Ultrametric Pseudodifferential Equations And Applications
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Ultrametric Pseudodifferential Equations And Applications
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Author : Andreĭ I︠U︡rʹevich Khrennikov
language : en
Publisher: Cambridge University Press
Release Date : 2018-04-26
Ultrametric Pseudodifferential Equations And Applications written by Andreĭ I︠U︡rʹevich Khrennikov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-26 with Mathematics categories.
Provides a novel interdisciplinary perspective on the state of the art of ultrametric pseudodifferential equations and their applications.
Mathematical Morphology And Its Applications To Signal And Image Processing
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Author : Bernhard Burgeth
language : en
Publisher: Springer
Release Date : 2019-06-19
Mathematical Morphology And Its Applications To Signal And Image Processing written by Bernhard Burgeth and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-19 with Computers categories.
This book contains the refereed proceedings of the 14th International Symposium on Mathematical Morphology, ISMM 2019, held in Saarbrücken, Germany, in July 2019. The 40 revised full papers presented together with one invited talk were carefully reviewed and selected from 54 submissions. The papers are organized in topical sections on Theory, Discrete Topology and Tomography, Trees and Hierarchies, Multivariate Morphology, Computational Morphology, Machine Learning, Segmentation, Applications in Engineering, and Applications in (Bio)medical Imaging.
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.
Pseudodifferential Equations Over Non Archimedean Spaces
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Author : W. A. Zúñiga-Galindo
language : en
Publisher: Springer
Release Date : 2017-01-08
Pseudodifferential Equations Over Non Archimedean Spaces written by W. A. Zúñiga-Galindo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-08 with Mathematics categories.
Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applications of p-adic wavelets.
Compound Renewal Processes
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Author : A. A. Borovkov
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-30
Compound Renewal Processes written by A. A. Borovkov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-30 with Mathematics categories.
Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.
Strongly Regular Graphs
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Author : Andries E. Brouwer
language : en
Publisher:
Release Date : 2022-01-13
Strongly Regular Graphs written by Andries E. Brouwer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-13 with Language Arts & Disciplines categories.
This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.
Coxeter Bialgebras
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Author : Marcelo Aguiar
language : en
Publisher: Cambridge University Press
Release Date : 2022-11-17
Coxeter Bialgebras written by Marcelo Aguiar and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-17 with Mathematics categories.
The goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimonoid and connect the two notions via a family of functors called Fock functors. These generalize similar functors connecting Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph opens a new chapter in Coxeter theory as well as in Hopf theory, connecting the two. It also relates fruitfully to many other areas of mathematics such as discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. It is carefully written, with effective use of tables, diagrams, pictures, and summaries. It will be of interest to students and researchers alike.
Higher Special Functions
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Author : Wolfgang Lay
language : en
Publisher: Cambridge University Press
Release Date : 2024-05-23
Higher Special Functions written by Wolfgang Lay and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-23 with Mathematics categories.
Higher special functions emerge from boundary eigenvalue problems of Fuchsian differential equations with more than three singularities. This detailed reference provides solutions for singular boundary eigenvalue problems of linear ordinary differential equations of second order, exploring previously unknown methods for finding higher special functions. Starting from the fact that it is the singularities of a differential equation that determine the local, as well as the global, behaviour of its solutions, the author develops methods that are both new and efficient and lead to functional relationships that were previously unknown. All the developments discussed are placed within their historical context, allowing the reader to trace the roots of the theory back through the work of many generations of great mathematicians. Particular attention is given to the work of George Cecil Jaffé, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.
Equivalents Of The Riemann Hypothesis Volume 3 Further Steps Towards Resolving The Riemann Hypothesis
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Author : Kevin Broughan
language : en
Publisher: Cambridge University Press
Release Date : 2023-10-12
Equivalents Of The Riemann Hypothesis Volume 3 Further Steps Towards Resolving The Riemann Hypothesis written by Kevin Broughan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-12 with Mathematics categories.
The Riemann hypothesis (RH) may be the most important outstanding problem in mathematics. This third volume on equivalents to RH comprehensively presents recent results of Nicolas, Rogers–Tao–Dobner, Polymath15, and Matiyasevich. Particularly interesting are derivations which show, assuming all zeros on the critical line are simple, that RH is decidable. Also included are classical Pólya–Jensen equivalence and related developments of Ono et al. Extensive appendices highlight key background results, most of which are proved. The book is highly accessible, with definitions repeated, proofs split logically, and graphical visuals. It is ideal for mathematicians wishing to update their knowledge, logicians, and graduate students seeking accessible number theory research problems. The three volumes can be read mostly independently. Volume 1 presents classical and modern arithmetic RH equivalents. Volume 2 covers equivalences with a strong analytic orientation. Volume 3 includes further arithmetic and analytic equivalents plus new material on RH decidability.
Equivalents Of The Riemann Hypothesis
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Author : Kevin Alfred Broughan
language : en
Publisher: Cambridge University Press
Release Date : 2017
Equivalents Of The Riemann Hypothesis written by Kevin Alfred Broughan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Riemann hypothesis categories.
This three-volume work presents the main known equivalents to the Riemann hypothesis, perhaps the most important problem in mathematics. Volume 3 covers new arithmetic and analytic equivalences from numerous studies in the field, such as Rogers and Tao, and presents derivations which show whether the Riemann hypothesis is decidable.