This book gives a rigorous treatment of selected topics in classical analysis, with many applications and examples. The exposition is at the undergraduate level, building on basic principles of advanced calculus without appeal to more sophisticated techniques of complex analysis and Lebesgue integration. Among the topics covered are Fourier series and integrals, approximation theory, Stirling's formula, the gamma function, Bernoulli numbers and polynomials, the Riemann zeta function, Tauberian theorems, elliptic integrals, ramifications of the Cantor set, and a theoretical discussion of differential equations including power series solutions at regular singular points, Bessel functions, hypergeometric functions, and Sturm comparison theory. Preliminary chapters offer rapid reviews of basic principles and further background material such as infinite products and commonly applied inequalities. This book is designed for individual study but can also serve as a text for second-semester courses in advanced calculus. Each chapter concludes with an abundance of exercises. Historical notes discuss the evolution of mathematical ideas and their relevance to physical applications. Special features are capsule scientific biographies of the major players and a gallery of portraits. Although this book is designed for undergraduate students, others may find it an accessible source of information on classical topics that underlie modern developments in pure and applied mathematics.
The modern subject of Bergman spaces is a masterful blend of complex function theory with functional analysis and operator theory. It has much in common with Hardy spaces but involves new elements such as hyperbolic geometry, reproducing kernels, and biharmonic Green functions. This book develops background material and provides a self-contained introduction to a broad range of old and new topics in Bergman spaces, including recent advances on interpolation and sampling, contractive zero-divisors, and invariant subspaces. It is accessible to anyone who has studied basic real and complex analysis at the graduate level.
Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry.
This volume contains articles on the history of Soviet mathematics, many of which are personal accounts by mathematicians who witnessed and contributed to the turbulent and glorious years of Moscow mathematics. The articles in the book focus on mathematical developments in that era, the personal lives of Russian mathematicians, and political events that shaped the course of scientific work in the Soviet Union. Important contributions include an article about Luzin and his school, based in part on documents that were released only after perestroika, and two articles on Kolmogorov. The volume concludes with annotated bibliographies in English and Russian for further reading. The revised edition is appended by an article of Tikhomirov, which provides an update and general overview of 20th-century Moscow mathematics, and it also includes an Index of Names. This book should appeal to mathematicians, historians, and anyone else interested in Soviet mathematical history.
In this definitive history, bestselling journalist Golenbock focuses on a particularly dominant period of the Yankees' past, when the Bronx Bombers won nine World Series titles on the strengths of such Hall of Famers as DiMaggio, Mantle, Berra, and Ford. Includes interviews of players and coaches, vintage photos, and a new introduction.
Encounters with mathematicians by A. P. Yushkevich The Moscow school of the theory of functions in the 1930s by S. S. Demidov About mathematics at Moscow State University in the late 1940s and early 1950s by E. M. Landis Reminiscences of Soviet mathematicians by B. A. Rosenfeld A. N. Kolmogorov by V. M. Tikhomirov On A. N. Kolmogorov by V. I. Arnold Pages of a mathematical autobiography (1942-1953) by M. M. Postnikov Markov and Bishop: An essay in memory of A. A. Markov (1903-1979) and E. Bishop (1928-1983) by B. A. Kushner Etude on life and automorphic forms in the Soviet Union by I. Piatetski-Shapiro On Soviet mathematics of the 1950s and 1960s by D. B. Fuchs In the other direction by A. B. Sossinsky A brief survey of the literature on the development of mathematics in the USSR by S. S. Demidov Russian bibliography by S. S. Demidov Moscow mathematics--Then and now by V. M. Tikhomirov Errata Index of names
Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. It contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It introduces non-specialists to a beautiful area of complex analysis and geometry.
This text provides an introduction to the applications and implementations of partial differential equations. The content is structured in three progressive levels which are suited for upper–level undergraduates with background in multivariable calculus and elementary linear algebra (chapters 1–5), first– and second–year graduate students who have taken advanced calculus and real analysis (chapters 6-7), as well as doctoral-level students with an understanding of linear and nonlinear functional analysis (chapters 7-8) respectively. Level one gives readers a full exposure to the fundamental linear partial differential equations of physics. It details methods to understand and solve these equations leading ultimately to solutions of Maxwell’s equations. Level two addresses nonlinearity and provides examples of separation of variables, linearizing change of variables, and the inverse scattering transform for select nonlinear partial differential equations. Level three presents rich sources of advanced techniques and strategies for the study of nonlinear partial differential equations, including unique and previously unpublished results. Ultimately the text aims to familiarize readers in applied mathematics, physics, and engineering with some of the myriad techniques that have been developed to model and solve linear and nonlinear partial differential equations.
It is the near future. Axel, a computer scientist, with broad, mechanically-inclined hobbies, is working on a prototype matter transmitter. It is erratic and, in an instant, he finds his consciousness has been transmitted across space. It has been received into the brain of a young, male humanoid immediately following the latter's brain-death from a traumatic wound; one that has not, however, left any long-term organic injuries: Axel of Earth has become Lexar of Nandroth. Lexar's race are called the Androthi. Their world has some geophysical similarities to Earth, and some similarity of life forms but with notable exceptions. The civilisations of the Androthi are roughly on the same technological level as 14th century Europe and Asia. Their overwhelming problem is that their world has been invaded by self-replicating robots, the mekkans, which have a highly advanced - and to living creatures deadly - technology. The mekkans are relatively few in number. They require, for their power and construction, minerals that they cannot easily find and mine. To obtain them, they have set about subjugating Nandroth and enslaving the Androthi, either by direct force or by fomenting internecine warfare. Their ultimate intention is to refuel their nuclear?powered space craft and continue their conquest of living worlds in the universe. Axel-Lexar's self-appointed task is to get his fellow Androthi to accept who and what he is, and to get them to help him create, with what resources are available, strategies to defeat the mekkans. Above all, he wants to destroy the mekkan's ability to threaten intelligent life forms on other worlds. The work deals, inter alia, with the nature of the linguistic problems faced by Axel on his becoming Lexar and the means by which he attempts to transform the local technology. He seeks to exploit special features of mekkan engineering and their rigid social structure, in order to subvert their seemingly unassailable power. But, in the meantime, there are defences to organise against the mekkans' highly advanced weapons, and battles to be fought against other Androthi nations who have become the mekkans' allies. To complicate his new life, he finds that Lexar is betrothed to the teenage daughter of the local Lord. She is a highly intelligent, independent and passionate individual, at first disbelieving, then suspicious and finally jealously protective.
Excellent illustrations and the latest technology from the clinic, practice and laboratory are compiled for both the practicing urologist and the researching cytopathologist in the book "Urinary Cytology." The completely revised and up-dated text in the new second edition reflects the first common effort of urologists, pathologists and cytopathologists to find a unified concept: from conventional cytology to electron microscopy toflow cytometry. The authors' main emphasis is on conveying practical techniques for the collection, concentration, fixation, staining and analysis of cellular material. They clearly discuss the circumstances under which new techniques are advisable and the relevance of these techniques when difficult questions of detail arise. At the same time, basic scientific principles arepresented in comprehensible form. The atlas section gives examples of urologic cytology, compares pathological with normal results, discusses the problems in differential diagnosis and points the way to solutions.
Drawing extensively on anthropological theory and ecological models of human adaptation, this book explores the growth of a food-producing economy in the period 5000-3000 BC.
This book provides a self-contained account of continuous-parameter time series, starting with second-order models. Integration with respect to orthogonal increment processes, spectral theory and linear prediction are treated in detail. Lévy-driven models are incorporated, extending coverage to allow for infinite variance, a variety of marginal distributions and sample paths having jumps. The necessary theory of Lévy processes and integration of deterministic functions with respect to these processes is developed at length. Special emphasis is given to the analysis of continuous-time ARMA processes.
A treasury of witty quotes and wild stories covering decades of baseball history. Baseball is a funny game. No other sport can compare to the national pastime’s vast catalog of silly quotations, unforgettable characters, memorable nicknames, and inventive pranks. Alphabetized by topic, The Funniest Baseball Book Ever captures the game in all its humorous glory. It’s simply the most complete, contemporary resource for over a century of the sport’s history. Also included are short profiles of such colorful characters as Casey Stengel, Bill Veeck, Jim Bouton, and Bill Lee. With over ninty percent of its material never before collected in a single volume, The Funniest Baseball Book Ever will entertain and surprise everyone from casual fans to diehards, from newcomers to veterans.
This is the vivid memoir of a man who was twenty-one at the outbreak of World War II. Having joined the RAFVR before the war, he was mobilized in August 1939 and after training became operational on 233 Squadron Coastal Command flying Hudsons from Leuchars, Aldergrove and St Eval. After fourteen months he was rested and was tasked with training navigators for the impending enlargement of Bomber Command.In 1944 he joined 625 Squadron flying Lancasters over German targets and eventually took command of B Flight and was promoted Squadron Leader. His memories of the many raids, his crew and operational flying during this period until the end of the war are truly gripping. After the German capitulation, Peter joined Shield Force bound for the Far-east and the night bombing of Japan. However before they could become operational the atom bomb put an end to the war in that theater. His unit was redirected to relieve Hong Kong and the final chapters give a unique insight into how the Japanese garrison was replaced by British law and order. This was a purely land operation carried out by the RAF without the presence of the Army.
This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
The death of Pope John Paul II and consequent election of Pope Benedict XVI has shed light on a political process that the world has not been privy to for almost twenty-six years. People from around the world gathered in St. Peter's Square, wondering who the next Vatican leader would be and how the election process really worked, while everyone from international news correspondents to local priests added their own opinions to the debate. In Heirs of the Fisherman, former Vatican insider John-Peter Pham presents a candid portrait of the modern Vatican, the only account to reveal the striking changes to papal succession procedures made by John Paul II. Blending political and ecclesiastical history, Pham goes beyond a mere description of the complex rituals to offer rare insight into the dramatic shifts inside the College of Cardinals, whose 100 members now hail from 50 nations around the globe. He takes us into the secret conclave, where the electors were kept under lock and key, until they had selected a new pope. He also includes a chapter devoted to the intrigues of the 20th century where the first conclave had an emperor's veto and the last was won by the first non-Italian in four centuries becauase the Italians were bitterly divided. With a new Preface, Afterword, and appendices that include an English translation of the last will and testament of Pope John Paul II, Heirs of the Fisherman is an illuminating history and must-have guide to this vitally important world event. It will continue to be an indispensable reference to observers of future Catholic Church politics.
A new assessment of the Battle of the Bulge, the largest and bloodiest battle fought by U.S. forces in World War II, offers a balanced perspective that considers both the German and American viewpoints and discusses the failings of intelligence; Hitler's strategic grasp; effects of weather and influence of terrain; and differences in weaponry, understanding of aerial warfare, and doctrine.
This is a detailed study of understanding in a second language, related to the actual lives of minority workers. The focus is on everyday interactions between these workers and the bureaucrats of the society in which they are now resident. It provides an important contribution to the debate about the function of language as a social practice, adding a new perspective to the psycholinguistic and experimental paradigms, currently existing in second language acquisition research.
This book is an extensively elaborated treatise on physical layer concepts of advanced mobile communications. Setting out from the author's own experience of university teaching for over three decades, the book covers the most fundamental aspects of physical layer transceivers for mobile communications ranging from approximation schemes such as sampling, the Fourier series and the Fourier transformation over multi-antenna techniques including aspects of curvilinear coordinate systems, tensor calculus, determinant computation rules, array antennas, spatial sampling, details on probability theory and information theory, optimum detection with soft outputs and spatial multiplexing to orthogonal frequency division multiplexing.
NAMED ONE OF THE BEST BOOKS OF THE YEAR BY PUBLISHERS WEEKLY New York Times bestselling author Peter F. Hamilton’s riveting new thriller combines the nail-biting suspense of a serial-killer investigation with clear-eyed scientific and social extrapolation to create a future that seems not merely plausible but inevitable. A century from now, thanks to a technology allowing instantaneous travel across light-years, humanity has solved its energy shortages, cleaned up the environment, and created far-flung colony worlds. The keys to this empire belong to the powerful North family—composed of successive generations of clones. Yet these clones are not identical. For one thing, genetic errors have crept in with each generation. For another, the original three clone “brothers” have gone their separate ways, and the branches of the family are now friendly rivals more than allies. Or maybe not so friendly. At least that’s what the murder of a North clone in the English city of Newcastle suggests to Detective Sidney Hurst. Sid is a solid investigator who’d like nothing better than to hand off this hot potato of a case. The way he figures it, whether he solves the crime or not, he’ll make enough enemies to ruin his career. Yet Sid’s case is about to take an unexpected turn: because the circumstances of the murder bear an uncanny resemblance to a killing that took place years ago on the planet St. Libra, where a North clone and his entire household were slaughtered in cold blood. The convicted slayer, Angela Tramelo, has always claimed her innocence. And now it seems she may have been right. Because only the St. Libra killer could have committed the Newcastle crime. Problem is, Angela also claims that the murderer was an alien monster. Now Sid must navigate through a Byzantine minefield of competing interests within the police department and the world’s political and economic elite . . . all the while hunting down a brutal killer poised to strike again. And on St. Libra, Angela, newly released from prison, joins a mission to hunt down the elusive alien, only to learn that the line between hunter and hunted is a thin one. BONUS: This edition includes an excerpt from Peter F. Hamilton’s The Abyss Beyond Dreams. Praise for Great North Road “A mesmerizing page-turner.”—Publishers Weekly (starred review) “A gripping saga that blends wilderness survival, police procedural, political and social intrigue, and dynastic sf into a mammoth tale featuring believable characters and exceptionally skilled storytelling.”—Library Journal (starred review) “A perfect introduction to [Hamilton’s] gifts for character design, dialogue, and sheer, big-idea-driven storytelling.”—Booklist (starred review) “Compelling and original . . . an awesome novel [with] plenty of action.”—SFRevu “One very compelling and entertaining science fiction novel.”—SF Site “Simply brilliant . . . an astonishing achievement.”—Tor.com
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