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The great mathematician G. H. Hardy told us that ¿Beauty is the ?rst test: there is no permanent place in the world for ugly mathematics¿ (see [24, p. 85]). It is clear why Hardy loved complex analysis: it is a very beautiful partofclassicalmathematics. ThetheoryofHilbertspacesandofoperatorson themisalmostasclassicalandisperhapsasbeautifulascomplexanalysis. The studyoftheHardy¿Hilbertspace(aHilbertspacewhoseelementsareanalytic functions), and of operators on that space, combines these two subjects. The interplay produces a number of extraordinarily elegant results. For example, very elementary concepts from Hilbert space provide simple proofs of the Poisson integral (Theorem 1. 1. 21 below) and Cauchy integral (Theorem 1. 1. 19) formulas. The fundamental theorem about zeros of fu- tions in the Hardy¿Hilbert space (Corollary 2. 4. 10) is the central ingredient of a beautiful proof that every continuous function on [0,1] can be uniformly approximated by polynomials with prime exponents (Corollary 2. 5. 3). The Hardy¿Hilbert space context is necessary to understand the structure of the invariant subspaces of the unilateral shift (Theorem 2. 2. 12). Conversely, pr- erties of the unilateral shift operator are useful in obtaining results on f- torizations of analytic functions (e. g. , Theorem 2. 3. 4) and on other aspects of analytic functions (e. g. , Theorem 2. 3. 3). The study of Toeplitz operators on the Hardy¿Hilbert space is the most natural way of deriving many of the properties of classical Toeplitz mat- ces (e. g. , Theorem 3. 3.

Feedstuff is a common standard for each kind of food for animals, which are in the charge of man and serve as food. Feed for livestock is of special interest. The quality of feed is responsible for the health of animals and indirectly for the quality of human nutrition. Agriculturally used plants, such as numerous grains, oil seeds and nuts, root crops, and to a smaller extent, many forage crops are susceptible to mycotoxin contamination. Fungal and in the end mycotoxin contaminated feed may be involved in modern livestock production practice (confined rearing on high-density diets) because plant feedstuff especially from multiple sources may be used for feeding. The mixing of mycotoxin contaminated pecan, walnut, or other nut meats into feedstuff is one example. The nuts are pressed to recover the oil while most of the toxin is concentrated in the residual meats. The press cake usually is diverted into animal feed channels. The amount of these (protein supplement) ingredients, while small, could cause problems in the health of animal and human. Available data suggest that the mold and mycotoxin problem is largely one of the worldwide feed management. Especially individual farm silos and feed troughs are major sites of toxin production in mold-contaminated feeds. Guidelines for the investigation and amelioration of feedstuff quality in different countries have been prepared. Mycotoxin contamination of feeds occurs as a result of crop invasion by field fungi.

Among all great ape species, the bonobo is still the least studied in both captivity and the wild. Nevertheless we have observed a considerable increase in knowledge across various fields of bonobo research in recent years. In part due to the ongoing peace process in the Democratic Republic of Congo, research and conservation activities on the bonobo have resumed and multiplied since 2001. Part One of The Bonobos: Behavior, Ecology, and Conservation focuses on scientific research. Behavioral studies in captivity propose to answer why bonobos have some unique characteristics such as high social status of females and flexible social relationships. The outcomes present important aspects to be investigated in running field studies. In the wild, analysis of population genetics across the bonobo's distribution range illuminates the species' evolutionary path and contributes to a global management plan. Site specific analysis reveals how genetics are used to re-identify individuals after an extended interruption of long-term research. Ecological studies at three independent sites, two in Salonga National Park, as well as one in the Luo Scientific Reserve, provide valuable information for the comprehension of ecological adaptation of bonobos. With the application of recent methods of mammalian feeding ecology as well as comparative approaches in other great ape species, these studies allow us to draw conclusions on ape ecological adaptation and evolution. Part Two of The Bonobos: Behavior, Ecology, and Conservation focuses on conservation. In overview, local and global aspects of the factors threatening the wild bonobo population are reviewed. Here the outcomes of large-scale efforts within the functioning ecosystem conservation paradigm focus on three landscapes within the range of the bonobo: the Salonga-Lukenie-Sankuru Landscape, the Maringa-Lopori-Wamba Landscape, and the Lac Télé-Lac Tumba Swamp Forest Landscape, are presented. Papers in thispart include the different aspects of various stakeholders and discuss the unique threats and actions taken to ensure bonobo survival. Pioneering the way, details from the first comprehensive assessment of bonobos in the Salonga National Park reveal a baseline from which to monitor future trends. Concerned about the indigenous' peoples aspects of conservation, an ethnographic study documents cultural, social, and economic practices for the purpose of reviving the local traditional knowledge to exemplify possible applications at the national level. To be inclusive of all aspects of range country concerns, the contributions of Kinshasa's bonobo sanctuary to national conservation efforts are presented. The outcome of these contributions taken together not only illuminate the current status of the bonobo but allow for critically designing the next steps for the continuation of its future.

This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

This series is intended for the rapidly increasing number of health care professionals who have rudimentary knowledge and experience in health care computing and are seeking opportunities to expand their horizons. It does not attempt to compete with the primers already on the market. Eminent international experts will edit, author, or contribute to each volume in order to provide comprehensive and current accounts of in- novations and future trends in this quickly evolving field. Each book will be practical, easy to use, and weIl referenced. Our aim is for the series to encompass all of the health professions by focusing on specific professions, such as nursing, in individual volumes. However, integrated computing systems are only one tool for improving communication among members of the health care team. Therefore, it is our hope that the series will stimulate professionals to explore additional me ans of fostering interdisciplinary exchange. This se ries springs from a professional collaboration that has grown over the years into a highly valued personal friendship. Our joint values put people first. If the Computers in Health Care series lets us share those values by helping health care professionals to communicate their ideas for the benefit of patients, then our efforts will have succeeded.

This work is aimed at an audience with asound mathematical background wishing to leam about the rapidly expanding field of mathematical finance. Its content is suitable particularly for graduate students in mathematics who have a background in measure theory and prob ability. The emphasis throughout is on developing the mathematical concepts re- quired for the theory within the context of their application. No attempt is made to cover the bewildering variety of novel (or 'exotic') financial instru- ments that now appear on the derivatives markets; the focus throughout remains on a rigorous development of the more basic options that lie at the heart of the remarkable range of current applications of martingale theory to financial markets. The first five chapters present the theory in a discrete-time framework. Stochastic calculus is not required, and this material should be accessible to anyone familiar with elementary probability theory and linear algebra. The basic idea of pricing by arbitrage (or, rather, by nonarbitrage) is presented in Chapter 1. The unique price for a European option in a single- period binomial model is given and then extended to multi-period binomial models. Chapter 2 intro duces the idea of a martingale measure for price pro- cesses. Following a discussion of the use of self-financing trading strategies to hedge against trading risk, it is shown how options can be priced using an equivalent measure for which the discounted price process is a mar- tingale.

Since the term "e;random ?eld'' has a variety of different connotations, ranging from agriculture to statistical mechanics, let us start by clarifying that, in this book, a random ?eld is a stochastic process, usually taking values in a Euclidean space, and de?ned over a parameter space of dimensionality at least 1. Consequently, random processes de?ned on countable parameter spaces will not 1 appear here. Indeed, even processes on R will make only rare appearances and, from the point of view of this book, are almost trivial. The parameter spaces we like best are manifolds, although for much of the time we shall require no more than that they be pseudometric spaces. With this clari?cation in hand, the next thing that you should know is that this book will have a sequel dealing primarily with applications. In fact, as we complete this book, we have already started, together with KW (Keith Worsley), on a companion volume [8] tentatively entitled RFG-A,or Random Fields and Geometry: Applications. The current volume-RFG-concentrates on the theory and mathematical background of random ?elds, while RFG-A is intended to do precisely what its title promises. Once the companion volume is published, you will ?nd there not only applications of the theory of this book, but of (smooth) random ?elds in general.

Algebraic curves are the graphs of polynomial equations in two vari- 3 ables, such as y3 + 5xy2 = x + 2xy. By focusing on curves of degree at most 3-lines, conics, and cubics-this book aims to fill the gap between the familiar subject of analytic geometry and the general study of alge- braic curves. This text is designed for a one-semester class that serves both as a a geometry course for mathematics majors in general and as a sequel to college geometry for teachers of secondary school mathe- matics. The only prerequisite is first-year calculus. On the one hand, this book can serve as a text for an undergraduate geometry course for all mathematics majors. Algebraic geometry unites algebra, geometry, topology, and analysis, and it is one of the most exciting areas of modem mathematics. Unfortunately, the subject is not easily accessible, and most introductory courses require a prohibitive amount of mathematical machinery. We avoid this problem by focusing on curves of degree at most 3. This keeps the results tangible and the proofs natural. It lets us emphasize the power of two fundamental ideas, homogeneous coordinates and intersection multiplicities.

My goal in writing this book has been to provide teachers and students of multi­ variate statistics with a unified treatment ofboth theoretical and practical aspects of this fascinating area. The text is designed for a broad readership, including advanced undergraduate students and graduate students in statistics, graduate students in bi­ ology, anthropology, life sciences, and other areas, and postgraduate students. The style of this book reflects my beliefthat the common distinction between multivariate statistical theory and multivariate methods is artificial and should be abandoned. I hope that readers who are mostly interested in practical applications will find the theory accessible and interesting. Similarly I hope to show to more mathematically interested students that multivariate statistical modelling is much more than applying formulas to data sets. The text covers mostly parametric models, but gives brief introductions to computer-intensive methods such as the bootstrap and randomization tests as well. The selection of material reflects my own preferences and views. My principle in writing this text has been to restrict the presentation to relatively few topics, but cover these in detail. This should allow the student to study an area deeply enough to feel comfortable with it, and to start reading more advanced books or articles on the same topic.

Although the ?rst decades of the 20th century saw some strong debates on set theory and the foundation of mathematics, afterwards set theory has turned into a solid branch of mathematics, indeed, so solid, that it serves as the foundation of the whole building of mathematics. Later generations, honest to Hilbert's dictum, "e;No one can chase us out of the paradise that Cantor has created for us"e; proved countless deep and interesting theorems and also applied the methods of set theory to various problems in algebra, topology, in?nitary combinatorics, and real analysis. The invention of forcing produced a powerful, technically sophisticated tool for solving unsolvable problems. Still, most results of the pre-Cohen era can be digested with just the knowledge of a commonsense introduction to the topic. And it is a worthy e?ort, here we refer not just to usefulness, but, ?rst and foremost, to mathematical beauty. In this volume we o?er a collection of various problems in set theory. Most of classical set theory is covered, classical in the sense that independence methods are not used, but classical also in the sense that most results come fromtheperiod,say,1920-1970.Manyproblemsarealsorelatedtoother?elds of mathematics such as algebra, combinatorics, topology, and real analysis. We do not concentrate on the axiomatic framework, although some - pects, such as the axiom of foundation or the role E of the axiom of choice, are elaborated.

About the first edition:"e;The text is geared to the needs of the beginning graduate student, covering with complete, well-written proofs the usual major branches of groups, rings, fields, and modules...[n]one of the material one expects in a book like this is missing, and the level of detail is appropriate for its intended audience."e; (Alberto Delgado, MathSciNet)"e;This text promotes the conceptual understanding of algebra as a whole, and that with great methodological mastery. Although the presentation is predominantly abstract...it nevertheless features a careful selection of important examples, together with a remarkably detailed and strategically skillful elaboration of the more sophisticated, abstract theories."e; (Werner Kleinert, Zentralblatt)For the new edition, the author has completely rewritten the text, reorganized many of the sections, and even cut or shortened material which is no longer essential. He has added a chapter on Ext and Tor, as well as a bit of topology.

Intended for nonspecialists with some knowledge of physics or engineering, The Quantum Beat covers a wide range of salient topics relevant to atomic clocks, treated in a broad intuitive manner with a minimum of mathematical formalism. Detailed descriptions are given of the design principles of the rubidium, cesium, hydrogen maser, and mercury ion standards; the revolutionary changes that the advent of the laser has made possible, such as laser cooling, optical pumping, the formation of "optical molasses," and the cesium "fountain" standard; and the time-based global navigation systems, Loran-C and the Global Positioning System. Also included are topics that bear on the precision and absolute accuracy of standards, such as noise, resonance line shape, the relativistic Doppler effect as well as more general relativistic notions of time relevant to synchronization of remote clocks, and time reversal symmetry.This edition retains the essentially didactic approach to the treatment of the development of atomic clocks in the first edition, but brings up to date the extraordinary developments in recent years, culminating in clocks based on quantum resonance at optical frequency in individual ions confined in miniature electromagnetic traps. These, together with advances in the generation of wide-band coherent frequency combs spanning the spectrum as far as the optical range, has made possible the direct measurement of phenomena occurring at optical frequencies! As a result of these recent advances, in addition to the time-based GPS and LORAN C navigation systems treated in the first edition, other important applications of a fundamental scientific interest have become feasible. These include satellite-borne tests of the theory of general relativity and the equivalence principle on which it is based.

As a student I discovered in our library a thin booklet by Frederick Mosteller entitled50 Challenging Problems in Probability. Itreferredtoas- plementary "e;regular textbook"e; by William Feller, An Introduction to Pro- bilityTheoryanditsApplications.SoItookthisonealong,too,andstartedon the ?rst of Mosteller's problems on the train riding home. From that evening, I caught on to probability. These two books were not primarily about abstract formalisms but rather about basic modeling ideas and about ways - often extremely elegant ones - to apply those notions to a surprising variety of empirical phenomena. Essentially, these books taught the reader the skill to "e;think probabilistically"e; and to apply simple probability models to real-world problems. The present book is in this tradition; it is based on the view that those cognitive skills are best acquired by solving challenging, nonstandard pro- bility problems. My own experience, both in learning and in teaching, is that challenging problems often help to develop, and to sharpen, our probabilistic intuition much better than plain-style deductions from abstract concepts.

The theory of convex optimization has been constantly developing over the past 30 years.  Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "e;anticonvex"e; and "e;convex-anticonvex"e; optimizaton problems.  This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity.  This manuscript will be of great interest for experts in this and related fields.

Due to the serious spoilage and health issues the presence of mycotoxins can cause, it's imperative that the food industry has a basic understanding fungi and their corresponding mycotoxins. An indispensable resource, Mycotoxins in Foodstuffs gives an in depth overview by listing the degree of contamination, concentration and country of origin/detection for each case of mycotoxin contamination for each commodity. In addition, the book shows whether or not food is predisposed for mycotoxin contamination.

This book is based on a two-semester course in ordinary di?erential eq- tions that I have taught to graduate students for two decades at the U- versity of Missouri. The scope of the narrative evolved over time from an embryonic collection of supplementary notes, through many classroom tested revisions, to a treatment of the subject that is suitable for a year (or more) of graduate study. If it is true that students of di?erential equations giveaway their point of viewbythewaytheydenotethederivativewith respecttotheindependent variable, then the initiated reader can turn to Chapter 1, note that I write x ?,not x , and thus correctly deduce that this book is written with an eye toward dynamical systems. Indeed, this book contains a thorough int- duction to the basic properties of di?erential equations that are needed to approach the modern theory of (nonlinear) dynamical systems. However, this is not the whole story. The book is also a product of my desire to demonstrate to my students that di?erential equations is the least insular of mathematical subjects, that it is strongly connected to almost all areas of mathematics, and it is an essential element of applied mathematics.

This new and completely revised edition brings several new elements to the reader. Each chapter begins with aseries of Major Study Topics and con- cludes with some Questions for Reviewand Discussion. I also have added a glossary to assist students with unfamiliar terms. This edition offers a greater emphasis on molecular biology and genetics than was present in either of the previous editions. The sequence of topics has also changed so that basic regulation and recombination are introduced early to provide a basis for subsequent discussion. I have preserved the pre- sentation of basic virology and genetic transfer processes while expanding coverage of plasmid molecular biology. All of what I would consider to be essential material occurs within the first 13chapters. The final four chapters are shorter, optional material and are not interdependent; they can be used in any order or omitted at an instructor's discretion. It is a pleasure to acknowledge the able assistance of the editorial and production staff of Springer-Verlag. I am also grateful to my colleagues who were so patient with my questions and to Rene Allard for his helpful com- ments on the first six chapters.