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Highlighting recent advances in variational and hemivariational inequalities with an emphasis on theory, numerical analysis and applications, this volume serves as an indispensable resource to graduate students and researchers interested in the latest results from recognized scholars in this relatively young and rapidly-growing field. Particularly, readers will find that the volume’s results and analysis present valuable insights into the fields of pure and applied mathematics, as well as civil, aeronautical, and mechanical engineering. Researchers and students will find new results on well posedness to stationary and evolutionary inequalities and their rigorous proofs. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities. Finally, the applications presented illustrate the use of these results in the study of miscellaneous mathematical models which describe the contact between deformable bodies and a foundation. This includes the modelling, the variational and the numerical analysis of the corresponding contact processes. Furthermore, it can be used as supplementary reading material for advanced specialized courses in mathematical modeling for students with a strong background knowledge on nonlinear analysis, numerical analysis, partial differential equations, and mechanics of continua.

Mathematics. --- Combinatorics. --- Mathematical Modeling and Industrial Mathematics. --- Operator Theory. --- Operator theory. --- Mathématiques --- Théorie des opérateurs --- Hemivariational inequalities. --- Relaxation methods (Mathematics). --- Variational inequalities (Mathematics). --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Variational inequalities (Mathematics) --- Inequalities, Hemivariational --- Inequalities, Variational (Mathematics) --- Mathematical models. --- Combinatorics --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- Functional analysis --- Math --- Science --- Calculus of variations --- Differential inequalities

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Thomas Hubauer addresses the challenge of providing reasonable interpretations of incomplete observational data in the context of imperfect domain models – a situation often encountered in the context of industrial diagnostics. To tackle this problem, the author proposes a novel approach called Relaxed Abduction, which is able to derive pragmatic interpretations in situations where existing methods either fail or provide overly complex solutions. To strengthen the link to applications in industrial diagnostics, he develops a methodology to structure diagnosis problems according to ISO 13379 and express it using multiple description logic knowledge bases. Contents Formalizing Diagnostics Using Description Logics Formalization and Properties of Relaxed Abduction Solving Diagnostic Problems Using Relaxed Abduction Incremental Diagnostics Target Groups Researchers and students of computer science, knowledge management, and applied mathematics Practitioners in the area of industrial diagnostics and maintenance The Author Thomas Hubauer is a Research Scientist at the R&D department of a large German engineering company. His topics of interest range from ontologies and reasoning to machine learning and data analytics.

Computer science. --- Computer science --- Computers. --- Applied mathematics. --- Engineering mathematics. --- Computer Science. --- Mathematics of Computing. --- Computing Methodologies. --- Appl.Mathematics/Computational Methods of Engineering. --- Mathematics. --- Engineering --- Engineering analysis --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Informatics --- Mathematics --- Relaxation methods (Mathematics) --- Robust optimization. --- Optimization, Robust --- RO (Robust optimization) --- Mathematical optimization --- Numerical analysis --- Artificial intelligence. --- Artificial Intelligence. --- Mathematical and Computational Engineering. --- Mathematical analysis --- AI (Artificial intelligence) --- Artificial thinking --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Science --- Computer science—Mathematics.