Horrocks Correspondence on a Quadric Surface

We extend the Horrocks correspondence between vector bundles and cohomology modules on the projective plane to the product of two projective lines. We introduce a set of invariants for a vector bundle on the product of two projective lines, which includes the first cohomology module of the bundle, and prove that there is a one to one correspondence between these sets of invariants and isomorphism classes of vector bundles without line bundle summands.Comment: 19 page

Horrocks Correspondence on ACM Varieties

We describe a vector bundle \sE on a smooth $n$-dimensional ACM variety in terms of its cohomological invariants H^i_*(\sE), $1\leq i \leq n-1$, and certain graded modules of "socle elements" built from \sE. In this way we give a generalization of the Horrocks correspondence. We prove existence theorems where we construct vector bundles from these invariants and uniqueness theorems where we show that these data determine a bundle up to isomorphisms. The cases of the quadric hypersurface in $\mathbb P^{n+1}$ and the Veronese surface in $\mathbb P^5$ are considered in more detail.Comment: 18 pages, not figure

The Bis(ferrocenyl)phosphenium Ion Revisited

The bis(ferrocenyl)phosphenium ion, [Fc2P]+, reported by Cowley et al. (J. Am. Chem. Soc. 1981, 103, 714–715), was the only claimed donor‐free divalent phosphenium ion. Our examination of the molecular and electronic structure reveals that [Fc2P]+ possesses significant intramolecular Fe⋅⋅⋅P contacts, which are predominantly electrostatic and moderate the Lewis acidity. Nonetheless, [Fc2P]+ undergoes complex formation with the Lewis bases PPh3 and IPr to give the donor–acceptor complexes [Fc2P(PPh3)]+ and [Fc2P(IPr)]+ (IPr=1,3‐bis(2,6‐diisopropylphenyl)imidazole‐2‐ylidene)

The water supercooled regime as described by four common water models

The temperature scale of simple water models in general does not coincide with the natural one. Therefore, in order to make a meaningful evaluation of different water models a temperature rescaling is necessary. In this paper we introduce a rescaling using the melting temperature and the temperature corresponding to the maximum of the heat capacity to evaluate four common water models (TIP4P-Ew, TIP4P-2005, TIP5P-Ew and Six-Sites) in the supercooled regime. Although all the models show the same general qualitative behavior, the TIP5P-Ew appears as the best representation of the supercooled regime when the rescaled temperature is used. We also analyze, using thermodynamic arguments, the critical nucleus size for ice growth. Finally, we speculate on the possible reasons why atomistic models do not usually crystalize while the coarse grained mW model do crystallize.Comment: 8 pages, 8 figure

The Planck-LFI instrument: analysis of the 1/f noise and implications for the scanning strategy

We study the impact of the 1/f noise on the PLANCK Low Frequency Instrument (LFI) osbervations (Mandolesi et al 1998) and describe a simple method for removing striping effects from the maps for a number of different scanning stategies. A configuration with an angle between telescope optical axis and spin-axis just less than 90 degrees (namely 85 degress) shows good destriping efficiency for all receivers in the focal plane, with residual noise degradation < 1-2 %. In this configuration, the full sky coverage can be achieved for each channel separately with a 5 degrees spin-axis precession to maintain a constant solar aspect angle.Comment: submitted to Astronomy and Astrophysics, 12 pages, 15 PostSript figure

Planck Low Frequency Instrument: Beam Patterns

The Low Frequency Instrument on board the ESA Planck satellite is coupled to the Planck 1.5 meter off-axis dual reflector telescope by an array of 27 corrugated feed horns operating at 30, 44, 70, and 100 GHz. We briefly present here a detailed study of the optical interface devoted to optimize the angular resolution (10 arcmin at 100 GHz as a goal) and at the same time to minimize all the systematics coming from the sidelobes of the radiation pattern. Through optical simulations, we provide shapes, locations on the sky, angular resolutions, and polarization properties of each beam.Comment: On behalf of the Planck collaboration. 3 pages, 1 figure. Article published in the Proceedings of the 2K1BC Experimental Cosmology at millimetre wavelength

SSADH variation in primates: Intra- and interspecific data on a gene with a potential role in human cognitive functions

In the present study we focus on the nucleotide and the inferred amino acid variation occurring in humans and other primate species for mitochondrial NAD(+)-dependent succinic semialdehyde dehydrogenase, a gene recently supposed to contribute to cognitive performance in humans. We determined 2527 bp of coding, intronic, and flanking sequences from chimpanzee, bonobo, gorilla, orangutan, gibbon, and macaque. We also resequenced the entire coding sequence on 39 independent chromosomes from Italian families. Four variable coding sites were genotyped in additional populations from Europe, Africa, and Asia. A test for constancy of the nonsynonymous vs. synonymous rates of nucleotide changes revealed that primates are characterized by largely variable d(N)/d(S) ratios. On a background of strong conservation, probably controlled by selective constraints, the lineage leading to humans showed a ratio increased to 0.42. Human polymorphic levels fall in the range reported for other genes, with a pattern of frequency and haplotype structure strongly suggestive of nonneutrality. The comparison with the primate sequences allowed inferring the ancestral state at all variable positions, suggesting that the c.538(C) allele and the associated functional variant is indeed a derived state that is proceeding to fixation. The unexpected pattern of human polymorphism compared to interspecific findings outlines the possibility of a recent positive selection on some variants relevant to new cognitive capabilities unique to humans

Interplanetary and Interstellar Dust Observed by the Wind/WAVES Electric Field Instrument

Observations of hypervelocity dust particles impacting the Wind spacecraft are reported here for the first time using data from the WindWAVES electric field instrument. A unique combination of rotating spacecraft, amplitude-triggered high-cadence waveform collection, and electric field antenna configuration allow the first direct determination of dust impact direction by any spacecraft using electric field data. Dust flux and impact direction data indicate that the observed dust is approximately micron-sized with both interplanetary and interstellar populations. Nanometer radius dust is not detected by Wind during times when nanometer dust is observed on the STEREO spacecraft and both spacecraft are in close proximity. Determined impact directions suggest that interplanetary dust detected by electric field instruments at 1 AU is dominated by particles on bound trajectories crossing Earths orbit, rather than dust with hyperbolic orbits