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This text bridges the gap between beginning and advanced calculus. It offers a systematic development of the real number system and careful treatment of mappings, sequences, limits, continuity, and metric spaces. 1963 edition.
This volume presents answers to some natural questions of a general analytic character that arise in the theory of Banach spaces. I believe that altogether too many of the results presented herein are unknown to the active abstract analysts, and this is not as it should be. Banach space theory has much to offer the prac titioners of analysis; unfortunately, some of the general principles that motivate the theory and make accessible many of its stunning achievements are couched in the technical jargon of the area, thereby making it unapproachable to one unwilling to spend considerable time and effort in deciphering the jargon. With this in mind, I have concentrated on presenting what I believe are basic phenomena in Banach spaces that any analyst can appreciate, enjoy, and perhaps even use. The topics covered have at least one serious omission: the beautiful and powerful theory of type and cotype. To be quite frank, I could not say what I wanted to say about this subject without increasing the length of the text by at least 75 percent. Even then, the words would not have done as much good as the advice to seek out the rich Seminaire Maurey-Schwartz lecture notes, wherein the theory's development can be traced from its conception. Again, the treasured volumes of Lindenstrauss and Tzafriri also present much of the theory of type and cotype and are must reading for those really interested in Banach space theory.
Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.
The field of modern logic is too extensive to be worked through by open cast mining. To open it up, we need to sink shafts and construct adits. This is the method of most text books: a systematic exposition of a number of main topics, supplemented by exercises to teach skill in the appurtenant techniques, lays a secure foundation for subsequent dis cussion of selected questions. Compared with this, the present treatment is more like a network of exploratory drillings to show that it would be worthwhile to start mining operations, or to work the existing shafts and adits, as the case may be. Within this metaphor we may also describe the inherent weakness of this conception: once a cavity is pierced, the duct's capacity will in general not be sufficient to carry away the discovered riches. But whether we are concerned with a new or an already worked mine - at any rate, the experience should stimulate us into either reviving an existing system of shafts or even, in particularly fortunate cases, designing a new ap proach.
In the past few decades, Magnetic Resonance Imaging (MRI) has become an indispensable tool in modern medicine, with MRI systems now available at every major hospital in the developed world. But for all its utility and prevalence, it is much less commonly understood and less readily explained than other common medical imaging techniques. Unlike optical, ultrasonic, X-ray (including CT), and nuclear medicine-based imaging, MRI does not rely primarily on simple transmission and/or reflection of energy, and the highest achievable resolution in MRI is orders of magnitude smaller that the smallest wavelength involved. In this book, MRI will be explained with emphasis on the magnetic fields required, their generation, their concomitant electric fields, the various interactions of all these fields with the subject being imaged, and the implications of these interactions to image quality and patient safety. Classical electromagnetics will be used to describe aspects from the fundamental phenomenon of nuclear precession through signal detection and MRI safety. Simple explanations and Illustrations combined with pertinent equations are designed to help the reader rapidly gain a fundamental understanding and an appreciation of this technology as it is used today, as well as ongoing advances that will increase its value in the future. Numerous references are included to facilitate further study with an emphasis on areas most directly related to electromagnetics.
This book constitutes the refereed proceedings of the 7th International Conference on Sequences and Their Applications, SETA 2012, held in Waterloo, Canada, in June 2012. The 28 full papers presented together with 2 invited papers in this volume were carefully reviewed and selected from 48 submissions. The papers are grouped in topical sections on perfect sequences; finite fields; boolean functions; Golomb 80th birthday session; linear complexity; frequency hopping; correlation of sequences; bounds on sequences, cryptography; aperiodic correlation; and Walsh transform.
This book discusses principles, methodology, and applications of microbiological laboratory techniques . It lays special emphasis on the use of various automated machines that are essential for medical microbiology and diagnostic labs. The book contains eleven major chapters. The first chapter describes the good lab practices which should be followed by the students in all biological, chemistry or microbiology laboratories. The next chapter describes manual and automated characterization of antibiotic resistant microbes, followed by a chapter on genomics based tools and techniques that are integral to research. Further chapters deal with other important techniques like immunology based techniques, spectrophotometry and its various types, MALDI-TOFF and microarrays, each with illustrations and detailed description of the protocols and applications. The book also gives certain important guidelines to the students about the planning the experiment and interpreting results. The book is highly informative and provides latest techniques. It is a handy compendium for graduate and post graduate students, as well as more advanced researchers.
Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi–Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi–Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and illustrations.
This book demonstrates that the concept of an instruction sequence offers a novel and useful viewpoint on issues relating to diverse subjects in computer science. Selected issues relating to well-known subjects from the theory of computation and the area of computer architecture are rigorously investigated in this book thinking in terms of instruction sequences. The subjects from the theory of computation, to wit the halting problem and non-uniform computational complexity, are usually investigated thinking in terms of a common model of computation such as Turing machines and Boolean circuits. The subjects from the area of computer architecture, to wit instruction sequence performance, instruction set architectures and remote instruction processing, are usually not investigated in a rigorous way at all.
