Algebraic varieties with automorphism groups of maximal rank

We confirm, to some extent, the belief that a projective variety X has the largest number (relative to the dimension of X) of independent commuting automorphisms of positive entropy only when X is birational to a complex torus or a quotient of a torus. We also include an addendum to an early paper though it is not used in the present paper.Comment: Mathematische Annalen (to appear

Magnetic-field dependence of the critical currents in a periodic coplanar array of narrow superconducting strip

We calculate the magnetic-field dependence of the critical current due to both geometrical edge barriers and bulk pinning in a periodic coplanar array of narrow superconducting strips. We find that in zero or low applied magnetic fields the critical current can be considerably enhanced by the edge barriers, but in modest applied magnetic fields the critical current reduces to that due to bulk pinning alone.Comment: 23 pages, 7 figure

The photometric properties of a vast stellar substructure in the outskirts of M33

We have surveyed $\sim40$sq.degrees surrounding M33 with CFHT MegaCam in the g and i filters, as part of the Pan-Andromeda Archaeological Survey. Our observations are deep enough to resolve the top 4mags of the red giant branch population in this galaxy. We have previously shown that the disk of M33 is surrounded by a large, irregular, low-surface brightness substructure. Here, we quantify the stellar populations and structure of this feature using the PAndAS data. We show that the stellar populations of this feature are consistent with an old population with $<[Fe/H]>\sim-1.6$dex and an interquartile range in metallicity of $\sim0.5$dex. We construct a surface brightness map of M33 that traces this feature to $\mu_V\simeq33$mags\,arcsec$^{-2}$. At these low surface brightness levels, the structure extends to projected radii of $\sim40$kpc from the center of M33 in both the north-west and south-east quadrants of the galaxy. Overall, the structure has an "S-shaped" appearance that broadly aligns with the orientation of the HI disk warp. We calculate a lower limit to the integrated luminosity of the structure of $-12.7\pm0.5$mags, comparable to a bright dwarf galaxy such as Fornax or AndII and slightly less than $1\$ of the total luminosity of M33. Further, we show that there is tentative evidence for a distortion in the distribution of young stars near the edge of the HI disk that occurs at similar azimuth to the warp in HI. The data also hint at a low-level, extended stellar component at larger radius that may be a M33 halo component. We revisit studies of M33 and its stellar populations in light of these new results, and we discuss possible formation scenarios for the vast stellar structure. Our favored model is that of the tidal disruption of M33 in its orbit around M31.Comment: Accepted for publication in ApJ. 17 figures. ApJ preprint forma

Ursinus College Bulletin Vol. 13, No. 4, January 1897

A digitized copy of the January 1897 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1121/thumbnail.jp

Ursinus College Bulletin Vol. 13, No. 9, June 1897

A digitized copy of the June 1897 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1126/thumbnail.jp

Ursinus College Bulletin Vol. 13, No. 10, July 1897

A digitized copy of the July 1897 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1127/thumbnail.jp

Ursinus College Bulletin Vol. 13, No. 6, March 1897

A digitized copy of the March 1897 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1123/thumbnail.jp

Ursinus College Bulletin Vol. 13, No. 3, December 1896

A digitized copy of the December 1896 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1120/thumbnail.jp

Ursinus College Bulletin Vol. 13, No. 5, February 1897

A digitized copy of the February 1897 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1122/thumbnail.jp

Ursinus College Bulletin Vol. 13, No. 2, November 1896

A digitized copy of the November 1896 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1119/thumbnail.jp