01243nam0-22003851i-450-9900013325304033210-8218-5156-X000133253FED01000133253(Aleph)000133253FED0100013325320000920d1994----km-y0itay50------baeng<<The >>Mathematical Legacy of Wilhelm MagnusGroups, geometry and special functionsEditors W. Abikoff, Joan S. Birman, K. Kuiken.Providence (RI)American Mathematical Societyc1994.x, 500 p.24 cmContemporary mathematics169Teoria dei gruppiCongressiFunzioni di una variabile complessaCongressi512.2Abikoff,WilliamBirman,Joans S.Brooklyn (ny),1992Kuiken,K.CONFERENCE ON THE LEGACY OF WILHELM MAGNUS, Brooklyn (NY), May 1-3, 1992350747ITUNINARICAUNIMARCBK990001332530403321C-1-(16912765MA1MA120EXX30-XXMathematical Legacy of Wilhelm Magnus375914UNINAING0104666nam 22006615 450 99646653200331620200704015627.03-319-95001-010.1007/978-3-319-95001-3(CKB)4100000006674951(DE-He213)978-3-319-95001-3(MiAaPQ)EBC6307125(PPN)230538150(EXLCZ)99410000000667495120180919d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierOperads of Wiring Diagrams[electronic resource] /by Donald Yau1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XI, 308 p. 437 illus.) Lecture Notes in Mathematics,0075-8434 ;21923-319-95000-2 Introduction -- Part I Wiring Diagrams -- Wiring Diagrams -- Generators and Relations -- Decomposition of Wiring Diagrams -- Finite Presentation -- Finite Presentation for Algebras over Wiring Diagrams -- Part II Undirected Wiring Diagrams -- Undirected Wiring Diagrams -- Generators and Relations -- Decomposition of Undirected Wiring Diagrams -- Finite Presentation for Undirected Wiring Diagrams -- Algebras of Undirected Wiring Diagrams -- Part III Maps Between Operads of Wiring Diagrams -- A Map from Normal to Undirected Wiring Diagrams -- A Map from Wiring Diagrams to Undirected Wiring Diagrams -- Problems.Wiring diagrams form a kind of graphical language that describes operations or processes with multiple inputs and outputs, and shows how such operations are wired together to form a larger and more complex operation. This monograph presents a comprehensive study of the combinatorial structure of the various operads of wiring diagrams, their algebras, and the relationships between these operads. The book proves finite presentation theorems for operads of wiring diagrams as well as their algebras. These theorems describe the operad in terms of just a few operadic generators and a small number of generating relations. The author further explores recent trends in the application of operad theory to wiring diagrams and related structures, including finite presentations for the propagator algebra, the algebra of discrete systems, the algebra of open dynamical systems, and the relational algebra. A partial verification of David Spivak’s conjecture regarding the quotient-freeness of the relational algebra is also provided. In the final part, the author constructs operad maps between the various operads of wiring diagrams and identifies their images. Assuming only basic knowledge of algebra, combinatorics, and set theory, this book is aimed at advanced undergraduate and graduate students as well as researchers working in operad theory and its applications. Numerous illustrations, examples, and practice exercises are included, making this a self-contained volume suitable for self-study.Lecture Notes in Mathematics,0075-8434 ;2192Category theory (Mathematics)Homological algebraDynamicsErgodic theoryInformation theoryNeural networks (Computer science) Category Theory, Homological Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11035Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XInformation and Communication, Circuitshttps://scigraph.springernature.com/ontologies/product-market-codes/M13038Mathematical Models of Cognitive Processes and Neural Networkshttps://scigraph.springernature.com/ontologies/product-market-codes/M13100Category theory (Mathematics).Homological algebra.Dynamics.Ergodic theory.Information theory.Neural networks (Computer science) .Category Theory, Homological Algebra.Dynamical Systems and Ergodic Theory.Information and Communication, Circuits.Mathematical Models of Cognitive Processes and Neural Networks.621.31924Yau Donaldauthttp://id.loc.gov/vocabulary/relators/aut721399MiAaPQMiAaPQMiAaPQBOOK996466532003316Operads of wiring diagrams1539999UNISA05184nam 22007935 450 991025458430332120200701035441.03-319-42496-310.1007/978-3-319-42496-5(CKB)3710000000926226(DE-He213)978-3-319-42496-5(MiAaPQ)EBC6301761(MiAaPQ)EBC5590579(Au-PeEL)EBL5590579(OCoLC)1066183857(PPN)196323908(EXLCZ)99371000000092622620161024d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierChaos: Concepts, Control and Constructive Use /by Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky2nd ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XI, 281 p. 119 illus.) Understanding Complex Systems,1860-08323-319-42495-5 Introduction -- Paradigm for Chaos -- Main Features of Chaotic Systems -- Reconstruction of Dynamical Systems -- Controlling Chaos -- Synchronization of Chaotic Systems -- Stochastic Resonance -- The Appearance of Regular Fluxes Without Gradients -- Quantum Manifestations of Classical chaoticity -- Tunneling and Chaos.This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.Understanding Complex Systems,1860-0832Statistical physicsDynamicsVibrationDynamicsSystem theoryComputational complexityPhysicsComplex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Vibration, Dynamical Systems, Controlhttps://scigraph.springernature.com/ontologies/product-market-codes/T15036Systems Theory, Controlhttps://scigraph.springernature.com/ontologies/product-market-codes/M13070Complexityhttps://scigraph.springernature.com/ontologies/product-market-codes/T11022Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Statistical physics.Dynamics.Vibration.Dynamics.System theory.Computational complexity.Physics.Complex Systems.Vibration, Dynamical Systems, Control.Systems Theory, Control.Complexity.Mathematical Methods in Physics.Statistical Physics and Dynamical Systems.003.857Bolotin Yuriiauthttp://id.loc.gov/vocabulary/relators/aut818779Tur Anatoliauthttp://id.loc.gov/vocabulary/relators/autYanovsky Vladimirauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910254584303321Chaos: Concepts, Control and Constructive Use2039151UNINA