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

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

Cohen strongly p-summing holomorphic mappings on Banach spaces

Let $E$ and $F$ be complex Banach spaces, $U$ be an open subset of $E$ and $1\leq p\leq\infty$. We introduce and study the notion of a Cohen strongly $p$-summing holomorphic mapping from $U$ to $F$, a holomorphic version of a strongly $p$-summing linear operator. For such mappings, we establish both Pietsch domination/factorization theorems and analyse their linearizations from $\mathcal{G}^\infty(U)$ (the canonical predual of $\mathcal{H}^\infty(U)$) and their transpositions on $\mathcal{H}^\infty(U)$. Concerning the space $\mathcal{D}_p^{\mathcal{H}^\infty}(U,F)$ formed by such mappings and endowed with a natural norm $d_p^{\mathcal{H}^\infty}$, we show that it is a regular Banach ideal of bounded holomorphic mappings generated by composition with the ideal of strongly $p$-summing linear operators. Moreover, we identify the space $(\mathcal{D}_p^{\mathcal{H}^\infty}(U,F^*),d_p^{\mathcal{H}^\infty})$ with the dual of the completion of tensor product space $\mathcal{G}^\infty(U)\otimes F$ endowed with the Chevet--Saphar norm $g_p$

Optimizing Adaptive Transmission Policies for Wireless Vehicular Communications

Abstract—The adoption of wireless vehicular communication technologies would strongly depend on the technologies transmission reliability, required by QoS demanding traffic safety applications, and the system’s scalability as the technology is gradually introduced. To this aim, this work proposes the use of opportunistic transmission policies that dynamically adapt the transmission parameters based on the operating conditions and potential traffic safety risks. The work analyses different configuration proposals with the aim to meeting the strong traffic safety QoS requirements, while maximizing the technology’s robustness and minimising channel congestion, which in turn is crucial to guarantee the future system’s scalability

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