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Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields (including the real and complex numbers) as representing a localization of the problems under consideration. We shall deal with global problems, all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational points.

My principal aim in writing this book was to present a wide range of astrophysical topics in sufficient depth to give the reader a general quantitative understanding of the subject. The book outlines cosmic events but does not portray them in detail-it provides aseries of astrophysical sketches. I think this approach befits the present uncertainties and changing views in astrophysics. The material is based on notes I prepared for a course aimed at seniors and beginning graduate students in physics and astronomy at Cornell. This course defined the level at which the book is written. For readers who are versed in physics but are unfamiliar with astronomical terminology, Appendix A is included. It gives a brief background of astronomical concepts and should be read before starting the main text. The first few chapters outline the scope of modern astrophysics and deal with elementary problems concerning the size and mass of cosmic objects. However, it soon becomes apparent that a broad foundation in physics is needed to proceed. This base is developed in Chapters 4 to 7 by using, as ex am pIes, specific astronomi- cal situations. Chapters 8 to 10 enlarge on the topics first outlined in Chapter I and show how we can obtain quantitative insights into the structure and evolution of stars, the dynamics of co~mic gases, and the large-scale behavior of the universe.

This text attempts to change the way we teach logic to beginning students. Instead of teaching logic as a subject in isolation, we regard it as a basic tool and show how to use it. We strive to give students a skill in the propo­ sitional and predicate calculi and then to exercise that skill thoroughly in applications that arise in computer science and discrete mathematics. We are not logicians, but programming methodologists, and this text reflects that perspective. We are among the first generation of scientists who are more interested in using logic than in studying it. With this text, we hope to empower further generations of computer scientists and math­ ematicians to become serious users of logic. Logic is the glue Logic is the glue that binds together methods of reasoning, in all domains. The traditional proof methods -for example, proof by assumption, con­ tradiction, mutual implication, and induction- have their basis in formal logic. Thus, whether proofs are to be presented formally or informally, a study of logic can provide understanding.

The title gives a reasonable ?rst-order approximation to what this book is about. To explain why, let's start with the expression "e;di?erential equations."e; These are essential in science and engineering, because the laws of nature t- ically result in equations relating spatial and temporal changes in one or more variables.Todevelopanunderstandingofwhatisinvolvedin?ndingsolutions, the book begins with problems involving derivatives for only one independent variable, and these give rise to ordinary di?erential equations. Speci?cally, the ?rst chapter considers initial value problems (time derivatives), and the second concentrates on boundary value problems (space derivatives). In the succeeding four chapters problems involving both time and space derivatives, partial di?erential equations, are investigated. This brings us to the next expression in the title: "e;numerical methods."e; This is a book about how to transform di?erential equations into problems that can be solved using a computer. The fact is that computers are only able to solve discrete problems and generally do this using ?nite-precision arithmetic. What this means is that in deriving and then using a numerical algorithmthecorrectnessofthediscreteapproximationmustbeconsidered,as must the consequences of round-o? error in using ?oating-point arithmetic to calculatetheanswer.Oneoftheinterestingaspectsofthesubjectisthatwhat appears to be an obviously correct numerical method can result in complete failure. Consequently, although the book concentrates on the derivation and use of numerical methods, the theoretical underpinnings are also presented andusedinthedevelopment.

The Journey Ahead At the heart of transcendental number theory lies an intriguing paradox: While essen- tially all numbers are transcendental, establishing the transcendence of a particular number is a monumental task. Thus transcendental numbers are an enigmatic species of number: We know they are all around us and yet it requires enormous effort to catch one. More often than not, they slip through our fingers and dissappear back into the dense jungle of numbers. Here we will venture to tame a few of these incredible creatures. In the pages ahead we offer an approach to transcendence that not only includes the intricate analysis but also the beautiful ideas behind the technical details. The phrase "e;classical transcendental number theory"e; in the title of this book refers to the most widely known results that were obtained in the nineteenth and early twentieth centuries. The reason for this focus is threefold. Firstly, this body of work requires only the mathematical techniques and tools familiar to advanced undergraduate mathematics students, and thus this area can be appreciated by a wide range of readers. Secondly, the ideas behind modem transcendence results are almost always an elaboration of the classical arguments we will explore here. And finally, and perhaps more importantly, this early work yields the transcendence of such admired and well-known numbers as e, rr, and even 2v'2.

Geometry of Biological Time deals with dynamics of processes that repeat themselves regularly. Such rhythmic return through a cycle of change is an ubiquitous principle of organization in living systems. In this revised and updated edition the author plans to extend the thread from 1980 to the present concentrating on areas which he personally feels have been interesting and where he feels there will be much activity in the future. This involves going through spatial biochemical, electrophysiological, and organismic dynamical systems and patterns that were discovered by pursuing the theme of phase singularities that the original book introduced. In particular the work on excitability in cell membranes has been thoroughly updated as have the references throughout the book.

This extensive volume began as a short course primarily geared toward toxicologists who want to expand their understanding of toxicologic pathology in order to be better study directors while also proving to be of great interest to other drug development scientists and regulatory reviewers. The overall goal is to help non-pathologists understand, contextualize, and communicate the pathology data and interpretations from the study pathologist in a practical and usable format. Within the book, readers will find an overview of general pathology concepts that include fundamental vocabulary and the basics of pathophysiological processes, along with numerous chapters devoted to pathology in specific organ systems as well as topics such as biomarkers, correlation of clinical pathology endpoints (chemistry and hematology) with microscopic changes, and well-known pathology findings for classes of toxic substances. Authoritative, practical, and comprehensive, Toxicologic Pathology for Non-Pathologists aims to help non-pathologists understand, converse in, and apply a basic understanding of pathology in their day-to-day careers.

The oceans are shrinking. They're not literally shrinking; warming in the last century has actually expanded the sea enough to threaten low-lying coastal lands that are vul- nerable to storm surge. During the same interval, however, events on land have increasingly affected the sea. Since in most ways the Earth is a closed system-a zero-sum planet in today's parlance-as terrestrial influence on the sea expands, the sea's influence on its own processes shrinks. Control of many crucial marine processes no longer resides within the sea. The evidence for this is abundant and, to anyone who is looking, unmis- takable. In recent decades scientists have witnessed unprecedented pertur- bations and increases in previously uncommon events that demonstrate growing terrestrial influences on the sea. Numerous marine species, from sea urchins to monk seals, have experienced devastating epidemics. The number of harmful algal blooms and jellyfishpopulation explosions is rising An hypoxic "e;dead zone"e; in the Gulf of Mexico off the mouth of the Mississippi Rivernow appears each year and grows to encompass an area as large as NewJersey. Live coral cover in shallow reefs in Florida,Jamaica, the Maldives and many other locations has severely declined. Deepwater reef- building corals, once widely distributed, have disappeared throughout much of their ranges. Researchers have discovered high concentrations of persis- tent organic pollutants in declining populations of beluga whales and polar bears, both high trophic level predators in marine food webs.

This volume is being published for two reasons. The first is to present a collection of previously published articles on the subject of programming methodology that have helped define the field and give it direction. It is hoped that the scientist in the field will find the volume useful as a reference, while the scientist in neighboring fields will find it useful in seriously acquainting himself with important ideas in programming methodology. The advanced student can also study it-either in a course or by himself -in order to learn significant material that may not appear in texts for some time. The second reason for this volume is to make public the nature and work on programming methodology of IFIP Working Group 2.3, hereafter called WG2.3. (IFIP stands for International Federation for Information Processing.) WG2.3 is one of many IFIP Working Groups that have been established to provide international forums for discussion of ideas in various areas. Generally, these groups publish proceedings of some of their meetings and occasionally they sponsor a larger conference that persons outside a group can attend. WG2.3 has been something of a maverick in this respect. From the beginning the group has shunned paperwork, reports, meetings, and the like. This has meant less pUblicity for IFIP and WG2.3, but on the other hand it has meant that meetings could be devoted almost wholly to scientific discussions.

One of the most exciting developments in modern physics has been the discovery of the new class of oxide materials with high superconducting transition temperature. Systems with Tc well above liquid nitrogen temperature are already a reality and higher Tc's are anticipated. Indeed, the idea of a room-temperature superconductor, which just a short time ago was considered science fiction, appears to be a distinctly possible outcome of materials research. To address the need to train students and scientists for research in this exciting field, Jeffrey W. Lynn and colleagues at the University of Maryland, College Park, as well as other superconductivity experts from around the U.S., taught a graduate-level course in the fall of 1987, from which the chapters in this book were drawn. Subjects included are: Survey of superconductivity (J. Lynn).- The theory of type-II superconductivity (D. Belitz).- The Josephson effect (P. Ferrell).- Crystallography (A. Santoro).- Electronic structure (C.P. Wang).- Magnetic properties and interactions (J. Lynn).- Synthesis and diamagnetic properties (R. Shelton).- Electron pairing (P. Allen).- Superconducting devices (F. Bedard).- Superconducting properties (J. Crow, N.-P. Ong).

There is a growing social interest in developing vision-based vehicle guidance systems for improving traffic safety and efficiency and the environment. Ex- amples of vision-based vehicle guidance systems include collision warning systems, steering control systems for tracking painted lane marks, and speed control systems for preventing rear-end collisions. Like other guidance systems for aircraft and trains, these systems are ex- pected to increase traffic safety significantly. For example, safety improve- ments of aircraft landing processes after the introduction of automatic guidance systems have been reported to be 100 times better than prior to installment. Although the safety of human lives is beyond price, the cost for automatic guidance could be compensated by decreased insurance costs. It is becoming more important to increase traffic safety by decreasing the human driver's load in our society, especially with an increasing population of senior people who continue to drive. The second potential social benefit is the improvement of traffic efficiency by decreasing the spacing between vehicles without sacrificing safety. It is reported, for example, that four times the efficiency is expected if the spacing between cars is controlled automatically at 90 cm with a speed of 100 kmjh compared to today's typical manual driving. Although there are a lot of tech- nical, psychological, and social issues to be solved before realizing the high- density jhigh-speed traffic systems described here, highly efficient highways are becoming more important because of increasing traffic congestion.

Mast cells and basophils are responsible for inflammatory and allergic reactions. As such, the signals that generate these responses and how their pathways of action work are the focus of much present day research into allergy and inflammation. This book focuses primarily on the molecular mechanisms that govern mast cell and basophil cell biology and function, as well as providing a comprehensive summary of the field of signal transduction and also giving insights into areas that have therapeutic potential. The book provides detailed insights into mast cell and basophil growth and development, their activation by allergens, including details of receptor activation and downstream events, and the regulators of morphology and degranulation. The metabolic pathways involved in prostaglandin and leukotriene production are discussed as is the role of transcription factors in mast cell growth and cytokine production. Written by leaders in the field, this volume will provide the reader with an up-to-date account of a topic where the rapid progress makes conventional information gathering difficult.

This IMA Volume in Mathematics and its Applications SINGULARITIES AND OSCILLATIONS is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1994-1995 IMA program on "e;Waves and Scattering. "e; We would like to thank Joseph Keller, Jeffrey Rauch, and Michael Taylor for their excellent work as organizers of the meeting. We would like to express our further gratitude to Rauch and Taylor, who served as editors of the proceedings. We also take this opportunity to thank the National Science Foun- dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. Avner Friedman Robert Gulliver v PREFACE Thestudyofsingularitiesand oscillationsofwaves has progressed along several fronts. A key common feature is the presence of a small scale in the solutions. Recent emphasis has been on nonlinear waves. Nonlinear problems are generally less amenable than linear problems to broad unified approaches. As a result there is a justifiable tendency to concentrate on problems of particular geometric or physical interest. This volume con- tains a multiplicity of approaches brought to bear on problems varying from the formation ofcaustics and the propagation ofwaves at a boundary to the examination ofviscous boundary layers. There is an examination of the foundations of the theory of high-frequency electromagnetic waves in a dielectric or semiconducting medium. Unifying themes are not entirely absent from nonlinear analysis.

Neuroimaging: Clinical and Physical Principles is destined to be the new benchmark among text/reference books for neuroradiology. Unique among all similar titles is this book's complete coverage of ALL imaging modalities and techniques used in modern neuroimaging, from MR (including up-to-the minute developments in fast MR, MRA, and FLAIR), to CT, ultrasonography, angiography, plain film, and myelography. Many topics that are covered little if at all in standard neuroimaging texts are given complete, state-of-the-art descriptions in this book, including: imaging of the head, neck, temporal bone, orbit, and sinuses; normal variants; imaging of pediatric neurologic diseases and developmental anomalies; imaging of trauma to the head, brain, and spine; interventional techniques, both intracranial and spinal; and sedation of both adult and pediatric patients. The book is rounded out with complete coverage of the Physical Principles that underlie modern Computed Tomography and Magnetic Resonance Imaging. The ten chapters in this section provide everything the radiologist must know such as; the physical basics of MR and CT; MR and CT contrast agents and their applications; hardware and safety issues; image acquisition and artifacts; and more! Each chapter is organized to provide fast answers to everyday clinical problems. Numerous tables and lists summarize imaging protocols and differential diagnoses for rapid reference, while the text of each chapter provides a thorough review of the state of the art neuroimaging procedures. Chapters reveal potential imaging findings for numerous conditions and direct the reader towards the imaging technique that will reveal the most informative results under each circumstance.

The young investigator with an idea has to negotiate many institutional, federal, and industrial challenges in order to get a product to market. Nowhere is described the steps in the development of new drugs, diagnos- tics, or devices; the person with an idea has nowhere to turn for information and details. The young investigator may understand the elements of basic and clinical research, but ordinarily has no insight into novel ways of finding research funding or how to explore to find the funding opportunities that are available. The young investigator has little knowledge of the mecha- nisms to bring an idea through the developmental phases to the market. There are other players in this complex endeavor with whom he or she has no contact, including those from industry, the Food and Drug Administration, and the legal community. Exposure to the philosophy of product develop- ment and to procedural information would be useful to the scientific com- munity, as would contact with those who have successfully taken an idea to a finished product. A first attempt to do this was the symposium on Idea to Product: The Process, sponsored by Serono Symposia USA and held No- vember 17 to 20, 1994, in Washington, D.C. This book comprises the pro- ceedings of that meeting. The editors are indebted to the many contributors to this volume, and we are especially grateful to Serono Symposia USA and to Leslie Nies and her staff for their expertise in organizing the symposium.

This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems. The relations between random matrix models and the theory of classical integrable systems have long been studied. These appear mainly in the deformation theory, when parameters characterizing the measures or the domain of localization of the eigenvalues are varied. The resulting differential equations determining the partition function and correlation functions are, remarkably, of the same type as certain equations appearing in the theory of integrable systems. They may be analyzed effectively through methods based upon the Riemann-Hilbert problem of analytic function theory and by related approaches to the study of nonlinear asymptotics in the large N limit. Associated with studies of matrix models are certain stochastic processes, the "e;Dyson processes"e;, and their continuum diffusion limits, which govern the spectrum in random matrix ensembles, and may also be studied by related methods. Random Matrices, Random Processes and Integrable Systems provides an in-depth examination of random matrices with applications over a vast variety of domains, including multivariate statistics, random growth models, and many others. Leaders in the field apply the theory of integrable systems to the solution of fundamental problems in random systems and processes using an interdisciplinary approach that sheds new light on a dynamic topic of current research.

"e;Complex Intelligent Systems and Applications"e; presents the most up-to-date advances in complex, software intensive and intelligent systems. Each self-contained chapter is the contribution of distinguished experts in areas of research relevant to the study of complex, intelligent, and software intensive systems. These contributions focus on the resolution of complex problems from areas of networking, optimization and artificial intelligence. The book is divided into three parts focusing on complex intelligent network systems, efficient resource management in complex systems, and artificial data mining systems. Through the presentation of these diverse areas of application, the volume provides insights into the multidisciplinary nature of complex problems. Throughout the entire book, special emphasis is placed on optimization and efficiency in resource management, network interaction, and intelligent system design. This book presents the most recent interdisciplinary results in this area of research and can serve as a valuable tool for researchers interested in defining and resolving the types of complex problems that arise in networking, optimization, and artificial intelligence.

Numerous studies have pointed to the key role of complement in the pathogenesis of retinal disease, particularly age-related macular degeneration (AMD). Reports about new gene associations and links to other physiological pathways are emerging almost on a weekly base. Several promising clinical candidates covering a wide area of potential treatment applications are in the pipelines of both industrial and academic groups. This indicates an increasing interest in complement as a therapeutic target. In view of these exciting discoveries, scientists from around the world convened at the First Aegean Conferences Conference on Inflammation and Retinal Disease: Complement Biology and Pathology (June 10-17, 2007) in Crete, Greece, to discuss recent advances in this rapidly-evolving field. This volume represents a collection of topics on the functions of complement in eye diseases, pathophysiology, protein structures, and complement therapeutics discussed during the conference. Our sincere thanks to the contributing authors for the time and effort they have devoted to writing what I consider exceptionally informative chapters in a book that will have a significant impact on the complement field. We would also like to express my thanks to Rodanthi Lambris for her assistance in collating the chapters and preparing the documents for publication and I gratefully acknowledge the generous help provided by Dimitrios Lambris in managing the organization of this meeting. Finally, I also thank Andrea Macaluso of Springer Publishers for her supervision in this book's production. John D. Lambris Anthony P.

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi's most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter's prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1Numerical ConditioningSpecial FunctionsInterpolation and Approximation Selected Works with Commentaries, Vol. 2Orthogonal Polynomials on the Real LineOrthogonal Polynomials on the SemicircleChebyshev QuadratureKronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3Linear Difference EquationsOrdinary Differential EquationsSoftwareHistory and BiographyMiscellaneaWorks of Werner Gautschi

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi's most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter's prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1Numerical ConditioningSpecial FunctionsInterpolation and Approximation Selected Works with Commentaries, Vol. 2Orthogonal Polynomials on the Real LineOrthogonal Polynomials on the SemicircleChebyshev QuadratureKronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3Linear Difference EquationsOrdinary Differential EquationsSoftwareHistory and BiographyMiscellaneaWorks of Werner Gautschi

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi's most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter's prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1Numerical ConditioningSpecial FunctionsInterpolation and Approximation Selected Works with Commentaries, Vol. 2Orthogonal Polynomials on the Real LineOrthogonal Polynomials on the SemicircleChebyshev QuadratureKronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3Linear Difference EquationsOrdinary Differential EquationsSoftwareHistory and BiographyMiscellaneaWorks of Werner Gautschi

Rates of childhood obesity are alarmingly high and increasing each year. Studies have shown that obese children are more likely to become obese adults and are likely to suffer with numerous health consequences like coronary heart disease, high blood pressure, and Type II diabetes, among others. Studies also indicate that television viewing and exposure to advertising for food products influences children's attitudes toward, food preferences and food purchase requests for foods with low nutritional value. It is important to better understand the role of media in childhood obesity and to learn how media may be used to address this issue in a positive way. This book focuses on communication and media research that can have an impact on reducing childhood obesity. Emphasis is placed on topics related to how the media communicate health-related messages about food, nutrition and diet that influence childhood obesity. Particular emphasis is on the new media, given the fact that media now have more central roles in socializing today's children and youth than ever before. Advertising and marketing messages reach young consumers through a variety of vehicles - broadcast and cable television, radio, magazines, computers through the Internet, music, cell phones - and in many different venues - homes, schools, child-care settings, grocery stores, shopping malls, theaters, sporting events, and even airports. In addition, given the disparity in obesity rates between children of color and the general population, special attention is given to research on media targeting these populations.