New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{?1/4}$ as time t goes to infinity. This improves the works of Selberg and da Silva (2017) [30] and Tesfahun (2017) [34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.     

A-posteriori KAM theory with optimal estimates for partially integrable systems

In this paper we present a-posteriori KAM results for existence of d-dimensional isotropic invariant tori for n-DOF Hamiltonian systems with additional $n?d$ independent first integrals in involution. We carry out a covariant formulation that does not require the use of action-angle variables nor symplectic reduction techniques. The main advantage is that we overcome the curse of dimensionality avoiding the practical shortcomings produced by the use of reduced coordinates, which may cause difficulties and underperformance when quantifying the hypotheses of the KAM theorem in such reduced coordinates. The results include ordinary and (generalized) iso-energetic KAM theorems. The approach is suitable to perform numerical computations and computer assisted proofs.     

Separation technique based on electrophoresis,chromatography and magnetism phenomena: the migration time and peak broadening

1. Download : Download high-res image (108KB)
2. Download : Download full-size image

     

Pericyclic reactions in the synthesis of new 5-aryl-5,6-dihydroquinolino[2,1-b]quinazolin-12-ones

1. Download high-res image (52KB)
2. Download full-size image

     

Unexpected formation of dinaphthoaza-17-crown-5 ether containing γ-aminopiperidine subunit

1. Download : Download high-res image (90KB)
2. Download : Download full-size image

     

DFT B3LYP/6-311+G* calculation study of a new nonclassical mechanism of electrophilic functionalization of aromatic C–H bond via aryl cation formation

1. Download : Download high-res image (84KB)
2. Download : Download full-size image

     

Going Off the Grid: Iterative Model Selection for Biclustered Matrix Completion

We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly minimizing an information criterion to select an appropriate amount of row and column smoothing, namely, to perform model selection. We also discuss how to exploit the special structure of the problem to scale up the estimation and model selection procedure via the Hutchinson estimator, combined with a stochastic Quasi-Newton approach. Supplementary material for this article is available online.