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Harmonic Analysis and Rational Approximation : Their Rôles in Signals, Control and Dynamical Systems
This book - an outgrowth of a topical summer school - sets out to introduce non-specialists from physics and engineering to the basic mathematical concepts of approximation and Fourier theory. After a general introduction, Part II of this volume contains basic material on the complex and harmonic analysis underlying the further developments presented. Part III deals with the essentials of approximation theory while Part IV completes the foundations by a tour of probability theory. Part V reviews some major applications in signal and control theory. In Part VI mathematical aspects of dynamical systems theory are discussed. Part VII, finally, is devoted to a modern approach to two physics problems: turbulence and the control and noise analysis in gravitational waves measurements.
Guidelines for the use of advanced numerical analysis
It is an authoritative guide that explains in detail the potential restrictions and pitfalls and so help engineers undertake advanced numerical analysis. It discusses the major approximations involved in nonlinear numerical analysis and describes some of the more popular constituitive models currently available and explores their strengths and weaknesses.
Graph-theoretic concepts in computer science ; Vol. 3787 ; 31st International Workshop, WG 2005, Metz, France, June 23-25, 2005, Revised Selected Papers
that aims to unite theory and practice by demonstrating how graph-theoretic concepts can be applied to various areas in Computer Science. This book provides results for various classes of graphs, graph computations, graph algorithms, and graph-theoretical applications in various fields.
Graph-theoretic concepts in computer science ; 46th International Workshop, WG 2020, Leeds, UK, June 24–26, 2020, Revised Selected Papers
This book constitutes the revised papers of the 46th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2020, held in Leeds, UK, in June 2020. The workshop was held virtually due to the COVID-19 pandemic. The 32 full papers presented in this volume were carefully reviewed and selected from 94 submissions. They cover a wide range of areas, aiming to present emerging research results and to identify and explore directions of future research of concepts on graph theory and how they can be applied to various areas in computer science.
Geometry of Müntz Spaces and Related Questions
Starting point and motivation for this volume is the classical Muentz theorem which states that the space of all polynomials on the unit interval, whose exponents have too many gaps, is no longer dense in the space of all continuous functions. The resulting spaces of Muentz polynomials are largely unexplored as far as the Banach space geometry is concerned and deserve the attention that the authors arouse. They present the known theorems and prove new results concerning, for example, the isomorphic and isometric classification and the existence of bases in these spaces. Moreover they state many open problems. Although the viewpoint is that of the geometry of Banach spaces they only assume that the reader is familiar with basic functional analysis. In the first part of the book the Banach spaces notions are systematically introduced and are later on applied for Muentz spaces. They include the opening and inclination of subspaces, bases and bounded approximation properties and versions of universality.
Geometric Properties for Incomplete Data
Computer vision and image analysis require interdisciplinary collaboration between mathematics and engineering. This book addresses the area of high-accuracy measurements of length, curvature, motion parameters and other geometrical quantities from acquired image data. It is a common problem that these measurements are incomplete or noisy, such that considerable efforts are necessary to regularise the data, to fill in missing information, and to judge the accuracy and reliability of these results. This monograph brings together contributions from researchers in computer vision, engineering and mathematics who are working in this area.
Generalized Bounds for Convex Multistage Stochastic Programs
The auther was involved in several industry projects in the field of power management, on the occasion of which I was repeatedly c- fronted with complex decision problems under uncertainty. Although usually hard to solve, I quickly learned to appreciate the benefit of stochastic progr- ming models and developed a strong interest in their theoretical properties. Motivated both by practical questions and theoretical concerns, I became p- ticularly interested in the art of finding tight bounds on the optimal value of a given model. The present work attempts to make a contribution to this important branch of stochastic optimization theory. In particular, it aims at extending some classical bounding methods to broader problem classes of practical relevance.
Galerkin Finite Element Methods for Parabolic Problems
This book provides insight in the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is based on first discretizing in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then applying some single step or multistep time stepping method. The concern is stability and error analysis of approximate solutions in various norms, and under various regularity assumptions on the exact solution.
Fuzzy and Rough Techniques in Medical Diagnosis and Medication
This volume provides readers with selected fuzzy and rough tools used to medical tasks, especially diagnosing and medication. To build a link between theoretical, mathematical excerpts and practical medical applications, the contents is formed as a sequence of occurrences in which a patient appears to be diagnosed and cured. The fuzzy and rough elements are inserted in the book in the order required by the presentation of medical substance to maintain the logical unity of the book’s essence. In conformity with this pattern the essay presents in turn some necessary elements of fuzzy set theory, the classical fuzzy diagnostic model with extensions, the fuzzy diagnostic model with clinical examinations extended throughout time based on distance theory, methods of drug effectiveness measurements and algorithms selecting the optimal medicine. As the complement, the solution of an approximation problem is suggested to find a curve that surrounds two-dimensional clock-like point sets with the little approximation error.
Fundamentals of computation theory ; 15th International symposium, FCT 2005, Lübeck, Gemany, August 17-20, 2005, Proceedings
This book constitutes the refereed proceedings of the 15th International Symposium Fundamentals of Computation Theory, FCT 2005, held in L]beck, Germany in August 2005. The 46 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 105 submissions. The papers are organized in topical sections on circuits, automata, complexity, approximability, computational and structural complexity, graphs and complexity, computational game theory, visual cryptography and computational geometry, query complexity, distributed systems, automata and formal languages, semantics, approximation algorithms, average case complexity, algorithms, graph algorithms, and pattern matching.
Fun with algorithms ; 4th International conference, FUN 2007, Castiglioncello, Italy, June 3-5, 2007, Proceedings
This book constitutes the refereed proceedings of the 4th International Conference on Fun with Algorithms, FUN 2007, held in Castiglioncello, Italy in June 2007.
Frontiers in Algorithmics ; 2nd Annual International Workshop, FAW 2008, Changsha, China, June 19-21, 2008, Proceeedings
This book constitutes the refereed proceedings of the Second International Frontiers of Algorithmics Workshop, FAW 2008, held in Changsha, China, in June 2008.The 33 revised full papers presented together with the abstracts of 3 invited talks were carefully reviewed and selected from 80 submissions. The papers were selected for 9 special focus tracks in the areas of biomedical informatics, discrete structures, geometric information processing and communication, games and incentive analysis.
Frontiers in Algorithmics ; 1st Annual International Workshop, FAW 2007, Lanzhou, China, August 1-3, 2007, Proceedings
This book constitutes the refereed proceedings of the First Annual International Frontiers of Algorithmics Workshop, FAW 2007, held in Lanzhou, China in August 2007. The 33 revised full papers presented were carefully reviewed and selected from 141 submissions.
Frontiers in Algorithmics ; 14th International Workshop, FAW 2020, Haikou, China, October 19-21, 2020, Proceedings
This book constitutes the proceedings of the 14th International Workshop on Frontiers in Algorithmics, FAW 2020, held in Haikou, China, in May 2020. The conference was held virtually due to the COVID-19 pandemic. The 12 full papers presented in this volume were carefully reviewed and selected from 15 submissions. The workshop provides a focused forum on current trends of research on algorithms, discrete structures, and their applications, and brings together international experts at the research frontiers in these areas to exchange ideas and to present significant new results. The papers detail graph theory, scheduling and algorithm and complexity.
Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Key Features The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal Examples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric tube formula The method of Diophantine approximation is used to study self-similar strings and flows Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions Throughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts, and discusses several open problems and extensions.
Finite Model Theory ; 2nd ed.
The book presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed-point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. Other topics include DATALOG languages, quantifiers and oracles, 0-1 laws, and optimization and approximation problems. The book is written in such a way that the respective parts on model theory and descriptive complexity theory may be read independently. This second edition is a thoroughly revised and enlarged version of the original text.
Finite Elements in Structural Analysis : Theoretical Concepts and Modeling Procedures in Statics and Dynamics of Structures
Introduces the basic concepts of the finite element method in the static and dynamic analysis of beam, plate, shell and solid structures, discussing how the method works, the characteristics of a finite element approximation and how to avoid the pitfalls of finite element modeling. Presenting the finite element theory as simply as possible, the book allows readers to gain the knowledge required when applying powerful FEA software tools. Further, it describes modeling procedures, especially for reinforced concrete structures, as well as structural dynamics methods, with a particular focus on the seismic analysis of buildings, and explores the modeling of dynamic systems. Featuring numerous illustrative examples, the book allows readers to easily grasp the fundamentals of the finite element theory and to apply the finite element method proficiently.
Finite Elements III : First-Order and Time-Dependent PDEs
Volume III is divided into 28 chapters. The first eight chapters focus on the symmetric positive systems of first-order PDEs called Friedrichs' systems. This part of the book presents a comprehensive and unified treatment of various stabilization techniques from the existing literature. It discusses applications to advection and advection-diffusion equations and various PDEs written in mixed form such as Darcy and Stokes flows and Maxwell's equations. The remainder of Volume III addresses time-dependent problems: parabolic equations (such as the heat equation), evolution equations without coercivity (Stokes flows, Friedrichs' systems), and nonlinear hyperbolic equations (scalar conservation equations, hyperbolic systems). It offers a fresh perspective on the analysis of well-known time-stepping methods. The last five chapters discuss the approximation of hyperbolic equations with finite elements. Here again a new perspective is proposed.
Finite Element Methods for Engineering Sciences : Theoretical Approach and Problem Solving Techniques
This self-tutorial offers a concise yet thorough grounding in the mathematics necessary for successfully applying FEMs to practical problems in science and engineering. The enlarged English-language edition, based on the original French, also contains a chapter on the approximation steps derived from the description of nature with differential equations and then applied to the specific model to be used.
Finite element analysis in geotechnical engineering ; Vol.1 : Theory
Provides the reader with a detailed insight into the use of the finite element method in geotechnical engineering. As specialist knowledge required to perform geotechnical finite element analysis is not normally part of a single engineering degree course, this lucid work will prove invaluable. It brings together essential information presented in a manner understandable to most engineers. Volume 1 presents the theory, assumptions and approximations involved in finite element analysis
