On a Lower Bound for ∥(4/3)k∥\|(4/3)^k\|

We prove, that $$\biggl\|\biggl(\frac43\biggr)^k\biggr\| >\biggl(\frac49\biggr)^k\qquad\text{for}\quad k\ge6,$$ where $\|\cdot\|$ is a distance to the nearest prime

ASTE Simultaneous HCN(4-3) and HCO+(4-3) Observations of the Two Luminous Infrared Galaxies NGC 4418 and Arp 220

We report the results of HCN(J=4-3) and HCO+(J=4-3) observations of two luminous infrared galaxies (LIRGs), NGC 4418 and Arp 220, made using the Atacama Submillimeter Telescope Experiment (ASTE). The ASTE wide-band correlator provided simultaneous observations of HCN(4-3) and HCO+(4-3) lines, and a precise determination of their flux ratios. Both galaxies showed high HCN(4-3) to HCO+(4-3) flux ratios of >2, possibly due to AGN-related phenomena. The J = 4-3 to J = 1-0 transition flux ratios for HCN (HCO+) are similar to those expected for fully thermalized (sub-thermally excited) gas in both sources, in spite of HCN's higher critical density. If we assume collisional excitation and neglect an infrared radiative pumping process, our non-LTE analysis suggests that HCN traces gas with significantly higher density than HCO+. In Arp 220, we separated the double-peaked HCN(4-3) emission into the eastern and western nuclei, based on velocity information. We confirmed that the eastern nucleus showed a higher HCN(4-3) to HCN(1-0) flux ratio, and thus contained a larger amount of highly excited molecular gas than the western nucleus.Comment: 21 pages, 4 figures, accepted for publication in PASJ (Vol.62, No.1, 2010 Feb 25 issue

The hyperplanes of the U (4)(3) near hexagon

Combining theoretical arguments with calculations in the computer algebra package GAP, we are able to show that there are 27 isomorphism classes of hyperplanes in the near hexagon for the group U (4)(3). We give an explicit construction of a representative of each class and we list several combinatorial properties of such a representative

Charge 4/3 leptons in cosmic rays

A cosmic ray counter telescope has been operated at zenith angles of 0, 40, 44, and 60 degs in order to look for charge 4/3 particles. A few million clean single cosmic rays of each zenith angle are analyzed