arXiv subjects
Publications and source records attributed to Masahiro Sugimoto.
Let $G$ be a finite group. K. Harada conjectured that the product of degrees of all irreducible characters of $G$ divides the product of lengths of all conjugacy classes of $G$. We verify this conjecture for finite general linear groups and finite unitary groups.
K. Harada conjectured for any finite group $G$, the product of sizes of all conjugacy classes is divisible by the product of degrees of all irreducible characters. We study this conjecture when $G$ is the general linear group over a finite field. We show the conjecture holds if the order of the field is sufficiently large.
We have carried out survey observations toward the Galactic plane at l~38 deg in the 12CO and 13CO J=1-0 lines using the Nobeyama Radio Observatory 45-m telescope. A wide area (0.8 x 0.8 deg) was mapped with high spatial resolution (17"). The line of sight samples the gas in both the Sagittarius arm and the inter-arm regions. The present observations reveal how the structure and physical conditions vary across a spiral arm. We classify the molecular gas in the line of sight into two distinct components based on its appearance: the bright and compact B component and the fainter and diffuse (i.e., more extended) D component. The B component is predominantly seen at the spiral arm velocities, while the D component dominates at the inter-arm velocities and is also found at the spiral arm velocities. We introduce the brightness distribution function and the brightness distribution index (BDI, which indicates the dominance of the B component) in order to quantify the map's appearance. The radial velocities of BDI peaks coincide with those of high 12CO J=3-2/12CO J=1-0 intensity ratio (i.e., warm gas) and H II regions, and tend to be offset from the line brightness peaks at lower velocities (i.e., presumably downstream side of the arm). Our observations reveal that the gas structure at small scales changes across a spiral arm: bright and spatially confined structures develop in a spiral arm, leading to star formation at downstream side, while extended emission dominates in the inter-arm region.