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New Mathematical Monographs

16615
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Phase Transitions in the Theory of Lattice Gases
90 折
出版日:2025/10/31 作者:Barry Simon (California Institute of Technology)  出版社:Cambridge University Press  裝訂:精裝
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K-stability of Fano Varieties
95 折
出版日:2025/04/30 作者:Chenyang (Princeton University Xu New Jersey)  出版社:Cambridge University Press  裝訂:精裝
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Abstract Chiral Polytopes
90 折
出版日:2025/04/30 作者:Daniel Pellicer (Universidad Nacional Autonoma de Mexico)  出版社:Cambridge University Press  裝訂:精裝
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Meromorphic Dynamics 2 Volume Hardback Set
95 折
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Reduction Theory and Arithmetic Groups
90 折
出版日:2022/10/31 作者:Joachim (Universitat Wien Schwermer Austria)  出版社:Cambridge University Press  裝訂:精裝
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Bruhat-Tits Theory:A New Approach
90 折
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Hardy Martingales:Stochastic Holomorphy, L^1-Embeddings, and Isomorphic Invariants
90 折
出版日:2022/07/31 作者:Paul F. X. Muller (Johannes Kepler Universitat Linz)  出版社:Cambridge University Press  裝訂:精裝
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Conformal Blocks, Generalized Theta Functions and the Verlinde Formula
90 折
出版日:2021/12/31 作者:Shrawan Kumar  出版社:Cambridge Univ Pr  裝訂:精裝
In 1988, E. Verlinde gave a remarkable conjectural formula for the dimension of conformal blocks over a smooth curve in terms of representations of affine Lie algebras. Verlinde's formula arose from physical considerations, but it attracted further attention from mathematicians when it was realized that the space of conformal blocks admits an interpretation as the space of generalized theta functions. A proof followed through the work of many mathematicians in the 1990s. This book gives an authoritative treatment of all aspects of this theory. It presents a complete proof of the Verlinde formula and full details of the connection with generalized theta functions, including the construction of the relevant moduli spaces and stacks of G-bundles. Featuring numerous exercises of varying difficulty, guides to the wider literature and short appendices on essential concepts, it will be of interest to senior graduate students and researchers in geometry, representation theory and theoretical p
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Factorization Algebras in Quantum Field Theory
95 折
出版日:2021/11/30 作者:Kevin Costello; Owen (University of Massachusetts Gwilliam Amherst)  出版社:Cambridge University Press  裝訂:平裝
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Factorization Algebras in Quantum Field Theory: Volume 2
90 折
出版日:2021/09/30 作者:Kevin Costello  出版社:Cambridge Univ Pr  裝訂:精裝
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this second volume, the authors show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies. Along with a systematic reworking of the Batalin–Vilkovisky formalism via derived geometry and factorization algebras, this book offers concrete examples from physics, ranging from angular momentum and Virasoro symmetries to a five-dimensional gauge theory.
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Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem
90 折
出版日:2021/04/30 作者:Michael A. Hill  出版社:Cambridge Univ Pr  裝訂:精裝
The long-standing Kervaire invariant problem in homotopy theory arose from geometric and differential topology in the 1960s and was quickly recognised as one of the most important problems in the field. In 2009 the authors of this book announced a solution to the problem, which was published to wide acclaim in a landmark Annals of Mathematics paper. The proof is long and involved, using many sophisticated tools of modern (equivariant) stable homotopy theory that are unfamiliar to non-experts. This book presents the proof together with a full development of all the background material to make it accessible to a graduate student with an elementary algebraic topology knowledge. There are explicit examples of constructions used in solving the problem. Also featuring a motivating history of the problem and numerous conceptual and expository improvements on the proof, this is the definitive account of the resolution of the Kervaire invariant problem.
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Singular Intersection Homology
90 折
出版日:2020/09/30 作者:Greg Friedman  出版社:Cambridge Univ Pr  裝訂:精裝
Intersection homology is a version of homology theory that extends Poincaré duality and its applications to stratified spaces, such as singular varieties. This is the first comprehensive expository book-length introduction to intersection homology from the viewpoint of singular and piecewise-linear chains. Recent breakthroughs have made this approach viable by providing intersection homology and cohomology versions of all the standard tools in the homology tool box, making the subject readily accessible to graduate students and researchers in topology as well as researchers from other fields. This text includes both new research material and new proofs of previously-known results in intersection homology, as well as treatments of many classical topics in algebraic and manifold topology. Written in a detailed but expository style, this book is suitable as an introduction to intersection homology or as a thorough reference.
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Representations of Solvable Lie Groups:Basic Theory and Examples
90 折
出版日:2020/04/30 作者:Didier Arnal  出版社:Cambridge Univ Pr  裝訂:精裝
The theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena. Combining basic theory and new results, this monograph is a fresh and self-contained exposition of group representations and harmonic analysis on solvable Lie groups. Covering a range of topics from stratification methods for linear solvable actions in a finite-dimensional vector space, to complete proofs of essential elements of Mackey theory and a unified development of the main features of the orbit method for solvable Lie groups, the authors provide both well-known and new examples, with a focus on those relevant to contemporary applications. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers.
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Potential Theory and Geometry on Lie Groups
90 折
出版日:2020/01/31 作者:N. Th. Varopoulos  出版社:Cambridge Univ Pr  裝訂:精裝
This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The first part describes the use of tools from potential theory to establish the classification and to show that the analytic and algebraic approaches to the classification are equivalent. Part II covers geometric theory of the same classification and a proof that it is equivalent to the algebraic approach. Part III is a new approach to the geometric classification that requires more advanced geometric technology, namely homotopy, homology and the theory of currents. Using these methods, a more direct, but also more sophisticated, approach to the equivalence of the geometric and algebraic classification is made. Background material is introduced gradually to familiarise readers with ideas from areas such as Lie groups, differential topology and probability, in particular, random walks on groups. Numerous open problems inspire students to explore further.
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Dirichlet Series and Holomorphic Functions in High Dimensions
90 折
出版日:2019/09/30 作者:Andreas Defant  出版社:Cambridge Univ Pr  裝訂:精裝
Over 100 years ago Harald Bohr identified a deep problem about the convergence of Dirichlet series, and introduced an ingenious idea relating Dirichlet series and holomorphic functions in high dimensions. Elaborating on this work, almost twnety years later Bohnenblust and Hille solved the problem posed by Bohr. In recent years there has been a substantial revival of interest in the research area opened up by these early contributions. This involves the intertwining of the classical work with modern functional analysis, harmonic analysis, infinite dimensional holomorphy and probability theory as well as analytic number theory. New challenging research problems have crystallized and been solved in recent decades. The goal of this book is to describe in detail some of the key elements of this new research area to a wide audience. The approach is based on three pillars: Dirichlet series, infinite dimensional holomorphy and harmonic analysis.
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Spectral Spaces
90 折
出版日:2019/05/31 作者:Max Dickmann  出版社:Cambridge Univ Pr  裝訂:精裝
Spectral spaces are a class of topological spaces. They are a tool linking algebraic structures, in a very wide sense, with geometry. They were invented to give a functional representation of Boolean algebras and distributive lattices and subsequently gained great prominence as a consequence of Grothendieck's invention of schemes. There are more than 1,000 research articles about spectral spaces, but this is the first monograph. It provides an introduction to the subject and is a unified treatment of results scattered across the literature, filling in gaps and showing the connections between different results. The book includes new research going beyond the existing literature, answering questions that naturally arise from this comprehensive approach. The authors serve graduates by starting gently with the basics. For experts, they lead them to the frontiers of current research, making this book a valuable reference source.
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Global Homotopy Theory
90 折
出版日:2018/11/30 作者:Stefan Schwede  出版社:Cambridge Univ Pr  裝訂:精裝
Equivariant homotopy theory started from geometrically motivated questions about symmetries of manifolds. Several important equivariant phenomena occur not just for a particular group, but in a uniform way for all groups. Prominent examples include stable homotopy, K-theory or bordism. Global equivariant homotopy theory studies such uniform phenomena, i.e. universal symmetries encoded by simultaneous and compatible actions of all compact Lie groups. This book introduces graduate students and researchers to global equivariant homotopy theory. The framework is based on the new notion of global equivalences for orthogonal spectra, a much finer notion of equivalence than is traditionally considered. The treatment is largely self-contained and contains many examples, making it suitable as a textbook for an advanced graduate class. At the same time, the book is a comprehensive research monograph with detailed calculations that reveal the intrinsic beauty of global equivariant phenomena.
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Factorization Algebras in Quantum Field Theory
90 折
出版日:2016/12/31 作者:Kevin Costello  出版社:Cambridge Univ Pr  裝訂:精裝
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.
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Discriminant Equations in Diophantine Number Theory
90 折
出版日:2016/10/01 作者:Jan-Hendrik Evertse  出版社:Cambridge Univ Pr  裝訂:精裝
Discriminant equations are an important class of Diophantine equations with close ties to algebraic number theory, Diophantine approximation and Diophantine geometry. This book is the first comprehensive account of discriminant equations and their applications. It brings together many aspects, including effective results over number fields, effective results over finitely generated domains, estimates on the number of solutions, applications to algebraic integers of given discriminant, power integral bases, canonical number systems, root separation of polynomials and reduction of hyperelliptic curves. The authors' previous title, Unit Equations in Diophantine Number Theory, laid the groundwork by presenting important results that are used as tools in the present book. This material is briefly summarized in the introductory chapters along with the necessary basic algebra and algebraic number theory, making the book accessible to experts and young researchers alike.
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The Theory of Hb Spaces
90 折
出版日:2016/09/30 作者:Emmanuel Fricain  出版社:Cambridge Univ Pr  裝訂:精裝
An H(b) space is defined as a collection of analytic functions that are in the image of an operator. The theory of H(b) spaces bridges two classical subjects, complex analysis and operator theory, which makes it both appealing and demanding. Volume 1 of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators and Clark measures. Volume 2 focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.
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The Theory of H(b) Spaces
90 折
出版日:2015/12/31 作者:Emmanuel Fricain  出版社:Cambridge Univ Pr  裝訂:精裝
An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding. The first volume of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators, and Clark measures. The second volume focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.
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Cubical Homotopy Theory
90 折
出版日:2015/09/30 作者:Brian A. Munson  出版社:Cambridge Univ Pr  裝訂:精裝
Graduate students and researchers alike will benefit from this treatment of classical and modern topics in homotopy theory of topological spaces with an emphasis on cubical diagrams. The book contains 300 examples and provides detailed explanations of many fundamental results. Part I focuses on foundational material on homotopy theory, viewed through the lens of cubical diagrams: fibrations and cofibrations, homotopy pullbacks and pushouts, and the Blakers–Massey Theorem. Part II includes a brief example-driven introduction to categories, limits and colimits, an accessible account of homotopy limits and colimits of diagrams of spaces, and a treatment of cosimplicial spaces. The book finishes with applications to some exciting new topics that use cubical diagrams: an overview of two versions of calculus of functors and an account of recent developments in the study of the topology of spaces of knots.
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Symplectic Topology and Floer Homology
90 折
出版日:2015/09/15 作者:Yong-Geun Oh  出版社:Cambridge Univ Pr  裝訂:精裝
Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory, including many examples of their applications to various problems in symplectic topology. The first volume covered the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.
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Symplectic Topology and Floer Homology
90 折
出版日:2015/08/31 作者:Yong-Geun Oh  出版社:Cambridge Univ Pr  裝訂:精裝
Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 1 covers the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory. One novel aspect of this treatment is the uniform treatment of both closed and open cases and a complete proof of the boundary regularity theorem of weak solutions of pseudo-holomorphic curves with totally real boundary conditions. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.
若需訂購本書,請電洽客服 02-25006600[分機130、131]。
Symplectic Topology and Floer Homology
90 折
出版日:2015/08/31 作者:Yong-Geun Oh  出版社:Cambridge Univ Pr  裝訂:精裝
Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 1 covers the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudo-holomorphic curve theory. One novel aspect of this treatment is the uniform treatment of both closed and open cases and a complete proof of the boundary regularity theorem of weak solutions of pseudo-holomorphic curves with totally real boundary conditions. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory, including many examples of their applications to various problems in symplectic topology. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.
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Pseudo-reductive Groups
90 折
出版日:2015/04/30 作者:Brian Conrad  出版社:Cambridge Univ Pr  裝訂:精裝
Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will value this book, as it develops tools likely to be used in tackling other problem
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Sobolev Spaces on Metric Measure Spaces ― An Approach Based on Upper Gradients
90 折
出版日:2015/03/31 作者:Juha Heinonen  出版社:Cambridge Univ Pr  裝訂:精裝
Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of metric measure spaces supporting a Poincaré inequality. This coherent treatment from first principles is an ideal introduction to the subject for graduate students and a useful reference for experts. It presents the foundations of the theory of such first-order Sobolev spaces, then explores geometric implications of the critical Poincaré inequality, and indicates numerous examples of spaces satisfying this axiom. A distinguishing feature of the book is its focus on vector-valued Sobolev spaces. The final chapters include proofs of several landmark theorems, including Cheeger's stability theorem for Poincaré inequalities under Gromov–Hausdorff convergence, and the Keith–Zhong self-improvement
若需訂購本書,請電洽客服 02-25006600[分機130、131]。
The Theory of H(b) Spaces
90 折
出版日:2014/07/01 作者:Emmanuel Fricain  出版社:Cambridge Univ Pr  裝訂:精裝
An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding. The first volume of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators, and Clark measures. The second volume focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.
若需訂購本書,請電洽客服 02-25006600[分機130、131]。
Categorical Homotopy Theory
90 折
出版日:2014/05/31 作者:Emily Riehl  出版社:Cambridge Univ Pr  裝訂:精裝
This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Par
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Differential Geometry of Singular Spaces and Reduction of Symmetry
90 折
出版日:2013/07/31 作者:J. Śniatycki  出版社:Cambridge Univ Pr  裝訂:精裝
In this book the author illustrates the power of the theory of subcartesian differential spaces for investigating spaces with singularities. Part I gives a detailed and comprehensive presentation of the theory of differential spaces, including integration of distributions on subcartesian spaces and the structure of stratified spaces. Part II presents an effective approach to the reduction of symmetries. Concrete applications covered in the text include reduction of symmetries of Hamiltonian systems, non-holonomically constrained systems, Dirac structures, and the commutation of quantization with reduction for a proper action of the symmetry group. With each application the author provides an introduction to the field in which relevant problems occur. This book will appeal to researchers and graduate students in mathematics and engineering.
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Non-Hausdorff Topology and Domain Theory ─ Selected Topics in Point-Set Topology
90 折
出版日:2013/05/31 作者:Jean Goubault-Larrecq  出版社:Cambridge Univ Pr  裝訂:精裝
This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff. For the first time in a single volume, this book covers basic material on metric and topological spaces, advanced material on complete partial orders, Stone duality, stable compactness, quasi-metric spaces and much more. An early chapter on metric spaces serves as an invitation to the topic (continuity, limits, compactness, completeness) and forms a complete introductory course by itself. Graduate students and researchers alike will enjoy exploring this treasure trove of results. Full proofs are given, as well as motivating ideas, clear explanations, illuminating examples, application exercises and some more challenging problems for more advanced readers.
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Homotopy Theory of Higher Categories
90 折
出版日:2011/11/30 作者:Carlos Simpson  出版社:Cambridge Univ Pr  裝訂:精裝
The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techn
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Entropy in Dynamical Systems
90 折
出版日:2011/06/20 作者:Tomasz Downarowicz  出版社:Cambridge Univ Pr  裝訂:精裝
This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon–McMillan–Breiman Theorem, the Ornstein–Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses symbolic extension entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research.
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出版日:2026/03/19 作者:Luís Saraiva(EDI)  出版社:Springer Nature  裝訂:精裝
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Essential Mathematics for Economics: A Student's Guide to Key Mathematical Techniques
滿額折
出版日:2026/03/14 作者:Vasileios Zikos  出版社:World Scientific Pub Co Inc  裝訂:平裝
優惠價: 1 2090
預購中
出版日:2026/03/14 作者:Vasileios Zikos  出版社:World Scientific Pub Co Inc  裝訂:精裝
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Mathematical Theory of Quantum Teleportation Protocols:An Introduction for Scientists and Engineers
90 折
出版日:2026/03/10 作者:Binayak S. Choudhury; Soumen Samanta  出版社:PBKTYFRL  裝訂:精裝
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Revenge in Seneca's Tragedies:Anger, Philosophy, and the Feminine
95 折
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