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Atomicity through Fractal Measure Theory

Mathematical and Physical Fundamentals with Applications

Authors: Gavriluţ, Alina, Mercheş, Ioan, Agop, Maricel

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eBook $84.99
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  • ISBN 978-3-030-29593-6
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Hardcover $109.99
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  • ISBN 978-3-030-29592-9
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About this book

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 potential applications in life sciences, are opened.

About the authors

Alina Gavrilut, PhD, is lecturer at the Faculty of  Mathematics, Alexandru Ioan Cuza University of Iasi,  Romania. Fields of competence: Mathematical Analysis – especially the Measure Theory, Nonlinear Dynamics and Quantum Physics.

Ioan Mercheş is an emeritus professor of theoretical physics at the Alexandru Ioan Cuza University of Iasi, Romania. He has co-authored 2 books published with Springer:  Mechanics: An Intensive Course (2012) and Electrodynamics: An Intensive Course (2016).

Maricel Agop is  professor of physics at the Gheorghe Asachi Technical University of Lasi, Romania.  He was awarded the title  “Doctor Honoris Causa” of the University “Vasile Alecsandri”, Bacau, Romania  (2013). Since 2018, he has been a correspondent member of the Academy of Romanian Scientists.

Table of contents (11 chapters)

Table of contents (11 chapters)
  • Several hypertopologies: A short overview

    Pages 1-7

    Gavriluţ, Alina (et al.)

  • A mathematical-physical approach on regularity in hit-and-miss hypertopologies for fuzzy set multifunctions

    Pages 9-19

    Gavriluţ, Alina (et al.)

  • Non-atomic set multifunctions

    Pages 21-35

    Gavriluţ, Alina (et al.)

  • Non-atomicity and the Darboux property for fuzzy and non-fuzzy Borel/Baire multivalued set functions

    Pages 37-50

    Gavriluţ, Alina (et al.)

  • Atoms and pseudo-atoms for set multifunctions

    Pages 51-69

    Gavriluţ, Alina (et al.)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-030-29593-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-030-29592-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Atomicity through Fractal Measure Theory
Book Subtitle
Mathematical and Physical Fundamentals with Applications
Authors
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-29593-6
DOI
10.1007/978-3-030-29593-6
Hardcover ISBN
978-3-030-29592-9
Edition Number
1
Number of Pages
XIII, 184
Number of Illustrations
1 b/w illustrations
Topics