Systems View of Coronavirus

No one envisioned the kinds of problems that emerged from the novel coronavirus nor had anyone considered its interactive scope. Now is the time to begin to redesign our processes and systems so that when confronted again we can cope and navigate better. Everyone needs to be a partner in these redesigns and each of the health, social, educational, and other systems must be integrated because it is their interconnections that coproduce and give meaning to our lives

No Open Cluster in the Ruprecht 93 Region

UBVI CCD photometry has been obtained for the Ruprecht 93 (Ru 93) region. We were unable to confirm the existence of an intermediate-age open cluster in Ru 93 from the spatial distribution of blue stars. On the other hand, we found two young star groups in the observed field: the nearer one (Ru 93 group) comprises the field young stars in the Sgr-Car arm at d ~ 2.1 kpc, while the farther one (WR 37 group) is the young stars around WR 37 at d ~ 4.8 kpc. We have derived an abnormal extinction law (Rv = 3.5) in the Ruprecht 93 region.Comment: 6 pages, 6 figures, JKAS 2010, in press (Aug issue

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