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For recursively generated shifts, we provide definitive answers to two outstanding problems in the theory of unilateral weighted shifts: the Subnormality Problem ({\bf SP}) (related to the Aluthge transform) and the Square Root Problem ({\bf SRP}) (which deals with Berger measures of subnormal shifts). We use the Mellin Transform and the theory of exponential polynomials to establish that ({\bf SP}) and ({\bf SRP}) are equivalent if and only if a natural functional equation holds for the canonically associated Mellin transform. For $p$--atomic measures with $p \le 6$, our main result provides a new and simple proof of the above-mentioned equivalence. Subsequently, we obtain an example of a $7$--atomic measure for which the equivalence fails. This provides a negative answer to a problem posed by G.R. Exner in 2009, and to a recent conjecture formulated by R.E. Curto et al in 2019.

The development of state-of-the-art spectrographs has ushered in a new era in the detection and characterization of exoplanetary systems. Our objective is to utilize the high-resolution and precision capabilities of the ESPRESSO instrument to detect and measure the broad-band transmission spectrum of HD 189733b's atmosphere. Additionally, we aim to employ an improved Rossiter-McLaughlin model to derive properties related to the velocity fields of the stellar surface and to constrain the orbital architecture. Our results demonstrate a high degree of precision in fitting the observed radial velocities during transit using the improved modeling of the Rossiter-McLaughlin effect. We tentatively detect the effect of differential rotation with a confidence level of $93.4 \%$ when considering a rotation period within the photometric literature values, and $99.6\%$ for a broader range of rotation periods. For the former, the amplitude of differential rotation ratio suggests an equatorial rotation period of $11.45\pm 0.09$ days and a polar period of $14.9\pm 2$. The addition of differential rotation breaks the latitudinal symmetry, enabling us to measure the true spin-orbit angle $ \psi \approx 13.6 \pm 6.9 ^\circ$ and the stellar inclination axis angle $ i_{\star} \approx 71.87 ^{+6.91^\circ}_{-5.55^\circ}$. Moreover, we determine a sub-solar amplitude of the convective blueshift velocity $V_{CB}$ $\approx$ $-211 ^{+69} _{-61}$ m$\,$s$ ^{-1}$, which falls within the expected range for a K-dwarf host star and is compatible with both runs. Finally, we successfully retrieved the transmission spectrum of HD 189733b from the high-resolution ESPRESSO data. We observe a significant decrease in radius with increasing wavelength, consistent with the phenomenon of super-Rayleigh scattering.

We study a general class of weighted shifts whose weights $\alpha$ are given by $\alpha_n = \sqrt{\frac{p^n + N}{p^n + D}}$, where $p > 1$ and $N$ and $D$ are parameters so that $(N,D) \in (-1, 1)\times (-1, 1)$. Some few examples of these shifts have appeared previously, usually as examples in connection with some property related to subnormality. In sectors nicely arranged in the unit square in $(N,D)$, we prove that these geometrically regular weighted shifts exhibit a wide variety of properties: moment infinitely divisible, subnormal, $k$- but not $(k+1)$-hyponormal, or completely hyperexpansive, and with a variety of well-known functions (such as Bernstein functions) interpolating their weights squared or their moment sequences. They provide subshifts of the Bergman shift with geometric, not linear, spacing in the weights which are moment infinitely divisible. This new family of weighted shifts provides a useful addition to the library of shifts with which to explore new definitions and properties.

We present an analysis of Sun-as-a-star observations from four different high-resolution, stabilized spectrographs -- HARPS, HARPS-N, EXPRES, and NEID. With simultaneous observations of the Sun from four different instruments, we are able to gain insight into the radial velocity precision and accuracy delivered by each of these instruments and isolate instrumental systematics that differ from true astrophysical signals. With solar observations, we can completely characterize the expected Doppler shift contributed by orbiting Solar System bodies and remove them. This results in a data set with measured velocity variations that purely trace flows on the solar surface. Direct comparisons of the radial velocities measured by each instrument show remarkable agreement with residual intra-day scatter of only 15-30 cm/s. This shows that current ultra-stabilized instruments have broken through to a new level of measurement precision that reveals stellar variability with high fidelity and detail. We end by discussing how radial velocities from different instruments can be combined to provide powerful leverage for testing techniques to mitigate stellar signals., Comment: 17 pages, 9 figures, accepted for publication

We followed-up with ESPRESSO the K0V star HIP 29442 (TOI-469), already known to host a validated sub-Neptune companion TOI-469.01. We aim to verify the planetary nature of TOI-469.01. We modelled radial velocity and photometric time series to measure the dynamical mass, radius, and ephemeris, and to characterise the internal structure and composition of TOI-469.01. We confirmed the planetary nature of TOI-469.01. Thanks to ESPRESSO we discovered two additional close-in companions. We also detected their low signal-to-noise transit signals in the TESS light curve. HIP 29442 is a compact multi-planet system, and the three planets have orbital periods $P_{\rm orb, b}=13.63083\pm0.00003$, $P_{\rm orb, c}=3.53796\pm0.00003$, and $P_{\rm orb, d}=6.42975^{+0.00009}_{-0.00010}$ days, and we measured their masses with high precision: $m_{\rm p, b}=9.6\pm0.8~M_{\oplus}$, $m_{\rm p, c}=4.5\pm0.3~M_{\oplus}$, and $m_{\rm p, d}=5.1\pm0.4~M_{\oplus}$. We measured radii and bulk densities of all the planets (the 3$\sigma$ confidence intervals are shown in parenthesis): $R_{\rm p, b}=3.48^{+0.07 (+0.19)}_{-0.08 (-0.28)} ~R_{\oplus}$ and $\rho_{\rm p, b}=1.3\pm0.2 (0.3) g~cm^{-3}$; $R_{\rm p, c}=1.58^{+0.10 (+0.30)}_{-0.11 (-0.34)}~R_{\oplus}$ and $\rho_{\rm p, c}=6.3^{+1.7 (+6.0)}_{-1.3 (-2.7)} g~cm^{-3}$; $R_{\rm p, d}=1.37\pm0.11^{(+0.32)}_{(-0.43)}~R_{\oplus}$ and $\rho_{\rm p, d}=11.0^{+3.4 (+21.0)}_{-2.4 (-6.3)} g~cm^{-3}$. We used the more conservative 3$\sigma$ confidence intervals for the radii as input to the interior structure modelling. We find that HIP 29442 $b$ appears as a typical sub-Neptune, likely surrounded by a gas layer of pure H-He with a mass of $0.27^{+0.24}_{-0.17} M_{\oplus}$ and a thickness of $1.4\pm0.5 R_{\oplus}$. For the innermost companions HIP 29442 $c$ HIP 29442 $d$, the model supports an Earth-like composition., Comment: Accepted for publication on A&A

We report the discovery of two warm sub-Neptunes transiting the bright (G = 9.5 mag) K-dwarf HD 15906 (TOI 461, TIC 4646810). This star was observed by the Transiting Exoplanet Survey Satellite (TESS) in sectors 4 and 31, revealing two small transiting planets. The inner planet, HD 15906 b, was detected with an unambiguous period but the outer planet, HD 15906 c, showed only two transits separated by $\sim$ 734 days, leading to 36 possible values of its period. We performed follow-up observations with the CHaracterising ExOPlanet Satellite (CHEOPS) to confirm the true period of HD 15906 c and improve the radius precision of the two planets. From TESS, CHEOPS and additional ground-based photometry, we find that HD 15906 b has a radius of 2.24 $\pm$ 0.08 R$_\oplus$ and a period of 10.924709 $\pm$ 0.000032 days, whilst HD 15906 c has a radius of 2.93$^{+0.07}_{-0.06}$ R$_\oplus$ and a period of 21.583298$^{+0.000052}_{-0.000055}$ days. Assuming zero bond albedo and full day-night heat redistribution, the inner and outer planet have equilibrium temperatures of 668 $\pm$ 13 K and 532 $\pm$ 10 K, respectively. The HD 15906 system has become one of only six multiplanet systems with two warm ($\lesssim$ 700 K) sub-Neptune sized planets transiting a bright star (G $\leq$ 10 mag). It is an excellent target for detailed characterisation studies to constrain the composition of sub-Neptune planets and test theories of planet formation and evolution., Comment: 30 pages, 20 figures, 11 tables (including appendix). Published in MNRAS

Our aim is to detect and characterise long-period companions around main sequence stars (spectral types late F to early M). We use the RV method to search for exoplanets around stars. The RV variations are measured with HARPS at the ESO 3.6 metre telescope. The true mass and inclination of our heavier companions are provided by astrometry, for which we use proper motions from Hipparcos and Gaia. Five Jupiter-mass exoplanets are reported to orbit HIP54597, BD-210397 (x2), HD74698, and HD94771 with 8.9 yr, 5.2 yr, 17.4 yr, 9.4 yr, and 5.9 yr orbits, and to have minimum masses of $2.01 \pm 0.03$, $0.7 \pm 0.1$, $2.4^{+1.5}_{-0.2}$, $0.40 \pm 0.06$, and $0.53 \pm 0.03 M_J$ respectively. HD74698 also hosts a highly irradiated Neptune in a 15 day orbit with a minimum mass of $0.07 \pm 0.01 M_J$. The mass of HIP54597 b can maximally increase by 10% - 30%, the minimum mass of HD74698 c is likely equal to its true mass, and BD-210397 c has a mass of $2.66^{+0.63}_{-0.32} M_J$. HD62364 hosts a brown dwarf with a true mass of $18.77^{+0.66}_{-0.63} M_J$ in an orbit of 14 yr. HD56380B, HD221638B, and HD33473C have minimum masses within the brown dwarf limits, in orbits of 8.9 yr, 16.6 yr, and 50 yr respectively; however, astrometric measurements reveal them to be stellar binaries, with masses of $375.3^{+8.6}_{-8.4}$, $110.0^{+3.9}_{-3.7}$, and $271.0^{+3.9}_{-3.8} M_J$. The orbits of the stellar binaries HD11938 and HD61383 are incomplete. The preliminary result for HD61383 is a 0.190 $M_{\odot}$ binary in a 39 yr orbit. The secondary of the binary system HD11938 has a mass of 0.33 $M_{\odot}$ - which is confirmed by a secondary peak in the CCF - and a preliminary period of 35 yr. The origin of the 3.0 yr RV signal of HD3964 is uncertain as it shows entanglement with the magnetic cycle of the star. We finally report one more star, HD11608, with a magnetic cycle that mimics a planetary signal., Comment: 22 pages, 32 figures, accepted for publication in A&A

The realizability problem is a well-known problem in the analysis of complex systems, which can be modeled as an infinite-dimensional moment problem. More precisely, as a truncated $K-$moment problem where $K$ is the space of all possible configurations of the components of the considered system. The power of this reformulation has been already exploited in \cite{KuLeSp11}, where necessary and sufficient conditions of Haviland type have been obtained for several instances of the realizability problem. In this article we exploit this same reformulation to apply to the realizability problem the recent advances obtained in \cite{CGIK2022} for the truncated moment problem for linear functionals on general unital commutative algebras. This provides alternative proofs and sometimes extensions of several results in \cite{KuLeSp11}, allowing to finally embed them in the unified framework for the infinite-dimensional truncated moment problem presented in \cite{CGIK2022}.

Small planets located at the lower mode of the bimodal radius distribution are generally assumed to be composed of iron and silicates in a proportion similar to that of the Earth. However, recent discoveries are revealing a new group of low-density planets that are inconsistent with that description. We intend to confirm and characterize the TESS planet candidate TOI-244.01, which orbits the bright ($K$ = 7.97 mag), nearby ($d$ = 22 pc), and early-type (M2.5 V) M-dwarf star GJ 1018 with an orbital period of 7.4 days. We used Markov Chain Monte Carlo methods to model 57 precise radial velocity measurements acquired by the ESPRESSO spectrograph together with TESS photometry and complementary HARPS data. We find TOI-244 b to be a super-Earth with a radius of $R_{\rm p}$ = 1.52 $\pm$ 0.12 $\rm R_{\oplus}$ and a mass of $M_{\rm p}$ = 2.68 $\pm$ 0.30 $\rm M_{\oplus}$. These values correspond to a density of $\rho$ = 4.2 $\pm$ 1.1 $\rm g \cdot cm^{-3}$, which is below what would be expected for an Earth-like composition. We find that atmospheric loss processes may have been efficient to remove a potential primordial hydrogen envelope, but high mean molecular weight volatiles such as water could have been retained. Our internal structure modeling suggests that TOI-244 b has a $479^{+128}_{-96}$ km thick hydrosphere over a 1.17 $\pm$ 0.09 $\rm R_{\oplus}$ solid structure composed of a Fe-rich core and a silicate-dominated mantle compatible with that of the Earth. On a population level, we find two tentative trends in the density-metallicity and density-insolation parameter space for the low-density super-Earths, which may hint at their composition. With a 8$\%$ precision in radius and 12$\%$ precision in mass, TOI-244 b is among the most precisely characterized super-Earths, which, together with the likely presence of an extended hydrosphere, makes it a key target for atmospheric observations., Comment: Accepted for publication in A&A

Social networks contribute to the distribution of social capital, defined as the relationships, norms of trust and reciprocity within a community or society that facilitate cooperation and collective action. Therefore, better positioned members in a social network benefit from faster access to diverse information and higher influence on information dissemination. A variety of methods have been proposed in the literature to measure social capital at an individual level. However, there is a lack of methods to quantify social capital at a group level, which is particularly important when the groups are defined on the grounds of protected attributes. To fill this gap, we propose to measure the social capital of a group of nodes by means of the effective resistance and emphasize the importance of considering the entire network topology. Grounded in spectral graph theory, we introduce three effective resistance-based measures of group social capital, namely group isolation, group diameter and group control, where the groups are defined according to the value of a protected attribute. We denote the social capital disparity among different groups in a network as structural group unfairness, and propose to mitigate it by means of a budgeted edge augmentation heuristic that systematically increases the social capital of the most disadvantaged group. In experiments on real-world networks, we uncover significant levels of structural group unfairness when using gender as the protected attribute, with females being the most disadvantaged group in comparison to males. We also illustrate how our proposed edge augmentation approach is able to not only effectively mitigate the structural group unfairness but also increase the social capital of all groups in the network., Comment: Accepted at International AAAI Conference on Web and Social Media (ICWSM) 2025. Please cite accordingly

A historical planet-search on a sample of 1647 nearby southern main sequence stars has been ongoing since 1998 with the CORALIE spectrograph at La Silla Observatory, with a backup subprogram dedicated to the monitoring of binary stars. We review 25 years of CORALIE measurements and search for Doppler signals consistent with stellar or brown dwarf companions to produce an updated catalog of both known and previously unpublished binary stars in the planet-search sample, assessing the binarity fraction of the stellar population and providing perspective for more precise planet-search in the binary sample. We perform new analysis on the CORALIE planet-search sample radial velocity measurements, searching for stellar companions and obtaining orbital solutions for both known and new binary systems. We perform simultaneous radial velocity and proper motion anomaly fits on the subset of these systems for which Hipparcos and Gaia astrometry measurements are available, obtaining accurate estimates of true mass for the companions. We find 218 stars in the CORALIE sample to have at least one stellar companion, 130 of which are not yet published in the literature and for which we present orbital solutions. The use of proper motion anomaly allow us to derive true masses for the stellar companions in 132 systems, which we additionally use to estimate stability regions for possible planetary companions on circumprimary or circumbinary orbits. Finally, we produce detection limit maps for each star in the sample and obtain occurrence rates of $0.43^{+0.23}_{-0.11}\%$ and $12.69^{+0.87}_{-0.77}\%$ for brown dwarf and stellar companions respectively in the CORALIE sample., Comment: 34 pages, 15 figures, accepted for publication in A&A

The criminalization of poverty has been widely denounced as a collective bias against the most vulnerable. NGOs and international organizations claim that the poor are blamed for their situation, are more often associated with criminal offenses than the wealthy strata of society and even incur criminal offenses simply as a result of being poor. While no evidence has been found in the literature that correlates poverty and overall criminality rates, this paper offers evidence of a collective belief that associates both concepts. This brief report measures the societal bias that correlates criminality with the poor, as compared to the rich, by using Natural Language Processing (NLP) techniques in Twitter. The paper quantifies the level of crime-poverty bias in a panel of eight different English-speaking countries. The regional differences in the association between crime and poverty cannot be justified based on different levels of inequality or unemployment, which the literature correlates to property crimes. The variation in the observed rates of crime-poverty bias for different geographic locations could be influenced by cultural factors and the tendency to overestimate the equality of opportunities and social mobility in specific countries. These results have consequences for policy-making and open a new path of research for poverty mitigation with the focus not only on the poor but on society as a whole. Acting on the collective bias against the poor would facilitate the approval of poverty reduction policies, as well as the restoration of the dignity of the persons affected.

The deceleration of global poverty reduction in the last decades suggests that traditional redistribution policies are losing their effectiveness. Alternative ways to work towards the #1 United Nations Sustainable Development Goal (poverty eradication) are required. NGOs have insistingly denounced the criminalization of poverty, and the social science literature suggests that discrimination against the poor (a phenomenon known as aporophobia) could constitute a brake to the fight against poverty. This paper describes a proposal for an agent-based model to examine the impact that aporophobia at the institutional level has on poverty levels. This aporophobia agent-based model (AABM) will first be applied to a case study in the city of Barcelona. The regulatory environment is central to the model, since aporophobia has been identified in the legal framework. The AABM presented in this paper constitutes a cornerstone to obtain empirical evidence, in a non-invasive way, on the causal relationship between aporophobia and poverty levels. The simulations that will be generated based on the AABM have the potential to inform a new generation of poverty reduction policies, which act not only on the redistribution of wealth but also on the discrimination of the poor.

This paper clarifies why bias cannot be completely mitigated in Machine Learning (ML) and proposes an end-to-end methodology to translate the ethical principle of justice and fairness into the practice of ML development as an ongoing agreement with stakeholders. The pro-ethical iterative process presented in the paper aims to challenge asymmetric power dynamics in the fairness decision making within ML design and support ML development teams to identify, mitigate and monitor bias at each step of ML systems development. The process also provides guidance on how to explain the always imperfect trade-offs in terms of bias to users.

Since 2005 ESO has been working with its community and industry to develop an extremely large optical/infrared telescope. ESO's Extremely Large Telescope, or ELT for short, is a revolutionary ground-based telescope that will have a 39-metre main mirror and will be the largest visible and infrared light telescope in the world. To address specific topics that are needed for the science operations and calibrations of the telescope, thirteen specific working groups were created to coordinate the effort between ESO, the instrument consortia, and the wider community. We describe here the goals of these working groups as well as their achievements so far., Comment: 8 pages, 4 figures

This is an extended version of our survey article, "Graph rules for recurrent neural network dynamics," to appear in the April 2023 edition of the Notices of the AMS. It includes additional results, derivations, figures, references, and a set of open questions., Comment: 32 pages (double-column), 25 figures, 2 tables

In this study we evaluated the task-based image quality of a low contrast clinical task for the abdomen protocol (e.g., pancreatic tumour) of three different CT vendors, exploiting three model-based iterative reconstruction (MBIR) levels. We used three CT systems equipped with a full, partial, advanced MBIR algorithms. Acquisitions were performed on a phantom at three dose levels. Acquisitions were reconstructed with a standard kernel, using filtered back projection algorithm (FBP) and three levels of the MBIR. The noise power spectrum (NPS), the normalized one (nNPS) and the task-based transfer function (TTF) were computed following the method proposed by the American Association of Physicists in Medicine task group report-233 (AAPM TG-233). Detectability index (d') of a small lesion (small feature; 100 HU and 5-mm diameter) was calculated using non-prewhitening with eye-filter model observer (NPWE).The nNPS, NPS and TTF changed differently depending on CT system. Higher values of d' were obtained with advanced-MBIR, followed by full-MBIR and partial-MBIR.Task-based image quality was assessed for three CT scanners of different vendors, considering a clinical question. Detectability can be a tool for protocol optimisation and dose reduction since the same dose levels on different scanners correspond to different d' values., Comment: 7 pages, 5 figures, 3 tables

This is a brief overview of results from [arXiv:2107.10244, ref 11], on network architectures that produce sequential dynamics in a special family of inhibition-dominated neural networks. It was written for SIAM DSWeb., Comment: 6 pages, 4 figures, appeared in SIAM DSWeb, 2022

Context. Radial velocity (RV) measurements induced by the presence of planets around late-type stars are contaminated by stellar signals that are of the order of a few meters per second in amplitude, even for the quietest stars. Those signals are induced by acoustic oscillations, convective granulation patterns, active regions co-rotating with the stellar surface, and magnetic activity cycles. Aims. This study investigates the properties of all coherent stellar signals seen on the Sun on timescales up to its sidereal rotational period. By combining HARPS and HARPS-N solar data spanning several years, we are able to clearly resolve signals on timescales from minutes to several months. Methods. We use a Markov Chain Monte Carlo (MCMC) mixture model to determine the quality of the solar data based on the expected airmass-magnitude extinction law. We then fit the velocity power spectrum of the cleaned and heliocentric RVs with all known variability sources, to recreate the RV contribution of each component. Results. After rejecting variations caused by poor weather conditions, we are able to improve the average intra-day root mean square (RMS) value by a factor of ~1.8. On sub-rotational timescales, we are able to fully recreate the observed RMS of the RV variations. In order to also include rotational components and their strong alias peaks introduced by nightly sampling gaps, the alias powers are accounted for by being redistributed to the central frequencies of the rotational harmonics. Conclusions. In order to enable a better understanding and mitigation of stellar activity sources, their respective impact on the total RV must be well-measured and characterized. We are able to recreate RV components up to rotational timescales, which can be further used to analyse the impact of each individual source of stellar signals on the detectability of exoplanets., Comment: Accepted for publication in A&A

We study the time-dependent moments and associated polynomials arising from the partial differential equation $\partial_t f = \nu\Delta f + g\cdot\nabla f + h\cdot f$, and consider in detail the dual equation. For the heat equation we find that several non-negative polynomials which are not sums of squares become sums of squares under the heat equation in finite time. We show that every non-negative polynomial in $\mathbb{R}[x,y,z]_{\leq 4}$ becomes a sum of squares in finite time under the heat equation. We solve the problem of moving atoms under the equation $\partial_t f = g\cdot\nabla f + h\cdot f$ with $f_0 = \mu_0$ being a finitely atomic measure. The time evolution $\mu_t = \sum_{i=1}^k c_i(t)\cdot \delta_{x_i(t)}$ of the atom positions $x_i(t)$ are described by the transport term $g\cdot\nabla$ and the time-dependent coefficients $c_i(t)$ have an explicit solution depending on $x_i(t)$, $h$, and $\mathrm{div}\, g$., Comment: Extended Results

We present radial velocity follow-up obtained with ESPRESSO of the M-type star LTT 1445A (TOI-455), for which a transiting planet b with an orbital period of~5.4 days was detected by TESS. We report the discovery of a second transiting planet (LTT 1445A c) and a third non-transiting candidate planet (LTT 1445A d) with orbital periods of 3.12 and 24.30 days, respectively. The host star is the main component of a triple M-dwarf system at a distance of 6.9 pc. We used 84 ESPRESSO high-resolution spectra to determine accurate masses of 2.3$\pm$0.3 $\mathrm{M}_\oplus$ and 1.0$\pm$0.2 $\mathrm{M}_\oplus$ for planets b and c and a minimum mass of 2.7$\pm$0.7 $\mathrm{M}_\oplus$ for planet d. Based on its radius of 1.43$\pm0.09$ $\mathrm{R}_\oplus$ as derived from the TESS observations, LTT 1445A b has a lower density than the Earth and may therefore hold a sizeable atmosphere, which makes it a prime target for the James Webb Space Telescope. We used a Bayesian inference approach with the nested sampling algorithm and a set of models to test the robustness of the retrieved physical values of the system. There is a probability of 85$\%$ that the transit of planet c is grazing, which results in a retrieved radius with large uncertainties at 1.60$^{+0.67}_{-0.34}$ $\mathrm{R}_\oplus$. LTT 1445A d orbits the inner boundary of the habitable zone of its host star and could be a prime target for the James Webb Space Telescope., Comment: 31 pages, 20 figures Accepted A&A

High-resolution spectroscopy studies of ultra-hot Jupiters have been key in our understanding of exoplanet atmospheres. Observing into the atmospheres of these giant planets allows for direct constraints on their atmospheric compositions and dynamics while laying the groundwork for new research regarding their formation and evolution environments. Two of the most well-studied ultra-hot Jupiters are WASP-76b and WASP-121b, with multiple detected chemical species and strong signatures of their atmospheric dynamics. We take a new look at these two exceptional ultra-hot Jupiters by reanalyzing the transit observations taken with ESPRESSO at the Very Large Telescope and attempt to detect additional species. To extract the planetary spectra of the two targets, we corrected for the telluric absorption and removed the stellar spectrum contributions. We then exploited new synthetic templates that were specifically designed for ultra-hot Jupiters in combination with the cross-correlation technique to unveil species that remained undetected by previous analyses. We add a novel detection of Ba+ to the known atmospheric compositions of WASP-76b and WASP-121b, the heaviest species detected to date in any exoplanetary atmosphere, with additional new detections of Co and Sr+ and a tentative detection of Ti+ for WASP-121b. We also confirm the presence of Ca+, Cr, Fe, H, Li, Mg, Mn, Na, and V on both WASP-76b and WASP-121b, with the addition of Ca, Fe+, and Ni for the latter. Finally, we also confirm the clear asymmetric absorption feature of Ca+ on WASP-121b, with an excess absorption at the bluer wavelengths and an effective planet radius beyond the Roche lobe. This indicates that the signal may arise from the escape of planetary atmosphere., Comment: 21 pages, 16 figures. Published in A&A Volume 666, October 2022 - Letter to the Editor

In this paper, we study the truncated matrix moment problem in one variable through recursive matrix extensions. \ We give necessary and sufficient conditions for a recursive matrix extension of finite data to be a matrix moment sequence in the classical cases of Hamburger, Stieltjes, and Hausdorff moment problems. \ We also discuss matricial subnormal completion and matricial $k$--hyponormal completion problems and provide an analog of Stampfli's Theorem on flat propagation for $2$--hyponormal matricial weighted shifts., Comment: 27 pages

An outline of J\"org Eschmeier's main mathematical contributions is organized both on a historical perspective, as well as on a few distinct topics. The reader can grasp from our essay the dynamics of spectral theory of commutative tuples of linear operators during the last half century. Some clear directions of future research are also underlined., Comment: 13 pages, 5 pictures