Translational tilings of the integers with long periods.

Kolountzakis, Mihail N.

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Adaptive tests for periodic signal detection with applications to laser vibrometry

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Initially motivated by a practical issue in target detection laser vibrometry, we are interested in the problem of periodic signal detection in a Gaussian fixed design regression framework. Assuming that the signal belongs to some periodic Sobolev ball and that the variance of the noise is known, we first consider the problem from a minimax point of view: we evaluate the so-called which corresponds to the minimal distance between the signal and zero so that the detection...

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The note presents a simple proof of a result due to F. Obersnel and P. Omari on the existence of periodic solutions with an arbitrary period of the first order scalar differential equation, provided equation has an n-periodic solution with the minimal period n > 1.