DC and JGS were partially supported by the grant MTM2014-59488-P (Spain) and ICMAT Severo Ochoa project SEV-2011-0087. JGS was partially supported by an AMS-Simons Travel Grant. AZ acknowledges partial support by NSF grant DMS-1056327. We thank Prin…

In this note, we show that there exist solutions of the Muskat problem which shift stability regimes in the following sense: they start stable, then …

Jodeit’s theorem [Jo] provides another approach to de Leeuw’s compactification by looking at extensions of Fourier multipliers. He proved that any Lp-bounded Fourier multiplier on Zn is the restriction of a Lp-bounded Fourier multiplier on Rn. To be…

Let H be a subgroup of some locally compact group G. Assume H is approximable by discrete subgroups and G admits neighborhood bases which are "almost…

This paper develops different discretization schemes for nonholonomic mechanical systems through a discrete geometric approach. The proposed methods …

Real time large scale streaming data pose major challenges to forecasting, in particular defying the presence of human experts to perform the corresp…

This article reviews several recently developed Lagrangian tools and shows how their combined use succeeds in obtaining a detailed description of pur…

This section is devoted to prove the main result of this paper:

Motivated by an equation arising in magnetohydrodynamics, we address the well-posedness theroy for the non-diffusive magneto-geostrophic equation. Na…

We now study the validity of our results of section 2 in the operator valued setting. Our models are the operator valued BMO in [23] and the large BMO spaces in [3]. Hence, assume that M is a —possibly noncommutative— von Neumann algebra equipped wi…

Given a measure $\mu$ of polynomial growth, we refine a deep result by David and Mattila to construct an atomic martingale filtration of $\mathrm{sup…

This paper shows finite time singularity formation for the Muskat problem in a stable regime. The framework we found is with a dry region, where the …

We classify symplectically foliated fillings of certain contact foliated manifolds. We show that up to symplectic deformation, the unique minimal sym…

We will prove our estimates for T⋆; the ones for T are completely analogous.

We obtain the off-diagonal Muckenhoupt-Wheeden conjecture for Calder\'on-Zygmund operators. Namely, given $1<p<q<\infty$ and a pair of weights $(u,v)…

We present two maximally superintegrable Hamiltonian systems ${\cal H}_\lambda$ and ${\cal H}_\eta$ that are defined, respectively, on an $N$-dimensi…

Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite…

In this paper we present and illustrate a general methodology to apply KAM theory in particular problems, based on an {\em a posteriori} approach. We…

We prove the existence of infinitely many mixing solutions for the Muskat problem in the fully unstable regime displaying a linearly degraded macrosc…

Neural networks are popular models for regression. They are often trained via back-propagation to find a value of the weights that correctly predicts…

We now demonstrate the bootstrap argument used to prove our goal. Theorem (5.1) tell us that the following estimate holds for k≥6:

We consider the 2D Boussinesq equations with a velocity damping term in a strip $\mathbb{T}\times[-1,1]$, with impermeable walls. In this physical sc…

Classification problems in security settings are usually contemplated as confrontations in which one or more adversaries try to fool a classifier to …

Motivated by a question of Rubel, we consider the problem of characterizing which noncompact hypersurfaces in $\RR^n$ can be regular level sets of a …

Let us say that an $n$-sided polygon is semi-regular if it is circumscriptible and its angles are all equal but possibly one, which is then larger th…

We will now state second order necessary conditions for optimal control problems applying a formalism similar to Hamiltonian formalism used for continuous-time systems. In order to be able to use duality of vectors and covectors we assume that M is …

We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary condition…

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