Remarks on the Emergence of Weak Euler Solutions in the Vanishing Viscosity Limit

Journal of Nonlinear Science - We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime $$L^2$$ weak...     

How to Utilize my App Reviews? A Novel Topics Extraction Machine Learning Schema for Strategic Business Purposes

Acquiring knowledge about users’ opinion and what they say regarding specific features within an app, constitutes a solid steppingstone for understanding their needs and concerns. App review utilization helps project management teams to identify threads and opportunities for app software maintenance, optimization and strategic marketing purposes. Nevertheless, app user review classification for identifying valuable gems of information for app software improvement, is a complex and multidimensional issue. It requires foresight and multiple combinations of sophisticated text pre-processing, feature extraction and machine learning methods to efficiently classify app reviews into specific topics. Against this backdrop, we propose a novel feature engineering classification schema that is capable to identify more efficiently and earlier terms-words within reviews that could be classified into specific topics. For this reason, we present a novel feature extraction method, the DEVMAX.DF combined with different machine learning algorithms to propose a solution in app review classification problems. One step further, a simulation of a real case scenario takes place to validate the effectiveness of the proposed classification schema into different apps. After multiple experiments, results indicate that the proposed schema outperforms other term extraction methods such as TF.IDF and χ² to classify app reviews into topics. To this end, the paper contributes to the knowledge expansion of research and practitioners with the purpose to reinforce their decision-making process within the realm of app reviews utilization.     

Inviscid Limit of Vorticity Distributions in the Yudovich Class

We prove that given initial data , forcing and any T > 0, the solutions u^ν of Navier-Stokes converge strongly in for any p ∈ [1, ∞) to the unique Yudovich weak solution u of the Euler equations. A consequence is that vorticity distribution functions converge to their inviscid counterparts. As a by-product of the proof, we establish continuity of the Euler solution map for Yudovich solutions in the L^p vorticity topology. The main tool in these proofs is a uniformly controlled loss of regularity property of the linear transport by Yudovich solutions. Our results provide a partial foundation for the Miller-Robert statistical equilibrium theory of vortices as it applies to slightly viscous fluids. © 2020 Wiley Periodicals LLC.     

Turbulent Cascade Direction and Lagrangian Time-Asymmetry

Journal of Nonlinear Science - We establish Lagrangian formulae for energy conservation anomalies involving the discrepancy between short-time two-particle dispersion forward and backward in time....     

Reaction de paiticipation d'amines tertiaires : applictions a la synthese d'aminoglycopyramosides

Methyl glycopyranosides with diallylamino and mesylate groups in $\text{trans}$ relationship undergo an intramolecular reaction in which the amino group assists the replacement of the mesylate group by a nucleophile. Such a reaction may result in a 1,2-shift of the nitrogen atom depending on which carbon atom of the intermediate aziridinium ion is attacked by the nucleophile. A further N,N-dideallylation using palladium on charcoal leads, for example, to chloro- or fluoroaminoglycopyranosides with a good regioselectivity.