Michael Oberguggenberger - Böcker

Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities. A workshop held at the Erwin-Schr dinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and general relativity, stochastic partial differential equations, and nonstandard analysis.The authors provide the latest research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models. The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical methods.

This work provides a comprehensive introduction to the non-linear theory of generalized functions (in the sense of Colombeau's construction) on differentiable manifolds. Particular emphasis is laid on a diffeomorphism invariant geometric approach to embedding the space of Schwartz distributions into algebras of generalized functions. The foundations of a "non-linear distributional geometry" are developed, supplying a solid base for an increasing number of applications of algebras of generalized functions to questions of a primarily geometric mature, in particular in mathematical physics. Applications of the resulting theory to symmetry-group analysis of differential equations and the theory of general relativity are presented in separate chapters. These features distinguish the present volume from earlier introductory texts and monographs on the subject.

This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis.

This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis.

This easy-to-follow textbook/reference presents a concise introduction to mathematical analysis from an algorithmic point of view, with a particular focus on applications of analysis and aspects of mathematical modelling.

This volumeaddressestheissueofuncertaintyincivilengineeringfromdesign toconstruction. Failures do occur in practice. Attributing them to a residual risk or a faulty execution of the projectdoesnotproperlycover the range of causes. A closer scrutiny of the design, the engineering model, the data, the soil-structure-interactionand the model assumptions is required. Usually, the uncertaintiesininitialandboundaryconditionsaswellasmaterialparameters are abundant. Current engineering practice often leaves these issues aside, despite the factthatnewscienti?c tools have been developed in the past decades that allow a rational description of uncertainties of all kinds, from model uncertainty to data uncertainty. It is the aim of this volume to have a critical look atcurrent engineering riskconcepts in order to raise awareness of uncertainty in numericalcom- tations, shortcomings of a strictly probabilistic safety concept, geotechnical models of failure mechanisms and their implications forconstruction mana- ment, execution,and the juristic questionas to who has to takeresponsibility. In addition, a number ofthe new procedures for modelling uncertaintyare- plained.Our central claim is that doubts and uncertainties must be openly - dressed in the design process. This contrasts certain tendencies in the en- neering community that, though incorporating uncertainties by one or the other way in the modelling process,claim to being able tocontrol them.

Der gewählte Zugang beinhaltet: Entwicklung der Grundlagen der Analysis aus algorithmischer Sichtweise, Vergegenständlichung der Theorie mittels MATLAB- und Maple-Programmen und Java-Applets, Behandlung grundlegender Konzepte und Verfahren der numerischen Analysis.

This volumeaddressestheissueofuncertaintyincivilengineeringfromdesign toconstruction. Failures do occur in practice. Attributing them to a residual risk or a faulty execution of the projectdoesnotproperlycover the range of causes. A closer scrutiny of the design, the engineering model, the data, the soil-structure-interactionand the model assumptions is required. Usually, the uncertaintiesininitialandboundaryconditionsaswellasmaterialparameters are abundant. Current engineering practice often leaves these issues aside, despite the factthatnewscienti?c tools have been developed in the past decades that allow a rational description of uncertainties of all kinds, from model uncertainty to data uncertainty. It is the aim of this volume to have a critical look atcurrent engineering riskconcepts in order to raise awareness of uncertainty in numericalcom- tations, shortcomings of a strictly probabilistic safety concept, geotechnical models of failure mechanisms and their implications forconstruction mana- ment, execution,and the juristic questionas to who has to takeresponsibility. In addition, a number ofthe new procedures for modelling uncertaintyare- plained.Our central claim is that doubts and uncertainties must be openly - dressed in the design process. This contrasts certain tendencies in the en- neering community that, though incorporating uncertainties by one or the other way in the modelling process,claim to being able tocontrol them.

Der gewählte Zugang beinhaltet: Entwicklung der Grundlagen der Analysis aus algorithmischer Sichtweise, Vergegenständlichung der Theorie mittels MATLAB- und Maple-Programmen und Java-Applets, Behandlung grundlegender Konzepte und Verfahren der numerischen Analysis.