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Time-Varying Vector Fields and Their Flows

Author: Saber Jafarpour

Publisher: Springer

Published: 2014-10-10

Total Pages: 119

ISBN-13: 3319101390

This short book provides a comprehensive and unified treatment of time-varying vector fields under a variety of regularity hypotheses, namely finitely differentiable, Lipschitz, smooth, holomorphic, and real analytic. The presentation of this material in the real analytic setting is new, as is the manner in which the various hypotheses are unified using functional analysis. Indeed, a major contribution of the book is the coherent development of locally convex topologies for the space of real analytic sections of a vector bundle, and the development of this in a manner that relates easily to classically known topologies in, for example, the finitely differentiable and smooth cases. The tools used in this development will be of use to researchers in the area of geometric functional analysis.

Time-Varying Vector Fields and Their Flows

Author: Saber Jafarpour

Publisher:

Published: 2014-10-31

Total Pages: 128

ISBN-13: 9783319101408

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Tautological Control Systems

Author: Andrew D. Lewis

Publisher: Springer

Published: 2014-07-22

Total Pages: 128

ISBN-13: 3319086383

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This brief presents a description of a new modelling framework for nonlinear/geometric control theory. The framework is intended to be—and shown to be—feedback-invariant. As such, Tautological Control Systems provides a platform for understanding fundamental structural problems in geometric control theory. Part of the novelty of the text stems from the variety of regularity classes, e.g., Lipschitz, finitely differentiable, smooth, real analytic, with which it deals in a comprehensive and unified manner. The treatment of the important real analytic class especially reflects recent work on real analytic topologies by the author. Applied mathematicians interested in nonlinear and geometric control theory will find this brief of interest as a starting point for work in which feedback invariance is important. Graduate students working in control theory may also find Tautological Control Systems to be a stimulating starting point for their research.

Advances in Visual Computing

Author: George Bebis

Publisher: Springer

Published: 2013-10-15

Total Pages: 793

ISBN-13: 3642419399

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The two volume sets LNCS 8033 and 8034 constitutes the refereed proceedings of the 9th International Symposium on Visual Computing, ISVC 2013, held in Rethymnon, Crete, Greece, in July 2013. The 63 revised full papers and 35 poster papers presented together with 32 special track papers were carefully reviewed and selected from more than 220 submissions. The papers are organized in topical sections: Part I (LNCS 8033) comprises computational bioimaging; computer graphics; motion, tracking and recognition; segmentation; visualization; 3D mapping, modeling and surface reconstruction; feature extraction, matching and recognition; sparse methods for computer vision, graphics and medical imaging; face processing and recognition. Part II (LNCS 8034) comprises topics such as visualization; visual computing with multimodal data streams; visual computing in digital cultural heritage; intelligent environments: algorithms and applications; applications; virtual reality.

Topological Obstructions to Stability and Stabilization

Author: Wouter Jongeneel

Publisher: Springer Nature

Published: 2023-05-16

Total Pages: 134

ISBN-13: 3031301331

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This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topology of an attractor, its domain of attraction, and the underlying manifold that is supposed to contain these sets. They present some proofs of known results in order to highlight assumptions and to develop extensions, and they provide new results showcasing the most effective methods to cope with these obstructions to stability and stabilization. Moreover, the book shows how Borsuk’s retraction theory and the index-theoretic methodology of Krasnosel’skii and Zabreiko underlie a large fraction of currently known results. This point of view reveals important open problems, and for that reason, this book is of interest to any researcher in control, dynamical systems, topology, or related fields.

Visualization Handbook

Author: Charles D. Hansen

Publisher: Elsevier

Published: 2011-08-30

Total Pages: 984

ISBN-13: 0080481647

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The Visualization Handbook provides an overview of the field of visualization by presenting the basic concepts, providing a snapshot of current visualization software systems, and examining research topics that are advancing the field. This text is intended for a broad audience, including not only the visualization expert seeking advanced methods to solve a particular problem, but also the novice looking for general background information on visualization topics. The largest collection of state-of-the-art visualization research yet gathered in a single volume, this book includes articles by a “who’s who of international scientific visualization researchers covering every aspect of the discipline, including: · Virtual environments for visualization · Basic visualization algorithms · Large-scale data visualization · Scalar data isosurface methods · Visualization software and frameworks · Scalar data volume rendering · Perceptual issues in visualization · Various application topics, including information visualization. * Edited by two of the best known people in the world on the subject; chapter authors are authoritative experts in their own fields; * Covers a wide range of topics, in 47 chapters, representing the state-of-the-art of scientific visualization.

Discontinuous Dynamical Systems on Time-varying Domains

Author: Albert C. J. Luo

Publisher: Springer Science & Business Media

Published: 2009-11-06

Total Pages: 234

ISBN-13: 3642002536

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"Discontinuous Dynamical Systems on Time-varying Domains" is the first monograph focusing on this topic. While in the classic theory of dynamical systems the focus is on dynamical systems on time-invariant domains, this book presents discontinuous dynamical systems on time-varying domains where the corresponding switchability of a flow to the time-varying boundary in discontinuous dynamical systems is discussed. From such a theory, principles of dynamical system interactions without any physical connections are presented. Several discontinuous systems on time-varying domains are analyzed in detail to show how to apply the theory to practical problems. The book can serve as a reference book for researchers, advanced undergraduate and graduate students in mathematics, physics and mechanics. Dr. Albert C. J. Luo is a professor at Southern Illinois University Edwardsville, USA. His research is involved in the nonlinear theory of dynamical systems. His main contributions are in the following aspects: a stochastic and resonant layer theory in nonlinear Hamiltonian systems, singularity on discontinuous dynamical systems, and approximate nonlinear theories for a deformable-body.

Nonlinear Control in the Year 2000

Author: Alberto Isidori

Publisher: Springer Science & Business Media

Published: 2000-11-17

Total Pages: 644

ISBN-13: 9781852333645

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Control of nonlinear systems, one of the most active research areas in control theory, has always been a domain of natural convergence of research interests in applied mathematics and control engineering. The theory has developed from the early phase of its history, when the basic tool was essentially only the Lyapunov second method, to the present day, where the mathematics ranges from differential geometry, calculus of variations, ordinary and partial differential equations, functional analysis, abstract algebra and stochastic processes, while the applications to advanced engineering design span a wide variety of topics, which include nonlinear controllability and observability, optimal control, state estimation, stability and stabilization, feedback equivalence, motion planning, noninteracting control, disturbance attenuation, asymptotic tracking. The reader will find in the book methods and results which cover a wide variety of problems: starting from pure mathematics (like recent fundamental results on (non)analycity of small balls and the distance function), through its applications to all just mentioned topics of nonlinear control, up to industrial applications of nonlinear control algorithms.

Geometric Analysis on Real Analytic Manifolds

Author: Andrew D. Lewis

Publisher: Springer Nature

Published: 2023-12-09

Total Pages: 323

ISBN-13: 3031379136

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This monograph provides some useful tools for performing global geometric analysis on real analytic manifolds. At the core of the methodology of the book is a variety of descriptions for the topologies for the space of real analytic sections of a real analytic vector bundle and for the space of real analytic mappings between real analytic manifolds. Among the various descriptions for these topologies is a development of geometric seminorms for the space of real analytic sections. To illustrate the techniques in the book, a number of fundamental constructions in differential geometry are shown to induce continuous mappings on spaces of real analytic sections and mappings. Aimed at researchers at the level of Doctoral students and above, the book introduces the reader to the challenges and opportunities of real analytic analysis and geometry.

In Situ Visualization for Computational Science

Author: Hank Childs

Publisher: Springer Nature

Published: 2022-05-04

Total Pages: 464

ISBN-13: 3030816273

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This book provides an overview of the emerging field of in situ visualization, i.e. visualizing simulation data as it is generated. In situ visualization is a processing paradigm in response to recent trends in the development of high-performance computers. It has great promise in its ability to access increased temporal resolution and leverage extensive computational power. However, the paradigm also is widely viewed as limiting when it comes to exploration-oriented use cases. Furthermore, it will require visualization systems to become increasingly complex and constrained in usage. As research efforts on in situ visualization are growing, the state of the art and best practices are rapidly maturing. Specifically, this book contains chapters that reflect state-of-the-art research results and best practices in the area of in situ visualization. Our target audience are researchers and practitioners from the areas of mathematics computational science, high-performance computing, and computer science that work on or with in situ techniques, or desire to do so in future.