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We derive the smoothed aggregation two-level method from the variational objective to minimize the final error after finishing the entire iteration. This contrasts to a standard variational two-level method, where the coarse-grid correction vector is chosen to minimize the error after coarse-grid correction procedure, which represents merely an intermediate stage of computing. Thus, we enforce the global minimization of the error. The method with smoothed prolongator is thus interpreted as a qualitatively...
The strong version of the Poincaré recurrence theorem states that for any probability space , any -measure preserving transformation and any almost every point of returns to infinitely many times. In [8] (see also [4]) the theorem has been proved for MV-algebras of some type. The present paper contains a remarkable strengthening of the result stated in [8].
A simple condition sufficient for non-oscillatory behavior of input/output systems is formulated and discussed.
Let be a reduced -dimensional complex space, for which the set of singularities consists of finitely many points. If denotes the set of smooth points, the author considers a holomorphic vector bundle , equipped with a Hermitian metric , where represents a closed analytic subset of complex codimension at least two. The results, surveyed in this paper, provide criteria for holomorphic extension of across , or across the singular points of if . The approach taken here is via the metric...
Abelovu cenu za matematiku získal v roce 2017 francouzský matematik Yves Meyer za rozvoj teorie waveletů. V článku se seznámíme s jeho vědeckým životopisem, hlavní myšlenkou teorie waveletů a jejich použitím v praxi.
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