A lower bound in Nehari's theorem on the polydisc

By theorems of Ferguson and Lacey (d=2) and Lacey and Terwilleger (d>2), Nehari's theorem is known to hold on the polydisc D^d for d>1, i.e., if H_\psi is a bounded Hankel form on H^2(D^d) with analytic symbol \psi, then there is a function \phi in L^\infty(\T^d) such that \psi is the Riesz projection of \phi. A method proposed in Helson's last paper is used to show that the constant C_d in the estimate \|\phi\|_\infty\le C_d \|H_\psi\| grows at least exponentially with d; it follows that there is no analogue of Nehari's theorem on the infinite-dimensional polydisc

Food Preservation by Freezing

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Tidal Remnants and Intergalactic HII Regions

We report the discovery of two small intergalactic HII regions in the loose group of galaxies around the field elliptical NGC 1490. The HII regions are located at least 100 kpc from any optical galaxy but are associated with a number of large HI clouds that are lying along an arc 500 kpc in length and that have no optical counterpart on the Digital Sky Survey. The sum of the HI masses of the clouds is almost 10^10 M_sun and the largest HI cloud is about 100 kpc in size. Deep optical imaging reveals a very low surface brightness counterpart to this largest HI cloud, making this one of the HI richest optical galaxies known (M_HI/L_V~200). Spectroscopy of the HII regions indicates that the abundance in these HII regions is only slightly sub-solar, excluding a primordial origin of the HI clouds. The HI clouds are perhaps remnants resulting from the tidal disruption of a reasonably sized galaxy, probably quite some time ago, by the loose group to which NGC1490 belongs. Alternatively, they are remnants of the merger that created the field elliptical NGC1490. The isolated HII regions show that star formation on a very small scale can occur in intergalactic space in gas drawn from galaxies by tidal interactions. Many such intergalactic small star formation regions may exist near tidally interacting galaxies.Comment: To appear in the proceedings of the IAU Symposium #217, Recycling Intergalactic and Interstellar Matter, eds. P.-A. Duc, J. Braine, and E. Brinks, 6 pages with low resolution figures. The full paper with high resolution images can be downloaded from http://www.astron.nl/~morganti/Papers/cloud.ps.g

Delta-like and gtl2 are reciprocally expressed, differentially methylated linked imprinted genes on mouse chromosome 12

AbstractThe distal portion of mouse chromosome 12 is imprinted. To date, however, Gtl2 is the only imprinted gene identified on chromosome 12. Gtl2 encodes multiple alternatively spliced transcripts with no apparent open reading frame. Using conceptuses with maternal or paternal uniparental disomy for chromosome 12 (UPD12), we found that Gtl2 is expressed from the maternal allele and methylated at the 5′ end of the silent paternal allele. A reciprocally imprinted gene, Delta-like (Dlk), with homology to genes involved in the Notch signalling pathway was identified 80kb upstream of Gtl2. Dlk was expressed exclusively from the paternal allele in both the embryo and placenta, but the CpG-island promoter of Dlk was completely unmethylated on both parental alleles. Rather, a paternally methylated region was identified in the last exon of the active Dlk allele. The proximity, reciprocal imprinting and methylation in this domain are reminiscent of the co-ordinately regulated Igf2–H19 imprinted domain on mouse chromosome 7. Like H19 and Igf2, Gtl2 and Dlk were found to be co-expressed in the same tissues throughout development, though not after birth. These results have implications for the regulation, function and evolution of imprinted domains