Rotational spectra of isotopic species of methyl cyanide, CH3_3CN, in their ground vibrational states up to terahertz frequencies

Methyl cyanide is an important trace molecule in star-forming regions. It is one of the more common molecules used to derive kinetic temperatures in such sources. As preparatory work for Herschel, SOFIA, and in particular ALMA we want to improve the rest frequencies of the main as well as minor isotopologs of methyl cyanide. The laboratory rotational spectrum of methyl cyanide in natural isotopic composition has been recorded up to 1.63 THz. Transitions with good signal-to-noise ratio could be identified for CH$_3$CN, $^{13}$CH$_3$CN, CH$_3^{13}$CN, CH$_3$C$^{15}$N, CH$_2$DCN, and $^{13}$CH$_3^{13}$CN in their ground vibrational states up to about 1.2 THz. The main isotopic species could be identified even in the highest frequency spectral recordings around 1.6 THz. The highest $J'$ quantum numbers included in the fit are 64 for $^{13}$CH$_3^{13}$CN and 89 for the main isotopic species. Greatly improved spectroscopic parameters have been obtained by fitting the present data together with previously reported transition frequencies. The present data will be helpful to identify isotopologs of methyl cyanide in the higher frequency bands of instruments such as the recently launched Herschel satellite, the upcoming airplane mission SOFIA or the radio telescope array ALMA.Comment: 13 pages, 2 figures, article appeared; CDMS links update

Subdifferential and optimality conditions for the difference of set-valued mappings

In this paper, an existence theorem of the subgradients for set-valued mappings, which introduced by Borwein (Math Scand 48:189-204, 1981), and relations between this subdifferential and the subdifferential introduced by Baier and Jahn (J Optim Theory Appl 100:233-240, 1999), are obtained. By using the concept of this subdifferential, the sufficient optimality conditions for generalized D. C. multiobjective optimization problems are established. And the necessary optimality conditions, which are the generalizations of that in Gadhi (Positivity 9:687-703, 2005), are also established. Moreover, by using a special scalarization function, a real set-valued optimization problem is introduced and the equivalent relations between the solutions are proved for the real set-valued optimization problem and a generalized D. C. multiobjective optimization problem