Using the relativistic Fermat’s principle, we establish a bridge between stationary–complete manifolds which satisfy observer-manifold condition and pre-Randers metrics, namely, Randers metrics without any restriction on one-form. As consequence, give description of causal ladder such spacetimes in terms elements associated with metric: its geodesics distance. We obtain, as applications this in...

The magnitude squared coherence (MSC) spectrum is an often used frequency-dependent measure for the linear dependency between two stationary processes, and the recent literature contain several contributions on how to form high-resolution data-dependent and adaptive MSC estimators, and on the efficient implementation of such estimators. In this work, we further this development with the present...

Spanning trees have been studied extensively and have many practical applications. From astronomers using spanning trees to find quasar superstructures, to biomedical engineers detecting actin fibers in cell images tree enumeration remains an interesting problem. In this paper we examine a simple, practical, algebraic approach for the enumeration of spanning trees in complete and non-complete g...

the non-commuting graph $nabla(g)$ of a non-abelian group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we 'll prove that if $g$ is a finite group with $nabla(g)congnabla(bs_{n})$, then $g cong bs_{n}$, where $bs_{n}$ is the symmetric group of degre...