Shape Smoothness And Invariant Stratification Of An Attracting Set For Delayed Monotone Positive Feedback

Author : Tibor Krisztin,Hans-Otto Walther,Jianhong Wu
Publisher : American Mathematical Soc.
Page : 526 pages
File Size : 42,9 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821871692

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Shape, Smoothness, and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback by Tibor Krisztin,Hans-Otto Walther,Jianhong Wu Pdf

This book contains recent results about the global dynamics defined by a class of delay differential equations which model basic feedback mechanisms and arise in a variety of applications such as neural networks. The authors describe in detail the geometric structure of a fundamental invariant set, which in special cases is the global attractor, and the asymptotic behavior of solution curves on it. The approach makes use of advanced tools which in recent years have been developed for the investigation of infinite-dimensional dynamical systems: local invariant manifolds and inclination lemmas for noninvertible maps, Floquet theory for delay differential equations, a priori estimates controlling the growth and decay of solutions with prescribed oscillation frequency, a discrete Lyapunov functional counting zeros, methods to represent invariant sets as graphs, and Poincaré-Bendixson techniques for classes of delay differential systems. Several appendices provide the general results needed in the case study, so the presentation is self-contained. Some of the general results are not available elsewhere, specifically on smooth infinite-dimensional centre-stable manifolds for maps. Results in the appendices will be useful for future studies of more complicated attractors of delay and partial differential equations.

Author : Tibor Krisztin,Hans-Otto Walther,Jianhong Wu
Publisher : American Mathematical Soc.
Page : 253 pages
File Size : 51,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821810743

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Shape, Smoothness and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback by Tibor Krisztin,Hans-Otto Walther,Jianhong Wu Pdf

This book contains recent results about the global dynamics defined by a class of delay differential equations which model basic feedback mechanisms and arise in a variety of applications such as neural networks. The authors describe in detail the geometric structure of a fundamental invariant set, which in special cases is the global attractor, and the asymptotic behavior of solution curves on it. The approach makes use of advanced tools which in recent years have been developed for the investigation of infinite-dimensional dynamical systems: local invariant manifolds and inclination lemmas for noninvertible maps, Floquet theory for delay differential equations, a priori estimates controlling the growth and decay of solutions with prescribed oscillation frequency, a discrete Lyapunov functional counting zeros, methods to represent invariant sets as graphs, and Poincaré-Bendixson techniques for classes of delay differential systems. Several appendices provide the general results needed in the case study, so the presentation is self-contained. Some of the general results are not available elsewhere, specifically on smooth infinite-dimensional centre-stable manifolds for maps. Results in the appendices will be useful for future studies of more complicated attractors of delay and partial differential equations.

Author : Teresa Faria,Pedro Freitas
Publisher : American Mathematical Soc.
Page : 404 pages
File Size : 48,6 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821871358

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Topics in Functional Differential and Difference Equations by Teresa Faria,Pedro Freitas Pdf

This volume contains papers written by participants at the Conference on Functional Differential and Difference Equations held at the Instituto Superior Técnico in Lisbon, Portugal. The conference brought together mathematicians working in a wide range of topics, including qualitative properties of solutions, bifurcation and stability theory, oscillatory behavior, control theory and feedback systems, biological models, state-dependent delay equations, Lyapunov methods, etc. Articles are written by leading experts in the field. A comprehensive overview is given of these active areas of current research. The book will be of interest to both theoretical and applied mathematical scientists.

Author : A. Canada,P. Drabek,A. Fonda
Publisher : Elsevier
Page : 752 pages
File Size : 50,9 Mb
Release : 2006-08-21
Category : Mathematics
ISBN : 0080463819

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Handbook of Differential Equations: Ordinary Differential Equations by A. Canada,P. Drabek,A. Fonda Pdf

This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. Covers a variety of problems in ordinary differential equations Pure mathematical and real world applications Written for mathematicians and scientists of many related fields

Author : K. Vajravelu
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 42,8 Mb
Release : 2001-04-30
Category : Mathematics
ISBN : 0792368673

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Differential Equations and Nonlinear Mechanics by K. Vajravelu Pdf

The book includes chapters written by well-known mathematicians and engineers. The topics include nonlinear differential equations, nonlinear dynamics, neural networks, modeling and dissipative processes, nonlinear ODE, nonlinear PDE, nonlinear mechanics, and fuzzy differential equations. The chapters are self-contained and contain new results. The book is suitable for anyone interested in pursuing research in the fields mentioned above.

Author : Jianhong Wu
Publisher : Walter de Gruyter
Page : 200 pages
File Size : 49,7 Mb
Release : 2001
Category : Mathematics
ISBN : 3110169886

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Introduction to Neural Dynamics and Signal Transmission Delay by Jianhong Wu Pdf

In the design of a neural network, either for biological modeling, cognitive simulation, numerical computation or engineering applications, it is important to investigate the network's computational performance which is usually described by the long-term behaviors, called dynamics, of the model equations. The purpose of this book is to give an introduction to the mathematical modeling and analysis of networks of neurons from the viewpoint of dynamical systems.

Author : John Mallet-Paret,Jianhong Wu,Huaiping Zhu,Yingfie Yi
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 46,6 Mb
Release : 2012-10-11
Category : Mathematics
ISBN : 9781461445227

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Infinite Dimensional Dynamical Systems by John Mallet-Paret,Jianhong Wu,Huaiping Zhu,Yingfie Yi Pdf

​This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation and applications of new developments of nonlinear analysis and other mathematical theories. Theories of the infinite dimensional dynamical systems have also found more and more important applications in physical, chemical, and life sciences. This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from University of Minnesota on the occasion of his 70th birthday, this collection reflects the pioneering work and influence of Professor Sell in a few core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifolds theory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows.​

Author : Christian Meyer
Publisher : American Mathematical Soc.
Page : 220 pages
File Size : 42,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821871811

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Modular Calabi-Yau Threefolds by Christian Meyer Pdf

The main subject of this book is the connection between Calabi-Yau threefolds and modular forms. The book presents the general theory and brings together the known results. It studies hundreds of new examples of rigid and non-rigid modular Calabi-Yau threefolds and correspondences between them. Conjectures about the possible levels of modular forms connected with Calabi-Yau threefolds are presented. Tables of newforms of weight four and large levels are compiled and included in the appendix.

Author : Arne Ledet
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 55,9 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821871803

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Brauer Type Embedding Problems by Arne Ledet Pdf

This monograph is concerned with Galois theoretical embedding problems of so-called Brauer type with a focus on 2-groups and on finding explicit criteria for solvability and explicit constructions of the solutions. Before considering questions of reducing the embedding problems and reformulating the solvability criteria, the author provides the necessary theory of Brauer groups, group cohomology and quadratic forms. The book will be suitable for students seeking an introduction to embedding problems and inverse Galois theory. It will also be a useful reference for researchers in the field.

Author : Eric T. Sawyer
Publisher : American Mathematical Soc.
Page : 219 pages
File Size : 41,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821871843

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Function Theory by Eric T. Sawyer Pdf

Author : Levent Tunçel
Publisher : American Mathematical Soc.
Page : 219 pages
File Size : 45,8 Mb
Release : 2016-05-05
Category : Electronic
ISBN : 9781470428112

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Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization by Levent Tunçel Pdf

Since the early 1960s, polyhedral methods have played a central role in both the theory and practice of combinatorial optimization. Since the early 1990s, a new technique, semidefinite programming, has been increasingly applied to some combinatorial optimization problems. The semidefinite programming problem is the problem of optimizing a linear function of matrix variables, subject to finitely many linear inequalities and the positive semidefiniteness condition on some of the matrix variables. On certain problems, such as maximum cut, maximum satisfiability, maximum stable set and geometric representations of graphs, semidefinite programming techniques yield important new results. This monograph provides the necessary background to work with semidefinite optimization techniques, usually by drawing parallels to the development of polyhedral techniques and with a special focus on combinatorial optimization, graph theory and lift-and-project methods. It allows the reader to rigorously develop the necessary knowledge, tools and skills to work in the area that is at the intersection of combinatorial optimization and semidefinite optimization. A solid background in mathematics at the undergraduate level and some exposure to linear optimization are required. Some familiarity with computational complexity theory and the analysis of algorithms would be helpful. Readers with these prerequisites will appreciate the important open problems and exciting new directions as well as new connections to other areas in mathematical sciences that the book provides.

Author : Carl R. Riehm
Publisher : American Mathematical Soc.
Page : 305 pages
File Size : 40,8 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 9780821885956

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Introduction to Orthogonal, Symplectic, and Unitary Representations of Finite Groups by Carl R. Riehm Pdf

Author : Marcelo Aguiar
Publisher : American Mathematical Soc.
Page : 201 pages
File Size : 44,8 Mb
Release : 2006
Category : Education
ISBN : 9780821853542

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Coxeter Groups and Hopf Algebras by Marcelo Aguiar Pdf

An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary background ideas making this work accessible to advanced graduate students. The later chapters culminate in a unified and conceptual construction of several Hopf algebras based on combinatorial objects which emerge naturally from the geometric viewpoint. This work lays a foundation and provides new insights for further development of the subject.

Author : James W. Cogdell,Henry H. Kim,James W. Cogdell, Henry H. Kim, and M. Ram Murty,M. Ram Murty
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 48,6 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 082187179X

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Lectures on Automorphic L-functions by James W. Cogdell,Henry H. Kim,James W. Cogdell, Henry H. Kim, and M. Ram Murty,M. Ram Murty Pdf

James W. Cogdell, Lectures on $L$-functions, converse theorems, and functoriality for $GL_n$: Preface Modular forms and their $L$-functions Automorphic forms Automorphic representations Fourier expansions and multiplicity one theorems Eulerian integral representations Local $L$-functions: The non-Archimedean case The unramified calculation Local $L$-functions: The Archimedean case Global $L$-functions Converse theorems Functoriality Functoriality for the classical groups Functoriality for the classical groups, II Henry H. Kim, Automorphic $L$-functions: Introduction Chevalley groups and their properties Cuspidal representations $L$-groups and automorphic $L$-functions Induced representations Eisenstein series and constant terms $L$-functions in the constant terms Meromorphic continuation of $L$-functions Generic representations and their Whittaker models Local coefficients and non-constant terms Local Langlands correspondence Local $L$-functions and functional equations Normalization of intertwining operators Holomorphy and bounded in vertical strips Langlands functoriality conjecture Converse theorem of Cogdell and Piatetski-Shapiro Functoriality of the symmetric cube Functoriality of the symmetric fourth Bibliography M. Ram Murty, Applications of symmetric power $L$-functions: Preface The Sato-Tate conjecture Maass wave forms The Rankin-Selberg method Oscillations of Fourier coefficients of cusp forms Poincare series Kloosterman sums and Selberg's conjecture Refined estimates for Fourier coefficients of cusp forms Twisting and averaging of $L$-series The Kim-Sarnak theorem Introduction to Artin $L$-functions Zeros and poles of Artin $L$-functions The Langlands-Tunnell theorem Bibliography

Author : Frank Hollander
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 49,7 Mb
Release : 2000
Category : Mathematics
ISBN : 0821844350

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Large Deviations by Frank Hollander Pdf

Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.