The Fokker-Planck (FP) model is one of the commonly used methods for studies of the dynamical evolution of dense spherical stellar systems such as globular clusters and galactic nuclei. The FP model is numerically stable in most cases, but we find that it encounters numerical difficulties rather often when the effects of tidal shocks are included in two-dimensional (energy and angular momentum space) version of the FP model or when the initial condition is extreme (e.g., a very large cluster mass and a small cluster radius). To avoid such a problem, we have developed a new integration scheme for a two-dimensional FP equation by adopting an Alternating Direction Implicit (ADI) method given in the Douglas-Rachford split form. We find that our ADI method reduces the computing time by a factor of ~2 compared to the fully implicit method, and resolves problems of numerical instability.

The H2S 22,0 - 21,1 line emission is observed to be strongly localized toward Sgr B2(M), and emissions from other positions in the more extended SgrB2 region are almost negligible. H2S is thought to form effectively by the passage of the C-type shocks but to be quickly transformed to SO2 or other sulfur species (Pineau des Forets et al. 1993). Such a shock may have enhanced the H2S abundance in Sgr B2(M), where massive star formation is taking place. But the negligible emission of H2S from other observed positions may indicate that these positions have not been affected by shocks enough to produce H2S, or if they have experienced shocks, H2S may have transformed already to other sulfur-containing species. The SO2 222,20 - 221,21 line was also observed to be detectable only toward the (M) position. The line intensity ratios of these two molecules appear to be very similar at Sgr B2(M) and IRAS 16239-2422, where the latter is a region of low-mass star formation. This may suggest that the shock environment in these two star-forming regions is similar and that the shock chemistry also proceeds in a similar fashion in these two different regions, if we accept shock formation of these two species.

The auroral observation has been started at Jang Bogo Station (JBS), Antarctica by using a visible All-sky camera (v-ASC) in 2018 to routinely monitor the aurora in association with the simultaneous observations of the ionosphere, thermosphere and magnetosphere at the station. In this article, the auroral observations are introduced with the analysis procedure to recognize the aurora from the v-ASC image data and to compute the auroral occurrences and the initial results on their spatial and temporal distributions are presented. The auroral occurrences are mostly confined to the northern horizon in the evening sector and extend to the zenith from the northwest to cover almost the entire sky disk over JBS at around 08 MLT (magnetic local time; 03 LT) and then retract to the northeast in the morning sector. At near the magnetic local noon, the occurrences are horizontally distributed in the northern sky disk, which shows the auroral occurrences in the cusp region. The results of the auroral occurrences indicate that JBS is located most of the time in the polar cap near the poleward boundary of the auroral oval in the nightside and approaches closer to the oval in the morning sector. At around 08 MLT (03 LT), JBS is located within the auroral oval and then moves away from it, finally being located in the cusp region at the magnetic local noon, which indicates that the location of JBS turns out to be ideal to investigate the variabilities of the poleward boundary of the auroral oval from long-term observations of the auroral occurrences. The future plan for the ground auroral observations near JBS is presented.