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The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems.
It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.Contents:IntroductionModels in Inverse ProblemsTikhonov Theory for Linear ProblemsTikhonov Theory for Nonlinear Inverse ProblemsNonsmooth OptimizationDirect Inversion MethodsBayesian Inference
Readership: Advanced undergraduates, graduates and researchers in applied mathematics, computational mathematics, optimization, statistics, natural science and engineering. It will appeal to those interested in inverse problems.
Key Features:A large part of the materials in the book is developed by the authors, and they have not been treated in other booksA comprehensive treatment of nonsmooth Tikhonov regularization, with a focus on value function calculus, parameter choice rules, computational algorithms, and an optimization approach to nonlinear inverse problemsA concise introduction to fast direct methods for inverse problems, e.g., MUSIC algorithm, direct sampling method, and Gel'fand–Levitan–Marchenko transformationA detailed illustration of uncertainty quantification for inverse problems via Bayesian inference, including model selection, Markov chain Monte Carlo and approximate Bayesian inferenceKeywords:Inverse Problems;Tikhonov Regularization;Nonsmooth Optimization;Direct Inversion;Bayesian InferenceReviews:
“The volume can be read by anyone with a basic knowledge of functional analysis and probability theory. Many examples where abstract theorems and algorithms are specialized for applied problems makes the book suitable for graduate courses on applied mathematics and inverse problems.”Zentralblatt MATH
The volume’s holistic representation of science, which includes the aims and values, knowledge, practices, techniques, and methodological rules (as well as science’s social and institutional contexts), mirrors its core aim to synthesize perspectives from the fields of philosophy of science and science education. The authors believe that this more integrated conception of nature of science in science education is both innovative and beneficial. They discuss in detail the implications for curriculum content, pedagogy, and learning outcomes, deploy numerous real-life examples, and detail the links between their ideas and curriculum policy more generally.
Leading researchers from industry and academia, as well as from government and private research institutions around the world summarize recent technical advances in chapters devoted to their individual contributions. In so doing, they examine a wide range of modern characterization techniques, from microscopy and spectroscopy to diffraction, thermal analysis, rheology, mechanical measurements and chromatography. These methods are compared with each other to assist in determining the best solution for both fundamental and applied problems, paying attention to the characterization of nanoscale miscibility and interfaces, both in blends involving copolymers and in immiscible blends. The thermodynamics, miscibility, phase separation, morphology and interfaces in polymer blends are also discussed in light of new insights involving the nanoscopic scale. Finally, the authors detail the processing-morphology-property relationships of polymer blends, as well as the influence of processing on the generation of micro and nano morphologies, and the dependence of these morphologies on the properties of blends. Hot topics such as compatibilization through nanoparticles, miscibility of new biopolymers and nanoscale investigations of interfaces in blends are also addressed.
With its application-oriented approach, handpicked selection of topics and expert contributors, this is an outstanding survey for anyone involved in the field of polymer blends for advanced technologies.