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Atomicity through Fractal Measure Theory

Mathematical and Physical Fundamentals with Applications

  • Alina Gavriluţ
  • Ioan Mercheş
  • Maricel Agop
Book

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Alina Gavriluţ, Ioan Mercheş, Maricel Agop
    Pages 1-7
  3. Alina Gavriluţ, Ioan Mercheş, Maricel Agop
    Pages 21-35
  4. Alina Gavriluţ, Ioan Mercheş, Maricel Agop
    Pages 51-69
  5. Alina Gavriluţ, Ioan Mercheş, Maricel Agop
    Pages 71-82
  6. Alina Gavriluţ, Ioan Mercheş, Maricel Agop
    Pages 83-103
  7. Alina Gavriluţ, Ioan Mercheş, Maricel Agop
    Pages 123-131
  8. Alina Gavriluţ, Ioan Mercheş, Maricel Agop
    Pages 133-162
  9. Back Matter
    Pages 181-184

About this book

Introduction

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.

Keywords

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 quantum measure theory multivalued analysis

Authors and affiliations

  • Alina Gavriluţ
    • 1
  • Ioan Mercheş
    • 2
  • Maricel Agop
    • 3
  1. 1.Faculty of MathematicsAlexandru Ioan Cuza UniversityIaşiRomania
  2. 2.Faculty of PhysicsAlexandru Ioan Cuza UniversityIaşiRomania
  3. 3.Physics Department, Gheorghe Asachi TechnicalUniversity of LasiIaşiRomania

Bibliographic information