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Exploring Scale Symmetry
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Book Synopsis Exploring Scale Symmetry by : Thomas Lowe
Download or read book Exploring Scale Symmetry written by Thomas Lowe and published by World Scientific. This book was released on 2021-02-18 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Exploring Musical Spaces by : Julian Hook
Download or read book Exploring Musical Spaces written by Julian Hook and published by Oxford University Press. This book was released on 2022-09-08 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring Musical Spaces is a comprehensive synthesis of mathematical techniques in music theory, written with the aim of making these techniques accessible to music scholars without extensive prior training in mathematics. The book adopts a visual orientation, introducing from the outset a number of simple geometric models--the first examples of the musical spaces of the book's title--depicting relationships among musical entities of various kinds such as notes, chords, scales, or rhythmic values. These spaces take many forms and become a unifying thread in initiating readers into several areas of active recent scholarship, including transformation theory, neo-Riemannian theory, geometric music theory, diatonic theory, and scale theory. Concepts and techniques from mathematical set theory, graph theory, group theory, geometry, and topology are introduced as needed to address musical questions. Musical examples ranging from Bach to the late twentieth century keep the underlying musical motivations close at hand. The book includes hundreds of figures to aid in visualizing the structure of the spaces, as well as exercises offering readers hands-on practice with a diverse assortment of concepts and techniques.
Download or read book Symmetry written by Kristopher Tapp and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets, permutations, and a proof of the Pythagorean Theorem. All of these topics serve a single compelling goal: understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us. The exposition is engaging, precise and rigorous. The theorems are visually motivated with intuitive proofs appropriate for the intended audience. Students from all majors will enjoy the many beautiful topics herein, and will come to better appreciate the powerful cumulative nature of mathematics as these topics are woven together into a single fascinating story about the ways in which objects can be symmetric.
Book Synopsis The Architecture of Music Volume 1.0 by : Greg Aranda, Architect
Download or read book The Architecture of Music Volume 1.0 written by Greg Aranda, Architect and published by The Great Wave Publishing Company. This book was released on 2018-09-22 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Architecture of Music Volume 1.0 is the most complete combined chord, scale, and mode encyclopedia for the guitar and piano ever created, an effort almost two decades in the making. The chord encyclopedia includes more than 300 unique chords, and depicts every possible way to play them on the guitar and piano. The scale and mode encyclopedia contains 5 scales (33 modes) in every key, as well as complete lists of chords included in the chord encyclopedia that you are able to play with every note, in every scale, in every key. The book's two new innovative diagrams, the interval diagram and linear circle of fifths, expose the architecture behind chords, scales, and modes, and explain basic music theory without the use of standard musical notation. The information contained within is meant to be used as a comprehensive reference guide and tool for exploring and analyzing chords, scales, and modes through musical improvisation and composition.
Book Synopsis Universal Themes of Bose-Einstein Condensation by : Nick P. Proukakis
Download or read book Universal Themes of Bose-Einstein Condensation written by Nick P. Proukakis and published by Cambridge University Press. This book was released on 2017-04-27 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering general theoretical concepts and the research to date, this book demonstrates that Bose-Einstein condensation is a truly universal phenomenon.
Book Synopsis Electroweak Symmetry Breaking And New Physics At The Tev Scale by : Timothy L Barklow
Download or read book Electroweak Symmetry Breaking And New Physics At The Tev Scale written by Timothy L Barklow and published by World Scientific. This book was released on 1997-05-05 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Hidden Symmetry of the 43 Octatonic Scales and 43 Tetrachords by : Dave Creamer
Download or read book The Hidden Symmetry of the 43 Octatonic Scales and 43 Tetrachords written by Dave Creamer and published by Bellasonic Publications LLC. This book was released on 2019-05-08 with total page 838 pages. Available in PDF, EPUB and Kindle. Book excerpt: In The Hidden Symmetry of 43 Octatonic Scales and 43 Tetrachords, Creamer provides an extensive explanation and analysis of his system of octatonic (eight-note) harmonizations and melodic organization as well as a series of exercises, complete musical examples and original compositions utilizing the system. While the book includes the diminished scale and all of the eight-note bebop scales, Creamer goes well beyond their traditional use in a jazz context and introduces a vast new musical language where all eight notes are utilized as scale tones creating thousands of chord combinations, tonal colors and melodic possibilities that can be used by improvisers and composers in any musical context for generating new ideas and expanding traditional harmonic and melodic approaches. Guitarists will also benefit from the inherit symmetrical fingerings of the system (eight-notes-per-two-strings) as well as full tablature for all examples have been provided. Much more than a series of possible mathematical combinations, the book is presented as a complete system, and while a thorough theoretical framework is presented for contextual understanding, the music is first and foremost the focus of the work as articulated in the book’s Foreward by Tuck Andress. Perhaps not since George Russell’s book, Lydian Chromatic Concept of Tonal Organization, has a book had such tremendous potential for modern composers and musicians.
Book Synopsis Scale Space and PDE Methods in Computer Vision by : Ron Kimmel
Download or read book Scale Space and PDE Methods in Computer Vision written by Ron Kimmel and published by Springer. This book was released on 2005-03-31 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Welcome to the proceedings of the 5th International Conference on Scale-Space and PDE Methods in Computer Vision. The scale-space concept was introduced by Iijima more than 40 years ago and became popular later on through the works of Witkin and Koenderink. It is at the junction of three major schools of thought in image processing and computer vision: the design of ?lters, axiomatic approaches based on partial di?erential equations (PDEs), and variational methods for image regularization. Scale-space ideas belong to the mathematically best-understood approaches in image analysis. They have entered numerous successful applications in medical imaging and a number of other ?elds where they often give results of very high quality. This conference followed biennial meetings held in Utrecht, Corfu, Vancouver and Skye. It took place in a little castle (Schl ̈ osschen Sch ̈ onburg) near the small town of Hofgeismar, Germany. Inspired by the very successful previous meeting at Skye, we kept the style of gathering people in a slightly remote and scenic place in order to encourage many fruitful discussions during the day and in the evening. Wereceived79fullpapersubmissionsofahighstandardthatischaracteristic for the scale-space conferences. Each paper was reviewed by three experts from the Program Committee, sometimes helped by additional reviewers. Based on theresultsofthesereviews,53paperswereaccepted.Weselected24manuscripts for oral presentation and 29 for poster presentation.
Book Synopsis Equidistribution Of Dynamical Systems: Time-quantitative Second Law by : Jozsef Beck
Download or read book Equidistribution Of Dynamical Systems: Time-quantitative Second Law written by Jozsef Beck and published by World Scientific. This book was released on 2020-10-05 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantized Number Theory, Fractal Strings And The Riemann Hypothesis: From Spectral Operators To Phase Transitions And Universality by : Hafedh Herichi
Download or read book Quantized Number Theory, Fractal Strings And The Riemann Hypothesis: From Spectral Operators To Phase Transitions And Universality written by Hafedh Herichi and published by World Scientific. This book was released on 2021-07-27 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures On Fractal Geometry by : Martina Zaehle
Download or read book Lectures On Fractal Geometry written by Martina Zaehle and published by World Scientific. This book was released on 2023-12-27 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Economic Risk in Hydrocarbon Exploration by : Ian Lerche
Download or read book Economic Risk in Hydrocarbon Exploration written by Ian Lerche and published by Elsevier. This book was released on 1999-01-08 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic Risk in Hydrocarbon Exploration provides a total framework for assessing the uncertainties associated with exploration risk from beginning to end. Numerous examples with accompanying microcomputer algorithms illustrate how to quantitatively approach economic risk. The text compares detailed assumptions and models of economic risk, and presents numerical examples throughout to facilitate hands-on calculations using popular spread-sheet packages on personal computers. Covers economic risk from exploration through production models Brings methods to a level where all can be done on a PC Analyzes numerical examples from the real world Removes "mystery" from how economics is done Addresses assumptions in models and shows how they influence projections
Download or read book Exploring Chaos written by Brian Davies and published by CRC Press. This book was released on 2018-05-04 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. It describes the theory of fractals, focusing on the importance of scaling and ordinary differential equations.
Book Synopsis The Weather and Climate by : Shaun Lovejoy
Download or read book The Weather and Climate written by Shaun Lovejoy and published by Cambridge University Press. This book was released on 2018-03-01 with total page 1186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in nonlinear dynamics, especially modern multifractal cascade models, allow us to investigate the weather and climate at unprecedented levels of accuracy. Using new stochastic modeling and data analysis techniques, this book provides an overview of the nonclassical, multifractal statistics. By generalizing the classical turbulence laws, emergent higher-level laws of atmospheric dynamics are obtained and are empirically validated over time-scales of seconds to decades and length-scales of millimetres to the size of the planet. In generalizing the notion of scale, atmospheric complexity is reduced to a manageable scale-invariant hierarchy of processes, thus providing a new perspective for modeling and understanding the atmosphere. This synthesis of state-of-the-art data and nonlinear dynamics is systematically compared with other analyses and global circulation model outputs. This is an important resource for atmospheric science researchers new to multifractal theory and is also valuable for graduate students in atmospheric dynamics and physics, meteorology, oceanography and climatology.
Book Synopsis The Garden Classroom by : Cathy James
Download or read book The Garden Classroom written by Cathy James and published by Shambhala Publications. This book was released on 2015-04-07 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Creative ways to use the garden to inspire learning, for kids ages 4-8 Packed with garden-based activities that promote science, math, reading, writing, imaginative play, and arts and crafts, The Garden Classroom offers a whole year of outdoor play and learning ideas—however big or small your garden. Every garden offers children a rich, sensory playground, full of interesting things to discover and learn about. There's a whole lot of science happening right before their eyes. The garden can also be a place to develop math and literacy skills, as the outdoors offers up plenty of invitations to weave learning into everyday gardening. The garden classroom is a place where plants grow, and where children grow too.
Book Synopsis Universe in a glass of iced-water. Exploration in off-the-wall physic by : Victor Christianto
Download or read book Universe in a glass of iced-water. Exploration in off-the-wall physic written by Victor Christianto and published by Infinite Study. This book was released on 2023-09-01 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various exploration in astrophysics has revealed many breakthroughs nowadays, not only with respect to James Webb Telescope, but also recent finding related to water and ice deposits in the Moon surface. Those new findings seem to bring us to new questions related to origin of Earth, Moon and the entire Universe.
Book Synopsis Elementary-Particle Physics by : National Research Council
Download or read book Elementary-Particle Physics written by National Research Council and published by National Academies Press. This book was released on 1998-04-01 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of the Physics in a New Era series of assessments of the various branches of the field, Elementary-Particle Physics reviews progress in the field over the past 10 years and recommends actions needed to address the key questions that remain unanswered. It explains in simple terms the present picture of how matter is constructed. As physicists have probed ever deeper into the structure of matter, they have begun to explore one of the most fundamental questions that one can ask about the universe: What gives matter its mass? A new international accelerator to be built at the European laboratory CERN will begin to explore some of the mechanisms proposed to give matter its heft. The committee recommends full U.S. participation in this project as well as various other experiments and studies to be carried out now and in the longer term.
