Pseudohermitian invariants and classification of CR mappings in generalized ellipsoids

We discuss the problem of classifying all local CR diffeomorphisms of a strictly pseudoconvex surface. Our method exploits the Tanaka--Webster pseudohermitian invariants, their transformation formulae, and the Chern--Moser invariants. Our main application concerns a class of generalized ellipsoids where we classify all local CR mappings.Comment: Accepted version, to appear on J. Math. Soc. Japa

Detectability of substellar companions around white dwarfs with Gaia

To date not a single-bona fide planet has been identified orbiting a single white dwarf. In fact we are ignorant about the final configuration of >95% of planetary systems. Theoretical models predict a gap in the final distribution of orbital periods, due to the opposite effects of stellar mass loss (planets pushed outwards) and tidal interactions (planets pushed inwards) during the RGB and the AGB stellar expansions. Over its five year primary mission, Gaia is expected to astrometrically detect the first (few tens of) WD massive planets/BDs giving first evidence that WD planets exist, at least those in wide orbits. In this article we present preliminary results of our simulations of what Gaia should be able to find in this field.Comment: Proceedings of the 19th European Workshop on White Dwarfs (Montr\'eal 11-15 August 2014). To appear on ASP Conference Series; 4 pages, 2 figure

The Gaia Data Release 1 parallaxes and the distance scale of Galactic planetary nebulae

In this paper we gauge the potentiality of Gaia in the distance scale calibration of planetary nebulae (PNe) by assessing the impact of DR1 parallaxes of central stars of Galactic PNe (CSPNe) against known physical relations. For selected PNe targets with state-of-the-art data on angular sizes and fluxes, we derive the distance-dependent parameters of the classical distance scales, i.e., physical radii and ionized masses, from DR1 parallaxes; we propagate the uncertainties in the estimated quantities and evaluate their statistical properties in the presence of large relative parallax errors; we populate the statistical distance scale diagrams with this sample and discuss its significance in light of existing data and current calibrations. We glean from DR1 parallaxes 8 CSPNe with S/N$>$1. We show that this set of potential calibrators doubles the number of extant trigonometric parallaxes (from HST and ground-based), and increases by two orders of magnitude the domain of physical parameters probed previously. We then use the combined sample of suitable trigonometric parallaxes to fit the physical-radius-to-surface-brightness relation. This distance scale calibration, although preliminary, appears solid on statistical grounds, and suggestive of new PNe physics. With the tenfold improvement in PNe number statistics and astrometric accuracy expected from future Gaia releases the new distance scale, already very intriguing, will be definitively constrained.Comment: New Astronomy, in pres

Isoperimetric inequality in the Grushin plane

We prove a sharp isoperimetric inequality in the Grushin plane and compute the corresponding isoperimetric set

John and uniform domains in generalized Siegel boundaries

Given the pair of vector fields $X=\partial_x+|z|^{2m}y\partial_t$ and $Y=\partial_y-|z|^{2m}x \partial_t,$ where $(x,y,t)= (z,t)\in\mathbb{R}^3=\mathbb{C}\times\mathbb{R}$, we give a condition on a bounded domain $\Omega\subset\mathbb{R}^3$ which ensures that $\Omega$ is an $(\epsilon,\delta)$-domain for the Carnot-Carath\'eodory metric. We also analyze the Ahlfors regularity of the natural surface measure induced at the boundary by the vector fields.Comment: Minor corrections and updated reference

Levi umbilical surfaces in complex space

We define a complex connection on a real hypersurface of \C^{n+1} which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in \C^{n+1}, $n\ge 2$, which are Levi umbilical and have non zero constant Levi curvature. It turns out that such surfaces are contained either in a sphere or in the boundary of a complex tube domain with spherical section.Comment: 18 page

DAS: a data management system for instrument tests and operations

The Data Access System (DAS) is a metadata and data management software system, providing a reusable solution for the storage of data acquired both from telescopes and auxiliary data sources during the instrument development phases and operations. It is part of the Customizable Instrument WorkStation system (CIWS-FW), a framework for the storage, processing and quick-look at the data acquired from scientific instruments. The DAS provides a data access layer mainly targeted to software applications: quick-look displays, pre-processing pipelines and scientific workflows. It is logically organized in three main components: an intuitive and compact Data Definition Language (DAS DDL) in XML format, aimed for user-defined data types; an Application Programming Interface (DAS API), automatically adding classes and methods supporting the DDL data types, and providing an object-oriented query language; a data management component, which maps the metadata of the DDL data types in a relational Data Base Management System (DBMS), and stores the data in a shared (network) file system. With the DAS DDL, developers define the data model for a particular project, specifying for each data type the metadata attributes, the data format and layout (if applicable), and named references to related or aggregated data types. Together with the DDL user-defined data types, the DAS API acts as the only interface to store, query and retrieve the metadata and data in the DAS system, providing both an abstract interface and a data model specific one in C, C++ and Python. The mapping of metadata in the back-end database is automatic and supports several relational DBMSs, including MySQL, Oracle and PostgreSQL.Comment: Accepted for pubblication on ADASS Conference Serie

Updates from FOTOSS: Highlights and Statistics from the OATo Photographic Plate Archive

This is a progress report of the on-going work related to the FOTOSS project (Valorizzazione scientifica dell’archivio di osservazioni FOTOgrafiche del Secolo Scorso di patrimonio dell’OATo). First, we give an up-to-date account of the status of the FOTOSS project, including preliminary informations on the number and characteristics of the digitized plate images; we then present a detailed explanation of the content and usage of the latest realization of the Master Plate Catalog (MPC), along with some general statistics based on the observations recorded in the MPC

NGP Reference Catalogue for the SPICA FGS

This document describes the properties of the NGP Reference Catalogue used for the WP1400 “Input Star Catalogue for the SPICA mission” study conducted by the OATo Team for Thales Alenia Space Italia (TASI) within the “FGS Feasibility Consolidation for SPICA Mission” project commissioned by ESA.This technical note describes the properties of the NGP Reference Catalogue used for the analysis presented by Spagna et al "Input Star Catalogue for SPICA mission" OATO-SPICA-FGS-TNO-001 (07/2020