This book presents basic atomic theory as given in first and second year courses at university. It demonstrates that the structure of the Periodic Table as we know it is based on sound principles. Throughout the book, theoretical concepts are presented, along with the experimental evidence for them. Foundations are laid in the introductory chapter, which deals with fundamental particles, electromagnetic radiation and Heisenberg's uncertainty principle. Atomic orbitals are then described, using a minimum of mathematics, followed by a discussion of the electron configurations of the elements. Further chapters reveal the relationships between the electronic configurations of the elements and some properties of their atoms; and the variations in the properties of their fluorides and oxides across the periods and down the groups of the Periodic Table. Ideal for the needs of undergraduate chemistry students, Tutorial Chemistry Texts is a major new series consisting of short, single topic or modular texts concentrating on the fundamental areas of chemistry taught in undergraduate science courses. Each book provides a concise account of the basic principles underlying a given subject, embodying an independent-learning philosophy and including worked examples.

Motivated by recent increased activity of research on time scales, the book provides a systematic approach to the study of the qualitative theory of boundedness, periodicity and stability of Volterra integro-dynamic equations on time scales. Researchers and graduate students who are interested in the method of Lyapunov functions/functionals, in the study of boundedness of solutions, in the stability of the zero solution, or in the existence of periodic solutions should be able to use this book as a primary reference and as a resource of latest findings. This book contains many open problems and should be of great benefit to those who are pursuing research in dynamical systems or in Volterra integro-dynamic equations on time scales with or without delays. Great efforts were made to present rigorous and detailed proofs of theorems. The book should serve as an encyclopedia on the construction of Lyapunov functionals in analyzing solutions of dynamical systems on time scales. The book is suitable for a graduate course in the format of graduate seminars or as special topics course on dynamical systems. The book should be of interest to investigators in biology, chemistry, economics, engineering, mathematics and physics.

Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.

The origin of these Studies dates from many years back. As a youth I was faced, as others are, by the problem of sex. Living partly in an Australian city where the ways of life were plainly seen, partly in the solitude of the bush, I was free both to contemplate and to meditate many things. A resolve slowly grew up within me: one main part of my life-work should be to make clear the problems of sex. That was more than twenty years ago. Since then I can honestly say that in all that I have done that resolve has never been very far from my thoughts. I have always been slowly working up to this central problem; and in a book published some three years ago—Man and Woman: a Study of Human Secondary Sexual Characters—I put forward what was, in my own eyes, an introduction to the study of the primary questions of sexual psychology. Now that I have at length reached the time for beginning to publish my results, these results scarcely seem to me large. As a youth, I had hoped to settle problems for those who came after; now I am quietly content if I do little more than state them. For even that, I now think, is much; it is at least the half of knowledge. In this particular field the evil of ignorance is magnified by our efforts to suppress that which never can be suppressed, though in the effort of suppression it may become perverted. I have at least tried to find out what are the facts, among normal people as well as among abnormal people; for, while it seems to me that the physician's training is necessary in order to ascertain the facts, the physician for the most part only obtains the abnormal facts, which alone bring little light. I have tried to get at the facts, and, having got at the facts, to look them simply and squarely in the face. If I cannot perhaps turn the lock myself, I bring the key which can alone in the end rightly open the door: the key of sincerity. That is my one panacea: sincerity.

Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.

The theory of surgery on manifolds has been generalized to categories of manifolds with group actions in several different ways. This book discusses some basic properties that such theories have in common. Special emphasis is placed on analogs of the fourfold periodicity theorems in ordinary surgery and the roles of standard general position hypotheses on the strata of manifolds with group actions. The contents of the book presuppose some familiarity with the basic ideas of surgery theory and transformation groups, but no previous knowledge of equivariant surgery is assumed. The book is designed to serve either as an introduction to equivariant surgery theory for advanced graduate students and researchers in related areas, or as an account of the authors' previously unpublished work on periodicity for specialists in surgery theory or transformation groups.

The theory of almost periodic functions is a very active field of research for scholars. This research monograph analyzes various classes of multi-dimensional metrically almost periodic type functions with values in complex Banach spaces. We provide many applications of our theoretical results to the abstract Volterra integro-differential inclusions in Banach spaces.

The central subject of this book is Almost Periodic Oscillations, the most common oscillations in applications and the most intricate for mathematical analysis. Prof. Akhmet's lucid and rigorous examination proves these oscillations are a "regular" component of chaotic attractors. The book focuses on almost periodic functions, first of all, as Stable (asymptotically) solutions of differential equations of different types, presumably discontinuous; and, secondly, as non-isolated oscillations in chaotic sets. Finally, the author proves the existence of Almost Periodic Oscillations (asymptotic and bi-asymptotic) by asymptotic equivalence between systems. The book brings readers' attention to contemporary methods for considering oscillations as well as to methods with strong potential for study of chaos in the future. Providing three powerful instruments for mathematical research of oscillations where dynamics are observable and applied, the book is ideal for engineers as well as specialists in electronics, computer sciences, robotics, neural networks, artificial networks, and biology. Distinctively combines results and methods of the theory of differential equations with thorough investigation of chaotic dynamics with almost periodic ingredients; Provides all necessary mathematical basics in their most developed form, negating the need for any additional sources for readers to start work in the area; Presents a unique method of investigation of discontinuous almost periodic solutions in its unified form, employed to differential equations with different types of discontinuity; Develops the equivalence method to its ultimate effective state such that most important theoretical problems and practical applications can be analyzed by the method.

This book presents a fully scientific account of the use of the golden ratio. It explores the observation that stable nucleides obey a number theory based general law. The discovery described in this book could be of seminal significance, also in other fields where the golden ratio is known to be of fundamental importance.