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Thierry De Pauw Washek F. Pfeffer 《Transactions of the American Mathematical Society》2007,359(12):5915-5929
In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector fields that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is finite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions.
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P. Neittaanmki J. Saranen A. R. Mitchell 《Mathematical Methods in the Applied Sciences》1981,3(1):328-335
In this paper a finite element approximation scheme for the system curl is considered. The use of pointwise approximation of the boundary condition leads to a nonconforming method. The error estimate is proved and numerically tested. 相似文献
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E.A. Feldman 《Topology》1973,12(3):201-227
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We characterize the n-dimensional vector fields (with or without null linear parts) which can be transformed, under conjugation or orbital equivalence, into their quasi-homogeneous parts of minimum degree and, therefore, have the same dynamics. We give several examples of nilpotent and degenerate systems. 相似文献
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Singularities of vector fields 总被引:8,自引:0,他引:8
Floris Takens 《Publications Mathématiques de L'IHéS》1974,43(1):47-100
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Thomas Eckl 《manuscripta mathematica》2002,107(1):59-71
A result of J. Wahl shows that the existence of a vector field vanishing on an ample divisor of a projective normal variety
X implies that X is a cone over this divisor. If X is smooth, X will be isomorphic to the n-dimensional projective space.
This paper is a first attempt to generalize Wahl's theorem to higher codimensions: Given a complex smooth projective threefold
X and a vector field on X vanishing on an irreducible and reduced curve which is the scheme theoretic intersection of two
ample divisors, X is isomorphic to the 3-dimensional projective space or the 3-dimensional quadric.
Received: 24 April 2001 相似文献
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Thierry Bouche 《Mathematische Zeitschrift》1995,218(1):519-526
This article was processed by the author using the Springer-Verlag TEX QPMZGHB macro package 1991. 相似文献
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In this paper, we consider an approximation problem which arose in optimal control theory. We seek conditions on a compact subset K of Euclidean n-space such that every continuous vector field on K may be uniformly approximated (on K) by vector fields with strictly positive integrating factors. We prove that such approximation is possible for all K in a particular subclass of the compact sets with topological dimension less than or equal to 1. 相似文献
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