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In a recent paper of the authors together with A. Aleman, it is shown that the Bloch space $\mathcal{B}$ in the unit disc has the following radicality property: if an analytic function $g$ satisfies that $g^n\in \mathcal{B}$, then $g^m\in \mathcal{B}$, for all $m\le n$. Since $\mathcal{B}$ coincides with the space $\mathcal{T}(A^p_\alpha)$ of analytic symbols $g$ such that the Volterra-type operator $T_gf(z)= \int_0^z f(\zeta)g'(\zeta)\,d\zeta$ is bounded on the classical weighted Bergman space $A^p_\alpha$, the radicality property was used to study the composition of paraproducts $T_g$ and $S_gf=T_fg$ on $A^p_{\alpha}$. Motivated by this fact, we prove that $\mathcal{T}(A^p_\omega)$ also has the radicality property, for any radial weight $\omega$. Unlike the classical case, the lack of a precise description of $\mathcal{T}(A^p_\omega)$ for a general radial weight, induces us to prove the radicality property for $A^p_\omega$ from precise norm-operator results for compositions of analytic paraproducts.

The Centaur (60558) Echeclus was discovered on March 03, 2000, orbiting between the orbits of Jupiter and Uranus. After exhibiting frequent outbursts, it also received a comet designation, 174P. If the ejected material can be a source of debris to form additional structures, studying the surroundings of an active body like Echeclus can provide clues about the formation scenarios of rings, jets, or dusty shells around small bodies. Stellar occultation is a handy technique for this kind of investigation, as it can, from Earth-based observations, detect small structures with low opacity around these objects. Stellar occultation by Echeclus was predicted and observed in 2019, 2020, and 2021. We obtain upper detection limits of rings with widths larger than 0.5 km and optical depth of $\tau$ = 0.02. These values are smaller than those of Chariklo's main ring; in other words, a Chariklo-like ring would have been detected. The occultation observed in 2020 provided two positive chords used to derive the triaxial dimensions of Echeclus based on a 3D model and pole orientation available in the literature. We obtained $a = 37.0\pm0.6$ km, $b = 28.4 \pm 0.5$ km, and $c= 24.9 \pm 0.4$ km, resulting in an area-equivalent radius of $30.0 \pm 0.5$ km. Using the projected limb at the occultation epoch and the available absolute magnitude ($\rm{H}_{\rm{v}} = 9.971 \pm 0.031$), we calculate an albedo of $p_{\rm{v}} = 0.050 \pm 0.003$. Constraints on the object's density and internal friction are also proposed., Comment: Accepted for publication on MNRAS

This work aims at constraining the size, shape, and geometric albedo of the dwarf planet candidate 2002 MS4 through the analysis of nine stellar occultation events. Using multichord detection, we also studied the object's topography by analyzing the obtained limb and the residuals between observed chords and the best-fitted ellipse. We predicted and organized the observational campaigns of nine stellar occultations by 2002 MS4 between 2019 and 2022, resulting in two single-chord events, four double-chord detections, and three events with three to up to sixty-one positive chords. Using 13 selected chords from the 8 August 2020 event, we determined the global elliptical limb of 2002 MS4. The best-fitted ellipse, combined with the object's rotational information from the literature, constrains the object's size, shape, and albedo. Additionally, we developed a new method to characterize topography features on the object's limb. The global limb has a semi-major axis of 412 $\pm$ 10 km, a semi-minor axis of 385 $\pm$ 17 km, and the position angle of the minor axis is 121 $^\circ$ $\pm$ 16$^\circ$. From this instantaneous limb, we obtained 2002 MS4's geometric albedo and the projected area-equivalent diameter. Significant deviations from the fitted ellipse in the northernmost limb are detected from multiple sites highlighting three distinct topographic features: one 11 km depth depression followed by a 25$^{+4}_{-5}$ km height elevation next to a crater-like depression with an extension of 322 $\pm$ 39 km and 45.1 $\pm$ 1.5 km deep. Our results present an object that is $\approx$138 km smaller in diameter than derived from thermal data, possibly indicating the presence of a so-far unknown satellite. However, within the error bars, the geometric albedo in the V-band agrees with the results published in the literature, even with the radiometric-derived albedo.

Context. Bright stellar positions are now known with an uncertainty below 1 mas thanks to Gaia DR2. Between 2019-2020, the Galactic plane will be the background of Jupiter. The dense stellar background will lead to an increase in the number of occultations, while the Gaia DR2 catalogue will reduce the prediction uncertainties for the shadow path. Aims. We observed a stellar occultation by the Galilean moon Europa (J2) and propose a campaign for observing stellar occultations for all Galilean moons. Methods. During a predicted period of time, we measured the light flux of the occulted star and the object to determine the time when the flux dropped with respect to one or more reference stars, and the time that it rose again for each observational station. The chords obtained from these observations allowed us to determine apparent sizes, oblatness, and positions with kilometre accuracy. Results. We present results obtained from the first stellar occultation by the Galilean moon Europa observed on 2017 March 31. The apparent fitted ellipse presents an equivalent radius of 1561.2 $\pm$ 3.6 km and oblatenesses 0.0010 $\pm$ 0.0028. A very precise Europa position was determined with an uncertainty of 0.8 mas. We also present prospects for a campaign to observe the future events that will occur between 2019 and 2021 for all Galilean moons. Conclusions. Stellar occultation is a suitable technique for obtaining physical parameters and highly accurate positions of bright satellites close to their primary. A number of successful events can render the 3D shapes of the Galilean moons with high accuracy. We encourage the observational community (amateurs included) to observe the future predicted events., Comment: 10 pages, 16 figures, 4 tables, A&A Letter doi:10.1051/0004-6361/201935500

As it is well known, the spectrum $ {\rm sp\,} \Gamma$ (of the adjacency matrix $A$) of a graph $\Gamma$, with $d$ distinct eigenvalues other than its spectral radius $\lambda_0$, usually provides a lot of information about the structure of $G$. Moreover, from ${\rm sp\,}\Gamma$ we can define the so-called predistance polynomials $p_0,\ldots,p_d\in {\mathbb R}_d[x]$, with ${\rm dgr\,} p_i=i$, $i=0,\ldots,d$, which are orthogonal with respect to the scalar product $\langle f, g\rangle_{\Gamma} =\frac{1}{n}{\rm tr\,}(f(A)g(A))$ and normalized in such a way that $\|p_i\|_{\Gamma}^2=p_i(\lambda_0)$. They can be seen as a generalization for any graph of the distance polynomials of a distance-regular graph. Going further, we consider the preintersection numbers $\xi_{ij}^h$ for $i,j,h\in\{0,\ldots,d\}$, which generalize the intersection numbers of a distance-regular graph, and they are the Fourier coefficients of $p_ip_j$ in terms of the basis $\{p_h\}_{0\le h\le d}$. The aim of this paper is to show that, for any graph $\Gamma$, the information contained in its spectrum, predistance polynomials, and preintersection numbers is equivalent. Also, we give some characterizations of distance-regularity which are based on the above concepts. For instance, we comment upon the so-called spectral excess theorem stating that a connected regular graph $G$ is distance-regular if and only if its spectral excess, which is the value of $p_d$ at $\lambda_0$, equals the average excess, that is, the mean of the numbers of vertices at extremal distance $d$ from every vertex.

In this paper we give sharp norm estimates for the Bergman operator acting from weighted mixed-norm spaces to weighted Hardy spaces in the ball, endowed with natural norms., Comment: Minor revisions

The local spectrum of a vertex set in a graph has been proven to be very useful to study some of its metric properties. It also has applications in the area of pseudo-distance-regularity around a set and can be used to obtain quasi-spectral characterizations of completely (pseudo-)regular codes. In this paper we study the relation between the local spectrum of a vertex set and the local spectrum of each of its subconstituents. Moreover, we obtain a new characterization for completely pseudo-regular codes, and consequently for completely regular codes, in terms of the relation between the local spectrum of an extremal set of vertices and the local spectrum of its antipodal set. We also present a new proof of the version of the Spectral Excess Theorem for extremal sets of vertices.