High Quality Content by WIKIPEDIA articles! In mathematics, the Schwarz–Ahlfors–Pick theorem is an extension of the Schwarz lemma for hyperbolic geometry, such as the Poincare half-plane model. It states that the Poincare metric is distance-decreasing on harmonic functions. The theorem states that every holomorphic function on the unit disk U, or the upper half-plane H, with distances defined by the Poincare metric, is a contraction mapping. That is, every such analytic mapping will not...
High Quality Content by WIKIPEDIA articles! In mathematics, the Schwarz–Ahlfors–Pick theorem is an extension of the Schwarz lemma for hyperbolic geometry, such as the Poincare half-plane model. It states that the Poincare metric is distance-decreasing on harmonic functions. The theorem states that every holomorphic function on the unit disk U, or the upper half-plane H, with distances defined by the Poincare metric, is a contraction mapping. That is, every such analytic mapping will not increase the distance between points. Stated more precisely: Theorem: (Schwarz–Ahlfors–Pick) For all holomorphic functions f:Urightarrow U, one has rho(f(z_1),f(z_2)) leq rho(z_1,z_2) for points z_1,z_2 in U and Poincare distance ?. For any tangent vector T, the hyperbolic length of the tangent vector does not increase: |f^*(T)| leq |T|.
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Предлагаемая книга освещает наиболее часто встречающуюся патологию желудочно-кишечного тракта, печени, поджелудочной железы, в диагностику которой существенный вклад вносит компьютерная томография. Представленный материал основан на многолетних собственных наблюдениях авторов и многочисленных литературных источниках последних лет. Большое внимание уделено применению контрастного усиления как...
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Дата выхода: сентябрь 2019
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