Design of some crystal and quasicrystal networks, based on rhombellane tiling,is presented. [1,1,1]Propellane,is a synthesized organic molecule; its hydrogenated form, the bicyclo[1.1.1]pentane,may be represented by the complete bipartite graph K2,3 which is the smallest rhombellane. Topology of translational and radial structures involving rhombellanes is described in terms of vertex symbol, c...

We construct a family of groups from suitable higher rank graphs which are dimensional generalizations the Thompson groups. introduce group invariants, inspired by K-theory C⁎-algebras, and show that many our not isomorphic to Brin-Thompson nV, when n≥2.

EINSTEIN’S equations (1936) yield maximum likelihood estimates of the w regional frequency distribution of crossovers in the tetrads from which a given sample of strands was derived, one per tetrad. But clearly, as with all estimates of universe parameters from sample statistics, other values within a certain range cannot be rejected; that range can be ascertained, for each tetrad-rank separate...

Abstract The tensor rank decomposition, or canonical polyadic is the decomposition of a into sum rank-1 tensors. condition number measures sensitivity summands with respect to structured perturbations. Those are perturbations preserving that decomposed. On other hand, angular up scaling. We show for random rank-2 tensors expected value infinite wide range choices density. Under mild additional ...

The matrix separation problem aims to separate a low-rank matrix and a sparse matrix from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications. Nuclear-norm minimization models have been proposed for matrix separation and proved to yield exact separations under suitable conditions. These models, however, typically require...

Simple method to improve traditional approaches to name taxa of higher ranks has been proposed. Instead of base name + postfixes (which vary between codes of nomenclature and sometimes not standardized at all), use numerical prefixes, where numbers designate the rank of taxon, from lowest (species = 1) to highest (kingdom = 7). This “numerical ranks” method is not only more simple and straightf...