Horizons Of Fractal Geometry And Complex Dimensions

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Horizons Of Fractal Geometry And Complex Dimensions
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Author : Robert G. Niemeyer
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-26
Horizons Of Fractal Geometry And Complex Dimensions written by Robert G. Niemeyer 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 2019-06-26 with Mathematics categories.
This volume contains the proceedings of the 2016 Summer School on Fractal Geometry and Complex Dimensions, in celebration of Michel L. Lapidus's 60th birthday, held from June 21–29, 2016, at California Polytechnic State University, San Luis Obispo, California. The theme of the contributions is fractals and dynamics and content is split into four parts, centered around the following themes: Dimension gaps and the mass transfer principle, fractal strings and complex dimensions, Laplacians on fractal domains and SDEs with fractal noise, and aperiodic order (Delone sets and tilings).
Horizons Of Fractal Geometry And Complex Dimensions
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Author : Robert G. Niemeyer
language : en
Publisher:
Release Date : 2019
Horizons Of Fractal Geometry And Complex Dimensions written by Robert G. Niemeyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Fractals categories.
This volume contains the proceedings of the 2016 Summer School on Fractal Geometry and Complex Dimensions, in celebration of Michel L. Lapidus's 60th birthday, held from June 21-29, 2016, at California Polytechnic State University, San Luis Obispo, California. The theme of the contributions is fractals and dynamics and content is split into four parts, centered around the following themes: Dimension gaps and the mass transfer principle, fractal strings and complex dimensions, Laplacians on fractal domains and SDEs with fractal noise, and aperiodic order (Delone sets and tilings).
Analysis Probability And Mathematical Physics On Fractals
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Author : Patricia Alonso Ruiz
language : en
Publisher: World Scientific
Release Date : 2020-02-26
Analysis Probability And Mathematical Physics On Fractals written by Patricia Alonso Ruiz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-26 with Mathematics categories.
In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.
An Invitation To Fractal Geometry
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Author : Michel L. Lapidus
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-31
An Invitation To Fractal Geometry written by Michel L. Lapidus and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-31 with Mathematics categories.
This book offers a comprehensive exploration of fractal dimensions, self-similarity, and fractal curves. Aimed at undergraduate and graduate students, postdocs, mathematicians, and scientists across disciplines, this text requires minimal prerequisites beyond a solid foundation in undergraduate mathematics. While fractal geometry may seem esoteric, this book demystifies it by providing a thorough introduction to its mathematical underpinnings and applications. Complete proofs are provided for most of the key results, and exercises of different levels of difficulty are proposed throughout the book. Key topics covered include the Hausdorff metric, Hausdorff measure, and fractal dimensions such as Hausdorff and Minkowski dimensions. The text meticulously constructs and analyzes Hausdorff measure, offering readers a deep understanding of its properties. Through emblematic examples like the Cantor set, the Sierpinski gasket, the Koch snowflake curve, and the Weierstrass curve, readers are introduced to self-similar sets and their construction via the iteration of contraction mappings. The book also sets the stage for the advanced theory of complex dimensions and fractal drums by gently introducing it via a variety of classical examples, including well-known fractal curves. By intertwining historical context with rigorous mathematical exposition, this book serves as both a stand-alone resource and a gateway to deeper explorations in fractal geometry.
Advances In Complex Geometry
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Author : Yanir A. Rubinstein
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-26
Advances In Complex Geometry written by Yanir A. Rubinstein 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 2019-08-26 with Mathematics categories.
This volume contains contributions from speakers at the 2015–2018 joint Johns Hopkins University and University of Maryland Complex Geometry Seminar. It begins with a survey article on recent developments in pluripotential theory and its applications to Kähler–Einstein metrics and continues with articles devoted to various aspects of the theory of complex manifolds and functions on such manifolds.
Exploring Scale Symmetry
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Author : Thomas Lowe
language : en
Publisher: World Scientific
Release Date : 2021-02-18
Exploring Scale Symmetry written by Thomas Lowe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-18 with Mathematics categories.
Welcome to the world of scale symmetry, the last elementary symmetry and the least explored!Find out how this long-neglected element transforms the traditional geometry of lines and planes into a rich landscape of trees, craggy mountains and rolling oceans.Enjoy a visual exploration through the intricate and elaborate structures of scale-symmetric geometry. See unique fractals, Mandelboxes, and automata and physical behaviors. Take part in the author's forage into the lesser-trodden regions of this landscape, and discover unusual and attractive specimens!You will also be provided with all the tools needed to recreate the structures yourself.Every example is new and developed by the author, and is chosen because it pushes the field of scale-symmetric geometry into a scarcely explored region. The results are complex and intricate but the method of generation is often simple, which allows it to be presented graphically without depending on too much mathematical syntax. If you are interested in the mathematics, science and art of scale symmetry, then read on!This is also a book for programmers and for hobbyists: those of us who like to dabble with procedural imagery and see where it leads.
Motivic Homotopy Theory And Refined Enumerative Geometry
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Author : Federico Binda
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-03-09
Motivic Homotopy Theory And Refined Enumerative Geometry written by Federico Binda 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 2020-03-09 with Education categories.
This volume contains the proceedings of the Workshop on Motivic Homotopy Theory and Refined Enumerative Geometry, held from May 14–18, 2018, at the Universität Duisburg-Essen, Essen, Germany. It constitutes an accessible yet swift introduction to a new and active area within algebraic geometry, which connects well with classical intersection theory. Combining both lecture notes aimed at the graduate student level and research articles pointing towards the manifold promising applications of this refined approach, it broadly covers refined enumerative algebraic geometry.
Contributions In Algebra And Algebraic Geometry
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Author : Shrikrishna G. Dani
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-10-07
Contributions In Algebra And Algebraic Geometry written by Shrikrishna G. Dani 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 2019-10-07 with Education categories.
This volume contains the proceedings of the International Conference on Algebra, Discrete Mathematics and Applications, held from December 9–11, 2017, at Dr. Babasaheb Ambedkar Marathwada University, Aurangabad (Maharashtra), India. Contemporary topics of research in algebra and its applications to algebraic geometry, Lie groups, algebraic combinatorics, and representation theory are covered. The articles are devoted to Leavitt path algebras, roots of elements in Lie groups, Hilbert's Nullstellensatz, mixed multiplicities of ideals, singular matrices, rings of integers, injective hulls of modules, representations of linear, symmetric groups and Lie algebras, the algebra of generic matrices and almost injective modules.
Topology And Geometry Of Biopolymers
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Author : Erica Flapan
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-03-05
Topology And Geometry Of Biopolymers written by Erica Flapan 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 2020-03-05 with Education categories.
This book contains the proceedings of the AMS Special Session on Topology of Biopolymers, held from April 21–22, 2018, at Northeastern University, Boston, MA. The papers cover recent results on the topology and geometry of DNA and protein knotting using techniques from knot theory, spatial graph theory, differential geometry, molecular simulations, and laboratory experimentation. They include current work on the following topics: the density and supercoiling of DNA minicircles; the dependence of DNA geometry on its amino acid sequence; random models of DNA knotting; topological models of DNA replication and recombination; theories of how and why proteins knot; topological and geometric approaches to identifying entanglements in proteins; and topological and geometric techniques to predict protein folding rates. All of the articles are written as surveys intended for a broad interdisciplinary audience with a minimum of prerequisites. In addition to being a useful reference for experts, this book also provides an excellent introduction to the fast-moving field of topology and geometry of biopolymers.
Advances In Harmonic Analysis And Partial Differential Equations
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Author : Donatella Danielli
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-04-09
Advances In Harmonic Analysis And Partial Differential Equations written by Donatella Danielli 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 2020-04-09 with Education categories.
This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Partial Differential Equations, held from April 21–22, 2018, at Northeastern University, Boston, Massachusetts. The book features a series of recent developments at the interface between harmonic analysis and partial differential equations and is aimed toward the theoretical and applied communities of researchers working in real, complex, and harmonic analysis, partial differential equations, and their applications. The topics covered belong to the general areas of the theory of function spaces, partial differential equations of elliptic, parabolic, and dissipative types, geometric optics, free boundary problems, and ergodic theory, and the emphasis is on a host of new concepts, methods, and results.