Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r) that one usually associates with such a group and hence with a simply-laced Coxeter-Dynkin diagram have a meaningful definition for the non-simply-laced diagrams, too, and as a byproduct we extend Saito's formula for the determinant of the Cartan matrix to all cases. Returning to invariant theory we show that for each irreducible representation i of a binary tetrahedral, octahedral, or icosahedral group one can find a homomorphism into a finite complex reflection group whose defining reflection representation restricts to i.Comment: 19 page

Oxygen Fugacity of the Upper Mantle of Mars. Evidence from the Partitioning Behavior of Vanadium in Y980459 (Y98) and other Olivine-Phyric Shergottites

Using partitioning behavior of V between olivine and basaltic liquid precisely calibrated for martian basalts, we determined the redox state of primitive (olivine-rich, high Mg#) martian basalts near their liquidus. The combination of oxidation state and incompatible element characteristics determined from early olivine indicates that correlations between fO2 and other geochemical characteristics observed in many martian basalts is also a fundamental characteristic of these primitive magmas. However, our data does not exhibit the range of fO2 observed in these previous studies.. We conclude that the fO2 for the martian upper mantle is approximately IW+1 and is incompatible-element depleted. It seems most likely (although clearly open to interpretation) that these mantle-derived magmas assimilated a more oxidizing (>IW+3), incompatible-element enriched, lower crustal component as they ponded at the base of the martian crust

Analysis of RR Lyrae Stars in the Northern Sky Variability Survey

We use data from the Northern Sky Variability Survey (NSVS), obtained from the first generation Robotic Optical Transient Search Experiment (ROTSE-I), to identify and study RR Lyrae variable stars in the solar neighborhood. We initially identified 1197 RRab (RR0) candidate stars brighter than the ROTSE median magnitude V = 14. Periods, amplitudes, and mean V magnitudes are determined for a subset of 1188 RRab stars with well defined light curves. Metallicities are determined for 589 stars by the Fourier parameter method and by the relationship between period, amplitude, and [Fe/H]. We comment upon the difficulties of clearly classifying RRc (RR1) variables in the NSVS dataset. Distances to the RRab stars are calculated using an adopted luminosity-metallicity relation with corrections for interstellar extinction. The 589 RRab stars in our final sample are used to study the properties of the RRab population within 5 kpc of the Sun. The Bailey diagram of period versus amplitude shows that the largest component of this sample belongs to Oosterhoff type I. Metal-rich ([Fe/H] > -1) RRab stars appear to be associated with the Galactic disk. Our metal-rich RRab sample may include a thin disk as well as a thick disk population, although the uncertainties are too large to establish this. There is some evidence among the metal-rich RRab stars for a decline in scale height with increasing [Fe/H], as was found by Layden (1995). The distribution of RRab stars with -1 < [Fe/H] < -1.25 indicates that within this metallicity range the RRab stars are a mixture of stars belonging to halo and disk populations.Comment: 68 pages, 26 figures, 9 tables, accepted to A

Comparative RNAi Screens in C. elegans and C. briggsae Reveal the Impact of Developmental System Drift on Gene Function

Although two related species may have extremely similar phenotypes, the genetic networks underpinning this conserved biology may have diverged substantially since they last shared a common ancestor. This is termed Developmental System Drift (DSD) and reflects the plasticity of genetic networks. One consequence of DSD is that some orthologous genes will have evolved different in vivo functions in two such phenotypically similar, related species and will therefore have different loss of function phenotypes. Here we report an RNAi screen in C. elegans and C. briggsae to identify such cases. We screened 1333 genes in both species and identified 91 orthologues that have different RNAi phenotypes. Intriguingly, we find that recently evolved genes of unknown function have the fastest evolving in vivo functions and, in several cases, we identify the molecular events driving these changes. We thus find that DSD has a major impact on the evolution of gene function and we anticipate that the C. briggsae RNAi library reported here will drive future studies on comparative functional genomics screens in these nematodes

Z7Z_7 Orbifold Models in M-Theory

Among $T^7/\Gamma$ orbifold compactifications of $M$-theory, we examine models containing the particle physics Standard Model in four-dimensional spacetimes, which appear as fixed subspaces of the ten-dimensional spacetimes at each end of the interval, $I^1\simeq S^1/Z_2$, spanning the $11^\text{th}$ dimension. Using the $Z_7$ projection to break the $E_8$ gauge symmetry in each of the four-planes and a limiting relation to corresponding heterotic string compactifications, we discuss the restrictions on the possible resulting gauge field and matter spectra. In particular, some of the states are non-local: they connect two four-dimensional Worlds across the $11^\text{th}$ dimension. We illustrate our programmable calculations of the matter field spectrum, including the anomalous U(1) factor which satisfies a universal Green-Schwarz relation, discuss a Dynkin diagram technique to showcase a model with $SU(3)\times SU(2)\times U(1)^5$ gauge symmetry, and discuss generalizations to higher order orbifolds.Comment: 23 pages, 2 figures, 4 tables; LaTeX 3 time

Molecular Composition of Carbonaceous Globules in the Bells (CM2) Chondrite

Some meteorites and IDPs contain micron-size carbonaceous globules that are associated with significant H and/or N isotopic anomalies. This has been interpreted as indicating that such globules may contain at least partial preserved organic species formed in the outer reaches of the proto-solar disk or the presolar cold molecular cloud. Owing to their small sizes, relatively little is known about their chemical compositions. Here we present in situ measurements of aromatic molecular species in organic globules from the Bells (CM2) chondrite by microprobe two-step laser mass spectrometry. This meteorite was chosen for study because we have previously found this meteorite to contain high abundances of globules that often occur in clusters. The Bells (CM2) globules are also noteworthy for having particularly high enrichments in H-2. and N-15. In this study, we identified individual globules and clusters of globules using native UV fluorescence

A study of 15N14N isotopic exchange over cobalt molybdenum nitrides

The 14N/15N isotopic exchange pathways over Co3Mo3N, a material of interest as an ammonia synthesis catalyst and for the development of nitrogen transfer reactions, have been investigated. Both the homomolecular and heterolytic exchange processes have been studied, and it has been shown that lattice nitrogen species are exchangeable. The exchange behavior was found to be a strong function of pretreatment with ca. 25% of lattice N atoms being exchanged after 40 min at 600 °C after N2 pretreatment at 700 °C compared to only 6% following similar Ar pretreatment. This observation, for which the potential contribution of adsorbed N species can be discounted, is significant in terms of the application of this material. In the case of the Co6Mo6N phase, regeneration to Co3Mo3N under 15N2 at 600 °C occurs concurrently with 14N15N formation. These observations demonstrate the reactivity of nitrogen in the Co–Mo–N system to be a strong function of pretreatment and worthy of further consideration

Dynamical Confirmation of SDSS Weak Lensing Scaling Laws

Galaxy masses can be estimated by a variety of methods; each applicable in different circumstances, and each suffering from different systematic uncertainties. Confirmation of results obtained by one technique with analysis by another is particularly important. Recent SDSS weak lensing measurements of the projected-mass correlation function reveal a linear relation between galaxy luminosities and the depth of their dark matter halos (measured on 260 \hinv kpc scales). In this work we use an entirely independent dynamical method to confirm these results. We begin by assembling a sample of 618 relatively isolated host galaxies, surrounded by a total of 1225 substantially fainter satellites. We observe the mean dynamical effect of these hosts on the motions of their satellites by assembling velocity difference histograms. Dividing the sample by host properties, we find significant variations in satellite velocity dispersion with host luminosity. We quantify these variations using a simple dynamical model, measuring \mtsd a dynamical mass within 260 \hinv kpc. The appropriateness of this mass reconstruction is checked by conducting a similar analysis within an N-body simulation. Comparison between the dynamical and lensing mass-to-light scalings shows reasonable agreement, providing some quantitative confirmation for the lensing results.Comment: 7 pages, 3 figures, accepted for publication in ApJ Letter