Curvatures and Curves in Hilbert Space.
David L. Ragozin (1980)
Mathematische Zeitschrift
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David L. Ragozin (1980)
Mathematische Zeitschrift
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Guessous, Mohamed (1997)
Journal of Convex Analysis
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Wojciech Kucharz (1987)
Mathematische Zeitschrift
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Sabadini, I. (2001)
Rendiconti del Seminario Matematico
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Changho Keem (1991)
Manuscripta mathematica
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Lothar Göttsche (1990)
Manuscripta mathematica
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Fernand Pelletier, Rebhia Saffidine (2013)
Annales de la faculté des sciences de Toulouse Mathématiques
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The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [5] and [4]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [3] and [6] for articulated arms and snakes in a finite dimensional Hilbert space.
Serge Randriambololona, Sergei Starchenko (2011)
Fundamenta Mathematicae
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We show that the first order structure whose underlying universe is ℂ and whose basic relations are all algebraic subsets of ℂ² does not have quantifier elimination. Since an algebraic subset of ℂ² is either of dimension ≤ 1 or has a complement of dimension ≤ 1, one can restate the former result as a failure of quantifier elimination for planar complex algebraic curves. We then prove that removing the planarity hypothesis suffices to recover quantifier elimination: the structure with...
E. Bujalance, J.J. Etayo, J.M. Gamboa (1987)
Mathematische Zeitschrift
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L.S. Hulburt (1891/92)
Bulletin of the New York Mathematical Society
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Henryk Żołądek (2011)
Banach Center Publications
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The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.
E. Odell, Th. Schlumprecht (1993)
Geometric and functional analysis
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Jan O. Kleppe (1996)
Journal für die reine und angewandte Mathematik
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Frank D. Grosshans (1986)
Mathematische Zeitschrift
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Jacek Bochnak, Gustave Efroymson (1980)
Mathematische Annalen
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Pierre Dèbes (1996)
Manuscripta mathematica
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Petruševski, Ljiljana (1989)
Publications de l'Institut Mathématique. Nouvelle Série
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