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Hausdorff Calculus
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Book Synopsis Hausdorff Calculus by : Yingjie Liang
Download or read book Hausdorff Calculus written by Yingjie Liang and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-03-04 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the fundamental concepts, methods, and applications of Hausdorff calculus, with a focus on its applications in fractal systems. Topics such as the Hausdorff diffusion equation, Hausdorff radial basis function, Hausdorff derivative nonlinear systems, PDE modeling, statistics on fractals, etc. are discussed in detail. It is an essential reference for researchers in mathematics, physics, geomechanics, and mechanics.
Book Synopsis Hausdorff Calculus by : Yingjie Liang
Download or read book Hausdorff Calculus written by Yingjie Liang and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-03-04 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the fundamental concepts, methods, and applications of Hausdorff calculus, with a focus on its applications in fractal systems. Topics such as the Hausdorff diffusion equation, Hausdorff radial basis function, Hausdorff derivative nonlinear systems, PDE modeling, statistics on fractals, etc. are discussed in detail. It is an essential reference for researchers in mathematics, physics, geomechanics, and mechanics.
Download or read book Set Theory written by Felix Hausdorff and published by American Mathematical Soc.. This book was released on 2021-08-24 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is a translation into English of the Third Edition of the classic German language work Mengenlehre by Felix Hausdorff published in 1937. From the Preface (1937): “The present book has as its purpose an exposition of the most important theorems of the theory of sets, along with complete proofs, so that the reader should not find it necessary to go outside this book for supplementary details while, on the other hand, the book should enable him to undertake a more detailed study of the voluminous literature on the subject. The book does not presuppose any mathematical knowledge beyond the differential and integral calculus, but it does require a certain maturity in abstract reasoning; qualified college seniors and first year graduate students should have no difficulty in making the material their own … The mathematician will … find in this book some things that will be new to him, at least as regards formal presentation and, in particular, as regards the strengthening of theorems, the simplification of proofs, and the removal of unnecessary hypotheses.”
Book Synopsis Hausdorff Measures by : C. A. Rogers
Download or read book Hausdorff Measures written by C. A. Rogers and published by Cambridge University Press. This book was released on 1998-10-22 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: When it was first published this was the first general account of Hausdorff measures, a subject that has important applications in many fields of mathematics. There are three chapters: the first contains an introduction to measure theory, paying particular attention to the study of non-s-finite measures. The second develops the most general aspects of the theory of Hausdorff measures, and the third gives a general survey of applications of Hausdorff measures followed by detailed accounts of two special applications. This edition has a foreword by Kenneth Falconer outlining the developments in measure theory since this book first appeared. Based on lectures given by the author at University College London, this book is ideal for graduate mathematicians with no previous knowledge of the subject, but experts in the field will also want a copy for their shelves.
Book Synopsis Paradoxes of Measures and Dimensions Originating in Felix Hausdorff's Ideas by : Janusz Czy?
Download or read book Paradoxes of Measures and Dimensions Originating in Felix Hausdorff's Ideas written by Janusz Czy? and published by World Scientific. This book was released on 1994 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, many ideas by Felix Hausdorff are described and contemporary mathematical theories stemming from them are sketched.
Book Synopsis Paradoxes of Measures and Dimensions Originating in Felix Hausdorff's Ideas by : Janusz Czyz
Download or read book Paradoxes of Measures and Dimensions Originating in Felix Hausdorff's Ideas written by Janusz Czyz and published by World Scientific. This book was released on 1994-01-14 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, many ideas by Felix Hausdorff are described and contemporary mathematical theories stemming from them are sketched. Contents:The Paradox of the SphereInaccessible Numbers and the Hierarchal Structure of Set TheoryThe Hausdorff Measures, Hausdorff Dimensions and FractalsThe Baker-Campbell-Hausdorff FormulaHausdorff MatricesAppendixReferences Readership: Mathematicians, logicians and mathematical physicists. Keywords:Banach-Tarski Paradox;Inaccessible Cardinals;Large Cardinals;Hausdorff Dimension;Fractal;Baker-Campbell-Hausdorff Formula;Lie Superalgebra;Lie Supergroup;Hausdorfd Matrix;Hausdorff Summation;Young-Hausdorff InequalityReview: “Each chapter concludes with an extensive bibliography on the subject. The book should be accessible to mathematicians, pure and applied, as well as to theoretical physicists.” Mathematics Abstracts
Book Synopsis The Exact Hausdorff Dimension in Random Recursive Constructions by : Siegfried Graf
Download or read book The Exact Hausdorff Dimension in Random Recursive Constructions written by Siegfried Graf and published by American Mathematical Soc.. This book was released on 1988 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hausdorff Approximations by : Bl. Sendov
Download or read book Hausdorff Approximations written by Bl. Sendov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point a1Ie.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Book Synopsis Fundamentals of Mathematical Analysis by : Adel N. Boules
Download or read book Fundamentals of Mathematical Analysis written by Adel N. Boules and published by Oxford University Press. This book was released on 2021-03-04 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Mathematical Analysis explores real and functional analysis with a substantial component on topology. The three leading chapters furnish background information on the real and complex number fields, a concise introduction to set theory, and a rigorous treatment of vector spaces. Fundamentals of Mathematical Analysis is an extensive study of metric spaces, including the core topics of completeness, compactness and function spaces, with a good number of applications. The later chapters consist of an introduction to general topology, a classical treatment of Banach and Hilbert spaces, the elements of operator theory, and a deep account of measure and integration theories. Several courses can be based on the book. This book is suitable for a two-semester course on analysis, and material can be chosen to design one-semester courses on topology or real analysis. It is designed as an accessible classical introduction to the subject and aims to achieve excellent breadth and depth and contains an abundance of examples and exercises. The topics are carefully sequenced, the proofs are detailed, and the writing style is clear and concise. The only prerequisites assumed are a thorough understanding of undergraduate real analysis and linear algebra, and a degree of mathematical maturity.
Book Synopsis Fourier Analysis and Hausdorff Dimension by : Pertti Mattila
Download or read book Fourier Analysis and Hausdorff Dimension written by Pertti Mattila and published by Cambridge University Press. This book was released on 2015-07-22 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past two decades there has been active interplay between geometric measure theory and Fourier analysis. This book describes part of that development, concentrating on the relationship between the Fourier transform and Hausdorff dimension. The main topics concern applications of the Fourier transform to geometric problems involving Hausdorff dimension, such as Marstrand type projection theorems and Falconer's distance set problem, and the role of Hausdorff dimension in modern Fourier analysis, especially in Kakeya methods and Fourier restriction phenomena. The discussion includes both classical results and recent developments in the area. The author emphasises partial results of important open problems, for example, Falconer's distance set conjecture, the Kakeya conjecture and the Fourier restriction conjecture. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.
Book Synopsis Hausdorff on Ordered Sets by : Felix Hausdorff
Download or read book Hausdorff on Ordered Sets written by Felix Hausdorff and published by American Mathematical Soc.. This book was released on with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Georg Cantor, the founder of set theory, published his last paper on sets in 1897. In 1900, David Hilbert made Cantor's Continuum Problem and the challenge of well-ordering the real numbers the first problem of his famous lecture at the international congress in Paris. Thus, as the nineteenth century came to a close and the twentieth century began, Cantor's work was finally receiving its due and Hilbert had made one of Cantor's most important conjectures his number one problem. It was time for the second generation of Cantorians to emerge. Foremost among this group were Ernst Zermelo and Felix Hausdorff. Zermelo isolated the Choice Principle, proved that every set could be well-ordered, and axiomatized the concept of set. He became the father of abstract set theory. Hausdorff eschewed foundations and developed set theory as a branch of mathematics worthy of study in its own right, capable of supporting both general topology and measure theory. He is recognized as the era's leading Cantorian. Hausdorff published seven articles in set theory during the period 1901-1909, mostly about ordered sets. This volume contains translations of these papers with accompanying introductory essays. They are highly accessible, historically significant works, important not only for set theory, but also for model theory, analysis and algebra. This book is suitable for graduate students and researchers interested in set theory and the history of mathematics. Also available from the AMS by Felix Hausdorff are the classic work, Grundzuge der Mengenlehre, and its English translation, Set Theory, as Volume 69 and Volume 119 in the AMS Chelsea Publishing series. Information for our distributors: Copublished with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
Book Synopsis Fractals and Fractional Calculus in Continuum Mechanics by : Alberto Carpinteri
Download or read book Fractals and Fractional Calculus in Continuum Mechanics written by Alberto Carpinteri and published by Springer. This book was released on 2014-05-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is characterized by the illustration of cases of fractal, self-similar and multi-scale structures taken from the mechanics of solid and porous materials, which have a technical interest. In addition, an accessible and self-consistent treatment of the mathematical technique of fractional calculus is provided, avoiding useless complications.
Book Synopsis Multi-Variable Calculus by : Yunzhi Zou
Download or read book Multi-Variable Calculus written by Yunzhi Zou and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-03-09 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a concise yet complete calculus textbook covering all essential topics in multi-variable calculus, including geometry in three-dimensional space, partial derivatives, maximum/minimum, multiple integrals and vector calculus as well as a chapter for ODE. All the chapters are constructed in a logical way to outline the essence of each topic and to address potential difficulties arising from learning.
Book Synopsis Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers by : Cédric Arhancet
Download or read book Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers written by Cédric Arhancet and published by Springer Nature. This book was released on 2022-05-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on recent research in noncommutative harmonic analysis treats the Lp boundedness of Riesz transforms associated with Markovian semigroups of either Fourier multipliers on non-abelian groups or Schur multipliers. The detailed study of these objects is then continued with a proof of the boundedness of the holomorphic functional calculus for Hodge–Dirac operators, thereby answering a question of Junge, Mei and Parcet, and presenting a new functional analytic approach which makes it possible to further explore the connection with noncommutative geometry. These Lp operations are then shown to yield new examples of quantum compact metric spaces and spectral triples. The theory described in this book has at its foundation one of the great discoveries in analysis of the twentieth century: the continuity of the Hilbert and Riesz transforms on Lp. In the works of Lust-Piquard (1998) and Junge, Mei and Parcet (2018), it became apparent that these Lp operations can be formulated on Lp spaces associated with groups. Continuing these lines of research, the book provides a self-contained introduction to the requisite noncommutative background. Covering an active and exciting topic which has numerous connections with recent developments in noncommutative harmonic analysis, the book will be of interest both to experts in no-commutative Lp spaces and analysts interested in the construction of Riesz transforms and Hodge–Dirac operators.
Book Synopsis Bulletin of the American Mathematical Society by : American Mathematical Society
Download or read book Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1908 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bulletin (new Series) of the American Mathematical Society by :
Download or read book Bulletin (new Series) of the American Mathematical Society written by and published by . This book was released on 1908 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt:
