Zero-Dimensional Commutative Rings


Book Description

This work presents advances in zero-dimensional commutative rings and commutative algebra. It illustrates the research frontier with 52 open problems together with comments on the relevant literature, and offers a comprehensive index for easy access to information. Wide-ranging developments in commutative ring theory are examined.




The Engineering Handbook


Book Description

First published in 1995, The Engineering Handbook quickly became the definitive engineering reference. Although it remains a bestseller, the many advances realized in traditional engineering fields along with the emergence and rapid growth of fields such as biomedical engineering, computer engineering, and nanotechnology mean that the time has come to bring this standard-setting reference up to date. New in the Second Edition 19 completely new chapters addressing important topics in bioinstrumentation, control systems, nanotechnology, image and signal processing, electronics, environmental systems, structural systems 131 chapters fully revised and updated Expanded lists of engineering associations and societies The Engineering Handbook, Second Edition is designed to enlighten experts in areas outside their own specialties, to refresh the knowledge of mature practitioners, and to educate engineering novices. Whether you work in industry, government, or academia, this is simply the best, most useful engineering reference you can have in your personal, office, or institutional library.




The Big Picture


Book Description

As a college student, author Captain Jack Jaknovich yearned to understand the world. To do so, he began writing. In The Big Picture, he presents a host of essays compiled over the years that explain how actions, reactions, and consequences of various interconnected events follow an identifiable pattern in the past that points toward a goal of evolution for life from Earth into the universe. The Big Picture discusses how businesses and nongovernmental organizations use governments, the media, and other sources to manipulate peoples fears to ensure profits for themselves and their associates. Jaknovich shows how this multi-pronged strategy causes people to fear independent travel, limit perspectives to that of mainstream media, and remain impassive regarding unethical practices. The essays include guidance for the psychological revolution needed to ensure the survival of life in a sustainable manner. Drawing on interpretations from many realms of thought and study, The Big Picture presents a study on existence and evolution that can help humans live longer, happier lives.




Algebraic Geometry


Book Description

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.




Dimensions, Embeddings, and Attractors


Book Description

This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part brings together a number of abstract embedding results, and provides a unified treatment of four definitions of dimension that arise in disparate fields: Lebesgue covering dimension (from classical 'dimension theory'), Hausdorff dimension (from geometric measure theory), upper box-counting dimension (from dynamical systems), and Assouad dimension (from the theory of metric spaces). These abstract embedding results are applied in the second part of the book to the finite-dimensional global attractors that arise in certain infinite-dimensional dynamical systems, deducing practical consequences from the existence of such attractors: a version of the Takens time-delay embedding theorem valid in spatially extended systems, and a result on parametrisation by point values. This book will appeal to all researchers with an interest in dimension theory, particularly those working in dynamical systems.




A new paradigm of reality?


Book Description

The vision that culture has historically offered about reality has failed to help humans to live fully or to achieve their potential. A knowledge revolution has been taking place in recent years that, once it is understood, can completely transform human beings, offering new solutions to personal and collective problems because their root causes have been identified at last. What we now know means that we can understand spiritual truths and their multiple dimensions without abandoning rationality. This new vision is strong enough to put an end to human suffering and boost inner peace, which is for what every being human yearns. New science sees an intelligent design in the whole Universe. Quantum physics has revolutionized our knowledge of reality. All scientists are now aware of the quantum "enigmas" but not everyone agrees on how to interpret them. This book offers an interpretation that might explain them, and one that is based on the idea of "science within consciousness". As you read the book, it will become evident that this interpretation most closely resembles the vision of reality that both the perennial wisdom of Humanity and the teachings of the great spiritual masters have offered us throughout history. The first part of the book outlines briefly what some of the leading thinkers on science and philosophy have to say about reality and how this new vision of the world is converging with what the perennial wisdom of Humanity has been saying throughout our history. The second part seeks to explain what can happen to us when we are exposed to this new knowledge and how all of us can change inside ourselves in the light of this information. This book aims to unite, not divide, helping Humanity to raise its level of consciousness, allowing us to live a higher quality life in accordance with our spiritual dimension.




The Fence Methods


Book Description

This book is about a recently developed class of strategies, known as the fence methods, which fits particularly well in non-conventional and complex model selection problems with practical considerations. The idea involves a procedure to isolate a subgroup of what are known as correct models, of which the optimal model is a member. This is accomplished by constructing a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is constructed, the optimal model is selected from amongst those within the fence according to a criterion which can be made flexible. In particular, the criterion of optimality can incorporate consideration of practical interest, thus making model selection a real life practice.Furthermore, this book introduces a data-driven approach, called adaptive fence, which can be used in a wide range of problems involving determination of tuning parameters, or constants. Instead of relying on asymptotic theory, the fence focuses on finite-sample performance, and computation. Such features are particularly suitable to statistics in the new era.




Entropy in Dynamical Systems


Book Description

This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon–McMillan–Breiman Theorem, the Ornstein–Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses symbolic extension entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research.




Methods of Algebraic Geometry: Volume 3


Book Description

All three volumes of Hodge and Pedoe's classic work have now been reissued. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.




Automated Deduction in Geometry


Book Description

This book constitutes the thoroughly refereed post-proceedings of the 4th International Workshop on Automated Deduction in Geometry, ADG 2002, held at Hagenberg Castle, Austria in September 2002. The 13 revised full papers presented were carefully selected during two rounds of reviewing and improvement. Among the issues addressed are theoretical and methodological topics, such as the resolution of singularities, algebraic geometry and computer algebra; various geometric theorem proving systems are explored; and applications of automated deduction in geometry are demonstrated in fields like computer-aided design and robotics.