Topology 90
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| Author | : Moreno Andreatta |
| Publisher | : CRC Press |
| Total Pages | : 130 |
| Release | : 2024-11-01 |
| Genre | : Mathematics |
| ISBN | : 1040156703 |
This book introduces path-breaking applications of concepts from mathematical topology to music-theory topics including harmony, chord progressions, rhythm, and music classification. Contributions address topics of voice leading, Tonnetze (maps of notes and chords), and automatic music classification. Focusing on some geometrical and topological aspects of the representation and formalisation of musical structures and processes, the book covers topological features of voice-leading geometries in the most recent advances in this mathematical approach to representing how chords are connected through the motion of voices, leading to analytically useful simplified models of high-dimensional spaces; It generalizes the idea of a Tonnetz, a geometrical map of tones or chords, and shows how topological aspects of these maps can correspond to many concepts from music theory. The resulting framework embeds the chord maps of neo-Riemannian theory in continuous spaces that relate chords of different sizes and includes extensions of this approach to rhythm theory. It further introduces an application of topology to automatic music classification, drawing upon both static topological representations and time-series evolution, showing how static and dynamic features of music interact as features of musical style. This volume will be a key resource for academics, researchers, and advanced students of music, music analyses, music composition, mathematical music theory, computational musicology, and music informatics. It was originally published as a special issue of the Journal of Mathematics and Music.
| Author | : Christodoulos A. Floudas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 4646 |
| Release | : 2008-09-04 |
| Genre | : Mathematics |
| ISBN | : 0387747583 |
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
| Author | : John L. Kelley |
| Publisher | : Courier Dover Publications |
| Total Pages | : 321 |
| Release | : 2017-03-07 |
| Genre | : Mathematics |
| ISBN | : 0486820661 |
Comprehensive text for beginning graduate-level students and professionals. "The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure." — Bulletin of the American Mathematical Society. 1955 edition.
| Author | : Antonio Villanacci |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 495 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1475736193 |
General equilibrium In this book we try to cope with the challenging task of reviewing the so called general equilibrium model and of discussing one specific aspect of the approach underlying it, namely, market completeness. With the denomination "general equilibrium" (from now on in short GE) we shall mainly refer to two different things. On one hand, in particular when using the expression "GE approach", we shall refer to a long established methodolog ical tradition in building and developing economic models, which includes, as of today, an enormous amount of contributions, ranging in number by several 1 thousands • On the other hand, in particular when using the expression "stan dard differentiable GE model", we refer to a very specific version of economic model of exchange and production, to be presented in Chapters 8 and 9, and to be modified in Chapters 10 to 15. Such a version is certainly formulated within the GE approach, but it is generated by making several quite restrictive 2 assumptions • Even to list and review very shortly all the collective work which can be ascribed to the GE approach would be a formidable task for several coauthors in a lifetime perspective. The book instead intends to address just a single issue. Before providing an illustration of its main topic, we feel the obligation to say a word on the controversial character of GE. First of all, we should say that we identify the GE approach as being based 3 on three principles .
| Author | : |
| Publisher | : |
| Total Pages | : 1036 |
| Release | : 1990 |
| Genre | : Aeronautics |
| ISBN | : |
| Author | : Steven R. Finch |
| Publisher | : Cambridge University Press |
| Total Pages | : 783 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 1108470599 |
Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 ..., and the natural logarithm base, e = 2.718 .... Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson-Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl-Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton-Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
| Author | : John G. Ratcliffe |
| Publisher | : Springer Nature |
| Total Pages | : 812 |
| Release | : 2019-10-23 |
| Genre | : Mathematics |
| ISBN | : 3030315975 |
This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately.
| Author | : Sofia Lambropoulou |
| Publisher | : Springer |
| Total Pages | : 481 |
| Release | : 2017-12-14 |
| Genre | : Mathematics |
| ISBN | : 3319681036 |
This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging). The main mathematical focus throughout the book is on algebraic modeling with particular emphasis on braid groups. The research methods include algebraic modeling using topological structures, such as knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address the simulation of polymer chains and ionic liquids, as well as the modeling of natural phenomena via topological surgery. The treatment of computational structures, including finite fields and cryptography, focuses on the development of novel techniques. These techniques can be applied to the design of algebraic specifications for systems modeling and verification. This book is the outcome of a workshop in connection with the research project Thales on Algebraic Modeling of Topological and Computational Structures and Applications, held at the National Technical University of Athens, Greece in July 2015. The reader will benefit from the innovative approaches to tackling difficult questions in topology, applications and interrelated research areas, which largely employ algebraic tools.
| Author | : Donald Bers |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 468 |
| Release | : 2012-12-06 |
| Genre | : Medical |
| ISBN | : 940100658X |
How is the heartbeat generated? What controls the strength of contraction of heart muscle? What are the links between cardiac structure and function? How does our understanding of skeletal and smooth muscle and non-muscle cells influence our thinking about force development in the heart? Are there important species differences in how contraction is regulated in the heart? How do the new molecular data fit together in understanding the heart beat? What goes wrong in ischemia, hypertrophy, and heart failure? This book paints a modern `portrait' of how the heart works and in this picture the author shows a close-up of the structural, biochemical, and physiological links between excitation and contraction. The author takes the reader through a series of important, interrelated topics with great clarity and continuity and also includes many useful illustrations and tables. The book starts by considering the cellular structures involved in excitation-contraction coupling and then described the characteristics of the myofilaments as the end effector of excitation-contraction coupling. A general scheme of calcium regulation is described and the possible sources and sinks of calcium are discussed in simple, but quantitative terms. The cardiac action potential and its many underlying currents are reviewed. Then the characteristics of some key calcium transport systems (calcium channels, sodium/calcium exchange and SR calcium uptake and release) are discussed in detail. This is then built into a more integrated picture of calcium regulation in succeeding chapters by detailed discussions of excitation-calcium coupling mechanisms (in skeletal, cardiac, and smooth muscle), the interplay between calcium regulatory processes, and finally mechanisms of cardiac inotropy, calcium overload, and dysfunction (e.g., ischemia, hypertrophy, and heart failure). Excitation-Contraction Coupling and Cardiac Contractile Force – Second Edition is an invaluable source of information for anyone who is interested in how the heart beat is controlled and especially suited for students of the cardiovascular system at all levels from medical/graduate students through senior investigators in related fields.
| Author | : Gerald Beer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 360 |
| Release | : 1993-10-31 |
| Genre | : Mathematics |
| ISBN | : 9780792325314 |
This monograph provides an introduction to the theory of topologies defined on the closed subsets of a metric space, and on the closed convex subsets of a normed linear space as well. A unifying theme is the relationship between topology and set convergence on the one hand, and set functionals on the other. The text includes for the first time anywhere an exposition of three topologies that over the past ten years have become fundamental tools in optimization, one-sided analysis, convex analysis, and the theory of multifunctions: the Wijsman topology, the Attouch--Wets topology, and the slice topology. Particular attention is given to topologies on lower semicontinuous functions, especially lower semicontinuous convex functions, as associated with their epigraphs. The interplay between convex duality and topology is carefully considered and a chapter on set-valued functions is included. The book contains over 350 exercises and is suitable as a graduate text. This book is of interest to those working in general topology, set-valued analysis, geometric functional analysis, optimization, convex analysis and mathematical economics.
