We present UBVI photometry of the old open cluster NGC 1193. Color-magnitude diagrams (CMDs) of this cluster show a well defined main sequence and a sparse red giant branch. For the inner region of r<50 arcsec, three blue straggler candidates are new
ly found in addition to the objects Kaluzny (1988) already found. The color-color diagrams show that the reddening value toward NGC 1193 is E(B-V) =0.19 +/- 0.04. From the ultraviolet excess measurement, we derived the metallicity to be [Fe/H]=-0.45 +/- 0.12. A distance modulus of (m-M)_0 =13.3 +/- 0.15 is obtained from zero age main sequence fitting with the empirically calibrated Hyades isochrone of Pinsonneault et al. (2004). CMD comparison with the Padova isochrones by Bertelli et al. (1994) gives an age of log t =9.7 +/- 0.1.
In this Paper, we have derived Cepheid period-luminosity (P-L) relations for the Large Magellanic Cloud (LMC) fundamental mode Cepheids, based on the data released from OGLE-III. We have applied an extinction map to correct for the extinction of thes
e Cepheids. In addition to the VIW band P-L relations, we also include JHK and four Spitzer IRAC band P-L relations, derived by matching the OGLE-III Cepheids to the 2MASS and SAGE datasets, respectively. We also test the non-linearity of the Cepheid P-L relations based on extinction-corrected data. Our results (again) show that the LMC P-L relations are non-linear in VIJH bands and linear in KW and the four IRAC bands, respectively.
We study an equation lying `mid-way between the periodic Hunter-Saxton and Camassa-Holm equations, and which describes evolution of rotators in liquid crystals with external magnetic field and self-interaction. We prove that it is an Euler equation o
n the diffeomorphism group of the circle corresponding to a natural right-invariant Sobolev metric. We show that the equation is bihamiltonian and admits both cusped, as well as smooth, traveling-wave solutions which are natural candidates for solitons. We also prove that it is locally well-posed and establish results on the lifespan of its solutions. Throughout the paper we argue that despite similarities to the KdV, CH and HS equations, the new equation manifests several distinctive features that set it apart from the other three.
