1,231 research outputs found
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
Sublingual isosorbide dinitrate to improve technetium-99m-teboroxime perfusion defect reversibility.
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 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 -Catalan trees, i.e. planar -ary trees. We also show that, if
one can construct a certain Markov chain on large -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
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