Functional Analysis

A novel, practical introduction to functional analysis In the twenty years since the first edition of Applied Functional Analysis was published, there has been an explosion in the number of books on functional analysis. Yet none of these offers the unique perspective of this new edition. Jean-Pierre Aubin updates his popular reference on functional analysis with new insights and recent discoveries-adding three new chapters on set-valued analysis and convex analysis, viability kernels and capture basins, and first-order partial differential equations. He presents, for the first time at an introductory level, the extension of differential calculus in the framework of both the theory of distributions and set-valued analysis, and discusses their application for studying boundary-value problems for elliptic and parabolic partial differential equations and for systems of first-order partial differential equations. To keep the presentation concise and accessible, Jean-Pierre Aubin introduces functional analysis through the simple Hilbertian structure. He seamlessly blends pure mathematics with applied areas that illustrate the theory, incorporating a broad range of examples from numerical analysis, systems theory, calculus of variations, control and optimization theory, convex and nonsmooth analysis, and more. Finally, a summary of the essential theorems as well as exercises reinforcing key concepts are provided. Applied Functional Analysis, Second Edition is an excellent and timely resource for both pure and applied mathematicians.

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.

Functional Foods Presenting cutting-edge information on new and emerging food engineering processes, Functional Foods , the second volume in the groundbreaking new series, “Bioprocessing in Food Science,” is an essential reference on the modeling, quality, safety, and technologies associated with food processing operations today. Functional Foods , the second volume in series, “Bioprocessing in Food Science,” is an up-to-date, comprehensive volume covering the preparation, processes and health benefits of functional foods. Written and edited by a team of experts in the field, this important new volume provides readers extensive knowledge about different types of traditional and commercially available functional foods from different sources, such as milk, meat, cereals, millets and fruits and vegetables. The main objective of this book is to disseminate knowledge about the recent technologies developed in the field of functional foods to students, researchers, and industry professionals. This will enable them to make crucial decisions regarding the adoption, implementation, economics, and constraints of the different technologies. As the demand for healthy food is increasing, manufacturers are searching for new possibilities for occupying a growing share in the rapidly changing food market. Covering the use of conventional and non-conventional sources, prebiotics, probiotics and many other topics, with emphasis on their functionality in food systems, this volume also provides insights on the specific packaging requirements for functional foods with maximum illustrations of how to enhance shelf life and create superior quality products. The authors and editors discuss the need for regulatory frameworks, government bodies, guidelines, and their challenges within the context of the functional food market. Whether for the veteran engineer or scientist, the student, or a manager or other technician working in the field, this volume is a must-have for any library. This outstanding new volume: Discusses an overview of functional foods including global regulations, legislations and packaging requirements Provides knowledge of functional ingredients and health benefits of functional foods from different plants, animals, and microbes sources Acquaints the readers about technological aspects for functional ingredients delivery Addresses the basic to advanced aspects of different functional foods, combining the requirements, health benefits and regulations, showcasing the development of functional food products with potential functional benefits Audience: Process and chemical engineers, chemists, engineers in other disciplines, managers, researchers, scientists, students, and teachers working in the field of food engineering and processing

Functional oxides have a wide variety of applications in the electronic industry. The discovery of new metal oxides with interesting and useful properties continues to drive much research in chemistry, physics, and materials science. In Functional Oxides five topical areas have been selected to illustrate the importance of metal oxides in modern materials chemistry: Noncentrosymmetric Inorganic Oxide Materials Geometrically Frustrated Magnetic Materials Lithium Ion Conduction in Oxides Thermoelectric Oxides Transition Metal Oxides – Magnetoresistance and Half-Metallicity The contents highlight structural chemistry, magnetic and electronic properties, ionic conduction and other emerging areas of importance, such as thermoelectricity and spintronics. Functional Oxides covers these complex concepts in a clear and accessible manner providing an excellent introduction to this broad subject area.

A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique «learn by doing» approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.

Functional Metabolism of Cells is the first comprehensive survey of metabolism, offering an in-depth examination of metabolism and regulation of carbohydrates, lipids, and amino acids. It provides a basic background on metabolic regulation and adaptation as well as the chemical logic of metabolism, and covers the interrelationship of metabolism to life processes of the whole organism. The book lays out a structured approach to the metabolic basis of disease, including discussion of the normal pathways of metabolism, altered pathways leading to disease, and use of molecular genetics in diagnosis and treatment of disease. It also takes a unique comparative approach in which human metabolism is a reference for metabolism in microorganisms and plant design, and presents novel coverage of development and aging, and human health and animal adaptation. The final chapter reviews the past and future promise of new genetic approaches to treatment and bioinformatics. This, the most exhaustive treatment of metabolism currently available, is a useful text for advanced undergraduates and graduates in biochemistry, cell/molecular biology, and biomedicine, as well as biochemistry instructors and investigators in related fields.

Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems. The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations. The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields of science, engineering, and economics. Functional Differential Equations: Advances and Applications also features: • Discussions on the classes of equations that cannot be solved to the highest order derivative, and in turn, addresses existence results and behavior types • Oscillatory motion and solutions that occur in many real-world phenomena as well as in man-made machines • Numerous examples and applications with a specific focus on ordinary differential equations and functional differential equations with finite delay • An appendix that introduces generalized Fourier series and Fourier analysis after periodicity and almost periodicity • An extensive Bibliography with over 550 references that connects the presented concepts to further topical exploration Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics. The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and dynamics processes. CONSTANTIN CORDUNEANU, PhD, is Emeritus Professor in the Department of Mathematics at The University of Texas at Arlington, USA. The author of six books and over 200 journal articles, he is currently Associate Editor for seven journals; a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Romanian Academy; and past president of the American Romanian Academy of Arts and Sciences. YIZENG LI, PhD, is Professor in the Department of Mathematics at Tarrant County College, USA. He is a member of the Society for Industrial and Applied Mathematics. MEHRAN MAHDAVI, PhD, is Professor in the Department of Mathematics at Bowie State University, USA. The author of numerous journal articles, he is a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Mathematical Association of America.

A comprehensive overview of the internationalisation of correspondence analysis Correspondence Analysis: Theory, Practice and New Strategies examines the key issues of correspondence analysis, and discusses the new advances that have been made over the last 20 years. The main focus of this book is to provide a comprehensive discussion of some of the key technical and practical aspects of correspondence analysis, and to demonstrate how they may be put to use. Particular attention is given to the history and mathematical links of the developments made. These links include not just those major contributions made by researchers in Europe (which is where much of the attention surrounding correspondence analysis has focused) but also the important contributions made by researchers in other parts of the world. Key features include: A comprehensive international perspective on the key developments of correspondence analysis. Discussion of correspondence analysis for nominal and ordinal categorical data. Discussion of correspondence analysis of contingency tables with varying association structures (symmetric and non-symmetric relationship between two or more categorical variables). Extensive treatment of many of the members of the correspondence analysis family for two-way, three-way and multiple contingency tables. Correspondence Analysis offers a comprehensive and detailed overview of this topic which will be of value to academics, postgraduate students and researchers wanting a better understanding of correspondence analysis. Readers interested in the historical development, internationalisation and diverse applicability of correspondence analysis will also find much to enjoy in this book.

This book introduces and details the key facets of Combined Analysis – an x-ray and/or neutron scattering methodology which combines structural, textural, stress, microstructural, phase, layer, or other relevant variable or property analyses in a single approach. The text starts with basic theories related to diffraction by polycrystals and some of the most common combined analysis instrumental set-ups are detailed. Also discussed are microstructures of powder diffraction profiles; quantitative phase analysis from the Rietveld analysis; residual stress analysis for isotropic and anisotropic materials; specular x-ray reflectivity, and the various associated models.

Everyday we face decisions that carry an element of risk and uncertainty. The ability to analyze, predict, and prepare for the level of risk entailed by these decisions is, therefore, one of the most constant and vital skills needed for analysts, scientists and managers. Risk analysis can be defined as a systematic use of information to identify hazards, threats and opportunities, as well as their causes and consequences, and then express risk. In order to successfully develop such a systematic use of information, those analyzing the risk need to understand the fundamental concepts of risk analysis and be proficient in a variety of methods and techniques. Risk Analysis adopts a practical, predictive approach and guides the reader through a number of applications. Risk Analysis: Provides an accessible and concise guide to performing risk analysis in a wide variety of fields, with minimal prior knowledge required. Adopts a broad perspective on risk, with focus on predictions and highlighting uncertainties beyond expected values and probabilities, allowing a more flexible approach than traditional statistical analysis. Acknowledges that expected values and probabilities could produce poor predictions – surprises may occur. Emphasizes the planning and use of risk analyses, rather than just the risk analysis methods and techniques, including the statistical analysis tools. Features many real-life case studies from a variety of applications and practical industry problems, including areas such as security, business and economy, transport, oil & gas and ICT (Information and Communication Technology). Forms an ideal companion volume to Aven’s previous Wiley text Foundations of Risk Analysis. Professor Aven’s previous book Foundations of Risk Analysis presented and discussed several risk analysis approaches and recommended a predictive approach. This new text expands upon this predictive approach, exploring further the risk analysis principles, concepts, methods and models in an applied format. This book provides a useful and practical guide to decision-making, aimed at professionals within the risk analysis and risk management field.