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Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems
Added 3/21/2008
Leszek Gasinski, Nikolaos Papageorgiou
Starting in the early 1980s, people using the tools of nonsmooth analysis developed some remarkable nonsmooth extensions of the existing critical point theory. Until now, however, no one had gathered these tools and results together into a unified, systematic survey of these advances.
This book fills that gap. It provides a complete presentation of nonsmooth critical point theory, then goes beyond it to study nonlinear second order boundary value problems. The authors do not limit their treatment to problems in variational form. They also examine in detail equations driven by the p-Laplacian, its generalizations, and their spectral properties, studying a wide variety of problems and illustrating the powerful tools of modern nonlinear analysis. The presentation includes many recent results, including some that were previously unpublished. Detailed appendices outline the fundamental mathematical tools used in the book, and a rich bibliography forms a guide to the relevant literature.
Most books addressing critical point theory deal only with smooth problems, linear or semilinear problems, or consider only variational methods or the tools of nonlinear operators. Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods for a wide variety of problems.
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Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified
Added 2/1/3191
Vincenzo Ancona, Bernard Gaveau
Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of higher dimension than the initial space. It simplifies the theory through easily identifiable and well-defined weight filtrations. It also avoids discussion of cohomological descent theory to maintain accessibility. Topics include classical Hodge theory, differential forms on complex spaces, and mixed Hodge structures on noncompact spaces.
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Compact Handbook of Computational Biology
Added 1/28/2008
A. Konopka, M. James C. Crabbe
The assimilation of computational methods into the life sciences has played an important role in advancing biological research. From sequencing genomes to discovering motifs in large collections of functionally equivalent sequences of nucleic acids and proteins, the value of powerful computational tools has become abundantly clear. The Compact Handbook of Computational Biology describes the foundational concepts, techniques, and challenges of biomolecular sequence analysis, biopolymer structure analysis and prediction, genomics, and molecular evolution.
Comprising contributions from renowned scientists, many of whom pioneered current methodologies, the Compact Handbook of Computational Biology offers interdisciplinary and authoritative coverage of methods for analysis of nucleic acid and protein sequences and structures, definition and detection of motifs in nucleic acid and protein sequences, protein structure prediction, and discrete modeling of biopolymers. Specific computational topics include computer-assisted research on protein folding, computer-assisted studies of DNA-protein interactions, computer-assisted genomics, proteomics, and comparative genomics, and computer-assisted studies of genome evolution at the molecular (DNA) level.
Offering a survey of specific algorithms that have proven successful in molecular biology, genomics, structural biology, and bioinformatics, this invaluable handbook is an authoritative source covering terminology, software, and applications of computational biology.
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Solvency: Models, Assessment and Regulation
Added 3/12/2008
Arne Sandstrom
Until now there were no published analyses of the recent solvency work conducted in Europe, specifically the risk categories proposed by the International Actuarial Association (IAA). Answering the insurance industry's demand in the wake of the EU Solvency II project, Solvency: Models, Assessment and Regulation provides a concrete summary and review of solvency and inspires additional work in the field.
Following an introduction to the concept, the first section of the book provides a historical review of solvency, detailing solvency regulation and accounting within the EU. A review of the steps leading to Solvency II looks at accounting, supervision, the actuarial field, the first phase of Solvency II, international approaches to banking, and the solvency systems of 12 major nations.
The second section explores the current basis for solvency modeling, focusing on the valuation of assets and liabilities, dependency and various conservative approaches, as well as a baseline and benchmark approach. This section also provides examples of risk structure and the effects of diversification.
The final section discusses groups and internal modeling as it relates to EU Solvency II. It addresses insurance groups, financial conglomerates, reinsurance, the importance of internal modeling and stress testing, and the current state of the second phase of EU Solvency II.
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Stochastic Processes in Science, Engineering and Finance
Added 2/15/2008
Frank Beichelt
Stochastic Processes in Science, Engineering, and Finance emphasizes applications in various fields. This book features numerous worked examples to represent the subject in a comprehensible, user-friendly way. It includes a self-contained review of probability-theoretic topics and provides a large number of exercises with solutions as well as important proofs and theoretically challenging examples for the mathematically interested reader. The text makes an ideal reference for senior undergraduate and graduate students in stochastic processes, practitioners, and researchers in mathematical finance, operations, industrial engineering, electrical engineering, and actuarial science.
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Technical Analysis of Stock Trends, Ninth Edition
Added 4/4/2008
Robert Edwards, John Magee, W.H.C. Bassetti
Based on the research and experience of Dow, Schabacker, and Edwards, Technical Analysis of Stock Trends, Ninth Edition presents proven techniques, methods, and procedures for success, even in today's unpredictable markets.
New and updated material on
· Dow Theory and long term investing, including new tables of performance and risk
· Magee's Basing Points Procedure, a previously little noticed gem
· The use of Edwards and Magee's methodology in the futures and commodities area
· The Turtle systems and procedures manual for futures trading
· More than 25 new charts, each an analysis and trading lesson in itself for the modern context
· Innovative connection to internet material which makes the book easier and more informative to use at edwards-magee.com
This irreplaceable guide presents a current perspective while maintaining the time proven material of the previous editions. Technical Analysis of Stock Trends, Ninth Edition features updated and to the moment material on Pragmatic Portfolio Theory, entry and stop setting procedures at all fractal scales and includes strategic and tactical procedures and techniques.
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A First Course in Fuzzy and Neural Control
Added 11/1/2007
Hung Nguyen, Nadipuram Prasad, Carol Walker, Elbert Walker
Although the use of fuzzy control methods has grown nearly to the level of classical control, the true understanding of fuzzy control lags seriously behind. Moreover, most engineers are well versed in either traditional control or in fuzzy control-rarely both. Each has applications for which it is better suited, but without a good understanding of both, engineers cannot make a sound determination of which technique to use for a given situation.
A First Course in Fuzzy and Neural Control is designed to build the foundation needed to make those decisions. It begins with an introduction to standard control theory, then makes a smooth transition to complex problems that require innovative fuzzy, neural, and fuzzy-neural techniques. For each method, the authors clearly answer the questions: What is this new control method? Why is it needed? How is it implemented? Real-world examples, exercises, and ideas for student projects reinforce the concepts presented.
Developed from lecture notes for a highly successful course titled The Fundamentals of Soft Computing, the text is written in the same reader-friendly style as the authors' popular A First Course in Fuzzy Logic text. A First Course in Fuzzy and Neural Control requires only a basic background in mathematics and engineering and does not overwhelm students with unnecessary material but serves to motivate them toward more advanced studies.
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Modeling MEMS and NEMS
Added 11/1/2007
John Pelesko, David Bernstein
Designing small structures necessitates an a priori understanding of various device behaviors. The way to gain such understanding is to construct, analyze, and interpret the proper mathematical model.
Through such models, Modeling MEMS and NEMS illuminates microscale and nanoscale phenomena, thereby facilitating the design and optimization of micro- and nanoscale devices. After some introductory material, a review of continuum mechanics, and a study of scaling, the book is organized around phenomena. Each chapter addresses a sequence of real devices that share a common feature. The authors abstract that feature from the devices and present the mathematical tools needed to model it. They construct, analyze, and interpret a series of models of increasing complexity, then at the end of the chapter, they return to one of the devices described, apply the model to it, and interpret the analysis.
In the beginning, the world of microdevices was dominated by experimental work and the development of fabrication techniques. As it matures, optimization and innovative designs are moving to the forefront. Modeling MEMS and NEMS not only provides the practical background and tools needed to design and optimize microdevices but it also helps develop the intuitive understanding that can lead to developing new and better designs and devices.
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Optimization Modelling: A Practical Approach
Added 2/15/2008
Ruhul Amin Sarker, Charles Newton
Although a useful and important tool, the potential of mathematical modelling for decision making is often neglected. Considered an art by many and weird science by some, modelling is not as widely appreciated in problem solving and decision making as perhaps it should be. And although many operations research, management science, and optimization books touch on modelling techniques, the short shrift they usually get in coverage is reflected in their minimal application to problems in the real world. Illustrating the important influence of modelling on the decision making process, Optimization Modelling: A Practical Approach helps you come to grips with a wide range of modelling techniques.
Highlighting the modelling aspects of optimization problems, the authors present the techniques in a clear and straightforward manner, illustrated by examples. They provide and analyze the formulation and modelling of a number of well-known theoretical and practical problems and touch on solution approaches. The book demonstrates the use of optimization packages through the solution of various mathematical models and provides an interpretation of some of those solutions. It presents the practical aspects and difficulties of problem solving and solution implementation and studies a number of practical problems. The book also discusses the use of available software packages in solving optimization models without going into difficult mathematical details and complex solution methodologies.
The emphasis on modelling techniques rather than solution algorithms sets this book apart. It is a single source for a wide range of methods, classic theoretical and practical problems, data collection and input preparation, the use of different optimization software, and practical issues of modelling, model solving, and implementation. The authors draw directly from their experience to provide lessons learned when applying modelling techniques to practical problem solving and implementation difficulties.
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Recent developments in the Navier-Stokes problem
Added 11/28/2007
P.G. Lemarie-Rieusset
The Navier-Stokes equations: fascinating, fundamentally important, and challenging,. Although many questions remain open, progress has been made in recent years. The regularity criterion of Caffarelli, Kohn, and Nirenberg led to many new results on existence and non-existence of solutions, and the very active search for mild solutions in the 1990's culminated in the theorem of Koch and Tataru that, in some ways, provides a definitive answer.
Recent Developments in the Navier-Stokes Problem brings these and other advances together in a self-contained exposition presented from the perspective of real harmonic analysis. The author first builds a careful foundation in real harmonic analysis, introducing all the material needed for his later discussions. He then studies the Navier-Stokes equations on the whole space, exploring previously scattered results such as the decay of solutions in space and in time, uniqueness, self-similar solutions, the decay of Lebesgue or Besov norms of solutions, and the existence of solutions for a uniformly locally square integrable initial value. Many of the proofs and statements are original and, to the extent possible, presented in the context of real harmonic analysis.
Although the existence, regularity, and uniqueness of solutions to the Navier-Stokes equations continue to be a challenge, this book is a welcome opportunity for mathematicians and physicists alike to explore the problem's intricacies from a new and enlightening perspective.
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A Practical Guide to Boundary Element Methods with the Software Library BEMLIB
Added 11/28/2007
C. Pozrikidis
The boundary-element method is a powerful numerical technique for solving partial differential equations encountered in applied mathematics, science, and engineering. The strength of the method derives from its ability to solve with notable efficiency problems in domains with complex and possibly evolving geometry where traditional methods can be demanding, cumbersome, or unreliable. This dual-purpose text provides a concise introduction to the theory and implementation of boundary-element methods, while simultaneously offering hands-on experience based on the software library BEMLIB.
BEMLIB contains four directories comprising a collection of FORTRAN 77 programs and codes on Green's functions and boundary-element methods for Laplace, Helmholtz, and Stokes flow problems. The software is freely available from the Internet site: http://bemlib.ucsd.edu
The first seven chapters of the text discuss the theoretical foundation and practical implementation of the boundary-element method. The material includes both classical topics and recent developments, such as methods for solving inhomogeneous, nonlinear, and time-dependent equations. The last five chapters comprise the BEMLIB user guide, which discusses the mathematical formulation of the problems considered, outlines the numerical methods, and describes the structure of the boundary-element codes.
A Practical Guide to Boundary Element Methods with the Software Library BEMLIB is ideal for self-study and as a text for an introductory course on boundary-element methods, computational mechanics, computational science, and numerical differential equations.
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Introduction to Quantum Control and Dynamics
Added 11/28/2007
Domenico D'Alessandro
The introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics. Exploring this emerging subject, Introduction to Quantum Control and Dynamics presents the mathematical concepts and fundamental physics behind the analysis and control of quantum dynamics, emphasizing the application of Lie algebra and Lie group theory.
After introducing the basics of quantum mechanics, the book derives a class of models for quantum control systems from fundamental physics. It examines the controllability and observability of quantum systems and the related problem of quantum state determination and measurement. The author also uses Lie group decompositions as tools to analyze dynamics and to design control algorithms. In addition, he describes various other control methods and discusses topics in quantum information theory that include entanglement and entanglement dynamics. The final chapter covers the implementation of quantum control and dynamics in several fields.
Armed with the basics of quantum control and dynamics, readers will invariably use this interdisciplinary knowledge in their mathematical, physics, and engineering work.
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Isometries on Banach Spaces: function spaces
Added 12/19/2007
Richard Fleming, James Jamison
Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one.
Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras.
This treatment provides a clear account of historically important results, exposes the principal methods of attack, and includes some results that are more recent and some that are lesser known. Unique in its focus, this book will prove useful for experts as well as beginners in the field and for those who simply want to acquaint themselves with this area of Banach space theory.
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Strain Solitons in Solids and How to Construct Them
Added 12/19/2007
Alexander Samsonov
Although the theory behind solitary waves of strain shows that they hold significant promise in nondestructive testing and a variety of other applications, an enigma has long persisted-the absence of observable elastic solitary waves in practice. Inspired by this apparent contradiction, Strain Solitons in Solids and How to Construct Them refines the existing theory, explores how to construct a powerful deformation pulse in a waveguide without plastic flow or fracture, and proposes a direct method of strain soliton generation, detection, and observation.
The author focuses on the theory, simulation, generation, and propagation of strain solitary waves in a nonlinearly elastic, straight cylindrical rod under finite deformations. He introduces the general theory of wave propagation in nonlinearly elastic solids and shows, from first principles, how its main ideas can lead to successful experiments. In doing so, he develops a new approach to solving the corresponding doubly dispersive equation (DDE) with dissipative terms, leading to new explicit and exact solutions. He also shows that the method is applicable to a variety of nonlinear problems.
First discovered in virtual reality, nonlinear waves and solitons in solids are finally moving into the genuine reality of physics, mechanics, and engineering. Strain Solitons in Solids and How to Construct Them shows how to balance the mathematics of the problem with the application of the results to experiments and ultimately to generating and observing solitons in solids.
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Linear and Quasilinear Complex Equations of Hyperbolic and Mixed Types
Added 11/28/2007
Guo Chun Wen
This volume deals with first and second order complex equations of hyperbolic and mixed types. Various general boundary value problems for linear and quasilinear complex equations are investigated in detail. To obtain results for complex equations of mixed types, some discontinuous boundary value problems for elliptic complex equations are discussed. Mixed complex equations are included in the quasilinear case, and the text considers both boundary value conditions in the general oblique derivative case and multiply connected domains. Complex analytical methods are used to investigate various problems as well. In particular, hyperbolic numbers and hyperbolic complex functions are introduced to handle hyperbolic complex equations. Researchers and graduate students in mathematical analysis will find this text indispensable.
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Functional Equations with Causal Operators
Added 11/28/2007
C. Corduneanu
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
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Calculus with Complex Numbers
Added 11/28/2007
John Reade
This practical treatment explains the applications complex calculus without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, differentiation, contour integration, finite and infinite real integrals, summation of series, and the fundamental theorem of algebra. The Residue Theorem for evaluating complex integrals is presented in a straightforward way, laying the groundwork for further study. A working knowledge of real calculus and familiarity with complex numbers is assumed. This book is useful for graduate students in calculus and undergraduate students of applied mathematics, physical science, and engineering.
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Interfacial Phenomena: Equilibrium and Dynamic Effects, Second Edition
Added 2/15/2008
Clarence Miller, P. Neogi
Since the publication of the first edition of Interfacial Phenomena, the interest in interfaces and surfactants has multiplied, along with their applications. Experimental and theoretical advances have provided scientists with greater insight into the structure, properties, and behavior of surfactant and colloid systems.
Emphasizing equilibrium phenomena, flow, transport, and stability,
Interfacial Phenomena: Equilibrium and Dynamic Effects, Second Edition presents a concise and current summary of the fundamental principles governing interfacial interactions. This new edition features updated and expanded topics in every chapter. It highlights key experimental techniques that have expanded the scope of our understanding, such as in mass transfer, microstructure determination in colloidal dispersions, and surfactant-polymer interactions.
Interfacial Phenomena, Second Edition reflects the progress scientists have made in understanding the surface chemistry and interfacial dynamics of colloid and surfactant systems. The book also illustrates the growing applicability of these systems in a variety of fields including pharmaceuticals, cosmetics, detergents, paints, agricultural chemicals, and foods.
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Microstructural Randomness and Scaling in Mechanics of Materials
Added 12/19/2007
Martin Ostoja-Starzewski
An area at the intersection of solid mechanics, materials science, and stochastic mathematics, mechanics of materials often necessitates a stochastic approach to grasp the effects of spatial randomness. Using this approach, Microstructural Randomness and Scaling in Mechanics of Materials explores numerous stochastic models and methods used in the mechanics of random media and illustrates these in a variety of applications.
The book first offers a refresher in several tools used in stochastic mechanics, followed by two chapters that outline periodic and disordered planar lattice (spring) networks. Subsequent chapters discuss stress invariance in classical planar and micropolar elasticity and cover several topics not yet collected in book form, including the passage of a microstructure to an effective micropolar continuum.
After forming this foundation in various methods of stochastic mechanics, the book focuses on problems of microstructural randomness and scaling. It examines both representative and statistical volume elements (RVEs/SVEs) as well as micromechanically based stochastic finite elements (SFEs). The author also studies nonlinear elastic and inelastic materials, the stochastic formulation of thermomechanics with internal variables, and wave propagation in random media.
The concepts discussed in this comprehensive book can be applied to many situations, from micro and nanoelectromechanical systems (MEMS/NEMS) to geophysics.
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Noncommutative Geometry and Cayley-smooth Orders
Added 1/7/2008
Lieven Bruyn
Noncommutative Geometry and Cayley-smooth Orders explains the theory of Cayley-smooth orders in central simple algebras over function fields of varieties. In particular, the book describes the étale local structure of such orders as well as their central singularities and finite dimensional representations.
After an introduction to partial desingularizations of commutative singularities from noncommutative algebras, the book presents the invariant theoretic description of orders and their centers. It proceeds to introduce étale topology and its use in noncommutative algebra as well as to collect the necessary material on representations of quivers. The subsequent chapters explain the étale local structure of a Cayley-smooth order in a semisimple representation, classify the associated central singularity to smooth equivalence, describe the nullcone of these marked quiver representations, and relate them to the study of all isomorphism classes of n-dimensional representations of a Cayley-smooth order. The final chapters study Quillen-smooth algebras via their finite dimensional representations.
Noncommutative Geometry and Cayley-smooth Orders provides a gentle introduction to one of mathematics' and physics' hottest topics.
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Power Investing With Basket Securities: The Investor's Guide to Exchange-Traded Funds
Added 12/19/2007
Peter Madlem, Larry Edwards
Tremendously versatile, basket securities have the potential to change the way money is managed. This book provides the proper definition of the basket security, a brief exploration of their true history, and powerful ways to exploit their advantages. The authors explore simple yet effective ways basket securities can be used in asset management strategies including trading the market, building a diversified core, or creating a thousand stock portfolio. They cover the broad array of currently available basket securities and discuss others that are on the horizon, what and when to buy and sell, and how to protect investments from market declines.
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Encyclopedic Dictionary of International Finance and Banking
Added 12/19/2007
Jae Shim, Michael Constas
The Encyclopedic Dictionary of International Finance and Banking is a practical reference of proven techniques, strategies, and approaches. It covers virtually all important topics dealing with multinational business finance, money, investments, financial planning, financial economics, and banking. In addition, it explores the application of computers, quantitative techniques and models, and economics to international finance and banking. You get:
o Clear definitions and explanations
o Step-by-step instructions
o Statistical data, Charts, exhibits, and diagrams
o Checklists
o Practical Applications
Shim presents the most current information, offers important directives, and explains the technical procedures involved in this dynamic field. This reference gives you the tools you need to diagnose and evaluate the financial situations you face on a daily basis and answers every question you may have. It provides real-life examples and suggestions for handling everyday problems.
WHAT THIS BOOK WILL DO FOR YOU
More than a dictionary, more than an encyclopedia, this working guide will help you quickly pinpoint:
o What to look for
o How to do it
o What to watch out for
o How to apply it in the complex world of business
o What to do
You'll find ratios, formulas, examples, applications, exhibits, charts, and rules of thumb to help you analyze and evaluate any multinational financial decision. You will find this Encyclopedic Dictionary practical, comprehensive, quick, and useful. In short, this is a veritable cookbook of guidelines, illustrations, and how-tos. Encyclopedic Dictionary of International Finance and Banking is the resource you will reach for again and again.
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Modelling, Simulation and Control of Non-linear Dynamical Systems: An Intelligent Approach Using Soft Computing and Fractal Theory
Added 12/19/2007
Patricia Melin, Oscar Castillo
These authors use soft computing techniques and fractal theory in this new approach to mathematical modeling, simulation and control of complexion-linear dynamical systems. First, a new fuzzy-fractal approach to automated mathematical modeling of non-linear dynamical systems is presented. It is illustrated with examples on the PROLOG programming language. Second, a new fuzzy-genetic approach to automated simulation of dynamical systems is presented. It is illustrated with examples in the MATLAB programming language. Third, a new method for model-based adaptive control using a neuro-fussy fractal approach is combined with the methods mentioned above. This method is illustrated with MATLAB. Finally, applications of these new methods are presented, in the areas such as biochemical processes, robotic systems, manufacturing, food industry and chemical processes.
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Numerical Methods for Finance
Added 1/7/2008
John Miller, David Edelman, John Appleby
Featuring international contributors from both industry and academia, Numerical Methods for Finance explores new and relevant numerical methods for the solution of practical problems in finance. It is one of the few books entirely devoted to numerical methods as applied to the financial field.
Presenting state-of-the-art methods in this area, the book first discusses the coherent risk measures theory and how it applies to practical risk management. It then proposes a new method for pricing high-dimensional American options, followed by a description of the negative inter-risk diversification effects between credit and market risk. After evaluating counterparty risk for interest rate payoffs, the text considers strategies and issues concerning defined contribution pension plans and participating life insurance contracts. It also develops a computationally efficient swaption pricing technology, extracts the underlying asset price distribution implied by option prices, and proposes a hybrid GARCH model as well as a new affine point process framework. In addition, the book examines performance-dependent options, variance reduction, Value at Risk (VaR), the differential evolution optimizer, and put-call-futures parity arbitrage opportunities.
Sponsored by DEPFA Bank, IDA Ireland, and Pioneer Investments, this concise and well-illustrated book equips practitioners with the necessary information to make important financial decisions.
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Pattern Discovery in Bioinformatics: Theory & Algorithms
Added 1/7/2008
Laxmi Parida
The computational methods of bioinformatics are being used more and more to process the large volume of current biological data. Promoting an understanding of the underlying biology that produces this data, Pattern Discovery in Bioinformatics: Theory and Algorithms provides the tools to study regularities in biological data.
Taking a systematic approach to pattern discovery, the book supplies sound mathematical definitions and efficient algorithms to explain vital information about biological data. It explores various data patterns, including strings, clusters, permutations, topology, partial orders, and boolean expressions. Each of these classes captures a different form of regularity in the data, providing possible answers to a wide range of questions. The book also reviews basic statistics, including probability, information theory, and the central limit theorem.
This self-contained book provides a solid foundation in computational methods, enabling the solution of difficult biological questions.
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Optimal Statistical Inference in Financial Engineering
Added 4/4/2008
Masanobu Taniguchi, Junichi Hirukawa, Kenichiro Tamaki
Until now, few systematic studies of optimal statistical inference for stochastic processes had existed in the financial engineering literature, even though this idea is fundamental to the field. Balancing statistical theory with data analysis, Optimal Statistical Inference in Financial Engineering examines how stochastic models can effectively describe actual financial data and illustrates how to properly estimate the proposed models.
After explaining the elements of probability and statistical inference for independent observations, the book discusses the testing hypothesis and discriminant analysis for independent observations. It then explores stochastic processes, many famous time series models, their asymptotically optimal inference, and the problem of prediction, followed by a chapter on statistical financial engineering that addresses option pricing theory, the statistical estimation for portfolio coefficients, and value-at-risk (VaR) problems via residual empirical return processes. The final chapters present some models for interest rates and discount bonds, discuss their no-arbitrage pricing theory, investigate problems of credit rating, and illustrate the clustering of stock returns in both the New York and Tokyo Stock Exchanges.
Basing results on a modern, unified optimal inference approach for various time series models, this reference underlines the importance of stochastic models in the area of financial engineering.
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Handbook of Finite Translation Planes
Added 4/4/2008
Norman Johnson, Vikram Jha, Mauro Biliotti
The Handbook of Finite Translation Planes provides a comprehensive listing of all translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and thorough sketches of the major relevant theorems.
From the methods of André to coordinate and linear algebra, the book unifies the numerous diverse approaches for analyzing finite translation planes. It pays particular attention to the processes that are used to study translation planes, including ovoid and Klein quadric projection, multiple derivation, hyper-regulus replacement, subregular lifting, conical distortion, and Hermitian sequences. In addition, the book demonstrates how the collineation group can affect the structure of the plane and what information can be obtained by imposing group theoretic conditions on the plane. The authors also examine semifield and division ring planes and introduce the geometries of two-dimensional translation planes.
As a compendium of examples, processes, construction techniques, and models, the Handbook of Finite Translation Planes equips readers with precise information for finding a particular plane. It presents the classification results for translation planes and the general outlines of their proofs, offers a full review of all recognized construction techniques for translation planes, and illustrates known examples.
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Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics
Added 3/21/2008
Victor Galaktionov, Sergey Svirshchevskii
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties.
This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders.
The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.
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Capillary Flows with Forming Interfaces
Added 4/4/2008
Yulii Damir Shikhmurzaev
Capillary Flows with Forming Interfaces explores numerous theoretical problems that arise in the mathematical description of capillary flows. It focuses on developing a unified approach to a variety of seemingly very different capillary flows of practical importance where classical fluid mechanics leads to nonphysical results.
The book begins with a review of the conceptual framework of fluid mechanics and then proceeds to analyze the roots of singularities, such as the moving contact-line problem and the capillary breakup problem. The author then examines how different singular flows can be described as particular cases of a general physical phenomenon of interface formation. He illustrates the developed mathematical models and experimentally verifies them through a number of example problems relevant to engineering applications.
The conceptual framework provided in this reference enables further progress in developing mathematical models of capillary flows.
The book also allows readers to make informed strategic choices regarding available numerical codes and the in-house development of these codes.
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Algorithmic Lie Theory for Solving Ordinary Differential Equations
Added 4/4/2008
Fritz Schwarz
Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete problems. Taking this approach, Algorithmic Lie Theory for Solving Ordinary Differential Equations serves as a valuable introduction for solving differential equations using Lie's theory and related results.
After an introductory chapter, the book provides the mathematical foundation of linear differential equations, covering Loewy's theory and Janet bases. The following chapters present results from the theory of continuous groups of a 2-D manifold and discuss the close relation between Lie's symmetry analysis and the equivalence problem. The core chapters of the book identify the symmetry classes to which quasilinear equations of order two or three belong and transform these equations to canonical form. The final chapters solve the canonical equations and produce the general solutions whenever possible as well as provide concluding remarks. The appendices contain solutions to selected exercises, useful formulae, properties of ideals of monomials, Loewy decompositions, symmetries for equations from Kamke's collection, and a brief description of the software system ALLTYPES for solving concrete algebraic problems.
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Mathematics of Quantum Computation and Quantum Technology
Added 4/4/2008
Goong Chen, Louis Kauffman, Samuel Lomonaco
Research and development in the pioneering field of quantum computing involve just about every facet of science and engineering, including the significant areas of mathematics and physics. Based on the firm understanding that mathematics and physics are equal partners in the continuing study of quantum science, Mathematics of Quantum Computation and Quantum Technology explores the rapid mathematical advancements made in this field in recent years.
Novel Viewpoints on Numerous Aspects of Quantum Computing and Technology
Edited by a well-respected team of experts, this volume compiles contributions from specialists across various disciplines. It contains four main parts, beginning with topics in quantum computing that include quantum algorithms and hidden subgroups, quantum search, algorithmic complexity, and quantum simulation. The next section covers quantum technology, such as mathematical tools, quantum wave functions, superconducting quantum computing interference devices (SQUIDs), and optical quantum computing. The section on quantum information deals with error correction, cryptography, entanglement, and communication. The final part explores topological quantum computation, knot theory, category algebra, and logic.
The Tools You Need to Tackle the Next Generation of Quantum Technology
This book facilitates both the construction of a common quantum language and the development of interdisciplinary quantum techniques, which will aid efforts in the pursuit of the ultimate goal-a "real" scalable quantum computer.
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Nonlinear Hyperbolic Waves in Multidimensions
Added 3/21/2008
Phoolan Prasad
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.
Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts in gas dynamics, a graphical presentation of the results of extensive numerical computations, and an extension of Fermat's principle. There is also a chapter containing approximate equations used to discuss stability of steady transonic flows.
Full of new and original results, Nonlinear Hyperbolic Waves in Multidimensions is your only opportunity to explore a full treatment of these recent findings in book form. The material presented in this volume will prove useful not only for solving practical problems, but also in raising many difficult but important mathematical questions that remain open.
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Optimal Traffic Control: Urban Intersections
Added 4/8/2008
Slobodan Guberinic, Gordana Senborn, Bratislav Lazic
Despite traffic circles, four-way stop signs, lights regulated by timers or sensors, and other methods, the management of urban intersections remains problematic. Consider that transportation systems have all the features of so-called complex systems: the great number of state and control variables, the presence of uncertainty and indeterminism, the complex interactions between subsystems, the necessity to optimize several optimization criteria, and active behavior of the controlled process, to name just a few. Therefore, a mathematical approach to these systems can resolve their complex issues more elegantly than other methods.
Addressing both efficiency and traffic safety issues, Optimal Traffic Control: Urban Intersections examines the traffic control optimization problem and presents a novel solution method. Using an approach based on control theory, graph theory, and combinatorial optimization, the authors derive a full mathematical description of the traffic control problem and enumerate all combinatorial aspects. The result is a set of algorithmic solutions to various problems along with computer implementation that you can incorporate into real traffic control systems for immediate results. The book concludes by evaluating how the choice of a complete set of signal groups influences intersection performance.
Although modern cities throughout the world have a unique character influenced by culture, geography, and population, most of them share one main feature: busy intersections and the issue of controlling the traffic traveling through them. The development of information technologies, especially computer and telecommunications techniques, has changed the complexity of the problem and influenced the development of new solutions. Clearly stating the issues and presenting a possible solution, this book shows you how to take full advantage of all the capabilities of microprocessor-based traffic signal controllers.
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Stochastic Hybrid Systems
Added 4/4/2008
Christos Cassandras, John Lygeros
Because they incorporate both time- and event-driven dynamics, stochastic hybrid systems (SHS) have become ubiquitous in a variety of fields, from mathematical finance to biological processes to communication networks to engineering. Comprehensively integrating numerous cutting-edge studies, Stochastic Hybrid Systems presents a captivating treatment of some of the most ambitious types of dynamic systems. Cohesively edited by leading experts in the field, the book introduces the theoretical basics, computational methods, and applications of SHS. It first discusses the underlying principles behind SHS and the main design limitations of SHS. Building on these fundamentals, the authoritative contributors present methods for computer calculations that apply SHS analysis and synthesis techniques in practice. The book concludes with examples of systems encountered in a wide range of application areas, including molecular biology, communication networks, and air traffic management. It also explains how to resolve practical problems associated with these systems. Stochastic Hybrid Systems achieves an ideal balance between a theoretical treatment of SHS and practical considerations. The book skillfully explores the interaction of physical processes with computerized equipment in an uncertain environment, enabling a better understanding of sophisticated as well as everyday devices and processes.
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Geometric Algebra and Applications to Physics
Added 4/4/2008
Venzo Sabbata, Bidyut Kumar Datta
Bringing geometric algebra to the mainstream of physics pedagogy, Geometric Algebra and Applications to Physics not only presents geometric algebra as a discipline within mathematical physics, but the book also shows how geometric algebra can be applied to numerous fundamental problems in physics, especially in experimental situations.
This reference begins with several chapters that present the mathematical fundamentals of geometric algebra. It introduces the essential features of postulates and their underlying framework; bivectors, multivectors, and their operators; spinor and Lorentz rotations; and Clifford algebra. The book also extends some of these topics into three dimensions. Subsequent chapters apply these fundamentals to various common physical scenarios. The authors show how Maxwell's equations can be expressed and manipulated via space-time algebra and how geometric algebra reveals electromagnetic waves' states of polarization. In addition, they connect geometric algebra and quantum theory, discussing the Dirac equation, wave functions, and fiber bundles. The final chapter focuses on the application of geometric algebra to problems of the quantization of gravity.
By covering the powerful methodology of applying geometric algebra to all branches of physics, this book provides a pioneering text for undergraduate and graduate students as well as a useful reference for researchers in the field.
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Differential Geometry and Topology of Curves
Added 4/4/2008
Yu Animov
Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.
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Theorems of Leray-Schauder Type And Applications
Added 4/4/2008
Donal O'Regan, Radu Precup
This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many applications of current interest in the theory of nonlinear differential equations are presented to complement the theory. The text is essentially self-contained, so it may also be used as an introduction to topological methods in nonlinear analysis. This volume will appeal to graduate students and researchers in mathematical analysis and its applications.
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Virtual Topology and Functor Geometry
Added 4/7/2008
Fred Van Oystaeyen
Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear introduction to noncommutative topology, Virtual Topology and Functor Geometry explores new aspects of these areas as well as more established facets of noncommutative algebra.
Presenting the material in an easy, colloquial style to facilitate understanding, the book begins with an introduction to category theory, followed by a chapter on noncommutative spaces. This chapter examines noncommutative lattices, noncommutative opens, sheaf theory, the generalized Stone space, and Grothendieck topology. The author then studies Grothendieck categorical representations to formulate an abstract notion of "affine open". The final chapter proposes a dynamical version of topology and sheaf theory, providing at least one solution of the problem of sheafification independent of generalizations of topos theory.
By presenting new ideas for the development of an intrinsically noncommutative geometry, this book fosters the further unification of different kinds of noncommutative geometry and the expression of observations that involve natural phenomena.
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Isometries in Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two
Added 4/7/2008
Richard Fleming, James Jamison
A continuation of the authors’ previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces. Picking up where the first volume left off, the book begins with a chapter on the Banach–Stone property. The authors consider the case where the isometry is from C0(Q, X) to C0(K, Y) so that the property involves pairs (X, Y) of spaces. The next chapter examines spaces X for which the isometries on LP(μ, X) can be described as a generalization of the form given by Lamperti in the scalar case. The book then studies isometries on direct sums of Banach and Hilbert spaces, isometries on spaces of matrices with a variety of norms, and isometries on Schatten classes. It subsequently highlights spaces on which the group of isometries is maximal or minimal. The final chapter addresses more peripheral topics, such as adjoint abelian operators and spectral isometries. Essentially self-contained, this reference explores a fundamental aspect of Banach space theory. Suitable for both experts and newcomers to the field, it offers many references to provide solid coverage of the literature on isometries.
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Engineering BGM
Added 4/7/2008
Alan Brace
Also known as the Libor market model, the Brace-Gatarek-Musiela (BGM) model is becoming an industry standard for pricing interest rate derivatives. Written by one of its developers, Engineering BGM builds progressively from simple to more sophisticated versions of the BGM model, offering a range of methods that can be programmed into production code to suit readers' requirements.
After introducing the standard lognormal flat BGM model, the book focuses on the shifted/displaced diffusion version. Using this version, the author develops basic ideas about construction, change of measure, correlation, calibration, simulation, timeslicing, pricing, delta hedging, barriers, callable exotics (Bermudans), and vega hedging. Subsequent chapters address cross-economy BGM, the adaptation of the BGM model to inflation, a simple tractable stochastic volatility version of BGM, and Brazilian options suitable for BGM analysis. An appendix provides notation and an extensive array of formulae.
The straightforward presentation of various BGM models in this handy book will help promote a robust, safe, and stable environment for calibrating, simulating, pricing, and hedging interest rate instruments.
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Algorithmic Combinatorics on Partial Words
Added 4/7/2008
Francine Blanchet-Sadri
The discrete mathematics and theoretical computer science communities have recently witnessed explosive growth in the area of algorithmic combinatorics on words. The next generation of research on combinatorics of partial words promises to have a substantial impact on molecular biology, nanotechnology, data communication, and DNA computing. Delving into this emerging research area, Algorithmic Combinatorics on Partial Words presents a mathematical treatment of combinatorics on partial words designed around algorithms and explores up-and-coming techniques for solving partial word problems as well as the future direction of research. This five-part book begins with a section on basics that covers terminology, the compatibility of partial words, and combinatorial properties of words. The book then focuses on three important concepts of periodicity on partial words: period, weak period, and local period. The next part describes a linear time algorithm to test primitivity on partial words and extends the results on unbordered words to unbordered partial words while the following section introduces some important properties of pcodes, details a variety of ways of defining and analyzing pcodes, and shows that the pcode property is decidable using two different techniques. In the final part, the author solves various equations on partial words, presents binary and ternary correlations, and covers unavoidable sets of partial words. Setting the tone for future research in this field, this book lucidly develops the central ideas and results of combinatorics on partial words.
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Discrete Dynamical Systems and Difference Equations with Mathematica
Added 4/7/2008
Mustafa R.S. Kulenovic, Orlando Merino
Following the work of Yorke and Li in 1975, the theory of discrete dynamical systems and difference equations developed rapidly. The applications of difference equations also grew rapidly, especially with the introduction of graphical-interface software that can plot trajectories, calculate Lyapunov exponents, plot bifurcation diagrams, and find basins of attraction.
Modern computer algebra systems have opened the door to the use of symbolic calculation for studying difference equations. This book offers an introduction to discrete dynamical systems and difference equations and presents the Dynamica software. Developed by the authors and based on Mathematica, Dynamica provides an easy-to-use collection of algebraic, numerical, and graphical tools and techniques that allow users to quickly gain the ability to:
· Find and classify the stability character of equilibrium and periodic points
· Perform semicycle analysis of solutions
· Calculate and visualize invariants
· Calculate and visualize Lyapunov functions and numbers
· Plot bifurcation diagrams
· Visualize stable and unstable manifolds
· Calculate Box Dimension
While it presents the essential theoretical concepts and results, the book's emphasis is on using the software. The authors present two sets of Dynamica sessions: one that serves as a tutorial of the different techniques, the other features case studies of well-known difference equations. Dynamica and notebooks corresponding to particular chapters are available for download from the Internet.
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Parallel Iterative Algorithms: From Sequential to Grid Computing
Added 4/7/2008
Jacques Mohcine Bahi, Sylvain Contassot-Vivier, Raphael Couturier
Focusing on grid computing and asynchronism, Parallel Iterative Algorithms explores the theoretical and practical aspects of parallel numerical algorithms. Each chapter contains a theoretical discussion of the topic, an algorithmic section that fully details implementation examples and specific algorithms, and an evaluation of the advantages and drawbacks of the algorithms. Several exercises also appear at the end of most chapters.
The first two chapters introduce the general features of sequential iterative algorithms and their applications to numerical problems. The book then describes different kinds of parallel systems and parallel iterative algorithms. It goes on to address both linear and nonlinear parallel synchronous and asynchronous iterative algorithms for numerical computation, with an emphasis on the multisplitting approach. The final chapter discusses the features required for efficient implementation of asynchronous iterative algorithms.
Providing the theoretical and practical knowledge needed to design and implement efficient parallel iterative algorithms, this book illustrates how to apply these algorithms to solve linear and nonlinear numerical problems in parallel environments, including local, distant, homogeneous, and heterogeneous clusters.
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Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures
Added 4/7/2008
Elias Camouzis, G. Ladas
Extending and generalizing the results of rational equations, Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures focuses on the boundedness nature of solutions, the global stability of equilibrium points, the periodic character of solutions, and the convergence to periodic solutions, including their periodic trichotomies. The book also provides numerous thought-provoking open problems and conjectures on the boundedness character, global stability, and periodic behavior of solutions of rational difference equations. After introducing several basic definitions and general results, the authors examine 135 special cases of rational difference equations that have only bounded solutions and the equations that have unbounded solutions in some range of their parameters. They then explore the seven known nonlinear periodic trichotomies of third order rational difference equations. The main part of the book presents the known results of each of the 225 special cases of third order rational difference equations. In addition, the appendices supply tables that feature important information on these cases as well as on the boundedness character of all fourth order rational difference equations. A Framework for Future Research The theory and techniques developed in this book to understand the dynamics of rational difference equations will be useful in analyzing the equations in any mathematical model that involves difference equations. Moreover, the stimulating conjectures will promote future investigations in this fascinating, yet surprisingly little known area of research.
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A.D. Alexandrov: Selected Works Part II: Intrinsic Geometry of Convex Surfaces
Added 4/7/2008
S.S. Kutateladze
A.D. Alexandrov is considered by many to be the father of intrinsic geometry, second only to Gauss in surface theory. That appraisal stems primarily from this masterpiece--now available in its entirely for the first time since its 1948 publication in Russian. Alexandrov's treatise begins with an outline of the basic concepts, definitions, and results relevant to intrinsic geometry. It reviews the general theory, then presents the requisite general theorems on rectifiable curves and curves of minimum length. Proof of some of the general properties of the intrinsic metric of convex surfaces follows. The study then splits into two almost independent lines: further exploration of the intrinsic geometry of convex surfaces and proof of the existence of a surface with a given metric. The final chapter reviews the generalization of the whole theory to convex surfaces in the Lobachevskii space and in the spherical space, concluding with an outline of the theory of nonconvex surfaces. Alexandrov's work was both original and extremely influential. This book gave rise to studying surfaces "in the large," rejecting the limitations of smoothness, and reviving the style of Euclid. Progress in geometry in recent decades correlates with the resurrection of the synthetic methods of geometry and brings the ideas of Alexandrov once again into focus. This text is a classic that remains unsurpassed in its clarity and scope.
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Handbook of Parallel Computing: Models, Algorithms and Applications
Added 5/5/2008
Sanguthevar Rajasekaran, John Reif
The ability of parallel computing to process large data sets and handle time-consuming operations has resulted in unprecedented advances in biological and scientific computing, modeling, and simulations. Exploring these recent developments, the Handbook of Parallel Computing: Models, Algorithms, and Applications provides comprehensive coverage on all aspects of this field.
The first section of the book describes parallel models. It covers evolving computational systems, the decomposable bulk synchronous model, parallel random access machine-on-chip architecture, the parallel disks model, mobile agents, fault-tolerant computing, hierarchical performance modeling, the partitioned optical passive star network, and the reconfigurable mesh model. The subsequent section on parallel algorithms examines networks of workstations, grid and packet scheduling, the derandomization technique, isosurface extraction and rendering, suffix trees, and mobile computing algorithmics. The final part of the text highlights an array of problems and offers ways to combat these challenges.
This volume provides an up-to-date assessment of the models and algorithms involved in applying parallel computing to a variety of fields, from computational biology to wireless networking.
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Operations Research and Management Science Handbook
Added 5/5/2008
A. Ravi Ravindran
Operations Research (OR) began as an interdisciplinary activity to solve complex military problems during World War II. Utilizing principles from mathematics, engineering, business, computer science, economics, and statistics, OR has developed into a full fledged academic discipline with practical application in business, industry, government and military. Currently regarded as a body of established mathematical models and methods essential to solving complicated management issues, OR provides quantitative analysis of problems from which managers can make objective decisions. Operations Research and Management Science (OR/MS) methodologies continue to flourish in numerous decision making fields. Featuring a mix of international authors, Operations Research and Management Science Handbook combines OR/MS models, methods, and applications into one comprehensive, yet concise volume. The first resource to reach for when confronting OR/MS difficulties, this text – Provides a single source guide in OR/MS Bridges theory and practice Covers all topics relevant to OR/MS Offers a quick reference guide for students, researchers and practitioners Contains unified and up-to-date coverage designed and edited with non-experts in mind Discusses software availability for all OR/MS techniques Includes contributions from a mix of domestic and international experts The 26 chapters in the handbook are divided into two parts. Part I contains 14 chapters that cover the fundamental OR/MS models and methods. Each chapter gives an overview of a particular OR/MS model, its solution methods and illustrates successful applications. Part II of the handbook contains 11 chapters discussing the OR/MS applications in specific areas. They include airlines, e-commerce, energy systems, finance, military, production systems, project management, quality control, reliability, supply chain management and water resources. Part II ends with a chapter on the future of OR/MS applications.
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Effective Computational Methods for Wave Propagation
Added 5/7/2008
Nikolaos Kampanis, Vassilios Dougalis, John Ekaterinaris
Due to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years. Exploring the latest developments in the field, Effective Computational Methods for Wave Propagation presents several modern, valuable computational methods used to describe wave propagation phenomena in selected areas of physics and technology. Featuring contributions from internationally known experts, the book is divided into four parts. It begins with the simulation of nonlinear dispersive waves from nonlinear optics and the theory and numerical analysis of Boussinesq systems. The next section focuses on computational approaches, including a finite element method and parabolic equation techniques, for mathematical models of underwater sound propagation and scattering. The book then offers a comprehensive introduction to modern numerical methods for time-dependent elastic wave propagation. The final part supplies an overview of high-order, low diffusion numerical methods for complex, compressible flows of aerodynamics. Concentrating on physics and technology, this volume provides the necessary computational methods to effectively tackle the sources of problems that involve some type of wave motion.
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Algebraic Statistics: Computational Commutative Algebra in Statistics
Added 5/7/2008
Giovanni Pistone, Eva Riccomagno, Henry Wynn
Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics.
It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model.
As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science.
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