The book offers a new approach to information theory that is more general then the classical approach by Shannon. The classical definition of information is given for an alphabet of symbols or for a set of mutually exclusive propositions (a partition of the probability space ) with corresponding probabilities adding up to 1. The new definition is given for an arbitrary cover of , i.e. for a set of possibly overlapping propositions. The generalized information concept is called novelty and it is accompanied by two new concepts derived from it, designated as information and surprise, which describe "opposite" versions of novelty, information being related more to classical information theory and surprise being related more to the classical concept of statistical significance. In the discussion of these three concepts and their interrelations several properties or classes of covers are defined, which turn out to be lattices. The book also presents applications of these new concepts, mostly in statistics and in neuroscience.

This book prepares students to execute the quantitative and computational needs of the finance industry. The quantitative methods are explained in detail with examples from real financial problems like option pricing, risk management, portfolio selection, etc. Codes are provided in R programming language to execute the methods. Tables and figures, often with real data, illustrate the codes. References to related work are intended to aid the reader to pursue areas of specific interest in further detail. The comprehensive background with economic, statistical, mathematical, and computational theory strengthens the understanding. The coverage is broad, and linkages between different sections are explained. The primary audience is graduate students, while it should also be accessible to advanced undergraduates. Practitioners working in the finance industry will also benefit.

Least squares estimation, when used appropriately, is a powerful research tool. A deeper understanding of the regression concepts is essential for achieving optimal benefits from a least squares analysis. This book builds on the fundamentals of statistical methods and provides appropriate concepts that will allow a scientist to use least squares as an effective research tool. This book is aimed at the scientist who wishes to gain a working knowledge of regression analysis. The basic purpose of this book is to develop an understanding of least squares and related statistical methods without becoming excessively mathematical. It is the outgrowth of more than 30 years of consulting experience with scientists and many years of teaching an appied regression course to graduate students. This book seves as an excellent text for a service course on regression for non-statisticians and as a reference for researchers. It also provides a bridge between a two-semester introduction to statistical methods and a thoeretical linear models course. This book emphasizes the concepts and the analysis of data sets. It provides a review of the key concepts in simple linear regression, matrix operations, and multiple regression. Methods and criteria for selecting regression variables and geometric interpretations are discussed. Polynomial, trigonometric, analysis of variance, nonlinear, time series, logistic, random effects, and mixed effects models are also discussed. Detailed case studies and exercises based on real data sets are used to reinforce the concepts. John O. Rawlings, Professor Emeritus in the Department of Statistics at North Carolina State University, retired after 34 years of teaching, consulting, and research in statistical methods. He was instrumental in developing, and for many years taught, the course on which this text is based. He is a Fellow of the American Statistical Association and the Crop Science Society of America. Sastry G. Pantula is Professor and Directory of Graduate Programs in the Department of Statistics at North Carolina State University. He is a member of the Academy of Outstanding Teachers at North Carolina State University. David A. Dickey is Professor of Statistics at North Carolina State University. He is a member of the Academy of Outstanding Teachers at North Carolina State University.

The present volume is comprised of contributions solicited from invitees to conferences held at the University of Houston, University of Jyv] askyl] a, and Xi'an Jiaotong University honoring the 70th birthday of Professor Roland Glowinski. Although scientists convened on three di?erent continents, the - itors prefer to view the meetings as single event. The three locales signify the fact Roland has friends, collaborators and admirers across the globe. The contents span a wide range of topics in contemporary applied mathematics rangingfrompopulationdynamics, to electromagnetics, to ?uidmechanics, to the mathematics of ?nance among others. However, they do not fully re?ect the breath and diversity of Roland's scienti?c interest. His work has always been at the intersection mathematics and scienti?c computing and their - plication to mechanics, physics, aeronautics, engineering sciences and more recently biology. He has made seminal contribution in the areas of methods for science computation, ?uid mechanics, numerical controls for distributed parameter systems, and solid and structural mechanics as well as shape - timization, stellar motion, electron transport, and semiconductor modeling. Two central themes arise from the corpus of Roland's work. The ?rst is that numerical methods should take advantage of the mathematical properties of themodel. Theyshouldbeportableandcomputablewithcomputingresources of the foreseeable future as well as with contemporary resources. The second theme is that whenever possible one should validate numerical with expe- mental data. The volume is written at an advanced scienti?c level and no e?ort has been made to make it self contained."

The present book deals with the issues of stability of Motion which most often are encountered in the analysis of scientific and technical problems. There are many comprehensive monographs on the theory of stability of motion, with each one devoted to a separate complicated issue of the theory. The main advantage of this book, however, is its simple yet simultaneous rigorous presentation of the concepts of the theory, which often are presented in the context of applied problems with detailed examples demonstrating effective methods of solving practical problems.

The goal of this book is to present the new trend of Computational Fluid Dynamics (CFD) for the 21 st Century. It consists of papers presented at a symposium honoring Prof. No buyuki Satofuka on the occasion of his 60th birthday. The symposium entitled Computational Fluid Dynamics fOT the 21st Century was held at Kyoto Institute of Technology (KIT) in Kyoto, Japan on July 15-17,2000. The symposium was hosted by KIT as a memorial event celebrating the 100 year anniversary of this establishment. The invited speakers were from Ja pan as weil as from the international community in Asia, Europe and North America. It is a great pleasure to dedicate this book to Prof. Satofuka in appreciation ofhis contributions to this field. During the last 30 years, Prof. Satofuka made many important contributions to CFD ad vancing the numerics and our understanding of flow physics in different regimes. The details of his contributions are discussed in the first chapter. The book contains chapters covering re lated topics with emphasis on new promising directions for the 21 st Century. The chapters of the book reflect the 10 sessions of the symposium on both the numerics and the applications including grid generation and adaptation, new numerical schemes, optimi zation techniques and parallel computations as weil as applications to multi-sc ale and multi physics problems, design and flow control and new topics beyond aeronautics. In the follow ing, the chapters of the book are introduced."

In his paper Theory of Communication [Gab46], D. Gabor proposed the use of a family of functions obtained from one Gaussian by time-and frequency shifts. Each of these is well concentrated in time and frequency; together they are meant to constitute a complete collection of building blocks into which more complicated time-depending functions can be decomposed. The application to communication proposed by Gabor was to send the coeffi cients of the decomposition into this family of a signal, rather than the signal itself. This remained a proposal-as far as I know there were no seri ous attempts to implement it for communication purposes in practice, and in fact, at the critical time-frequency density proposed originally, there is a mathematical obstruction; as was understood later, the family of shifted and modulated Gaussians spans the space of square integrable functions [BBGK71, Per71] (it even has one function to spare [BGZ75] . . . ) but it does not constitute what we now call a frame, leading to numerical insta bilities. The Balian-Low theorem (about which the reader can find more in some of the contributions in this book) and its extensions showed that a similar mishap occurs if the Gaussian is replaced by any other function that is "reasonably" smooth and localized. One is thus led naturally to considering a higher time-frequency density.

The year 2000 is the centenary year of the publication of Bachelier's thesis which - together with Harry Markovitz Ph.D. dissertation on portfolio selection in 1952 and Fischer Black's and Myron Scholes' solution of an option pricing problem in 1973 - is considered as the starting point of modern finance as a mathematical discipline. On this remarkable anniversary the workshop on mathematical finance held at the University of Konstanz brought together practitioners, economists and mathematicians to discuss the state of the art. Apart from contributions to the known discrete, Brownian, and LA(c)vy process models, first attempts to describe a market in a reasonable way by a fractional Brownian motion model are presented, opening many new aspects for practitioners and new problems for mathematicians. As most dynamical financial problems are stochastic filtering or control problems many talks presented adaptations of control methods and techniques to the classical financial problems in a [ portfolio selection a [ irreversible investment a [ risk sensitive asset allocation a [ capital asset pricing a [ hedging contingent claims a [ option pricing a [ interest rate theory. The contributions of practitioners link the theoretical results to the steadily increasing flow of real world problems from financial institutions into mathematical laboratories. The present volume reflects this exchange of theoretical and applied results, methods and techniques that made the workshop a fruitful contribution to the interdisciplinary work in mathematical finance.

The problems of conditional optimization of the uniform (or C-) norm for polynomials and rational functions arise in various branches of science and technology. Their numerical solution is notoriously difficult in case of high degree functions. The book develops the classical Chebyshev's approach which gives analytical representation for the solution in terms of Riemann surfaces. The techniques born in the remote (at the first glance) branches of mathematics such as complex analysis, Riemann surfaces and Teichmuller theory, foliations, braids, topology are applied to approximation problems. The key feature of this book is the usage of beautiful ideas of contemporary mathematics for the solution of applied problems and their effective numerical realization. This is one of the few books where the computational aspects of the higher genus Riemann surfaces are illuminated. Effective work with the moduli spaces of algebraic curves provides wide opportunities for numerical experiments in mathematics and theoretical physics.

In 2008, November 23-28, the workshop of "Classical Problems on Planar Polynomial Vector Fields " was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincare for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert's 16th problem. These problems had been posed more than 110 years ago. Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincare and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert's 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.

This book is devoted to current advances in the field of nonlinear mathematical physics and modeling of critical phenomena that can lead to catastrophic events. Pursuing a multidisciplinary approach, it gathers the work of scientists who are developing mathematical and computational methods for the study and analysis of nonlinear phenomena and who are working actively to apply these tools and create conditions to mitigate and reduce the negative consequences of natural and socio-economic disaster risk. This book summarizes the contributions of the International School and Workshop on Nonlinear Mathematical Physics and Natural Hazards, organized within the framework of the South East Europe Network in Mathematical and Theoretical Physics (SEENET MTP) and supported by UNESCO. It was held at the Bulgarian Academy of Sciences from November 28 to December 2, 2013. The contributions are divided into two major parts in keeping with the scientific program of the meeting. Among the topics covered in Part I (Nonlinear Mathematical Physics towards Critical Phenomena) are predictions and correlations in self organized criticality, space-time structure of extreme current and activity events in exclusion processes, quantum spin chains and integrability of many-body systems, applications of discriminantly separable polynomials, MKdV-type equations, and chaotic behavior in Yang-Mills theories. Part II (Seismic Hazard and Risk) is devoted to probabilistic seismic hazard assessment, seismic risk mapping, seismic monitoring, networking and data processing in Europe, mainly in South-East Europe. The book aims to promote collaboration at the regional and European level to better understand and model phenomena that can cause natural and socio-economic disasters, and to contribute to the joint efforts to mitigate the negative consequence of natural disasters. This collection of papers reflects contemporary efforts on capacity building through developing skills, exchanging knowledge and practicing mathematical methods for modeling nonlinear phenomena, disaster risk preparedness and natural hazards mitigation. The target audience includes students and researchers in mathematical and theoretical physics, earth physics, applied physics, geophysics, seismology and earthquake danger and risk mitigation.

Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches covers recent developments in optimization techniques for addressing several computational chemistry and biology problems. A tantalizing problem that cuts across the fields of computational chemistry, biology, medicine, engineering and applied mathematics is how proteins fold. Global and local optimization provide a systematic framework of conformational searches for the prediction of three-dimensional protein structures that represent the global minimum free energy, as well as low-energy biomolecular conformations. Each contribution in the book is essentially expository in nature, but of scholarly treatment. The topics covered include advances in local and global optimization approaches for molecular dynamics and modeling, distance geometry, protein folding, molecular structure refinement, protein and drug design, and molecular and peptide docking. Audience: The book is addressed not only to researchers in mathematical programming, but to all scientists in various disciplines who use optimization methods in solving problems in computational chemistry and biology.

This book focuses on problems at the interplay between the theory of partitions and optimal transport with a view toward applications. Topics covered include problems related to stable marriages and stable partitions, multipartitions, optimal transport for measures and optimal partitions, and finally cooperative and noncooperative partitions. All concepts presented are illustrated by examples from game theory, economics, and learning.

Since the introduction of genetic algorithms in the 1970s, an enormous number of articles together with several significant monographs and books have been published on this methodology. As a result, genetic algorithms have made a major contribution to optimization, adaptation, and learning in a wide variety of unexpected fields. Over the years, many excellent books in genetic algorithm optimization have been published; however, they focus mainly on single-objective discrete or other hard optimization problems under certainty. There appears to be no book that is designed to present genetic algorithms for solving not only single-objective but also fuzzy and multiobjective optimization problems in a unified way. Genetic Algorithms And Fuzzy Multiobjective Optimization introduces the latest advances in the field of genetic algorithm optimization for 0-1 programming, integer programming, nonconvex programming, and job-shop scheduling problems under multiobjectiveness and fuzziness. In addition, the book treats a wide range of actual real world applications. The theoretical material and applications place special stress on interactive decision-making aspects of fuzzy multiobjective optimization for human-centered systems in most realistic situations when dealing with fuzziness. The intended readers of this book are senior undergraduate students, graduate students, researchers, and practitioners in the fields of operations research, computer science, industrial engineering, management science, systems engineering, and other engineering disciplines that deal with the subjects of multiobjective programming for discrete or other hard optimization problems under fuzziness. Real world research applications are used throughout the book to illustrate the presentation. These applications are drawn from complex problems. Examples include flexible scheduling in a machine center, operation planning of district heating and cooling plants, and coal purchase planning in an actual electric power plant.

Practical quantum computing still seems more than a decade away, and researchers have not even identified what the best physical implementation of a quantum bit will be. There is a real need in the scientific literature for a dialogue on the topic of lessons learned and looming roadblocks. This reprint from Quantum Information Processing is dedicated to the experimental aspects of quantum computing and includes articles that 1) highlight the lessons learned over the last 10 years, and 2) outline the challenges over the next 10 years. The special issue includes a series of invited articles that discuss the most promising physical implementations of quantum computing. The invited articles were to draw grand conclusions about the past and speculate about the future, not just report results from the present.

The scientific monograph of a survey kind presented to the reader's attention deals with fundamental ideas and basic schemes of optimization methods that can be effectively used for solving strategic planning and operations manage ment problems related, in particular, to transportation. This monograph is an English translation of a considerable part of the author's book with a similar title that was published in Russian in 1992. The material of the monograph embraces methods of linear and nonlinear programming; nonsmooth and nonconvex optimization; integer programming, solving problems on graphs, and solving problems with mixed variables; rout ing, scheduling, solving network flow problems, and solving the transportation problem; stochastic programming, multicriteria optimization, game theory, and optimization on fuzzy sets and under fuzzy goals; optimal control of systems described by ordinary differential equations, partial differential equations, gen eralized differential equations (differential inclusions), and functional equations with a variable that can assume only discrete values; and some other methods that are based on or adjoin to the listed ones."

This unique book on the subject addresses fundamental problems and will be the standard reference for a long time to come. The authors have different scientific origins and combine these successfully, creating a text aimed at graduate students and researchers that can be used for courses and seminars.

This book extends classical Hermite-Hadamard type inequalities to the fractional case via establishing fractional integral identities, and discusses Riemann-Liouville and Hadamard integrals, respectively, by various convex functions. Illustrating theoretical results via applications in special means of real numbers, it is an essential reference for applied mathematicians and engineers working with fractional calculus. Contents Introduction Preliminaries Fractional integral identities Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals Hermite-Hadamard inequalities involving Hadamard fractional integrals

After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein's special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry. It will be demonstrated that, in full analogy to classical mechanics where barycentric coordinates are related to the Newtonian mass, barycentric coordinates are related to the Einsteinian relativistic mass in hyperbolic geometry. Contrary to general belief, Einstein's relativistic mass hence meshes up extraordinarily well with Minkowski's four-vector formalism of special relativity. In Euclidean geometry, barycentric coordinates can be used to determine various triangle centers. While there are many known Euclidean triangle centers, only few hyperbolic triangle centers are known, and none of the known hyperbolic triangle centers has been determined analytically with respect to its hyperbolic triangle vertices. In his recent research, the author set the ground for investigating hyperbolic triangle centers via hyperbolic barycentric coordinates, and one of the purposes of this book is to initiate a study of hyperbolic triangle centers in full analogy with the rich study of Euclidean triangle centers. Owing to its novelty, the book is aimed at a large audience: it can be enjoyed equally by upper-level undergraduates, graduate students, researchers and academics in geometry, abstract algebra, theoretical physics and astronomy. For a fruitful reading of this book, familiarity with Euclidean geometry is assumed. Mathematical-physicists and theoretical physicists are likely to enjoy the study of Einstein's special relativity in terms of its underlying hyperbolic geometry. Geometers may enjoy the hunt for new hyperbolic triangle centers and, finally, astronomers may use hyperbolic barycentric coordinates in the velocity space of cosmology.

This volume of High Performance Computing in Science and Engineering is fully dedicated to the final report of KONWIHR, the Bavarian Competence Network for Technical and Scientific High Performance Computing. It includes the transactions of the final KONWIHR workshop, that was held at Technische Universitat Munchen, October 14-15, 2004, as well as additional reports of KONWIHR research groups. KONWIHR was established by the Bavarian State Government in order to support the broad application of high performance computing in science and technology throughout the country. KONWIHR is a supporting action to the installation of the German supercomputer Hitachi SR 8000 in the Leibniz Computing Center of the Bavarian Academy of Sciences. The report covers projects from basic research in computer science to develop tools for high performance computing as well as applications from biology, chemistry, electrical engineering, geology, mathematics, physics, computational fluid dynamics, materials science and computer science."

This interdisciplinary thesis involves the design and analysis of coordination algorithms on networks, identification of dynamic networks and estimation on networks with random geometries with implications for networks that support the operation of dynamic systems, e.g., formations of robotic vehicles, distributed estimation via sensor networks. The results have ramifications for fault detection and isolation of large-scale networked systems and optimization models and algorithms for next generation aircraft power systems. The author finds novel applications of the methodology in energy systems, such as residential and industrial smart energy management systems.

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020) Mariusz Lemanczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021) Miroslava Antic, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is kept as low as at all possible and deeper questions related to the mathematical foundations of scattering theory are passed by. It should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. The book is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.