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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)

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
Creator
Contributor
Author
Subject
Language
eng
Summary
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.--
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)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-030-29593-6
Instantiates
Publication
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 Mathematical-physical approach on regularity in hit-and-miss hypertologies for fuzzy set multifunctions -- 3. Non-atomic set multifunctions -- 4. Non-atomicity and the Darboux property for fuzzy and non-fuzzy Borel/Baire multivalued set functions -- 5. Atoms and pseudo-atoms 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 non-additive set malfunctions -- 10. Extended atomicity through non-differentiability and its physical implications -- 11. On a multifractal theory of motion in a non-differentiable space. Toward a possible multifractal theory of measure -- List of symbols -- Index
Control code
978-3-030-29593-6
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, non-commercial 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)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-030-29593-6
Publication
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 Mathematical-physical approach on regularity in hit-and-miss hypertologies for fuzzy set multifunctions -- 3. Non-atomic set multifunctions -- 4. Non-atomicity and the Darboux property for fuzzy and non-fuzzy Borel/Baire multivalued set functions -- 5. Atoms and pseudo-atoms 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 non-additive set malfunctions -- 10. Extended atomicity through non-differentiability and its physical implications -- 11. On a multifractal theory of motion in a non-differentiable space. Toward a possible multifractal theory of measure -- List of symbols -- Index
Control code
978-3-030-29593-6
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, non-commercial 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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