Some notions of subharmonicity over the quaternions

This works introduces several notions of subharmonicity for real-valued functions of one quaternionic variable. These notions are related to the theory of slice regular quaternionic functions introduced by Gentili and Struppa in 2006. The interesting properties of these new classes of functions are studied and applied to construct the analogs of Green's functions.Comment: 16 page

Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

Abstract Starting from a kinetic BGK-model for a rarefied polyatomic gas, based on a molecular structure of discrete internal energy levels, an asymptotic Chapman-Enskog procedure is developed in the asymptotic continuum limit in order to derive consistent fluid-dynamic equations for macroscopic fields at Navier-Stokes level. In this way, the model allows to treat the gas as a mixture of mono-atomic species. Explicit expressions are given not only for dynamical pressure, but also for shear stress, diffusion velocities, and heat flux. The analysis is shown to deal properly also with a mixture of reactive gases, endowed for simplicity with translational degrees of freedom only, in which frame analogous results can be achieved

Shock wave structure of multi-temperature Euler equations from kinetic theory for a binary mixture

A multi-temperature hydrodynamic limit of kinetic equations is employed for the analysis of the steady shock problem in a binary mixture. Numerical results for varying parameters indicate possible occurrence of either smooth profiles or of weak solutions with one or two discontinuities. \ua9 2014 Springer Science+Business Media Dordrecht

Regular vs. classical M\"obius transformations of the quaternionic unit ball

The regular fractional transformations of the extended quaternionic space have been recently introduced as variants of the classical linear fractional transformations. These variants have the advantage of being included in the class of slice regular functions, introduced by Gentili and Struppa in 2006, so that they can be studied with the useful tools available in this theory. We first consider their general properties, then focus on the regular M\"obius transformations of the quaternionic unit ball B, comparing the latter with their classical analogs. In particular we study the relation between the regular M\"obius transformations and the Poincar\'e metric of B, which is preserved by the classical M\"obius transformations. Furthermore, we announce a result that is a quaternionic analog of the Schwarz-Pick lemma.Comment: 14 page

Kinetic models for reactive mixtures: Problems and applications

Problems related to physical consistency and practical application of kinetic BGK models for reactive mixtures are investigated. In particular, two approximation strategies are discussed, relevant to the different physical scenarios of slow and fast chemical reactions, respectively. The former is tested versus the steady shock problem in comparison to available hydrodynamic results. For the latter, allowing for an explicit proof of the H-theorem, a preliminary sample is shown of the space homogeneous calculations in progress

Covid-19 and ENT practice: Our experience: ENT outpatient department, ward and operating room management during the SARS-CoV-2 pandemic

Coronavirus COVID-19 SARS-CoV-2 ENT Otolaryngolog

Random planar trees and the Jacobian conjecture

We develop a probabilistic approach to the celebrated Jacobian conjecture, which states that any Keller map (i.e. any polynomial mapping $F\colon \mathbb{C}^n \to \mathbb{C}^n$ whose Jacobian determinant is a nonzero constant) has a compositional inverse which is also a polynomial. The Jacobian conjecture may be formulated in terms of a problem involving labellings of rooted trees; we give a new probabilistic derivation of this formulation using multi-type branching processes. Thereafter, we develop a simple and novel approach to the Jacobian conjecture in terms of a problem about shuffling subtrees of $d$-Catalan trees, i.e. planar $d$-ary trees. We also show that, if one can construct a certain Markov chain on large $d$-Catalan trees which updates its value by randomly shuffling certain nearby subtrees, and in such a way that the stationary distribution of this chain is uniform, then the Jacobian conjecture is true. Finally, we show that the subtree shuffling conjecture is true in a certain asymptotic sense, and thereafter use our machinery to prove an approximate version of the Jacobian conjecture, stating that inverses of Keller maps have small power series coefficients for their high degree terms.Comment: 36 pages, 4 figures. Section 2.5 added, Section 3 expanded, further minor edit