Expert judgment is invaluable for assessing products, systems, and situations for which measurements or test results are sparse or nonexistent. Eliciting and Analyzing Expert Judgment: A Practical Guide takes the reader step by step through the techniques of eliciting and analyzing expert judgment, with special attention given to helping the reader develop elicitation methods and tools adaptable to a variety of unique situations and work areas. The analysis procedures presented in the book may require a basic understanding of statistics and probabilities, but the authors have provided detailed explanations of the techniques used and have taken special care to define all statistical jargon. Originally published in 1991, this book is designed so that those familiar with the use of expert judgment can quickly find the material appropriate for their advanced background.

Statisticians know that the clean data sets that appear in textbook problems have little to do with real-life industry data. To better prepare their students for all types of statistical careers, academic statisticians now strive to use data sets from real-life statistical problems. This book contains 20 case studies that use actual data sets that have not been simplified for classroom use. Each case study is a collaboration between statisticians from academe and from business, industry, or government. This book is the result of a collaborative workshop of statisticians focusing on academic-industrial partnerships. The cases come from a wide variety of application areas, including biology/environment, medical and health care, pharmaceutical, marketing and survey research, and manufacturing.

This monograph deals with aspects of the computer programming process that involve techniques derived from mathematical logic. The author focuses on proving that a given program produces the intended result whenever it halts, that a given program will eventually halt, that a given program is partially correct and terminates, and that a system of rewriting rules always halts. Also, the author describes the intermediate behavior of a given program, and discusses constructing a program to meet a given specification.

As this monograph shows, the purpose of cardinal spline interpolation is to bridge the gap between the linear spline and the cardinal series. The author explains cardinal spline functions, the basic properties of B-splines, including B- splines with equidistant knots and cardinal splines represented in terms of B-splines, and exponential Euler splines, leading to the most important case and central problem of the book - cardinal spline interpolation, with main results, proofs, and some applications. Other topics discussed include cardinal Hermite interpolation, semi-cardinal interpolation, finite spline interpolation problems, extremum and limit properties, equidistant spline interpolation applied to approximations of Fourier transforms, and the smoothing of histograms.

In the field of combinatorial optimization problems, the Vehicle Routing Problem (VRP) is one of the most challenging. Defined more than 40 years ago, the problem involves designing the optimal set of routes for fleets of vehicles for the purpose of serving a given set of customers. Interest in VRP is motivated by its practical relevance as well as its considerable difficulty. The Vehicle Routing Problem covers both exact and heuristic methods developed for the VRP and some of its main variants, emphasizing the practical issues common to VRP. The book is composed of three parts containing contributions from well-known experts. The first part covers basic VRP, known more commonly as capacitated VRP.

This book studies the use of scientific computation as a tool in attacking a number of mathematical problems and conjectures. In this case, scientific computation refers primarily to computations that are carried out with a large number of significant digits, for calculations associated with a variety of numerical techniques such as the (second) Remez algorithm in polynomial and rational approximation theory, Richardson extrapolation of sequences of numbers, the accurate finding of zeros of polynomials of large degree, and the numerical approximation of integrals by quadrature techniques. The goal of this book is not to delve into the specialized field dealing with the creation of robust and reliable software needed to implement these high-precision calculations, but rather to emphasize the enormous power that existing software brings to the mathematician's arsenal of weapons for attacking mathematical problems and conjectures.

The global approach to nonlinear renewal theory is integrated with the author's own local approach. Both the theory and its applications are placed in perspective by including a discussion of the linear renewal theorem and its applications to the sequential probability ratio test. Applications to repeated significance tests, to tests with power one, and to sequential estimation are also included. The monograph is self- contained for readers with a working knowledge of measure-theoretic probability and intermediate statistical theory.

Mathematical theories of populations have appeared both implicitly and explicitly in many important studies of populations, human populations as well as populations of animals, cells and viruses. They provide a systematic way for studying a population's underlying structure. A basic model in population age structure is studied and then applied, extended and modified, to several population phenomena such as stable age distributions, self-limiting effects, and two-sex populations. Population genetics are studied with special attention to derivation and analysis of a model for a one-locus, two-allele trait in a large randomly mating population. The dynamics of contagious phenomena in a population are studied in the context of epidemic diseases.

Many fundamental combinatorial problems, arising in such diverse fields as artificial intelligence, logic, graph theory, and linear algebra, can be formulated as Boolean constraint satisfaction problems (CSP). This book is devoted to the study of the complexity of such problems. The authors' goal is to develop a framework for classifying the complexity of Boolean CSP in a uniform way. In doing so, they bring out common themes underlying many concepts and results in both algorithms and complexity theory. The results and techniques presented here show that Boolean CSP provide an excellent framework for discovering and formally validating ‘global’ inferences about the nature of computation. This book presents a novel and compact form of a compendium that classifies an infinite number of problems by using a rule-based approach. This enables practitioners to determine whether or not a given problem is known to be computationally intractable.

Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.

Algebraic Theory of Automata Networks investigates automata networks as algebraic structures and develops their theory in line with other algebraic theories. Automata networks are investigated as products of automata, and the fundamental results in regard to automata networks are surveyed and extended, including the main decomposition theorems of Letichevsky, and of Krohn and Rhodes. The text summarizes the most important results of the past four decades regarding automata networks and presents many new results discovered since the last book on this subject was published. Several new methods and special techniques are discussed, including characterization of homomorphically complete classes of automata under the cascade product; products of automata with semi-Letichevsky criterion and without any Letichevsky criteria; automata with control words; primitive products and temporal products; network completeness for digraphs having all loop edges; complete finite automata network graphs with minimal number of edges; and emulation of automata networks by corresponding asynchronous ones.

A study of the art and science of solving elliptic problems numerically, with an emphasis on problems that have important scientific and engineering applications, and that are solvable at moderate cost on computing machines.

H-infinity control originated from an effort to codify classical control methods, where one shapes frequency response functions for linear systems to meet certain objectives. H-infinity control underwent tremendous development in the 1980s and made considerable strides toward systematizing classical control. This book addresses the next major issue of how this extends to nonlinear systems. At the core of nonlinear control theory lie two partial differential equations (PDEs). One is a first-order evolution equation called the information state equation, which constitutes the dynamics of the controller. One can view this equation as a nonlinear dynamical system. Much of this volume is concerned with basic properties of this system, such as the nature of trajectories, stability, and, most important, how it leads to a general solution of the nonlinear H-infinity control problem.

Toeplitz systems arise in a variety of applications in mathematics, scientific computing, and engineering, including numerical partial and ordinary differential equations, numerical solutions of convolution-type integral equations, stationary autoregressive time series in statistics, minimal realization problems in control theory, system identification problems in signal processing, and image restoration problems in image processing. This practical book introduces current developments in using iterative methods for solving Toeplitz systems based on the preconditioned conjugate gradient method. The authors focus on the important aspects of iterative Toeplitz solvers and give special attention to the construction of efficient circulant preconditioners. Applications of iterative Toeplitz solvers to practical problems are addressed, enabling readers to use the book s methods and algorithms to solve their own problems. An appendix containing the MATLABA® programs used to generate the numerical results is included. Students and researchers in computational mathematics and scientific computing will benefit from this book.

Developed over the course of many years of on-the-job projects involving HVAC energy auditing, testing/balancing and cost estimating, and refined through feedback from thousands of engineers and technicians who have used them, the forms contained in this manual are concise, comprehensive, and optimally organized for easy reference. Complete sets of forms are provided for all aspects of testing and balancing, energy auditing, indoor quality diagnosis, and load calculations. The first edition, entitled HVAC Energy Audit & Balancing Forms Manual compiled these time-saving forms for the first time in a single reference. This enhanced second edition adds a new chapter on technical management, providing procedures for achieving thorough, systematic and accurate problem solving, troubleshooting and decision making in building systems management and contracting.