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Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.
As science integrates the in-depth knowledge of the physical world accumulated over the past three centuries, it will be channeled into a new and exciting line of inquiry that acknowledges the expanded reality of consciousness as a creative force in the universe and the spiritual creative power embodied in our own minds. This book summarizes the thoughts of an inquisitive, but open-minded, scientist. What I present here is a theory that looks promising, not scientific proof. It should not be surprising, however, if some of what I propose coincides with theories propounded by others who claim a more intimate relationship with the Almighty. After all, if I am on the right track, and if they are, it would be worrisome if we were not, ultimately, in agreement. All I ask is that you seriously consider the logic of my theory, especially if it challenges you to question what you were taught - in Sunday school, in catechism or, dare I say, in physics class. I offer this book, not as a theological treatise, but as a short, readable exposition of a worldview that can bring sense and purpose into individual lives, and tolerance and peace to a planet whose future is in serious jeopardy - in large part because of the irrational dogmatism of both religion and science. If I am correct, we are literally all one being (God) in many individual forms. Why, then, would we continue to harm one another?
The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications. From the reviews: "I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." --MATHEMATICAL REVIEWS
Mathematically rigorous exposition of the basic theory of marked point processes and piecewise deterministic stochastic processes Point processes are constructed from scratch with detailed proofs Includes applications with examples and exercises in survival analysis, branching processes, ruin probabilities, sports (soccer), finance and risk management, and queueing theory Accessible to a wider cross-disciplinary audience
Problems of Point Blast Theory covers all the main topics of modern theory with the exception of applications to nova and supernova outbursts. All the presently known theoretical results are given and problems which are still to be resolved are indicated. A special feature of the book is the sophisticated mathematical approach. Of interest to specialists and graduate students working in hydrodynamics, explosion theory, plasma physics, mathematical physics, and applied mathematics.
The purpose of this series is to help make contemporary European philosophy intelligible to a wider audience in the English-speaking world, and to suggest its interest and importance in particular to those trained in analytical philosophy.
This book presents some of the latest research in critical point theory, describing methods and presenting the newest applications. Coverage includes extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. Applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations.
The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland’s variational principle.
This book develops the central aspect of fixed point theory – the topological fixed point index – to maximal generality, emphasizing correspondences and other aspects of the theory that are of special interest to economics. Numerous topological consequences are presented, along with important implications for dynamical systems. The book assumes the reader has no mathematical knowledge beyond that which is familiar to all theoretical economists. In addition to making the material available to a broad audience, avoiding algebraic topology results in more geometric and intuitive proofs. Graduate students and researchers in economics, and related fields in mathematics and computer science, will benefit from this book, both as a useful reference and as a well-written rigorous exposition of foundational mathematics. Numerous problems sketch key results from a wide variety of topics in theoretical economics, making the book an outstanding text for advanced graduate courses in economics and related disciplines.
How does science work? Does it tell us what the world is “really” like? What makes it different from other ways of understanding the universe? In Theory and Reality, Peter Godfrey-Smith addresses these questions by taking the reader on a grand tour of more than a hundred years of debate about science. The result is a completely accessible introduction to the main themes of the philosophy of science. Examples and asides engage the beginning student, a glossary of terms explains key concepts, and suggestions for further reading are included at the end of each chapter. Like no other text in this field, Theory and Reality combines a survey of recent history of the philosophy of science with current key debates that any beginning scholar or critical reader can follow. The second edition is thoroughly updated and expanded by the author with a new chapter on truth, simplicity, and models in science.