‎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.

This study aims at presenting a numerical model for predicting grout flow and penetration length into the jointed rock mass using Universal Distinct Element Code (UDEC). The numerical model is validated using practical data and analytical method for grouting process. Input data for the modeling, including geomechanical parameters along with grout properties, were obtained from a case study. The...

The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...

Abstract: In this paper, the transmission zero at s radius and the minimum phase radius of a linear time-invariant (LTI) system are introduced. The former radius gives a measure of how “near” a LTI system is from having a transmission zero at a specified point s ∈ C in the complex plane, and the latter radius measures how “near” a minimum phase system is to a nonminimum phase system. Formulas f...

electromagnetic forming is a high energy rate forming process in which an electromagnetic lorentz body force is used for deformation of products.  in this article, electromagnetic forming process was simulated for the assembly of parts as an innovative method.  the effect of important process parameters such as discharge energy, radius and width of rectangular groove on the strength of the asse...

We propose some refinements for the second inequality in $$ \frac{1}{2}\left\Vert A\right\Vert \le w(A)\le \left\Vert A\right\Vert, where A ∈ B(H). In particular, if is hyponormal, then, by refining Young with Kantorovich constant K K(⋅, ⋅), we show that \frac{1}{2{\operatorname{inf}}_{\left\Vert x\right\Vert =1}\zeta (x)}\left|\left\Vert A\right.\right|++\left|\left.{A}^{\ast}\right\Vert \righ...

We study various inequalities for numerical radius and Berezin number of a bounded linear operator on Hilbert space. It is proved that the pure two-isometry 1 Crawford 0. In particular, we show any scalar-valued non-constant inner function θ, Toeplitz Tθ Hardy space 0, respectively. also shown multiplicative class isometries sub-multiplicative commutants shift. have illustrated these results wi...