Advances In Non Archimedean Analysis And Applications
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Advances In Non Archimedean Analysis And Applications
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Author : W. A. Zúñiga-Galindo
language : en
Publisher: Springer Nature
Release Date : 2021-12-02
Advances In Non Archimedean Analysis And Applications written by W. A. Zúñiga-Galindo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-02 with Mathematics categories.
This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its applications. Featuring new techniques developed by leading experts in the field, it highlights the relevance and depth of this important area of mathematics, in particular its expanding reach into the physical, biological, social, and computational sciences as well as engineering and technology. In the last forty years the connections between non-Archimedean mathematics and disciplines such as physics, biology, economics and engineering, have received considerable attention. Ultrametric spaces appear naturally in models where hierarchy plays a central role – a phenomenon known as ultrametricity. In the 80s, the idea of using ultrametric spaces to describe the states of complex systems, with a natural hierarchical structure, emerged in the works of Fraunfelder, Parisi, Stein and others. A central paradigm in the physics of certain complex systems – for instance, proteins – asserts that the dynamics of such a system can be modeled as a random walk on the energy landscape of the system. To construct mathematical models, the energy landscape is approximated by an ultrametric space (a finite rooted tree), and then the dynamics of the system is modeled as a random walk on the leaves of a finite tree. In the same decade, Volovich proposed using ultrametric spaces in physical models dealing with very short distances. This conjecture has led to a large body of research in quantum field theory and string theory. In economics, the non-Archimedean utility theory uses probability measures with values in ordered non-Archimedean fields. Ultrametric spaces are also vital in classification and clustering techniques. Currently, researchers are actively investigating the following areas: p-adic dynamical systems, p-adic techniques in cryptography, p-adic reaction-diffusion equations and biological models, p-adic models in geophysics, stochastic processes in ultrametric spaces, applications of ultrametric spaces in data processing, and more. This contributed volume gathers the latest theoretical developments as well as state-of-the art applications of non-Archimedean analysis. It covers non-Archimedean and non-commutative geometry, renormalization, p-adic quantum field theory and p-adic quantum mechanics, as well as p-adic string theory and p-adic dynamics. Further topics include ultrametric bioinformation, cryptography and bioinformatics in p-adic settings, non-Archimedean spacetime, gravity and cosmology, p-adic methods in spin glasses, and non-Archimedean analysis of mental spaces. By doing so, it highlights new avenues of research in the mathematical sciences, biosciences and computational sciences.
Advances In Non Archimedean Analysis And Applications
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Author : W. A. Zúñiga-Galindo
language : en
Publisher:
Release Date : 2021
Advances In Non Archimedean Analysis And Applications written by W. A. Zúñiga-Galindo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its applications. Featuring new techniques developed by leading experts in the field, it highlights the relevance and depth of this important area of mathematics, in particular its expanding reach into the physical, biological, social, and computational sciences as well as engineering and technology. In the last forty years the connections between non-Archimedean mathematics and disciplines such as physics, biology, economics and engineering, have received considerable attention. Ultrametric spaces appear naturally in models where hierarchy plays a central role - a phenomenon known as ultrametricity. In the 80s, the idea of using ultrametric spaces to describe the states of complex systems, with a natural hierarchical structure, emerged in the works of Fraunfelder, Parisi, Stein and others. A central paradigm in the physics of certain complex systems - for instance, proteins - asserts that the dynamics of such a system can be modeled as a random walk on the energy landscape of the system. To construct mathematical models, the energy landscape is approximated by an ultrametric space (a finite rooted tree), and then the dynamics of the system is modeled as a random walk on the leaves of a finite tree. In the same decade, Volovich proposed using ultrametric spaces in physical models dealing with very short distances. This conjecture has led to a large body of research in quantum field theory and string theory. In economics, the non-Archimedean utility theory uses probability measures with values in ordered non-Archimedean fields. Ultrametric spaces are also vital in classification and clustering techniques. Currently, researchers are actively investigating the following areas: p-adic dynamical systems, p-adic techniques in cryptography, p-adic reaction-diffusion equations and biological models, p-adic models in geophysics, stochastic processes in ultrametric spaces, applications of ultrametric spaces in data processing, and more. This contributed volume gathers the latest theoretical developments as well as state-of-the art applications of non-Archimedean analysis. It covers non-Archimedean and non-commutative geometry, renormalization, p-adic quantum field theory and p-adic quantum mechanics, as well as p-adic string theory and p-adic dynamics. Further topics include ultrametric bioinformation, cryptography and bioinformatics in p-adic settings, non-Archimedean spacetime, gravity and cosmology, p-adic methods in spin glasses, and non-Archimedean analysis of mental spaces. By doing so, it highlights new avenues of research in the mathematical sciences, biosciences and computational sciences.
Advances In Non Archimedean Analysis
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Author : Helge Glöckner
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-05-20
Advances In Non Archimedean Analysis written by Helge Glöckner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-20 with Mathematics categories.
This volume contains the Proceedings of the 13th International Conference on p-adic Functional Analysis, held from August 12–16, 2014, at the University of Paderborn, Paderborn, Germany. The articles included in this book feature recent developments in various areas of non-Archimedean analysis, non-Archimedean functional analysis, representation theory, number theory, non-Archimedean dynamical systems and applications. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
Nonarchimedean Functional Analysis
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Author : Peter Schneider
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Nonarchimedean Functional Analysis written by Peter Schneider and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book grew out of a course which I gave during the winter term 1997/98 at the Universitat Munster. The course covered the material which here is presented in the first three chapters. The fourth more advanced chapter was added to give the reader a rather complete tour through all the important aspects of the theory of locally convex vector spaces over nonarchimedean fields. There is one serious restriction, though, which seemed inevitable to me in the interest of a clear presentation. In its deeper aspects the theory depends very much on the field being spherically complete or not. To give a drastic example, if the field is not spherically complete then there exist nonzero locally convex vector spaces which do not have a single nonzero continuous linear form. Although much progress has been made to overcome this problem a really nice and complete theory which to a large extent is analogous to classical functional analysis can only exist over spherically complete field8. I therefore allowed myself to restrict to this case whenever a conceptual clarity resulted. Although I hope that thi8 text will also be useful to the experts as a reference my own motivation for giving that course and writing this book was different. I had the reader in mind who wants to use locally convex vector spaces in the applications and needs a text to quickly gra8p this theory.
Advances In Ultrametric Analysis
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Author : Alain Escassut
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-03-26
Advances In Ultrametric Analysis written by Alain Escassut and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-26 with Mathematics categories.
Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of -adic series, rational maps on the projective line over , non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, -modules with a convex base, non-compact Trace class operators and Schatten-class operators in -adic Hilbert spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in Levi-Civita fields, ultrametric spectra of commutative non-unital Banach rings, classes of non-Archimedean Köthe spaces, -adic Nevanlinna theory and applications, and sub-coordinate representation of -adic functions. Moreover, a paper on the history of -adic analysis with a comparative summary of non-Archimedean fields is presented. Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
Advances In Ultrametric Analysis
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Author : Khodr Shamseddine
language : en
Publisher: American Mathematical Soc.
Release Date : 2013
Advances In Ultrametric Analysis written by Khodr Shamseddine and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
This volume contains papers based on lectures given at the 12th International Conference on p-adic Functional Analysis, which was held at the University of Manitoba on July 2-6, 2012. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
Mathematics Without Boundaries
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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2014-09-17
Mathematics Without Boundaries written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-17 with Mathematics categories.
The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.
Catherine Beneteau Alberto A Condori Constanze Liaw William T Ross And Alan A Sola
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Author : Catherine Bénéteau:
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-12-22
Catherine Beneteau Alberto A Condori Constanze Liaw William T Ross And Alan A Sola written by Catherine Bénéteau: and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-22 with Mathematics categories.
This volume contains the Proceedings of the Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, held from June 29–July 3, 2015, at the Institut Mittag-Leffler, Djursholm, Sweden. The conference brought together experienced researchers and promising young mathematicians from many countries to discuss recent progress made in function theory, model spaces, completeness problems, and Carleson measures. This volume contains articles covering cutting-edge research questions, as well as longer survey papers and a report on the problem session that contains a collection of attractive open problems in complex and harmonic analysis.
Causality The P Adic Theory
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Author : Vladimir Anashin
language : en
Publisher: Springer Nature
Release Date : 2025-04-24
Causality The P Adic Theory written by Vladimir Anashin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-24 with Mathematics categories.
This book delves into the mathematical theory of causal functions over discrete time, offering a fresh perspective on causality beyond its philosophical roots. By exploring the intricate world of p-adic 1-Lipschitz functions, this volume bridges the gap between abstract mathematical concepts and their practical applications in fields such as automata theory, combinatorics, and applied computer science. Readers will uncover a wealth of insights as the book investigates key topics including the nature of causal functions, the role of discrete time in causality, and the application of non-Archimedean metrics. With contributions from eminent scholars, this work invites readers to ponder critical questions: How do we define causality in mathematical terms? What are the implications of using p-adic analysis in understanding complex systems especially quantum ones? The author's unique approach makes this book an essential read for anyone interested in the intersection of mathematics and real-world applications. Ideal for researchers and practitioners with a background in mathematics, computer science, or physics, this book is a valuable resource for those seeking to deepen their understanding of causal functions. Whether you're a scholar exploring theoretical perspectives or a professional looking to apply these concepts practically, this volume offers a comprehensive guide to navigating the complexities of causality. Part of an ongoing series on advanced mathematical theories, it is an indispensable addition to any academic library.
Automated Reasoning
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Author : Christoph Benzmüller
language : en
Publisher: Springer Nature
Release Date : 2024-07-01
Automated Reasoning written by Christoph Benzmüller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-01 with Computers categories.
Infotext (nur auf Basis des Vorgängers): This two-volume set of LNAI 14739-14740 constitute the proceedings of the 12th International Joint Conference on Automated Reasoning, IJCAR 2024, held in Nancy, France, during July 3-6, 2024. The 39 full research papers and 6 short papers presented in this book were carefully reviewed and selected from 115 submissions. The papers focus on the following topics: theorem proving and tools; SAT, SMT and Quantifier Elimination; Intuitionistic Logics and Modal Logics; Calculi, Proof Theory and Decision Procedures; and Unification, Rewriting and Computational Models. This book is open access.