Potential theory grew out of mathematical physics, in particular out of the theory of gravitation and the theory of electrostatics. Mathematical physicists such as Poisson and Green introduced some of the central ideas of the subject. A mathematician with a general knowledge of analysis may find it useful to begin his study of classical potential theory by looking at its physical origins. Sections 2, 5 and 6 of these Notes give in part heuristic arguments based on physical considerations. These heuristic arguments suggest mathematical theorems and provide the mathematician with the problem of finding the proper hypotheses and mathematical proofs. These Notes are based on a one-semester course given by the author at Brown University in 1971. On the part of the reader, they assume a knowledge of Real Function Theory to the extent of a first year graduate course. In addition some elementary facts regarding harmonic functions are aS$umed as known. For convenience we have listed these facts in the Appendix. Some notation is also explained there. Essentially all the proofs we give in the Notes are for Euclidean 3-space R3 and Newtonian potentials ~.
A development of some of the principal applications of function theory in several complex variables to Banach algebras. The authors do not presuppose any knowledge of several complex variables on the part of the reader, and all relevant material is developed within the text. Furthermore, the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. This third edition contains new material on maximum modulus algebras and subharmonicity, the hull of a smooth curve, integral kernels, perturbations of the Stone-Weierstrass Theorem, boundaries of analytic varieties, polynomial hulls of sets over the circle, areas, and the topology of hulls. The authors have also included a new chapter commenting on history and recent developments, as well as an updated and expanded reading list.
During the past twenty years many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. On the one hand, function theory has been used to answer algebraic questions such as the question of the existence of idempotents in a Banach algebra. On the other hand, concepts arising from the study of Banach algebras such as the maximal ideal space, the Silov boundary, Gleason parts, etc. have led to new questions and to new methods of proof in function theory. Roughly one third of this book isconcerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. We presuppose no knowledge of severalcomplex variables on the part of the reader but develop the necessary material from scratch. The remainder of the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. For n > I no complete theory exists but many important particular problems have been solved. Throughout, our aim has been to make the exposition elementary and self-contained. We have cheerfully sacrificed generality and completeness all along the way in order to make it easier to understand the main ideas.
This book introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space.
This lecture series was presented by a consortium of universities in conjunction with the U.S. Air Force Office of Scientific Research during the period 1967-1969 in Washington, D.C. and at the University of Maryland. The series of lectures was devoted to active basic areas of contemporary analysis which is important in or shows potential in real-world applications. Each lecture presents a survey and critical review of aspects of the specific area addressed, with emphasis on new results, open problems, and applications. This volume contains nine lectures in the series; subsequent lectures will also be published.
What about those who'd drowned in the convoy since midnight? They were dead... their dreams quashed by a devastating event. Poof! Gone! One minute breathing... the next not. What about loved ones who were awaiting their arrival in America? Their dreams were quashed, too, weren't they? How were the dead ones chosen? And the survivors? Some would say it was their destiny, the work of an omniscient God. Surely, purpose and meaning mattered, though, or why would God even cause their existence to occur, if only to end for some in such a questionable and unfathomable fate? Those other ships were sunk by German U-boat torpedoes, but not Johnny's? No one was given a choice... yet, he survived to write this autobiography.
Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form. It is not abstraction for its own sake, but abstraction for the sake of efficiency, power and insight. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics. It did this by exposing the mathematical structure of geometry, and by providing the tools to analyse it. This is typical of the way algebra is applied; it is the best and purest form of application because it reveals the simplest and most universal mathematical structures. The present book aims to foster a proper appreciation of algebra by showing abstraction at work on concrete problems, the classical problems of construction by straightedge and compass. These problems originated in the time of Euclid, when geometry and number theory were paramount, and were not solved until th the 19 century, with the advent of abstract algebra. As we now know, alge bra brings about a unification of geometry, number theory and indeed most branches of mathematics. This is not really surprising when one has a historical understanding of the subject, which I also hope to impart.
During the last two decades several remarkable new results were discovered about harmonic measure in the complex plane. This book provides a careful survey of these results and an introduction to the branch of analysis which contains them. Many of these results, due to Bishop, Carleson, Jones, Makarov, Wolff and others, appear here in paperback for the first time. The book is accessible to students who have completed standard graduate courses in real and complex analysis. The first four chapters provide the needed background material on univalent functions, potential theory, and extremal length, and each chapter has many exercises to further inform and teach the readers.
A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book provides a broad view of these subjects at the level of calculus, without being a calculus book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history with mathematics. He covers the main ideas of Euclid, but with 2000 years of extra insights attached. Presupposing only high school algebra, it can be read by any well prepared student entering university. Moreover, this book will be popular with graduate students and researchers in mathematics due to its attractive and unusual treatment of fundamental topics. A set of well-written exercises at the end of each section allows new ideas to be instantly tested and reinforced.
Long respected as the most comprehensive nurse anesthesia resource available, this new edition continues the tradition of bringing together leading experts to create a balanced reference that applies scientific principles to today’s clinical anesthesia practice. Inside you’ll find a solid introduction to the equipment and patient care techniques unique to nurse anesthesia side-by-side with the cutting-edge research and application of evidence necessary to prepare you for tomorrow. Over 700 tables and boxes highlight the most essential information in a quick, easy-to-reference format. An easy-to-use organization with basic principles covered first, followed by individual chapters for each surgical specialty, ensures you have the information you need to build your knowledge. Over 650 figures of anatomy, nurse anesthesia procedures, and equipment enhance your understanding of complex information. Expert CRNA authors provide the most up-to-date and relevant clinical information you’ll use in daily practice. The latest pharmacology information on pharmacokinetics, drug delivery systems, opiate antagonists, and key induction drugs to keep you up-to-date. Thoroughly updated references make finding the latest and most important research in the field quick and simple. New chapters address legal issues, neonatal anesthesia, anesthesia education, clinical monitoring, regional anesthesia, unexpected complications, and more. Expanded coverage of chemistry and physics as well as immunology makes these difficult fundamental topics easier to understand and apply to everyday practice. Over 100 new images enhance your understanding of difficult anesthesia concepts.
The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.
Completely updated edition, written by a close-knit author team Presents a unique approach to stroke - integrated clinical management that weaves together causation, presentation, diagnosis, management and rehabilitation Includes increased coverage of the statins due to clearer evidence of their effectiveness in preventing stroke Features important new evidence on the preventive effect of lowering blood pressure Contains a completely revised section on imaging Covers new advances in interventional radiology
Counterexamples are remarkably effective for understanding the meaning, and the limitations, of mathematical results. Fornaess and Stensones look at some of the major ideas of several complex variables by considering counterexamples to what might seem like reasonable variations or generalizations. The first part of the book reviews some of the basics of the theory, in a self-contained introduction to several complex variables. The counterexamples cover a variety of important topics: the Levi problem, plurisubharmonic functions, Monge-Ampere equations, CR geometry, function theory, and the $\bar\partial$ equation. The book would be an excellent supplement to a graduate course on several complex variables.
This book discusses a variety of problems which are usually treated in a second course on the theory of functions of one complex variable, the level being gauged for graduate students. It treats several topics in geometric function theory as well as potential theory in the plane, covering in particular: conformal equivalence for simply connected regions, conformal equivalence for finitely connected regions, analytic covering maps, de Branges' proof of the Bieberbach conjecture, harmonic functions, Hardy spaces on the disk, potential theory in the plane. A knowledge of integration theory and functional analysis is assumed.
This book describes the way in which the human brain is supplied with blood and how the brain uses this to provide nutrients, primarily oxygen and glucose, to brain cells in order to maintain healthy brain function. In particular, it focuses on the quantitative nature of blood flow and metabolism. The book covers models of blood flow and metabolism and how these can be measured using a variety of imaging and non-imaging techniques. It also examines how cerebral blood flow is controlled in response to a wide variety of challenges and how it changes with normal physiological variation and in response to a large number of pathological conditions, including stroke and dementia.As the first substantial book for over ten years in a fast-changing field, it highlights how the subject has progressed in the last couple of decades. It tackles the subject in a quantitative way, underlining its importance in both technical and clinical fields. Audiences with a technical or clinical background, especially researchers and postgraduate students in biomedical engineering or medicine, will find this a valuable read.
An introduction to the variational methods used to formulate and solve mathematical and physical problems, allowing the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency, laying as it does the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, as well as computer science.
Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. The book bases its discussion of algorithms on a generalisation of the division algorithm for polynomials in one variable that was only discovered in the 1960's. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have let to some interesting applications, for example in robotics and in geometric theorem proving. In preparing this new edition, the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem.
Never before has a comprehensive history of the pancreas like History of the Pancreas been published. It not only is a historical review of the science of medicine, it is liberally interspersed with anecdotal vignettes of the researchers who have worked on this organ. Much of it, such as the discovery of the duct of Wirsüng, of the islets of Langerhans, of insulin, gastrin and their tumors, reads like the adverture, which it is. This book, divided into 14 chapters, is written in a narrative style and is easily readable, as glimpses of the investigators, those who failed as well as those who succeeded, adds both perspective and human interest. Each chapter is completely referenced, totaling over 1500 references. As a reference book for students, teachers, investigators, writers, its detailed hjistorical documentation is unique. From the pre-Christian era of Asia Minor, to Greece, Rome, Europe and America, to the explosive progress in Japan, the history is there. History of the Pancreas: Mysteries of a Hidden Organ fills a gap.
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.