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

Solar and Heliospheric Physics with the Square Kilometre Array

The fields of solar radiophysics and solar system radio physics, or radio heliophysics, will benefit immensely from an instrument with the capabilities projected for SKA. Potential applications include interplanetary scintillation (IPS), radio-burst tracking, and solar spectral radio imaging with a superior sensitivity. These will provide breakthrough new insights and results in topics of fundamental importance, such as the physics of impulsive energy releases, magnetohydrodynamic oscillations and turbulence, the dynamics of post-eruptive processes, energetic particle acceleration, the structure of the solar wind and the development and evolution of solar wind transients at distances up to and beyond the orbit of the Earth. The combination of the high spectral, time and spatial resolution and the unprecedented sensitivity of the SKA will radically advance our understanding of basic physical processes operating in solar and heliospheric plasmas and provide a solid foundation for the forecasting of space weather events.Comment: 15 pages, Proceedings of Advancing Astrophysics with the Square Kilometre Array (AASKA14). 9 -13 June, 2014. Giardini Naxos, Italy. Online at http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=215, id.16

Tanaka Theorem for Inelastic Maxwell Models

We show that the Euclidean Wasserstein distance is contractive for inelastic homogeneous Boltzmann kinetic equations in the Maxwellian approximation and its associated Kac-like caricature. This property is as a generalization of the Tanaka theorem to inelastic interactions. Consequences are drawn on the asymptotic behavior of solutions in terms only of the Euclidean Wasserstein distance

On Proper Polynomial Maps of C2.\mathbb{C}^2.

Two proper polynomial maps $f_1, f_2 \colon \mathbb{C}^2 \longrightarrow \mathbb{C}^2$ are said to be \emph{equivalent} if there exist $\Phi_1, \Phi_2 \in \textrm{Aut}(\mathbb{C}^2)$ such that $f_2=\Phi_2 \circ f_1 \circ \Phi_1$. We investigate proper polynomial maps of arbitrary topological degree $d \geq 2$ up to equivalence. Under the further assumption that the maps are Galois coverings we also provide the complete description of equivalence classes. This widely extends previous results obtained by Lamy in the case $d=2$.Comment: 15 pages. Final version, to appear in Journal of Geometric Analysi

The Scintillating Tail of Comet C/2020 F3 (Neowise)

Context. The occultation of a radio source by the plasma tail of a comet can be used to probe structure and dynamics in the tail. Such occultations are rare, and the occurrence of scintillation, due to small-scale density variations in the tail, remains somewhat controversial. Aims. A detailed observation taken with the Low-Frequency Array (LOFAR) of a serendipitous occultation of the compact radio source 3C196 by the plasma tail of comet C/2020 F3 (Neowise) is presented. 3C196 tracked almost perpendicularly behind the tail, providing a unique profile cut only a short distance downstream from the cometary nucleus itself. Methods. Interplanetary scintillation (IPS) is observed as the rapid variation of the intensity received of a compact radio source due to density variations in the solar wind. IPS in the signal received from 3C196 was observed for five hours, covering the full transit behind the plasma tail of comet C/2020 F3 (Neowise) on 16 July 2020, and allowing an assessment of the solar wind in which the comet and its tail are embedded. Results. The results reveal a sudden and strong enhancement in scintillation which is unequivocally attributable to the plasma tail. The strongest scintillation is associated with the tail boundaries, weaker scintillation is seen within the tail, and previously-unreported periodic variations in scintillation are noted, possibly associated with individual filaments of plasma. Furthermore, contributions from the solar wind and comet tail are separated to measure a sharp decrease in the velocity of material within the tail, suggesting a steep velocity shear resulting in strong turbulence along the tail boundaryComment: Accepted for publication in Astronomy and Astrophysics, 8 pages, 9 figure

LOFAR observations of the quiet solar corona

The quiet solar corona emits meter-wave thermal bremsstrahlung. Coronal radio emission can only propagate above that radius, $R_\omega$, where the local plasma frequency eqals the observing frequency. The radio interferometer LOw Frequency ARray (LOFAR) observes in its low band (10 -- 90 MHz) solar radio emission originating from the middle and upper corona. We present the first solar aperture synthesis imaging observations in the low band of LOFAR in 12 frequencies each separated by 5 MHz. From each of these radio maps we infer $R_\omega$, and a scale height temperature, $T$. These results can be combined into coronal density and temperature profiles. We derived radial intensity profiles from the radio images. We focus on polar directions with simpler, radial magnetic field structure. Intensity profiles were modeled by ray-tracing simulations, following wave paths through the refractive solar corona, and including free-free emission and absorption. We fitted model profiles to observations with $R_\omega$ and $T$ as fitting parameters. In the low corona, $R_\omega < 1.5$ solar radii, we find high scale height temperatures up to 2.2e6 K, much more than the brightness temperatures usually found there. But if all $R_\omega$ values are combined into a density profile, this profile can be fitted by a hydrostatic model with the same temperature, thereby confirming this with two independent methods. The density profile deviates from the hydrostatic model above 1.5 solar radii, indicating the transition into the solar wind. These results demonstrate what information can be gleaned from solar low-frequency radio images. The scale height temperatures we find are not only higher than brightness temperatures, but also than temperatures derived from coronograph or EUV data. Future observations will provide continuous frequency coverage, eliminating the need for local hydrostatic density models

LOFAR tied-array imaging and spectroscopy of solar S bursts

Context. The Sun is an active source of radio emission that is often associated with energetic phenomena ranging from nanoflares to coronal mass ejections (CMEs). At low radio frequencies (&lt;100 MHz), numerous millisecond duration radio bursts have been reported, such as radio spikes or solar S bursts (where S stands for short). To date, these have neither been studied extensively nor imaged because of the instrumental limitations of previous radio telescopes. Aims. Here, LOw Frequency ARray (LOFAR) observations were used to study the spectral and spatial characteristics of a multitude of S bursts, as well as their origin and possible emission mechanisms. Methods. We used 170 simultaneous tied-array beams for spectroscopy and imaging of S bursts. Since S bursts have short timescales and fine frequency structures, high cadence (~50 ms) tied-array images were used instead of standard interferometric imaging, that is currently limited to one image per second. Results. On 9 July 2013, over 3000 S bursts were observed over a time period of ~8 h. S bursts were found to appear as groups of short-lived (&lt;1 s) and narrow-bandwidth (~2.5 MHz) features, the majority drifting at ~3.5 MHz s-1 and a wide range of circular polarisation degrees (2−8 times more polarised than the accompanying Type III bursts). Extrapolation of the photospheric magnetic field using the potential field source surface (PFSS) model suggests that S bursts are associated with a trans-equatorial loop system that connects an active region in the southern hemisphere to a bipolar region of plage in the northern hemisphere. Conclusions. We have identified polarised, short-lived solar radio bursts that have never been imaged before. They are observed at a height and frequency range where plasma emission is the dominant emission mechanism, however, they possess some of the characteristics of electron-cyclotron maser emission

Electronic and structural properties of superconducting MgB2_2, CaSi2_2 and related compounds

We report a detailed study of the electronic and structural properties of the 39K superconductor \mgbtwo and of several related systems of the same family, namely \mgalbtwo, \bebtwo, \casitwo and \cabesi. Our calculations, which include zone-center phonon frequencies and transport properties, are performed within the local density approximation to the density functional theory, using the full-potential linearized augmented plane wave (FLAPW) and the norm-conserving pseudopotential methods. Our results indicate essentially three-dimensional properties for these compounds; however, strongly two-dimensional $\sigma$-bonding bands contribute significantly at the Fermi level. Similarities and differences between \mgbtwo and \bebtwo (whose superconducting properties have not been yet investigated) are analyzed in detail. Our calculations for \mgalbtwo show that metal substitution cannot be fully described in a rigid band model. \casitwo is studied as a function of pressure, and Be substitution in the Si planes leads to a stable compound similar in many aspects to diborides.Comment: Revised version, Phys.Rev.B in pres

LOFAR tied-array imaging of Type III solar radio bursts

Context. The Sun is an active source of radio emission which is often associated with energetic phenomena such as solar flares and coronal mass ejections (CMEs). At low radio frequencies (< 100 MHz), the Sun has not been imaged extensively because of