Abstract: The real decentralized fixed mode radius measures how “near” a decentralized LTI system is from having a decentralized fixed mode (DFM) present. In this paper, some properties of the real DFM radius are discussed, a procedure for computing the actual system parametric perturbations that achieve the real DFM radius is presented, and the real DFM radius is extended to deal with structur...

Denote the joint numerical radius of an m-tuple of bounded operators A = (A1, . . . , Am) by w(A). We give a complete description of maps f satisfying w(A − B) = w(f(A) − f(B)) for any two m-tuples of operators A = (A1, . . . , Am) and B = (B1, . . . , Bm). We also characterize linear isometries for the joint numerical radius, and maps preserving the joint numerical range of A. AMS Classificati...

In diverse branches of mathematics, several inequalities have been studied and applied. this article, we improve Furuta’s inequality. Subsequently, apply improvement to obtain new radius that not reported in the current literature. Numerical examples illustrate main findings.

This article is devoted to studying some new numerical radius inequalities for Hilbert space operators. Our analysis enables us improve an earlier bound due Kittaneh. It shown, among other, that if $A\in \mathcal{B}(\mathcal{H})$, then \[ \frac{1}{8}\left( {{\left\| A+{{A}^{*}} \right\|}^{2}}+{{\left\| A-{{A}^{*}} \right\|}^{2}} \right)\le \omega ^{2}\left( A \right) \le \left\| \frac{{{\left| ...

The purpose of this research paper is to introduce new Cauchy–Schwarz inequalities that are valid in semi-Hilbert spaces, which generalizations Hilbert spaces. We demonstrate how these can be employed derive novel A-numerical radius inequalities, where A denotes a positive semidefinite operator complex space. Some our expand upon the existing literature on numerical with space operators, import...

in this paper, direct numerical simulation of two-phase incompressible gas-liquid flow for simulation of bubble motion in a microtube is presented. microtube radius is 10 µm. the interface is tracked using volume of fluid (vof) method with continuous surface force (csf) model. the flow is solved using a finite volume scheme, based on piso algorithm. numerical simulation is performed on a axisym...