ISSN:
0020-7608
Schlagwort(e):
linear operator
;
banach algebra
;
general topology
;
asymptotic analysis
;
chemical network systems
;
Chemistry
;
Theoretical, Physical and Computational Chemistry
Quelle:
Wiley InterScience Backfile Collection 1832-2000
Thema:
Chemie und Pharmazie
Notizen:
By extending the methodology given in Parts I and II of this series of articles, certain dynamical systems of chemical kinetic equations are analyzed in the setting of the Banach algebra B(B) of all bounded operators acting on a Banach space B. In this article, we proceed from the general setting of B(B), which played a central role in Part II, toward its specific application to the dynamical systems. In our analysis, crucial initial steps are taken by (i) equipping the abstract space B with the “positive quadrant,” which we denote by Γ(∝+n), and by (ii) investigating the asymptotic behavior of the solution χε(t) of the initial-value problem $dx(t)/dt = Tx(t), x(0)=\xi \in \Gamma(R^{+n})\subset {\cal B} \hbox{, where } T \in {\bf B}({\cal B})$ is suitably specified for our application purposes. The main theorem and its two specialized versions, together with the notions of Γ-semipositive operators and semipositive matrices presented here, serve as fundamental tools for the analysis of a class of dynamical systems of chemical kinetic equations whose examples were illustratively treated in the previous parts of this series of articles. The techniques developed here for an asymptotic analysis of chemical kinetic dynamical systems will be linked and unified with those for the asymptotic analysis of quantum mechanical systems in a forthcoming part of this series of articles. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 149-163, 1997
Materialart:
Digitale Medien
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