A Tale Of Two Fractals
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A Tale Of Two Fractals
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Author : A.A. Kirillov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-23
A Tale Of Two Fractals written by A.A. Kirillov 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 2013-04-23 with Mathematics categories.
Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.
Russian Fractals In Indigenous Artifacts
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Author : Abdul Karim Bangura
language : en
Publisher: Vernon Press
Release Date : 2025-06-22
Russian Fractals In Indigenous Artifacts written by Abdul Karim Bangura and has been published by Vernon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-22 with Art categories.
This book is the first comprehensive work on Russian Fractals in indigenous artifacts. While existing works focus on universal phenomena, such as liquid crystal or finance, none explore the intersection between Fractals and Russia. 'Russian Fractals in Indigenous Artifacts' therefore investigates how indigenous Russian cultures have a wonderful Fractal heritage that was originally tied to socially just and ecologically sustainable social practices, including those of indigenous northern groups such as the Yakut. Fractal designs originally allowed unalienated value, both human and nonhuman, to be visible, thereby enabling just and sustainable living. This book also examines how the tsarist elite encouraged the creation of unique creative masterpieces, developing and strengthening traditional crafts and art of indigenous people—hence, Fabergé, or imperial architecture. Today, the challenge for contemporary Russia is to reestablish the relationship between the social and ecological sustainability of indigenous cultures and practices, for which we can now provide modeling and analysis. Lay attempts at this have only limited success, as they have based the attempts on a purely religious basis, which recognizes the ecological aspects but often succumbs to authoritarian nationalism. However, the freely accession of indigenous peoples to Russia for the sake of national liberation has had a positive effect on enriching them with spirituality and creativity by Fractal artifacts through friendly exchanges with one another. In 'Russian Fractals in Indigenous Artifacts,' Bangura and Zhigun express why there is a need for a forward-thinking Fractal renaissance in Russia, bringing together contemporary computational and scientific analyses with these ecologically and socially sustainable traditions.
The Butterfly In The Quantum World
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Author : Indubala I Satija
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2016-09-06
The Butterfly In The Quantum World written by Indubala I Satija and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-06 with Science categories.
Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, is the first book ever to tell the story of the "Hofstadter butterfly", a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What happens if you immerse a crystal in a magnetic field? What energies can the electrons take on? From 1930 onwards, physicists struggled to answer this question, until 1974, when graduate student Douglas Hofstadter discovered that the answer was a graph consisting of nothing but copies of itself nested down infinitely many times. This wild mathematical object caught the physics world totally by surprise, and it continues to mesmerize physicists and mathematicians today. The butterfly plot is intimately related to many other important phenomena in number theory and physics, including Apollonian gaskets, the Foucault pendulum, quasicrystals, the quantum Hall effect, and many more. Its story reflects the magic, the mystery, and the simplicity of the laws of nature, and Indu Satija, in a wonderfully personal style, relates this story, enriching it with a vast number of lively historical anecdotes, many photographs, beautiful visual images, and even poems, making her book a great feast, for the eyes, for the mind and for the soul.
Assouad Dimension And Fractal Geometry
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Author : Jonathan M. Fraser
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-29
Assouad Dimension And Fractal Geometry written by Jonathan M. Fraser 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 2020-10-29 with Mathematics categories.
The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.
Advances In Applied Analysis
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Author : Sergei V. Rogosin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-21
Advances In Applied Analysis written by Sergei V. Rogosin 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 2012-08-21 with Mathematics categories.
This book contains survey papers based on the lectures presented at the 3rd International Winter School “Modern Problems of Mathematics and Mechanics” held in January 2010 at the Belarusian State University, Minsk. These lectures are devoted to different problems of modern analysis and its applications. An extended presentation of modern problems of applied analysis will enable the reader to get familiar with new approaches of mostly interdisciplinary character. The results discussed are application oriented and present new insight into applied problems of growing importance such as applications to composite materials, anomalous diffusion, and fluid dynamics.
Geometry Of Mobius Transformations Elliptic Parabolic And Hyperbolic Actions Of Sl2 R With Dvd Rom
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Author : Vladimir V Kisil
language : en
Publisher: World Scientific
Release Date : 2012-06-19
Geometry Of Mobius Transformations Elliptic Parabolic And Hyperbolic Actions Of Sl2 R With Dvd Rom written by Vladimir V Kisil and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-19 with Mathematics categories.
This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F Klein, who defined geometry as a study of invariants under a transitive group action.The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered./a
Topics In Clifford Analysis
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Author : Swanhild Bernstein
language : en
Publisher: Springer Nature
Release Date : 2019-10-15
Topics In Clifford Analysis written by Swanhild Bernstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-15 with Mathematics categories.
Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.
Fractal Geometry And Stochastics Vi
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Author : Uta Freiberg
language : en
Publisher: Springer Nature
Release Date : 2021-03-23
Fractal Geometry And Stochastics Vi written by Uta Freiberg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-23 with Mathematics categories.
This collection of contributions originates from the well-established conference series "Fractal Geometry and Stochastics" which brings together researchers from different fields using concepts and methods from fractal geometry. Carefully selected papers from keynote and invited speakers are included, both discussing exciting new trends and results and giving a gentle introduction to some recent developments. The topics covered include Assouad dimensions and their connection to analysis, multifractal properties of functions and measures, renewal theorems in dynamics, dimensions and topology of random discrete structures, self-similar trees, p-hyperbolicity, phase transitions from continuous to discrete scale invariance, scaling limits of stochastic processes, stemi-stable distributions and fractional differential equations, and diffusion limited aggregation. Representing a rich source of ideas and a good starting point for more advanced topics in fractal geometry, the volume will appeal to both established experts and newcomers.
Science And Technology Of Polymers And Advanced Materials
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Author : Omari V. Mukbaniani
language : en
Publisher: CRC Press
Release Date : 2019-09-02
Science And Technology Of Polymers And Advanced Materials written by Omari V. Mukbaniani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-02 with Science categories.
Increasing interest in lightweight and high-performance materials is leading to significant research activity in the area of polymers and composites. One recent focus is to develop multifunctional materials that have more than one property tailored as to the specified design requirements, in addition to achieving low density. The possibility of simultaneously tailoring several desired properties is attractive but very challenging, and it requires significant advancement in the science and technology of high-performance functional polymers and composites. This volume presents a selection of new approaches in the field of composites and nanomaterials, polymer synthesis and applications, and materials and their properties. Some composites/nanocomposites and interfaces are explored as well, some with medical applications. The authors also look at simulations and modeling, synthesis involving photochemistry, self-assembled hydrogels, and sol-gel processing.
The Colours Of Infinity
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Author : Nigel Lesmoir-Gordon
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-20
The Colours Of Infinity written by Nigel Lesmoir-Gordon 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 2010-10-20 with Mathematics categories.
A geometry able to include mountains and clouds now exists. I put it together in 1975, but of course it incorporates numerous pieces that have been around for a very long time. Like everything in science, this new geometry has very, very deep and long roots. Benoît B. Mandelbrot Introduction This enhanced and expanded edition of THE COLOURS OF INFINITY features an additional chapter on the money markets by the fractal master himself, Professor Benoît Mandelbrot. The DVD of the film associated with this book has been re-mastered especially for this edition with exquisite new fractal animations, which will take your breath away! Driven by the curious enthusiasm that engulfs many fractalistas, in 1994, Nigel Lesmoir-Gordon overcame enormous obstacles to raise the finance for, then shoot and edit the groundbreaking TV documentary from which this book takes its name. The film has been transmitted on TV channels in over fifty countries around the world. This book is not just a celebration of the discovery of the Mandelbrot set, it also brings fractal geometry up to date with a gathering of the thoughts and enthusiasms of the foremost writers and researchers in the field. As Ian Stewart makes clear in the opening chapter, there were antecedents for fractal geometry before 1975 when Mandelbrot gave the subject its name and began to develop the underlying theory.