q-series and L-functions related to half-derivatives of the Andrews--Gordon identity

Studied is a generalization of Zagier's q-series identity. We introduce a generating function of L-functions at non-positive integers, which is regarded as a half-differential of the Andrews--Gordon q-series. When q is a root of unity, the generating function coincides with the quantum invariant for the torus knot.Comment: 21 pages, related papers can be found from http://gogh.phys.s.u-tokyo.ac.jp/~hikami

The redox-active drug metronidazole and thiol-depleting garlic compounds act synergistically in the protist parasite Spironucleus vortens

Spironucleus vortens is a protozoan parasite associated with significant mortalities in the freshwater angelfish, Pterophyllum scalare. Control of this parasite is especially problematic due to restrictions on the use of the drug of choice, metronidazole (MTZ), on fish farms. Use of garlic (Allium sativum) is undergoing a renaissance following experimental validations of its antimicrobial efficiency. Ajoene ((E,Z)-4,5,9-trithiadodeca-1,6,11-triene 9-oxide), is a stable transformation product of allicin, the primary biologically active component of garlic. In the current study, an ajoene oil crude extract had a minimum inhibitory concentration (MIC) of 40 μg/ml against S. vortens. GC-MS and NMR spectroscopy revealed this ajoene extract contained a mixture of the (E) and (Z)-ajoene isomers along with diallyl disulphide (DADS) and diallyl trisulphide (DATS). The only component of the ajoene crude oil found to substantially inhibit S. vortens growth by optical density monitoring (Bioscreen C Reader) was (Z)-ajoene (MIC 16 μg/ml). Ajoene oil acted in synergy with MTZ in vitro, reducing the individual MIC of this drug (4 μg/ml) by 16-fold, and that of ajoene oil by 200-fold with a fractional inhibitory concentration (FIC) index of 0.263. This synergistic interaction was confirmed in vivo. S. vortens-infected P. scalare angelfish dosed orally with 0.5% (v/w) MTZ combined with 0.05% (v/w) ajoene displayed a significant reduction in faecal trophozoite count, whilst those fed on 0.5% MTZ flakes (half the recommended oral dose) alone did not. This study demonstrates for the first time the synergistic interaction between the synthetic drug MTZ and natural ajoene oil both in vitro and in vivo. Future work should evaluate the potential synergy of ajoene and MTZ against MTZ-resistant bacteria and protists

The Law of the Sea: International Law Implications of the U.S. Refusal to Sign the Treaty

This study is undertaken to show the impact of the international law aspects of the Law of the Sea Treaty as they relate to the U.S. failure to sign the Treaty. The U.S. has embarked on a course of action, by its refusal to sign the Treaty, that can have major impact on day-to-day national policy issues as they relate to international law governing a state\u27s behavior. The U.S., in refusing to sign the Treaty because of the deep seabed provisions, and yet claiming other provisions as reflecting customary law, is probably correct as viewed in today\u27s realities

Suppressed CO emission and high G/D ratios in z=2 galaxies with sub-solar gas-phase metallicity

We study a population of significantly sub-solar enrichment galaxies at z=1.99, to investigate how molecular gas, dust and star-formation relate in low-metallicity galaxies at the peak epoch of star-formation. We target our sample with several deep ALMA and VLA datasets, and find no individual detections of CO[4-3], CO[1-0] or dust, in stark contrast to the >60% detection rate expected for solar-enrichment galaxies with these MS Halpha SFRs. We find that both low and high density molecular gas (traced by CO[1-0] and CO[4-3] respectively) are affected by the low enrichment, showing sample average (stacked) luminosity deficits >0.5-0.7 dex below expectations. This is particularly pertinent for the use of high-J CO emission as a proxy of instantaneous star-formation rate. Our individual galaxy data and stacked constraints point to a strong inverse dependence ∝Zγ of gas-to-dust ratios (G/D) and CO-to-H2 conversion factors (aco) on metallicity at z∼2, with γG/D<-2.2 and γαCO<-0.8, respectively. We quantify the importance of comparing G/D and aco vs. metallicity trends from the literature on a common, suitably normalised metallicity scale. When accounting for systematic offsets between different metallicity scales, our z∼2 constraints on these scaling relations are consistent with the corresponding relations for local galaxies. However, among those local relations, we favour those with a steep/double power-law dependence of G/D on metallicity. Finally, we discuss the implications of these findings for (a) gas mass measurements for sub-M∗ galaxies, and (b) efforts to identify the characteristic galaxy mass scale contributing most to the comoving molecular gas density at z=2

The [C II] emission as a molecular gas mass tracer in galaxies at low and high redshift

We present ALMA Band 9 observations of the [C II]158um emission for a sample of 10 main-sequence galaxies at redshift z ~ 2, with typical stellar masses (log M*/Msun ~ 10.0 - 10.9) and star formation rates (~ 35 - 115 Msun/yr). Given the strong and well understood evolution of the interstellar medium from the present to z = 2, we investigate the behaviour of the [C II] emission and empirically identify its primary driver. We detect [C II] from six galaxies (four secure, two tentative) and estimate ensemble averages including non detections. The [C II]-to-infrared luminosity ratio (L[C II]/LIR) of our sample is similar to that of local main-sequence galaxies (~ 2 x 10^-3), and ~ 10 times higher than that of starbursts. The [C II] emission has an average spatial extent of 4 - 7 kpc, consistent with the optical size. Complementing our sample with literature data, we find that the [C II] luminosity correlates with galaxies' molecular gas mass, with a mean absolute deviation of 0.2 dex and without evident systematics: the [C II]-to-H2 conversion factor (alpha_[C II] ~ 30 Msun/Lsun) is largely independent of galaxies' depletion time, metallicity, and redshift. [C II] seems therefore a convenient tracer to estimate galaxies' molecular gas content regardless of their starburst or main-sequence nature, and extending to metal-poor galaxies at low and high redshifts. The dearth of [C II] emission reported for z > 6 - 7 galaxies might suggest either a high star formation efficiency or a small fraction of UV light from star formation reprocessed by dust

Merger driven star-formation activity in Cl J1449+0856 at z=1.99 as seen by ALMA and JVLA

We use ALMA and JVLA observations of the galaxy cluster Cl J1449+0856 at z=1.99, in order to study how dust-obscured star-formation, ISM content and AGN activity are linked to environment and galaxy interactions during the crucial phase of high-z cluster assembly. We present detections of multiple transitions of 12CO, as well as dust continuum emission detections from 11 galaxies in the core of Cl J1449+0856. We measure the gas excitation properties, star-formation rates, gas consumption timescales and gas-to-stellar mass ratios for the galaxies. We find evidence for a large fraction of galaxies with highly-excited molecular gas, contributing >50% to the total SFR in the cluster core. We compare these results with expectations for field galaxies, and conclude that environmental influences have strongly enhanced the fraction of excited galaxies in this cluster. We find a dearth of molecular gas in the galaxies' gas reservoirs, implying a high star-formation efficiency (SFE) in the cluster core, and find short gas depletion timescales τ<0.1-0.4 Gyrs for all galaxies. Interestingly, we do not see evidence for increased specific star-formation rates (sSFRs) in the cluster galaxies, despite their high SFEs and gas excitations. We find evidence for a large number of mergers in the cluster core, contributing a large fraction of the core's total star-formation compared with expectations in the field. We conclude that the environmental impact on the galaxy excitations is linked to the high rate of galaxy mergers, interactions and active galactic nuclei in the cluster core