In the second edition of this highly successful book, the authors once again aim to equip the reader with up-to-date information. This book, containing more than 200 cadaveric photos and 200 illustrations, aims to familiarize physicians practicing botulinum neurotoxin type A (BoNT-A) and filler injection with the anatomy of the facial mimetic muscles, vessels, and soft tissues in order to enable them to achieve optimum cosmetic results while avoiding possible adverse events. Anatomic considerations of importance when administering BoNT-A and fillers are identified and in addition invaluable clinical guidelines are provided, highlighting, for example, the preferred injection points for BoNT-A and the adequate depth of filler injection. Unique insights are also offered into the differences between Asians and Caucasians with regard to relevant anatomy. The contributing authors include an anatomist who offers distinctive anatomic perspectives on BoNT-A and filler treatments and three expert physicians from different specialties, namely a dermatologist, a plastic surgeon, and a cosmetic physician, who share insights gained during extensive clinical experience in the use of BoNT-A and fillers.

This atlas deals with the standard technique used for reconstructing the mandible and the maxilla - the fibula flap. The reader will find useful information on all issues that are important in the surgical procedure, including the use of CAD-CAM technology (Computer Assisted Technology), bone synthesis and flap modelling.

This second edition of Probability With Statistical Applications offers a practical introduction to probability for undergraduates at all levels with different backgrounds and views towards applications. Calculus is a prerequisite for understanding the basic concepts, however the book is written with a sensitivity to students’ common difficulties with calculus that does not obscure the thorough treatment of the probability content. The first six chapters of this text neatly and concisely cover the material traditionally required by most undergraduate programs for a first course in probability.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas­ sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe­ matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface A wide range of problems exists in classical and quantum physics, engi­ neering, and applied mathematics in which special functions arise. The procedure followed in most texts on these topics (e. g. , quantum mechanics, electrodynamics, modern physics, classical mechanics, etc. ) is to formu­ late the problem as a differential equation that is related to one of several special differential equations (Hermite's, Bessel's, Laguerre's, Legendre's, etc. )

The bulk of the present book has not been published previously though Chapters II and IV are based in part on two earlier papers of mine: "The Influence of Harald H!1lffding's Philosophy on Niels Bohr's Interpretation of Quantum Mechanics", which appeared in Danish Yearbook of Philosophy, 1979, and "The Bohr-H!1lffding Relationship Reconsidered", published in Studies in History and Philosophy of Science, 1988. These two papers comple­ ment each other, and in order to give the whole issue a more extended treatment I have sought, in the present volume by drawing on relevant historical material, to substantiate the claim that H!1lffding was Bohr's mentor. Besides containing a detailed account of Bohr's philosophy, the book, at the same time, serves the purpose of making H!1lffding' s ideas and historical significance better known to a non-Danish readership. During my work on this book I have consulted the Royal Danish Library; the National Archive of Denmark and the Niels Bohr Archive, Copenhagen, in search of relevant material. I am grateful for permission to use and quote material from these sources. Likewise, I am indebted to colleagues and friends for commenting upon the manuscript: I am especially grateful to Professor Henry Folse for our many discussions during my visit to New Orleans in November-December 1988 and again here in Elsinore in July 1990.

The Second Law of Thermodynamics has been called the most important law of nature: It is the law that gives a direction to processes that is not inherent in the laws of motion, that says the state of the universe is driven to thermal equilibrium. Its mathematical formulation is simple: The entropy of a closed system cannot decrease. Since the recognition that macroscopic phenomena have an atomic basis, it has remained a fundamental problem to reconcile the increase of entropy with the known reversibility of all the laws of microscopic physics. Professor Michael Mackey of McGill University here explores the dynamical basis for the Second Law, that is, he seeks to illuminate the fundamental dynamical properties required for the construction of a successful statistical mechanics. Aimed at physicists and applied mathematicians with an interest in the foundations of statistical mechanics, the book includes such new material as: a demonstration that the black body radiation law can be deduced from maximal entropy principles; a discussion of sufficient conditions for the existence of at least one state of thermodynamic equilibrium; a description of the behavior of entropy in asymptotically periodic systems; a necessary and sufficient condition for the evolution of entropy to a global maximum; and a presen- tation of the three main types of ergodic theorems and their proofs. He also explores the potential role of incomplete knowledge of dynamical variables, measurement imprecision, and the effects of noise in giving rise to entropy increases.

The Schrodinger equation is the basic equation of quantum theory. The study of this equation plays an exceptionally important role in modern physics. From a mathematician's point of view the Schrodinger equation is as inexhaustible as mathematics itself.