Download or read book Function Theory of One Complex Variable written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 2006 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples andexercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem,and the Bergman kernel. The authors also treat $Hp$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.

Download or read book Kvant Selecta Combinatorics I written by Serge Tabachnikov and published by American Mathematical Soc.. This book was released on 2001 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of articles translated from Russian editions of the journal "Kvant"--T.p. verso.

Download or read book Gaseous Molecular Ions written by Eugen Illenberger and published by Springer Science & Business Media. This book was released on 1992-05-26 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the matter in our solar system, and, probably, within the whole universe, exists in the form of ionized particles. On the other hand, in our natural environ ment, gaseous matter generally consists of neutral atoms and molecules. Only under certain conditions, such as within the path oflightning or in several technical devices (e. g. gas discharges, rocket engines, etc. ) will some of the atoms and molecules be ionized. It is also believed that the chemistry of the earth's troposphere predomi nantly proceeds via reactions between neutral particles. (The complex system of atmospheric chemistry will be treated in one of the forthcoming volumes to this series. ) Why, then, are ions considered so important that hundreds oflaboratories all over the world (including some of the most prestigious) are involved in research pro grams on ions, covering many different facets, from biochemistry to physics? One may obtain as many different answers as there are research groups busy in this field. There is, however, one simple, common feature which makes it attractive to work with ions: since they carry one or more net elementary charges, they can easily be gui ded, focused or separated by appropriate electric and magnetic fields, and, last but not least, they can easily be detected. Apart from these advantages, which are welcome and appreciated by the researcher, the study of molecular ions can provide insight into very fundamental aspects of the general behavior of molecules.

Download or read book Development of the Commonwealth of Puerto Rico written by Luis Muñoz Marín and published by . This book was released on 1973 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book National Institutes of Health Consensus Development Conference Summary written by and published by . This book was released on 1977 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Introduction to Morse Theory written by Yukio Matsumoto and published by American Mathematical Soc.. This book was released on 2002 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite-dimensional Morse theory is easier to present fundamental ideas than in infinite-dimensional Morse theory, which is theoretically more involved. However, finite-dimensional Morse theory has its own significance. This volume explains the finte-dimensional Morse theory.

Download or read book Gastroenterology and Nutrition written by Josef Neu and published by Elsevier Health Sciences. This book was released on 2018-07-06 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dr. Richard Polin's Neonatology Questions and Controversies series highlights the most challenging aspects of neonatal care, offering trustworthy guidance on up-to-date diagnostic and treatment options in the field. In each volume, renowned experts address the clinical problems of greatest concern to today's practitioners, helping you handle difficult practice issues and provide optimal, evidence-based care to every patient. - Stay fully up to date in this fast-changing field with Gastroenterology and Nutrition, 3rd Edition. - Emerging knowledge about the basic developmental physiology of upper intestinal motility as it relates to reflux and feeding tolerance, and immaturities in motility by altering composition of feedings and pharmacologic means. - New content on genetics and pharmacology, the role of inflammation in systemic diseases in other organs as well as necrotizing enterocolitis, optimizing administration of lipids to preterm infants, and administering lipids to infants who are at high risk for complications secondary to suboptimal lipid therapies. - Current coverage of the composition of human milk and clinical trials that address the efficacy of donor milk in comparison to formula and own mother's milk. - Consistent chapter organization to help you find information quickly and easily. - The most authoritative advice available from world-class neonatologists who share their knowledge of new trends and developments in neonatal care. Purchase each volume individually, or get the entire 7-volume set!Gastroenterology and NutritionHematology, Immunology and GeneticsHemodynamics and CardiologyInfectious Disease and Pharmacology New Volume!Nephrology and Fluid/Electrolyte PhysiologyNeurologyThe Newborn Lung

Download or read book Classroom Discourse and the Space of Learning written by Ference Marton and published by Routledge. This book was released on 2004-05-20 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classroom Discourse and the Space of Learning is about learning in schools and the central role of language in learning. The investigations of learning it reports are based on two premises: First, whatever you are trying to learn, there are certain necessary conditions for succeeding--although you cannot be sure that learning will take place when those conditions are met, you can be sure that no learning will occur if they are not. The limits of what is possible to learn is what the authors call "the space of learning." Second, language plays a central role in learning--it does not merely convey meaning, it also creates meaning. The book explicates the necessary conditions for successful learning and employs investigations of classroom discourse data to demonstrate how the space of learning is linguistically constituted in the classroom. Classroom Discourse and the Space of Learning: *makes the case that an understanding of how the space of learning is linguistically constituted in the classroom is best achieved through investigating "classroom discourse" and that finding out what the conditions are for successful learning and bringing them about should be the teacher's primary professional task. Thus, it is fundamentally important for teachers and student teachers to be given opportunities to observe different teachers teaching the same thing, and to analyze and reflect on whether the classroom discourse in which they are engaged maximizes or minimizes the conditions for learning; *is both more culturally situated and more generalizable than many other studies of learning in schools. Each case of classroom teaching clearly demonstrates how the specific language, culture, and pedagogy molds what is happening in the classroom, yet at the same time it is possible to generalize from these culturally specific examples the necessary conditions that must be met for the development of any specific capability regardless of where the learning is taking place and what other conditions might be present; and *encompasses both theory and practice--providing a detailed explication of the theory of learning underlying the analyses of classroom teaching reported, along with close analyses of a number of authentic cases of classroom teaching driven by classroom discourse data which have practical relevance for teachers. Intended for researchers and graduate students in education, teacher educators, and student teachers, Classroom Discourse and the Space of Learning is practice- and content-oriented, theoretical, qualitative, empirical, and focused on language, and links teaching and learning in significant new ways.

Download or read book Advances in Moduli Theory written by Kenji Ueno and published by American Mathematical Soc.. This book was released on 2002 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The word ``moduli'' in the sense of this book first appeared in the epoch-making paper of B. Riemann, Theorie der Abel'schen Funktionen, published in 1857. Riemann defined a Riemann surface of an algebraic function field as a branched covering of a one-dimensional complex projective space, and found out that Riemann surfaces have parameters. This work gave birth to the theory of moduli. However, the viewpoint regarding a Riemann surface as an algebraic curve became the mainstream,and the moduli meant the parameters for the figures (graphs) defined by equations. In 1913, H. Weyl defined a Riemann surface as a complex manifold of dimension one. Moreover, Teichmuller's theory of quasiconformal mappings and Teichmuller spaces made a start for new development of the theory ofmoduli, making possible a complex analytic approach toward the theory of moduli of Riemann surfaces. This theory was then investigated and made complete by Ahlfors, Bers, Rauch, and others. However, the theory of Teichmuller spaces utilized the special nature of complex dimension one, and it was difficult to generalize it to an arbitrary dimension in a direct way. It was Kodaira-Spencer's deformation theory of complex manifolds that allowed one to study arbitrary dimensional complex manifolds.Initial motivation in Kodaira-Spencer's discussion was the need to clarify what one should mean by number of moduli. Their results, together with further work by Kuranishi, provided this notion with intrinsic meaning. This book begins by presenting the Kodaira-Spencer theory in its original naiveform in Chapter 1 and introduces readers to moduli theory from the viewpoint of complex analytic geometry. Chapter 2 briefly outlines the theory of period mapping and Jacobian variety for compact Riemann surfaces, with the Torelli theorem as a goal. The theory of period mappings for compact Riemann surfaces can be generalized to the theory of period mappings in terms of Hodge structures for compact Kahler manifolds. In Chapter 3, the authors state the theory of Hodge structures, focusingbriefly on period mappings. Chapter 4 explains conformal field theory as an application of moduli theory. This is the English translation of a book originally published in Japanese. Other books by Kenji Ueno published in this AMS series, Translations of Mathematical Monographs, include An Introduction toAlgebraic Geometry, Volume 166, Algebraic Geometry 1: From Algebraic Varieties to Schemes, Volume 185, and Algebraic Geometry 2: Sheaves and Cohomology, Volume 197.

Download or read book The Geometry of Domains in Space written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans lations-have both shaped and guided this development. In particular, the Fourier transform and the theory of translation invariant operators (convolution transforms) have played a central role in this analysis. Much modern work in analysis takes place on a domain in space. In this context the tools, perforce, must be different. No longer can we expect there to be symmetries. Correspondingly, there is no longer any natural way to apply the Fourier transform. Pseudodifferential operators and Fourier integral operators can playa role in solving some of the problems, but other problems require new, more geometric, ideas. At a more basic level, the analysis of a smoothly bounded domain in space requires a great deal of preliminary spadework. Tubular neighbor hoods, the second fundamental form, the notion of "positive reach", and the implicit function theorem are just some of the tools that need to be invoked regularly to set up this analysis. The normal and tangent bundles become part of the language of classical analysis when that analysis is done on a domain. Many of the ideas in partial differential equations-such as Egorov's canonical transformation theorem-become rather natural when viewed in geometric language. Many of the questions that are natural to an analyst-such as extension theorems for various classes of functions-are most naturally formulated using ideas from geometry.

Download or read book The Evolution Problem in General Relativity written by Sergiu Klainerman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this work is to revisit the proof of the global stability of Minkowski space by D. Christodoulou and S. Klainerman, [Ch-KI]. We provide a new self-contained proof of the main part of that result, which concerns the full solution of the radiation problem in vacuum, for arbitrary asymptotically flat initial data sets. This can also be interpreted as a proof of the global stability of the external region of Schwarzschild spacetime. The proof, which is a significant modification of the arguments in [Ch-Kl], is based on a double null foliation of spacetime instead of the mixed null-maximal foliation used in [Ch-Kl]. This approach is more naturally adapted to the radiation features of the Einstein equations and leads to important technical simplifications. In the first chapter we review some basic notions of differential geometry that are sys tematically used in all the remaining chapters. We then introduce the Einstein equations and the initial data sets and discuss some of the basic features of the initial value problem in general relativity. We shall review, without proofs, well-established results concerning local and global existence and uniqueness and formulate our main result. The second chapter provides the technical motivation for the proof of our main theorem.

Download or read book Necessary Conditions of Learning written by Ference Marton and published by Routledge. This book was released on 2014-06-20 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Necessary Conditions of Learning presents a research approach (phenomenography) and a theory (the variation theory of learning) introduced and developed by Ference Marton and taken up by his wide and varied following around the world—together with their practical applications in educational contexts. Reflecting Marton’s whole lifetime's work, the unique and significant contribution of this book is to offer an evidence-based answer to the questions "How do we make novel meanings our own?" and "How do we learn to see things in more powerful ways?" The presentation makes use of hundreds of empirical studies carried out in Europe and Asia which build on the theory. The line of reasoning and the way in which the examples are put together is consistent with the theory—it is both presented and applied. The main argument is that in order to learn we have to discern, and to discern the intended ideas we must be presented with carefully structured variation, against a background of invariance. We then go through processes of contrast, generalization, and fusion in order to make sense. These insights form a practical framework for those who design teaching and teaching materials. Necessary Conditions of Learning is a major original work for which scholars of pedagogical theory have been waiting a long time.

Download or read book The Implicit Function Theorem written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2012-11-26 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for C^k functions, (ii) formulations in other function spaces, (iii) formulations for non- smooth functions, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash--Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex story, and is intimately bound up with the development of fundamental ideas in analysis and geometry. This entire development, together with mathematical examples and proofs, is recounted for the first time here. It is an exciting tale, and it continues to evolve. "The Implicit Function Theorem" is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas.

Download or read book The Annenbergs written by John E. Cooney and published by Simon & Schuster. This book was released on 1982 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is the colorful and dramatic biography of two of America's most controversial entrepreneurs: Moses Louis Annenberg, 'the racing wire king, ' who built his fortune in racketeering, invested it in publishing, and lost much of it in the biggest tax evasion case in United States history; and his son, Walter, launcher of TV Guide and Seventeen magazines and former ambassador to Great Britain."--Jacket.

Download or read book Research in Education written by James H. McMillan and published by Addison-Wesley Educational Publishers. This book was released on 1997 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Legal Writer written by Gerald Lebovits and published by . This book was released on 2016 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: