Provides an in-depth discussion of Koszul duality in the relative context over a base ring
Presents generalization of the Poincare-Birkhoff-Witt theorem to the relative context
Adds a whole new "relative" dimension to the Koszul duality studies existing in the literature
This research monograph develops the theory of relative nonhomogeneous Koszul duality. Koszul duality is a fundamental phenomenon in homological algebra and related areas of mathematics, such as algebraic topology, algebraic geometry, and representation theory. Koszul duality is a popular subject of contemporary research.
This book, written by one of the world's leading experts in the area, includes the homogeneous and nonhomogeneous quadratic duality theory over a nonsemisimple, noncommutative base ring, the Poincare?Birkhoff?Witt theorem generalized to this context, and triangulated equivalences between suitable exotic derived categories of modules, curved DG comodules, and curved DG contramodules. The thematic example, meaning the classical duality between the ring of differential operators and the de Rham DG algebra of differential forms, involves some of the most important objects of study in the contemporary algebraic and differential geometry. For the first time in the history of Koszul duality the derived D-\Omega duality is included into a general framework. Examples highly relevant for algebraic and differential geometry are discussed in detail.
Leonid Positselski received his Ph.D. in Mathematics from Harvard University in 1998. He did his postdocs at the Institute for Advanced Study (Princeton), Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette), Max-Planck-Institut fuer Mathematik (Bonn), the University of Stockholm, and the Independent University of Moscow in 1998-2003. He taught as an Associate Professor at the Mathematics Faculty of the National Research University Higher School of Economics in Moscow in 2011-2014. In Spring 2014 he moved from Russia to Israel, and since 2018 he work as a Researcher at the Institute of Mathematics of the Czech Academy of Sciences in Prague.
He is an algebraist specializing in homological algebra. His research papers span a wide area including algebraic geometry, representation theory, commutative algebra, algebraic K-theory, and algebraic number theory.
He is the author of four books and memoirs, including "Quadratic Algebras" (joint with A. Polishchuk, AMS University Lecture Series, 2005), "Homological algebra of semimodules and semicontramodules: Semi-infinite homological algebra of associative algebraic structures" (Monografie Matematyczne IMPAN, Birkhauser Basel, 2010), "Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence" (AMS Memoir, 2011), and "Weakly curved A-infinity algebras over a topological local ring" (Memoir of the French Math. Society, 2018-19).
Series Title : Frontiers in Mathematics
Copyright : 2021
Number of Pages : XXX, 283
Category Theory, Homological Algebra
About this book
This book serves as a textbook in real analysis. It focuses on the fundamentals of the structural properties of metric spaces and analytical properties of functions defined between such spaces. Topics include sets, functions and cardinality, real numbers, analysis on R, topology of the real line, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.
ATUL RAZDAN served at the Department of Mathematics, University of Delhi, India, from 2004?2008. He started his career as Lecturer in 1995 at Indira Gandhi National Open University (IGNOU), New Delhi, India, until 2004. His area of research is algebra on which he has published several papers in journals of international repute.
V. RAVICHANDRAN is Professor of Mathematics at the National Institute of Technology, Tiruchirappalli, India. Earlier, he held positions at Universiti Sains Malaysia (2004?2007 and 2011?2012) and the University of Delhi, India (2007?2018). He specializes in geometric function theory and has published more than 150 research papers. Since 2004, he has been serving as Editor of the Bulletin of the Malaysian Mathematical Sciences Society.
ISBN 9789811683824
Number of Pages 477
Hardcover:
9783030924027
This book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation. The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes. The text introduces new asymptotic recurrent algorithms of phase space reduction. It also addresses both effective conditions of weak convergence for distributions of hitting times as well as convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes. The book also contains a comprehensive bibliography of major works in the field. It provides an effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications.
Preface.- List of symbols.- Introduction.- Part ITimes for Regularly Perturbed Semi-Markov Processes.- Flows of Rare Events for Regularly Perturbed Semi-Markov Processes.- Generalizations of Limit Theorems for First-Rare-Event Times.- First-Rare-Event Times for Perturbed Risk Processes.- First-Rare-Event Times for Perturbed Closed Queuing Systems.- First-Rare-Event Times for Perturbed M/M-Type Queuing Systems.- Part II: Hitting Times and Phase Space Reduction for Perturbed Semi-Markov Processes.- Asymptotically Comparable Functions.- Perturbed Semi-Markov Processes and Reduction of Phase Space.- Asymptotics of Hitting Times for Perturbed Semi-Markov Processes.- Asymptotics for Expectations of Hitting Times for Perturbed Semi-Markov Processes.- Generalizations and Examples of Limit Theorems for Hitting Times.- Limit Theorems for Randomly Stopped Stochastic Processes.- Methodological and Bibliographical Notes.- References.- Index.
Provides a snapshot of a popular emerging topic
Presents new research and contextual literature review
Suitable for researchers and mixed-level classes
This book is the second volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation.
The second volume presents a complete classification of ergodic theorems for alternating regenerative processes, including more than twenty-five such theorems. The text addresses new asymptotic recurrent algorithms of phase space reduction for multi-alternating regenerative processes modulating by regularly and singularly perturbed finite semi-Markov processes. It also features a new study of super-long, long, and short time ergodic theorems for these processes.
The book also contains a comprehensive bibliography of major works in the field. It provides an effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications.
Dmitrii Silvestrov: Candidate of Science [PhD], (1969, Kiev University), Doctor of Science (1972, Kiev University). Professor at Kiev University (1974-1992), Malardalen University (1999-2009) and Stockholm University from 2009. At present, professor emeritus at Stockholm and Malardalen Universities. The main areas of research is Stochastic Processes and their Applications. The author of 13 books and more than 170 research papers. Supervised 22 doctoral students who subsequently obtained PhD degrees.
Copyright : 2022
Number of Pages : XIV, 410
Number of Illustrations : 5 b/w illustrations, 5 illustrations in colour
Probability Theory, Stochastic Processes
A Creative Journey through the Fjords of Mathematical Analysis for Beginners
Convenes problems in Advanced Calculus with solutions that favor creativity
Covers all the classical topics seen in first-year Calculus and Mathematical Analysis courses
Offers a theoretical background in every chapter, with relevant definitions and theorems for self-study
This book convenes a collection of carefully selected problems in mathematical analysis, crafted to achieve maximum synergy between analytic geometry and algebra and favoring mathematical creativity in contrast to mere repetitive techniques. With eight chapters, this work guides the student through the basic principles of the subject, with a level of complexity that requires good use of imagination.
In this work, all the fundamental concepts seen in a first-year Calculus course are covered. Problems touch on topics like inequalities, elementary point-set topology, limits of real-valued functions, differentiation, classical theorems of differential calculus (Rolle, Lagrange, Cauchy, and l’Hospital), graphs of functions, and Riemann integrals and antiderivatives. Every chapter starts with a theoretical background, in which relevant definitions and theorems are provided; then, related problems are presented. Formalism is kept at a minimum, and solutions can be found at the end of each chapter.
Instructors and students of Mathematical Analysis, Calculus and Advanced Calculus aimed at first-year undergraduates in Mathematics, Physics and Engineering courses can greatly benefit from this book, which can also serve as a rich supplement to any traditional textbook on these subjects as well.
Paolo Toni is a Teacher of Mathematics and Physics, retired from Liceo Scientifico E. Fermi in Padua, Italy, with prolific research activities on didactics of mathematics. He obtained a Mathematics degree (1972) from the University of Firenze and authored a few books, beginning with recreational mathematics. For many years, Prof. Toni took an active role in mathematical competitions in his home country, having co-created, directed, and promoted the “Citta di Padova” Mathematical Competition, aimed at students of secondary level.
Pier Domenico Lamberti is a Full Professor in Mathematical Analysis at the University of Padua, Italy. He got a PhD in Mathematics from the University of Padua (2003), and has been visiting researcher at the University of Cardiff, UK; University of Athens, Greece; and Complutense University of Madrid, Spain. His research interests lie in mathematical analysis, with focus on partial differential equations, spectral theory, theory of functions spaces, functional analysis, calculus of variations, and homogenization theory.
Giacomo Drago is a Teacher of Mathematics and Physics at Istituto Tecnico Economico Calvi in Padua, Italy. He obtained a Master degree in Mathematics (2011) from the University of Padua, Italy. As a student, he distinguished himself in the national finals of three consecutive editions (2004-2006) of the Kangourou Mathematics Competitions.
Series Title : Problem Books in Mathematics
Copyright : 2022
Number of Pages : XVII, 270
Number of Illustrations : 171 b/w illustrations
Real Functions, Analysis
Sheds light on the deepest mysteries of Quantum Mechanics
Authored by world-leaders in quantum theory and beyond
Published in honor of Dieter Zeh, pioneer of decoherence theory
Quantum theory is at the foundation of the physical description of our world. One of the people who contributed significantly to our conceptual understanding of this theory was Heinz-Dieter Zeh (1932-2018). He was the pioneer of the process of decoherence, through which the classical appearance of our world can be understood. This volume presents a collection of essays dedicated to his memory, written by distinguished scientists and scholars. They cover all aspects of the interpretation of quantum theory in general and the quantum-to-classical transition in particular. This volume provides illuminating reading to anyone seeking a deep understanding of quantum theory and its relevance to the foundations of physics.
Claus Kiefer is a professor of theoretical physics at the University of Cologne. He does research on quantum gravity and the foundations of quantum theory as well as studying black holes and more general cosmological questions. In 2009, his essay, "Does Time Exist in Quantum Gravity?", was awarded second prize by the Foundational Questions Institute, New York. In 2012, his essay, "Can Effects of Quantum Gravity Be Observed in the Cosmic Microwave Background?" (written together with Manuel Kramer), was awarded first prize by the Gravity Research Foundation, Wellesley Hills, USA.
Series Title : Fundamental Theories of Physics
Copyright : 2022
Number of Pages : XII, 314
Number of Illustrations : 6 b/w illustrations, 21 illustrations in colour
Quantum Physics, Philosophical Foundations of Physics and Astronomy, Philosophy of Science