The Center And Cyclicity Problems

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The Center and Cyclicity Problems

Author : Valery Romanovski
Publisher : Springer Science & Business Media
ISBN 13 : 0817647279
Total Pages : 336 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis The Center and Cyclicity Problems by : Valery Romanovski

Download or read book The Center and Cyclicity Problems written by Valery Romanovski and published by Springer Science & Business Media. This book was released on 2009-04-29 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a computational algebra approach, this comprehensive text addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The book gives the main properties of ideals in polynomial rings and their affine varieties followed by a discussion on the theory of normal forms and stability of differential equations. It contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography, making it a suitable graduate textbook as well as research reference.

Computer Algebra in Scientific Computing

Author : Vladimir P. Gerdt
Publisher : Springer
ISBN 13 : 364232973X
Total Pages : 374 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Computer Algebra in Scientific Computing by : Vladimir P. Gerdt

Download or read book Computer Algebra in Scientific Computing written by Vladimir P. Gerdt and published by Springer. This book was released on 2012-08-30 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2012, held in Maribor, Slovenia, in September 2012. The 28 full papers presented were carefully reviewed and selected for inclusion in this book. One of the main themes of the CASC workshop series, namely polynomial algebra, is represented by contributions devoted to new algorithms for computing comprehensive Gröbner and involutive systems, parallelization of the Gröbner bases computation, the study of quasi-stable polynomial ideals, new algorithms to compute the Jacobson form of a matrix of Ore polynomials, a recursive Leverrier algorithm for inversion of dense matrices whose entries are monic polynomials, root isolation of zero-dimensional triangular polynomial systems, optimal computation of the third power of a long integer, investigation of the complexity of solving systems with few independent monomials, the study of ill-conditioned polynomial systems, a method for polynomial root-finding via eigen-solving and randomization, an algorithm for fast dense polynomial multiplication with Java using the new opaque typed method, and sparse polynomial powering using heaps.

Control and Inverse Problems

Author : Kaïs Ammari
Publisher : Springer Nature
ISBN 13 : 3031356756
Total Pages : 276 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Control and Inverse Problems by : Kaïs Ammari

Download or read book Control and Inverse Problems written by Kaïs Ammari and published by Springer Nature. This book was released on 2023-09-26 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas. The chapters are based on talks given at the spring school "Control & Inverse Problems” held in Monastir, Tunisia in May 2022. In addition to providing a snapshot of these two areas, chapters also highlight breakthroughs on more specific topics, such as: Controllability of dynamical systems Information transfer in multiplier equations Nonparametric instrumental regression Control of chained systems The damped wave equation Control and Inverse Problems will be a valuable resource for both established researchers as well as more junior members of the community.

Extended Abstracts Spring 2018

Author : Andrei Korobeinikov
Publisher : Springer Nature
ISBN 13 : 3030252612
Total Pages : 282 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Extended Abstracts Spring 2018 by : Andrei Korobeinikov

Download or read book Extended Abstracts Spring 2018 written by Andrei Korobeinikov and published by Springer Nature. This book was released on 2019-09-03 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains extended abstracts outlining selected presentations delivered by participants of the joint international multidisciplinary workshop MURPHYS-HSFS-2018 (MUltiRate Processes and HYSteresis; Hysteresis and Slow-Fast Systems), dedicated to the mathematical theory and applications of the multiple scale systems, the systems with hysteresis and general trends in the dynamical systems theory. The workshop was jointly organized by the Centre de Recerca Matemàtica (CRM), Barcelona, and the Collaborative Research Center 910, Berlin, and held at the Centre de Recerca Matemàtica in Bellaterra, Barcelona, from May 28th to June 1st, 2018. This was the ninth workshop continuing a series of biennial meetings started in Ireland in 2002, and the second workshop of this series held at the CRM. Earlier editions of the workshops in this series were held in Cork, Pechs, Suceava, Lutherstadt and Berlin. The collection includes brief research articles reporting new results, descriptions of preliminary work, open problems, and the outcome of work in groups initiated during the workshop. Topics include analysis of hysteresis phenomena, multiple scale systems, self-organizing nonlinear systems, singular perturbations and critical phenomena, as well as applications of the hysteresis and the theory of singularly perturbed systems to fluid dynamics, chemical kinetics, cancer modeling, population modeling, mathematical economics, and control. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active research areas.

Geometric Configurations of Singularities of Planar Polynomial Differential Systems

Author : Joan C. Artés
Publisher : Springer Nature
ISBN 13 : 3030505707
Total Pages : 699 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Geometric Configurations of Singularities of Planar Polynomial Differential Systems by : Joan C. Artés

Download or read book Geometric Configurations of Singularities of Planar Polynomial Differential Systems written by Joan C. Artés and published by Springer Nature. This book was released on 2021-07-19 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the global study of finite and infinite singularities of planar polynomial differential systems, with special emphasis on quadratic systems. While results covering the degenerate cases of singularities of quadratic systems have been published elsewhere, the proofs for the remaining harder cases were lengthier. This book covers all cases, with half of the content focusing on the last non-degenerate ones. The book contains the complete bifurcation diagram, in the 12-parameter space, of global geometrical configurations of singularities of quadratic systems. The authors’ results provide - for the first time - global information on all singularities of quadratic systems in invariant form and their bifurcations. In addition, a link to a very helpful software package is included. With the help of this software, the study of the algebraic bifurcations becomes much more efficient and less time-consuming. Given its scope, the book will appeal to specialists on polynomial differential systems, pure and applied mathematicians who need to study bifurcation diagrams of families of such systems, Ph.D. students, and postdoctoral fellows.

Mathematical Sciences with Multidisciplinary Applications

Author : Bourama Toni
Publisher : Springer
ISBN 13 : 3319313231
Total Pages : 641 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Mathematical Sciences with Multidisciplinary Applications by : Bourama Toni

Download or read book Mathematical Sciences with Multidisciplinary Applications written by Bourama Toni and published by Springer. This book was released on 2016-08-19 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the fourth in a multidisciplinary series which brings together leading researchers in the STEAM-H disciplines (Science, Technology, Engineering, Agriculture, Mathematics and Health) to present their perspective on advances in their own specific fields, and to generate a genuinely interdisciplinary collaboration that transcends parochial subject-matter boundaries. All contributions are carefully edited, peer-reviewed, reasonably self-contained, and pedagogically crafted for a multidisciplinary readership. Contributions are drawn from a variety of fields including mathematics, statistics, game theory and behavioral sciences, biomathematics and physical chemistry, computer science and human-centered computing. This volume is dedicated to Professor Christiane Rousseau, whose work inspires the STEAM-H series, in recognition of her passion for the mathematical sciences and her on-going initiative, the Mathematics of Planet Earth paradigm of interdisciplinarity. The volume's primary goal is to enhance interdisciplinary understanding between these areas of research by showing how new advances in a particular field can be relevant to open problems in another and how many disciplines contribute to a better understanding of relevant issues at the interface of mathematics and the sciences. The main emphasis is on important methods, research directions and applications of analysis within and beyond each field. As such, the volume aims to foster student interest and participation in the STEAM-H domain, as well as promote interdisciplinary research collaborations. The volume is valuable as a reference of choice and a source of inspiration for a broad spectrum of scientists, mathematicians, research students and postdoctoral fellows.

Global Bifurcation Theory and Hilbert’s Sixteenth Problem

Author : V. Gaiko
Publisher : Springer Science & Business Media
ISBN 13 : 1441991689
Total Pages : 199 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Global Bifurcation Theory and Hilbert’s Sixteenth Problem by : V. Gaiko

Download or read book Global Bifurcation Theory and Hilbert’s Sixteenth Problem written by V. Gaiko and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk "Mathematical problems" at the Second Interna tional Congress of Mathematicians in Paris. The talk covered practically all directions of mathematical thought of that time and contained a list of 23 problems which determined the further development of mathema tics in many respects (1, 119]. Hilbert's Sixteenth Problem (the second part) was stated as follows: Problem. To find the maximum number and to determine the relative position of limit cycles of the equation dy Qn(X, y) -= dx Pn(x, y)' where Pn and Qn are polynomials of real variables x, y with real coeffi cients and not greater than n degree. The study of limit cycles is an interesting and very difficult problem of the qualitative theory of differential equations. This theory was origi nated at the end of the nineteenth century in the works of two geniuses of the world science: of the Russian mathematician A. M. Lyapunov and of the French mathematician Henri Poincare. A. M. Lyapunov set forth and solved completely in the very wide class of cases a special problem of the qualitative theory: the problem of motion stability (154]. In turn, H. Poincare stated a general problem of the qualitative analysis which was formulated as follows: not integrating the differential equation and using only the properties of its right-hand sides, to give as more as possi ble complete information on the qualitative behaviour of integral curves defined by this equation (176].

Nonlinear Systems, Vol. 1

Author : Victoriano Carmona
Publisher : Springer
ISBN 13 : 3319667661
Total Pages : 424 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Nonlinear Systems, Vol. 1 by : Victoriano Carmona

Download or read book Nonlinear Systems, Vol. 1 written by Victoriano Carmona and published by Springer. This book was released on 2018-09-15 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.

Practical Applications of Intelligent Systems

Author : Yinglin Wang
Publisher : Springer Science & Business Media
ISBN 13 : 3642256589
Total Pages : 754 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Practical Applications of Intelligent Systems by : Yinglin Wang

Download or read book Practical Applications of Intelligent Systems written by Yinglin Wang and published by Springer Science & Business Media. This book was released on 2012-02-02 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Sixth International Conference on Intelligent System and Knowledge Engineering presents selected papers from the conference ISKE 2011, held December 15-17 in Shanghai, China. This proceedings doesn’t only examine original research and approaches in the broad areas of intelligent systems and knowledge engineering, but also present new methodologies and practices in intelligent computing paradigms. The book introduces the current scientific and technical advances in the fields of artificial intelligence, machine learning, pattern recognition, data mining, information retrieval, knowledge-based systems, knowledge representation and reasoning, multi-agent systems, natural-language processing, etc. Furthermore, new computing methodologies are presented, including cloud computing, service computing and pervasive computing with traditional intelligent methods. The proceedings will be beneficial for both researchers and practitioners who want to utilize intelligent methods in their specific research fields. Dr. Yinglin Wang is a professor at the Department of Computer Science and Engineering, Shanghai Jiao Tong University, China; Dr. Tianrui Li is a professor at the School of Information Science and Technology, Southwest Jiaotong University, China.

13th Chaotic Modeling and Simulation International Conference

Author : Christos H. Skiadas
Publisher : Springer Nature
ISBN 13 : 3030707954
Total Pages : 1080 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis 13th Chaotic Modeling and Simulation International Conference by : Christos H. Skiadas

Download or read book 13th Chaotic Modeling and Simulation International Conference written by Christos H. Skiadas and published by Springer Nature. This book was released on 2021-12-14 with total page 1080 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gathering the proceedings of the 13th CHAOS2020 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences. The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies.

Reaction Kinetics: Exercises, Programs and Theorems

Author : János Tóth
Publisher : Springer
ISBN 13 : 1493986430
Total Pages : 469 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Reaction Kinetics: Exercises, Programs and Theorems by : János Tóth

Download or read book Reaction Kinetics: Exercises, Programs and Theorems written by János Tóth and published by Springer. This book was released on 2018-09-18 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fifty years ago, a new approach to reaction kinetics began to emerge: one based on mathematical models of reaction kinetics, or formal reaction kinetics. Since then, there has been a rapid and accelerated development in both deterministic and stochastic kinetics, primarily because mathematicians studying differential equations and algebraic geometry have taken an interest in the nonlinear differential equations of kinetics, which are relatively simple, yet capable of depicting complex behavior such as oscillation, chaos, and pattern formation. The development of stochastic models was triggered by the fact that novel methods made it possible to measure molecules individually. Now it is high time to make the results of the last half-century available to a larger audience: students of chemistry, chemical engineering and biochemistry, not to mention applied mathematics. Based on recent papers, this book presents the most important concepts and results, together with a wealth of solved exercises. The book is accompanied by the authors’ Mathematica package, ReactionKinetics, which helps both students and scholars in their everyday work, and which can be downloaded from http://extras.springer.com/ and also from the authors’ websites. Further, the large set of unsolved problems provided may serve as a springboard for individual research.

Integrability of Dynamical Systems: Algebra and Analysis

Author : Xiang Zhang
Publisher : Springer
ISBN 13 : 9811042268
Total Pages : 380 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Integrability of Dynamical Systems: Algebra and Analysis by : Xiang Zhang

Download or read book Integrability of Dynamical Systems: Algebra and Analysis written by Xiang Zhang and published by Springer. This book was released on 2017-03-30 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on the Darboux theory of integrability and local integrability together with their applications. It summarizes the classical results of Darboux integrability and its modern development together with their related Darboux polynomials and their applications in the reduction of Liouville and elementary integrabilty and in the center—focus problem, the weakened Hilbert 16th problem on algebraic limit cycles and the global dynamical analysis of some realistic models in fields such as physics, mechanics and biology. Although it can be used as a textbook for graduate students in dynamical systems, it is intended as supplementary reading for graduate students from mathematics, physics, mechanics and engineering in courses related to the qualitative theory, bifurcation theory and the theory of integrability of dynamical systems.

Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles

Author : Maoan Han
Publisher : Springer Science & Business Media
ISBN 13 : 1447129180
Total Pages : 408 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles by : Maoan Han

Download or read book Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles written by Maoan Han and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior.

Computer Algebra in Scientific Computing

Author : Andreas Weber
Publisher : MDPI
ISBN 13 : 3039217305
Total Pages : 160 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Computer Algebra in Scientific Computing by : Andreas Weber

Download or read book Computer Algebra in Scientific Computing written by Andreas Weber and published by MDPI. This book was released on 2019-11-04 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although scientific computing is very often associated with numeric computations, the use of computer algebra methods in scientific computing has obtained considerable attention in the last two decades. Computer algebra methods are especially suitable for parametric analysis of the key properties of systems arising in scientific computing. The expression-based computational answers generally provided by these methods are very appealing as they directly relate properties to parameters and speed up testing and tuning of mathematical models through all their possible behaviors. This book contains 8 original research articles dealing with a broad range of topics, ranging from algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers over methods for certifying the isolated zeros of polynomial systems to computer algebra problems in quantum computing.

Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem

Author : Robert Roussarie
Publisher : Springer Science & Business Media
ISBN 13 : 9783764359003
Total Pages : 230 pages
Book Rating : 4.3/5 (59 download)

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Book Synopsis Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem by : Robert Roussarie

Download or read book Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem written by Robert Roussarie and published by Springer Science & Business Media. This book was released on 1998-05-19 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets. The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations. - - - The book as a whole is a well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in the recently developed methods. The book, reflecting the current state of the art, can also be used for teaching special courses. (Mathematical Reviews)

Computer Algebra in Scientific Computing

Author : Matthew England
Publisher : Springer
ISBN 13 : 3030268314
Total Pages : 479 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Computer Algebra in Scientific Computing by : Matthew England

Download or read book Computer Algebra in Scientific Computing written by Matthew England and published by Springer. This book was released on 2019-08-15 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019, held in Moscow, Russia, in August 2019. The 28 full papers presented together with 2 invited talks were carefully reviewed and selected from 44 submissions. They deal with cutting-edge research in all major disciplines of computer algebra. The papers cover topics such as polynomial algebra, symbolic and symbolic-numerical computation, applications of symbolic computation for investigating and solving ordinary differential equations, applications of CASs in the investigation and solution of celestial mechanics problems, and in mechanics, physics, and robotics.

Bifurcations and Periodic Orbits of Vector Fields

Author : Dana Schlomiuk
Publisher : Springer Science & Business Media
ISBN 13 : 9401582386
Total Pages : 483 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Bifurcations and Periodic Orbits of Vector Fields by : Dana Schlomiuk

Download or read book Bifurcations and Periodic Orbits of Vector Fields written by Dana Schlomiuk and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last thirty years were a period of continuous and intense growth in the subject of dynamical systems. New concepts and techniques and at the same time new areas of applications of the theory were found. The 31st session of the Seminaire de Mathematiques Superieures (SMS) held at the Universite de Montreal in July 1992 was on dynamical systems having as its center theme "Bifurcations and periodic orbits of vector fields". This session of the SMS was a NATO Advanced Study Institute (ASI). This ASI had the purpose of acquainting the participants with some of the most recent developments and of stimulating new research around the chosen center theme. These developments include the major tools of the new resummation techniques with applications, in particular to the proof of the non-accumulation of limit-cycles for real-analytic plane vector fields. One of the aims of the ASI was to bring together methods from real and complex dy namical systems. There is a growing awareness that an interplay between real and complex methods is both useful and necessary for the solution of some of the problems. Complex techniques become powerful tools which yield valuable information when applied to the study of the dynamics of real vector fields. The recent developments show that no rigid frontiers between disciplines exist and that interesting new developments occur when ideas and techniques from diverse disciplines are married. One of the aims of the ASI was to show these multiple interactions at work.