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Author: Ulrich Langer
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110548488
Category : Mathematics
Languages : en
Pages : 262
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Book Description
This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.
Author: Ulrich Langer
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110548488
Category : Mathematics
Languages : en
Pages : 262
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Book Description
This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.
Author: Roger Penrose
Publisher: Cambridge University Press
ISBN: 9780521347860
Category : Mathematics
Languages : en
Pages : 516
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Book Description
In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant methods may be used to elucidate the structure and properties of space-time. In volume 1, Two-spinor calculus and relativistic fields, the calculus of 2-spinors is introduced and developed. Volume 2, Spinor and twistor methods in space-time geometry, introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. This work will be of great value to all those studying relativity, differential geometry, particle physics and quantum field theory from beginning graduate students to experts in these fields.
Author: Vidar Thomee
Publisher: Springer Science & Business Media
ISBN: 3662033593
Category : Mathematics
Languages : en
Pages : 310
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Book Description
My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.
Author: S. W. Hawking
Publisher: Cambridge University Press
ISBN: 1139810952
Category : Science
Languages : en
Pages : 406
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Book Description
Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.
Author: C. J. S. Clarke
Publisher: Cambridge University Press
ISBN: 9780521437967
Category : Science
Languages : en
Pages : 196
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Book Description
The different possible singularities are defined and the mathematical methods needed to extend the space-time are described in detail in this book. Results obtained (many appearing here for the first time) show that singularities are associated with a lack of smoothness in the Riemann tensor.
Author: Oscar Perpinan Lamigueiro
Publisher: CRC Press
ISBN: 1466565225
Category : Mathematics
Languages : en
Pages : 206
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Book Description
Code and Methods for Creating High-Quality Data Graphics A data graphic is not only a static image, but it also tells a story about the data. It activates cognitive processes that are able to detect patterns and discover information not readily available with the raw data. This is particularly true for time series, spatial, and space-time datasets. Focusing on the exploration of data with visual methods, Displaying Time Series, Spatial, and Space-Time Data with R presents methods and R code for producing high-quality graphics of time series, spatial, and space-time data. Practical examples using real-world datasets help you understand how to apply the methods and code. The book illustrates how to display a dataset starting with an easy and direct approach and progressively adding improvements that involve more complexity. Each of the book’s three parts is devoted to different types of data. In each part, the chapters are grouped according to the various visualization methods or data characteristics. Web Resource Along with the main graphics from the text, the author’s website offers access to the datasets used in the examples as well as the full R code. This combination of freely available code and data enables you to practice with the methods and modify the code to suit your own needs.
Author: Claes Johnson
Publisher: Courier Corporation
ISBN: 0486131599
Category : Mathematics
Languages : en
Pages : 290
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Book Description
An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
Author: J. R. Guerci
Publisher: Artech House
ISBN: 9781580536998
Category : Science
Languages : en
Pages : 212
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Book Description
This authoritative, leading-edge resource gives you a comprehensive overview of sample rate conversion (SRC) and its applications in software configurable radios. The book helps you understand the limits of feasible systems for sample rate conversion, as well as the limits of interpolation. You get sound advice on selecting the appropriate types of SRC for specific applications, and assistance in handling the trade-off between hardware complexity and the clock rate of a system. From an introduction to software radio and a refresher on the fundamentals of sampling and sample rate conversion, to discussions on block signal processing and well-known and novel structures for sample rate conversion, the book offers you practical guidance that enables you to quickly find solutions for your challenging projects in the field. This first-of-its-kind reference concludes with a list of questions that - when answered - helps to design a system for sample rate conversion. Over 890 equations and 90 illustrations support key topics throughout the book.
Author: Fabio Cardone
Publisher: Springer Science & Business Media
ISBN: 1402062834
Category : Science
Languages : en
Pages : 499
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Book Description
This volume provides a detailed discussion of the mathematical aspects and physical applications of a new geometrical structure of space-time, based on a generalization ("deformation") of the usual Minkowski space, as supposed to be endowed with a metric whose coefficients depend on the energy. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism.
Author: Dietrich Henckel
Publisher: Springer Science & Business Media
ISBN: 9400764251
Category : Political Science
Languages : en
Pages : 332
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Book Description
Time has become an increasingly important topic in urban studies and urban planning. The spatial-temporal interplay is not only of relevance for the theory of urban development and urban politics, but also for urban planning and governance. The space-time approach focuses on the human being with its various habits and routines in the city. Understanding and taking those habits into account in urban planning and public policies offers a new way to improve the quality of life in our cities. Adapting the supply and accessibility of public spaces and services to the inhabitants’ space-time needs calls for an integrated approach to the physical design of urban space and to the organization of cities. In the last two decades the body of practical and theoretical work on urban space-time topics has grown substantially. The book offers a state of the art overview of the theoretical reasoning, the development of new analytical tools, and practical experience of the space-time design of public cities in major European countries. The contributions were written by academics and practitioners from various fields exploring space-time research and planning.
