Atomicity through Fractal Measure Theory
Mathematical and Physical Fundamentals with Applications
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Beschreibung
This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory. Applications to quantum physics and, more generally, to the fractal theory of the motion, are highlighted. The study details the atomicity problem through key concepts, such as the atom/pseudoatom, atomic/nonatomic measures, and different types of non-additive set-valued multifunctions. Additionally, applications of these concepts are brought to light in the study of the dynamics of complex systems.
The first chapter prepares the basics for the next chapters. In the last chapter, applications of atomicity in quantum physics are developed and new concepts, such as the fractal atom are introduced. The mathematical perspective is presented first and the discussion moves on to connect measure theory and quantum physics through quantum measure theory. New avenues of research, such as fractal/multifractal measuretheory with potential applications in life sciences, are opened.
This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory. Applications to quantum physics and, more generally, to the fractal theory of the motion, are highlighted. The study details the atomicity problem through key concepts, such as the atom/pseudoatom, atomic/nonatomic measures, and different types of non-additive set-valued multifunctions. Additionally, applications of these concepts are brought to light in the study of the dynamics of complex systems.
The first chapter prepares the basics for the next chapters. In the last chapter, applications of atomicity in quantum physics are developed and new concepts, such as the fractal atom are introduced. The mathematical perspective is presented first and the discussion moves on to connect measure theory and quantum physics through quantum measure theory. New avenues of research, such as fractal/multifractal measure theory with potentialapplications in life sciences, are opened.
Features step-by-step tutorials help the reader conceptualize quickly Contains a special chapter on next generation Flash prepares readers for the future Includes ten tips on how to protect flash sites from hackers
Autor*in
Alina Gavriluţ
Themen in »Atomicity through Fractal Measure Theory«
non additive measure atom pseudo atom nonatomicity fractality nonlinear dynamics hypertopologies fuzzy set multifunctions non-atomic set multifunctions atomicity Gould integrability Alexandroff theorem Vietoris topology fractal measure theory multifractal theory
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“The book is addressed to a wide range of researchers in physics and mathematics and related areas using multivalued analysis.” (Ivan Podvigin, zbMATH 1445.81004, 2020)
“The book is intended by the authors ‘for graduate and postgraduate students, teachers, and all researchers in physics and mathematics’. … I would recommend this book, much more narrowly, to mathematicians working in measure theory and to physicists who are already quantum field theory practitioners wishing to think on their work in measure-theoretic terms.” (Vladimir García-Morales, Mathematical Reviews, September, 2020)
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