We investigate the long-time properties of the two-dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size ?. Under the classical Miles-Howard stability condition on the Richardson number, we prove that the system experiences a shear-buoyancy instability: the density variation and velocity undergo an O(t-1/2) inviscid damping while the vorticity and density gradient grow as O(t1/2). The result holds at least until the natural, nonlinear timescale t??-2.

Preservation of the angle of reflection when an internal gravity wave hits a sloping boundary generates a focusing mechanism if the angle between the direction of propagation of the incident wave and the horizontal is close to the slope inclination (near-critical reflection). This paper provides an explicit description of the leading approximation of the unique Leray solution to the near-critical reflection of internal waves from a slope in the form of a beam wave.

This contribution outlines current research aimed at developing models for personalized type 2 diabetes mellitus (T2D) prevention in the framework of the European project PRAESIIDIUM (Physics Informed Machine Learn-ing-Based Prediction and Reversion of Impaired Fasting Glucose Management) aimed at building a digital twin for preventing T2D in patients at risk.

This article is concerned with the rigorous justification of the hydrostatic limit for continuously stratified incompressible fluids under the influence of gravity. The main peculiarity of this work with respect to previous studies is that no (regularizing) viscosity contribution is added to the fluid-dynamics equations and only diffusivity effects are included.

Dissolution of drug from its solid form to a dissolved form is an important consideration in the design and optimization of drug delivery devices, particularly owing to the abundance of emerging compounds that are extremely poorly soluble. When the solid dosage form is encapsulated, for example by the porous walls of an implant, the impact of the encapsulant drug transport properties is a further confounding issue. In such a case, dissolution and diffusion work in tandem to control the release of drug.

We study the consistency and the oracle properties of the adaptive Lasso estimator for the coefficients of a linear AR(p) time series with a strictly stationary white noise (not necessarily described by i.i.d. r.v.'s). We apply the results to INAR(p) time series and to the non-parametric inference of the fertility function of a Hawkes point process. We present some numerical simulations to emphasize the advantages of the proposed procedure with respect to more classical ones and finally we apply it to a set of epidemiological data

A new technique for nonparametric regression of multichannel signals is presented. The technique is based on the use of the Rational-Dilation Wavelet Transform (RADWT), equipped with a tunable Q-factor able to provide sparse representations of functions with different oscillations persistence. In particular, two different frames are obtained by two RADWT with different Q-factors that give sparse representations of functions with low and high resonance.

In recent years there has been a growing interest in frame based de-noising procedures. The advantage of frames with respect to classical orthonor- mal bases (e.g. wavelet, Fourier, polynomial) is that they can furnish an efficient representation of a more broad class of signals. For example, signals which have fast oscillating behavior as sonar, radar, EEG, stock market, audio and speech are much more well represented by a frame (with similar oscillating characteristic) than by a classical wavelet basis, although the frame representation for such kind of signals can be not properly sparse.