A generalization of Bohr's Equivalence Theorem

Based on a generalization of Bohr's equivalence relation for general Dirichlet series, in this paper we study the sets of values taken by certain classes of equivalent almost periodic functions in their strips of almost periodicity. In fact, the main result of this paper consists of a result like Bohr's equivalence theorem extended to the case of these functions.Comment: Because of a mistake detected in one of the references, the previous version of this paper has been modified by the authors to restrict the scope of its application to the case of existence of an integral basi

Bohr's equivalence relation in the space of Besicovitch almost periodic functions

Based on Bohr's equivalence relation which was established for general Dirichlet series, in this paper we introduce a new equivalence relation on the space of almost periodic functions in the sense of Besicovitch, $B(\mathbb{R},\mathbb{C})$, defined in terms of polynomial approximations. From this, we show that in an important subspace $B^2(\mathbb{R},\mathbb{C})\subset B(\mathbb{R},\mathbb{C})$, where Parseval's equality and Riesz-Fischer theorem holds, its equivalence classes are sequentially compact and the family of translates of a function belonging to this subspace is dense in its own class.Comment: Because of a mistake detected in one of the references, the equivalence relation which is inspired by that of Bohr is revised to adapt correctly the situation in the general case. arXiv admin note: text overlap with arXiv:1801.0803

Measuring cortical connectivity in Alzheimer's disease as a brain neural network pathology: Toward clinical applications

Objectives: The objective was to review the literature on diffusion tensor imaging as well as resting-state functional magnetic resonance imaging and electroencephalography (EEG) to unveil neuroanatomical and neurophysiological substrates of Alzheimer’s disease (AD) as a brain neural network pathology affecting structural and functional cortical connectivity underlying human cognition. Methods: We reviewed papers registered in PubMed and other scientific repositories on the use of these techniques in amnesic mild cognitive impairment (MCI) and clinically mild AD dementia patients compared to cognitively intact elderly individuals (Controls). Results: Hundreds of peer-reviewed (cross-sectional and longitudinal) papers have shown in patients with MCI and mild AD compared to Controls (1) impairment of callosal (splenium), thalamic, and anterior–posterior white matter bundles; (2) reduced correlation of resting state blood oxygen level-dependent activity across several intrinsic brain circuits including default mode and attention-related networks; and (3) abnormal power and functional coupling of resting state cortical EEG rhythms. Clinical applications of these measures are still limited. Conclusions: Structural and functional (in vivo) cortical connectivity measures represent a reliable marker of cerebral reserve capacity and should be used to predict and monitor the evolution of AD and its relative impact on cognitive domains in pre-clinical, prodromal, and dementia stages of AD. (JINS, 2016, 22, 138–163

A new young stellar cluster embedded in a molecular cloud in the far outer Galaxy

We report the discovery of a new young stellar cluster and molecular cloud located in the far outer Galaxy, seen towards IRAS 06361-0142, and we characterise their properties. Near-infrared images were obtained with VLT/ISAAC through JHKs filters, millimetre line observations of CO(1-0) were obtained with SEST, and VLA 6 cm continuum maps obtained from archive data. The cloud and cluster are located at a distance of 7 kpc and a Galactocentric distance of 15 kpc, well in the far outer Galaxy. Morphologically, IRAS 06361-0142 appears as a cluster of several tens of stars surrounded by a nearly spherical nebular cavity centred at the position of the IRAS source. The cluster appears composed of low and intermediate-mass, young reddened stars with a large fraction having cleared the inner regions of their circumstellar discs responsible for (H - Ks) colour excess. The observations are compatible with a 4 Myr cluster with variable spatial extinction between Av = 6 and Av = 13.Comment: 6 pages, 6 figure

Improving evapotranspiration in a land surface model using biophysical variables derived from MSG/SEVIRI satellite

Monitoring evapotranspiration over land is highly dependent on the surface state and vegetation dynamics. Data from spaceborn platforms are desirable to complement estimations from land surface models. The success of daily evapotranspiration monitoring at continental scale relies on the availability, quality and continuity of such data. The biophysical variables derived from SEVIRI on board the geostationary satellite Meteosat Second Generation (MSG) and distributed by the Satellite Application Facility on Land surface Analysis (LSA-SAF) are particularly interesting for such applications, as they aimed at providing continuous and consistent daily time series in near-real time over Africa, Europe and South America. In this paper, we compare them to monthly vegetation parameters from a database commonly used in numerical weather predictions (ECOCLIMAP-I), showing the benefits of the new daily products in detecting the spatial and temporal (seasonal and inter-annual) variability of the vegetation, especially relevant over Africa. We propose a method to handle Leaf Area Index (LAI) and Fractional Vegetation Cover (FVC) products for evapotranspiration monitoring with a land surface model at 3–5 km spatial resolution. The method is conceived to be applicable for near-real time processes at continental scale and relies on the use of a land cover map. We assess the impact of using LSA-SAF biophysical variables compared to ECOCLIMAP-I on evapotranspiration estimated by the land surface model H-TESSEL. Comparison with in-situ observations in Europe and Africa shows an improved estimation of the evapotranspiration, especially in semi-arid climates. Finally, the impact on the land surface modelled evapotranspiration is compared over a north–south transect with a large gradient of vegetation and climate in Western Africa using LSA-SAF radiation forcing derived from remote sensing. Differences are highlighted. An evaluation against remote sensing derived land surface temperature shows an improvement of the evapotranspiration simulations

Deuterium and 15^{15}N fractionation in N2_2H+^+ during the formation of a Sun-like star

Although chemical models predict that the deuterium fractionation in N$_2$H$^+$ is a good evolutionary tracer in the star formation process, the fractionation of nitrogen is still a poorly understood process. Recent models have questioned the similar evolutionary trend expected for the two fractionation mechanisms in N$_2$H$^+$, based on a classical scenario in which ion-neutral reactions occurring in cold gas should have caused an enhancement of the abundance of N$_2$D$^+$, $^{15}$NNH$^+$, and N$^{15}$NH$^+$. In the framework of the ASAI IRAM-30m large program, we have investigated the fractionation of deuterium and $^{15}$N in N$_2$H$^+$ in the best known representatives of the different evolutionary stages of the Sun-like star formation process. The goal is to ultimately confirm (or deny) the classical "ion-neutral reactions" scenario that predicts a similar trend for D and $^{15}$N fractionation. We do not find any evolutionary trend of the $^{14}$N/$^{15}$N ratio from both the $^{15}$NNH$^+$ and N$^{15}$NH$^+$ isotopologues. Therefore, our findings confirm that, during the formation of a Sun-like star, the core evolution is irrelevant in the fractionation of $^{15}$N. The independence of the $^{14}$N/$^{15}$N ratio with time, found also in high-mass star-forming cores, indicates that the enrichment in $^{15}$N revealed in comets and protoplanetary disks is unlikely to happen at core scales. Nevertheless, we have firmly confirmed the evolutionary trend expected for the H/D ratio, with the N$_2$H$^+$/N$_2$D$^+$ ratio decreasing before the pre-stellar core phase, and increasing monotonically during the protostellar phase. We have also confirmed clearly that the two fractionation mechanisms are not related.Comment: 9 pages, 2 figures, accepted for publication in MNRA

Shedding light on the formation of the pre-biotic molecule formamide with ASAI

Formamide (NH2CHO) has been proposed as a pre-biotic precursor with a key role in the emergence of life on Earth. While this molecule has been observed in space, most of its detections correspond to high-mass star-forming regions. Motivated by this lack of investigation in the low-mass regime, we searched for formamide, as well as isocyanic acid (HNCO), in 10 low- and intermediate-mass pre-stellar and protostellar objects. The present work is part of the IRAM Large Programme ASAI (Astrochemical Surveys At IRAM), which makes use of unbiased broadband spectral surveys at millimetre wavelengths. We detected HNCO in all the sources and NH2CHO in five of them. We derived their abundances and analysed them together with those reported in the literature for high-mass sources. For those sources with formamide detection, we found a tight and almost linear correlation between HNCO and NH2CHO abundances, with their ratio being roughly constant -between 3 and 10- across 6 orders of magnitude in luminosity. This suggests the two species are chemically related. The sources without formamide detection, which are also the coldest and devoid of hot corinos, fall well off the correlation, displaying a much larger amount of HNCO relative to NH2CHO. Our results suggest that, while HNCO can be formed in the gas phase during the cold stages of star formation, NH2CHO forms most efficiently on the mantles of dust grains at these temperatures, where it remains frozen until the temperature rises enough to sublimate the icy grain mantles. We propose hydrogenation of HNCO as a likely formation route leading to NH2CHO.Comment: 26 pages, 9 figures. Accepted by Monthly Notices of the Royal Astronomical Societ

The census of interstellar complex organic molecules in the Class I hot corino of SVS13-A

We present the first census of the interstellar Complex Organic Molecules (iCOMs) in the low-mass Class I protostar SVS13-A, obtained by analysing data from the IRAM-30m Large Project ASAI (Astrochemical Surveys At IRAM). They consist of an high-sensitivity unbiased spectral survey at the 1mm, 2mm and 3mm IRAM bands. We detected five iCOMs: acetaldehyde (CH$_3$CHO), methyl formate (HCOOCH$_3$), dimethyl ether (CH$_3$OCH$_3$), ethanol (CH$_3$CH$_2$OH) and formamide (NH$_2$CHO). In addition we searched for other iCOMs and ketene (H$_2$CCO), formic acid (HCOOH) and methoxy (CH$_3$O), whose only ketene was detected. The numerous detected lines, from 5 to 37 depending on the species, cover a large upper level energy range, between 15 and 254 K. This allowed us to carry out a rotational diagram analysis and derive rotational temperatures between 35 and 110 K, and column densities between $3\times 10^{15}$ and $1\times 10^{17}$ cm$^{-2}$ on the 0."3 size previously determined by interferometric observations of glycolaldehyde. These new observations clearly demonstrate the presence of a rich chemistry in the hot corino towards SVS13-A. The measured iCOMs abundances were compared to other Class 0 and I hot corinos, as well as comets, previously published in the literature. We find evidence that (i) SVS13-A is as chemically rich as younger Class 0 protostars, and (ii) the iCOMs relative abundances do not substantially evolve during the protostellar phase.Comment: 24 pages, MNRAS in pres