In this talk, we give a criterion for a companion matrix to be reducible and give a complete characterization of reducible companion matrices. We also consider properties of the numerical ranges of reducible companion matrices. To be more precise, if C is an n-by-n reducible companion matrix which is unitarily equivalent to the direct sum of A and B, we study properties of the numerical ranges ...

A numerical simulation has been carried out to study the detonability characteristics of two- phase unconfined clouds. The parameters equivalence ratio, turbulence, shape, volume and uniformity of the cloud and the delay time distribution are recognized and introduced as the most important factors determining the reactivity of the cloud and influencing the initiation of a successful detonation....

A numerical simulation has been carried out to study the detonability characteristics of two- phase unconfined clouds. The parameters equivalence ratio, turbulence, shape, volume and uniformity of the cloud and the delay time distribution are recognized and introduced as the most important factors determining the reactivity of the cloud and influencing the initiation of a successful detonation....

‎let $n$ and $k$ be two positive integers‎, ‎$kleq n$ and $a$ be an $n-$square quaternion matrix‎. ‎in this paper‎, ‎some results on the $k-$numerical range of $a$ are investigated‎. ‎moreover‎, ‎the notions of $k$-numerical radius‎, ‎right $k$-spectral radius and $k$-norm of $a$ are introduced‎, ‎and some of their algebraic properties are studied‎.