A free boundary problem associated with the isoperimetric inequality

This paper proves a 30 year old conjecture that disks and annuli are the only domains where analytic content - the uniform distance from $\bar{z}$ to analytic functions - achieves its lower bound. This problem is closely related to several well-known free boundary problems, in particular, Serrin's problem about laminar flow of incompressible viscous fluid for multiply-connected domains, and Garabedian's problem on the shape of electrified droplets. Some further ramifications and open questions, including extensions to higher dimensions, are also discussed

Internal Migration and Regional Population Dynamics in Europe: Romanian Case Study

The report analyses population migration and change in Romania over the period 1984-1994. The analysis of population change is conducted for 2948 communes and towns, the finest administrative division for which population data are available. The lack of migration data on the level of communes and towns makes in-depth analysis of the migration for small spatial units impossible. For that reason analysis of the patterns of migration is conducted for 40 Judete (also referred to as counties or regions) and the capital city of Bucharest, i.e. 41 units altogether. Council of Europe Publishing, F-67075 Strasbourg - Cedex, France

Direct Observation of Martensitic Phase-Transformation Dynamics in Iron by 4D Single-Pulse Electron Microscopy

The in situ martensitic phase transformation of iron, a complex solid-state transition involving collective atomic displacement and interface movement, is studied in real time by means of four-dimensional (4D) electron microscopy. The iron nanofilm specimen is heated at a maximum rate of ∼10^(11) K/s by a single heating pulse, and the evolution of the phase transformation from body-centered cubic to face-centered cubic crystal structure is followed by means of single-pulse, selected-area diffraction and real-space imaging. Two distinct components are revealed in the evolution of the crystal structure. The first, on the nanosecond time scale, is a direct martensitic transformation, which proceeds in regions heated into the temperature range of stability of the fcc phase, 1185−1667 K. The second, on the microsecond time scale, represents an indirect process for the hottest central zone of laser heating, where the temperature is initially above 1667 K and cooling is the rate-determining step. The mechanism of the direct transformation involves two steps, that of (barrier-crossing) nucleation on the reported nanosecond time scale, followed by a rapid grain growth typically in ∼100 ps for 10 nm crystallites

The Planetary Nebula Luminosity Function at the Dawn of Gaia

The [O III] 5007 Planetary Nebula Luminosity Function (PNLF) is an excellent extragalactic standard candle. In theory, the PNLF method should not work at all, since the luminosities of the brightest planetary nebulae (PNe) should be highly sensitive to the age of their host stellar population. Yet the method appears robust, as it consistently produces < 10% distances to galaxies of all Hubble types, from the earliest ellipticals to the latest-type spirals and irregulars. It is therefore uniquely suited for cross-checking the results of other techniques and finding small offsets between the Population I and Population II distance ladders. We review the calibration of the method and show that the zero points provided by Cepheids and the Tip of the Red Giant Branch are in excellent agreement. We then compare the results of the PNLF with those from Surface Brightness Fluctuation measurements, and show that, although both techniques agree in a relative sense, the latter method yields distances that are ~15% larger than those from the PNLF. We trace this discrepancy back to the calibration galaxies and argue that, due to a small systematic error associated with internal reddening, the true distance scale likely falls between the extremes of the two methods. We also demonstrate how PNLF measurements in the early-type galaxies that have hosted Type Ia supernovae can help calibrate the SN Ia maximum magnitude-rate of decline relation. Finally, we discuss how the results from space missions such as Kepler and Gaia can help our understanding of the PNLF phenomenon and improve our knowledge of the physics of local planetary nebulae.Comment: 12 pages, invited review at the conference "The Fundamental Cosmic Distance Scale: State of the Art and Gaia Perspective", to appear in Astrophysics and Space Scienc

The ionization mechanism of NGC 185: how to fake a Seyfert galaxy?

NGC 185 is a dwarf spheroidal satellite of the Andromeda galaxy. From mid-1990s onwards it was revealed that dwarf spheroidals often display a varied and in some cases complex star formation history. In an optical survey of bright nearby galaxies, NGC 185 was classified as a Seyfert galaxy based on its emission line ratios. However, although the emission lines in this object formally place it in the category of Seyferts, it is probable that this galaxy does not contain a genuine active nucleus. NGC 185 was not detected in radio surveys either in 6 or 20 cm, or X-ray observations, which means that the Seyfert-like line ratios may be produced by stellar processes. In this work, we try to identify the possible ionization mechanisms for this galaxy. We discussed the possibility of the line emissions being produced by planetary nebulae (PNe), using deep spectroscopy observations obtained with GMOS-N, at Gemini. Although the fluxes of the PNe are high enough to explain the integrated spectrum, the line ratios are very far from the values for the Seyfert classification. We then proposed that a mixture of supernova remnants and PNe could be the source of the ionization, and we show that a composition of these two objects do mimic Seyfert-like line ratios. We used chemical evolution models to predict the supernova rates and to support the idea that these supernova remnants should be present in the galaxy.Comment: 9 pages, 7 figures, accepted for publication in MNRA

A multi-photon Stokes-parameter invariant for entangled states

We consider the Minkowskian norm of the n-photon Stokes tensor, a scalar invariant under the group realized by the transformations of stochastic local quantum operations and classical communications (SLOCC). This invariant is offered as a candidate entanglement measure for n-qubit states and discussed in relation to measures of quantum state entanglement for certain important classes of two-qubit and three-qubit systems. This invariant can be directly estimated via a quantum network, obviating the need to perform laborious quantum state tomography. We also show that this invariant directly captures the extent of entanglement purification due to SLOCC filters.Comment: 9 pages, 0 figures, Accepted for publication in Physical Review

Caravan politics in the depoliticised city:Applying and opposing exceptional measures for Dutch Traveller, Sinti, and Roma caravan sites

This article analyses the depoliticisation of Dutch caravan politics, which has resulted in massive pitch shortages threatening the existence of the specific caravan housing culture of Dutch Travellers, Sinti and Roma groups. The rationality underlying the repressive governance of caravans is understood as a depoliticised affirmation of technocratic solutions to an unwanted and racialised housing culture. However, as in many other European countries, Dutch authorities have been summoned to work on Roma and Traveller inclusion programmes and address pitch shortages. The increased pressure on the Dutch government culminated in 2018 when it adopted a new framework that prohibits any further measures to repress caravan culture. In what follows, a situated account of depoliticised caravan politics – and resistance to it (i.e. re-politicisation efforts) – is presented by examining the case of Teersdijk, a large campsite in the city of Nijmegen

Relaxation of nonlinear oscillations in BCS superconductivity

The diagonal case of the $sl(2)$ Richardson-Gaudin quantum pairing model \cite{Richardson1,Richardson2,Richardson3,Richardson4,Richardson5,Richardson6,G audin76} is known to be solvable as an Abel-Jacobi inversion problem \cite{SOV,Kuznetzov,Kuz1,Kuz2,Kuz3,Kuz4,Kuz5,YAKE04}. This is an isospectral (stationary) solution to a more general integrable hierarchy, in which the full time evolution can be written as isomonodromic deformations. Physically, the more general solution is appropriate when the single-particle electronic spectrum is subject to external perturbations. The asymptotic behavior of the nonlinear oscillations in the case of elliptic solutions is derived