Algebraic density property of Danilov-Gizatullin surfaces

A Danilov-Gizatullin surface is an affine surface $V$ which is the complement of an ample section $S$ of a Hirzebruch surface. The remarkable theorem of Danilov and Gizatullin states that the isomorphism class of $V$ depends only on the self-intersection number $S^2$. In this paper we apply their theorem to present $V$ as the quotient of an affine threefold by a torus action, and to prove that the Lie algebra generated by the complete algebraic vector fields on $V$ coincides with the set of all algebraic vector fields.Comment: 12 page

A Schwarz Method for the Magnetotelluric Approximation of Maxwell's equations

The magnetotelluric approximation of the Maxwell's equations is used to model the propagation of low frequency electro-magnetic waves in the Earth's subsurface, with the purpose of reconstructing the presence of mineral or oil deposits. We propose a classical Schwarz method for solving this magnetotelluric approximation of the Maxwell equations, and prove its convergence using maximum principle techniques. This is not trivial, since solutions are complex valued, and we need a new result that the magnetotelluric approximations satisfy a maximum modulus principle for our proof. We illustrate our analysis with numerical experiments.Comment: 9 pages, 3 figure

Planck Intermediate Results. XXXVI. Optical identification and redshifts of Planck SZ sources with telescopes at the Canary Islands Observatories

We present the results of approximately three years of observations of Planck Sunyaev-Zeldovich (SZ) sources with telescopes at the Canary Islands observatories as part of the general optical follow-up programme undertaken by the Planck collaboration. In total, 78 SZ sources are discussed. Deep-imaging observations were obtained for most of these sources; spectroscopic observations in either in long-slit or multi-object modes were obtained for many. We effectively used 37.5 clear nights. We found optical counterparts for 73 of the 78 candidates. This sample includes 53 spectroscopic redshift determinations, 20 of them obtained with a multi-object spectroscopic mode. The sample contains new redshifts for 27 Planck clusters that were not included in the first Planck SZ source catalogue (PSZ1).Comment: 15 pages, 14 figures, accepted for publication in A&

VizieR Online Data Catalog: 1Jy northern AGN sample (Planck+, 2016)

The complete sample presented in this paper consists of 104 northern and equatorial radio-loud AGN. It includes all AGN with declination >=-10° that have a measured average radio flux density at 37GHz exceeding 1Jy. Most of the sample sources have been monitored at Metsahovi Radio Observatory for many years, and the brightest sources have been observed for up to 30yr. (1 data file)

VizieR Online Data Catalog: Planck Catalogue of Galactic cold clumps (PGCC) (Planck+, 2016)

The Planck Catalogue of Galactic Cold Clumps (PGCC) is a list of 13188 Galactic sources and 54 sources located in the Small and Large Magellanic Clouds. The sources have been identified in Planck data as sources colder than their environment. It has been built using the 48 months Planck data at 857, 545, and 353GHz combined with the 3THz IRAS data. (1 data file)