Short paper on the extraction of semantic statements ?la Wikidata ( like " Ottawa ", " is capital of ", " Canada " ) from free text, or open domain relation extraction.
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This image is a modified version of the previous with the same title, extension : pdf The image has been given by the photographer Steve Surfman, as indicated, and was previously appropriately ( ? ) tagged for Open Domain.
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Other results include the Markov Kakutani fixed-point theorem ( 1936-1938 ) and the Ryll-Nardzewski fixed-point theorem ( 1967 ) for continuous affine self-mappings of compact convex sets, as well as the Earle Hamilton fixed-point theorem ( 1968 ) for holomorphic self-mappings of open domains.
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Owing respectively to Green's theorem and the divergence theorem, such a field is necessarily a conservative one, and it is free from sources or sinks, having net flux equal to zero through any open domain without holes . ( These two observations combine as real and imaginary parts in Cauchy's integral theorem . ) In fluid dynamics, such a vector field is a potential flow.
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Uniformization by parallel slit domains holds for arbitrary connected open domains in "'C "'; conjectured ( Koebe's " Kreisnormierungsproblem " ) that a similar statement was true for uniformization by circular domains . proved Koebe's conjecture when the number of boundary components is countable; although proved for wide classes of domains, the conjecture remains open when the number of boundary components is uncountable . also considered the limiting case of osculating or tangential circles which has continued to be actively studied in the theory of circle packing.
