concept of KM-fuzzy metric spaces to  a larger ...

For an ordered set { } k w w w W , , , 2 1  = of vertices and a vertex v in a connected graph G, the (metric) representation of v with respect to W is the k-vector r(v/W) = (d(v, w1), d(v, w2), ..., d(v, wk)), where d(x, y)representsthe distance between the vertices x and y. A resolving set of minimum cardinality is called a minimum resolving set or abasis and the cardinality of a basis for G ...

Interference temperature has been proposed by the FCC as a metric for interference analysis. The purpose of the metric is to demystify and remove the subjective context that has been the basis of interference analysis within the regulatory agencies. The development of an interference metric is critical if more intensive, dynamic use of the spectrum is desired. There has been very little specifi...

The geometric structural complexity of spatial objects does not render an intuitive distance metric on the data space that measures spatial proximity. However, such a metric provides a formal basis for analytical work in transformation-based multidimensional spatial access methods, including locality preservation of the underlying transformation and distance-based spatial queries. We study the ...