From the Introduction: " Marston Morse was born in 1892, so that he was 33 years old when in 1925 his paper Relations between the critical points of a real-valued function of n independent variables appeared in the Transactions of the American Mathematical Society. Thus Morse grew to maturity just at the time when the subject of Analysis Situs was being shaped by such masters as Poincare, Veblen, L. E. J. Brouwer, G. D. Birkhoff, Lefschetz and Alexander, and it was Morse's genius and destiny to discover one of the most beautiful and far-reaching relations between this fledgling and Analysis; a relation which is now known as Morse Theory. In retrospect all great ideas take on a certain simplicity and inevitability, partly because they shape the whole subsequent development of the subject. And so to us, today, Morse Theory seems natural and inevitable. This whole flight of ideas was of course acclaimed by the mathematical World...it eventually earned him practically every honor of the mathematical community, over twenty honorary degrees, the National Science Medal, the Legion of Honor of France, ..."

Starting from an undergraduate level, this book systematically develops the basics of * Calculus on manifolds, vector bundles, vector fields and differential forms, * Lie groups and Lie group actions, * Linear symplectic algebra and symplectic geometry, * Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

The purpose of this book is to provide an up-to-date introduction to the time-domain finite element methods for Maxwell's equations involving metamaterials. Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials has attracted significant attention from researchers across many disciplines. Thanks to enormous efforts on the part of engineers and physicists, metamaterials present great potential applications in antenna and radar design, sub-wavelength imaging, and invisibility cloak design. Hence the efficient simulation of electromagnetic phenomena in metamaterials has become a very important issue and is the subject of this book, in which various metamaterial modeling equations are introduced and justified mathematically. The development and practical implementation of edge finite element methods for metamaterial Maxwell's equations are the main focus of the book. The book finishes with some interesting simulations such as backward wave propagation and time-domain cloaking with metamaterials.

This volume contains a collection of papers dedicated to Professor Eckhard Platen to celebrate his 60th birthday, which occurred in 2009. The contributions have been written by a number of his colleagues and co-authors. All papers have been - viewed and presented as keynote talks at the international conference "Quantitative Methods in Finance" (QMF) in Sydney in December 2009. The QMF Conference Series was initiated by Eckhard Platen in 1993 when he was at the Australian - tional University (ANU) in Canberra. Since joining UTS in 1997 the conference came to be organised on a much larger scale and has grown to become a signi?cant international event in quantitative ?nance. Professor Platen has held the Chair of Quantitative Finance at the University of Technology, Sydney (UTS) jointly in the Faculties of Business and Science since 1997. Prior to this appointment, he was the Founding Head of the Centre for Fin- cial Mathematics at the Institute of Advanced Studies at ANU, a position to which he was appointed in 1994. Eckhard completed a PhD in Mathematics at the Technical University in Dresden in 1975 and in 1985 obtained his Doctor of Science degree (Habilitation degree in the German system) from the Academy of Sciences in Berlin where he headed the Stochastics group at the Weierstrass Institute.

This book focuses on the theoretical aspects of small strain theory of elastoplasticity with hardening assumptions. It provides a comprehensive and unified treatment of the mathematical theory and numerical analysis. It is divided into three parts, with the first part providing a detailed introduction to plasticity, the second part covering the mathematical analysis of the elasticity problem, and the third part devoted to error analysis of various semi-discrete and fully discrete approximations for variational formulations of the elastoplasticity. This revised and expanded edition includes material on single-crystal and strain-gradient plasticity. In addition, the entire book has been revised to make it more accessible to readers who are actively involved in computations but less so in numerical analysis. Reviews of earlier edition: "The authors have written an excellent book which can be recommended for specialists in plasticity who wish to know more about the mathematical theory, as well as those with a background in the mathematical sciences who seek a self-contained account of the mechanics and mathematics of plasticity theory." (ZAMM, 2002) "In summary, the book represents an impressive comprehensive overview of the mathematical approach to the theory and numerics of plasticity. Scientists as well as lecturers and graduate students will find the book very useful as a reference for research or for preparing courses in this field." (Technische Mechanik) "The book is professionally written and will be a useful reference to researchers and students interested in mathematical and numerical problems of plasticity. It represents a major contribution in the area of continuum mechanics and numerical analysis." (Math Reviews)

This multidisciplinary volume is the second in the STEAM-H series to feature invited contributions on mathematical applications in naval engineering. Seeking a more holistic approach that transcends current scientific boundaries, leading experts present interdisciplinary instruments and models on a broad range of topics. Each chapter places special emphasis on important methods, research directions, and applications of analysis within the field. Fundamental scientific and mathematical concepts are applied to topics such as microlattice materials in structural dynamics, acoustic transmission in low Mach number liquid flow, differential cavity ventilation on a symmetric airfoil, Kalman smoother, metallic foam metamaterials for vibration damping and isolation, seal whiskers as a bio-inspired model for the reduction of vortex-induced vibrations, multidimensional integral for multivariate weighted generalized Gaussian distributions, minimum uniform search track placement for rectangular regions, antennas in the maritime environment, the destabilizing impact of non-performers in multi-agent groups, inertial navigation accuracy with bias modeling. Carefully peer-reviewed and pedagogically presented for a broad readership, this volume is perfect to graduate and postdoctoral students interested in interdisciplinary research. Researchers in applied mathematics and sciences will find this book an important resource on the latest developments in naval engineering. In keeping with the ideals of the STEAM-H series, this volume will certainly inspire interdisciplinary understanding and collaboration.

Verena Puchner evaluates and compares statistical matching and selected SAE methods. Due to the fact that poverty estimation at regional level based on EU-SILC samples is not of adequate accuracy, the quality of the estimations should be improved by additionally incorporating micro census data. The aim is to find the best method for the estimation of poverty in terms of small bias and small variance with the aid of a simulated artificial "close-to-reality" population. Variables of interest are imputed into the micro census data sets with the help of the EU-SILC samples through regression models including selected unit-level small area methods and statistical matching methods. Poverty indicators are then estimated. The author evaluates and compares the bias and variance for the direct estimator and the various methods. The variance is desired to be reduced by the larger sample size of the micro census.

Whatdoasupernovaexplosioninouterspace,?owaroundanairfoil and knocking in combustion engines have in common? The physical and chemical mechanisms as well as the sizes of these processes are quite di?erent. So are the motivations for studying them scienti?cally. The super- 8 nova is a thermo-nuclear explosion on a scale of 10 cm. Astrophysicists try to understand them in order to get insight into fundamental properties of the universe. In ?ows around airfoils of commercial airliners at the scale of 3 10 cm shock waves occur that in?uence the stability of the wings as well as fuel consumption in ?ight. This requires appropriate design of the shape and structure of airfoils by engineers. Knocking occurs in combustion, a chemical 1 process, and must be avoided since it damages motors. The scale is 10 cm and these processes must be optimized for e?ciency and environmental conside- tions. The common thread is that the underlying ?uid ?ows may at a certain scale of observation be described by basically the same type of hyperbolic s- tems of partial di?erential equations in divergence form, called conservation laws. Astrophysicists, engineers and mathematicians share a common interest in scienti?c progress on theory for these equations and the development of computational methods for solutions of the equations. Due to their wide applicability in modeling of continua, partial di?erential equationsareamajor?eldofresearchinmathematics. Asubstantialportionof mathematical research is related to the analysis and numerical approximation of solutions to such equations. Hyperbolic conservation laws in two or more spacedimensionsstillposeoneofthemainchallengestomodernmathematics.

Nuclear engineering has undergone extensive progress over the years. In the past century, colossal developments have been made and with specific reference to the mathematical theory and computational science underlying this discipline, advances in areas such as high-order discretization methods, Krylov Methods and Iteration Acceleration have steadily grown. Nuclear Computational Science: A Century in Review addresses these topics and many more; topics which hold special ties to the first half of the century, and topics focused around the unique combination of nuclear engineering, computational science and mathematical theory. Comprising eight chapters, Nuclear Computational Science: A Century in Review incorporates a number of carefully selected issues representing a variety of problems, providing the reader with a wealth of information in both a clear and concise manner. The comprehensive nature of the coverage and the stature of the contributing authors combine to make this a unique landmark publication. Targeting the medium to advanced level academic, this book will appeal to researchers and students with an interest in the progression of mathematical theory and its application to nuclear computational science.

On the occasion of his 60th birthday in October 2009, friends, collaborators, and admirers of Wolfgang Dahmen have organized this volume which touches on va- ous of his research interests. This volume will provide an easy to read excursion into many important topics in applied and computational mathematics. These include nonlinear and adaptive approximation, multivariate splines, subdivision schemes, multiscale and wavelet methods, numerical schemes for partial differential and boundary integral equations, learning theory, and high-dimensional integrals. College Station, Texas, USA Ronald A. DeVore Paderborn, Germany Angela Kunoth June 2009 vii Acknowledgements We are deeply grateful to Dr. Martin Peters and Thanh-Ha Le Thi from Springer for realizing this book project and to Frank Holzwarth for technical support. ix Contents Introduction: Wolfgang Dahmen's mathematical work...1 Ronald A. DeVore and Angela Kunoth 1 Introduction ...1 2 The early years: Classical approximation theory...2 3 Bonn, Bielefeld, Berlin, and multivariate splines ...2 3. 1 Computer aided geometric design ...3 3. 2 Subdivision and wavelets ...4 4 Wavelet and multiscale methods for operator equations...5 4. 1 Multilevel preconditioning ...5 4. 2 Compression of operators...5 5 Adaptive solvers ...6 6 Constructionandimplementation...7 7 Hyperbolic partial differential equations and conservation laws ...8 8 Engineering collaborations ...9 9 Thepresent ...9 10 Finalremarks...10 Publications by Wolfgang Dahmen (as of summer 2009)...10 The way things were in multivariate splines: A personal view...19 Carl de Boor 1 Tensor product spline interpolation...19 2 Quasiinterpolation ...20 3 MultivariateB-splines ...21 4 Kergininterpolation ...

This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

A new starting-point and a new method are requisite, to insure a complete [classi?cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di?cult execution und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and H. S. White (1917) [129] The history of classifying combinatorial objects is as old as the history of the objects themselves. In the mid-19th century, Kirkman, Steiner, and others became the fathers of modern combinatorics, and their work - on various objects, including (what became later known as) Steiner triple systems - led to several classi?cation results. Almost a century earlier, in 1782, Euler [180] published some results on classifying small Latin squares, but for the ?rst few steps in this direction one should actually go at least as far back as ancient Greece and the proof that there are exactly ?ve Platonic solids. One of the most remarkable achievements in the early, pre-computer era is the classi?cation of the Steiner triple systems of order 15, quoted above. An onerous task that, today, no sensible person would attempt by hand calcu- tion. Because, with the exception of occasional parameters for which com- natorial arguments are e?ective (often to prove nonexistence or uniqueness), classi?cation in general is about algorithms and computation.

The aquatic coastal zone is one of the most challenging targets for environmental remote sensing. Properties such as bottom reflectance, spectrally diverse suspended sediments and phytoplankton communities, diverse benthic communities, and transient events that affect surface reflectance (coastal blooms, runoff, etc.) all combine to produce an optical complexity not seen in terrestrial or open ocean systems. Despite this complexity, remote sensing is proving to be an invaluable tool for "Case 2" waters. This book presents recent advances in coastal remote sensing with an emphasis on applied science and management. Case studies of the operational use of remote sensing in ecosystem studies, monitoring, and interfacing remote sensing/science/management are presented. Spectral signatures of phytoplankton and suspended sediments are discussed in detail with accompanying discussion of why blue water (Case 1) algorithms cannot be applied to Case 2 waters. Audience This book is targeted for scientists and managers interested in using remote sensing in the study or management of aquatic coastal environments. With only limited discussion of optics and theory presented in the book, such researchers might benefit from the detailed presentations of aquatic spectral signatures, and to operational management issues. While not specifically written for remote sensing scientists, it will prove to be a useful reference for this community for the current status of aquatic coastal remote sensing.

Continuamentenasconoifatti 1 aconfusionedelleteorie 2 Carlo Dossi Electromagnetism is withoutany doubt a fascinating area of physics, engineering and mathematics. Since the early pioneeringworks ofAmpere, Faraday, and Maxwell, the scienti?cliteratureon this subject has become immense, and books devoted to almost all of its aspects have been published in the meantime. However, webelievethatthereisstillsomeplacefornew booksdealingwithel- tromagnetism, particularly if they are focused on more speci?c models, or try to mix different levels of analysis: rigorous mathematical results, sound numerical appro- mation schemes, real-life examples from physics and engineering. The complete mathematical description of electromagnetic problems is provided by the celebrated Maxwell equations, a system of partial differential equations - pressed interms ofphysical quantitiesliketheelectric?eld, themagnetic?eld and the currentdensity.Maxwell'scontributiontotheformulationofthese equationsisrelated to the introductionof a speci?c term, called displacement current, that he proposed to add to the set of equations generally assumed to hold at that time, in order to ensure the conservation of the electric charge. The presence of the displacement current permits to describe one of the most - portant phenomenon in electromagnetism, namely, wave propagation; however, in many interesting applications the propagation speed of the wave is very high with respect to the ratio of some typical length and time scale of the considered device, and therefore the dominant aspect becomes the diffusionof the electromagnetic ?elds. When the focus is on diffusioninstead of propagation, from the modelingpointof view this corresponds to neglecting the time derivative of the electric induction (i.e., thedisplacement current introducedby Maxwell)or, alternatively,neglectingthe time derivative of the magnetic induction.

The presence of uncertainty in a system description has always been a critical issue in control. The main objective of Randomized Algorithms for Analysis and Control of Uncertain Systems, with Applications (Second Edition) is to introduce the reader to the fundamentals of probabilistic methods in the analysis and design of systems subject to deterministic and stochastic uncertainty. The approach propounded by this text guarantees a reduction in the computational complexity of classical control algorithms and in the conservativeness of standard robust control techniques. The second edition has been thoroughly updated to reflect recent research and new applications with chapters on statistical learning theory, sequential methods for control and the scenario approach being completely rewritten. Features: * self-contained treatment explaining Monte Carlo and Las Vegas randomized algorithms from their genesis in the principles of probability theory to their use for system analysis; * development of a novel paradigm for (convex and nonconvex) controller synthesis in the presence of uncertainty and in the context of randomized algorithms; * comprehensive treatment of multivariate sample generation techniques, including consideration of the difficulties involved in obtaining identically and independently distributed samples; * applications of randomized algorithms in various endeavours, such as PageRank computation for the Google Web search engine, unmanned aerial vehicle design (both new in the second edition), congestion control of high-speed communications networks and stability of quantized sampled-data systems. Randomized Algorithms for Analysis and Control of Uncertain Systems (second edition) is certain to interest academic researchers and graduate control students working in probabilistic, robust or optimal control methods and control engineers dealing with system uncertainties. The present book is a very timely contribution to the literature. I have no hesitation in asserting that it will remain a widely cited reference work for many years. M. Vidyasagar

This edited volume consists of twelve contributions related to the EU Marie Curie Transfer of Knowledge Project Cooperation of Estonian and Norwegian Scienti c Centres within Mathematics and its Applications, CENS-CMA (2005-2009), - der contract MTKD-CT-2004-013909, which ?nanced exchange visits to and from CENS, the Centre for Nonlinear Studies at the Institute of Cybernetics of Tallinn University of Technology in Estonia. Seven contributions describe research highlights of CENS members, two the work of members of CMA, the Centre of Mathematics for Applications,Univ- sity of Oslo, Norway, as the partner institution of CENS in the Marie Curie project, and three the ?eld of work of foreign research fellows, who visited CENS as part of theproject. Thestructureofthebookre?ectsthedistributionofthetopicsaddressed: Part I Waves in Solids Part II Mesoscopic Theory Part III Exploiting the Dissipation Inequality Part IV Waves in Fluids Part V Mathematical Methods The papers are written in a tutorial style, intended for non-specialist researchers and students, where the authors communicate their own experiences in tackling a problem that is currently of interest in the scienti?c community. The goal was to produce a book, which highlights the importance of applied mathematics and which can be used for educational purposes, such as material for a course or a seminar. To ensure the scienti?c quality of the contributions, each paper was carefully - viewed by two international experts. Special thanks go to all authors and referees, without whom making this book would not have been possible.

Programming Finite Elements in Java (TM) teaches the reader how to programme the algorithms of the finite element method (FEM) in Java (TM). The compact, simple code helps the student to read the algorithms, to understand them and thus to be able to refine them. All of the main aspects of finite element techniques are considered: finite element solution; generation of finite element meshes; and visualization of finite element models and results with Java 3D (TM). The step-by-step presentation includes algorithm programming and code explanation at each point. Problems and exercises are provided for each chapter, with Java (TM) source code and problem data sets available from http://extras.springer.com/2010/978-1-84882-971-8.

Argumentation is all around us. Letters to the Editor often make points of cons- tency, and "Why" is one of the most frequent questions in language, asking for r- sons behind behaviour. And argumentation is more than 'reasoning' in the recesses of single minds, since it crucially involves interaction. It cements the coordinated social behaviour that has allowed us, in small bands of not particularly physically impressive primates, to dominate the planet, from the mammoth hunt all the way up to organized science. This volume puts argumentation on the map in the eld of Arti cial Intelligence. This theme has been coming for a while, and some famous pioneers are chapter authors, but we can now see a broader systematic area emerging in the sum of topics and results. As a logician, I nd this intriguing, since I see AI as 'logic continued by other means', reminding us of broader views of what my discipline is about. Logic arose originally out of re ection on many-agent practices of disputation, in Greek Ant- uity, but also in India and China. And logicians like me would like to return to this broader agenda of rational agency and intelligent interaction. Of course, Aristotle also gave us a formal systems methodology that deeply in uenced the eld, and eventually connected up happily with mathematical proof and foundations.

The Third Conference on Applied Mathematics and Scienti?c Computing took place June 23-27, 2003 on island of Brijuni, Croatia. The main goal of the conference was to interchange ideas among applied mathematicians in the broadest sense both from and outside academia, as well as experts from other areas who apply different mathematical techniques. During the meeting there were invited and contributed talksand software presentations. Invited presentations were given by active researchers from the ?eldsof approximation theory, numerical methods for differential equations and numericallinear algebra. These proceedings contain research and review papers by invited speakers and selected contributed papers from the ?elds of applied and numerical mathematics. A particular aim of the conference was to encourage young scientists to present results of their research. Traditionally, the best presentation given by PhD student was rewarded. This year awardee was Luka Grubisi ? c ' (University of Hagen, Hagen, Germany) and we congratulate him for this achievement. It would be hard to organize the conference without generous support of the Croatian Ministry of Science and Technology and we acknowledge it. We are also indebted to themainorganizer, Department of Mathematics, University of Zagreb.Motivating beautiful nature should bealso mentioned.And,attheend, we are thankful to Drs. JosipTambaca ? and Ivica Nakic ' for giving this book its ?nal shape.

? DoesP=NP. In just ?ve symbols Dick Karp -in 1972-captured one of the deepest and most important questions of all time. When he ?rst wrote his famous paper, I think it's fair to say he did not know the depth and importance of his question. Now over three decades later, we know P=NP is central to our understanding of compu- tion, it is a very hard problem, and its resolution will have potentially tremendous consequences. This book is a collection of some of the most popular posts from my blog- Godel Lost Letter andP=NP-which I started in early 2009. The main thrust of the blog, especially when I started, was to explore various aspects of computational complexity around the famousP=NP question. As I published posts I branched out and covered additional material, sometimes a timely event, sometimes a fun idea, sometimes a new result, and sometimes an old result. I have always tried to make the posts readable by a wide audience, and I believe I have succeeded in doing this.

Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.

In January 2012 an Oberwolfach workshop took place on the topic of recent developments in the numerics of partial differential equations. Focus was laid on methods of high order and on applications in Computational Fluid Dynamics. The book covers most of the talks presented at this workshop.

Computer Science and Operations Research continue to have a synergistic relationship and this book represents the results of the cross-fertilization between OR/MS and CS/AI. It is this interface of OR/CS that makes possible advances that could not have been achieved in isolation. Taken collectively, these articles are indicative of the state of the art in the interface between OR/MS and CS/AI and of the high-caliber research being conducted by members of the INFORMS Computing Society.

The present volume celebrates the 60th birthday of Professor Giovanni Paolo Galdi and honors his remarkable contributions to research in the ?eld of Mathematical Fluid Mechanics. The book contains a collection of 35 peer reviewed papers, with authors from 20 countries, re?ecting the worldwide impact and great inspiration by his work over the years. These papers were selected from invited lectures and contributed talks presented at the International Conference on Mathematical Fluid Mechanics held in Estoril, Portugal, May 21-25, 2007 and organized on the oc- sion of Professor Galdi's 60th birthday. We express our gratitude to all the authors and reviewers for their important contributions. Professor Galdi devotes his career to research on the mathematical analysis of the Navier-Stokes equations and non-Newtonian ?ow problems, with special emphasis on hydrodynamic stability and ?uid-particle interactions, impressing the worldwide mathematical communities with his results. His numerous contributions have laid down signi?cant milestones in these ?elds, with a great in?uence on interdis- plinary research communities. He has advanced the careers of numerous young researchers through his generosity and encouragement, some directly through int- lectual guidance and others indirectly by pairing them with well chosen senior c- laborators. A brief review of Professor Galdi's activities and some impressions by colleagues and friends are included here.

This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.