Given a conservative dynamical system of classical physics, how does one find a variational principle for it? Is there a canonical recipe for such a principle? The case of particle mechanics was settled by Lagrange in 1788; this text treats continuous systems. Recipes devised are algebraic in nature, and this book develops all the mathematical tools found necessary after the minute examination of the adiabatic fluid dynamics in the introduction. These tools include: Lagrangian and Hamiltonian formalisms, Legendre transforms, dual spaces of Lie algebras and associated 2-cocycles; and linearized and Z2-graded versions of all of these. The following typical physical systems, together with their Hamiltonian structures, are discussed: Classical Magnetohydro-dynamics with its Hall deformation; Multifluid Plasma; Superfluid He-4 (both irrotational and rotating) and 3He-A; Quantum fluids; Yang-Mills MHD; Spinning fluids; Spin Glass; Extended YM Plasma; A Lattice Gas. Detailed motivations, easy-to-follow arguments, open problems, and over 300 exercises help the reader.

Survival data or more general time-to-event data occur in many areas, including medicine, biology, engineering, economics, and demography, but previously standard methods have requested that all time variables are univariate and independent. This book extends the field by allowing for multivariate times. Applications where such data appear are survival of twins, survival of married couples and families, time to failure of right and left kidney for diabetic patients, life history data with time to outbreak of disease, complications and death, recurrent episodes of diseases and cross-over studies with time responses. As the field is rather new, the concepts and the possible types of data are described in detail and basic aspects of how dependence can appear in such data is discussed. Four different approaches to the analysis of such data are presented. The multi-state models where a life history is described as the subject moving from state to state is the most classical approach. The Markov models make up an important special case, but it is also described how easily more general models are set up and analyzed. Frailty models, which are random effects models for survival data, made a second approach, extending from the most simple shared frailty models, which are considered in detail, to models with more complicated dependence structures over individuals or over time. Marginal modelling has become a popular approach to evaluate the effect of explanatory factors in the presence of dependence, but without having specified a statistical model for the dependence. Finally, the completely non-parametric approach to bivariate censored survival data is described. This book is aimed at investigators who need to analyze multivariate survival data, but due to its focus on the concepts and the modelling aspects, it is also useful for persons interested in such data, but not having a statistical education. It can be used as a textbook for a graduate course in multivariate survival data. It is made from an applied point of view and covers all essential aspects of applying multivariate survival models. Also more theoretical evaluations, like asymptotic theory, are described, but only to the extent useful in applications and for understanding the models. For reading the book, it is useful, but not necessary, to have an understanding of univariate survival data. Philip Hougaard is a statistician at the pharmaceutical company Novo Nordisk. He has a Ph.D. in nonlinear regression models and is Doctor of Science based on a thesis on frailty models. He is associate editor of Biometrics and Lifetime Data Analysis. He has published over 80 papers in the statistical and medical literature.

Rationality - as opposed to 'ad-hoc' - and asymptotics - to emphasize the fact that perturbative methods are at the core of the theory - are the two main concepts associated with the Rational Asymptotic Modeling (RAM) approach in fluid dynamics when the goal is to specifically provide useful models accessible to numerical simulation via high-speed computing. This approach has contributed to a fresh understanding of Newtonian fluid flow problems and has opened up new avenues for tackling real fluid flow phenomena, which are known to lead to very difficult mathematical and numerical problems irrespective of turbulence. With the present scientific autobiography the author guides the reader through his somewhat non-traditional career; first discovering fluid mechanics, and then devoting more than fifty years to intense work in the field. Using both personal and general historical contexts, this account will be of benefit to anyone interested in the early and contemporary developments of an important branch of theoretical and computational fluid mechanics.

The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "Equilibrium Problems and Variational Models," which was held in Erice (Sicily) in the period June 23 - July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order deriva tives, geometric aspects, distance functions and log-quadratic proximal methodology. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others. As noted in the previous book "Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models," edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to han dle problems whose equilibrium conditions are not obtained by the mini mization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) con dition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation."

This book is intended as an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The first part explains how to use computer algebra for applications in solid-state simulation, based on the GAP computer algebra package. Computer algebra enables us to easily obtain various group theoretical properties, such as the representations, character tables, and subgroups. Furthermore it offers a new perspective on material design, which could be executed in a mathematically rigorous and systematic way. The second part then analyzes the relation between the structural symmetry and the electronic structure in C60 (as an example of a system without periodicity). The principal object of the study was to illustrate the hierarchical change in the quantum-physical properties of the molecule, which correlates to the reduction in the symmetry (as it descends down in the ladder of subgroups). The book also presents the computation of the vibrational modes of the C60 by means of the computer algebra. In order to serve the common interests of researchers, the details of the computations (the required initial data and the small programs developed for the purpose) are explained in as much detail as possible.

The purpose of this book is to honor the fundamental contributions to many different areas of statistics made by Barry Arnold. Distinguished and active researchers highlight some of the recent developments in statistical distribution theory, order statistics and their properties, as well as inferential methods associated with them. Applications to survival analysis, reliability, quality control, and environmental problems are emphasized.

The first part of this volume gathers the lecture notes of the courses of the "XVII Escuela Hispano-Francesa", held in Gijon, Spain, in June 2016. Each chapter is devoted to an advanced topic and presents state-of-the-art research in a didactic and self-contained way. Young researchers will find a complete guide to beginning advanced work in fields such as High Performance Computing, Numerical Linear Algebra, Optimal Control of Partial Differential Equations and Quantum Mechanics Simulation, while experts in these areas will find a comprehensive reference guide, including some previously unpublished results, and teachers may find these chapters useful as textbooks in graduate courses. The second part features the extended abstracts of selected research work presented by the students during the School. It highlights new results and applications in Computational Algebra, Fluid Mechanics, Chemical Kinetics and Biomedicine, among others, offering interested researchers a convenient reference guide to these latest advances.

This volume contains the invited contributions to the Spring 2012 seminar series at Virginia State University on Mathematical Sciences and Applications. It is a thematic continuation of work presented in Volume 24 of the Springer Proceedings in Mathematics & Statistics series. Contributors present their own work as leading researchers to advance their specific fields and induce a genuine interdisciplinary interaction. Thus all articles therein are selective, self-contained, and are pedagogically exposed to foster student interest in science, technology, engineering and mathematics, stimulate graduate and undergraduate research, as well as collaboration between researchers from different areas. The volume features new advances in mathematical research and its applications: anti-periodicity; almost stochastic difference equations; absolute and conditional stability in delayed equations; gamma-convergence and applications to block copolymer morphology; the dynamics of collision and near-collision in celestial mechanics; almost and pseudo-almost limit cycles; rainbows in spheres and connections to ray, wave and potential scattering theory; null-controllability of the heat equation with constraints; optimal control for systems subjected to null-controllability; the Galerkin method for heat transfer in closed channels; wavelet transforms for real-time noise cancellation; signal, image processing and machine learning in medicine and biology; methodology for research on durability, reliability, damage tolerance of aerospace materials and structures at NASA Langley Research Center. The volume is suitable and valuable for mathematicians, scientists and research students in a variety of interdisciplinary fields, namely physical and life sciences, engineering and technology including structures and materials sciences, computer science for signal, image processing and machine learning in medicine.

Semi-infinite optimization is a vivid field of active research. Recently semi infinite optimization in a general form has attracted a lot of attention, not only because of its surprising structural aspects, but also due to the large number of applications which can be formulated as general semi-infinite programs. The aim of this book is to highlight structural aspects of general semi-infinite programming, to formulate optimality conditions which take this structure into account, and to give a conceptually new solution method. In fact, under certain assumptions general semi-infinite programs can be solved efficiently when their bi-Ievel structure is exploited appropriately. After a brief introduction with some historical background in Chapter 1 we be gin our presentation by a motivation for the appearance of standard and general semi-infinite optimization problems in applications. Chapter 2 lists a number of problems from engineering and economics which give rise to semi-infinite models, including (reverse) Chebyshev approximation, minimax problems, ro bust optimization, design centering, defect minimization problems for operator equations, and disjunctive programming."

This book introduces readers to the lattice Boltzmann method (LBM) for solving transport phenomena - flow, heat and mass transfer - in a systematic way. Providing explanatory computer codes throughout the book, the author guides readers through many practical examples, such as: * flow in isothermal and non-isothermal lid-driven cavities; * flow over obstacles; * forced flow through a heated channel; * conjugate forced convection; and * natural convection. Diffusion and advection-diffusion equations are discussed, together with applications and examples, and complete computer codes accompany the sections on single and multi-relaxation-time methods. The codes are written in MatLab. However, the codes are written in a way that can be easily converted to other languages, such as FORTRANm Python, Julia, etc. The codes can also be extended with little effort to multi-phase and multi-physics, provided the physics of the respective problem are known. The second edition of this book adds new chapters, and includes new theory and applications. It discusses a wealth of practical examples, and explains LBM in connection with various engineering topics, especially the transport of mass, momentum, energy and molecular species. This book offers a useful and easy-to-follow guide for readers with some prior experience with advanced mathematics and physics, and will be of interest to all researchers and other readers who wish to learn how to apply LBM to engineering and industrial problems. It can also be used as a textbook for advanced undergraduate or graduate courses on computational transport phenomena

This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, ever y entry is followed by a cross-reference to other related subject entries in the dictionary.

The feasibility to extract porous medium parameters from acoustic recordings is investigated. The thesis gives an excellent discussion of our basic understanding of different wave modes, using a full-waveform and multi-component approach. Focus lies on the dependency on porosity and permeability where especially the latter is difficult to estimate. In this thesis, this sensitivity is shown for interface-wave and reflected-wave modes. For each of the pseudo-Rayleigh and pseudo-Stoneley interface waves unique estimates for permeability and porosity can be obtained when impedance and attenuation are combined.
The pseudo-Stoneley wave is most sensitive to permeability: both the impedance and the attenuation are controlled by the fluid flow. Also from reflected-wave modes unique estimates for permeability and porosity can be obtained when the reflection coefficients of different reflected modes are combined. In this case the sensitivity to permeability is caused by subsurface heterogeneities generating mesoscopic fluid flow at seismic frequencies. The results of this thesis suggest that estimation of in-situ permeability is feasible, provided detection is carried out with multi-component measurements. The results of this thesis argely affect geotechnical and reservoir engineering practices.

This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered.

This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered.

Wiley-Interscience Series in Discrete Mathematics and Optimization Advisory
Editors: Ronald L. Graham, Jan Karel Lenstra, and Robert E. Tarjan

Discrete mathematics, the study of finite structures, is one of the fastest-growing areas in mathematics. The wide applicability of its evolving techniques points to the rapidity with which the field is moving from its beginnings to its maturity, and reflects the ever-increasing interaction between discrete mathematics and computer science. This Series provides broad coverage of discrete mathematics and optimization, ranging over such fields as combinatorics, graph theory, enumeration, and the analysis of algorithms. "The Wiley-Interscience Series in Discrete Mathematics and Optimization" will be a substantial part of the record of the extraordinary development of this field. A complete listing of the titles in the Series appears on the inside front cover of this book.

"[Integer and Combinatorial Optimization] is a major contribution to the literature of discrete programming. This text should be required reading for anybody who intends to research this area or even just to keep abreast of developments."
--"Times Higher Education Supplement," London

"An extensive but extremely well-written graduate text covering integer programming."
--"American Mathematical Monthly"

Recent titles in the Series include:

"Integer and Combinatorial Optimization" George L. Nemhauser and Laurence A. Wolsey 1988 (0 471-82819-X) 763 pp.

"Introduction to the Theory of Error-Correcting Codes" Second Edition Vera Pless
For mathematicians, engineers, and computer scientists, here is an introduction to the theory of error-correctingcodes, focusing on linear block codes. The book considers such codes as Hamming and Golay codes, correction of double errors, use of finite fields, cyclic codes, B.C.H. codes, weight distributions, and design of codes. In a second edition of the book, Pless offers thoroughly expanded coverage of nonbinary and cyclic codes. Some proofs have been simplified, and there are many more examples and problems. 1989 (0 471-61884-5) 224 pp.

Recently, analogies between laboratory physics (e.g. quantum optics and condensed matter) and gravitational/cosmological phenomena such as black holes have attracted an increasing interest. This book contains a series of selected lectures devoted to this new and rapidly developing field. Various analogies connecting (apparently) different areas in physics are presented in order to bridge the gap between them and to provide an alternative point of view.

This book deals with asymptotic solutions of linear and nonlinear equa- tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) ~ o. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp- totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) ~ 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob- lems of mathematical physics; certain specific formulas were obtained by differ- ent methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ter- nov [113], J. Schwinger [107, 108], E. J. Heller [53], G. A. Hagedorn [50, 51], V. N. Bayer, V. M. Katkov [21], N. A. Chernikov [35] and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume [106] write in its preface: "One can hope that in the near future a computational pro- cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed.

Experience gained during a ten-year long involvement in modelling, program ming and application in nonlinear optimization helped me to arrive at the conclusion that in the interest of having successful applications and efficient software production, knowing the structure of the problem to be solved is in dispensable. This is the reason why I have chosen the field in question as the sphere of my research. Since in applications, mainly from among the nonconvex optimization models, the differentiable ones proved to be the most efficient in modelling, especially in solving them with computers, I started to deal with the structure of smooth optimization problems. The book, which is a result of more than a decade of research, can be equally useful for researchers and stu dents showing interest in the domain, since the elementary notions necessary for understanding the book constitute a part of the university curriculum. I in tended dealing with the key questions of optimization theory, which endeavour, obviously, cannot bear all the marks of completeness. What I consider the most crucial point is the uniform, differential geometric treatment of various questions, which provides the reader with opportunities for learning the structure in the wide range, within optimization problems. I am grateful to my family for affording me tranquil, productive circumstances. I express my gratitude to F."

This volume comprises the proceedings of the International Workshop on Eco logical Goal Functions, held at the Schleswig-Holstein Cultural Center of Salzau, August 30 -September 4, 1996. The conference - first in a series - intended to be convened at Salzau at 1 -2 year intervals to address various aspects of theo retical and application-oriented ecology, was initiated, organized and carried out under the auspices of the Ecology Center of the Kiel University. It featured key note addresses, invited lectures, submitted papers, and posters. 32 contributions written by authors from eight countries, were selected to be presented in this book. From the very rich discussions of the workshop, some general characteristics emerged which might become important for a deeper understanding of the nature of evolving systems or, in other words, systems with a history, described by variables with a high degree of interdependence. These characteristics include the following: Speaking of 'goal functions' is a convenient 'fa on de parler', since a logical analysis of the formal structure of teleological and causal explanations shows that both are analogous with regard to the inherent structural typology and the basic mode of explanation. Teleological interpretations introduce motives or objectives of actors into the set of 'antecedens' conditions relevant for system evolution, and are consequently a subset of causal interpretations."

In this edition, the scope and character of the monograph did not change with respect to the first edition. Taking into account the rapid development of the field, we have, however, considerably enlarged its contents. Chapter 4 includes two additional sections 4.4 and 4.6 on theory and algorithms of D.C. Programming. Chapter 7, on Decomposition Algorithms in Nonconvex Optimization, is completely new. Besides this, we added several exercises and corrected errors and misprints in the first edition. We are grateful for valuable suggestions and comments that we received from several colleagues. R. Horst, P.M. Pardalos and N.V. Thoai March 2000 Preface to the First Edition Many recent advances in science, economics and engineering rely on nu merical techniques for computing globally optimal solutions to corresponding optimization problems. Global optimization problems are extraordinarily di verse and they include economic modeling, fixed charges, finance, networks and transportation, databases and chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environment al engineering. Due to the existence of multiple local optima that differ from the global solution all these problems cannot be solved by classical nonlinear programming techniques. During the past three decades, however, many new theoretical, algorith mic, and computational contributions have helped to solve globally multi extreme problems arising from important practical applications."

Complementarity theory is a new domain in applied mathematics and is concerned with the study of complementarity problems. These problems represent a wide class of mathematical models related to optimization, game theory, economic engineering, mechanics, fluid mechanics, stochastic optimal control etc. The book is dedicated to the study of nonlinear complementarity problems by topological methods. Audience: Mathematicians, engineers, economists, specialists working in operations research and anybody interested in applied mathematics or in mathematical modeling.

The stochastic gravitational-wave background (SGWB) is by far the most difficult source of gravitational radiation detect. At the same time, it is the most interesting and intriguing one. This book describes the initial detection of the SGWB and describes the underlying mathematics behind one of the most amazing discoveries of the 21st century. On the experimental side it would mean that interferometric gravitational wave detectors work even better than expected. On the observational side, such a detection could give us information about the very early Universe, information that could not be obtained otherwise. Even negative results and improved upper bounds could put constraints on many cosmological and particle physics models.

This volume features selected and peer-reviewed articles from the Pan-American Advanced Studies Institute (PASI). The chapters are written by international specialists who participated in the conference. Topics include developments based on breakthroughs in the mathematical understanding of phenomena describing systems in highly inhomogeneous and disordered media, including the KPZ universality class (describing the evolution of interfaces in two dimensions), random walks in random environment and percolative systems. PASI fosters a collaboration between North American and Latin American researchers and students. The conference that inspired this volume took place in January 2012 in both Santiago de Chile and Buenos Aires. Researchers and graduate students will find timely research in probability theory, statistical physics and related disciplines.

In 1970, Manfred Eigen initiated the study of the origin of self-reproducing systems of macromolecules and their evolution. Large-scale nucleotide sequencing (with computer methods) was introduced from 1977. The authors of this book, the first edition of which appeared (in Russian) in 1985, have been engaged in the research of the evolution of molecular genetic regulatory systems ever since those pioneering years. The book considers many fundamental problems of molecular biology, evolution, molecular genetic organization, the structure and function of macromolecules, always with the underlying motive of developing a unified theory. It describes many original, theoretical results as well as computational methods.

Another Calculus book? As long as students find calculus scary, the failure rate in mathematics is higher than in all other subjects, and as long as most people mistakenly believe that only geniuses can learn and understand mathematics, there will always be room for a new book of Calculus. We call it Calculus Light.

This book is designed for a one semester course in "light" calculus - mostly single variable, meant to be used by undergraduate students without a wide mathematical background and who do not major in mathematics but study subjects such as engineering, biology or management information systems.

The first chapter contains a historical background of calculus. Every scientific achievement involves people and therefore characterized by victories and disappointments, intrigues and hope. All of these elements exist in the story behind calculus and when you add the time dimension, starting 2400 years ago, it is a saga. We hope the reader enjoys reading this chapter as much as we enjoyed the writing.

In addition to classic calculus the book provides tools for practical applications such as Fourier series, Lagrange multipliers and elementary numerical methods.