Mathematical Properties of a Class of Four-dimensional Neutral Signature Metrics

While the Lorenzian and Riemanian metrics for which all polynomial scalar curvature invariants vanish (the VSI property) are well-studied, less is known about the four-dimensional neutral signature metrics with the VSI property. Recently it was shown that the neutral signature metrics belong to two distinct subclasses: the Walker and Kundt metrics. In this paper we have chosen an example from each of the two subcases of the Ricci-flat VSI Walker metrics respectively. To investigate the difference between the metrics we determine the existence of a null, geodesic, expansion-free, shear-free and vorticity-free vector, and classify these spaces using their infinitesimal holonomy algebras. The geometric implications of the holonomy algebras are further studied by identifying the recurrent or covariantly constant null vectors, whose existence is required by the holonomy structure in each example. We conclude the paper with a simple example of the equivalence algorithm for these pseudo-Riemannian manifolds, which is the only approach to classification that provides all necessary information to determine equivalence.Comment: 18 page

Exactly solvable model with two conductor-insulator transitions driven by impurities

We present an exact analysis of two conductor-insulator transitions in the random graph model. The average connectivity is related to the concentration of impurities. The adjacency matrix of a large random graph is used as a hopping Hamiltonian. Its spectrum has a delta peak at zero energy. Our analysis is based on an explicit expression for the height of this peak, and a detailed description of the localized eigenvectors and of their contribution to the peak. Starting from the low connectivity (high impurity density) regime, one encounters an insulator-conductor transition for average connectivity 1.421529... and a conductor-insulator transition for average connectivity 3.154985.... We explain the spectral singularity at average connectivity e=2.718281... and relate it to another enumerative problem in random graph theory, the minimal vertex cover problem.Comment: 4 pages revtex, 2 fig.eps [v2: new title, changed intro, reorganized text

P01.50. Influence of dietary red palm oil on antioxidant status in male Wistar rats

Journal articleAntioxidant status in male rats following the dietary consumption of red palm oil (RPO) was investigated. Male wistar rats were randomly divided into three groups. Group 1 (n=5) received no RPO supplementation and served as the control while group 2 (n=6) and 3 (n=6) received 2ml and 4ml RPO respectively. Plasma total polyphenols, plasma antioxidant capacity i.e. oxygen radical absorbance capacity (ORAC), ferric reducing antioxidant power (FRAP) as well as liver and erythrocyte antioxidant enzymes [catalase (CAT), glutathione peroxidase (GPx) and superoxide dismutase (SOD)] levels were determined using established techniques. Our results showed no significant differences (p<0.05) in total polyphenols, ORAC and FRAP in palm oil fed groups when compared with the control group. Catalase levels significantly increased (p<0.05) at both 2ml and 4ml RPO in the liver and erythrocyte. There was no significant difference in the liver GPx levels in palm oil fed groups while erythrocyte GPx level significantly increased at 4ml RPO when compared with the control group. Red palm oil did not significantly increase (p<0.05) liver and erythrocyte SOD levels in all the groups when compared with the control group. In conclusion, red palm oil increased the levels of liver and erythrocyte catalase as well as erythrocyte glutathione peroxidase level and hence, its dietary consumption could help to boost antioxidant status in the body and thus promote good health

Analysis and test evaluation of the dynamic response and stability of three advanced turboprop models

Results of dynamic response and stability wind tunnel tests of three 62.2 cm (24.5 in) diameter models of the Prop-Fan, advanced turboprop, are presented. Measurements of dynamic response were made with the rotors mounted on an isolated nacelle, with varying tilt for nonuniform inflow. One model was also tested using a semi-span wing and fuselage configuration for response to realistic aircraft inflow. Stability tests were performed using tunnel turbulence or a nitrogen jet for excitation. Measurements are compared with predictions made using beam analysis methods for the model with straight blades, and finite element analysis methods for the models with swept blades. Correlations between measured and predicted rotating blade natural frequencies for all the models are very good. The IP dynamic response of the straight blade model is reasonably well predicted. The IP response of the swept blades is underpredicted and the wing induced response of the straight blade is overpredicted. Two models did not flutter, as predicted. One swept blade model encountered an instability at a higher RPM than predicted, showing predictions to be conservative

An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation

Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for this problem using the l_inf norm, and we present an optimal linear time algorithm based on novel formalism. Moreover, given a precomputation in time O(n log n) consisting of a labeling of all extrema, we compute any optimal segmentation in constant time. We compare experimentally its performance to two piecewise linear segmentation heuristics (top-down and bottom-up). We show that our algorithm is faster and more accurate. Applications include pattern recognition and qualitative modeling.Comment: This is the extended version of our ICDM'05 paper (arXiv:cs/0702142

The north-south asymmetry of the ALFALFA HI velocity width function

The number density of extragalactic 21-cm radio sources as a function of their spectral line-widths -- the HI width function (HIWF) -- is a sensitive tracer of the dark matter halo mass function (HMF). The $\Lambda$ cold dark matter model predicts that the HMF should be identical everywhere provided it is sampled in sufficiently large volumes, implying that the same should be true of the HIWF. The ALFALFA 21-cm survey measured the HIWF in northern and southern Galactic fields and found a systematically higher number density in the north. At face value, this is in tension with theoretical predictions. We use the Sibelius-DARK N-body simulation and the semi-analytical galaxy formation model GALFORM to create a mock ALFALFA survey. We find that the offset in number density has two origins: the sensitivity of the survey is different in the two fields, which has not been correctly accounted for in previous measurements; and the $1/V_{\mathrm{eff}}$ algorithm used for completeness corrections does not fully account for biases arising from spatial clustering in the galaxy distribution. The latter is primarily driven by a foreground overdensity in the northern field within $30\,\mathrm{Mpc}$, but more distant structure also plays a role. We provide updated measurements of the ALFALFA HIWF (and HIMF) correcting for the variations in survey sensitivity. Only when systematic effects such as these are understood and corrected for can cosmological models be tested against the HIWF.Comment: MNRAS accepte

KIC 10449976: discovery of an extreme-helium subdwarf in the Kepler field

Optical spectroscopy of the blue star KIC 10449976 shows that it is an extremely helium-rich subdwarf with effective temperature T=40000+/-300 K and surface gravity log g=5.3+/-0.1. Radial-velocity measurements over a five-day timescale show an upper variability limit of ~50+/-20 km/s. Kepler photometry of KIC 10449976 in both long and short cadence modes shows evidence for a periodic modulation on a timescale of ~3.9 days. We have examined the possibility that this modulation is not astrophysical but conclude it is most likely real. We discuss whether the modulation could be caused by a low-mass companion, by stellar pulsations, or by spots. The identification of any one of these as cause has important consequences for understanding the origin of helium-rich subdwarfs.Comment: Accepted by MNRA

The scatter about the "Universal" dwarf spheroidal mass profile: A kinematic study of the M31 satellites, And V and And VI

While the satellites of the Milky Way (MW) have been shown to be largely consistent in terms of their mass contained within one half--light radius (M_{half}) with a "Universal" mass profile, a number of M31 satellites are found to be inconsistent with such relations, and seem kinematically colder in their central regions than their MW cousins. In this work, we present new kinematic and updated structural properties for two M31 dSphs, And V and And VI using data from the Keck Low Resolution Imaging Spectrograph (LRIS) and the DEep Imaging Multi-Object Spectrograph (DEIMOS) instruments and the Subaru Suprime-Cam imager. We measure systemic velocities of v_r=-393.1+/-4.2km/s and -344.8+/-2.5km/s, and dispersions of sigma_v=11.5{+5.3}{-4.4}km/s and sigma_v=9.4{+3.2}{-2.4}km/s for And V and And VI respectively, meaning these two objects are consistent with the trends in sigma_v and r_{half} set by their MW counterparts. We also investigate the nature of this scatter about the MW dSph mass profiles for the "Classical" (i.e. M_V<-8) MW and M31 dSphs. When comparing both the "classical" MW and M31 dSphs to the best--fit mass profiles in the size--velocity dispersion plane, we find general scatter in both the positive (i.e. hotter) and negative (i.e. colder) directions from these profiles. However, barring one exception (CVnI) only the M31 dSphs are found to scatter towards a colder regime, and, excepting the And I dSph, only MW objects scatter to hotter dispersions. We also note that the scatter for the combined population is greater than expected from measurement errors alone. We assess this divide in the context of the differing disc-to-halo mass (i.e. stars and baryons to total virial mass) ratios of the two hosts and argue that the underlying mass profiles for dSphs differ from galaxy to galaxy, and are modified by the baryonic component of the host.Comment: 15 pages, 8 figures. Small modifications made for referee report. Accepted for publication in MNRAS (29/06/2011