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Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p-torsion-structure is an additional, useful tool. For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for the fine description of various structures. For low dimensions the moduli of supersingular abelian varieties is by now well understood. In this book we provide a description of the supersingular locus in all dimensions, in particular we compute the dimension of it: it turns out to be equal to Äg.g/4Ü, and we express the number of components as a class number, thus completing a long historical line where special cases were studied and general results were conjectured (Deuring, Hasse, Igusa, Oda-Oort, Katsura-Oort).
Group theory --- Abelian varieties --- Algebraic varieties --- Moduli theory --- Classification theory --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Abelse varieteiten --- Coefficiententheorie --- Theorie des coefficients --- Varieties Abelian --- Variétés abéliennes --- Algebraic geometry. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Algebraic varieties - Classification theory
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P. Dolbeault: Résidus et courants.- D. Mumford: Varieties defined by quadratic equations.- A. Néron: Hauteurs et théorie des intersections.- A. Seidenberg: Report on analytic product.- C.S. Seshadri: Moduli of p-vector bundles over an algebraic curve.- O. Zariski: Contributions to the problem of equi-singularity.
Algebraic varieties -- Classification theory -- Congresses. --- Algebraic varieties. --- Congruences and residues. --- Geometry, Projective. --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Mathematics. --- Algebraic geometry. --- Algebraic topology. --- Algebraic Geometry. --- Algebraic Topology. --- Geometry, algebraic. --- Algebraic geometry --- Topology
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Differential geometry. Global analysis --- Algebraic varieties --- Vector bundles --- Classification theory --- Congresses. --- 51 --- -Vector bundles --- -Fiber spaces (Mathematics) --- Varieties, Algebraic --- Geometry, Algebraic --- Linear algebraic groups --- Mathematics --- -Congresses --- Congresses --- -Mathematics --- 51 Mathematics --- -51 Mathematics --- Fiber spaces (Mathematics) --- Classification theory&delete& --- Algebraic varieties - Classification theory - Congresses. --- Vector bundles - Congresses.
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This monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs). Flatness and backstepping techniques and their generalization to PDEs with higher-dimensional spatial domain lie at the core of this treatise. This includes the development of systematic late lumping design procedures and the deduction of semi-numerical approaches using suitable approximation methods. Theoretical developments are combined with both simulation examples and experimental results to bridge the gap between mathematical theory and control engineering practice in the rapidly evolving PDE control area. The text is divided into five parts featuring: - a literature survey of paradigms and control design methods for PDE systems - the first principle mathematical modeling of applications arising in heat and mass transfer, interconnected multi-agent systems, and piezo-actuated smart elastic structures - the generalization of flatness-based trajectory planning and feedforward control to parabolic and biharmonic PDE systems defined on general higher-dimensional domains - an extension of the backstepping approach to the feedback control and observer design for parabolic PDEs with parallelepiped domain and spatially and time varying parameters - the development of design techniques to realize exponentially stabilizing tracking control - the evaluation in simulations and experiments Control of Higher-Dimensional PDEs — Flatness and Backstepping Designs is an advanced research monograph for graduate students in applied mathematics, control theory, and related fields. The book may serve as a reference to recent developments for researchers and control engineers interested in the analysis and control of systems governed by PDEs.
Algebraic varieties -- Classification theory. --- Distributed parameter systems --- Differential equations, Partial --- Nonlinear control theory --- Mechanical Engineering --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Mechanical Engineering - General --- Distributed parameter systems. --- Nonlinear control theory. --- Differential equations, Partial. --- Partial differential equations --- Systems, Distributed parameter --- Engineering. --- System theory. --- Control engineering. --- Control. --- Systems Theory, Control. --- Control theory --- Engineering systems --- System analysis --- Nonlinear theories --- Systems theory. --- Control and Systems Theory. --- Systems, Theory of --- Systems science --- Science --- Control engineering --- Control equipment --- Engineering instruments --- Automation --- Programmable controllers --- Philosophy
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