On conjectures and problems of Ruzsa concerning difference graphs of S-units

Given a finite nonempty set of primes S, we build a graph $\mathcal{G}$ with vertex set $\mathbb{Q}$ by connecting x and y if the prime divisors of both the numerator and denominator of x-y are from S. In this paper we resolve two conjectures posed by Ruzsa concerning the possible sizes of induced nondegenerate cycles of $\mathcal{G}$, and also a problem of Ruzsa concerning the existence of subgraphs of $\mathcal{G}$ which are not induced subgraphs.Comment: 15 page

The VVV Survey reveals classical Cepheids tracing a young and thin stellar disk across the Galaxy's bulge

Solid insight into the physics of the inner Milky Way is key to understanding our Galaxy's evolution, but extreme dust obscuration has historically hindered efforts to map the area along the Galactic mid-plane. New comprehensive near-infrared time-series photometry from the VVV Survey has revealed 35 classical Cepheids, tracing a previously unobserved component of the inner Galaxy, namely a ubiquitous inner thin disk of young stars along the Galactic mid-plane, traversing across the bulge. The discovered period (age) spread of these classical Cepheids implies a continuous supply of newly formed stars in the central region of the Galaxy over the last 100 million years.Comment: Accepted for publication in The Astrophysical Journal Letters. Near-IR finding charts of the Cepheids are available at the following URL: http://www.astro.puc.cl/~idekany/pub/inner_disk_ceph_fc.pn

Orbital Magnetism and Current Distribution of Two-Dimensional Electrons under Confining Potential

The spatial distribution of electric current under magnetic field and the resultant orbital magnetism have been studied for two-dimensional electrons under a harmonic confining potential V(\vecvar{r})=m \omega_0^2 r^2/2 in various regimes of temperature and magnetic field, and the microscopic conditions for the validity of Landau diamagnetism are clarified. Under a weak magnetic field (\omega_c\lsim\omega_0, \omega_c being a cyclotron frequency) and at low temperature (T\lsim\hbar\omega_0), where the orbital magnetic moment fluctuates as a function of the field, the currents are irregularly distributed paramagnetically or diamagnetically inside the bulk region. As the temperature is raised under such a weak field, however, the currents in the bulk region are immediately reduced and finally there only remains the diamagnetic current flowing along the edge. At the same time, the usual Landau diamagnetism results for the total magnetic moment. The origin of this dramatic temperature dependence is seen to be in the multiple reflection of electron waves by the boundary confining potential, which becomes important once the coherence length of electrons gets longer than the system length. Under a stronger field (\omega_c\gsim\omega_0), on the other hand, the currents in the bulk region cause de Haas-van Alphen effect at low temperature as T\lsim\hbar\omega_c. As the temperature gets higher (T\gsim\hbar\omega_c) under such a strong field, the bulk currents are reduced and the Landau diamagnetism by the edge current is recovered.Comment: 15 pages, 11 figure

Effects of Magnetic Field on Josephson Current in SNS System

The effect of a magnetic field on Josephson current has been studied for a superconductor/normal-metal/superconductor (SNS) system, where N is a two-dimensional electron gas in a confining potential. It is found that the dependence of Josephson currents on the magnetic field are sensitive to the width of the normal metal. If the normal metal is wide and contains many channels (subbands), the current on a weak magnetic field shows a dependence similar to a Fraunhofer-pattern in SIS system and, as the field gets strong, it shows another type of oscillatory dependence on the field resulting from the Aharonov-Bohm interference between the edge states. As the number of channels decreases (i.e. normal metal gets narrower), however, the dependence in the region of the weak field deviates from a clear Fraunhofer pattern and the amplitude of the oscillatory dependence in the region of the strong field is reduced.Comment: 14 pages, 9 figure

The Orbit of the New Milky Way Globular Cluster FSR1716 =VVV-GC05

Indexación: Scopus.We use deep, multi-epoch near-IR images of the VISTA Variables in the Via Lictea (VVV) Survey to measure proper motions (PMs) of stars in the Milky Way globular cluster (GC) FSR1716 = VVV-GC05. The colormagnitude diagram of this object, made by using PM-selected members, shows an extended horizontal branch, nine confirmed RR Lyrae (RRL) members in the instability strip, and possibly several hotter stars extending to the blue. Based on the fundamental-mode (ab-type) RRL stars that move coherently with the cluster, we confirmed that FSR1716 is an Oosterhoff I GC with a mean period aPabn = 0.574 days. Intriguingly, we detect tidal extensions to both sides of this cluster in the spatial distribution of PM-selected member stars. Also, one of the confirmed RRabs is located -11 arcmin in projection from the cluster center, suggesting that FSR1716 may be losing stars due to the gravitational interaction with the Galaxy. We also measure radial velocities (RVs) for five cluster red giants selected using the PMs. The combination of RVs and PMs allow us to compute for the first time the orbit of this GC, using an updated Galactic potential. The orbit results to be confined within|Zmax| < 2.0 kpc, and has eccentricity 0.4 < e < 0.6, with perigalactic distance 1.5 < Rperi (kpc) < 2.3, and apogalactic distance 5.3 < Rapo (kpc) < 6.4. We conclude that, in agreement with its relatively low metallicity ([Fe/H] =-1.4 dex), this is an inner-halo GC plunging into the disk of the Galaxy. As such, this is a unique object with which to test the dynamical processes that contribute to the disruption of Galactic GCs. © 2018. The American Astronomical Society. All rights reserved.https://iopscience.iop.org/article/10.3847/1538-4357/aacd0

Cryptotomography: reconstructing 3D Fourier intensities from randomly oriented single-shot diffraction patterns

We reconstructed the 3D Fourier intensity distribution of mono-disperse prolate nano-particles using single-shot 2D coherent diffraction patterns collected at DESY's FLASH facility when a bright, coherent, ultrafast X-ray pulse intercepted individual particles of random, unmeasured orientations. This first experimental demonstration of cryptotomography extended the Expansion-Maximization-Compression (EMC) framework to accommodate unmeasured fluctuations in photon fluence and loss of data due to saturation or background scatter. This work is an important step towards realizing single-shot diffraction imaging of single biomolecules.Comment: 4 pages, 4 figure

Multi-wavelength study of the low-luminosity outbursting young star HBC 722

HBC 722 (V2493 Cyg) is a young eruptive star in outburst since 2010. It is an FU Orionis-type object with an atypically low outburst luminosity. Because it was well characterized in the pre-outburst phase, HBC 722 is one of the few FUors where we can learn about the physical changes and processes associated with the eruption. We monitored the source in the BVRIJHKs bands from the ground, and at 3.6 and 4.5 $\mu$m from space with the Spitzer Space Telescope. We analyzed the light curves and the spectral energy distribution by fitting a series of steady accretion disk models at many epochs. We also analyzed the spectral properties of the source based on new optical and infrared spectra. We also mapped HBC 722 and its surroundings at millimeter wavelengths. From the light curve analysis we concluded that the first peak of the outburst in 2010 September was due to an abrupt increase of the accretion rate in the innermost part of the system. This was followed by a long term process, when the brightening was mainly due to a gradual increase of the accretion rate and the emitting area. Our new observations show that the source is currently in a constant plateau phase. We found that around the peak the continuum was bluer and the H$\alpha$ profile changed significantly between 2012 and 2013. The source was not detected in the millimeter continuum, but we discovered a flattened molecular gas structure with a diameter of 1700 au and mass of 0.3 M$_{\odot}$ centered on HBC 722. While the first brightness peak could be interpreted as a rapid fall of piled-up material from the inner disk onto the star, the later monotonic flux rise suggests the outward expansion of a hot component according to the theory of Bell & Lin (1994). Our study of HBC 722 demonstrated that accretion-related outbursts can occur in young stellar objects even with very low mass disks, in the late Class II phase.Comment: 11 pages, 7 figures, 3 online tables. Accepted for publication in the A&

A systematic review on health resilience to economic crises

Background The health effects of recent economic crises differ markedly by population group. The objective of this systematic review is to examine evidence from longitudinal studies on factors influencing resilience for any health outcome or health behaviour among the general population living in countries exposed to financial crises. Methods We systematically reviewed studies from six electronic databases (EMBASE, Global Health, MEDLINE, PsycINFO, Scopus, Web of Science) which used quantitative longitudinal study designs and included: (i) exposure to an economic crisis; (ii) changes in health outcomes/behaviours over time; (iii) statistical tests of associations of health risk and/or protective factors with health outcomes/behaviours. The quality of the selected studies was appraised using the Quality Assessment Tool for Quantitative Studies. PRISMA reporting guidelines were followed. Results From 14,584 retrieved records, 22 studies met the eligibility criteria. These studies were conducted across 10 countries in Asia, Europe and North America over the past two decades. Ten socio-demographic factors that increased or protected against health risk were identified: gender, age, education, marital status, household size, employment/occupation, income/ financial constraints, personal beliefs, health status, area of residence, and social relations. These studies addressed physical health, mortality, suicide and suicide attempts, mental health, and health behaviours. Women’s mental health appeared more susceptible to crises than men’s. Lower income levels were associated with greater increases in cardiovascular disease, mortality and worse mental health. Employment status was associated with changes in mental health. Associations with age, marital status, and education were less consistent, although higher education was associated with healthier behaviours. Conclusions Despite widespread rhetoric about the importance of resilience, there was a dearth of studies which operationalised resilience factors. Future conceptual and empirical research is needed to develop the epidemiology of resilience