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Quantum Isometry Groups
by Debashish Goswami Jyotishman BhowmickThis book offers an up-to-date overview of the recently proposed theory of quantum isometry groups. Written by the founders, it is the first book to present the research on the "quantum isometry group", highlighting the interaction of noncommutative geometry and quantum groups, which is a noncommutative generalization of the notion of group of isometry of a classical Riemannian manifold. The motivation for this generalization is the importance of isometry groups in both mathematics and physics. The framework consists of Alain Connes' "noncommutative geometry" and the operator-algebraic theory of "quantum groups". The authors prove the existence of quantum isometry group for noncommutative manifolds given by spectral triples under mild conditions and discuss a number of methods for computing them. One of the most striking and profound findings is the non-existence of non-classical quantum isometry groups for arbitrary classical connected compact manifolds and, by using this, the authors explicitly describe quantum isometry groups of most of the noncommutative manifolds studied in the literature. Some physical motivations and possible applications are also discussed.
Quantum Mathematical Physics
by Felix Finster Johannes Kleiner Christian Röken Jürgen TolksdorfQuantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.
Quantum Monte Carlo Methods: Algorithms for Lattice Models
by J. E. Gubernatis N. Kawashima P. WernerFeaturing detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in quantum Monte Carlo techniques.
R for Programmers: Mastering the Tools
by Dan ZhangUnlike other books about R, written from the perspective of statistics, this book is written from the perspective of programmers, providing a channel for programmers with expertise in other programming languages to quickly understand R. The contents are divided into four parts: the basics of R, the server of R, databases and big data, and the appendices, which introduce the installation of Java, various databases, and Hadoop. Because this is a reference book, there is no special sequence for reading all the chapters. Anyone new to the subject who wishes to master R comprehensively can simply follow the chapters in sequence.
Rabi N. Bhattacharya
by Manfred Denker Edward C. WaymireThis volume presents some of the most influential papers published by Rabi N. Bhattacharya, along with commentaries from international experts, demonstrating his knowledge, insight, and influence in the field of probability and its applications. For more than three decades, Bhattacharya has made significant contributions in areas ranging from theoretical statistics via analytical probability theory, Markov processes, and random dynamics to applied topics in statistics, economics, and geophysics. Selected reprints of Bhattacharya's papers are divided into three sections: Modes of Approximation, Large Times for Markov Processes, and Stochastic Foundations in Applied Sciences. The accompanying articles by the contributing authors not only help to position his work in the context of other achievements, but also provide a unique assessment of the state of their individual fields, both historically and for the next generation of researchers. Rabi N. Bhattacharya: Selected Papers will be a valuable resource for young researchers entering the diverse areas of study to which Bhattacharya has contributed. Established researchers will also appreciate this work as an account of both past and present developments and challenges for the future.
Random Graphs, Geometry and Asymptotic Structure
by Michael Krivelevich Konstantinos Panagiotou Mathew Penrose Colin McdiarmidThe theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.
Random-Like Bi-level Decision Making
by Jiuping Xu Zongmin Li Zhimiao TaoAmong the various multi-level formulations of mathematical models in decision making processes, this book focuses on the bi-level model. Being the most frequently used, the bi-level model addresses conflicts which exist in multi-level decision making processes. From the perspective of bi-level structure and uncertainty, this book takes real-life problems as the background, focuses on the so-called random-like uncertainty, and develops the general framework of random-like bi-level decision making problems. The random-like uncertainty considered in this book includes random phenomenon, random-overlapped random (Ra-Ra) phenomenon and fuzzy-overlapped random (Ra-Fu) phenomenon. Basic theory, models, algorithms and practical applications for different types of random-like bi-level decision making problems are also presented in this book.
Random Matrix Theory with an External Source
by Edouard Brézin Shinobu HikamiThis is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the Gromov-Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.
Random Walks on Reductive Groups
by Yves Benoist Jean-François QuintThe classical theory of Random Walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple - or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
Randomization in Clinical Trials
by John M. Lachin William F. RosenbergerPraise for the First Edition "All medical statisticians involved in clinical trials should read this book..." - Controlled Clinical Trials Featuring a unique combination of the applied aspects of randomization in clinical trials with a nonparametric approach to inference, Randomization in Clinical Trials: Theory and Practice, Second Edition is the go-to guide for biostatisticians and pharmaceutical industry statisticians. Randomization in Clinical Trials: Theory and Practice, Second Edition features: Discussions on current philosophies, controversies, and new developments in the increasingly important role of randomization techniques in clinical trials A new chapter on covariate-adaptive randomization, including minimization techniques and inference New developments in restricted randomization and an increased focus on computation of randomization tests as opposed to the asymptotic theory of randomization tests Plenty of problem sets, theoretical exercises, and short computer simulations using SAS® to facilitate classroom teaching, simplify the mathematics, and ease readers' understanding Randomization in Clinical Trials: Theory and Practice, Second Edition is an excellent reference for researchers as well as applied statisticians and biostatisticians. The Second Edition is also an ideal textbook for upper-undergraduate and graduate-level courses in biostatistics and applied statistics. William F. Rosenberger, PhD, is University Professor and Chairman of the Department of Statistics at George Mason University. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, and author of over 80 refereed journal articles, as well as The Theory of Response-Adaptive Randomization in Clinical Trials, also published by Wiley. John M. Lachin, ScD, is Research Professor in the Department of Epidemiology and Biostatistics as well as in the Department of Statistics at The George Washington University. A Fellow of the American Statistical Association and the Society for Clinical Trials, Dr. Lachin is actively involved in coordinating center activities for clinical trials of diabetes. He is the author of Biostatistical Methods: The Assessment of Relative Risks, Second Edition, also published by Wiley.
Ranking of Multivariate Populations: A Permutation Approach with Applications
by Livio Corain Rosa Arboretti Stefano BonniniRanking of Multivariate Populations: A Permutation Approach with Applications presents a novel permutation-based nonparametric approach for ranking several multivariate populations. Using data collected from both experimental and observation studies, it covers some of the most useful designs widely applied in research and industry investigations, such as multivariate analysis of variance (MANOVA) and multivariate randomized complete block (MRCB) designs. <P><P>The first section of the book introduces the topic of ranking multivariate populations by presenting the main theoretical ideas and an in-depth literature review. The second section discusses a large number of real case studies from four specific research areas: new product development in industry, perceived quality of the indoor environment, customer satisfaction, and cytological and histological analysis by image processing. A web-based nonparametric combination global ranking software is also described. <P><P>Designed for practitioners and postgraduate students in statistics and the applied sciences, this application-oriented book offers a practical guide to the reliable global ranking of multivariate items, such as products, processes, and services, in terms of the performance of all investigated products/prototypes.
Rarefied Gas Dynamics
by Felix SharipovAimed at both researchers and professionals who deal with this topic in their routine work, this introduction provides a coherent and rigorous access to the field including relevant methods for practical applications. No preceding knowledge of gas dynamics is assumed.
Rational Bases and Generalized Barycentrics
by Eugene WachspressThis three-part volume explores theory for construction of rational interpolation functions for continuous patchwork approximation. Authored by the namesake of the Wachspress Coordinates, the book develops construction of basis functions for a broad class of elements which have widespread graphics and finite element application. Part one is the 1975 book "A Rational Finite Element Basis" (with minor updates and corrections) written by Dr. Wachspress. Part two describes theoretical advances since 1975 and includes analysis of elements not considered previously. Part three consists of annotated MATLAB programs implementing theory presented in Parts one and two.
Rationality and Operators
by Susumu CatoThis unique book develops an operational approach to preference and rationality as the author employs operators over binary relations to capture the concept of rationality. A preference is a basis of individual behavior and social judgment and is mathematically regarded as a binary relation on the set of alternatives. Traditionally, an individual/social preference is assumed to satisfy completeness and transitivity. However, each of the two conditions is often considered to be too demanding; and then, weaker rationality conditions are introduced by researchers. This book argues that the preference rationality conditions can be captured mathematically by "operators," which are mappings from the set of operators to itself. This operational approach nests traditional concepts in individual/social decision theory and clarifies the underlying formal structure of preference rationality. The author also applies his approach to welfare economics. The core problem of 'new welfare economics,' developed by Kaldor, Hicks, and Samuelson, is the rationality of social preference. In this book the author translates the social criteria proposed by those three economists into operational forms, which provide new insights into welfare economics extending beyond 'new welfare economics. '
Rationality Problems in Algebraic Geometry
by Gian Pietro Pirola Alessandro Verrarita Pardini Alexander Kuznetsov Brendan Hassett Arnaud BeauvilleProviding an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel-Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.
Ready Common Core, Mathematics Instruction [Grade] 2
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Ready Common Core, Mathematics Instruction [Grade] 5
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Ready Mathematics Practice and Problem Solving [Grade] 6
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Real Analysis
by Peter A. LoebThis textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors. The first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach. The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. To correctly discuss weak limits of measures, one needs the notion of a topological space rather than just a metric space, so general topology is introduced in terms of a base of neighborhoods at a point. The development of results then proceeds in parallel with results for metric spaces, where the base is generated by balls centered at a point. The text concludes with appendices on covering theorems for higher dimensions and a short introduction to nonstandard analysis including important applications to probability theory and mathematical economics.
Real Analysis
by Emmanuele DibenedettoThe second edition of this classic textbook presents a rigorous and self-contained introduction to real analysis with the goal of providing a solid foundation for future coursework and research in applied mathematics. Written in a clear and concise style, it covers all of the necessary subjects as well as those often absent from standard introductory texts. Each chapter features a "Problems and Complements" section that includes additional material that briefly expands on certain topics within the chapter and numerous exercises for practicing the key concepts. The first eight chapters explore all of the basic topics for training in real analysis, beginning with a review of countable sets before moving on to detailed discussions of measure theory, Lebesgue integration, Banach spaces, functional analysis, and weakly differentiable functions. More topical applications are discussed in the remaining chapters, such as maximal functions, functions of bounded mean oscillation, rearrangements, potential theory, and the theory of Sobolev functions. This second edition has been completely revised and updated and contains a variety of new content and expanded coverage of key topics, such as new exercises on the calculus of distributions, a proof of the Riesz convolution, Steiner symmetrization, and embedding theorems for functions in Sobolev spaces. Ideal for either classroom use or self-study, Real Analysis is an excellent textbook both for students discovering real analysis for the first time and for mathematicians and researchers looking for a useful resource for reference or review.
Real Options Illustrated
by Linda PetersThis book explains the standard Real Options Analysis (ROA) literature in a straightforward, step by step manner without the use of complex mathematics. A lot of ROA literature is described through partial differential equations, probabilitydensity functions and simulation techniques, all of which may be unconvincing in the applicable qualities ROA possesses. Using this book, the reader will have a better grasp about how ROA works and will be able to provide his or her judgment about ROA, since all the basics, as well as its positive and negative qualities, are discussed. Real Options Illustrated provides practitioners with a real options framework and encourages readers to study the methodology using the in-depth explanations. This introduction to ROA is sufficient to equip readers with ROA basics, enabling them to perform future independent research. From this book, readers can judge whether ROA is of any value to their field.
Real-Time Progressive Hyperspectral Image Processing
by Chein-I ChangThe book covers the most crucial parts of real-time hyperspectral image processing: causality and real-time capability. Recently, two new concepts of real time hyperspectral image processing, Progressive HyperSpectral Imaging (PHSI) and Recursive HyperSpectral Imaging (RHSI). Both of these can be used to design algorithms and also form an integral part of real time hyperpsectral image processing. This book focuses on progressive nature in algorithms on their real-time and causal processing implementation in two major applications, endmember finding and anomaly detection, both of which are fundamental tasks in hyperspectral imaging but generally not encountered in multispectral imaging. This book is written to particularly address PHSI in real time processing, while a book, Recursive Hyperspectral Sample and Band Processing: Algorithm Architecture and Implementation (Springer 2016) can be considered as its companion book.
Recapturing Space: New Middle-Range Theory in Spatial Demography
by Frank M. Howell Jeremy R. Porter Stephen A. MatthewsWith a unique focus on middle-range theory, this book details the application of spatial analysis to demographic research as a way of integrating and better understanding the different transitional components of the overall demographic transition. This book first details key concepts and measures in modern spatial demography and shows how they can be applied to middle-range theory to better understand people, places, communities and relationships throughout the world. Next, it shows middle-range theory in practice, from using spatial data as a proxy for social science statistics to examining the effect of "fracking" in Pennsylvania on the formation of new coalitions among environmental advocacy organizations. The book also traces future developments and offers some potential solutions to promoting and facilitating instruction in spatial demography. This volume is an ideal resource for advanced undergraduate and graduate students enrolled in courses involving spatial analyses in the social sciences, from sociology and political science to economics and educational research. In addition, scholars and others interested in the role that geographic context plays in relation to their research will find this book a helpful guide in further developing their work.
Recent Advances in Game Theory and Applications
by Leon A. Petrosyan Vladimir V. MazalovThis contributed volume contains fourteen papers based on selected presentations from the European Conference on Game Theory SING11-GTM 2015, held at Saint Petersburg State University in July 2015, and the Networking Games and Management workshop, held at the Karelian Research Centre of the Russian Academy of Sciences in Petrozvavodsk, Russia, also in July 2015. These papers cover a wide range of topics in game theory, including recent advances in areas with high potential for future work, as well as new developments on classical results. Some of these include A new approach to journal ranking using methods from social choice theory; A differential game of a duopoly in which two firms are competing for market share in an industry with network externalities; The impact of information propagation in the model of tax audits; A voting model in which the results of previous votes can affect the process of coalition formation in a decision-making body; The Selten-Szidarovsky technique for the analysis of Nash equilibria of games with an aggregative structure; Generalized nucleoli and generalized bargaining sets for games with restricted cooperation; Bayesian networks and games of deterrence; and A new look at the study of solutions for games in partition function form. The maturity and vitality of modern-day game theory are reflected in the new ideas, novel applications, and contributions of young researchers represented in this collection. It will be of interest to anyone doing theoretical research in game theory or working on one its numerous applications.
Recent Advances in Mathematical Sciences
by Adem Kılıçman Hari M. Srivastava M. Mursaleen Zanariah Abdul MajidThis book features selected papers from The Seventh International Conference on Research and Education in Mathematics that was held in Kuala Lumpur, Malaysia from 25 - 27th August 2015. With chapters devoted to the most recent discoveries in mathematics and statistics and serve as a platform for knowledge and information exchange between experts from academic and industrial sectors, it covers a wide range of topics, including numerical analysis, fluid mechanics, operation research, optimization, statistics and game theory. It is a valuable resource for pure and applied mathematicians, statisticians, engineers and scientists, and provides an excellent overview of the latest research in mathematical sciences.