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Free Boundary Problems : Theory and Applications
This book gathersa collection of refereed articles containing original result srepo- ing the recent originalcontributions of the lectures and communications presented at the Free Boundary Problems (FBP2005) Conference that took place at the University of Coimbra, Portugal, from 7 to 12 of June 2005. They deal with the Mathematics of a broad class of models and problems involving nonlinear partial diferentialequationsarising inPhysics, Engineering, Biology and Finance. Among the main topics, the talks considered free boundary problems in biomedicine, in porous media, in thermodynamic modeling.
Frames and Bases : An Introductory Course
During the last several years, frames have become increasingly popular; they have appeared in a large number of applications, and several concrete constructions of frames of various types have been presented. Most of these constructions were based on quite direct methods rather than the classical sufficient conditions for obtaining a frame. Consequently, there is a need for an updated book on frames, which moves the focus from the classical approach to a more constructive one.
Fracture Mechanics : With an Introduction to Micromechanics
Concerned with the fundamental concepts and methods of fracture mechanics and micromechanics, Fracture Mechanics primarily focuses on the mechanical description of fracture processes; however, material specific aspects are also discussed. The presentation of continuum mechanical and phenomenological foundations is followed by an introduction into classical failure hypotheses. A major part of the book is devoted to linear elastic and elastic-plastic fracture mechanics. Further subjects are creep fracture, dynamic fracture mechanics, damage mechanics, probabilistic fracture mechanics, failure of thin films and fracture of piezoelectric materials. The book also contains an extensive introduction into micromechanics.
Fracture Mechanics : Inverse Problems and Solutions
This book presents, in a unified manner, a variety of topics in Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve two-dimensional and three-dimensional crack problems.
Fractional-in-time semilinear parabolic equations and applications
This book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source, generally of arbitrary growth in the unknown function, a time derivative in the sense of Caputo and the presence of a large class of diffusion operators. The global regularity problem is then treated separately and the analysis is extended to some systems of fractional kinetic equations, including prey-predator models of Volterra–Lotka type and chemical reactions models, all of them possibly containing some fractional kinetics.
Fractional order systems and applications in engineering
Covers the fundamentals of fractional calculus together with some analytical and numerical techniques, and provides MATLAB® codes for the simulation of fractional-order control (FOC) systems. The use of fractional calculus can improve and generalize well-established control methods and strategies. Many different FOC schemes are presented for control and dynamic systems problems. These extend to the challenging control engineering design problems of robust and nonlinear control. Practical material relating to a wide variety of applications including, among others, mechatronics, civil engineering, irrigation and water management, and biological systems is also provided.
Fractals in Biology and Medicine : Beyond Planting Trees
This volume it highlights the potential that fractal geometry offers for elucidating and explaining the complex make-up of cells, tissues and biological organisms either in normal or in pathological conditions, including the structural changes that occur in tumours. It helps develop the concepts, questions and methods required in research on fractal biology and natural phenomena and to evidence the pitfalls of a too simplistic application of these principles in investigating topical subjects of biology and medicine. It discusses present and future applications of fractal geometry, bringing together cellular and molecular biology, engineering, mathematics, physics, medicine and other disciplines and allowing an interdisciplinary vision.
Fractal Behaviour of the Earth System
In this volume a collection of - pers considers the fractal behavior of the Earth's continental crust. Surface gravity anomalies are known to exhibit power-law spectral behavior under a wide range of conditions and scales. La Manna utilize multifractal models to explain the behavior of well logs from the main KTB borehole in Germany.
Fourier Series in Control Theory
Fourier Series in Control Theory successfully gathers all of the available theory of these "nonharmonic Fourier series" in one place, combining published results with new results, to create a unique source of such material for practicing applied mathematicians, engineers, and other scientific professionals.Starting with an overview of the problems of observability, controllability, and stabilization of linear systems and their interconnections, the text contains complete proofs along with a short, simplified, presentation of some properties of Bessel functions for the convenience of the reader. Only basic knowledge of functional analysis is required.
Foundations of Quantum Theory : From Classical Concepts to Operator Algebras
This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.
Foundations of generic optimization : Vol.1 : A combinatorial approach to epistasis
This is a comprehensive overview of the basics of fuzzy control, which also brings together some recent research results in soft computing, in particular fuzzy logic using genetic algorithms and neural networks. This book offers researchers not only a solid background but also a snapshot of the current state of the art in this field.
Foundations and applications of MIS : A model theory approach
Foundations and Applications of MIS presents a unique systems theory approach to management information system (MIS) development. The development is driven by the need to eliminate ambiguity in specification, design and construction of the application software. Further, the authors show that the considerable effort being expanded nowadays on validation, verification and testing, as required in current software engineering practices, will be reduced. The approach also reinforces the belief that MIS development is independent of software development. The work presents an approach that provides a theoretical foundation for MIS development from the systems theoretic viewpoint along with practical applications ranging from a transaction processing system to a solver system. Both formal systems theory and automatic system generation based on the authors' newly extended Prolog offer a significant increase in the efficiency of specification, design and production of the application software, as well as an increase in the functional reliability of the software produced. The book assumes a working knowledge of elementary set theory, logic, and familiarity with some systems concepts, such as the automaton model.
Foreign Exchange Rate Forecasting using Artificial Neural Networks
In this monograph, the authors try to apply artificial neural networks (ANNs) to exchange rates forecasting. Selection of the ANN approach for - change rates forecasting is because of ANNs’ unique features and powerful pattern recognition capability. Unlike most of the traditional model-based forecasting techniques, ANNs are a class of data-driven, self-adaptive, and nonlinear methods that do not require specific assumptions on the und- lying data generating process. These features are particularly appealing for practical forecasting situations where data are abundant or easily available, even though the theoretical model or the underlying relationship is - known. Furthermore, ANNs have been successfully applied to a wide range of forecasting problems in almost all areas of business, industry and engineering.
Fixed point theory for decomposable sets
This book attempts to show the present stage of "decomposable analysis" from the point of view of fixed point theory. The book is split into three parts, beginning with the background of functional analysis, proceeding to the theory of multifunctions and lastly, the decomposability property.Mathematicians and students working in functional, convex and nonlinear analysis, differential inclusions and optimal control should find this book of interest. A good background in fixed point theory is assumed as is a background in topology.
Finite Zeros in discrete time control systems
The book starts with definition of invariant zeros and goes as far as a general characterization of output-zeroing inputs and the corresponding solutions, explicit formulas for maximal output-nulling invariant subspaces and for the zero dynamics. The objective of this book is to render the reader familiar with a certain method of analysis of multivariable zeros (which goes beyond the classical approach) and related problems. The minimal mathematical background that is required from the reader is a working knowledge of linear algebra and difference equations.
Finite Mixture and Markov Switching Models
The prominence of finite mixture modelling is greater than ever. Many important statistical topics like clustering data, outlier treatment, or dealing with unobserved heterogeneity involve finite mixture models in some way or other. The area of potential applications goes beyond simple data analysis and extends to regression analysis and to non-linear time series analysis using Markov switching models.It is the first time that the Bayesian perspective of finite mixture modelling is systematically presented in book form. It is argued that the Bayesian approach provides much insight in this context and is easily implemented in practice. Although the main focus is on Bayesian inference, the author reviews several frequentist techniques, especially selecting the number of components of a finite mixture model, and discusses some of their shortcomings compared to the Bayesian approach. The aim of this book is to impart the finite mixture and Markov switching approach to statistical modelling to a wide-ranging community. This includes not only statisticians, but also biologists, economists, engineers, financial agents, market researcher, medical researchers or any other frequent user of statistical models. This book should help newcomers to the field to understand how finite mixture and Markov switching models are formulated, what structures they imply on the data, what they could be used for, and how they are estimated.
Finite Elements in Structural Analysis : Theoretical Concepts and Modeling Procedures in Statics and Dynamics of Structures
Introduces the basic concepts of the finite element method in the static and dynamic analysis of beam, plate, shell and solid structures, discussing how the method works, the characteristics of a finite element approximation and how to avoid the pitfalls of finite element modeling. Presenting the finite element theory as simply as possible, the book allows readers to gain the knowledge required when applying powerful FEA software tools. Further, it describes modeling procedures, especially for reinforced concrete structures, as well as structural dynamics methods, with a particular focus on the seismic analysis of buildings, and explores the modeling of dynamic systems. Featuring numerous illustrative examples, the book allows readers to easily grasp the fundamentals of the finite element theory and to apply the finite element method proficiently.
Finite Elements III : First-Order and Time-Dependent PDEs
Volume III is divided into 28 chapters. The first eight chapters focus on the symmetric positive systems of first-order PDEs called Friedrichs' systems. This part of the book presents a comprehensive and unified treatment of various stabilization techniques from the existing literature. It discusses applications to advection and advection-diffusion equations and various PDEs written in mixed form such as Darcy and Stokes flows and Maxwell's equations. The remainder of Volume III addresses time-dependent problems: parabolic equations (such as the heat equation), evolution equations without coercivity (Stokes flows, Friedrichs' systems), and nonlinear hyperbolic equations (scalar conservation equations, hyperbolic systems). It offers a fresh perspective on the analysis of well-known time-stepping methods. The last five chapters discuss the approximation of hyperbolic equations with finite elements. Here again a new perspective is proposed.
Finite Element Methods in Civil and Mechanical Engineering : A Mathematical Introduction
The finite element method is widely employed for numerical simulations in engineering and science due to its accuracy and efficiency. This concise introduction to the mathematical theory of the finite element method presents a selection of applications in civil and mechanical engineering including beams, elastic membranes, the wave equation, heat transfer, seepage in embankment, soil consolidation, incompressible fluids, and linear elasticity.
Finite element methods : Parallel-sparse statics and Eigen-Solutions
FEM, and the associated computer software are widely recognized as some of the most effective tools for solutions of large-scale engineering applications. Efficient equation and eigen-solvers play critical roles in solving these problems. Sparse matrix technologies have evolved and are now mature enough that all popular and commercialized FEM codes have inserted sparse solvers into their software. So far, however, few books include detailed discussion and explanation of sparse equation-solvers and Lanczos domain decomposition (DD) or finite element formulation for parallel computing purposes. The material in Finite Element Methods: Parallel-Sparse Statics and Eigen-Solutions has evolved over the past several years from the author's research work and his graduate courses.
