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

Multifaceted Mathematicians

This report attempts to provide an overview of some of the mathematicians who have combined their mathematical knowledge with other academic and non-academic specialities. The various examples given, many of them included in the well-known MacTutor History of Mathematics archive, corroborate the fact that although the idea of the typical polymath has receded with the passage of time, until the end of the Renaissance, most well-known mathematicians were also well-versed in a number of different sciences such as philosophy, astronomy, and physics. We also highlight other, less common combinations of knowledge, in famous mathematicians who were experts in other disciplines or activities of a totally disparate nature

Evolution and excitation conditions of outflows in high-mass star-forming regions

Theoretical models suggest that massive stars form via disk-mediated accretion, with bipolar outflows playing a fundamental role. A recent study toward massive molecular outflows has revealed a decrease of the SiO line intensity as the object evolves. The present study aims at characterizing the variation of the molecular outflow properties with time, and at studying the SiO excitation conditions in outflows associated with massive YSOs. We used the IRAM30m telescope to map 14 massive star-forming regions in the SiO(2-1), SiO(5-4) and HCO+(1-0) outflow lines, and in several dense gas and hot core tracers. Hi-GAL data was used to improve the spectral energy distributions and the L/M ratio, which is believed to be a good indicator of the evolutionary stage of the YSO. We detect SiO and HCO+ outflow emission in all the sources, and bipolar structures in six of them. The outflow parameters are similar to those found toward other massive YSOs. We find an increase of the HCO+ outflow energetics as the object evolve, and a decrease of the SiO abundance with time, from 10^(-8) to 10^(-9). The SiO(5-4) to (2-1) line ratio is found to be low at the ambient gas velocity, and increases as we move to high velocities, indicating that the excitation conditions of the SiO change with the velocity of the gas (with larger densities and/or temperatures for the high-velocity gas component). The properties of the SiO and HCO+ outflow emission suggest a scenario in which SiO is largely enhanced in the first evolutionary stages, probably due to strong shocks produced by the protostellar jet. As the object evolves, the power of the jet would decrease and so does the SiO abundance. During this process, however, the material surrounding the protostar would have been been swept up by the jet, and the outflow activity, traced by entrained molecular material (HCO+), would increase with time.Comment: 31 pages, 10 figures and 5 tables (plus 2 figures and 3 tables in the appendix). Accepted for publication in A&A. [Abstract modified to fit the arXiv requirements.

Molecules with a peptide link in protostellar shocks: a comprehensive study of L1157

Interstellar molecules with a peptide link -NH-C(=O)-, like formamide (NH$_2$CHO), acetamide (NH$_2$COCH$_3$) and isocyanic acid (HNCO) are particularly interesting for their potential role in pre-biotic chemistry. We have studied their emission in the protostellar shock regions L1157-B1 and L1157-B2, with the IRAM 30m telescope, as part of the ASAI Large Program. Analysis of the line profiles shows that the emission arises from the outflow cavities associated with B1 and B2. Molecular abundance of $\approx~(0.4-1.1)\times 10^{-8}$ and $(3.3-8.8)\times 10^{-8}$ are derived for formamide and isocyanic acid, respectively, from a simple rotational diagram analysis. Conversely, NH$_2$COCH$_3$ was not detected down to a relative abundance of a few $\leq 10^{-10}$. B1 and B2 appear to be among the richest Galactic sources of HNCO and NH$_2$CHO molecules. A tight linear correlation between their abundances is observed, suggesting that the two species are chemically related. Comparison with astrochemical models favours molecule formation on ice grain mantles, with NH$_2$CHO generated from hydrogenation of HNCO.Comment: 11 pages, 9 figures. Accepted for publication in MNRAS Main Journal. Accepted 2014 August 19, in original form 2014 July

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 $g_p$