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Probability Theory
This book is intended as an introduction to Probability Theory and Mathematical Statistics for students in mathematics, the physical sciences, engineering, and related fields. It is based on the author’s 25 years of experience teaching probability and is squarely aimed at helping students overcome common difficulties in learning the subject. The focus of the book is an explanation of the theory, mainly by the use of many examples. Whenever possible, proofs of stated results are provided. All sections conclude with a short list of problems. The book also includes several optional sections on more advanced topics. This textbook would be ideal for use in a first course in Probability Theory. Contents: Probabilities Conditional Probabilities and Independence Random Variables and Their Distribution Operations on Random Variables Expected Value, Variance, and Covariance Normally Distributed Random Vectors Limit Theorems Mathematical Statistics Appendix Bibliography Index
Nonstandard Analysis
Currently, nonstandard analysis is barely considered in university teaching. The author argues that nonstandard analysis is valuable not only for teaching, but also for understanding standard analysis and mathematics itself. An axiomatic approach wich pays attention to different language levels (for example, in the distinction between sums of ones and the natural numbers of the theory) leads naturally to a nonstandard theory. For motivation historical ideas of Leibniz can be taken up. The book contains an elaborated concept that follows this approach and is suitable, for example, as a basis for a lecture-supplementary course. The monograph part presents all major approaches to nonstandard an...
Extending Intersection Homology Type Invariants to Non-Witt Spaces
Intersection homology theory provides a way to obtain generalized Poincare duality, as well as a signature and characteristic classes, for singular spaces. For this to work, one has had to assume however that the space satisfies the so-called Witt condition. We extend this approach to constructing invariants to spaces more general than Witt spaces.
Probability in Banach Spaces, 9
The papers contained in this volume are an indication of the topics th discussed and the interests of the participants of The 9 International Conference on Probability in Banach Spaces, held at Sandjberg, Denmark, August 16-21, 1993. A glance at the table of contents indicates the broad range of topics covered at this conference. What defines research in this field is not so much the topics considered but the generality of the ques tions that are asked. The goal is to examine the behavior of large classes of stochastic processes and to describe it in terms of a few simple prop erties that the processes share. The reward of research like this is that occasionally one can gain deep insight, ev...
Bioengineering of the Skin
Through continuous research and development of modern instrumentation, it is now possible to visualize minute structures of the skin surface not visible to the human eye. Bioengineering of the Skin: Skin Surface Imaging and Analysis, written by an internationally based group of scientists, addresses engineering techniques for visualizing and analyzing skin surface images and profiles. This skin bioengineering reference offers comprehensive information about the technology of instruments in this field and the art of applying them in experimental studies. It explains what the instruments measure and why and when they should be used in skin research and product testing.
Dry Skin and Moisturizers
Dry Skin and Moisturizers: Chemistry and Function presents new information relating to skin biochemistry and pathological changes seen in various dry skin disorders. The book examines the pharmacology of ingredients in moisturizing preparations, providing a broad overview of formulations as well as detailed information on ingredients. Featuring contributions from leading researchers from around the world, the book also outlines general principles for testing and evaluation of effects on the skin, with particular emphasis on safety assessment. This comprehensive book is divided into five parts. Part I, Dry Skin and Moisturizers, offers an introduction to this fascinating topic, while Part II,...
Radially Symmetric Patterns of Reaction-Diffusion Systems
Includes a paper that studies bifurcations of stationary and time-periodic solutions to reaction-diffusion systems. This title develops a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns.
Invariants of Boundary Link Cobordism
An $n$-dimensional $\mu$-component boundary link is a codimension $2$ embedding of spheres $L=\sqcup_{\mu}S DEGREESn \subset S DEGREES{n+2}$ such that there exist $\mu$ disjoint oriented embedded $(n+1)$-manifolds which span the components of $L$. This title proceeds to compute the isomorphism class of $C_{
Allergic to Life
This easy-to-read title provides a comprehensive discussion of the major changes in daily life that have led to states of increased bodily inflammation. Indeed, today there is an epidemic of allergic and autoimmune disease in the first and developing world. While outdoor climate change is now considered common knowledge, the impact of longer work hours, artificial lighting, increased food shelf life, and changes to the microbiome all have made a large impact in increasing allergies worldwide. An allergy, best defined as a “damaging response from the Immune system due to a substance in the environment,” starts with warning signals, or generalized "symptoms," that are caused by something i...
High Dimensional Probability
What is high dimensional probability? Under this broad name we collect topics with a common philosophy, where the idea of high dimension plays a key role, either in the problem or in the methods by which it is approached. Let us give a specific example that can be immediately understood, that of Gaussian processes. Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. Assuming some regularity on the covariance, one tried to take advantage of the structure of the index set. Around 1970 it was understood, in particular by Dudley, Feldman, Gross, and Segal that a more abstract and intrinsic point of view was much more fruitful. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process. This shift in perspective subsequently lead to a considerable clarification of many aspects of Gaussian process theory, and also to its applications in other settings.
