First Laboratory Detection of N13CO-and Semiexperimental Equilibrium Structure of the NCO-Anion

The cyanate anion (NCO-) is a species of considerable astrophysical relevance. It is widely believed to be embedded in interstellar ices present in young stellar objects but has not yet been detected in the dense gas of the interstellar medium. Here we report highly accurate laboratory measurements of the rotational spectrum of the N13CO-isotopologue at submillimeter wavelengths along with the detection of three additional lines of the parent isotopologue up to 437.4 GHz. With this new data, the rotational spectrum of both isotopologues can be predicted to better 0.25 km s-1in equivalent radial velocity up to 1 THz, more than adequate for an astronomical search in any source. Moreover, a semiexperimental equilibrium structure of the anion is derived by combining the experimental ground-state rotational constants of the two isotopologues with theoretical vibrational corrections, obtained by using the coupled-cluster method with inclusion of single and double excitations and perturbative inclusion of triple excitations (CCSD(T)). The estimated accuracy of the two bond distances is on the order of 5 × 10-4Å: a comparison to the values obtained by geometry optimization with the CCSD(T) method and the use of a composite scheme, including additivity and basis-set extrapolation techniques, reveals that this theoretical procedure is very accurate

Grid-Obstacle Representations with Connections to Staircase Guarding

In this paper, we study grid-obstacle representations of graphs where we assign grid-points to vertices and define obstacles such that an edge exists if and only if an $xy$-monotone grid path connects the two endpoints without hitting an obstacle or another vertex. It was previously argued that all planar graphs have a grid-obstacle representation in 2D, and all graphs have a grid-obstacle representation in 3D. In this paper, we show that such constructions are possible with significantly smaller grid-size than previously achieved. Then we study the variant where vertices are not blocking, and show that then grid-obstacle representations exist for bipartite graphs. The latter has applications in so-called staircase guarding of orthogonal polygons; using our grid-obstacle representations, we show that staircase guarding is \textsc{NP}-hard in 2D.Comment: To appear in the proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

DC3_3N observations towards high-mass star-forming regions

We present the study of deuteration of cyanoacetylene (HC$_3$N) towards a sample of 28 high-mass star-forming cores divided into different evolutionary stages, from starless to evolved protostellar cores. We report for the first time the detection of DC$_3$N towards 15 high-mass cores. The abundance ratios of DC$_3$N with respect HC$_3$N range in the interval 0.003$-$0.022, lower than those found in low-mas protostars and dark clouds. No significant trend with the evolutionary stage, or with the kinetic temperature of the region, has been found. We compare the level of deuteration of HC$_3$N with those of other molecules towards the same sample, finding weak correlation with species formed only or predominantly in gas phase (N$_2$H$^+$ and HNC, respectively), and no correlation with species formed only or predominantly on dust grains (CH$_3$OH and NH$_3$, respectively). We also present a single-dish map of DC$_3$N towards the protocluster IRAS 05358+3543, which shows that DC$_3$N traces an extended envelope ($\sim$0.37 pc) and peaks towards two cold condensations separated from the positions of the protostars and the dust continuum. The observations presented in this work suggest that deuteration of HC$_3$N is produced in the gas of the cold outer parts of massive star-forming clumps, giving us an estimate of the deuteration factor prior to the formation of denser gas.Comment: Accepted in Monthly Notices of the Royal Astronomical Society -- 11 pages, 7 Figures, 2 Tables. Version with some typos correcte

High resolution infrared and Raman spectra of 13C12CD2: The CD stretching fundamentals and associated combination and hot bands

11 pags.; 4 figs.; 9 tabs.© 2015 AIP Publishing LLC. Infrared and Raman spectra of mono 13C fully deuterated acetylene, 13C12CD2, have been recorded and analysed to obtain detailed information on the C—D stretching fundamentals and associated combination, overtone, and hot bands. Infrared spectra were recorded at an instrumental resolution ranging between 0.006 and 0.01 cm−1 in the region 1800–7800 cm−1. Sixty new bands involving the ν 1 and ν 3 C—D stretching modes also associated with the ν 4 and ν 5 bending vibrations have been observed and analysed. In total, 5881 transitions have been assigned in the investigated spectral region. In addition, the Q branch of the ν 1 fundamental was recorded using inverse Raman spectroscopy, with an instrumental resolution of about 0.003 cm−1. The transitions relative to each stretching mode, i.e., the fundamental band, its first overtone, and associated hot and combination bands involving bending states with υ 4 + υ 5 up to 2 were fitted simultaneously. The usual Hamiltonian appropriate to a linear molecule, including vibration and rotation l-type and the Darling–Dennison interaction between υ 4 = 2 and υ 5 = 2 levels associated with the stretching states, was adopted for the analysis. The standard deviation for each global fit is ≤0.0004 cm−1, of the same order of magnitude of the measurement precision. Slightly improved parameters for the bending and the ν 2 manifold have been also determined. Precise values of spectroscopic parameters deperturbed from the resonance interactions have been obtained. They provide quantitative information on the anharmonic character of the potential energy surface, which can be useful, in addition to those reported in the literature, for the determination of a general anharmonic force field for the molecule. Finally, the obtained values of the Darling–Dennison constants can be valuable for understanding energy flows between independent vibrations.The Bologna authors acknowledge the Università di Bologna and the financial support of the Ministero dell’ Istruzione dell’Università e della Ricerca (PRIN 2012 “Spettroscopia e Tecniche computazionali per la ricerca Astrofisica, atmosferica e Radioastronomica”). D.B. and R.Z.M. acknowledge the financial support of the Ministry of Economy and Competitiveness through Research Grant No. FIS2012-38175.Peer Reviewe

Factorization methods for Noncommutative KP and Toda hierarchy

We show that the solution space of the noncommutative KP hierarchy is the same as that of the commutative KP hierarchy owing to the Birkhoff decomposition of groups over the noncommutative algebra. The noncommutative Toda hierarchy is introduced. We derive the bilinear identities for the Baker--Akhiezer functions and calculate the $N$-soliton solutions of the noncommutative Toda hierarchy.Comment: 7 pages, no figures, AMS-LaTeX, minor corrections, final version to appear in Journal of Physics

Field Representations of Vector Supersymmetry

We study some field representations of vector supersymmetry with superspin Y=0 and Y=1/2 and nonvanishing central charges. For Y=0, we present two multiplets composed of four spinor fields, two even and two odd, and we provide a free action for them. The main differences between these two multiplets are the way the central charge operators act and the compatibility with the Majorana reality condition on the spinors. One of the two is related to a previously studied spinning particle model. For Y=1/2, we present a multiplet composed of one even scalar, one odd vector and one even selfdual two-form, which is a truncation of a known representation of the tensor supersymmetry algebra in Euclidean spacetime. We discuss its rotation to Minkowski spacetime and provide a set of dynamical equations for it, which are however not derived from a Lagrangian. We develop a superspace formalism for vector supersymmetry with central charges and we derive our multiplets by superspace techniques. Finally, we discuss some representations with vanishing central charges.Comment: 37 page