A Sino-German 6cm polarisation survey of the Galactic plane - VIII. Small-diameter sources

Information of small-diameter sources is extracted from the Sino-German 6cm polarisation survey of the Galactic plane carried out with the Urumqi 25-m telescope. We performed two-dimensional elliptical Gaussian fits to the 6cm maps to obtain a list of sources with total-intensity and polarised flux densities. The source list contains 3832 sources with a fitted diameter smaller than 16 arcmin and a peak flux density exceeding 30 mJy, so about 5 times the rms noise, of the total-intensity data. The cumulative source count indicates completeness for flux densities exceeding about 60 mJy. We identify 125 linearly polarised sources at 6cm with a peak polarisation flux density greater than 10 mJy, so about 3 times the rms noise, of the polarised-intensity data. Despite lacking compact steep spectrum sources, the 6cm catalogue lists about 20 percent more sources than the Effelsberg 21cm source catalogue at the same angular resolution and for the same area. Most of the faint 6cm sources must have a flat spectrum and are either HII regions or extragalactic. When compared with the Green Bank 6cm (GB6) catalogue, we obtain higher flux densities for a number of extended sources with complex structures. Polarised 6cm sources density are uniformly distributed in Galactic latitude. Their number density decreases towards the inner Galaxy. More than 80 percent of the polarised sources are most likely extragalactic. With a few exceptions, the sources have a higher percentage polarisation at 6cm than at 21cm. Depolarisation seems to occur mostly within the sources with a minor contribution from the Galactic foreground emission.Comment: A&A accepted, 9 pages, 5 figures, Tables 1 and 2 are accessible from http://zmtt.bao.ac.cn/6cm

An approximation theory for the identification of nonlinear distributed parameter systems

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed