Atomicity through Fractal Measure Theory Mathematical and Physical Fundamentals with Applications 1st Edition by Alina Gavrilut,Ioan Merches,Maricel Agop ISBN 3030295958 978-3030295950

Atomicity through Fractal Measure Theory Mathematical and Physical Fundamentals with Applications 1st Edition by Alina Gavriluţ, Ioan Mercheş, Maricel Agop – Ebook PDF Instant Download/Delivery: 3030295958, 978-3030295950

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Product details:

ISBN 10: 3030295958 

ISBN 13: 978-3030295950

Author: Alina Gavriluţ, Ioan Mercheş, Maricel Agop

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.

Table of contents:

1. Front Matter
2. Several Hypertopologies: A Short Overview
3. A Mathematical-Physical Approach on Regularity in Hit-and-Miss Hypertopologies for Fuzzy Set Multifunctions
4. Non-Atomic Set Multifunctions
5. Non-Atomicity and the Darboux Property for Fuzzy and Non-Fuzzy Borel/Baire Multivalued Set Functions
6. Atoms and Pseudo-Atoms for Set Multifunctions
7. Gould Integrability on Atoms for Set Multifunctions
8. Continuity Properties and Alexandroff Theorem in Vietoris Topology
9. Approximation Theorems for Fuzzy Set Multifunctions in Vietoris Topology: Physical Implications of Regularity
10. Atomicity via Regularity for Non-Additive Set Multifunctions
11. Extended Atomicity Through Non-Differentiability and Its Physical Implications
12. On a Multifractal Theory of Motion in a Non-Differentiable Space: Toward a Possible Multifractal Theory of Measure
13. Back Matter

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Tags: Alina Gavrilut, Ioan Merches, Maricel Agop, Atomicity through, Fractal Measure Theory, Mathematical and Physical Fundamentals