Existence and Uniqueness of Positive Solutions for a System of Multi-order Fractional Differential Equations

In this paper, we study a class of ruin problems, in which premiums and claims are dependent. Under the assumption that premium income is a stochastic process, we raise the model that premiums and claims are dependent, give its numerical characteristics and the ruin probability of the individual risk model in the surplus process. In addition, we promote the number of insurance policies to a Poisson process with parameter λ, using martingale methods to obtain the upper bound of the ultimate ruin probability.

Candidate members of the Pal 5, GD-1, Cetus Polar and Orphan tidal stellar halo streams from SDSS DR9, LAMOST DR3 and APOGEE catalogs

We present candidate members of the Pal 5, GD-1, Cetus Polar and Orphan tidal stellar streams found in LAMOST DR3, SDSS DR9 and APOGEE catalogs. In LAMOST DR3, we find 20, 4 and 24 high confidence candidates of tidal streams GD-1, Cetus Polar and Orphan respectively. We also list 59, 118 and 10 high confidence candidates of tidal streams Cetus Polar, Orphan and Pal 5, respectively from the SDSS DR9 spectroscopic catalog. Furthermore, we find seven high confidence candidates of the Pal 5 tidal stream in the APOGEE data. Compared with SDSS, the new candidates from LAMOST DR3 are brighter, so that together, more of the color-magnitude diagram, including the giant branch, can be explored. Analysis of the SDSS data shows that there are three metallicity peaks associated with the Orphan stream which also exhibit some spatial separation. The LAMOST data confirm multiple metallicities in this stream. The metallicity, given by the higher resolution APOGEE instrument, of the Pal 5 tidal stream is [Fe/H] ,- -1.2, higher than that given earlier by SDSS spectra. Many previously unidentified stream members are tabulated here for the first time, along with existing members, allowing future researchers to further constrain the orbits of these objects as they move within the Galaxy＇s dark matter potential.

The Inclination, Pitch Angle and Forbidden Radius of Spiral Arms of PGC 35105

We have studied some properties including surface brightness in the u, g, r, i, and z bands of the nearly face-on galaxy PGC 35105. By subtracting a model surface brightness distribution from the observed image we obtain the residual image that shows only the spiral arms freed from the contamination by the bulge. From this we measured the the inclination, pitch angle, and forbidden radius （identified with the innermost point of the arm） for each of the two arms; and that for each of the five observing bands. We found these three parameters are largely independent of the observing band.

Multi-frequency VLBI Observations of NRAO 150

We present multi-frequency, high resolution, radio structures of NRAO 150 with VLBA and EVN array respectively, both of which show a very collimated one-sided jet structure beyond an angular distance of 80 mas. Model fitting is performed for observations at 2.3 GHz and 8.4 GHz which reveal the source to be consisting of several components at position angle -30°. According to the light curves at 4.8 GHz, 8.0 GHz and 14.5 GHz an outburst is currently occurring in its rising stage, which suggests that a new component is probably in the course of forming. Spectral analysis reveals that the new component probably has a higher spectral index. The maximum proper motion of -0.46 mas yr-1 is expected if we suppose that the new component is moving away from core at the beginning of the flaring.