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Author: Thomas Lowe
Publisher: World Scientific
ISBN: 9813278560
Category : Mathematics
Languages : en
Pages : 253
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Book Description
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.
Author: Thomas Lowe
Publisher: World Scientific
ISBN: 9813278560
Category : Mathematics
Languages : en
Pages : 253
Get Book Here
Book Description
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.
Author: Malke Rosenfeld
Publisher: Heinemann Educational Books
ISBN: 9780325074702
Category : Education
Languages : en
Pages : 0
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Book Description
"Kids love to move. But how do we harness all that kinetic energy effectively for math learning? In Math on the Move, Malke Rosenfeld shows how pairing math concepts and whole body movement creates opportunities for students to make sense of math in entirely new ways. Malke shares her experience creating dynamic learning environments by: exploring the use of the body as a thinking tool, highlighting mathematical ideas that are usefully explored with a moving body, providing a range of entry points for learning to facilitate a moving math classroom. ..."--Publisher description.
Author: Howard Baer
Publisher: Cambridge University Press
ISBN: 1009289845
Category : Science
Languages : en
Pages : 557
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Book Description
This OA text develops the basic concepts of supersymmetry for experimental and phenomenological particle physicists and graduate students.
Author: Annick LESNE
Publisher: Springer Science & Business Media
ISBN: 364215123X
Category : Science
Languages : en
Pages : 406
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Book Description
During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.
Author: Martina Zaehle
Publisher: World Scientific
ISBN: 9811283354
Category : Mathematics
Languages : en
Pages : 141
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Book Description
This book is based on a series of lectures at the Mathematics Department of the University of Jena, developed in the period from 1995 up to 2015. It is completed by additional material and extensions of some basic results from the literature to more general metric spaces.This book provides a clear introduction to classical fields of fractal geometry, which provide some background for modern topics of research and applications. Some basic knowledge on general measure theory and on topological notions in metric spaces is presumed.
Author: Timothy L Barklow
Publisher: World Scientific
ISBN: 9814499072
Category : Science
Languages : en
Pages : 749
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Book Description
This is an expanded version of the report by the Electroweak Symmetry Breaking and Beyond the Standard Model Working Group which was contributed to Particle Physics — Perspectives and Opportunities, a report of the Division of Particles and Fields Committee for Long Term Planning. One of the Working Group's primary goals was to study the phenomenology of electroweak symmetry breaking and attempt to quantify the “physics reach” of present and future colliders. Their investigations encompassed the Standard Model — with one doublet of Higgs scalars — and approaches to physics beyond the Standard Model. These include models of low-energy supersymmetry, dynamical electroweak symmetry breaking, and a variety of extensions of the Standard Model with new particles and interactions. The Working Group also considered signals of new physics in precision measurements arising from virtual processes and examined experimental issues associated with the study of electroweak symmetry breaking and the search for new physics at present and future hadron and lepton colliders.This volume represents an important contribution to the efforts being made to advance the frontiers of particle physics.
Author: Jozsef Beck
Publisher: World Scientific
ISBN: 9811225575
Category : Mathematics
Languages : en
Pages : 448
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Book Description
We know very little about the time-evolution of many-particle dynamical systems, the subject of our book. Even the 3-body problem has no explicit solution (we cannot solve the corresponding system of differential equations, and computer simulation indicates hopelessly chaotic behaviour). For example, what can we say about the typical time evolution of a large system starting from a stage far from equilibrium? What happens in a realistic time scale? The reader's first reaction is probably: What about the famous Second Law (of thermodynamics)?Unfortunately, there are plenty of notorious mathematical problems surrounding the Second Law. (1) How to rigorously define entropy? How to convert the well known intuitions (like 'disorder' and 'energy spreading') into precise mathematical definitions? (2) How to express the Second Law in forms of a rigorous mathematical theorem? (3) The Second Law is a 'soft' qualitative statement about entropy increase, but does not say anything about the necessary time to reach equilibrium.The object of this book is to answer questions (1)-(2)-(3). We rigorously prove a Time-Quantitative Second Law that works on a realistic time scale. As a by product, we clarify the Loschmidt-paradox and the related reversibility/irreversibility paradox.
Author: Cristian Suteanu
Publisher: Springer Nature
ISBN: 3031157338
Category : Science
Languages : en
Pages : 329
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Book Description
This book provides up-to-date, in-depth and accessible information on the concept of scale, and focuses on its applications in geography, Earth science, environmental science, and other fields in which the environment plays a significant role. Although the book presents methods and applications as a response to practical challenges, it is primarily concept-centered: it identifies a set of distinct, yet related notions of “scale”, analyzing and elucidating their evolving meanings in a systematic way. Concepts are defined with a focus on their practical operational applicability, and the introduction of methods is supported by concrete examples. The book links theoretical insights to illustrating applications, involving a broad range of themes, from maps, fractals, and chaos theory to fine art and literature. It approaches the subject in a spatial, temporal, and spatio-temporal context, including a wide diversity of spatial features from Earth and other planets, as well as time series and space-time patterns. This monograph is expected to be useful especially because in practice the various scale-focused concepts are not neatly separated and immiscible. It is therefore helpful for scholars in physical and human geography, Earth and environmental sciences, and other fields, to benefit from a clear conceptual framework that distinguishes and illuminates the various scale-related concepts and their interconnections. Selected chapters can also support a deeper understanding of the concept of scale for graduate and undergraduate students in geography, the natural sciences, and the humanities. Information on recommended additional literature and comments about specific sources offer a guide to further reading on the topics addressed in the book.
Author: Hafedh Herichi
Publisher: World Scientific
ISBN: 9813230819
Category : Mathematics
Languages : en
Pages : 494
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Book Description
Studying the relationship between the geometry, arithmetic and spectra of fractals has been a subject of significant interest in contemporary mathematics. This book contributes to the literature on the subject in several different and new ways. In particular, the authors provide a rigorous and detailed study of the spectral operator, a map that sends the geometry of fractal strings onto their spectrum. To that effect, they use and develop methods from fractal geometry, functional analysis, complex analysis, operator theory, partial differential equations, analytic number theory and mathematical physics.Originally, M L Lapidus and M van Frankenhuijsen 'heuristically' introduced the spectral operator in their development of the theory of fractal strings and their complex dimensions, specifically in their reinterpretation of the earlier work of M L Lapidus and H Maier on inverse spectral problems for fractal strings and the Riemann hypothesis.One of the main themes of the book is to provide a rigorous framework within which the corresponding question 'Can one hear the shape of a fractal string?' or, equivalently, 'Can one obtain information about the geometry of a fractal string, given its spectrum?' can be further reformulated in terms of the invertibility or the quasi-invertibility of the spectral operator.The infinitesimal shift of the real line is first precisely defined as a differentiation operator on a family of suitably weighted Hilbert spaces of functions on the real line and indexed by a dimensional parameter c. Then, the spectral operator is defined via the functional calculus as a function of the infinitesimal shift. In this manner, it is viewed as a natural 'quantum' analog of the Riemann zeta function. More precisely, within this framework, the spectral operator is defined as the composite map of the Riemann zeta function with the infinitesimal shift, viewed as an unbounded normal operator acting on the above Hilbert space.It is shown that the quasi-invertibility of the spectral operator is intimately connected to the existence of critical zeros of the Riemann zeta function, leading to a new spectral and operator-theoretic reformulation of the Riemann hypothesis. Accordingly, the spectral operator is quasi-invertible for all values of the dimensional parameter c in the critical interval (0,1) (other than in the midfractal case when c =1/2) if and only if the Riemann hypothesis (RH) is true. A related, but seemingly quite different, reformulation of RH, due to the second author and referred to as an 'asymmetric criterion for RH', is also discussed in some detail: namely, the spectral operator is invertible for all values of c in the left-critical interval (0,1/2) if and only if RH is true.These spectral reformulations of RH also led to the discovery of several 'mathematical phase transitions' in this context, for the shape of the spectrum, the invertibility, the boundedness or the unboundedness of the spectral operator, and occurring either in the midfractal case or in the most fractal case when the underlying fractal dimension is equal to ½ or 1, respectively. In particular, the midfractal dimension c=1/2 is playing the role of a critical parameter in quantum statistical physics and the theory of phase transitions and critical phenomena.Furthermore, the authors provide a 'quantum analog' of Voronin's classical theorem about the universality of the Riemann zeta function. Moreover, they obtain and study quantized counterparts of the Dirichlet series and of the Euler product for the Riemann zeta function, which are shown to converge (in a suitable sense) even inside the critical strip.For pedagogical reasons, most of the book is devoted to the study of the quantized Riemann zeta function. However, the results obtained in this monograph are expected to lead to a quantization of most classic arithmetic zeta functions, hence, further 'naturally quantizing' various aspects of analytic number theory and arithmetic geometry.The book should be accessible to experts and non-experts alike, including mathematics and physics graduate students and postdoctoral researchers, interested in fractal geometry, number theory, operator theory and functional analysis, differential equations, complex analysis, spectral theory, as well as mathematical and theoretical physics. Whenever necessary, suitable background about the different subjects involved is provided and the new work is placed in its proper historical context. Several appendices supplementing the main text are also included.
Author: Barrett Williams
Publisher: Barrett Williams
ISBN:
Category : Mathematics
Languages : en
Pages : 113
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Book Description
**Exploring the Infinite Possibilities Unlock the Mysteries of Mathematics** Dive into a world where numbers weave patterns of breathtaking beauty and equations reveal the secrets of the universe. "Exploring the Infinite Possibilities" is a captivating journey through the landscape of mathematics, offering a fresh and insightful perspective on a subject often shrouded in mystery and complexity. Begin your exploration with the aesthetic allure of mathematics, where the harmony of numbers and the elegance of patterns and symmetry spark a sense of wonder. Venture into the rich history of mathematical thought, tracing its evolution from ancient civilizations, through the intellectual fervor of the Renaissance, to the innovations that define modern mathematics today. Discover the boundless nature of infinity, uncover the mysteries of fractals and chaos theory, and delve into the intriguing realm of transfinite numbers. Wander through the natural world, where the Fibonacci sequence and the Golden Ratio manifest in mesmerizing forms and patterns, and explore the symmetrical beauty inherent in biological structures. Unravel the intricacies of mathematical proofs, from historical breakthroughs to contemporary challenges that drive mathematical discovery. Appreciate mathematics as a universal language, bridging the gap between the abstract and the tangible, and see its unifying power in science. From the elegance of Euclidean geometry to the peculiarities of non-Euclidean spaces, geometric concepts open the door to endless possibilities. Explore the hidden symmetries in abstract algebra, the enigmatic nature of prime numbers, and the profound impacts of calculus—the mathematics of change. Venture into the realms of mathematical analysis, probability, and statistics, uncovering the profound insights these fields offer into our world. Engage with the foundations of mathematical logic and embark on a journey through the digital age, where algorithms and machine learning reshape our lives. "Exploring the Infinite Possibilities" is not just a book—it's an inspiring odyssey into a vibrant mathematical universe. Whether you're a curious enthusiast or a seasoned mathematician, this book invites you to continue the great journey of mathematical exploration, inspiring future generations and highlighting the global impact of mathematics.
