Results 291 to 300 of about 244,761 (318)
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Cech Homology Characterizations of Infinite Dimensional Manifolds
American Journal of Mathematics, 1981Let \(X\) denote a locally compact ANR. It is shown that \(X\) is a \(Q\)-manifold if and only if \(X\) has the disjoint disks property and the disjoint Čech carriers property. This result can be regarded as the infinite- dimensional version of the known fact that when \(n\geq 5\), a generalized n-manifold Y is a topological \(n\)-manifold if and only ...
R. Daverman, J. Walsh
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Pontryagin Maximum Principle for Control Systems on Infinite Dimensional Manifolds
Set-Valued and Variational Analysis, 2014We discuss a mathematical framework for analysis of optimal control problems on infinite-dimensional manifolds. Such problems arise in study of dynamic optimization for partial differential equations with some symmetry.
Robert Kipka, Yu. S. Ledyaev
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Birkhoffian Systems in Infinite Dimensional Manifolds
Journal of Dynamics and Differential Equations, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oliva, Waldyr M., Terra, Gláucio
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Infinite-Dimensional Flag Manifolds in Integrable Systems
Acta Applicandae Mathematicae, 1995The authors present several instances where infinite-dimensional flag varieties and their holomorphic line bundles play a role in integrable systems. They describe the correspondence between flag varieties and Darboux transformations for the KP hierarchy and the \(n\)th KdV hierarchy, construct solutions of the \(n\)th MKdV hierarchy from the space of ...
Helminck, G.F., Helminck, A.G.
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On Complex Infinite-Dimensional Grassmann Manifolds
Complex Analysis and Operator Theory, 2008We investigate geometric properties of Grassmann manifolds and their complexifications in an infinite-dimensional setting. Specific structures of quaternionic type are constructed on these complexifications by a direct method that does not require any use of the cotangent bundles.
Daniel Beltiţă, José E. Galé
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Infinite Dimensional Groups and Manifolds
2004The volume is a collection of refereed research papers on infinite dimensional groups and manifolds in mathematics and quantum physics. Topics covered are: new classes of Lie groups of mappings, the Burgers equation, the Chern-Weil construction in infinite dimensions, the hamiltonian approach to quantum field theory, and different aspects of large N ...
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Beckner Inequality on Finite- and Infinite-Dimensional Manifolds*
Chinese Annals of Mathematics, Series B, 2006The authors use the dimension-free Harnack inequality, the coupling method, and Bakry-Emery's argument in order to present some explicit lower bounds for the constant of the Beckner type inequality on compact manifolds. As applications, the Beckner inequality and the transportation cost inequality are established for a class of continuous spin systems.
Deng, Pingji, Wang, Fengyu
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Brownian motion in infinite dimensional manifolds
Applied Mathematics & Optimization, 1985zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fundamental Results on Infinite-Dimensional Manifolds
2020In this chapter, we prove fundamental results on manifolds modeled on Hilbert space (more generally an infinite-dimensional normed linear space E such that E ≈ EN or \(E\approx E_f^N\)) or the Hilbert cube. We also prove the Toru’nczyk Factor Theorem, that is, for each complete metrizable ANR X with weight \(\leqslant \tau \) (\(\leqslant \aleph _0\)),
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