In this note, we rigorously justify a singular approximation of the incompressible Navier-Stokes equations. Our approximation combines two classical approximations of the incompressible Euler equations: a standard relaxation approximation, but with a diffusive scaling, and the Euler-Poisson equations in the quasineutral regime.

We consider a coperative control approach to address safety and optimality issues for simple model of a car-like robot. The approach makes use of optimal syntheses and Krasovskii solutions to discontinuous ODEs.

We provide a general approach to deal with entropy solutions to scalar conservation laws presenting nonclassical shocks.

We consider a hybrid control system and general optimal control problems for this system. We suppose that the switching strategy imposes restrictions on control sets and we provide necessary conditions for an optimal hybrid trajectory, stating a Hybrid Necessary Principle (HNP). Our result generalizes various necessary principles available in the literature.

In this article an accurate and efficient technique for tissue typing is presented. The proposed technique is based on Canonical Correlation Analysis, a statistical method able to simultaneously exploit the spectral and spatial information characterizing the Magnetic Resonance Spectroscopic Imaging (MRSI) data. Recently, Canonical Correlation Analysis has been successfully applied to other types of biomedical data, such as functional MRI data.

Accurate quantitation of Magnetic Resonance Spectroscopy (MRS) signals is an essential step before converting the estimated signal parameters, such as frequencies, damping factors, and amplitudes, into biochemical quantities (concentration, pH). Several subspace-based parameter estimators have been developed for this task, which are efficient and accurate time-domain algorithms. However, they suffer from a serious drawback: they allow only a limited inclusion of prior knowledge which is important for accuracy and resolution.

Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in function of the alphabets.