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Advances in Discrete Differential Geometry

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ISBN: 9783662504468 9783662504475 Year: Pages: 439 DOI: 10.1007/978-3-662-50447-5 Language: English
Publisher: Springer Nature
Subject: Mathematics
Added to DOAB on : 2017-02-03 18:41:25
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This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics.The authors take a closer look at discrete models in differentialgeometry and dynamical systems. Their curves are polygonal, surfacesare made from triangles and quadrilaterals, and time is discrete.Nevertheless, the difference between the corresponding smooth curves,surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture.This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.

Boundary Value Problems, Weyl Functions, and Differential Operators

Authors: --- ---
Book Series: Monographs in Mathematics ISBN: 9783030367145 Year: Pages: 772 DOI: 10.1007/978-3-030-36714-5 Language: English
Publisher: Springer Nature
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-02-04 11:21:15
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This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.

Scaling of Differential Equations

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Book Series: Simula SpringerBriefs on Computing ISBN: 9783319327259 9783319327266 Year: Pages: 138 DOI: 10.1007/978-3-319-32726-6 Language: English
Publisher: Springer Nature
Subject: Mathematics
Added to DOAB on : 2017-01-24 17:59:55
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The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models.Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics.The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically.This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.

Random Differential Equations in Scientific Computing

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ISBN: 9788376560267 Year: Pages: 650 DOI: 10.2478/9788376560267 Language: English
Publisher: De Gruyter
Subject: Mathematics
Added to DOAB on : 2014-03-05 13:15:31
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This book is a holistic and self-contained treatment of the analysis and numerics of random differential equations from a problem-centred point of view. An interdisciplinary approach is applied by considering state-of-the-art concepts of both dynamical systems and scientific computing. The red line pervading this book is the two-fold reduction of a random partial differential equation disturbed by some external force as present in many important applications in science and engineering. First, the random partial differential equation is reduced to a set of random ordinary differential equations in the spirit of the method of lines. These are then further reduced to a family of (deterministic) ordinary differential equations. The monograph will be of benefit, not only to mathematicians, but can also be used for interdisciplinary courses in informatics and engineering.

Multidimensional Inverse and Ill-Posed Problems for Differential Equations

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Book Series: Inverse and Ill-Posed Problems Series ISSN: 1381-4524 ISBN: 9783110271478 Year: Volume: 4 Pages: 139,00 DOI: 10.1515/9783110271478 Language: English
Publisher: De Gruyter
Subject: Mathematics
Added to DOAB on : 2019-06-27 13:08:38
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This monograph is devoted to statements of multidimensional inverse problems, in particular to methods of their investigation. Questions of the uniqueness of solution, solvability and stability are studied. Methods to construct a solution are given and, in certain cases, inversion formulas are given as well. Concrete applications of the theory developed here are also given. Where possible, the author has stopped to consider the method of investigation of the problems, thereby sometimes losing generality and quantity of the problems, which can be examined by such a method. The book should be of interet to researchers in the field of applied mathematics, geophysics and mathematical biology.

Finite Difference Computing with PDEs: A Modern Software Approach

Authors: ---
Book Series: Texts in Computational Science and Engineering ISSN: 1611-0994 / 2197-179X ISBN: 9783319554556 9783319554563 Year: Pages: 507 DOI: https://doi.org/10.1007/978-3-319-55456-3 Language: English
Publisher: Springer Nature
Subject: Computer Science
Added to DOAB on : 2017-11-24 13:03:18
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This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Manifolds - Current Research Areas

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ISBN: 9789535128717 9789535128724 9789535141228 Year: Pages: 160 DOI: 10.5772/63138 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:49

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Differential geometry is a very active field of research and has many applications to areas such as physics and gravity, for example. The papers in this book cover a number of subjects which will be of interest to workers in these areas. It is hoped that the papers here will be able to provide a useful resource for researchers with regard to current fields of research in this important area.

Numerical methods for the inverse dynamics simulation of underactuated mechanical systems

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Book Series: Schriftenreihe des Instituts für Mechanik, Karlsruher Institut für Technologie ISSN: 23634936 ISBN: 9783731506263 Year: Volume: 5 Pages: XVII, 224 p. DOI: 10.5445/KSP/1000065049 Language: ENGLISH
Publisher: KIT Scientific Publishing
Subject: Technology (General)
Added to DOAB on : 2019-07-30 20:02:00
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The present work deals with the inverse dynamics simulation of underactuated multibody systems. In particular, the study focuses on solving trajectory tracking control problems of differentially flat underactuated systems. The use of servo constraints provides an approach to formulate trajectory tracking control problems of underacutated systems, which are also called underactuated servo constraint problems.

Hardy Inequalities on Homogeneous Groups

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Book Series: Progress in Mathematics ISBN: 9783030028954 Year: Pages: 571 DOI: 10.1007/978-3-030-02895-4 Language: English
Publisher: Springer Nature
Subject: Mathematics
Added to DOAB on : 2020-02-04 11:21:19
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This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Non-Isothermal Kinetic Methods: Workbook and Laboratory Manual

Authors: --- --- --- --- et al.
Book Series: Textbooks 1: Max Planck Research Library for the History and Development of Knowledge ISBN: 9783844246933 Year: Pages: 73 Language: English
Publisher: Edition Open Access
Added to DOAB on : 2017-03-07 12:28:46
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In the modern world of ever-advancing technologies, actual tests of products and processes are more and more often preceded, if not replaced, by computer modeling. This saves the time and resources required for actual tests, and enables a better understanding of processes that occur in the course of tests. Preliminary computer modeling favors prudent planning of experiments. Calculations in thermal analysis are used everywhere, for example, in estimating the efficiency of thermal insulation of pipelines and in estimating the critical overheating conditions for some chemical substances under which their decomposition, self-heating, explosion, and so forth, occurs. This methodical manual focuses on a small aspect of calculations in thermal analysis dealing with constructing kinetic models from thermogravimetry and differential scanning calorimetry experimental data.

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