Download or read book Dichotomies and Stability in Nonautonomous Linear Systems written by Yu. A. Mitropolsky and published by CRC Press. This book was released on 2002-10-10 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov functions with variable sign, expressed in quadratic forms, to the solution of this problem. The authors explore the preservation of invariant tori of dynamic systems under perturbation. This volume is a classic contribution to the literature on stability theory and provides a useful source of reference for postgraduates and researchers.
Download or read book Dichotomies in Stability Theory written by W. A. Coppel and published by Springer. This book was released on 2006-11-15 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Ordinary Differential Equations in Abstract Spaces and Applications written by Everaldo M. Bonotto and published by John Wiley & Sons. This book was released on 2021-09-15 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES AND APPLICATIONS Explore a unified view of differential equations through the use of the generalized ODE from leading academics in mathematics Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces. The book covers applications to other types of differential equations, including Measure Functional Differential Equations (measure FDEs). It presents a uniform collection of qualitative results of Generalized ODEs and offers readers an introduction to several theories, including ordinary differential equations, impulsive differential equations, functional differential equations, dynamical equations on time scales, and more. Throughout the book, the focus is on qualitative theory and on corresponding results for other types of differential equations, as well as the connection between Generalized Ordinary Differential Equations and impulsive differential equations, functional differential equations, measure differential equations and dynamic equations on time scales. The book’s descriptions will be of use in many mathematical contexts, as well as in the social and natural sciences. Readers will also benefit from the inclusion of: A thorough introduction to regulated functions, including their basic properties, equiregulated sets, uniform convergence, and relatively compact sets An exploration of the Kurzweil integral, including its definitions and basic properties A discussion of measure functional differential equations, including impulsive measure FDEs The interrelationship between generalized ODEs and measure FDEs A treatment of the basic properties of generalized ODEs, including the existence and uniqueness of solutions, and prolongation and maximal solutions Perfect for researchers and graduate students in Differential Equations and Dynamical Systems, Generalized Ordinary Differential Equations in Abstract Spaces and Applications will also earn a place in the libraries of advanced undergraduate students taking courses in the subject and hoping to move onto graduate studies.
Download or read book Stability of Nonautonomous Differential Equations written by Luis Barreira and published by Springer. This book was released on 2007-09-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Download or read book Linear Systems And Exponential Dichotomy And Structure Of Sets Of Hyperbolic Points written by Zhensheng Lin and published by World Scientific. This book was released on 2000-04-28 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, the theory of stability is based on linear differential systems, which are simple and important systems in ordinary differential equations. The research on differential equations and on the theory of stability will, to a certain extent, be influenced by the research on linear differential systems. For differential linear equation systems, there are still many historical open questions attracting mathematicians. This book deals with the theory of linear differential systems developed around the notion of exponential dichotomies. The first author advanced the theory of stability through his research in this field.Several new important results on linear differential systems are presented. They concern exponential dichotomy and the structure of the sets of hyperbolic points. The book has five chapters: Chapter 1 introduces some necessary classical results on the linear differential systems, and the following chapters discuss exponential dichotomy, spectra of almost periodic linear systems, the Floquet theory for quasi periodic linear systems and the structure of sets of hyperbolic points. This book is a very useful reference in the area of the stability theory of ordinary differential equations and the theory of dynamic systems.
Download or read book Time Variant Systems and Interpolation written by Israel Gohberg and published by Springer Science & Business Media. This book was released on 1992 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Six papers deal with interrelated problems of modern operator theory, complex analysis, and system theory at a level accessible to advanced mathematicians and engineers. They provide a cross-section of recent advances in the understanding of the theory of time-varying systems and time-varying of analogues of interpolation problems. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Social Bonds as Freedom written by Paul Dumouchel and published by Berghahn Books. This book was released on 2015-08-01 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Central to discussions of multiculturalism and minority rights in modern liberal societies is the idea that the particular demands of minority groups contradict the requirements of equality, anonymity, and universality for citizenship and belonging. The contributors to this volume question the significance of this dichotomy between the universal and the particular, arguing that it reflects how the modern state has instituted the basic rights and obligations of its members and that these institutions are undergoing fundamental transformations under the pressure of globalization. They show that the social bonds uniting groups constitute the means of our freedom, rather than obstacles to achieving the universal.
Download or read book Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities written by Vladimir Andreevich I?A?kubovich and published by World Scientific. This book was released on 2004 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the Kalman-Yakubovich lemma on solvability of matrix inequalities are presented and discussed in detail. It is shown how the tools developed can be applied to stability investigations of relay control systems, gyroscopic systems, mechanical systems with a Coulomb friction, nonlinear electrical circuits, cellular neural networks, phase-locked loops, and synchronous machines.
Download or read book Frequency Domain Criteria for Absolute Stability written by Dmitry Altshuller and published by Springer. This book was released on 2012-07-25 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Frequency Domain Criteria for Absolute Stability focuses on recently-developed methods of delay-integral-quadratic constraints to provide criteria for absolute stability of nonlinear control systems. The known or assumed properties of the system are the basis from which stability criteria are developed. Through these methods, many classical results are naturally extended, particularly to time-periodic but also to nonstationary systems. Mathematical prerequisites including Lebesgue-Stieltjes measures and integration are first explained in an informal style with technically more difficult proofs presented in separate sections that can be omitted without loss of continuity. The results are presented in the frequency domain – the form in which they naturally tend to arise. In some cases, the frequency-domain criteria can be converted into computationally tractable linear matrix inequalities but in others, especially those with a certain geometric interpretation, inferences concerning stability can be made directly from the frequency-domain inequalities. The book is intended for applied mathematicians and control systems theorists. It can also be of considerable use to mathematically-minded engineers working with nonlinear systems.
Download or read book nonlinear analysis and applications written by V. Lakshmikantham and published by CRC Press. This book was released on 2020-11-25 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book attempts to put together the works of a wide range of mathematical scientists. It consists of the proceedings of the Seventh Conference on "Nonlinear Analysis and Applications" including papers that were delivered as invited talks and research reports.
Download or read book Control Methods in PDE Dynamical Systems written by Fabio Ancona and published by American Mathematical Soc.. This book was released on 2007 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: While rooted in controlled PDE systems, this 2005 AMS-IMS-SIAM Summer Research Conference sought to reach out to a rather distinct, yet scientifically related, research community in mathematics interested in PDE-based dynamical systems. Indeed, this community is also involved in the study of dynamical properties and asymptotic long-time behavior (in particular, stability) of PDE-mixed problems. It was the editors' conviction that the time had become ripe and the circumstances propitious for these two mathematical communities--that of PDE control and optimization theorists and that of dynamical specialists--to come together in order to share recent advances and breakthroughs in their respective disciplines. This conviction was further buttressed by recent discoveries that certain energy methods, initially devised for control-theoretic a-priori estimates, once combined with dynamical systems techniques, yield wholly new asymptotic results on well-established, nonlinear PDE systems, particularly hyperb These expectations are now particularly well reflected in the contributions to this volume, which involve nonlinear parabolic, as well as hyperbolic, equations and their attractors; aero-elasticity, elastic systems; Euler-Korteweg models; thin-film equations; Schrodinger equations; beam equations; etc. in addition, the static topics of Helmholtz and Morrey potentials are also prominently featured. A special component of the present volume focuses on hyperbolic conservation laws, to take advantage of recent theoretical advances with significant implications also on applied problems. in all these areas, the reader will find state-of-the-art accounts as stimulating starting points for further research.
Download or read book Functional Analytic Methods for Evolution Equations written by Giuseppe Da Prato and published by Springer. This book was released on 2004-08-30 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.
Download or read book Lyapunov Functions in Differential Games written by Vladislav I Zhukovskiy and published by CRC Press. This book was released on 2003-01-16 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "arsenal" has been supplied by stability theory. This approach, which combines dynamic programming and the Lyapunov function method, leads to coefficient criteria, or ratios of the game math model parameters with which optimal strategies of the players not only exist but their analytical form can be specified. In this book coefficient criteria are derived for numerous new and relevant problems in the theory of linear-quadratic multi-player differential games. Those criteria apply when the players formulate their strategies independently (non co-operative games) and use non-Nash equilibria or when the game model recognizes noise, perturbation and other uncertainties of which only their ranges are known (differential games under uncertainty). This text is useful for researchers, engineers and students of applied mathematics, control theory and the engineering sciences.
Download or read book Evolution Equations and Their Applications in Physical and Life Sciences written by G Lumer and published by CRC Press. This book was released on 2000-11-08 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of lectures on linear partial differntial equations and semigroups, nonlinear equations, stochastic evolutionary processes, and evolution problems from physics, engineering and mathematical biology. The contributions come from the 6th International Conference on Evolution Equations and Their Applications in Physical and Life Sciences, held in Bad Herrenalb, Germany.
Download or read book The Dichotomy of Leadership written by Jocko Willink and published by St. Martin's Press. This book was released on 2018-09-25 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: THE INSTANT #1 NATIONAL BESTSELLER From the #1 New York Times bestselling authors of Extreme Ownership comes a new and revolutionary approach to help leaders recognize and attain the leadership balance crucial to victory. With their first book, Extreme Ownership (published in October 2015), Jocko Willink and Leif Babin set a new standard for leadership, challenging readers to become better leaders, better followers, and better people, in both their professional and personal lives. Now, in THE DICHOTOMY OF LEADERSHIP, Jocko and Leif dive even deeper into the unchartered and complex waters of a concept first introduced in Extreme Ownership: finding balance between the opposing forces that pull every leader in different directions. Here, Willink and Babin get granular into the nuances that every successful leader must navigate. Mastering the Dichotomy of Leadership requires understanding when to lead and when to follow; when to aggressively maneuver and when to pause and let things develop; when to detach and let the team run and when to dive into the details and micromanage. In addition, every leader must: · Take Extreme Ownership of everything that impacts their mission, yet utilize Decentralize Command by giving ownership to their team. · Care deeply about their people and their individual success and livelihoods, yet look out for the good of the overall team and above all accomplish the strategic mission. · Exhibit the most important quality in a leader—humility, but also be willing to speak up and push back against questionable decisions that could hurt the team and the mission. With examples from the authors’ combat and training experiences in the SEAL teams, and then a demonstration of how each lesson applies to the business world, Willink and Babin clearly explain THE DICHOTOMY OF LEADERSHIP—skills that are mission-critical for any leader and any team to achieve their ultimate goal: VICTORY.
Download or read book The Manifesto for Teaching Online written by Sian Bayne and published by MIT Press. This book was released on 2020-09-15 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: An update to a provocative manifesto intended to serve as a platform for debate and as a resource and inspiration for those teaching in online environments. In 2011, a group of scholars associated with the Centre for Research in Digital Education at the University of Edinburgh released “The Manifesto for Teaching Online,” a series of provocative statements intended to articulate their pedagogical philosophy. In the original manifesto and a 2016 update, the authors counter both the “impoverished” vision of education being advanced by corporate and governmental edtech and higher education’s traditional view of online students and teachers as second-class citizens. The two versions of the manifesto were much discussed, shared, and debated. In this book, Siân Bayne, Peter Evans, Rory Ewins, Jeremy Knox, James Lamb, Hamish Macleod, Clara O'Shea, Jen Ross, Philippa Sheail and Christine Sinclair have expanded the text of the 2016 manifesto, revealing the sources and larger arguments behind the abbreviated provocations. The book groups the twenty-one statements (“Openness is neither neutral nor natural: it creates and depends on closures”; “Don’t succumb to campus envy: we are the campus”) into five thematic sections examining place and identity, politics and instrumentality, the primacy of text and the ethics of remixing, the way algorithms and analytics “recode” educational intent, and how surveillance culture can be resisted. Much like the original manifestos, this book is intended as a platform for debate, as a resource and inspiration for those teaching in online environments, and as a challenge to the techno-instrumentalism of current edtech approaches. In a teaching environment shaped by COVID-19, individuals and institutions will need to do some bold thinking in relation to resilience, access, teaching quality, and inclusion.
Download or read book Optimal Control of the Growth of Wealth of Nations written by E.N. Chukwu and published by CRC Press. This book was released on 2003-01-23 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students and researchers in applied mathematics and applied economics can use this introductory-level graduate text. It looks at the current problems of the development of the global economy by studying the dynamics of key economic variables, such as gross national product, interest rates, employment, value of capital stock, prices (inflation) and
