arXiv subjects

Angelo B. Mingarelli

Publications and source records attributed to Angelo B. Mingarelli.

21 records · Page 2Linked to original sources

arXiv2007

A study of fuzzy and many-valued logics in cellular automata

In this paper we provide an analytical study of the theory of multi-valued and fuzzy cellular automata where the fuzziness appears as the result of the application of an underlying multi-valued or continuous logic as opposed to standard logic as used conventionally. Using the disjunctive normal form of any one of the 255 ECA's so defined, we modify the underlying logic structure and redefine the ECA within the framework of this new logic. The idea here is to show that the evolution of space-time diagrams of ECA's under even a probabilistic logic can exhibit non-chaotic behavior. This is looked at specifically for Probabilistic Rule 110, in contrast with Boolean Rule 110 which is known to be capable of universal computation.

cs.LO↗

arXiv2007

Asymptotic solutions of forced nonlinear second order differential equations and their extensions

Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear differential equations on a half-axis. In addition, we extend the methods and present new similar results for integral equations and Volterra-Stieltjes integral equations, a framework whose benefits include the unification of second order difference and differential equations. In so doing, we enlarge the class of nonlinearities and in some cases remove the distinction between superlinear, sublinear, and linear differential equations that is normally found in the literature. An update of papers, past and present, in the theory of Volterra-Stieltjes integral equations is also presented.

math.CA↗

arXiv2006

A glimpse into the life and times of F.V.Atkinson

We review the life and scientific work of F.V Atkinson, mathematician. The article consists of a brief overview of his academic and professional life followed by an extensive compilation of his life's work, some unpublished. He is best remembered for his contributions to Number Theory (mean value theorems for the Riemann zeta function on the critical line), his work in operator theory (index theorems for abstract Fredholm operators), and his seminal work in many areas of differential equations (multiparameter spectral theory, Sturm-Liouville theory, asymptotics etc.)

math.CA↗