Almost convergence of complex uncertain double sequences

Convergence of real sequences, as well as complex sequences are studied by B. Liu and X. Chen respectively in uncertain environment. In this treatise, we extend the study of almost convergence by introducing double sequences of complex uncertain variable. Almost convergence with respect to almost surely, mean, measure, distribution and uniformly almost surely are presented and interrelationships among them are studied and depicted in the form of a diagram. We also define almost Cauchy sequence in the same format and establish some results. Conventionally we have, every convergent sequence is a Cauchy sequence and the converse case is not true in general. But taking complex uncertain variable in a double sequence, we find that a complex uncertain double sequence is a almost Cauchy sequence if and only if it is almost convergent. Some suitable examples and counter examples are properly placed to make the paper self sufficient.

The Fast Radio Burst Dispersion Measure Distribution

We compare the dispersion measure (DM) statistics of FRBs detected by the ASKAP and Parkes radio telescopes. We jointly model their DM distributions, exploiting the fact that the telescopes have different survey fluence limits but likely sample the same underlying population. After accounting for the effects of instrumental temporal and spectral resolution of each sample, we find that a fit between the modelled and observed DM distribution, using identical population parameters, provides a good fit to both distributions. Assuming a one-to-one mapping between DM and redshift for an homogeneous intergalactic medium (IGM), we determine the best-fit parameters of the population spectral index, $\hat{\alpha }$, and the power-law index of the burst energy distribution, $\hat{\gamma }$, for different redshift evolutionary models. Whilst the overall best-fit model yields $\hat{\alpha }=2.2_{-1.0}^{+0.7}$ and $\hat{\gamma }=2.0_{-0.1}^{+0.3}$, for a strong redshift evolutionary model, when we admit the further constraint of α = 1.5 we favour the best fit $\hat{\gamma }=1.5 \pm 0.2$ and the case of no redshift evolution. Moreover, we find no evidence that the FRB population evolves faster than linearly with respect to the star formation rate over the DM (redshift) range for the sampled population.

A climate network perspective of the intertropical convergence zone

The intertropical convergence zone (ITCZ) is an important component of the tropical rain belt. Climate models continue to struggle to adequately represent the ITCZ and differ substantially in its simulated response to climate change. Here we employ complex network approaches, which extract spatio-temporal variability patterns from climate data, to better understand differences in the dynamics of the ITCZ in state-of-the-art global circulation models (GCMs). For this purpose, we study simulations with 14 GCMs in an idealized slab-ocean aquaplanet setup from TRACMIP – the Tropical Rain belts with an Annual cycle and a Continent Model Intercomparison Project. We construct network representations based on the spatial correlation pattern of monthly surface temperature anomalies and study the zonal mean patterns of different topological and spatial network characteristics. Specifically, we cluster the GCMs by means of their zonal network measure distribution utilizing hierarchical clustering. We find that in the control simulation, the zonal network measure distribution is able to pick up model differences in the tropical SST contrast, the ITCZ position and the strength of the Southern Hemisphere Hadley cell. Although we do not find evidence for consistent modifications in the network structure tracing the response of the ITCZ to global warming in the considered model ensemble, our analysis demonstrates that coherent variations of the global SST field are linked with ITCZ dynamics. This suggests that climate networks can provide a new perspective on ITCZ dynamics and model differences therein.

An X-ray activity cycle on the young solar-like star ɛ Eridani

Chromospheric Ca II activity cycles are frequently found in late-type stars, but no systematic programs have been created to search for their coronal X-ray counterparts. The typical time scale of Ca II activity cycles ranges from years to decades. Therefore, long-lasting missions are needed to detect the coronal counterparts. The XMM-Newton satellite has so far detected X-ray cycles in five stars. A particularly intriguing question is at what age (and at what activity level) X-ray cycles set in. To this end, in 2015 we started the X-ray monitoring of the young solar-like star ɛ Eridani, previously observed on two occasions: in 2003 and in early 2015, both by XMM-Newton. With an age of 440 Myr, it is one of the youngest solar-like stars with a known chromospheric Ca II cycle. We collected the most recent Mount Wilson S-index data available for ɛ Eridani, starting from 2002, including previously unpublished data. We found that the Ca II cycle lasts 2.92 ± 0.02 yr, in agreement with past results. From the long-term XMM-Newton lightcurve, we find clear and systematic X-ray variability of our target, consistent with the chromospheric Ca II cycle. The average X-ray luminosity is 2 × 1028erg s−1, with an amplitude that is only a factor of 2 throughout the cycle. We apply a new method to describe the evolution of the coronal emission measure distribution of ɛ Eridani in terms of solar magnetic structures: active regions, cores of active regions, and flares covering the stellar surface at varying filling fractions. Combinations of these three types of magnetic structures can only describe the observed X-ray emission measure of ɛ Eridani if the solar flare emission measure distribution is restricted to events in the decay phase. The interpretation is that flares in the corona of ɛ Eridani last longer than their solar counterparts. We ascribe this to the lower metallicity of ɛ Eridani. Our analysis also revealed that the X-ray cycle of ɛ Eridani is strongly dominated by cores of active regions. The coverage fraction of cores throughout the cycle changes by the same factor as the X-ray luminosity. The maxima of the cycle are characterized by a high percentage of covering fraction of the flares, consistent with the fact that flaring events are seen in the corresponding short-term X-ray lightcurves predominately at the cycle maxima. The high X-ray emission throughout the cycle of ɛ Eridani is thus explained by the high percentage of magnetic structures on its surface.

The ionic composition of the local absorber towards 3C 273

ABSTRACT Hot ionized gas is observed in the local vicinity of our galaxy through spectral absorption features. The most common hypothesis is that this gas forms a halo surrounding our Milky Way, in collisional ionization equilibrium. In this paper, we investigate the elemental abundance of this hot and ionized local gas. We use a 2.4 Ms stacked X-ray spectrum of the bright blazar 3C 273 and probe the local absorption features. Using ion-by-ion fitting of the X-ray absorption lines, we derive the column density of each ionization species. Based on the column densities, we reconstruct the absorption measure distribution, namely the hydrogenic column density as a function of temperature. We report the elemental abundances of C, N, Ne, and Fe relative to solar O. Previous measurements of local X-ray emission lines in conjunction with the present column densities indicate a scale height of 1–80 kpc and hydrogen number density of 10−4–10−3 cm−3 for the hot ionized gas. Additionally, we detect He-like O lines from the quasar broad line region with velocities of 6400 ± 1500 km s−1.

The Variable Rotation Measure Distribution in 3C 273 on Parsec Scales

We briefly review how opacity affects the observed polarization in synchrotron emitting jets. We show some new multi-frequency observations of 3C 273 made with the VLBA in 1999–2000, which add significantly to the available rotation measure (RM) observations of this source. Our findings can be summarized as follows: (1) The transverse gradient in RM is amply confirmed. This implies a toroidal component to the magnetic field, which in turn requires a current of 1017–1018 A flowing down the jet. (2) The net magnetic field in the jet is longitudinal; however, whether or not the longitudinal component is vector-ordered is an open question. (3) The RM distribution is variable on timescales of months to years. We attribute this to the motion of superluminal components behind a turbulent Faraday screen that surrounds the jet. (4) Finally, we suggest that Faraday rotation measurements at higher resolution and higher frequencies, with the Event Horizon Telescope, may enable useful constraints to be placed on the accretion rate onto the central black hole.