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This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries. With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics. This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry. Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises. Authors Georg Glaeser, born 1955, got his PhD and habilitation in geometry at the Vienna University of Technology, 1998-2023 full professor of geometry at the University of Applied Arts Vienna. Author and coauthor of more than a dozen books on geometry, mathematics, computational geometry, computer graphics, and photography. Hellmuth Stachel, born 1942, got his PhD and habilitation in geometry in Graz. 1978 full professor at the Mining University Leoben, 1980-2011 full professor of geometry at the Vienna University of Technology. Coauthor of several books on mathematics and computational geometry and of more than 180 articles on geometry. Boris Odehnal, born 1973, got his PhD and habilitation in geometry at the Vienna University of Technology. 2011-2012 professor at the Dresden University of Technology, from 2023 full professor of geometry at the University of Applied Arts Vienna. Author of several dozens of publications on geometry.

Geometry. --- Mathematics. --- Applications of Mathematics. --- Conic sections. --- Conics, Spherical.

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This book deals with the prediction of possible future scenarios concerning the COVID-19 pandemic. Based on the well-known SIR model by Kermack and McKendrick a compartment model is established. This model comprises its own assumptions, transition rates and transmission dynamics, as well as a corresponding system of ordinary differential equations. Making use of numerical methods and a nonstandard-finite-difference scheme, two submodels are implemented in Matlab in order to make parameter estimations and compare different scenarios with each other. About the author Sarah Marie Treibert is a research assistant at the Chair of Applied Mathematics / Numerical Analysis of the University of Wuppertal (Bergische Universität Wuppertal). Her focus is on Epidemic Modelling.

Mathematics --- toegepaste wiskunde --- wiskunde --- Mathematics. --- Applications of Mathematics. --- Pandèmia de COVID-19, 2020 --- -Models matemàtics --- Previsió

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This book, the second of two volumes, presents significant applications for understanding modern analysis. It empowers young researchers with key techniques and applications to explore various subfields of this broad subject and introduces relevant frameworks for immediate deployment. The applications list begins with Degree Theory, a useful tool for studying nonlinear equations. Chapter 2 deals with Fixed Point Theory, and Chapter 3 introduces Critical Point Theory. Chapter 4 presents the main spectral properties of linear, nonlinear, anisotropic, and double-phase differential operators. Chapter 5 covers semilinear and nonlinear elliptic equations with different boundary conditions, while Chapter 6 addresses dynamic systems monitored by ordinary and partial differential equations. Chapter 7 delves into optimal control problems, and Chapter 8 discusses some economic models, providing a brief presentation of Game Theory and Nash equilibrium. By offering a clear and comprehensive overview of modern analysis tools and applications, this work can greatly benefit mature graduate students seeking research topics, as well as experienced researchers interested in this vast and rich field of mathematics.

Functional analysis. --- Topology. --- Mathematical optimization. --- Calculus of variations. --- Mathematics. --- Functional Analysis. --- Calculus of Variations and Optimization. --- Applications of Mathematics.

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The book provides the latest research results on measuring Credit Rating Migration by mathematical methods. It brings about most popular mathematical models, methods and applications on this area, especially presents the latest development on structure models. It is systematically collects the models, methods and results in this area. The book first introduced the financial background and preliminary mathematical theory. Then two mainstream mathematical models for measuring default risks, the reduced form model and structure model, are presented. The structure model for measuring credit rating migration risks is the main part of the book and authors prove the existence, uniqueness, regularities, asymptotic behavior, traveling wave and other properties of the solutions of the model. The structural credit rating migration model is also extended to more general case, such as stochastic interest rate, multiple ratings, region switch and so on. Some credit derivatives, and numerical analysis, parameter calibration and estimate of the migration boundary of the models are given in the last two chapters. The book focuses on theoretical financial investigators, especially financial mathematical researchers and students. The book is involved various mathematical models, such as PDE, numerical simulation etc., some of them are interesting mathematical problems, so that, and a good reference book to study mathematical modeling in credit rating migration. It might also be used as a textbook for students in financial credit risks.

Mathematical analysis --- Mathematics --- analyse (wiskunde) --- toegepaste wiskunde --- wiskunde --- Mathematics. --- Mathematical analysis. --- Applications of Mathematics. --- Analysis. --- Credit ratings.

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This book is the first comprehensive guide to logic-based Benders decomposition (LBBD), a general and versatile method for breaking large, complex optimization problems into components that are small enough for practical solution. The author introduces logic-based Benders decomposition for optimization, which substantially generalizes the classical Benders method. It can reduce solution times by orders of magnitude and allows decomposition to be applied to a much wider variety of optimization problems. On the theoretical side, this book provides a full account of inference duality concepts that underlie LBBD, as well as a description of how LBBD can be combined with stochastic and robust optimization, heuristic methods, and decision diagrams. It also clarifies the connection between LBBD and combinatorial Benders cuts for mixed integer programming. On the practical side, it explains how LBBD has been applied to a rapidly growing variety of problem domains. After describing basic theory, this book provides a comprehensive review of the rapidly growing literature that describes these applications, in each case explaining how LBBD is adapted to the problem at hand. In doing so this work provides a sourcebook of ideas for applying LBBD to new problems as they arise.

Mathematical optimization. --- Operations research. --- Mathematics. --- Production management. --- Optimization. --- Operations Research and Decision Theory. --- Applications of Mathematics. --- Operations Management.