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Control theory. --- Hilbert space. --- Théorie de la commande --- Espace de Hilbert --- Control theory --- Théorie de la commande
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Geometry, Differential. --- Hilbert space. --- Mathematical physics. --- Quantum field theory --- Quantum theory --- Mathematics.
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Hilbert space --- Kernel functions --- Linear operators --- Hilbert, Espaces de --- Noyaux (analyse fonctionnelle) --- Opérateurs linéaires. --- Systèmes, Théorie des --- Opérateurs linéaires. --- Systèmes, Théorie des --- Algorithms. --- Interpolation. --- System theory.
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The main purpose of this book is to present the basic theory and some recent de velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be trans lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties). The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively.
Banach [Espaces de ] --- Banach [Ruimten van ] --- Banach spaces --- Cauchy [Probleem van ] --- Cauchy [Problème de ] --- Cauchy problem --- Differentiaalvergelijkingen --- Differential equations --- Equations différentielles --- Hilbert [Espace d' ] --- Hilbert [Ruimte van ] --- Hilbert space --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Calculus --- Differential equations. --- Ordinary Differential Equations. --- 517.91 Differential equations
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Stochastic processes --- Partial differential equations --- Heat equation --- Stochastic partial differential equations --- Filters (Mathematics) --- Équation de la chaleur. --- Équations aux dérivées partielles stochastiques. --- Filtres (mathématiques) --- Banach spaces, Stochastic differential equations in --- Hilbert spaces, Stochastic differential equations in --- SPDE (Differential equations) --- Stochastic differential equations in Banach spaces --- Stochastic differential equations in Hilbert spaces --- Differential equations, Partial --- Diffusion equation --- Heat flow equation --- Differential equations, Parabolic --- Mathematics
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This is an introductory text on numerical weather prediction (numerically modelling the general circulation of the atmosphere), utilizing the spectral transform method. The book covers finite difference methods and time-differencing schemes; the theoretical development of the spectral transform method (using spherical surfaces rather than grids for determining variation in the elements of weather); physical processes; current issues in dynamical and physical initiation; and data analysis. Several practical examples of the spectral transform method are included.
Numerical weather forecasting. --- Spectral theory (Mathematics) --- Mathematical weather forecasting --- Physical weather forecasting --- Weather forecasting --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Weather forecasting. --- Forecasting, Weather --- Short range weather forecasting --- Weather --- Weather prediction --- Geophysical prediction --- Forecasting
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Geometry --- Geometry, Hyperbolic. --- Géométrie hyperbolique. --- Hyperbolic spaces. --- Espaces hyperboliques. --- Spectral theory (Mathematics) --- Théorie spectrale (mathématiques) --- Asymptotic expansions. --- Développements asymptotiques. --- Asymptotic expansions --- Geometry, Hyperbolic --- Hyperbolic spaces --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry --- Asymptotic developments --- Asymptotes --- Convergence --- Difference equations --- Divergent series --- Functions --- Numerical analysis
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Spectral theory (Mathematics) --- Finite difference methods --- Spectre (Mathématiques) --- Finite differences --- 519.63 --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Differences, Finite --- Finite difference method --- Numerical analysis --- Finite differences. --- Spectral theory (Mathematics).
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This work has grown out of the lecture notes that were prepared for a series of seminars on some selected topics in quantum logic. The seminars were delivered during the first semester of the 1993/1994 academic year in the Unit for Foundations of Science of the Department of History and Foundations of Mathematics and Science, Faculty of Physics, Utrecht University, The Netherlands, while I was staying in that Unit on a European Community Research Grant, and in the Center for Philosophy of Science, University of Pittsburgh, U. S. A. , where I was staying during the 1994/1995 academic year as a Visiting Fellow on a Fulbright Research Grant, and where I also was supported by the Istvan Szechenyi Scholarship Foundation. The financial support provided by these foundations, by the Center for Philosophy of Science and by the European Community is greatly acknowledged, and I wish to thank D. Dieks, the professor of the Foundations Group in Utrecht and G. Massey, the director of the Center for Philosophy of Science in Pittsburgh for making my stay at the respective institutions possible. I also wish to thank both the members of the Foundations Group in Utrecht, especially D. Dieks, C. Lutz, F. Muller, J. Uffink and P. Vermaas and the participants in the seminars at the Center for Philosophy of Science in Pittsburgh, especially N. Belnap, J. Earman, A. Janis, J. Norton, and J.
Quantum logic --- Quantum field theory --- Hilbert space. --- Quantum field theory. --- Quantum logic. --- Mathematical physics. --- Quantum physics. --- Functional analysis. --- Elementary particles (Physics). --- Philosophy and science. --- Theoretical, Mathematical and Computational Physics. --- Quantum Physics. --- Functional Analysis. --- Elementary Particles, Quantum Field Theory. --- Philosophy of Science. --- Science and philosophy --- Science --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Physical mathematics --- Mathematics --- Banach spaces --- Hyperspace --- Inner product spaces --- Algebraic logic --- Mathematical physics
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