UBVI CCD Photometry of the Open Cluster NGC 4609 and Hogg 15

UBVI CCD photometry is obtained for the open clusters NGC 4609 and Hogg 15 in Crux. For NGC 4609, CCD data are presented for the first time. From new photometry we derive the reddening, distance modulus and age of each cluster - NGC 4609 : E(B-V) = 0.37 +/- 0.03, V_0 - M_V = 10.60 +/- 0.08, log tau = 7.7 +/- 0.1; Hogg 15 : E(B-V) = 1.13 +/- 0.11, V_0 - M_V = 12.50 +/- 0.15, log tau <= 6.6. The young age of Hogg 15 strongly implies that WR 47 is a member of the cluster. We have also determined the mass function of these clusters and have obtained a normal slope (Gamma = -1.2 +/- 0.3) for NGC 4609 and a somewhat shallow slope (Gamma = -0.95 +/- 0.5) for Hogg 15.Comment: 12 pages, 14 figures, JKAS, in pres

Linear Connections on Graphs

In recent years, discrete spaces such as graphs attract much attention as models for physical spacetime or as models for testing the spirit of non-commutative geometry. In this work, we construct the differential algebras for graphs by extending the work of Dimakis et al and discuss linear connections and curvatures on graphs. Especially, we calculate connections and curvatures explicitly for the general nonzero torsion case. There is a metric, but no metric-compatible connection in general except the complete symmetric graph with two vertices.Comment: 22pages, Latex file, Some errors corrected, To appear in J. Math. Phy

Scattering measurements on natural and model trees

The acoustical back scattering from a simple scale model of a tree has been experimentally measured. The model consisted of a trunk and six limbs, each with 4 branches; no foliage or twigs were included. The data from the anechoic chamber measurements were then mathematically combined to construct the effective back scattering from groups of trees. Also, initial measurements have been conducted out-of-doors on a single tree in an open field in order to characterize its acoustic scattering as a function of azimuth angle. These measurements were performed in the spring, prior to leaf development. The data support a statistical model of forest scattering; the scattered signal spectrum is highly irregular but with a remarkable general resemblance to the incident signal spectrum. Also, the scattered signal's spectra showed little dependence upon scattering angle