This book deals with the theory of linear ordinary differential operators of arbitrary order. Unlike treatments that focus on spectral theory, this work centers on the construction of special eigenfunctions (generalized Jost solutions) and on the inverse problem: the problem of reconstructing the operator from minimal data associated to the special eigenfunctions. In the second order case this program includes spectral theory and is equivalent to quantum mechanical scattering theory; the essential analysis involves only the bounded eigenfunctions. For higher order operators, bounded eigenfunctions are again sufficient for spectral theory and quantum scattering theory, but they are far from sufficient for a successful inverse theory. The authors give a complete and self-contained theory of the inverse problem for an ordinary differential operator of any order. The theory provides a linearization for the associated nonlinear evolution equations, including KdV and Boussinesq. The authors also discuss Darboux-Bäcklund transformations, related first-order systems and their evolutions, and applications to spectral theory and quantum mechanical scattering theory. Among the book's most significant contributions are a new construction of normalized eigenfunctions and the first complete treatment of the self-adjoint inverse problem in order greater than two. In addition, the authors present the first analytic treatment of the corresponding flows, including a detailed description of the phase space for Boussinesq and other equations. The book is intended for mathematicians, physicists, and engineers in the area of soliton equations, as well as those interested in the analytical aspects of inverse scattering or in the general theory of linear ordinary differential operators. This book is likely to be a valuable resource to many. Required background consists of a basic knowledge of complex variable theory, the theory of ordinary differential equations, linear algebra, and functional analysis. The authors have attempted to make the book sufficiently complete and self-contained to make it accessible to a graduate student having no prior knowledge of scattering or inverse scattering theory. The book may therefore be suitable for a graduate textbook or as background reading in a seminar.
The authors show how to interpret recent results of Moser and Veselov on discrete versions of a class of classical integrable systems, in terms of a loop group framework. In this framework the discrete systems appear as time-one maps of integrable Hamiltonian flows. Earlier results of Moser on isospectral deformations of rank 2 extensions of a fixed matrix, can also be incorporated into their scheme.
Deals with the theory of linear ordinary differential operators of arbitrary order. This book centers on the construction of special eigenfunctions and on the inverse problem. It is suitable for mathematicians, physicists, and engineers in the area of soliton equations, as well as those interested in the analytical aspects of inverse scattering.
Deals with the theory of linear ordinary differential operators of arbitrary order. This book centers on the construction of special eigenfunctions and on the inverse problem. It is suitable for mathematicians, physicists, and engineers in the area of soliton equations, as well as those interested in the analytical aspects of inverse scattering.
This book deals with the theory of linear ordinary differential operators of arbitrary order. Unlike treatments that focus on spectral theory, this work centers on the construction of special eigenfunctions (generalized Jost solutions) and on the inverse problem: the problem of reconstructing the operator from minimal data associated to the special eigenfunctions. In the second order case this program includes spectral theory and is equivalent to quantum mechanical scattering theory; the essential analysis involves only the bounded eigenfunctions. For higher order operators, bounded eigenfunctions are again sufficient for spectral theory and quantum scattering theory, but they are far from sufficient for a successful inverse theory. The authors give a complete and self-contained theory of the inverse problem for an ordinary differential operator of any order. The theory provides a linearization for the associated nonlinear evolution equations, including KdV and Boussinesq. The authors also discuss Darboux-Bäcklund transformations, related first-order systems and their evolutions, and applications to spectral theory and quantum mechanical scattering theory. Among the book's most significant contributions are a new construction of normalized eigenfunctions and the first complete treatment of the self-adjoint inverse problem in order greater than two. In addition, the authors present the first analytic treatment of the corresponding flows, including a detailed description of the phase space for Boussinesq and other equations. The book is intended for mathematicians, physicists, and engineers in the area of soliton equations, as well as those interested in the analytical aspects of inverse scattering or in the general theory of linear ordinary differential operators. This book is likely to be a valuable resource to many. Required background consists of a basic knowledge of complex variable theory, the theory of ordinary differential equations, linear algebra, and functional analysis. The authors have attempted to make the book sufficiently complete and self-contained to make it accessible to a graduate student having no prior knowledge of scattering or inverse scattering theory. The book may therefore be suitable for a graduate textbook or as background reading in a seminar.
The authors show how to interpret recent results of Moser and Veselov on discrete versions of a class of classical integrable systems, in terms of a loop group framework. In this framework the discrete systems appear as time-one maps of integrable Hamiltonian flows. Earlier results of Moser on isospectral deformations of rank 2 extensions of a fixed matrix, can also be incorporated into their scheme.
The Hellenistic period—the nearly three centuries between the death of Alexander the Great, in 323 B.C., and the suicide of the Egyptian queen Kleopatra VII (the famous "Cleopatra"), in 30 B.C.—is one of the most complex and exciting epochs of ancient Greek art. The unprecedented geographic sweep of Alexander's conquests changed the face of the ancient world forever, forging diverse cultural connections and exposing Greek artists to a host of new influences and artistic styles. This beautifully illustrated volume examines the rich diversity of art forms that arose through the patronage of the royal courts of the Hellenistic kingdoms, placing special emphasis on Pergamon, capital of the Attalid dynasty, which ruled over large parts of Asia Minor. With its long history of German-led excavations, Pergamon provides a superb paradigm of a Hellenistic capital, appointed with important civic institutions—a great library, theater, gymnasium, temples, and healing center—that we recognize today as central features of modern urban life. The military triumphs of Alexander and his successors led to the expansion of Greek culture out from the traditional Greek heartland to the Indus River Valley in the east and as far west as the Strait of Gibraltar. These newly established Hellenistic kingdoms concentrated wealth and power, resulting in an unparalleled burst of creativity in all the arts, from architecture and sculpture to seal engraving and glass production. Pergamon and the Hellenistic Kingdoms of the Ancient World brings together the insights of a team of internationally renowned scholars, who reveal how the art of Classical Greece was transformed during this period, melding with predominantly Eastern cultural traditions to yield new standards and conventions in taste and style.
The world saw Carlos Pena and Alexa Vega enjoying the success of their acting careers--Carlos on Nickelodeon's Big Time Rush and Alexa in the Spy Kids movies. But what they didn't see was the question both Carlos and Alexa were asking in the midst of all that fame and fortune: What's the point of it all anyway? Overflowing with both laughter and honest reflections, What If Love Is the Point? shares Carlos and Alexa PenaVegas' incredible story--from the red carpet, Spy Kids movies, and Big Time Rush to Dancing with the Stars to marriage and their greatest adventure, parenthood. Join them as they: Offer an inspiring window into how God builds young faith and strengthens it into lasting love Give insight into how to put God at the center of relationships, family, and career Explore why society's expectations never fulfill our true needs Share ideas for resisting the hustle of today's culture and finding true rest Carlos and Alexa believe that following Jesus was what they were made for--and they believe it's what you were made for too. If you find yourself asking, "Isn't there more to life than this?," lean in to their remarkable story of tender faith, God's persistent work, and learning why love is always the point of it all. Praise for What If Love Is the Point?: "This is more than a book. It's a story of freedom, hope, redemption, and love. Being in the public eye, I understand the struggles they faced (and continue to face), individually and as a couple. I recognize myself in a lot of the stories they share. What If Love Is the Point? helped me heal from life's wounds. It taught me that I'm not alone and I know this book will help so many others grow their faith and live out love. I didn't want it to end." —Sam Acho, author of Let the World See You, analyst at ESPN, and nine-year NFL linebacker
This book concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give nonzero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go to infinity. A particular classof families of equations is considered, where the answer exhibits a new kind of behavior not seen in most work known until now. The techniques include Laplace transform and the method of stationary phase, and a combinatorial technique for estimating the contributions of terms in an infinite series expansion for the solution. Addressed primarily to researchers inalgebraic geometry, ordinary differential equations and complex analysis, the book will also be of interest to applied mathematicians working on asymptotics of singular perturbations and numerical solution of ODE's.
Every January, from 1996 to 2016, while I was suffering with summer in Rio I received snowy news from the Sundance Festival through Carlos Brandão and his partner Myrna. In those 20 years, Carlos and Myrna were my main source of information about independent world cinema. It is a great joy to see all this material gathered in a book. Carlos was a passionate researcher and, along with Myrna, an experienced reporter. Their interviews and reports on films and directors that have passed through Sundance have the mark of someone who saw everything up close. And knew how to tell it. Carlos Alberto Mattos – Film Critic When Robert Redford founded the nonprofit Sundance Institute in 1981, the intense creativity of American independent cinema in the 70’s was too distant. The Festival came to redefine the characteristics of a cinema that was becoming more conservative and less daring, as a reflection of the Reagan years. Betting on risk and dissonant and plural voices, Sundance knew how to reveal innovative directors and organize “Script Development Programs” in different parts of the world, starting with Brazil. The geopolitics of independent cinema would never be the same. Sundance marked the resumption of Brazilian Cinema after the disastrous government of President Collor. It was one of the first international festival to embrace our cinematography at that time and few critics and journalists followed this movement as closely as Carlos Augusto Brandão. With his inseparable Myrna, Carlos foresaw what was still under construction. He covered the Festival from the start, collecting precious interviews from young new-comers. I cannot remember Sundance without thinking about Carlos, his remarks and always relevant and sensitive questions, publishing stories that dimensioned the revival of Brazilian Cinema. These testimonies comprise this precious "20 Years of Independent Cinema". The interviews gathered here tell not only the story of the renaissance of independent cinema in different latitudes, but also speak of the intense passion that Carlos had for cinema. His texts make him both a witness and co-author of a cinema in transformation. Walter Salles – Film-Maker
The main message emerging from this new comprehensive global assessment is that premature death and disease can be prevented through healthier environments--and to a significant degree. Analysing the latest data on the environment-disease nexus and the devastating impact of environmental hazards and risks on global health, backed up by expert opinion, this report covers more than 130 diseases and injuries. The analysis shows that 23% of global deaths (and 26% of deaths among children under five) are due to modifiable environmental factors--and therefore can be prevented. Stroke, ischaemic heart disease, diarrhoea and cancers head the list. People in low-income countries bear the greatest disease burden, with the exception of noncommunicable diseases. The report's unequivocal evidence should add impetus to coordinating global efforts to promote healthy environments--often through well-established, cost-effective interventions. This analysis will inform those who want to better understand the transformational spirit of the Sustainable Development Goals agreed by Heads of State in September 2015. The results of the analysis underscore the pressing importance of stronger intersectoral action to create healthier environments that will contribute to sustainably improving the lives of millions around the world."--Page 4 of cover.
The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies ..., new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series offers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. The water and wastewater industry has undergone many changes in recent years. Of particular importance has been a renewed emphasis on improving resource management with tighter regulatory controls setting new targets on pricing, industry efficiency and loss reduction for both water and wastewater with more stringent environmental discharge conditions for wastewater. Meantime, the demand for water and wastewater services grows as the population increases and wishes for improved living conditions involving, among other items, domestic appliances that use water. Consequently, the installed infrastructure of the industry has to be continuously upgraded and extended, and employed more effectively to accommodate the new demands, both in throughput and in meeting the new regulatory conditions. Investment in fixed infrastructure is capital-intensive and slow to come on-stream. One outcome of these changes and demands is that the industry is examining the potential benefits of, and in many cases using, more advanced control systems.
Finally! A step-by-step guide to the keys that unlock the doors to Hollywood. Opening the Doors to Hollywood has all the information you'll ever need in order to tap into the $500 million spent yearly in Hollywood on acquiring and developing projects. Discover how to: Find a story Rewrite it Option it Package it Pitch it Write it Sell it to film and television companies Complete with a reference section that includes guilds/unions, libraries, sample contracts, seminars and workshops, trade publications, and writers' organizations, Opening the Doors to Hollywood is invaluable to any writer.
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.