Functional Analysis Methods for Reliability Models

The theorems of Hawking and Penrose show that space-times are likely to contain incomplete geodesics. Such geodesics are said to end at a singularity if it is impossible to continue the space-time and geodesic without violating the usual topological and smoothness conditions on the space-time. In this book the different possible singularities are defined, and the mathematical methods needed to extend the space-time are described in detail. The results obtained (many appearing here for the first time) show that singularities are associated with a lack of smoothness in the Riemann tensor. While the Friedmann singularity is analysed as an example, the emphasis is on general theorems and techniques rather than on the classification of particular exact solutions.

Despite its remote and seemingly rigorous environment, the Antarctic is the world's most important habitat for seals, currently supporting more seals than all other parts of the world combined. As various national Antarctic programmes were established to study these animals, the need to standardize techniques became apparent. This book, arising from work by the Scientific Committee on Antarctic Research (Group of Specialists on Seals), gives a detailed account of well-tried and, where possible, agreed methodologies, techniques, procedures and rationale for the collection and initial analysis of data on the biology and population ecology of Antarctic seals. This volume will not only help facilitate comparisons between different regions of Antarctica, but will also provide a guide for those studying seals in other parts of the world and those carrying out research on other large mammal species.

Within both the social and environmental sciences, much of the data collected is within a spatial context and requires statistical analysis for interpretation. The purpose of this book is to describe current methods for the analysis of spatial data. Methods described include data description, map interpolation, and exploratory and explanatory analyses. The book also examines spatial referencing, and methods for detecting problems, assessing their seriousness and taking appropriate action are discussed. This is an important text for any discipline requiring a broad overview of current theoretical and applied work for the analysis of spatial data sets. It will be of particular use to research workers and final year undergraduates in the fields of geography, environmental sciences and social sciences.

The calculus of variations has been an active area of mathematics for over 300 years. Its main use is to find stable critical points of functions for the solution of problems. To find unstable values, new approaches (Morse theory and min-max methods) were developed, and these are still being refined to overcome difficulties when applied to the theory of partial differential equations. Here, Professor Ghoussoub describes a point of view that may help when dealing with such problems. Building upon min-max methods, he systematically develops a general theory that can be applied in a variety of situations. In so doing he also presents a whole array of duality and perturbation methods. The prerequisites for following this book are relatively few; an appendix sketching certain methods in analysis makes the book reasonably self-contained. Consequently, it should be accessible to all mathematicians, pure or applied, economists and engineers working in nonlinear analysis or optimization.

This is the first comprehensive, yet clearly presented, account of statistical methods for analysing spherical data. The analysis of data, in the form of directions in space or of positions of points on a spherical surface, is required in many contexts in the earth sciences, astrophysics and other fields, yet the methodology required is disseminated throughout the literature. Statistical Analysis of Spherical Data aims to present a unified and up-to-date account of these methods for practical use. The emphasis is on applications rather than theory, with the statistical methods being illustrated throughout the book by data examples.

Observations of ocean circulation have increased as a result of international field programmes and of remote sensing systems on artificial earth satellites. Oceanographers are increasingly turning to inverse methods for combining these observations with numerical models of ocean circulation. Professor Bennett's work explores the potential for inverse theory, emphasizing possibilities rather than expedient or rudimentary applications. In addition to interpolating the data and adding realism to the model solutions, the methods can yield estimates for unobserved flow variables, forcing fields, and model parameters. Inverse formulations can resolve ill-posed modelling problems, lead to design criteria for oceanic observing systems, and enable the testing of models as scientific hypothesis. Exercises of varying difficulty rehearse technical skills and supplement the central theoretical development. Thus this book will be invaluable for environmental scientists and engineers, advanced underg

The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical but have little to do with what is described these days as real analysis. Most of the results described in this book have a dual formulation; they have a 'discrete version' related to a finitely generated discrete group, and a continuous version related to a Lie group. The authors chose to centre this book around Lie groups but could quite easily have pushed it in several other directions as it interacts with opetators, and probability theory, as well as with group theory. This book will serve as an excellent basis for graduate courses in Lie groups, Markov chains or potential theory.

This book presents statistical methods for analysis of the duration of events. The primary focus is on models for single-spell data, events in which individual agents are observed for a single duration. Some attention is also given to multiple-spell data. The first part of the book covers model specification, including both structural and reduced form models and models with and without neglected heterogeneity. The book next deals with likelihood based inference about such models, with sections on full and semiparametric specification. A final section treats graphical and numerical methods of specification testing. This is the first published exposition of current econometric methods for the study of duration data.

Based on methods of actual product developments from Goodyear Aerospace and Hewlett-Packard, this engrossing book provides specific guidelines plus a wealth of data for rapid and efficient development

This book provides students and research workers in the biological, medical and social sciences with the statistical background needed to collect and analyse data in an intelligent and critical manner. Key examples and case studies are used to illustrate commonly encountered research problems and to explain how they may be solved or even avoided altogether. Professor Manly also presents a clear understanding of the opportunities and limitations of different research designs, as well as an introduction to some new methods of analysis that are proving increasingly popular. Topics covered include the differences between observational and experimental studies; the design of sample surveys; multiple regression and its generalizations to log-linear and logistic models; experimental and quasi-experimental designs; interrupted time series; computer intensive methods of statistical inference; and the ethical considerations of research. In the final chapter, there is a useful discussion of how t

The Compendium of Organic Synthetic Methods series facilitates the working chemist's search for the most useful functional group transformations in organic chemistry. Drawn from an exhaustive survey o

A complete revision to the theory, practice and applications of factor analysis in chemistry--a mathematical technique for studying matrices of data. Methods of factor analysis that are quicker, more

Structured methodologies are a popular and powerful tool in information systems development. Many different ones exist, each employing a number of models and so a specification must be converted from one form to another during the development process. To solve this problem, Dr Tse proposes in this 1991 book a unifying framework behind popular structured models. He approaches the problem from the viewpoints of algebra and category theory. He not only develops the frameworks but also illustrates their practical and theoretical usefulness. Thus this book will provide insight for software engineers into how methodologies can be formalised and will open up a range of applications and problems for theoretical computer scientists.

Presented in this document is a class of deterministic models describing the dynamics of two plant species whose characteristics are common to the majority of annual plants that have a seedbank. Formulated in terms of elementary dynamical systems, these models were developed in response to four major questions on the long-term outcomes of binary mixtures of plant species: Is ultimate coexistence possible? If not, which strain will win? Does the mixture approach an equilibrium? If so, how long does the mixture take to attain it? The book gives a detailed account of model construction, analysis and application to field data obtained from long-term trials. In the particular case study modelled, the species involved are two pastural strains whose dynamics have critical agricultural and economic implications for the areas in which they are found, including North America, the Mediterranean region and Australia. This study will be valuable to researchers and students in mathematical biology a

The Statistical Analysis of Discrete Data provides an up-to-date introduction to methods for analyzing discrete data. The text covers both single-sample problems and problems with structured means whi

The advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric res

This is a concise graduate level introduction to analytical functional methods in quantum field theory. Functional integral methods provide relatively simple solutions to a wide range of problems in quantum field theory. After introducing the basic mathematical background, this book goes on to study applications and consequences of the formalism to the study of series expansions, measure, phase transitions, physics on spaces with nontrivial topologies, stochastic quantisation, fermions, QED, non-abelian gauge theories, symmetry breaking, the effective potential, finite temperature field theory, instantons and compositeness. Serious attention is paid to the shortcomings of the conventional formalism (e.g. problems of measure) as well as detailed appraisal of the ambiguities of series summation. This book will be of great use to graduate students in theoretical physics wishing to learn the use of functional integrals in quantum field theory. It will also be a useful reference for researc

This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be id

Treats linear regression diagnostics as a tool for application of linear regression models to real-life data. Presentation makes extensive use of examples to illustrate theory. Assesses the effect of

Bray's monograph considers the multivariate form of analysis of variance (MANOVA). The primary emphasis of the book is on methods for interpreting MANOVA statistical analyses. These are illustrated th

This introduction to mathematical methods that are useful for studying population phenomena is intended for advanced undergraduate and graduate students, and will be accessible to scientists who do not have a strong mathematics background. The material is graded in mathematical difficulty. The earlier parts of the book involve elementary diference equations while later chapters present topics that require more mathematical preparation. Models of total population and population age structure are first derived and studied, and then models of random population events are presented in terms of Markov chains. The last two chapters deal with mathematical methods used to uncover qualitative behaviour of more complicated difference equations. Each chapter begins with a simple model, usually of some historical interest, that defines the primary goals of the chapter. Exercises, for which solutions are provided, illustrate material in the text and also deal with models more advanced than those de

These notes originate from a one semester course which forms part of the "Math Methods" cycle at Brown. In the hope that these notes might prove useful for reference purposes several additional sectio

This short book sets out the principles of the methods commonly employed in obtaining numerical solutions to mathematical equations and shows how they are applied in solving particular types of equations. Now that computing facilities are available to most universities, scientific and engineering laboratories and design shops, an introduction to numerical method is an essential part of the training of scientists and engineers. A course on the lines of Professor Wilkes's book is given to graduate or undergraduate students of mathematics, the physical sciences and engineering at many universities and the number will increase. By concentrating on the essentials of his subject and giving it a modern slant, Professor Wilkes has written a book that is both concise and that covers the needs of a great many users of digital computers; it will serve also as a sound introduction for those who need to consult more detailed works.

How to spot patterns, identify opportunities, and grow your technical analysis skillsThe Trading Methodologies of W.D. Gann, Second Edition is a detailed yet accessible guide for trading, forecasting, and investing—using the principles of technical analysis to identify opportunities for profit. Beginning in the early 20th century, W.D. Gann developed pioneering methods of technical analysis that continue to hold value for modern traders. Gann’s insights on interpreting market conditions and recognizing patterns are a valuable addition to any trader’s strategy. The often cryptic nature of Gann’s original publications, however, prove challenging to modern readers. This valuable guide demystifies Gann’s techniques, providing clear and concise explanations and easy-to-follow instructions for today’s traders and investors. Expert trader and technical analyst Hima Reddy draws from her extensive experience to provide a systematic approach to Gann’s methodologies. This revised second edition i

Dynamic stability analysis enables the determination of unstable regions, which adversely affect a structure's durability. Unlike conventional cable-strut frameworks, tensegrity structures are characterized by a system of internal forces that hold the elements in stable equilibrium, so the initial prestress crucially affects the distribution of unstable regions. This book presents both theoretical background and examples to make a full qualitative and quantitative assessment of these structures possible. First, a geometrically non-linear model and the methods used to evaluate the behavior of tensegrity structures are explained, before a broad spectrum of different planar and spatial design solutions is considered. The book moves step-by-step from the simplest two-dimensional structure, for which solutions can be presented in explicit form, to more complex tensegrity structures such as domes, towers, and plates.

Transform any organization with proven strategies and tools for innovation Bringing together a wealth of experience from 60+ distinguished global thought leaders, How to Create Innovation is a comprehensive guide to becoming a leader in innovation and an organization that plays to win, containing all of the working methods, separate business innovation models, and processes you need to transform your organization digitally. The book includes 50+ ready-to-use tools, models, and canvases which you can download and start applying to your organization immediately. Written by Stefan F. Dieffenbacher, founder of an international award-winning consulting agency, the book draws upon Dieffenbacher's experiences working with clients like Amazon, BMW, Google, and Pfizer to deliver a one-stop, end-to-end solution to innovative transformation. In this book, readers will learn how to: Uncover opportunities by finding your niche and devising a more nuanced business strategyLead culture change by reco

Approximately 1 in 54 children in the U.S. will be diagnosed with an autism spectrum disorder (ASD) and that number is expected to rise, according to the CDC. Applied Behavior Analysis (ABA) is one of the most common interventions for those with ASD. One of the biggest problems facing the field of ABA-based interventions is ineffectiveness of intervention approaches due to the rigid application of ABA-based interventions. A Progressive Approach to Applied Behavior Analysis: The Autism Partnership Method provides practicing behavior analysts (e.g., BCBA, BCaBA, RBTs) and other clinicians with an in-depth introduction to a Progressive Approach to ABA and how it applies to common teaching methods within ABA-based interventions. This includes research and guidelines for implementing a Progressive Approach to ABA potentially increasing the likelihood of meaningful outcomes for the individuals with ASD. This will become the guide for practitioners on how to implement clinical judgement using

As the world becomes increasingly connected, it is also more exposed to a myriad of cyber threats. We need to use multiple types of tools and techniques to learn and understand the evolving threat landscape. Data is a common thread linking various types of devices and end users. Analyzing data across different segments of cybersecurity domains, particularly data generated during cyber-attacks, can help us understand threats better, prevent future cyber-attacks, and provide insights into the evolving cyber threat landscape. This book takes a data oriented approach to studying cyber threats, showing in depth how traditional methods such as anomaly detection can be extended using data analytics and also applies data analytics to non-traditional views of cybersecurity, such as multi domain analysis, time series and spatial data analysis, and human-centered cybersecurity.