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...

A simple algorithm is presented for the tensorial reduction of oneloop diagrams with massless external momenta. At most rank one tensor integrals with the initial number of denominators appear, plus, eventually, higher rank integrals with less denominators. The number of Gram determinants in the tensorial decomposition is then reduced, giving a better numerical stability of the results. In some...

Abstract We study the structure and compute stable rank of $C^{*}$ -algebras finite higher-rank graphs. completely determine -algebra when $k$ -graph either contains no cycle with an entrance or is cofinal. also exactly which finite, locally convex -graphs yield unital stably -algebras. give several examples to illustrate our results.

The envelope, EðAÞ, of a complex square matrix A is a region in the complex plane that contains the spectrum of A and is contained in the numerical range of A. The envelope is compact but not necessarily convex or connected. The connected components of EðAÞ have the potential of isolating the eigenvalues of A, leading us to study its geometry, boundary, and number of components. We also examine...

A generalized directions-of-arrival (DOAs) estimation algorithm is developed for the rank-one (point source) and higher-rank (distributed source) signal models. For higher-rank signals, the integral steering vector is deduced to be a Schur-Hadamard product comprising the steering vector of rank-one source and a real matrix according to the symmetry assumption of angular signal intensity. And th...

The reconstruction of high-dimensional sparse signals is a challenging task in a wide range of applications. In order to deal with high-dimensional problems, efficient sparse fast Fourier transform algorithms are essential tools. The second and third authors have recently proposed a dimension-incremental approach, which only scales almost linear in the number of required sampling values and alm...

Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix M , the goal is to compute a matrix M ′ of given rank r in a linear or affine subspace E of matrices (usually encoding a specific structure) such that the Frobenius distance ‖M −M ′‖ is small. We propose a Newton-like iteration for solving ...