Radio galaxies provide a means to determine the coordinate distance, the luminosity distance, the dimensionless luminosity distance, or the angular size distance to sources with redshifts as large as two. Dimensionless coodinate distances for 55 supernovae and 20 radio galaxies are presented and discussed here. The radio galaxy results are consistent with those obtained using supernovae, sugges...

This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning, functional analysis and geometric measure theory. The key aspect of the kernel distance developed here is its interpretation as an L2 distance between probability mea...

This paper describes and studies generalizations of the well known double ring network structures. Two classes of structures are studied, the N2R(p; q) and N2R(p; q; r) structures, of which the former is a special case of the well known Generalized Petersen Graphs. Basic properties of these structures are shown, indicating that they form a suitable base for future access network infrastructures...

Pulse dipolar electron paramagnetic resonance spectroscopy (PDS) is continuously furthering the understanding of chemical and biological assemblies through distance measurements in nanometer range. New paramagnets pulse sequences can provide structural insights not accessible other techniques. In pursuit alternative spin centers for PDS, we synthesized a low-spin CoII complex bearing nitroxide ...

By the relative distance of points p and q of a convex body C we mean the ratio of the Euclidean length of the segment pq to the half of the Euclidean length of a longest chord of C parallel to pq. We show that in the boundary of every plane convex body there exist seven points in pairwise relative distances at least 2 3 . We also give an estimate in case of three points. Finding sets of points...

This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning, functional analysis and geometric measure theory. The key aspect of the kernel distance developed here is its interpretation as an L2 distance between probability mea...

Forest edges affect many aspects of plant communities, causing changes in microclimate, species composition, and community structure. However, the direct role of edges in regulating forest regeneration is relatively unknown. The pattern of tree establishment across a forest-old field edge was experimentally examined to determine the response of three tree species to the edge gradient. We placed...

I t is the purpose of this note to prove a theorem concerning distances between points of a metric spacej under transformations of the space into itself. The distance between two points p and q of a metric space is denoted by d(p, q). The point into which a point p is taken by n applications of a transformation T is denoted by pn, that is, T takes p to pi, pi to p2, and so on. If d(p, q) is les...

An H(p, q)-labeling of a graph G is a vertex mapping f : VG → VH such that the distance (in the graph H) of f(u) and f(v) is at least p (at least q) if the vertices u and v are adjacent in G (are at distance two in G, respectively). This notion generalizes the notions of L(p, q)and C(p, q)-labelings of graphs studied as a graph model of the Frequency Assignment Problem. We study the computation...