An up-to-date, comprehensive account of major issues in finitemixture modeling This volume provides an up-to-date account of the theory andapplications of modeling via finite mixture distributions. With anemphasis on the applications of mixture models in both mainstreamanalysis and other areas such as unsupervised pattern recognition,speech recognition, and medical imaging, the book describes theformulations of the finite mixture approach, details itsmethodology, discusses aspects of its implementation, andillustrates its application in many common statisticalcontexts. Major issues discussed in this book include identifiabilityproblems, actual fitting of finite mixtures through use of the EMalgorithm, properties of the maximum likelihood estimators soobtained, assessment of the number of components to be used in themixture, and the applicability of asymptotic theory in providing abasis for the solutions to some of these problems. The author alsoconsiders how the EM algorithm can be scaled to handle the fittingof mixture models to very large databases, as in data miningapplications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and patternrecognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied andtheoretical statisticians as well as for researchers in the manyareas in which finite mixture models can be used to analyze data.

Equations for aerodynamic quantities of interest in equilibrium isentropic one-dimensional flows and for properties across plane showck waves in arbitrary of planetary gases are derived under the assumption that the gases obey the perfect gas law. This assumption restricts the range of applicability of the equations to conditions for which the onset of chemical dissociation or ionization has not been reached although no requirement for the gases to be calorically perfect is imposed. Analytic functions used to specify the variation of specific heats with temperature are consistent with the assumption that molecular vibrations behave like harmonic oscillators and are independent of rotational degrees of freedom. Simplified equations giving approximate results over more limited ranges of the variables are also presented. Sample comparisons of the aerodynamic behavior of a number of pure gases are made. It is shown that while some of the flow quantities characterizing aerodynamic flows are very sensitive to gas composition, the stagnation pressure coefficients for a number of gases differ by only a few percent from one gas to another.

Liquids and Liquid Mixtures, Third Edition explores the equilibrium properties of liquids and liquid mixtures and relates them to the properties of the constituent molecules using the methods of statistical thermodynamics. Topics covered include the critical state, fluid mixtures at high pressures, and the statistical thermodynamics of fluids and mixtures. This book consists of eight chapters and begins with an overview of the liquid state and the thermodynamic properties of liquids and liquid mixtures, including vapor pressure and heat capacities. The discussion then turns to the thermodynamics of and inequalities at the critical point; measurement of thermodynamic functions in the critical region; experimental values of the critical exponents; and scaling of the free energy. The change of thermodynamic functions with composition is the subject of the next two chapters, followed by an analysis of fluid mixtures at high pressures. The final chapter is devoted to the statistical thermodynamics of fluids and mixtures, paying particular attention to the thermodynamic properties in terms of the forces between the molecules; the balance of intermolecular potentials between like and unlike molecules; and phase behavior. This monograph will be of interest to students and researchers in the fields of chemistry and chemical engineering.

Advanced Thermodynamics Engineering, Second Edition is designed for readers who need to understand and apply the engineering physics of thermodynamic concepts. It employs a self-teaching format that reinforces presentation of critical concepts, mathematical relationships, and equations with concrete physical examples and explanations of application

This book deals with the kinetic modelling of gas mixtures. It extends the existing literature in mathematics for one species of gas to the case of gas mixtures. This is more realistic in applications. The presented model for gas mixtures is proven to be consistent meaning it satisfies the conservation laws, it admits an entropy and an equilibrium state. Furthermore, we can guarantee the existence, uniqueness and positivity of solutions. Moreover, the model is used for different applications, for example in plasma physics, for fluids with a small deviation from equilibrium and in the case of polyatomic gases.

New developments in assessing and managing risk are discussed in this volume. Addressing both practitioners in the banking sector and research institutions, the book provides a manifold view on the most-discussed topics in finance. Among the subjects treated are important issues such as: risk measures and allocation of risks, factor modeling, risk premia in the hedge funds industry and credit risk management. The volume provides an overview of recent developments as well as future trends in the area of risk assessment.

In this newly revised 5th Edition of Chemical and Engineering Thermodynamics, Sandler presents a modern, applied approach to chemical thermodynamics and provides sufficient detail to develop a solid understanding of the key principles in the field. The text confronts current information on environmental and safety issues and how chemical engineering principles apply in biochemical engineering, bio-technology, polymers, and solid-state-processing. This book is appropriate for the undergraduate and graduate level courses.

The most comprehensive, single-volume guide to conductingexperiments with mixtures "If one is involved, or heavily interested, in experiments onmixtures of ingredients, one must obtain this book. It is, as wasthe first edition, the definitive work." -Short Book Reviews (Publication of the International StatisticalInstitute) "The text contains many examples with worked solutions and with itsextensive coverage of the subject matter will prove invaluable tothose in the industrial and educational sectors whose work involvesthe design and analysis of mixture experiments." -Journal of the Royal Statistical Society "The author has done a great job in presenting the vitalinformation on experiments with mixtures in a lucid and readablestyle. . . . A very informative, interesting, and useful book on animportant statistical topic." -Zentralblatt fur Mathematik und Ihre Grenzgebiete Experiments with Mixtures shows researchers and students how todesign and set up mixture experiments, then analyze the data anddraw inferences from the results. Virtually every technique thathas appeared in the literature of mixtures can be found here, andcomputing formulas for each method are provided with completelyworked examples. Almost all of the numerical examples are takenfrom real experiments. Coverage begins with Scheffe latticedesigns, introducing the use of independent variables, and endswith the most current methods. New material includes: * Multiple response cases * Residuals and least-squares estimates * Categories of components: Mixtures of mixtures * Fixed as well as variable values for the major componentproportions * Leverage and the Hat Matrix * Fitting a slack-variable model * Estimating components of variances in a mixed model using ANOVAtable entries * Clarification of blocking mates and choice of mates * Optimizing several responses simultaneously * Biplots for multiple responses