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Wavelets, Their Friends, and what They Can Do for You
These notes introduce the central concepts surrounding wavelets and their applications. By focusing on the essential ideas and arguments, the authors enable readers to get to the heart of the matter as quickly as possible. A list of references guides readers interested in further study to the appropriate places in the literature for detailed proofs and real applications. The authors begin with the notion of time-frequency analysis, present the multiresolution analysis and basic wavelet construction, introduce the many friends, relatives, and mutations of wavelets, and finally give a selection of applications. This book is suitable for beginning graduate students and above. A preliminary chapter containing some of the prerequisite concepts and definitions is included for reference.
"Moonshine" of Finite Groups
This is an almost verbatim reproduction of the author's lecture notes written in 1983-84 at Ohio State University, Columbus. A substantial update is given in the bibliography. Over the last 20 plus years there has been energetic activity in the field of finite simple group theory related to the monster simple group. Most notably, influential works have been produced in the theory of vertex operator algebras from research that was stimulated by the moonshine of the finite groups. Still, we can ask the same questions now that we did 30-40 years ago: What is the monster simple group? Is it really related to the theory of the universe as it was vaguely so envisioned? What lies behind the moonshine phenomena of the monster group? It may appear that we have only scratched the surface. These notes are primarily reproduced for the benefit of readers who wish to start learning about modular functions used in moonshine.
Basic Noncommutative Geometry
"Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological alg...
The Cambridge Companion to Rossini
Publisher Description
Splitting Methods for Partial Differential Equations with Rough Solutions
Operator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convection-diffusion equations. Common for these equations is the prevalence of rough, or non-smooth, solutions, e.g., shocks. Rigorous analysis is presented, showing that both semi-discrete and fully discrete splitting methods converge. For conservation laws, s...
Gioachino Rossini
Giochino Rossini: A Research and Information Guide is designed as a tool for those beginning to study the life and works of Gioachino Rossini as well as for those who wish to explore beyond the established biographies and commentaries. The first edition was published in 2001, and represented a survey of some 878 publications relating to the composer’s life and works. The second edition is revised and updated to include the more than 150 books and articles written in the field of Rossini studies since then. Contents range from sources published in the early decades of the nineteenth century to works currently in progress. General subject areas include Rossini's biography, historical and analytical studies of his operatic and non-operatic compositions, his personal and professional associations, and the reassessment of his role in the development of nineteenth-century music.
Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry
The Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Kontsevich later refined Duflo's result in the framework of deformation quantization and also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. This book, which arose from a series of lectures by Damien Calaque at ETH, derives these two isomorphisms from a Duflo-type result for $Q$-manifolds. All notions mentio...
Fanfare for a City
Fanfare for a City invites us to listen to the sounds of Paris during the Second Empire (1852–1870), a regime that oversaw dramatic social change in the French capital. By exploring the sonic worlds of exhibitions, cafés, streets, and markets, Jacek Blaszkiewicz shows how the city's musical life shaped urban narratives about le nouveau Paris: a metropolis at a crossroads between its classical, Roman past and its capitalist, imperial future. At the heart of the narrative is "Baron" Haussmann, the engineer of imperial urbanism and the inspiration for a range of musical responses to modernity, from the enthusiastic to the nostalgic. Drawing on theoretical approaches from historical musicology, urban sociology, and sound studies to shed light on newly surfaced archival material, Fanfare for a City argues that urbanism was a driving force in how nineteenth-century music was produced, performed, and policed.
The Castrato
The Castrato is a nuanced exploration of why innumerable boys were castrated for singing between the mid-sixteenth and late-nineteenth centuries. It shows that the entire foundation of Western classical singing, culminating in bel canto, was birthed from an unlikely and historically unique set of desires, public and private, aesthetic, economic, and political. In Italy, castration for singing was understood through the lens of Catholic blood sacrifice as expressed in idioms of offering and renunciation and, paradoxically, in satire, verbal abuse, and even the symbolism of the castrato’s comic cousin Pulcinella. Sacrifice in turn was inseparable from the system of patriarchy—involving teachers, patrons, colleagues, and relatives—whereby castrated males were produced not as nonmen, as often thought nowadays, but as idealized males. Yet what captivated audiences and composers—from Cavalli and Pergolesi to Handel, Mozart, and Rossini—were the extraordinary capacities of castrato voices, a phenomenon ultimately unsettled by Enlightenment morality. Although the castrati failed to survive, their musicality and vocality have persisted long past their literal demise.
Changing the Score
This study seeks to explore the role and significance of aria insertion, the practice that allowed singers to introduce music of their own choice into productions of Italian operas. Each chapter investigates the art of aria insertion during the nineteenth century from varying perspectives, beginning with an overview of the changing fortunes of the practice, followed by explorations of individual prima donnas and their relationship with particular insertion arias: Carolina Ungher's difficulties in finding a "perfect" aria to introduce into Donizetti's Marino Faliero; Guiditta Pasta's performance of an aria from Pacini's Niobe in a variety of operas, and the subsequent fortunes of that particu...
