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Topological Groups: Yesterday, Today, Tomorrow

ISBN: 9783038422686 9783038422693 Year: Pages: VIII, 220 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics
Added to DOAB on : 2016-12-05 09:30:44
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In 1900, David Hilbert asked whether each locally euclidean topological group admits a Lie group structure. This was the fifth of his famous 23 questions which foreshadowed much of the mathematical creativity of the twentieth century. It required half a century of effort by several generations of eminent mathematicians until it was settled in the affirmative. These efforts resulted over time in the Peter-Weyl Theorem, the Pontryagin-van Kampen Duality Theorem for locally compact abelian groups, and finally the solution of Hilbert 5 and the structure theory of locally compact groups, through the combined work of Andrew Gleason, Kenkichi Iwasawa, Deane Montgomery, and Leon Zippin. For a presentation of Hilbert 5 see the 2014 book “Hilbert’s Fifth Problem and Related Topics” by the winner of a 2006 Fields Medal and 2014 Breakthrough Prize in Mathematics, Terence Tao.It is not possible to describe briefly the richness of the topological group theory and the many directions taken since Hilbert 5. The 900 page reference book in 2013 “The Structure of Compact Groups” by Karl H. Hofmann and Sidney A. Morris, deals with one aspect of compact group theory. There are several books on profinite groups including those written by John S. Wilson (1998) and by Luis Ribes and ‎Pavel Zalesskii (2012). The 2007 book “The Lie Theory of Connected Pro-Lie Groups” by Karl Hofmann and Sidney A. Morris, demonstrates how powerful Lie Theory is in exposing the structure of infinite-dimensional Lie groups.The study of free topological groups initiated by A.A. Markov, M.I. Graev and S. Kakutani, has resulted in a wealth of interesting results, in particular those of A.V. Arkhangelʹskiĭ and many of his former students who developed this topic and its relations with topology. The book “Topological Groups and Related Structures” by Alexander Arkhangelʹskii and Mikhail Tkachenko has a diverse content including much material on free topological groups. Compactness conditions in topological groups, especially pseudocompactness as exemplified in the many papers of W.W. Comfort, has been another direction which has proved very fruitful to the present day.

Harmonic Oscillators and Two-by‑two Matrices in Symmetry Problems in Physics

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ISBN: 9783038425007 9783038425014 Year: Pages: X, 360 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics
Added to DOAB on : 2017-10-02 11:58:37
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This book consists of the articles published in the special issues of this Symmetry journal based on two-by-two matrices and harmonic oscillators. The book also contains additional articles published by the guest editor in this Symmetry journal. They are of course based on harmonic oscillators and/or two-by-two matrices. The subject of symmetry is based on exactly soluble problems in physics, and the physical theory is not soluble unless it is based on oscillators and/or two-by-two matrices. The authors of those two special issues were aware of this environment when they submitted their articles. This book could therefore serve as an example to illustrate this important aspect of symmetry problems in physics.

Fuzzy Mathematics

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ISBN: 9783038973225 9783038973232 Year: Pages: 286 DOI: 10.3390/books978-3-03897-323-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General) --- Mathematics
Added to DOAB on : 2018-11-28 11:26:53
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This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems.The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value.

Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century

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ISBN: 9783038977469 Year: Pages: 260 DOI: 10.3390/books978-3-03897-747-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Physics (General)
Added to DOAB on : 2019-04-05 11:17:10
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For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for non-commutative harmonic analysis, applied to locally-compact, non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring non-commutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.

Interactions between Group Theory, Symmetry and Cryptology

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ISBN: 9783039288021 / 9783039288038 Year: Pages: 164 DOI: 10.3390/books978-3-03928-803-8 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-06-09 16:38:57
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Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.

Carbohydrate Intake in Non-communicable Disease Prevention and Treatment

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ISBN: 9783038978183 9783038978190 Year: Pages: 156 DOI: 10.3390/books978-3-03897-819-0 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Biology --- Nutrition and Food Sciences
Added to DOAB on : 2019-04-25 16:37:17
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In 2011, carbohydrates provided 63% of the dietary energy intake to the world&rsquo;s population. Historically, carbohydrate-rich diets have been associated with good health and longevity but there has been a move away from traditional carbohydrate-rich diets, with refined carbohydrate taking much criticism for contributing to non-communicable disease. The aim of this Special Issue is to discuss the appropriate use of environmentally sustainable carbohydrate-rich foods in the modern diet in developing and developed countries in the context of prevention and treatment of non-communicable disease.

Solid Catalysts for the Upgrading of Renewable Sources

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ISBN: 9783038975724 Year: Pages: 226 DOI: 10.3390/books978-3-03897-573-1 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Chemistry (General) --- Science (General)
Added to DOAB on : 2019-04-05 11:07:22
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The use of solid catalysts for the upgrade of renewable sources gives the opportunity to combine the two main cores of green chemistry, that is, on the one hand, the set-up of sustainable processes and, on the other, the use of biomass-derived materials. Solid catalysts have taken on a leading role in traditional petrochemical processes and could represent a key tool in new biorefinery-driven technologies.

Health Promotion in Children and Adolescents through Sport and Physical Activities

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ISBN: 9783038978862 9783038978879 Year: Pages: 158 DOI: 10.3390/books978-3-03897-887-9 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Medicine (General) --- Sports Medicine
Added to DOAB on : 2019-06-26 08:44:06
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I made the important decision to manage a Special Issue, because I believe it to be extremely important to focus on children’s and adolescents’ physiological and psychological development. I aimed to collect research that investigates the role of physical activity and sport on physical and mental well-being, with a particular focus on practical implications, innovation, tools, and technique. This Special Issue, “Health Promotion in Children and Adolescents through Sport and Physical Activities” addresses pediatric exercise science as a key scientific discipline able to help future generations live longer and better. It is already clear that sedentariness and a low level of muscular strength and power significantly affects cognitive functions and daily relations, but it is interesting to understand the key determinants and how we can help practitioners better manage these concerns in their patients. Authors were invited to submit letters, original research papers, case studies, meta-analyses, and systematic reviews.

Innovative Geo-Information Tools for Governance

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ISBN: 9783039213375 9783039213382 Year: Pages: 186 DOI: 10.3390/books978-3-03921-338-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General)
Added to DOAB on : 2019-12-09 11:49:15
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In current times, highly complex and urgent policy problems—e.g., climate change, rapid urbanization, equitable access to key services, land rights, and massive human resettlement—challenge citizens, NGOs, private corporations, and governments at all levels. These policy problems, often called ‘wicked’, involve multiple causal factors, anticipated and unanticipated effects, as well as high levels of disagreement among stakeholders about the nature of the problem and the appropriateness of solutions. Given the wickedness of such policy problems, interdisciplinary and longitudinal research is required, integrating and harnessing the diverse skills and knowledge of urban planners, anthropologists, geographers, geo-information scientists, economists, and others. This Special Issue promotes innovative concepts, methods, and tools, as well as the role of geo-information, to help (1) analyze alternative policy solutions, (2) facilitate stakeholder dialogue, and (3) explore possibilities for tackling wicked problems related to climate change, rapid urbanization, equitable access to key services (such as water and health), land rights, and human resettlements in high-, middle-, and low-income countries in the North and South. Such integrative approaches can deepen our understanding of how different levels of government and governance reach consensus, despite diverging beliefs and preferences. Due to the particularly complex spatiotemporal characteristics of wicked policy problems, innovative concepts, alternative methods, and new geo-information tools play a significant role.

Youth Studies and Generations: Values, Practices and Discourses on Generations

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ISBN: 9783039283262 9783039283279 Year: Pages: 262 DOI: 10.3390/books978-3-03928-327-9 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Social Sciences --- Sociology --- Ethnology
Added to DOAB on : 2020-04-07 23:07:09
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There is currently much discourse about generations in the public sphere. A sequence of letters conflates generations and age cohorts born in the last few decades (generation “X”, “Y” or “Z”) as well as multiple categories are used to describe today’s young people as a generation that is distinct from its predecessors. Despite the popularity of generational labels in media, politics, or even academia, the use of generation as a conceptual tool in youth studies has been controversial. This Special Issue allows readers to better understand the key issues regarding the use of generation as a theoretical concept and/or as a social category in the field of youth studies, shedding light on the controversies, trends, and cautions that go through it.

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