Odd-parity perturbations of self-similar Vaidya spacetime

We carry out an analytic study of odd-parity perturbations of the self-similar Vaidya space-times that admit a naked singularity. It is found that an initially finite perturbation remains finite at the Cauchy horizon. This holds not only for the gauge invariant metric and matter perturbation, but also for all the gauge invariant perturbed Weyl curvature scalars, including the gravitational radiation scalars. In each case, `finiteness' refers to Sobolev norms of scalar quantities on naturally occurring spacelike hypersurfaces, as well as pointwise values of these quantities.Comment: 28 page

Primary Xanthoma of the Mandible: Report of a Rare Case

Xanthoma is a lesion most commonly seen in soft tissues such as the skin, subcutis, or tendon sheaths. Xanthoma formation is often associated with primary or secondary hyperlipidemia. Primary bone xanthomas are extremely rare benign bone lesions not associated with hyperlipidemia, histopathologically characterized by histiocytes, abundant lipid containing macrophages (foam cells), and multinucleated giant cells. Cholesterol clefts can be found in the medullary bone. Less than ten cases of xanthoma in the mandible have been reported. We present a rare primary intrabony xanthoma in a normolipidemic patient

Bulk and surface energetics of lithium hydride crystal: benchmarks from quantum Monte Carlo and quantum chemistry

We show how accurate benchmark values of the surface formation energy of crystalline lithium hydride can be computed by the complementary techniques of quantum Monte Carlo (QMC) and wavefunction-based molecular quantum chemistry. To demonstrate the high accuracy of the QMC techniques, we present a detailed study of the energetics of the bulk LiH crystal, using both pseudopotential and all-electron approaches. We show that the equilibrium lattice parameter agrees with experiment to within 0.03 %, which is around the experimental uncertainty, and the cohesive energy agrees to within around 10 meV per formula unit. QMC in periodic slab geometry is used to compute the formation energy of the LiH (001) surface, and we show that the value can be accurately converged with respect to slab thickness and other technical parameters. The quantum chemistry calculations build on the recently developed hierarchical scheme for computing the correlation energy of a crystal to high precision. We show that the hierarchical scheme allows the accurate calculation of the surface formation energy, and we present results that are well converged with respect to basis set and with respect to the level of correlation treatment. The QMC and hierarchical results for the surface formation energy agree to within about 1 %.Comment: 16 pages, 4 figure

A Project Based Approach to Statistics and Data Science

In an increasingly data-driven world, facility with statistics is more important than ever for our students. At institutions without a statistician, it often falls to the mathematics faculty to teach statistics courses. This paper presents a model that a mathematician asked to teach statistics can follow. This model entails connecting with faculty from numerous departments on campus to develop a list of topics, building a repository of real-world datasets from these faculty, and creating projects where students interface with these datasets to write lab reports aimed at consumers of statistics in other disciplines. The end result is students who are well prepared for interdisciplinary research, who are accustomed to coping with the idiosyncrasies of real data, and who have sharpened their technical writing and speaking skills

Patient reactions to a web-based cardiovascular risk calculator in type 2 diabetes: a qualitative study in primary care.

Use of risk calculators for specific diseases is increasing, with an underlying assumption that they promote risk reduction as users become better informed and motivated to take preventive action. Empirical data to support this are, however, sparse and contradictory

Spherically symmetric perfect fluid in area-radial coordinates

We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. We show that analytic mass functions describe a static regular centre in these coordinates. In this case, a central singularity can not be realized without an infinite discontinuity in the central density. We construct mass functions involving fluid dynamics at the centre and investigate the relationship between those and the nature of the singularities.Comment: Accepted by CQG. LaTex file, 14 pages, no figure

Speculations on the application of foliar 13C discrimination to reveal groundwater dependency of vegetation and provide estimates of root depth and rates of groundwater use

© Author(s) 2018. Groundwater-dependent vegetation is globally distributed, having important ecological, social, and economic value. Along with the groundwater resources upon which it depends, this vegetation is under increasing threat through excessive rates of groundwater extraction. In this study we examined one shallow-rooted and two deep-rooted tree species at multiple sites along a naturally occurring gradient in depth-to-groundwater. We measured (i) stable isotope ratios of leaves (δ 13C), xylem, and groundwater (δ 2H and δ 18O); and (ii) leaf-vein density. We established that foliar discrimination of 13C (Δ13C) is a reliable indicator of groundwater use by vegetation and can also be used to estimate rooting depth. Through comparison with a continental-scale assessment of foliar Δ13C, we also estimated the upper limits to annual rates of groundwater use. We conclude that maximum rooting depth for both deep-rooted species ranged between 9.4 and 11.2 m and that annual rates of groundwater use ranged from ca. 1400 to 1700 mm for Eucalyptus camaldulensis and from 600 to 900 mm for Corymbia opaca. Several predictions about hydraulic and leaf traits arising from the conclusion that these two species made extensive use of groundwater were supported by additional independent studies of these species in central Australia