Bücher veröffentlicht von Birkhauser

New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions.This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others.Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.

This monograph presents an original method to unify the mathematical theories of well-posed problems and contact mechanics. The author uses a new concept called the Tykhonov triple to develop a well-posedness theory in which every convergence result can be interpreted as a well-posedness result. This will be useful for studying a wide class of nonlinear problems, including fixed-point problems, inequality problems, and optimal control problems. Another unique feature of the manuscript is the unitary treatment of mathematical models of contact, for which new variational formulations and convergence results are presented. Well-Posed Nonlinear Problems will be a valuable resource for PhD students and researchers studying contact problems. It will also be accessible to interested researchers in related fields, such as physics, mechanics, engineering, and operations research.

This volume contains a collection of articles on state-of-the-art developments in the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Seventeenth International Conference on Integral Methods in Science and Engineering, held virtually in July 2022, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical, electrical, and petroleum engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential working tool.

This open access book covers the main topics for a course on the differential geometry of curves and surfaces. Unlike the common approach in existing textbooks, there is a strong focus on variational problems, ranging from elastic curves to surfaces that minimize area, or the Willmore functional. Moreover, emphasis is given on topics that are useful for applications in science and computer graphics. Most often these applications are concerned with finding the shape of a curve or a surface that minimizes physically meaningful energy. Manifolds are not introduced as such, but the presented approach provides preparation and motivation for a follow-up course on manifolds, and topics like the Gauss-Bonnet theorem for compact surfaces are covered.

Architekten müssen sich immer wieder auch mit der theoretischen Grundlage ihres Faches auseinandersetzen, die über eine kunsthistorische Betrachtung hinausgeht. ¿Was ist Architektur?¿ oder ¿Was ist ein Architekt?¿ kann nur von der Produzentenseite unter historischen und vergleichenden Gesichtspunkten beantwortet werden.

In The Digital, a Continent?, the author argues in favor of a way of thinking about digital technology that draws on the new materialism. She uses photosynthesis and nuclear fission as examples of processes that are as artificial as they are natural to explain how digital technology can be viewed within the paradigm of a "communicative physics" in which poetics interacts with mathematical thinking. The author concludes that we can better understand ourselves and digital technology by developing notions of the multifaceted ways energy, form, and intellect interact in global architectonics. Theoretical consideration of digital technology Visual language and science New volume in the Applied Virtuality Book Series

In his 1979 essay The Postmodern Condition: A Report on Knowledge philosopher Jean-François Lyotard noted that the advent of the computer opened up a stage of progress in which knowledge has become a commodity. Modernity and postmodernity appear as two stages of a process resulting from the conflict of science and narrative. As science attempts to distance itself from narrative, it must create its own legitimacy. This paper takes up this challenge with a focus on the question of imagery. The image is precisely what modern science seeks to free itself from in its quest for absolute transparency. This transparency is examined from the perspective of architecture, drawing on arguments from philosophy, quantum mechanics, theology and information theory. Natural science in the context of postmodernism Quantum mechanics and information theory New volume in the Applied Virtuality Book Series

In this book, the editors focus on architecture and communication from various different perspectives - taking into account that the term "architecture" is used for buildings as well as in the context of computer software. Data and software also impact on our cities; raw data, however, do not convey any information - in order to generate information and communication they have to be organized and must make sense to the reader. The contributions avoid clear separation of the various communication spheres of their disciplines. Instead, they use the wide range of approaches to explore meanings - an ambitious aim that leaves the destination wide open; the reader is invited to share in this adventure.