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

Early Diagnosis of Neurodegenerative Diseases: What Has Been Undertaken to Promote the Transition from PET to Fluorescence Tracers

Alzheimer's Disease (AD) and Parkinson's Disease (PD) represent two among the most frequent neurodegenerative diseases worldwide. A common hallmark of these pathologies is the misfolding and consequent aggregation of amyloid proteins into soluble oligomers and insoluble beta-sheet-rich fibrils, which ultimately lead to neurotoxicity and cell death. After a hundred years of research on the subject, this is the only reliable histopathological feature in our hands. Since AD and PD are diagnosed only once neuronal death and the first symptoms have appeared, the early detection of these diseases is currently impossible. At present, there is no effective drug available, and patients are left with symptomatic and inconclusive therapies. Several reasons could be associated with the lack of effective therapeutic treatments. One of the most important factors is the lack of selective probes capable of detecting, as early as possible, the most toxic amyloid species involved in the onset of these pathologies. In this regard, chemical probes able to detect and distinguish among different amyloid aggregates are urgently needed. In this article, we will review and put into perspective results from ex vivo and in vivo studies performed on compounds specifically interacting with such early species. Following a general overview on the three different amyloid proteins leading to insoluble beta-sheet-rich amyloid deposits (amyloid beta(1-42) peptide, Tau, and alpha-synuclein), a list of the advantages and disadvantages of the approaches employed to date is discussed, with particular attention paid to the translation of fluorescence imaging into clinical applications. Furthermore, we also discuss how the progress achieved in detecting the amyloids of one neurodegenerative disease could be leveraged for research into another amyloidosis. As evidenced by a critical analysis of the state of the art, substantial work still needs to be conducted. Indeed, the early diagnosis of neurodegenerative diseases is a priority, and we believe that this review could be a useful tool for better investigating this field