The Resource Atomicity through Fractal Measure Theory : Mathematical and Physical Fundamentals with Applications, by Alina Gavriluţ, Ioan Mercheş, Maricel Agop, (electronic resource)
Atomicity through Fractal Measure Theory : Mathematical and Physical Fundamentals with Applications, by Alina Gavriluţ, Ioan Mercheş, Maricel Agop, (electronic resource)
Resource Information
The item Atomicity through Fractal Measure Theory : Mathematical and Physical Fundamentals with Applications, by Alina Gavriluţ, Ioan Mercheş, Maricel Agop, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Atomicity through Fractal Measure Theory : Mathematical and Physical Fundamentals with Applications, by Alina Gavriluţ, Ioan Mercheş, Maricel Agop, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multivalued nonadditive 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 nonadditive setvalued 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.
 Language
 eng
 Edition
 1st ed. 2019.
 Extent
 1 online resource (XIII, 184 pages)
 Contents

 Preface
 1. Short hypertopologies. A short overview
 2. A Mathematicalphysical approach on regularity in hitandmiss hypertologies for fuzzy set multifunctions
 3. Nonatomic set multifunctions
 4. Nonatomicity and the Darboux property for fuzzy and nonfuzzy Borel/Baire multivalued set functions
 5. Atoms and pseudoatoms for set multifunctions
 6. Gould integrability on atoms for set multifunctions
 7. Continuity properties and the Alexandroff theorem in Vietoris topology
 8. Approximation theorems for fuzzy set multifunctions in Vietoris topology. Physical implications of regularity 9. Atomicity via regularity for nonadditive set malfunctions
 10. Extended atomicity through nondifferentiability and its physical implications
 11. On a multifractal theory of motion in a nondifferentiable space. Toward a possible multifractal theory of measure
 List of symbols
 Index
 Isbn
 9783030295936
 Label
 Atomicity through Fractal Measure Theory : Mathematical and Physical Fundamentals with Applications
 Title
 Atomicity through Fractal Measure Theory
 Title remainder
 Mathematical and Physical Fundamentals with Applications
 Statement of responsibility
 by Alina Gavriluţ, Ioan Mercheş, Maricel Agop
 Language
 eng
 Summary
 This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multivalued nonadditive 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 nonadditive setvalued 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.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Gavriluţ, Alina
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName

 Mercheş, Ioan
 Agop, Maricel
 Series statement
 Springer eBooks.
 http://library.link/vocab/subjectName

 Measure theory
 Quantum physics
 Mathematical physics
 Label
 Atomicity through Fractal Measure Theory : Mathematical and Physical Fundamentals with Applications, by Alina Gavriluţ, Ioan Mercheş, Maricel Agop, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Preface  1. Short hypertopologies. A short overview  2. A Mathematicalphysical approach on regularity in hitandmiss hypertologies for fuzzy set multifunctions  3. Nonatomic set multifunctions  4. Nonatomicity and the Darboux property for fuzzy and nonfuzzy Borel/Baire multivalued set functions  5. Atoms and pseudoatoms for set multifunctions  6. Gould integrability on atoms for set multifunctions  7. Continuity properties and the Alexandroff theorem in Vietoris topology  8. Approximation theorems for fuzzy set multifunctions in Vietoris topology. Physical implications of regularity 9. Atomicity via regularity for nonadditive set malfunctions  10. Extended atomicity through nondifferentiability and its physical implications  11. On a multifractal theory of motion in a nondifferentiable space. Toward a possible multifractal theory of measure  List of symbols  Index
 Control code
 9783030295936
 Dimensions
 unknown
 Edition
 1st ed. 2019.
 Extent
 1 online resource (XIII, 184 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783030295936
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 1 illustration
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1126284417
 Label
 Atomicity through Fractal Measure Theory : Mathematical and Physical Fundamentals with Applications, by Alina Gavriluţ, Ioan Mercheş, Maricel Agop, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Preface  1. Short hypertopologies. A short overview  2. A Mathematicalphysical approach on regularity in hitandmiss hypertologies for fuzzy set multifunctions  3. Nonatomic set multifunctions  4. Nonatomicity and the Darboux property for fuzzy and nonfuzzy Borel/Baire multivalued set functions  5. Atoms and pseudoatoms for set multifunctions  6. Gould integrability on atoms for set multifunctions  7. Continuity properties and the Alexandroff theorem in Vietoris topology  8. Approximation theorems for fuzzy set multifunctions in Vietoris topology. Physical implications of regularity 9. Atomicity via regularity for nonadditive set malfunctions  10. Extended atomicity through nondifferentiability and its physical implications  11. On a multifractal theory of motion in a nondifferentiable space. Toward a possible multifractal theory of measure  List of symbols  Index
 Control code
 9783030295936
 Dimensions
 unknown
 Edition
 1st ed. 2019.
 Extent
 1 online resource (XIII, 184 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783030295936
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 1 illustration
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1126284417
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