This book features survey and research papers from The Abel Symposium 2011: Algebras, quivers and representations, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like, commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in representation theory of quivers and algebras.

"Algebras, Quivers and Representations" is targeted at researchers and graduate students in algebra, representation theory and triangulate categories. "

The new book series "The Science and Art of Simulation" (SAS) addresses computer simulations as a scientific activity and engineering artistry (in the sense of a techne). The first volume is devoted to three topics: 1. The Art of Exploring Computer Simulations Philosophy began devoting attention to computer simulations at a relatively early stage. Since then, the unquestioned point of view has been that computer simulation is a new scientific method; the philosophy of simulation is therefore part of the philosophy of science. The first section of this volume discusses this implicit, unchallenged assumption by addressing, from different perspectives, the question of how to explore (and how not to explore) research on computer simulations. Scientists discuss what is still lacking or considered problematic, while philosophers draft new directions for research, and both examine the art of exploring computer simulations. 2. The Art of Understanding Computer Simulations The results of computer simulations are integrated into both political and social decisions. It is implicitly assumed that the more detailed, and consequently more realistic, a computer simulation is, the more useful it will be in decision-making. However, this idea is by no means justified. Different types of computer simulations have to be differentiated, which in turn requires the specific skill of understanding computer simulation results. The articles in this section examine the capabilities and limits of simulation results in political and social contexts, exploring the art of understanding computer simulation results. 3. The Art of Knowing through Computer Simulations? The advent of computer simulation in today's scientific practices challenges the order of science. What kind of knowledge is gained through computer simulations is the key question in this section. Computer simulations are often compared to experiments or to arguments, and the transformation of our traditional scientific notions might be more challenging than expected - these Ideas are put forward in the third section to conceptualize the art of knowing through computer simulations.

This monograph explains the theory of quantum waveguides, that is, dynamics of quantum particles confined to regions in the form of tubes, layers, networks, etc. The focus is on relations between the confinement geometry on the one hand and the spectral and scattering properties of the corresponding quantum Hamiltonians on the other. Perturbations of such operators, in particular, by external fields are also considered. The volume provides a unique summary of twenty-five years of research activity in this area and indicates ways in which the theory can develop further. The book is fairly self-contained. While it requires some broader mathematical physics background, all the basic concepts are properly explained and proofs of most theorems are given in detail, so there is no need for additional sources. Without a parallel in the literature, the monograph by Exner and Kovarik guides the reader through this new and exciting field.

This vital new resource offers engineers and researchers a window on important new technology that will supersede the barcode and is destined to change the face of logistics and product data handling. In the last two decades, radio-frequency identification has grown fast, with accelerated take-up of RFID into the mainstream through its adoption by key users such as Wal-Mart, K-Mart and the US Department of Defense. RFID has many potential applications due to its flexibility, capability to operate out of line of sight, and its high data-carrying capacity. Yet despite optimistic projections of a market worth $25 billion by 2018, potential users are concerned about costs and investment returns. Clearly demonstrating the need for a fully printable chipless RFID tag as well as a powerful and efficient reader to assimilate the tag's data, this book moves on to describe both. Introducing the general concepts in the field including technical data, it then describes how a chipless RFID tag can be made using a planar disc-loaded monopole antenna and an asymmetrical coupled spiral multi-resonator. The tag encodes data via the "spectral signature" technique and is now in its third-generation version with an ultra-wide band (UWB) reader operating at between 5 and 10.7GHz.

The main body of this book is devoted to statistical physics, whereas much less emphasis is given to thermodynamics. In particular, the idea is to present the most important outcomes of thermodynamics - most notably, the laws of thermodynamics - as conclusions from derivations in statistical physics. Special emphasis is on subjects that are vital to engineering education. These include, first of all, quantum statistics, like the Fermi-Dirac distribution, as well as diffusion processes, both of which are fundamental to a sound understanding of semiconductor devices. Another important issue for electrical engineering students is understanding of the mechanisms of noise generation and stochastic dynamics in physical systems, most notably in electric circuitry. Accordingly, the fluctuation-dissipation theorem of statistical mechanics, which is the theoretical basis for understanding thermal noise processes in systems, is presented from a signals-and-systems point of view, in a way that is readily accessible for engineering students and in relation with other courses in the electrical engineering curriculum, like courses on random processes.

The primary objective of this book is to study some of the research topics in the area of analysis of complex surveys which have not been covered in any book yet. It discusses the analysis of categorical data using three models: a full model, a log-linear model and a logistic regression model. It is a valuable resource for survey statisticians and practitioners in the field of sociology, biology, economics, psychology and other areas who have to use these procedures in their day-to-day work. It is also useful for courses on sampling and complex surveys at the upper-undergraduate and graduate levels. The importance of sample surveys today cannot be overstated. From voters' behaviour to fields such as industry, agriculture, economics, sociology, psychology, investigators generally resort to survey sampling to obtain an assessment of the behaviour of the population they are interested in. Many large-scale sample surveys collect data using complex survey designs like multistage stratified cluster designs. The observations using these complex designs are not independently and identically distributed - an assumption on which the classical procedures of inference are based. This means that if classical tests are used for the analysis of such data, the inferences obtained will be inconsistent and often invalid. For this reason, many modified test procedures have been developed for this purpose over the last few decades.

Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion "Samuelson" market model (also known as the Black-Scholes model because it is used in that most famous theory), instead opting for models that allowed minimax approaches to complement or replace stochastic methods. Among the most fruitful models were those utilizing game-theoretic tools and the so-called interval market model. Over time, these models have slowly but steadily gained influence in the financial community, providing a useful alternative to classical methods. A self-contained monograph, The Interval Market Model in Mathematical Finance: Game-Theoretic Methods assembles some of the most important results, old and new, in this area of research. Written by seven of the most prominent pioneers of the interval market model and game-theoretic finance, the work provides a detailed account of several closely related modeling techniques for an array of problems in mathematical economics. The book is divided into five parts, which successively address topics including: * probability-free Black-Scholes theory; * fair-price interval of an option; * representation formulas and fast algorithms for option pricing; * rainbow options; * tychastic approach of mathematical finance based upon viability theory. This book provides a welcome addition to the literature, complementing myriad titles on the market that take a classical approach to mathematical finance. It is a worthwhile resource for researchers in applied mathematics and quantitative finance, and has also been written in a manner accessible to financially-inclined readers with a limited technical background.

This thesis focuses on the dynamics of autonomous Boolean networks, on the basis of Boolean logic functions in continuous time without external clocking. These networks are realized with integrated circuits on an electronic chip as a field programmable gate array (FPGA) with roughly 100,000 logic gates, offering an extremely flexible model system. It allows fast and cheap design cycles and large networks with arbitrary topologies and coupling delays. The author presents pioneering results on theoretical modeling, experimental realization, and selected applications. In this regard, three classes of novel dynamic behavior are investigated: (i) Chaotic Boolean networks are proposed as high-speed physical random number generators with high bit rates. (ii) Networks of periodic Boolean oscillators are home to long-living transient chimera states, i.e., novel patterns of coexisting domains of spatially coherent (synchronized) and incoherent (desynchronized) dynamics. (iii) Excitable networks exhibit cluster synchronization and can be used as fast artificial Boolean neurons whose spiking patterns can be controlled. This work presents the first experimental platform for large complex networks, which will facilitate exciting future developments.

This book covers essential Microsoft EXCEL (R)'s computational skills while analyzing introductory physics projects. Topics of numerical analysis include; multiple graphs on the same sheet, calculation of descriptive statistical parameters, a 3-point interpolation, the Euler and the Runge-Kutter methods to solve equations of motion, the Fourier transform to calculate the normal modes of a double pendulum, matrix calculations to solve coupled linear equations of a DC circuit, animation of waves and Lissajous figures, electric and magnetic field calculations from the Poisson equation and its 3D surface graphs, variational calculus such as Fermat's least traveling time principle and the least action principle. Nelson's stochastic quantum dynamics is also introduced to draw quantum particle trajectories.

This book provides the reader with a background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for advanced undergraduate or graduate students with a firm background in stochastics. Alongside the theoretical foundation, ready-to-implement algorithms and many examples make this book a valuable tool for anyone who is applying the methodology.

The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.

This book covers a wide spectrum of systems such as linear and nonlinear multivariable systems as well as control problems such as disturbance, uncertainty and time-delays. The purpose of this book is to provide researchers and practitioners a manual for the design and application of advanced discrete-time controllers. The book presents six different control approaches depending on the type of system and control problem. The first and second approaches are based on Sliding Mode control (SMC) theory and are intended for linear systems with exogenous disturbances. The third and fourth approaches are based on adaptive control theory and are aimed at linear/nonlinear systems with periodically varying parametric uncertainty or systems with input delay. The fifth approach is based on Iterative learning control (ILC) theory and is aimed at uncertain linear/nonlinear systems with repeatable tasks and the final approach is based on fuzzy logic control (FLC) and is intended for highly uncertain systems with heuristic control knowledge. Detailed numerical examples are provided in each chapter to illustrate the design procedure for each control method. A number of practical control applications are also presented to show the problem solving process and effectiveness with the advanced discrete-time control approaches introduced in this book.

This textbook offers a readily comprehensible introduction to classical Newtonian gravitation, which is fundamental for an understanding of classical mechanics and is particularly relevant to Astrophysics. The opening chapter recalls essential elements of vectorial calculus, especially to provide the formalism used in subsequent chapters. In chapter two Classical Newtonian gravity theory for one point mass and for a generic number N of point masses is then presented and discussed. The theory for point masses is naturally extended to the continuous case. The third chapter addresses the paradigmatic case of spherical symmetry in the mass density distribution (central force), with introduction of the useful tool of qualitative treatment of motion. Subsequent chapters discuss the general case of non-symmetric mass density distribution and develop classical potential theory, with elements of harmonic theory, which is essential to understand the potential development in series of the gravitational potential, the subject of the fourth chapter. Finally, in the last chapter the specific case of motion of a satellite around the earth is considered. Examples and exercises are presented throughout the book to clarify aspects of the theory. The book is aimed at those who wish to progress further beyond an initial bachelor degree, onward to a master degree, and a PhD. It is also a valuable resource for postgraduates and active researchers in the field.

This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical optimization models, is introduced to model and solve continuous nonlinear optimization applications. More than 15 real nonlinear optimization applications in algebraic and GAMS representation are presented which are used to illustrate the performances of the algorithms described in this book. Theoretical and computational results, methods, and techniques effective for solving nonlinear optimization problems, are detailed through the algorithms MINOS, KNITRO, CONOPT, SNOPT and IPOPT which work in GAMS technology.

Problems of Point Blast Theory covers all the main topics of modern theory with the exception of applications to nova and supernova outbursts. All the presently known theoretical results are given and problems which are still to be resolved are indicated. A special feature of the book is the sophisticated mathematical approach. Of interest to specialists and graduate students working in hydrodynamics, explosion theory, plasma physics, mathematical physics, and applied mathematics.

The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation.

"Nonlinear Partial Differential Equations for Scientists and Engineers, Third Edition, "improves onanalready highlycomplete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, research reference, or self-study guide."

The volume presents a selection of in-depth studies and state-of-the-art surveys of several challenging topics that are at the forefront of modern applied mathematics, mathematical modeling, and computational science. These three areas represent the foundation upon which the methodology of mathematical modeling and computational experiment is built as a ubiquitous tool in all areas of mathematical applications. This book covers both fundamental and applied research, ranging from studies of elliptic curves over finite fields with their applications to cryptography, to dynamic blocking problems, to random matrix theory with its innovative applications. The book provides the reader with state-of-the-art achievements in the development and application of new theories at the interface of applied mathematics, modeling, and computational science.

This book aims at fostering interdisciplinary collaborations required to meet the modern challenges of applied mathematics, modeling, and computational science. At the same time, the contributions combine rigorous mathematical and computational procedures and examples from applications ranging from engineering to life sciences, providing a rich ground for graduate student projects.

This book presents the latest research advances in complex network structure analytics based on computational intelligence (CI) approaches, particularly evolutionary optimization. Most if not all network issues are actually optimization problems, which are mostly NP-hard and challenge conventional optimization techniques. To effectively and efficiently solve these hard optimization problems, CI based network structure analytics offer significant advantages over conventional network analytics techniques. Meanwhile, using CI techniques may facilitate smart decision making by providing multiple options to choose from, while conventional methods can only offer a decision maker a single suggestion. In addition, CI based network structure analytics can greatly facilitate network modeling and analysis. And employing CI techniques to resolve network issues is likely to inspire other fields of study such as recommender systems, system biology, etc., which will in turn expand CI's scope and applications. As a comprehensive text, the book covers a range of key topics, including network community discovery, evolutionary optimization, network structure balance analytics, network robustness analytics, community-based personalized recommendation, influence maximization, and biological network alignment. Offering a rich blend of theory and practice, the book is suitable for students, researchers and practitioners interested in network analytics and computational intelligence, both as a textbook and as a reference work.

This textbook teaches advanced undergraduate and first-year graduate students in Engineering and Applied Sciences to gather and analyze empirical observations (data) in order to aid in making design decisions. While science is about discovery, the primary paradigm of engineering and "applied science" is design. Scientists are in the discovery business and want, in general, to understand the natural world rather than to alter it. In contrast, engineers and applied scientists design products, processes, and solutions to problems. That said, statistics, as a discipline, is mostly oriented toward the discovery paradigm. Young engineers come out of their degree programs having taken courses such as "Statistics for Engineers and Scientists" without any clear idea as to how they can use statistical methods to help them design products or processes. Many seem to think that statistics is only useful for demonstrating that a device or process actually does what it was designed to do. Statistics courses emphasize creating predictive or classification models - predicting nature or classifying individuals, and statistics is often used to prove or disprove phenomena as opposed to aiding in the design of a product or process. In industry however, Chemical Engineers use designed experiments to optimize petroleum extraction; Manufacturing Engineers use experimental data to optimize machine operation; Industrial Engineers might use data to determine the optimal number of operators required in a manual assembly process. This text teaches engineering and applied science students to incorporate empirical investigation into such design processes. Much of the discussion in this book is about models, not whether the models truly represent reality but whether they adequately represent reality with respect to the problems at hand; many ideas focus on how to gather data in the most efficient way possible to construct adequate models. Includes chapters on subjects not often seen together in a single text (e.g., measurement systems, mixture experiments, logistic regression, Taguchi methods, simulation) Techniques and concepts introduced present a wide variety of design situations familiar to engineers and applied scientists and inspire incorporation of experimentation and empirical investigation into the design process. Software is integrally linked to statistical analyses with fully worked examples in each chapter; fully worked using several packages: SAS, R, JMP, Minitab, and MS Excel - also including discussion questions at the end of each chapter. The fundamental learning objective of this textbook is for the reader to understand how experimental data can be used to make design decisions and to be familiar with the most common types of experimental designs and analysis methods.

Mathematical Modeling for Complex Fluids and Flows provides researchers and engineering practitioners encountering fluid flows with state-of-the-art knowledge in continuum concepts and associated fluid dynamics. In doing so it supplies the means to design mathematical models of these flows that adequately express the engineering physics involved. It exploits the implicit link between the turbulent flow of classical Newtonian fluids and the laminar and turbulent flow of non-Newtonian fluids such as those required in food processing and polymeric flows.

The book develops a descriptive mathematical model articulated through continuum mechanics concepts for these non-Newtonian, viscoelastic fluids and turbulent flows. Each complex fluid and flow is examined in this continuum context as well as in combination with the turbulent flow of viscoelastic fluids. Some details are also explored via kinetic theory, especially viscoelastic fluids and their treatment with the Boltzmann equation. Both solution and modeling strategies for turbulent flows are laid out using continuum concepts, including a description of constructing polynomial representations and accounting for non-inertial and curvature effects.

Ranging from fundamental concepts to practical methodology, and including discussion of emerging technologies, this book is ideal for those requiring a single-source assessment of current practice in this intricate yet vital field.

This book contains the most recent progress in data assimilation in meteorology, oceanography and hydrology including land surface. It spans both theoretical and applicative aspects with various methodologies such as variational, Kalman filter, ensemble, Monte Carlo and artificial intelligence methods. Besides data assimilation, other important topics are also covered including targeting observation, sensitivity analysis, and parameter estimation. The book will be useful to individual researchers as well as graduate students for a reference in the field of data assimilation.

Starting from fundamentals of classical stability theory, an overview is given of the transition phenomena in subsonic, wall-bounded shear flows. At first, the consideration focuses on elementary small-amplitude velocity perturbations of laminar shear layers, i.e. instability waves, in the simplest canonical configurations of a plane channel flow and a flat-plate boundary layer. Then the linear stability problem is expanded to include the effects of pressure gradients, flow curvature, boundary-layer separation, wall compliance, etc. related to applications. Beyond the amplification of instability waves is the non-modal growth of local stationary and non-stationary shear flow perturbations which are discussed as well. The volume continues with the key aspect of the transition process, that is, receptivity of convectively unstable shear layers to external perturbations, summarizing main paths of the excitation of laminar flow disturbances. The remainder of the book addresses the instability phenomena found at late stages of transition. These include secondary instabilities and nonlinear features of boundary-layer perturbations that lead to the final breakdown to turbulence. Thus, the reader is provided with a step-by-step approach that covers the milestones and recent advances in the laminar-turbulent transition. Special aspects of instability and transition are discussed through the book and are intended for research scientists, while the main target of the book is the student in the fundamentals of fluid mechanics. Computational guides, recommended exercises, and PowerPoint multimedia notes based on results of real scientific experiments supplement the monograph. These are especially helpful for the neophyte to obtain a solid foundation in hydrodynamic stability. To access the supplementary material go to extras.springer.com and type in the ISBN for this volume.

This volume collects recent advances in nonlinear delay systems, with an emphasis on constructive generalized Lyapunov and predictive approaches that certify stability properties. The book is written by experts in the field and includes two chapters by Miroslav Krstic, to whom this volume is dedicated. This volume is suitable for all researchers in mathematics and engineering who deal with nonlinear delay control problems and students who would like to understand the current state of the art in the control of nonlinear delay systems.

This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty.

This comprehensive work explores interfacial instability and pattern formation in dynamic systems away from the equilibrium state in solidification and crystal growth. Further, this significantly expanded 2nd edition introduces and reviews the progress made during the last two decades. In particular, it describes the most prominent pattern formation phenomena commonly observed in material processing and crystal growth in the framework of the previously established interfacial wave theory, including free dendritic growth from undercooled melt, cellular growth and eutectic growth in directional solidification, as well as viscous fingering in Hele-Shaw flow. It elucidates the key problems, systematically derives their mathematical solutions by pursuing a unified, asymptotic approach, and finally carefully examines these results by comparing them with the available experimental results. The asymptotic approach described here will be useful for the investigation of pattern formation phenomena occurring in a much broader class of inhomogeneous dynamical systems. In addition, the results on global stability and selection mechanisms of pattern formation will be of particular interest to researchers working on material processing and crystal growth. The stability mechanisms of a curved front and the pattern formation have been fundamental subjects in the areas of condensed-matter physics, materials science, crystal growth, and fluid mechanics for some time now. This book offers a stimulating and insightful introduction for all physicists, engineers and applied mathematicians working in the fields of soft condensed-matter physics, materials science, mechanical and chemical engineering, fluid dynamics, and nonlinear sciences.