Authors :
Debopam Ghosh
Volume/Issue :
Volume 5 - 2020, Issue 8 - August
Google Scholar :
http://bitly.ws/9nMw
Scribd :
https://bit.ly/2Z8fAz6
DOI :
10.38124/IJISRT20AUG601
Abstract :
The present article addresses the issue of determining the most stable configuration pair(s) of a Matrix Shell,
and thereby, of determining the set of most stable configurations of the associated Matrix Shell System. The problem is
resolved using the criteria of spectral proximity w.r.t. the Ordered Eigenspectrum of a defined Baseline Matrix (both for
Individual constituent Matrix Shells and the Matrix Shell System) and quantified in terms of an appropriate Proximity
Function, the article presents the analytic expressions of the Matrix Shell Baseline elements, corresponding to
A n A n A n A n (0,2 ), (0,2 1), (1,2 ), (1,2 1) and
A t n A t n ( ,2 ), ( ,2 1) where
t 2
, type Matrix Shells and defines the
Baseline Matrices in terms of these Baseline elements, the article then provides a mathematical framework to determine
the most stable Configuration pair(s) of constituent Matrix Shells and the set of most stable configurations of the Matrix
Shell System and concludes with demonstration of the working of the presented framework through hypothetical examples
based case studies
Keywords :
Matrix Shell, Matrix Shell System, State-Interaction Matrix, Matrix Shell Baseline elements.
The present article addresses the issue of determining the most stable configuration pair(s) of a Matrix Shell,
and thereby, of determining the set of most stable configurations of the associated Matrix Shell System. The problem is
resolved using the criteria of spectral proximity w.r.t. the Ordered Eigenspectrum of a defined Baseline Matrix (both for
Individual constituent Matrix Shells and the Matrix Shell System) and quantified in terms of an appropriate Proximity
Function, the article presents the analytic expressions of the Matrix Shell Baseline elements, corresponding to
A n A n A n A n (0,2 ), (0,2 1), (1,2 ), (1,2 1) and
A t n A t n ( ,2 ), ( ,2 1) where
t 2
, type Matrix Shells and defines the
Baseline Matrices in terms of these Baseline elements, the article then provides a mathematical framework to determine
the most stable Configuration pair(s) of constituent Matrix Shells and the set of most stable configurations of the Matrix
Shell System and concludes with demonstration of the working of the presented framework through hypothetical examples
based case studies
Keywords :
Matrix Shell, Matrix Shell System, State-Interaction Matrix, Matrix Shell Baseline elements.
