Stability of barycentric interpolation formulas

The barycentric interpolation formula defines a stable algorithm for evaluation at points in [−1, 1] of polynomial interpolants through data on Chebyshev grids. Here it is shown that for evaluation at points in the complex plane outside [−1, 1], the algorithm becomes unstable and should be replaced by the alternative modified Lagrange or "first barycentric" formula dating to Jacobi in 1825. This difference in stability confirms the theory published by N. J. Higham in 2004 (IMA J. Numer. Anal., v. 24) and has practical consequences for computation with rational functions

The Deuterium Abundance in the z=0.7 absorber towards QSO PG1718+4807

We report a further analysis of the ratio of deuterium to hydrogen (D/H) using HST spectra of the z=0.701 Lyman limit system towards the QSO PG1718+481. Initial analyses of this absorber found it gave a high D/H value, 1.8 - 3.1 \times 10^{-4} (Webb et al. 1998), inconsistent with several higher redshift measurements. It is thus important to critically examine this measurement. By analysing the velocity widths of the DI, HI and metal lines present in this system, Kirkman et al. (2001) report that the additional absorption in the blue wing of the lya line can not be DI, with a confidence level of 98%. Here we present a more detailed analysis, taking into account possible wavelength shifts between the three sets of HST spectra used in the analysis. We find that the constraints on this system are not as strong as those claimed by Kirkman et al. The discrepancy between the parameters of the blue wing absorption and the parameters expected for DI is marginally worse than 1 sigma. Tytler et al.(1999) commented on the first analysis of Webb et al.(1997,1998), reporting the presence of a contaminating lower redshift Lyman limit system, with log[N(HI)] = 16.7 at z=0.602, which biases the N(HI) estimate for the main system. Here we show that this absorber actually has log[N(HI)] < 14.6 and does not impact on the estimate of N(HI) in the system of interest at z = 0.701. The purpose of the present paper is to highlight important aspects of the analysis which were not explored in previous studies, and hence help refine the methods used in future analyses of D/H in quasar spectra.Comment: 11 pages, 9 figures. Accepted by MNRA

Gypsy moths and American dog ticks: Space partners

An experiment intended for the space shuttle and designed to investigate the effects of weightlessness and total darkness on gypsy moth eggs and engorged American dog ticks is described. The objectives are: (1) to reevaluate the effects of zero gravity on the termination of diapause/hibernation of embryonated gypsy moth eggs, (2) to determine the effect of zero gravity on the ovipositions and subsequent hatch from engorged female American dog ticks that have been induced to diapause in the laboratory, and (3) to determine whether morphological or biochemical changes occur in the insects under examination. Results will be compared with those from a similar experiment conducted on Skylab 4

A TiO study of the black-hole binary GRO J0422+32 in a very low state

We present 53 simultaneous photometric (I band) and spectroscopic (6900-9500 Angstroms) observations of J0422+32, taken during December 1997. From these we determine that J0422+32 was in its lowest state yet observed, at I=20.44+/-0.08. Using relative spectrophotometry, we show that it is possible to correct very accurately for telluric absorption. Following this, we use the TiO bands at 7055 Angstroms and 7589 Angstroms for a radial velocity study and thereby obtain a semi-amplitude of 378+/-16kms-1, which yields f(M)=1.191+/-0.021M_solar and q=9.0+2.2-2.7, consistent with previous observations. We further demonstrate that this little explored method is very powerful for such systems. We also determine a new orbital ephemeris of HJD=2450274.4156+/-0.0009 + 0.2121600+/-0.0000002E. We see some evidence for an ellipsoidal modulation, from which we determine the orbital inclination of J0422+32 to be less than 45 degrees. We therefore calculate a minimum mass for the primary of 2.22M_solar, consistent with a black hole, but not necessarily the super-massive one proposed by Beekman et al (1997). We obtain an M4-5 spectral type for the secondary star and determine that the secondary contributes 38+/-2% of the flux that we observe from J0422+32 over the range 6950-8400 Angstroms. From this we calculate the distance to the system to be 1.39+/-0.15kpc.Comment: (1) Department of Physics, Keele University, Keele, Staffordshire, ST5 5BG (2) Department of Astrophysics, Nuclear Physics Laboratory, Keble Road, Oxfo rd, OX1 3RH Accepted, to appear in MNRAS 8 pages, 5 figure

Functional Nanocomposite Coatings for Use in Food Packaging

Plastics are a class of materials known for their cost and property advantages, increasing significantly in their usage worldwide. Unfortunately, these benefits come with an increasingly concerning environmental impact. A combination of inadequate disposal options and combinations of materials have led to environmental disasters that will impact generations. One of the worst areas for plastic waste is food packaging. Plastic as a material generally excels at durability and longevity, but as food packaging, it outlives its intended purpose by several orders of magnitude. This leads to plastic food packaging materials sitting in landfill or leading to the environment for hundreds of years. Because of this, there is a strong motivation to develop food packaging materials that are biodegradable, yet still maintain the properties that make plastic better than other classes of materials. Food packaging has many forms, but in general, the most important aspects are cost, mechanical, and oxygen and water barrier properties. To achieve an end-product that excels in these aspects, combinations of materials called composites may be developed. Nanocomposites are a subcategory of composites composed of a matrix material and nanomaterials, separate phases that interact with one another in a number of ways. This research is focused on increasing the mechanical and barrier properties of polyvinyl alcohol, the most commercially-viable biodegradable polymer. The nanomaterials used were graphene oxide (GO) and cellulose nanofibers (CNF) for mechanical and barrier reinforcement. Five sample compositions were produced: a control PVA, CNF, 1 wt% GO, 5 wt% GO, and 10 wt% GO, which were drawn down on uncoated paper and cast by themselves. Testing of these nanocomposites included oxygen transmission, mechanical, and thermal property analysis, and various solvent-interaction testing including absorption of water and oil, Cobb testing, and water vapor permeation. With the addition of CNF and GO to PVA, there was an observed increase in barrier properties through a reduction of hydrophilicity and water absorption, and oxygen permeability

The American Dream in Crisis: How Student Debt Impacts the Educational Experiences of Black Students

In a society riddled with inequities, student debt can be viewed as a crisis for which long term solutions are a necessity. For Black students, student debt has detrimental effects on their overall college experience, including negative implications on their economic status, academic performance, emotional/mental well-being, as well as inhibiting social/civic engagement. This research will highlight the financial disadvantages that Black students undergo, which leads to an oppressive cycle of student debt and limits social mobility. With the stressors of student debt, Black students lose out on engaging socially with peers, as well as having enough time to focus on their academics. From continuous anxiety to constrained decision-making in order to get the most of their education, often these students will choose less satisfying careers with better wages –all in order to maximize the “return on investment” from their intake of student debt –

Isospectral deformations of closed Riemannian manifolds with different scalar curvature

We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds, more precisely, on $S^n\times T^m$, where $T^m$ is a torus of dimension $m\ge 2$ and $S^n$ is a sphere of dimension $n\ge 4$. These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.Comment: amstex, 10 pages, no figure