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Averaging method (Differential equations) --- Fourier series --- Series, Orthogonal
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Numerical solutions of differential equations --- Mathematical physics --- Differential geometry. Global analysis --- Differential equations, Nonlinear --- Differentiable dynamical systems --- Averaging method (Differential equations) --- Equations différentielles non linéaires --- Dynamique différentiable --- Méthode des moyennes (Equations différentielles) --- Numerical solutions --- Solutions numériques --- Differentiable dynamical systems. --- Numerical solutions. --- Averaging method (Differential equations). --- Equations différentielles non linéaires --- Dynamique différentiable --- Méthode des moyennes (Equations différentielles) --- Solutions numériques --- Numerical analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Method of averaging (Differential equations) --- Differential equations, Nonlinear - Numerical solutions
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Thermodynamically constrained averaging theory provides a consistent method for upscaling conservation and thermodynamic equations for application in the study of porous medium systems. The method provides dynamic equations for phases, interfaces, and common curves that are closely based on insights from the entropy inequality. All larger scale variables in the equations are explicitly defined in terms of their microscale precursors, facilitating the determination of important parameters and macroscale state equations based on microscale experimental and computational analysis. The method requires that all assumptions that lead to a particular equation form be explicitly indicated, a restriction which is useful in ascertaining the range of applicability of a model as well as potential sources of error and opportunities to improve the analysis.
Averaging method (Differential equations). --- Differential equations, Linear. --- Porous. --- Porous materials --- Thermodynamics --- Chemical & Materials Engineering --- Engineering & Applied Sciences --- Materials Science --- Mathematical models --- Mathematics --- Porous materials. --- Porous media --- Earth sciences. --- Geology --- Mineralogy. --- Geophysics. --- Thermodynamics. --- Earth Sciences. --- Geophysics/Geodesy. --- Quantitative Geology. --- Statistical methods. --- Materials --- Porosity --- Physical geography. --- GeologyxMathematics. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Physical geology --- Crystallography --- Minerals --- Geography --- Geology—Statistical methods. --- Geological physics --- Terrestrial physics --- Earth sciences
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This book provides a concise and accessible overview of model averaging, with a focus on applications. Model averaging is a common means of allowing for model uncertainty when analysing data, and has been used in a wide range of application areas, such as ecology, econometrics, meteorology and pharmacology. The book presents an overview of the methods developed in this area, illustrating many of them with examples from the life sciences involving real-world data. It also includes an extensive list of references and suggestions for further research. Further, it clearly demonstrates the links between the methods developed in statistics, econometrics and machine learning, as well as the connection between the Bayesian and frequentist approaches to model averaging. The book appeals to statisticians and scientists interested in what methods are available, how they differ and what is known about their properties. It is assumed that readers are familiar with the basic concepts of statistical theory and modelling, including probability, likelihood and generalized linear models.
Averaging method (Differential equations) --- Mathematical statistics. --- Ecology. --- Statistical methods. --- Statistics. --- Statistical Theory and Methods. --- Theoretical Ecology/Statistics. --- Biostatistics. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Balance of nature --- Biology --- Bionomics --- Ecological processes --- Ecological science --- Ecological sciences --- Environment --- Environmental biology --- Oecology --- Environmental sciences --- Population biology --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Ecology --- Statistics . --- Ecology . --- Biological statistics --- Biometrics (Biology) --- Biostatistics --- Biomathematics
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Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction. Chapters on Periodic Averaging and Hyperbolicity, Classical (first level) Normal Form Theory, Nilpotent (classical) Normal Form, and Higher Level Normal Form Theory are entirely new and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are surveys on invariant manifolds in Appendix C and averaging for PDEs in Appendix E. Since the first edition, the book has expanded in length and the third author, James Murdock has been added. Review of First Edition "One of the most striking features of the book is the nice collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with profuse, illuminating diagrams." - Mathematical Reviews.
Differential equations, Nonlinear --- Differentiable dynamical systems. --- Averaging method (Differential equations) --- Numerical solutions. --- Method of averaging (Differential equations) --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Numerical analysis --- Numerical solutions --- Differential equations, partial. --- Global analysis (Mathematics). --- Dynamical Systems and Ergodic Theory. --- Partial Differential Equations. --- Theoretical, Mathematical and Computational Physics. --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Partial differential equations --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Mathematical physics. --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Physical mathematics --- Physics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics
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Differential geometry. Global analysis --- Operational research. Game theory --- Averaging method (Differential equations) --- Large deviations. --- Attractors (Mathematics) --- Differential equations --- Méthode des moyennes (Equations différentielles) --- Grandes déviations --- Attracteurs (Mathématiques) --- Equations différentielles --- Qualitative theory. --- Théorie qualitative --- 51 <082.1> --- Mathematics--Series --- Moyennes, Méthode des (équations différentielles) --- Attracteurs (mathématiques) --- Équations différentielles --- Large deviations --- Théorie qualitative. --- Qualitative theory --- Méthode des moyennes (Equations différentielles) --- Grandes déviations --- Attracteurs (Mathématiques) --- Equations différentielles --- Théorie qualitative --- Deviations, Large --- Limit theorems (Probability theory) --- Statistics --- 517.91 Differential equations --- Method of averaging (Differential equations) --- Differential equations, Nonlinear --- Attracting sets (Mathematics) --- Attractors of a dynamical system --- Dynamical system, Attractors of --- Sets, Attracting (Mathematics) --- Differentiable dynamical systems --- Numerical solutions --- 517.91 --- Grandes déviations. --- Numerical solutions&delete&
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