Horizons Of Fractal Geometry And Complex Dimensions

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Horizons of Fractal Geometry and Complex Dimensions

Robert G. Niemeyer
Horizons of Fractal Geometry and Complex Dimensions Book PDF

Author : Robert G. Niemeyer
Publisher : Unknown
Page : 320 pages
File Size : 46,5 Mb
Release : 2019
Category : Fractals
ISBN : 1470453150

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Horizons of Fractal Geometry and Complex Dimensions by Robert G. Niemeyer Pdf

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

Robert G. Niemeyer,Erin P. J. Pearse,John A. Rock,Tony Samuel
Horizons of Fractal Geometry and Complex Dimensions Book PDF

Author : Robert G. Niemeyer,Erin P. J. Pearse,John A. Rock,Tony Samuel
Publisher : American Mathematical Soc.
Page : 302 pages
File Size : 53,8 Mb
Release : 2019-06-26
Category : Fractals
ISBN : 9781470435813

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Horizons of Fractal Geometry and Complex Dimensions by Robert G. Niemeyer,Erin P. J. Pearse,John A. Rock,Tony Samuel Pdf

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).

Fractal Geometry and Number Theory

Michel L. Lapidus,Machiel van Frankenhuysen
Fractal Geometry and Number Theory Book PDF

Author : Michel L. Lapidus,Machiel van Frankenhuysen
Publisher : Springer Science & Business Media
Page : 277 pages
File Size : 53,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461253143

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Fractal Geometry and Number Theory by Michel L. Lapidus,Machiel van Frankenhuysen Pdf

A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B.) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which form a sequence which we assume to be infinite. Important information about the geometry of . c is contained in its geometric zeta function (c(8) = L lj. j=l 2 Introduction We assume throughout that this function has a suitable meromorphic ex tension. The central notion of this book, the complex dimensions of a fractal string . c, is defined as the poles of the meromorphic extension of (c.

Analysis, Probability And Mathematical Physics On Fractals

Patricia Alonso Ruiz,Joe Po-chou Chen,Luke G Rogers,Alexander Teplyaev
Analysis Probability And Mathematical Physics On Fractals Book PDF

Author : Patricia Alonso Ruiz,Joe Po-chou Chen,Luke G Rogers,Alexander Teplyaev
Publisher : World Scientific
Page : 594 pages
File Size : 54,5 Mb
Release : 2020-02-26
Category : Mathematics
ISBN : 9789811215544

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Analysis, Probability And Mathematical Physics On Fractals by Patricia Alonso Ruiz,Joe Po-chou Chen,Luke G Rogers,Alexander Teplyaev Pdf

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.

Fractal Geometry, Complex Dimensions and Zeta Functions

Michel L. Lapidus,Machiel van Frankenhuijsen
Fractal Geometry Complex Dimensions and Zeta Functions Book PDF

Author : Michel L. Lapidus,Machiel van Frankenhuijsen
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 42,5 Mb
Release : 2007-08-08
Category : Mathematics
ISBN : 9780387352084

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Fractal Geometry, Complex Dimensions and Zeta Functions by Michel L. Lapidus,Machiel van Frankenhuijsen Pdf

Number theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to apply to the geometric, spectral and dynamic zeta functions associated with a fractal.

Advances in Complex Geometry

Yanir A. Rubinstein,Bernard Shiffman
Advances in Complex Geometry Book PDF

Author : Yanir A. Rubinstein,Bernard Shiffman
Publisher : American Mathematical Soc.
Page : 259 pages
File Size : 42,6 Mb
Release : 2019-08-26
Category : Geometry
ISBN : 9781470443337

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Advances in Complex Geometry by Yanir A. Rubinstein,Bernard Shiffman Pdf

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

Thomas Lowe
Exploring Scale Symmetry Book PDF

Author : Thomas Lowe
Publisher : World Scientific
Page : 253 pages
File Size : 55,9 Mb
Release : 2021-02-18
Category : Mathematics
ISBN : 9789813278561

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Exploring Scale Symmetry by Thomas Lowe Pdf

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.

Topology and Geometry of Biopolymers

Erica Flapan,Helen Wong
Topology and Geometry of Biopolymers Book PDF

Author : Erica Flapan,Helen Wong
Publisher : American Mathematical Soc.
Page : 246 pages
File Size : 42,8 Mb
Release : 2020-03-05
Category : Education
ISBN : 9781470448400

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Topology and Geometry of Biopolymers by Erica Flapan,Helen Wong Pdf

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.

Motivic Homotopy Theory and Refined Enumerative Geometry

Federico Binda,Marc Levine,Manh Toan Nguyen,Oliver Röndigs
Motivic Homotopy Theory and Refined Enumerative Geometry Book PDF

Author : Federico Binda,Marc Levine,Manh Toan Nguyen,Oliver Röndigs
Publisher : American Mathematical Soc.
Page : 267 pages
File Size : 40,9 Mb
Release : 2020-03-09
Category : Education
ISBN : 9781470448981

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Motivic Homotopy Theory and Refined Enumerative Geometry by Federico Binda,Marc Levine,Manh Toan Nguyen,Oliver Röndigs Pdf

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

Shrikrishna G. Dani,Surender K. Jain,Jugal K. Verma,Meenakshi P. Wasadikar
Contributions in Algebra and Algebraic Geometry Book PDF

Author : Shrikrishna G. Dani,Surender K. Jain,Jugal K. Verma,Meenakshi P. Wasadikar
Publisher : American Mathematical Soc.
Page : 147 pages
File Size : 47,9 Mb
Release : 2019-10-07
Category : Education
ISBN : 9781470447359

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Contributions in Algebra and Algebraic Geometry by Shrikrishna G. Dani,Surender K. Jain,Jugal K. Verma,Meenakshi P. Wasadikar Pdf

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.

K-theory in Algebra, Analysis and Topology

Guillermo Cortiñas,Charles A. Weibel
K theory in Algebra Analysis and Topology Book PDF

Author : Guillermo Cortiñas,Charles A. Weibel
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 49,6 Mb
Release : 2024-07-02
Category : Education
ISBN : 9781470450267

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K-theory in Algebra, Analysis and Topology by Guillermo Cortiñas,Charles A. Weibel Pdf

This volume contains the proceedings of the ICM 2018 satellite school and workshop K-theory conference in Argentina. The school was held from July 16–20, 2018, in La Plata, Argentina, and the workshop was held from July 23–27, 2018, in Buenos Aires, Argentina. The volume showcases current developments in K-theory and related areas, including motives, homological algebra, index theory, operator algebras, and their applications and connections. Papers cover topics such as K-theory of group rings, Witt groups of real algebraic varieties, coarse homology theories, topological cyclic homology, negative K-groups of monoid algebras, Milnor K-theory and regulators, noncommutative motives, the classification of C∗-algebras via Kasparov's K-theory, the comparison between full and reduced C∗-crossed products, and a proof of Bott periodicity using almost commuting matrices.

Categorical, Homological and Combinatorial Methods in Algebra

Ashish K. Srivastava,André Leroy,Ivo Herzog,Pedro A. Guil Asensio
Categorical Homological and Combinatorial Methods in Algebra Book PDF

Author : Ashish K. Srivastava,André Leroy,Ivo Herzog,Pedro A. Guil Asensio
Publisher : American Mathematical Soc.
Page : 357 pages
File Size : 47,6 Mb
Release : 2020-06-23
Category : Education
ISBN : 9781470443689

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Categorical, Homological and Combinatorial Methods in Algebra by Ashish K. Srivastava,André Leroy,Ivo Herzog,Pedro A. Guil Asensio Pdf

This book contains the proceedings of the AMS Special Session, in honor of S. K. Jain's 80th birthday, on Categorical, Homological and Combinatorial Methods in Algebra held from March 16–18, 2018, at Ohio State University, Columbus, Ohio. The articles contained in this volume aim to showcase the current state of art in categorical, homological and combinatorial aspects of algebra.

Advances in Harmonic Analysis and Partial Differential Equations

Donatella Danielli,Irina Mitrea
Advances in Harmonic Analysis and Partial Differential Equations Book PDF

Author : Donatella Danielli,Irina Mitrea
Publisher : American Mathematical Soc.
Page : 200 pages
File Size : 47,9 Mb
Release : 2020-04-09
Category : Education
ISBN : 9781470448967

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Advances in Harmonic Analysis and Partial Differential Equations by Donatella Danielli,Irina Mitrea Pdf

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.

Centenary of the Borel Conjecture

Marion Scheepers,Ondřej Zindulka
Centenary of the Borel Conjecture Book PDF

Author : Marion Scheepers,Ondřej Zindulka
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 54,7 Mb
Release : 2020-09-04
Category : Education
ISBN : 9781470450991

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Centenary of the Borel Conjecture by Marion Scheepers,Ondřej Zindulka Pdf

Borel's Conjecture entered the mathematics arena in 1919 as an innocuous remark about sets of real numbers in the context of a new covering property introduced by Émile Borel. In the 100 years since, this conjecture has led to a remarkably rich adventure of discovery in mathematics, producing independent results and the discovery of countable support iterated forcing, developments in infinitary game theory, deep connections with infinitary Ramsey Theory, and significant impact on the study of topological groups and topological covering properties. The papers in this volume present a broad introduction to the frontiers of research that has been spurred on by Borel's 1919 conjecture and identify fundamental unanswered research problems in the field. Philosophers of science and historians of mathematics can glean from this collection some of the typical trends in the discovery, innovation, and development of mathematical theories.

Trends in Set Theory

Samuel Coskey,Grigor Sargsyan
Trends in Set Theory Book PDF

Author : Samuel Coskey,Grigor Sargsyan
Publisher : American Mathematical Soc.
Page : 207 pages
File Size : 50,5 Mb
Release : 2020-06-18
Category : Education
ISBN : 9781470443320

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Trends in Set Theory by Samuel Coskey,Grigor Sargsyan Pdf

This volume contains the proceedings of Simon Fest, held in honor of Simon Thomas's 60th birthday, from September 15–17, 2017, at Rutgers University, Piscataway, New Jersey. The topics covered showcase recent advances from a variety of main areas of set theory, including descriptive set theory, forcing, and inner model theory, in addition to several applications of set theory, including ergodic theory, combinatorics, and model theory.