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Mathematical Control Theory : An Introduction
Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems.
Mathematical and Computational Models for Congestion Charging
This book presents rigorous treatments of issues related to congestion pricing. The chapters describe recent advances in areas such as mathematical and computational models for predicting traffic congestion, determining when, where, and how much to levy tolls, and analyzing the impact of tolls on transporation systems. The analyses and methodologies developed in this book provide Mechanisms that aid in determining and comparing congestion pricing schemes; Methodologies for evaluating the efficiency of existing and proposed congestion pricing schemes; A means to predict the impact of pricing on urban transporation systems; and Information essential to the financial and political success of congestion pricing programs.
Mathematical Analysis I
The purpose of the volume is to provide a support for a first course in Mathematical Analysis, along the lines of the recent Programme Specifications for mathematical teaching in European universities. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques.
Mathematical Analysis : Linear and Metric Structures and Continuity
The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators.
Mathematica for Theoretical Physics : Electrodynamics, Quantum Mechanics, General Relativity, and Fractals
Mathematica for Theoretical Physics: Electrodynamics, Quantum Mechanics, General Relativity, and Fractals This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A brief glossary of terms and functions is contained in the appendices.
Mathematica for Theoretical Physics : Classical Mechanics and Nonlinear Dynamics
Mathematica for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A brief glossary of terms and functions is contained in the appendices.
Masonry Constructions : Mechanical Models and Numerical Applications
This monograph firstly provides a detailed description of the constitutive equation of masonry-like materials, clearly setting out its most important features. It then goes on to provide a numerical procedure to solve the equilibrium problem of masonry solids.
Martingale Methods in Financial Modelling
This book provides a comprehensive, self-contained and up-to-date treatment of the main topics in the theory of option pricing. The first part of the text starts with discrete-time models of financial markets, including the Cox-Ross-Rubinstein binomial model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendix containing all the necessary results is included. This model setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing is presented. The second part of the text is devoted to the term structure modelling and the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice.
Maple and Mathematica : A Problem Solving Approach for Mathematics
the history of mathematics there are many situations in which cal- lations were performed incorrectly for important practical applications. the history of computing the number began in Egypt and Babylon about 2000 years BC, since then many mathematicians have calculated (e. g. , Archimedes, Ptolemy, Vi` ete, etc. ). In modern mathematics there exist computers that can perform various mathematical operations for which humans are incapable. Therefore the computers can be used to verify the results obtained by humans, to discovery new results, to - prove the result sthatahumancanobtain without anytechnology
Managing Critical Infrastructure Risks
At the beginning of each year, there is a deluge of top-10 lists on just about every subject you can imagine. A top-10 list of biggest news stories, best-selling books, most popular music and movies, richest companies, and best places to visit or live. It seems everyone has his or her own top-10 list, reflecting, perhaps, differences in regional, national, and cultural values. Companies and governments most often tend to focus their top-10 lists on economic priorities, or priorities related to national defense, security, public health, and new infrastructure. This year, 2007, was no exception. Yet, increasingly, we see governments, private organizations, and companies advocating a new type of prioritization. This framework needs to reach beyond the realms of economics, world trade, and corporate management to include the environment, stakeholders, public preferences, and social goals. Moreover, corporations and individuals are not only interested in generic 10-best lists; they want lists tailored to their values, goals, and current economic and social state. For example, the U. S.
Malliavin Calculus for Lévy Processes with Applications to Finance
While the original works on Malliavin calculus aimed to study the smoothness of densities of solutions to stochastic differential equations, this book has another goal. It portrays the most important and innovative applications in stochastic control and finance, such as hedging in complete and incomplete markets, optimisation in the presence of asymmetric information and also pricing and sensitivity analysis. In a self-contained fashion, both the Malliavin calculus with respect to Brownian motion and general Lévy type of noise are treated. Besides, forward integration is included and indeed extended to general Lévy processes. The forward integration is a recent development within anticipative stochastic calculus that, together with the Malliavin calculus, provides new methods for the study of insider trading problems.
MacLaurins Physical Dissertations
The Scottish mathematician Colin MacLaurin (1698-1746) is best known for developing and extending Newton’s work in calculus, geometry and gravitation; his 2-volume work "Treatise of Fluxions" (1742) was the first systematic exposition of Newton’s methods. It is well known that MacLaurin was awarded prizes by the Royal Academy of Sciences, Paris, for his earlier work on the collision of bodies (1724) and the tides (1740); however, the contents of these essays are less familiar – although some of the material is discussed in the Treatise of Fluxions - and the essays themselves often hard to obtain.
Machine Learning in Document Analysis and Recognition
The objective of Document Analysis and Recognition (DAR) is to recognize the text and graphicalcomponents of a document and to extract information. With ?rst papers dating back to the 1960’s, DAR is a mature but still gr- ing research?eld with consolidated and known techniques. Optical Character Recognition (OCR) engines are some of the most widely recognized pr- ucts of the research in this ?eld, while broader DAR techniques are nowadays studied and applied to other industrial and o?ce automation systems. In the machine learning community, one of the most widely known - search problems addressed in DAR is recognition of unconstrained handwr- ten characters which has been frequently used in the past as a benchmark for evaluating machine learning algorithms, especially supervised classi?ers.
Logical Foundations for Rule-Based Systems
Presents logical foundations for rule-based systems, as seen by the Author. An attempt has been made to provide an in-depth discussion of logical and other aspects of such systems, including languages for knowledge representation, inference mechanisms, inference control, design and verification.
Linkage in Evolutionary Computation
The whole volume consisting of 19 chapters is divided into 3 parts: Models and Theories; Operators and Frameworks; Applications. This edited volume will serve as a useful guide and reference for researchers who are currently working in the area of linkage. For postgraduate research students, this volume will serve as a good source of reference. It is also suitable as a text for a graduate level course focusing on linkage issues.
Linear Models and Generalizations : Least Squares and Alternatives
Gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and offers a selection of classical and modern algebraic results that are useful in research work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results aboutthe de?niteness ofmatrices,especially forthe di?erences ofmatrices, which enable superiority comparisons of two biased estimates to be made for the ?rst time. We have attempted to provide a uni?ed theory of inference from linear models with minimal assumptions
Linear Functional Analysis
This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations.
Lie theory ; Vol.230 : Harmonic analysis on symmetric spaces, general Plancherel theorems
Van den Ban’s introductory chapter explains the basic setup of a reductive symmetric space along with a careful study of the structure theory, particularly for the ring of invariant differential operators for the relevant class of parabolic subgroups. Advanced topics for the formulation and understanding of the proof are covered, including Eisenstein integrals, regularity theorems, Maass–Selberg relations, and residue calculus for root systems. Schlichtkrull provides a cogent account of the basic ingredients in the harmonic analysis on a symmetric space through the explanation and definition of the Paley–Wiener theorem. Approaching the Plancherel theorem through an alternative viewpoint, the Schwartz space, Delorme bases his discussion and proof on asymptotic expansions of eigenfunctions and the theory of intertwining integrals.
Le choix bayésien: Principes et pratique
Covers the so-called Bayesian approach to statistical inference and in particular its decision-making aspects. The bases of this axiomatics (choice of the a priori, optimal decisions, tests and regions of confidence) are discussed in detail, as well as more recent openings of Bayesian analysis such as the choice of models, the use of numerical methods. Stochastic approximation (MCMC), the theory of noninformative laws (Berger-Bernardo axioms) and the relation to the classical theory of admissibility. Each chapter is completed by an extensive series of exercises of increasing difficulty and by bibliographical notes on the themes addressed. This book can be used in a Master's program in Applied Mathematics, Biometrics, Econometrics or any other program that uses quantitative information processing techniques. It only requires a basic course in probability theory and mathematical statistics as a preliminary.
Large Eddy Simulation for Incompressible Flows : An Introduction
First concise textbook on Large-Eddy Simulation, a very important method in scientific computing and engineeringFrom the foreword to the third edition written by Charles Meneveau: ".
