Displaying similar documents to “Solitons and Gibbs Measures for Nonlinear Schrödinger Equations ”

On the order equivalence relation of binary association measures

Mariusz Paradowski (2015)

International Journal of Applied Mathematics and Computer Science

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Over a century of research has resulted in a set of more than a hundred binary association measures. Many of them share similar properties. An overview of binary association measures is presented, focused on their order equivalences. Association measures are grouped according to their relations. Transformations between these measures are shown, both formally and visually. A generalization coefficient is proposed, based on joint probability and marginal probabilities. Combining association...

Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation

Nikolay Tzvetkov, Nicola Visciglia (2013)

Annales scientifiques de l'École Normale Supérieure

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Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.

Region of interest contrast measures

Václav Remeš, Michal Haindl (2018)

Kybernetika

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A survey of local image contrast measures is presented and a new contrast measure for measuring the local contrast of regions of interest is proposed. The measures validation is based on the gradual objective contrast decreasing on medical test images in both grayscale and color. The performance of the eleven most frequented contrast measures is mutually compared and their robustness to different types of image degradation is analyzed. Since the contrast measures can be both global,...

Can interestingness measures be usefully visualized?

Robert Susmaga, Izabela Szczech (2015)

International Journal of Applied Mathematics and Computer Science

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The paper presents visualization techniques for interestingness measures. The process of measure visualization provides useful insights into different domain areas of the visualized measures and thus effectively assists their comprehension and selection for different knowledge discovery tasks. Assuming a common domain form of the visualized measures, a set of contingency tables, which consists of all possible tables having the same total number of observations, is constructed. These...

Long time dynamics for the one dimensional non linear Schrödinger equation

Nicolas Burq, Laurent Thomann, Nikolay Tzvetkov (2013)

Annales de l’institut Fourier

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In this article, we first present the construction of Gibbs measures associated to nonlinear Schrödinger equations with harmonic potential. Then we show that the corresponding Cauchy problem is globally well-posed for rough initial conditions in a statistical set (the support of the measures). Finally, we prove that the Gibbs measures are indeed invariant by the flow of the equation. As a byproduct of our analysis, we give a global well-posedness and scattering result for the L 2 critical...