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Analysis and Simulation of Chaotic Systems (Applied Mathematical Sciences #94)

Beginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable models for further mathematical analysis or computer simulations. For the most part, derivations are based on perturbation methods, and the majority of the text is devoted to careful derivations of implicit function theorems, the method of averaging, and quasi-static state approximation methods. The duality between stability and perturbation is developed and used, relying heavily on the concept of stability under persistent disturbances. Relevant topics about linear systems, nonlinear oscillations, and stability methods for difference, differential-delay, integro-differential and ordinary and partial differential equations are developed throughout the book. For the second edition, the author has restructured the chapters, placing special emphasis on introductory materials in Chapters 1 and 2 as distinct from presentation materials in Chapters 3 through 8. In addition, more material on bifurcations from the point of view of canonical models, sections on randomly perturbed systems, and several new computer simulations have been added.

Analysis and Simulation of Contact Problems (Lecture Notes in Applied and Computational Mechanics #27)

This carefully edited book offers a state-of-the-art overview on formulation, mathematical analysis and numerical solution procedures of contact problems. The contributions collected in this volume summarize the lectures presented by leading scientists in the area of contact mechanics, during the 4th Contact Mechanics International Symposium (CMIS) held in Hannover, Germany, 2005.

Analysis and Simulation of Electrical and Computer Systems (Lecture Notes in Electrical Engineering #452)

This book addresses selected topics in electrical engineering, electronics and mechatronics that have posed serious challenges for both the scientific and engineering communities in recent years. The topics covered range from mathematical models of electrical and electronic components and systems, to simulation tools implemented for their analysis and further developments; and from multidisciplinary optimization, signal processing methods and numerical results, to control and diagnostic techniques. By bridging theory and practice in the modeling, design and optimization of electrical, electromechanical and electronic systems, and by adopting a multidisciplinary perspective, the book provides researchers and practitioners with timely and extensive information on the state of the art in the field — and a source of new, exciting ideas for further developments and collaborations. The book presents selected results of the XIII Scientific Conference on Selected Issues of Electrical Engineering and Electronics (WZEE 2016), held on May 04–08, 2016, in Rzeszów, Poland. The Conference was organized by the Rzeszów Division of Polish Association of Theoretical and Applied Electrical Engineering (PTETiS) in cooperation with the Faculty of Electrical and Computer Engineering of the Rzeszów University of Technology.

Analysis and Simulation of Fluid Dynamics (Advances in Mathematical Fluid Mechanics)

This volume collects the contributions of a Conference held in June 2005 at the laboratoire Paul Painleve (UMR CNRS 8524) in Lille, France. The meeting was intended to review hot topics and future trends in fluid dynamics, with the objective to foster exchanges of various viewpoints (e.g. theoretical, and numerical) on the addressed questions. It comprises a collection of research articles on recent advances in the analysis and simulation of fluid dynamics.

Analysis and Simulation of Multifield Problems (Lecture Notes in Applied and Computational Mechanics #12)

The analysis and simulation of multifield problems have recently become one of the most actual and vivid areas of research. Although the individual subproblems of complex technical and physical phenomena often are understood separately, their interaction and coupling create not only new difficulties but also a complete new level and quality of interacting coupled field problems. Presented by leading experts this book includes recent results in these fields from the International Conference on Multifield Problems, April 8-10, 2002 at the University of Stuttgart, Germany.

Analysis and Synthesis of Dynamical Systems with Time-Delays (Lecture Notes in Control and Information Sciences #387)

Time-delay occurs in many dynamical systems such as biological systems, chemical systems, metallurgical processing systems, nuclear reactor, long transmission lines in pneumatic, hydraulic systems and electrical networks. Especially, in recent years, time-delay which exists in networked control s- temshasbroughtmorecomplexproblemintoanewresearcharea.Frequently, itisasourceofthegenerationofoscillation,instabilityandpoorperformance. Considerable e?ort has been applied to di?erent aspects of linear time-delay systems during recent years. Because the introduction of the delay factor renders the system analysis more complicated, in addition to the di?culties caused by the perturbation or uncertainties, in the control of time-delay s- tems, the problems of robust stability and robust stabilization are of great importance. This book presents some basic theories of stability and stabilization of systems with time-delay, which are related to the main results in this book. More attention will be paid on synthesis of systems with time-delay. That is, sliding mode control of systems with time-delay; networked control systems with time-delay; networked data fusion with random delay.

Analysis and Synthesis of Logics: How to Cut and Paste Reasoning Systems (Applied Logic Series #35)

Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature. The issue of preservation of properties is addressed.

Analysis and Synthesis of Nonlinear Control Systems: A Convex Optimisation Approach (Studies in Systems, Decision and Control #408)

This book presents a modern perspective on the modelling, analysis, and synthesis ideas behind convex-optimisation-based control of nonlinear systems: it embeds them in models with convex structures.Analysis and Synthesis of Nonlinear Control Systems begins with an introduction to the topic and a discussion of the problems to be solved. It then explores modelling via convex structures, including quasi-linear parameter-varying, Takagi–Sugeno models, and linear fractional transformation structures. The authors cover stability analysis, addressing Lyapunov functions and the stability of polynomial models, as well as the performance and robustness of the models. With detailed examples, simulations, and programming code, this book will be useful to instructors, researchers, and graduate students interested in nonlinear control systems.

Analysis and Thermomechanics: A Collection of Papers Dedicated to W. Noll on His Sixtieth Birthday

Analysis and Topology in Nonlinear Differential Equations: A Tribute to Bernhard Ruf on the Occasion of his 60th Birthday (Progress in Nonlinear Differential Equations and Their Applications #85)

This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in João Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60th birthday, is perceptible throughout the collection by the choice of themes and techniques. The many contributors consider modern topics in the calculus of variations, topological methods and regularity analysis, together with novel applications of partial differential equations. In keeping with the tradition of the workshop, emphasis is given to elliptic operators inserted in different contexts, both theoretical and applied. Topics include semi-linear and fully nonlinear equations and systems with different nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi type. Also treated are analytic aspects as well as applications such as diffusion problems in mathematical genetics and finance and evolution equations related to electromechanical devices.

Analysis and Visualization Tools for Constraint Programming: Constraint Debugging (Lecture Notes in Computer Science #1870)

Coordinating production across a supply chain, designing a new VLSI chip, allocating classrooms or scheduling maintenance crews at an airport are just a few examples of complex (combinatorial) problems that can be modeled as a set of decision variables whose values are subject to a set of constraints. The decision variables may be the time when production of a particular lot will start or the plane that a maintenance crew will be working on at a given time. Constraints may range from the number of students you can ?t in a given classroom to the time it takes to transfer a lot from one plant to another.Despiteadvancesincomputingpower,manyformsoftheseandother combinatorial problems have continued to defy conventional programming approaches. Constraint Logic Programming (CLP) ?rst emerged in the mid-eighties as a programming technique with the potential of signi?cantly reducing the time it takes to develop practical solutions to many of these problems, by combining the expressiveness of languages such as Prolog with the compu- tional power of constrained search. While the roots of CLP can be traced to Monash University in Australia, it is without any doubt in Europe that this new software technology has gained the most prominence, bene?ting, among other things, from sustained funding from both industry and public R&D programs over the past dozen years. These investments have already paid o?, resulting in a number of popular commercial solutions as well as the creation of several successful European startups.

Analysis, Applications, and Computations: Proceedings of the 13th ISAAC Congress, Ghent, Belgium, 2021 (Trends in Mathematics)

This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium.The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.

Analysis - Arbeitsbuch: Bezüge zwischen Schul- und Hochschulmathematik – sichtbar gemacht in Aufgaben mit kommentierten Lösungen

Schulmathematik und universitäre Mathematik – zwei getrennte Welten? Das vorliegende Buch begegnet dieser Frage mit einem neuen Konzept: Es bietet Schnittstellenaufgaben, die in den zentralen Themenbereichen der Analysis vielfältige Bezüge zwischen Schul- und Hochschulmathematik herstellen und diese für das Mathematiklernen nutzbar machen.- Schnittstellenaufgaben greifen Vorstellungen aus der Schulmathematik auf und nutzen diese, um Begriffsbildungen und Konzepte der Hochschulmathematik besser zu verstehen. - Umgekehrt zeigen sie, dass die Instrumente der Hochschulmathematik Möglichkeiten bieten, Schulmathematik tiefer zu durchdringen und sie auch dort zu erklären, wo in der Schule Plausibilitätsbetrachtungen genügen müssen. Ausführliche kommentierte Lösungsvorschläge unterstützen dabei den Lernprozess.

Analysis as a Life: Dedicated to Heinrich Begehr on the Occasion of his 80th Birthday (Trends in Mathematics)

This is a book comprising selected papers of colleagues and friends of Heinrich Begehr on the occasion of his 80th birthday. It aims at being a tribute to the excellent achievements of Heinrich Begehr in complex analysis and complex differential equations, and especially to his prominent role as one of the creators and long-time leader of the International Society for Analysis, its Applications and Computation (ISAAC).

Analysis as a Tool in Mathematical Physics: In Memory of Boris Pavlov (Operator Theory: Advances and Applications #276)

Boris Pavlov (1936-2016), to whom this volume is dedicated, was a prominent specialist in analysis, operator theory, and mathematical physics. As one of the most influential members of the St. Petersburg Mathematical School, he was one of the founders of the Leningrad School of Non-self-adjoint Operators. This volume collects research papers originating from two conferences that were organized in memory of Boris Pavlov: “Spectral Theory and Applications”, held in Stockholm, Sweden, in March 2016, and “Operator Theory, Analysis and Mathematical Physics – OTAMP2016” held at the Euler Institute in St. Petersburg, Russia, in August 2016. The volume also includes water-color paintings by Boris Pavlov, some personal photographs, as well as tributes from friends and colleagues.

Analysis at Large: Dedicated to the Life and Work of Jean Bourgain

​Analysis at Large is dedicated to Jean Bourgain whose research has deeply influenced the mathematics discipline, particularly in analysis and its interconnections with other fields. In this volume, the contributions made by renowned experts present both research and surveys on a wide spectrum of subjects, each of which pay tribute to a true mathematical pioneer. Examples of topics discussed in this book include Bourgain’s discretized sum-product theorem, his work in nonlinear dispersive equations, the slicing problem by Bourgain, harmonious sets, the joint spectral radius, equidistribution of affine random walks, Cartan covers and doubling Bernstein type inequalities, a weighted Prékopa-Leindler inequality and sumsets with quasicubes, the fractal uncertainty principle for the Walsh-Fourier transform, the continuous formulation of shallow neural networks as Wasserstein-type gradient flows, logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrödinger operators, polynomial equations in subgroups, trace sets of restricted continued fraction semigroups, exponential sums, twisted multiplicativity and moments, the ternary Goldbach problem, as well as the multiplicative group generated by two primes in Z/QZ.It is hoped that this volume will inspire further research in the areas of analysis treated in this book and also provide direction and guidance for upcoming developments in this essential subject of mathematics.

Analysis Band 1: Ein Lernbuch für den sanften Wechsel von der Schule zur Uni. Von Studenten mitentwickelt

In diesem Analysisbuch wird besonders viel Wert darauf gelegt, die Anfängerschwierigkeiten zu berücksichtigen: Alle neuen Begriffe werden ausführlich motiviert, die Beweisstrukturen werden so transparent wie möglich gemacht. Während der Vorbereitung gab es eine besonders intensive Zusammenarbeit mit einer Gruppe von Studierenden; alles, was ihrer Meinung nach zum besseren Verständnis hätte gesagt werden können, ist aufgenommen worden. Das Buch enthält zahlreiche Übungsaufgaben und Tipps zur Lösung. Die vollständigen, ausführlichen Lösungen zu den Übungsaufgaben findet man auf der Verlagswebsite. Das Buch ist auch zum Selbststudium geeignet. Schon im Text gibt es zahlreiche Fragen zum Mitdenken, und nach jedem Kapitel findet man - für spätere Prüfungsvorbereitungen - eine Sammlung von Verständnisfragen.Es werden auch viele Fragen angesprochen, die nicht direkt zur Analysis gehören: Grundlagen der Logik, Computeralgebrasysteme, Mathematik und Realität usw.

Analysis Band 1: Ein Lernbuch für den sanften Wechsel von der Schule zur Uni

In diesem Analysisbuch wird besonders viel Wert darauf gelegt, die Anfängerschwierigkeiten zu berücksichtigen: Alle neuen Begriffe werden ausführlich motiviert, die Beweisstrukturen werden so transparent wie möglich gemacht. Während der Vorbereitung gab es eine besonders intensive Zusammenarbeit mit einer Gruppe von Studierenden; alles, was ihrer Meinung nach zum besseren Verständnis hätte gesagt werden können, ist aufgenommen worden. Das Buch enthält viele Übungsaufgaben, deren ausführliche Lösungen als Online-Service zum Buch auf der speziell dafür eingerichteten Internetseite zu finden sind. Der Text wurde für die vorliegende 4. Auflage vom Autor noch einmal systematisch durchgesehen und in vielen Details verbessert.

Analysis Band 1: Ein Lernbuch für den sanften Wechsel von der Schule zur Uni. Von Studenten mitentwickelt

In diesem Analysisbuch wird besonders viel Wert darauf gelegt, die Anfängerschwierigkeiten zu berücksichtigen: Alle neuen Begriffe werden ausführlich motiviert, die Beweisstrukturen werden so transparent wie möglich gemacht. Während der Vorbereitung gab es eine besonders intensive Zusammenarbeit mit einer Gruppe von Studierenden; alles, was ihrer Meinung nach zum besseren Verständnis hätte gesagt werden können, ist aufgenommen worden. Das Buch enthält viele Übungsaufgaben, deren ausführliche Lösungen als Online-Service zum Buch auf der speziell dafür eingerichteten Internetseite zu finden sind. Der Text wurde für die vorliegende 5. Auflage vom Autor noch einmal systematisch durchgesehen und mit einem weiteren Lösungsweg zur Konstruktion von reellen Zahlen ergänzt.

Analysis Band 1: Ein Lernbuch für den sanften Wechsel von der Schule zur Uni

Die reellen Zahlen - Folgen und Reihen - Metrische Räume - Differentiation In diesem Analysisbuch wird besonders viel Wert darauf gelegt, die Anfängerschwierigkeiten zu berücksichtigen: Alle neuen Begriffe werden ausführlich motiviert, die Beweisstrukturen werden so transparent wie möglich gemacht. Während der Vorbereitung gab es eine besonders intensive Zusammenarbeit mit einer Gruppe von Studierenden; alles, was ihrer Meinung nach zum besseren Verständnis hätte gesagt werden können, ist aufgenommen worden. Das Buch enthält viele Übungsaufgaben, deren ausführliche Lösungen als Online-Service zum Buch auf der speziell dafür eingerichteten Internetseite zu finden sind.

Analysis Band 2: Ein Lernbuch

Das Buch ist im Stil der Analysis 1 geschrieben: Alles wird sehr ausführlich motiviert und entwickelt, und wieder gab es eine besonders intensive Zusammenarbeit mit Studierenden. Neben dem üblichen Stoff einer Analysis 2 (Funktionenräume, Integration, Differentialrechnung für Funktionen in mehreren Veränderlichen) enthält das Buch eine Reihe von Besonderheiten, die es sonst in keinem Lehrbuch gibt. Zum Beispiel ist der Satz von Liouville enthalten, durch den garantiert wird, dass gewisse einfache Funktionen nicht geschlossen integriert werden können. Im Kapitel "Anwendungen der Integralrechnung" gibt es einen Abschnitt zur Zahlentheorie, in dem Transzendenzbeweise für konkrete Zahlen - unter anderem für die Zahl e - geführt werden; in diesem Kapitel wird auch der Existenzsatz von Picard-Lindelöf behandelt. Und schließlich gibt es noch einen ausführlichen Anhang zum Thema "Englisch für Mathematiker": Was muss man beachten, wenn man sich auf Englisch über Mathematik unterhalten möchte? In der 2.Auflage wurde der Text an vielen Stellen korrigiert, und in Kapitel 6 (Integration) wurde ein Abschnitt überarbeitet.

Analysis Band 2: Ein Lernbuch

Das Buch ist im Stil der Analysis 1 geschrieben: Alles wird sehr ausführlich motiviert und entwickelt. Es gab wieder eine besonders intensive Zusammenarbeit mit Studierenden. Das Buch enthält eine Reihe von Besonderheiten, die es sonst in keinem Lehrbuch gibt. Zum Beispiel wird der Satz von Liouville gezeigt, durch den garantiert wird, dass gewisse einfache Funktionen nicht geschlossen integriert werden können. Im Kapitel zur Zahlentheorie gibt es Beweise für die Transzendenz von e und die Irrationalität der Kreiszahl p. Einmalig dürften auch der Bairesche Kategoriensatz und der Existenzsatz von Picard-Lindelöf in einer Analysis 2 sein. Und schließlich hat es noch nie das hier bereitgestellte "Englisch für Mathematiker" gegeben.

Analysis by Its History (Undergraduate Texts in Mathematics)

This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

Analysis, Control and Optimization of Complex Dynamic Systems (Gerad 25th Anniversary Ser.)

Analysis, Control and Optimization of Complex Dynamic Systems gathers in a single volume a spectrum of complex dynamic systems related papers written by experts in their fields, and strongly representative of current research trends. Complex systems present important challenges, in great part due to their sheer size which makes it difficult to grasp their dynamic behavior, optimize their operations, or study their reliability. Yet, we live in a world where, due to increasing inter-dependencies and networking of systems, complexity has become the norm. With this in mind, the volume comprises two parts. The first part is dedicated to a spectrum of complex problems of decision and control encountered in the area of production and inventory systems. The second part is dedicated to large scale or multi-agent system problems occurring in other areas of engineering such as telecommunication and electric power networks, as well as more generic context.

Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games (Lecture Notes in Economics and Mathematical Systems #529)

Focuses on the analysis, optimization and controllability of time-discrete dynamical systems and games under the aspect of stability, controllability and (for games) cooperative and non-cooperative treatment. The investigation of stability is based on Lyapunov's method which is generalized to non-autonomous systems. Optimization and controllability of dynamical systems is treated, among others, with the aid of mapping theorems such as implicit function theorem and inverse mapping theorem. Dynamical games are treated as cooperative and non-cooperative games and are used in order to deal with the problem of carbon dioxide reduction under economic aspects. The theoretical results are demonstrated by various applications.