The fundamental group and torsion group of Beauville surfaces

We give a survey on the fundamental group of surfaces isogenous to a higher product. If the surfaces are regular, e.g. if they are Beauville surfaces, the first homology group is a finite group. We present a MAGMA script which calculates the first homology groups of regular surfaces isogenous to a product.Comment: 14 pages; MAGMA script included; v2: minor corrections, final version to appear in the Proceedings of the Conference "Beauville Surfaces and Groups", Newcastle University (UK), 7-9th June 201

A Rapid X-ray Flare from Markarian 501

We present X-ray observations of the BL Lacertae (BL Lac) object Markarian 501 (Mrk 501), taken with the Rossi X-ray Timing Explorer in 1998 May as part of a multi-wavelength campaign. The X-ray light curve shows a very rapid flare in which the 2-10 keV flux increased by ~60% in <200 seconds. This rapid rise is followed by a drop-off in the 2-10 keV flux of ~40% in <600 seconds. The 10-15 keV variation in this flare is roughly a factor of two on similar time-scales. During the rise of the flare, the 3-15 keV spectral index hardened from 2.02 +/- 0.03 to 1.87 +/- 0.04, where it remained during the decay of the flare. This is the fastest variation ever seen in X-rays from Mrk 501 and among the fastest seen at any wavelength for this object. The shift in the energy at which the spectral power peaks (from 30 keV during the flare) is also among the most rapid shifts seen from this object. This flare occurs during an emission state (2-10 keV flux approximately 1.2e-10 erg cm^-2 s^-1) that is approximately 25% of the peak flux observed in 1997 April from this object but which is still high compared to its historical average X-ray flux. The variations in the hardness ratio are consistent with the low energy variations leading those at high energies during the development and decay of the flare. This pattern is rare among high frequency peaked BL Lac objects like Mrk 501, but has been seen recently in two other TeV emitting BL Lacs, Mrk 421 and PKS 2155-304. The hard lag is consistent with a flare dominated by the acceleration time-scale for a simple relativistic shock model of flaring.Comment: 11 pages, 3 figures, accepted for publication in Astrophys. J. Letter

On surfaces with p_g=2, q=1 and K^2=5

We consider minimal surfaces of general type with $p_g = 2$, $q = 1$ and $K^2 = 5$. We provide a stratification of the corresponding moduli space and we give some bounds for the number and the dimensions of its irreducible components.Comment: 25 pages. To appear in Rendiconti del Circolo Matematico di Palerm

Quasi-linear diffusion driving the synchrotron emission in active galactic nuclei

We study the role of the quasi-linear diffusion (QLD) in producing X-ray emission by means of ultra-relativistic electrons in AGN magnetospheric flows. We examined two regions: (a) an area close to the black hole and (b) the outer magnetosphere. The synchrotron emission has been studied for ultra-relativistic electrons and was shown that the QLD generates the soft and hard X-rays, close to the black hole and on the light cylinder scales respectively. By considering the cyclotron instability, we show that despite the short synchrotron cooling timescales, the cyclotron modes excite transverse and longitudinal-transversal waves. On the other hand, it is demonstrated that the synchrotron reaction force and a force responsible for the conservation of the adiabatic invariant tend to decrease the pitch angles, whereas the diffusion, that pushes back on electrons by means of the aforementioned waves, tends to increase the pitch angles. By examining the quasi-stationary state, we investigate a regime in which these two processes are balanced and a non-vanishing value of pitch angles is created.Comment: 4 pages, 3 figure

Nutrition, physical activity, and other lifestyle factors in the prevention of cognitive decline and dementia

Multiple factors combined are currently recognized as contributors to cognitive decline. The main independent risk factor for cognitive impairment and dementia is advanced age followed by other determinants such as genetic, socioeconomic, and environmental factors, including nutrition and physical activity. In the next decades, a rise in dementia cases is expected due largely to the aging of the world population. There are no hitherto effective pharmaceutical therapies to treat age-associated cognitive impairment and dementia, which underscores the crucial role of prevention. A relationship among diet, physical activity, and other lifestyle factors with cognitive function has been intensively studied with mounting evidence supporting the role of these determinants in the development of cognitive decline and dementia, which is a chief cause of disability globally. Several dietary patterns, foods, and nutrients have been investigated in this regard, with some encouraging and other disappointing results. This review presents the current evidence for the effects of dietary patterns, dietary components, some supplements, physical activity, sleep patterns, and social engagement on the prevention or delay of the onset of age-related cognitive decline and dementia. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Evaluation of proprioception and postural control at a minimum 1 year follow-up after ankle capsuloligamentous lateralplasty with Brostrom technique: A cohort study

Recovery of postural control and proprioception in patients affected by chronic ankle instability (CAI) and operated on capsulo-ligaments reconstructive surgery lacks of objective assessment. The aim of this study was to evaluate long-term post-surgical postural and proprioceptive control through the DPPS device in a cohort of patients operated on ligaments reconstruction through the modified Brostrom procedure at a minimum follow up of 12 months.Eleven patients with post-traumatic lateral CAI, operated of external capsulo-ligamentous complex repair according to Brostrom technique at a minimum follow-up of 1 year were enrolled. Physical examination and American Orthopaedics Foot and Ankle Society (AOFAS) ankle-hindfoot score. Proprioceptive and postural stability was assessed by DPPS - Delos Postural Proprioceptive System, linked to a computer with a specific software and including a flat table, an electronic unstable proprioceptive board, a Delos Vertical Controller, a monitor and a horizontal bar fitted with an infra-red sensor for hand support.Patients were 5 males and 6 females, mean age of 38.4 ± 12 years. Mean BMI of the patients was 26.8 ± 4.4. Mean follow up was 13.4 ± 2.1. The mean value of (AOFAS) clinical score was 90.3/100. Mean Static Stability Index (SSI) with open eyes was 87.7% (±7.6) in the operated leg and 90.4% (±6.1) in the contra-lateral. SSI with closed eyes was 64.5% (±11.2) in the operated leg and 61.6% (±16.8) in the contra-lateral. Mean Dynamic Stability Index (DSI) without restrictions was 56.2% (±14.6) in the operated leg and 56.8% (±10.6) in the contra-lateral. DSI with restricted upper limbs, had a mean value of 56.3% (±11.4) in the operated leg and 58.1% (±11.9) in the contra-lateral.Re-tensioning capsular-ligamentous surgery of the external compartment for CAI allow to recovery proprioceptive and postural control on the operated side, comparable with data from the contralateral limb and from the healthy population of the same age and sex

Surfaces containing a family of plane curves not forming a fibration

We complete the classification of smooth surfaces swept out by a 1-dimensional family of plane curves that do not form a fibration. As a consequence, we characterize manifolds swept out by a 1-dimensional family of hypersurfaces that do not form a fibration.Comment: Author's post-print, final version published online in Collect. Mat

Limits to Quantum Gravity Effects from Observations of TeV Flares in Active Galaxies

We have used data from the TeV gamma-ray flare associated with the active galaxy Markarian 421 observed on 15 May 1996 to place bounds on the possible energy-dependence of the speed of light in the context of an effective quantum gravitational energy scale. The possibility of an observable time dispersion in high energy radiation has recently received attention in the literature, with some suggestions that the relevant energy scale could be less than the Planck mass and perhaps as low as 10^16 GeV. The limits derived here indicate this energy scale to be in excess of 4x10^16 GeV at the 95% confidence level. To the best of our knowledge, this constitutes the first convincing limit on such phenomena in this energy regime.Comment: 6 pages, including 2 figure

Correlated variability of Mkn 421 at X-ray and TeV wavelengths on timescales of hours

Mkn 421 was observed for about two days with BeppoSAX, prior to and partly overlapping the start of a 1 week continuous exposure with ASCA in April 1998, as part of a world-wide multiwavelength campaign. A pronounced, well defined, flare observed in X-rays was also observed simultaneously at TeV energies by the Whipple Observatory's 10 m gamma-ray telescope. These data provide the first evidence that the X-ray and TeV intensities are well correlated on time-scales of hours.Comment: 4 pages, 1 figure, presented at the VERITAS Workshop on the TeV Astrophysics of Extragalactic Object