Displaying similar documents to “The behaviour of the Gaussian beam in an anisotropic medium with an interface between two media.”

The Gaussian zoo.

Renze, John, Wagon, Stan, Wick, Brian (2001)

Experimental Mathematics

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Gaussian Integers

Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, Yasunari Shidama (2013)

Formalized Mathematics

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Gaussian integer is one of basic algebraic integers. In this article we formalize some definitions about Gaussian integers [27]. We also formalize ring (called Gaussian integer ring), Z-module and Z-algebra generated by Gaussian integer mentioned above. Moreover, we formalize some definitions about Gaussian rational numbers and Gaussian rational number field. Then we prove that the Gaussian rational number field and a quotient field of the Gaussian integer ring are isomorphic. ...

Geometric influences II: Correlation inequalities and noise sensitivity

Nathan Keller, Elchanan Mossel, Arnab Sen (2014)

Annales de l'I.H.P. Probabilités et statistiques

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In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as the KKL theorem, hold for the new definition in Gaussian space. In this paper we prove Gaussian analogues of two of the central applications of influences: Talagrand’s lower bound on the correlation of increasing subsets of the discrete cube, and the Benjamini–Kalai–Schramm (BKS) noise sensitivity...

SURE shrinkage of gaussian paths and signal identification

Nicolas Privault, Anthony Réveillac (2011)

ESAIM: Probability and Statistics

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Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.