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Cost-Based Oracle Fundamentals
In Cost-Based Oracle Fundamentals, the first book in a series of three, Jonathan Lewis—one of the foremost authorities in this field—describes the most commonly used parts of the model, what the optimizer does with your statistics, and why things go wrong. With this information, you'll be in a position to fix entire problem areas, not just single SQL statements, by adjusting the model or creating more truthful statistics.
Correlated Data Analysis : Modeling, Analytics, and Applications
Presents some recent developments in correlated data analysis. It utilizes the class of dispersion models as marginal components in the formulation of joint models for correlated data. This enables the book to handle a broader range of data types than those analyzed by traditional generalized linear models.
Cooperative stochastic differential games
Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises.
Convexity and Well-Posed Problems
This book deals mainly with the study of convex functions and their behavior from the point of view of stability with respect to perturbations. We shall consider convex functions from the most modern point of view: a function is de?ned to be convex whenever its epigraph, the set of the points lying above the graph, is a convex set. Thus many of its properties can be seen also as properties of a certain convex set related to it. Moreover, we shall consider extended real valued functions.
Convex Polyhedra
Convex Polyhedra is one of the classics in geometry. There simply is no other book with so many of the aspects of the theory of 3-dimensional convex polyhedra in a comparable way, and in anywhere near its detail and completeness. It is the definitive source of the classical field of convex polyhedra and contains the available answers to the question of the data uniquely determining a convex polyhedron. This question concerns all data pertinent to a polyhedron, e.g. the lengths of edges, areas of faces, etc. This vital and clearly written book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method.
Convex functions and their applications : A contemporary approach ; 2nd ed.
This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some of the most advanced topics. The new edition includes considerably more material emphasizing the rich applicability of convex analysis to concrete examples. Chapters 4, 5, and 6 are entirely new, covering important topics such as the Hardy-Littlewood-Pólya-Schur theory of majorization, matrix convexity, and the Legendre-Fenchel-Moreau duality theory.
Convex Functions and their Applications : A Contemporary Approach ; 1st ed.
Convex functions play an important role in many branches of mathematics, as well as other areas of science and engineering. The present text is aimed to a thorough introduction to contemporary convex function theory, which entails a powerful and elegant interaction between analysis and geometry. A large variety of subjects are covered, from one real variable case (with all its mathematical gems) to some of the most advanced topics such as the convex calculus, Alexandrov’s Hessian, the variational approach of partial differential equations, the Prékopa-Leindler type inequalities and Choquet's theory.
Convex Functional Analysis
This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems.
Convex and Discrete Geometry
Gives an overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers.
Convergence and Applications of Newton-type Iterations
Recent results in local convergence and semi-local convergence analysis constitute a natural framework for the theoretical study of iterative methods. This monograph provides a comprehensive study of both basic theory and new results in the area. Each chapter contains new theoretical results and important applications in engineering, modeling dynamic economic systems, input-output systems, optimization problems, and nonlinear and linear differential equations. Several classes of operators are considered, including operators without Lipschitz continuous derivatives, operators with high order derivatives, and analytic operators. Each section is self-contained. Examples are used to illustrate the theory and exercises are included at the end of each chapter.
Controlled Markov Processes and Viscosity Solutions
This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. Stochastic control problems are treated using the dynamic programming approach. It approachs stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function. For controlled Markov diffusion processes, this becomes a nonlinear partial differential equation of second order, called a Hamilton-Jacobi-Bellman (HJB) equation. Typically, the value function is not smooth enough to satisfy the HJB equation in a classical sense. Viscosity solutions provide framework in which to study HJB equations, and to prove continuous dependence of solutions on problem data. The theory is illustrated by applications from engineering, management science, and financial economics.
Control of Turbulent and Magnetohydrodynamic Channel Flows : Boundary Stabilization and State Estimation
This monograph presents new constructive design methods for boundary stabilization and boundary estimation for several classes of benchmark problems in flow control, with potential applications to turbulence control, weather forecasting, and plasma control. The basis of the approach used in the work is the recently developed continuous backstepping method for parabolic partial differential equations, expanding the applicability of boundary controllers for flow systems from low Reynolds numbers to high Reynolds number conditions. Efforts in flow control over the last few years have led to a wide range of developments in many different directions, but most implementable developments thus far have been obtained using discretized versions of the plant models and finite-dimensional control techniques. In contrast, the design methods examined in this book are based on the “continuum” version of the backstepping approach, applied to the PDE model of the flow.
Control of Spatially Structured Random Processes and Random Fields with Applications
This book is devoted to the study and optimization of spatiotemporal stochastic processes, that is, processes which develop simultaneously in space and time under random influences. These processes are seen to occur almost everywhere when studying the global behavior of complex systems.Classical stochastic dynamic optimization forms the framework of the book. Taken as a whole, the project undertaken in the book is to establish optimality or near-optimality for Markovian policies in the control of spatiotemporal Markovian processes. The authors apply this general principle to different frameworks of Markovian systems and processes. Depending on the structure of the systems and the surroundings of the model classes the authors arrive at different levels of simplicity for the policy classes which encompass optimal or nearly optimal policies. A set of examples accompanies the theoretical findings, and these examples should demonstrate some important application areas for the theorems discussed.
Control of Coupled Partial Differential Equations
Contains selected contributions originating from the ‘Conference on Optimal Control of Coupled Systems of Partial Differential Equations’, held at the ‘Mathematisches Forschungsinstitut Oberwolfach’ in April 2005.
Contributions to the Science of Text and Language : Word Length Studies and Related Issues
This volume contains a collection of contributions to the science of language, focusing on the study of word length in particular. Within a synergetic framework, the word turns out to be a central linguistic unit, as is clearly outlined in the Editorâs preface. The bookâs first chapter is an extensive introduction to the history and state of the art of word length studies.The studies included unify contributions from three important linguistic fields, namely, linguistics and text analysis, mathematics and statistics, and corpus and data base design, which together give a comprehensive approach to the quantitative study of text and language and word length studies.
Contributions to Nonlinear Analysis : A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday
This volume represents a broad survey of current research in the fields of nonlinear analysis and nonlinear differential equations.It is concerned with the existence and uniform decay rates of solutions of the waveequation with a sourceterm and subject to nonlinear boundary damping.
Continuum Thermomechanics
The general goal of this book is to deduce rigorously, from the first principles, the partial differential equations governing the thermodynamic processes undergone by continuum media under forces and heat. Solids and fluids are considered in a unified framework. Reacting mixtures of fluids are also included for which general notions of thermodynamics are recalled, such as the Gibbs equilibrium theory.Linear approximate models are mathematically obtained by calculating the derivatives of the constitutive response functions. They include the classical models for linear vibrations of thermoelastic solids and also for wave propagation in fluids (dissipative and non-dissipative acoustics and internal gravity waves).
Continuous time processes for finance : Switching, self-exciting, fractional and other recent dynamics
This book explores recent topics in quantitative finance with an emphasis on applications and calibration to time-series. This last aspect is often neglected in the existing mathematical finance literature while it is crucial for risk management. The first part of this book focuses on switching regime processes that allow to model economic cycles in financial markets. After a presentation of their mathematical features and applications to stocks and interest rates, the estimation with the Hamilton filter and Markov Chain Monte-Carlo algorithm (MCMC) is detailed. A second part focuses on self-excited processes for modeling the clustering of shocks in financial markets.
Continuous Semigroups of Holomorphic Self-maps of the Unit Disc
The book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions. The book includes precise descriptions of the behavior of trajectories, backward orbits, petals and boundary behavior in general, aiming to give a rather complete picture of all interesting phenomena that occur. In order to fulfill this task, we choose to introduce a new point of view, which is mainly based on the intrinsic dynamical aspects of semigroups in relation with the hyperbolic distance and a deep use of Carathéodory prime ends topology and Gromov hyperbolicity theory.
Continuous Optimization : Current Trends and Modern Applications
The search for the best possible performance is inherent in human nature. Individuals, enterprises and governments all seek optimal—that is, the best—possible solutions of problems that they meet. Evidently, continuous optimization plays an increasingly significant role in everyday management and technical decisions in science, engineering and commerce. The collection of 16 refereed papers in this book covers a diverse number of topics and provides a good picture of recent research in continuous optimization. The first part of the book presents substantive survey articles in a number of important topic areas of continuous optimization. Most of the papers in the second part present results on the theoretical aspects as well as numerical methods of continuous optimization. The papers in the third part are mainly concerned with applications of continuous optimization.
