Shape maps for second order partial differential equations

We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a congruence volume whose collapse we study through an appropriate evolution equation, akin to Raychaudhuri's equation. We develop the necessary geometric framework on a suitable jet space in which the shape maps appear naturally associated with certain linear connections. Explicit computations are given, along with a nontrivial example

Acid Rain: Multilateral and Bilateral Approaches to Transboundary Pollution under International Law

This article seeks to examine the difficult problem of acid rain in an international law context. It begins by discussing the environmental difficulties that may be created by acid rain. Within this context, the authors then discuss the development of customary international law relevant to the question of acid rain. Following this, the authors move to a more specific discussion of multilateral and bilateral arrangements dealing with transboundary pollution with special emphasis on American-Canadian relations. Finally, the authors conclude by assessing the difficulties associated with the development of legal standards in this areaCette étude  cherchera à examiner l'énorme probleme des précipitations acides à l'intérieur d'un contexte de droit international. L'auteur premièrement discutera des difficultés environnementales que crée les précipitations acides, et puis, il notera le développement coutumier du droit international qui sefit autour du problème de précipitations acides. Par après, on apercevra l'étude prendre une note plus spécifique détaillant les arrangements bilatéraux et multilatéraux de la pollution transfrontière, avec une emphase spéciale sur les relations américo-canadiennes. En dernier, l'auteur évaluera les problèmes associés au développement des standards légaux dans cette region

solveME: fast and reliable solution of nonlinear ME models.

BackgroundGenome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints.ResultsHere, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models using a quad-precision NLP solver (Quad MINOS). Our method was up to 45 % faster than binary search for six significant digits in growth rate. We also develop a fast, quad-precision flux variability analysis that is accelerated (up to 60× speedup) via solver warm-starts. Finally, we employ the tools developed to investigate growth-coupled succinate overproduction, accounting for proteome constraints.ConclusionsJust as genome-scale metabolic reconstructions have become an invaluable tool for computational and systems biologists, we anticipate that these fast and numerically reliable ME solution methods will accelerate the wide-spread adoption of ME models for researchers in these fields

Tangent bundle geometry induced by second order partial differential equations

We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection type'. Whereas for ODEs the decomposition is intrinsic, for PDEs it is necessary to specify a closed 1-form on the manifold of independent variables, together with a transverse local vector field. The resulting decomposition provides several natural curvature operators. The harmonic map equation is examined, and in this case both the 1-form and the vector field arise naturally

The Southern 2MASS AGN Survey: spectroscopic follow-up with 6dF

The Two Micron All-Sky Survey (2MASS) has provided a uniform photometric catalog to search for previously unknown red AGN and QSOs. We have extended the search to the southern equatorial sky by obtaining spectra for 1182 AGN candidates using the 6dF multifibre spectrograph on the UK Schmidt Telescope. These were scheduled as auxiliary targets for the 6dF Galaxy Redshift Survey. The candidates were selected using a single color cut of J - Ks > 2 to Ks ~ 15.5 and a galactic latitude of |b|>30 deg. 432 spectra were of sufficient quality to enable a reliable classification. 116 sources (or ~27%) were securely classified as type 1 AGN, 20 as probable type 1s, and 57 as probable type 2 AGN. Most of them span the redshift range 0.05<z<0.5 and only 8 (or ~6%) were previously identified as AGN or QSOs. Our selection leads to a significantly higher AGN identification rate amongst local galaxies (>20%) than in any previous galaxy survey. A small fraction of the type 1 AGN could have their optical colors reddened by optically thin dust with A_V<2 mag relative to optically selected QSOs. A handful show evidence for excess far-IR emission. The equivalent width (EW) and color distributions of the type 1 and 2 AGN are consistent with AGN unified models. In particular, the EW of the [OIII] emission line weakly correlates with optical--near-IR color in each class of AGN, suggesting anisotropic obscuration of the AGN continuum. Overall, the optical properties of the 2MASS red AGN are not dramatically different from those of optically-selected QSOs. Our near-IR selection appears to detect the most near-IR luminous QSOs in the local universe to z~0.6 and provides incentive to extend the search to deeper near-IR surveys.Comment: 57 pages, 12 figures, 4 tables, to appear in vol.27/4 of Publications of the Astronomical Society of Australia (PASA

Hair Bundle Morphology on Surviving Hair Cells of the Chick Basilar Papilla Exposed to Intense Sound

Exposure to intense sound produces a well-defined patch lesion on the chick basilar papilla in which 30-35% of the short hair cells are lost. The present study compares various aspects of sensory hair bundle morphology on surviving hair cells in the patch lesion with hair bundles from matched locations on nonexposed control papilla immediately after removal from the exposure and 12-days post exposure. The height and thickness of the hairs, the total number of hairs in the bundle, the width of the bundle, and the area and perimeter of the apical surface of the hair cell were quantified from scanning electron microscope photomicrographs. An attempt was also made to determine if there was a consistent microstructure to the pattern of hair cell loss within the lesion area. Similar observations in 12-day recovered ears are also presented. The results indicated that stereocilia height increased and width decreased on surviving hair cells in the exposed ear. The width of the hair bundle, the hair cell surface area, and perimeter also decreased. However, the number of hairs per cell remained unchanged, and there was no evidence of any consistent organization to the hair cell loss within the patch across a number of specimens. These observations indicated that the hair bundles on short hair cells underwent changes as a consequence of intense sound exposure.The results after 12 days of recovery were complicated by developmental changes on the papilla and incomplete maturation of the newly regenerated hair cells. It remains to be seen whether these changes were the result of cell sampling in the sound-damaged ear or were due to true structural alterations within the sensory hairs themselves

Homogeneous variational problems: a minicourse

A Finsler geometry may be understood as a homogeneous variational problem, where the Finsler function is the Lagrangian. The extremals in Finsler geometry are curves, but in more general variational problems we might consider extremal submanifolds of dimension $m$. In this minicourse we discuss these problems from a geometric point of view.Comment: This paper is a written-up version of the major part of a minicourse given at the sixth Bilateral Workshop on Differential Geometry and its Applications, held in Ostrava in May 201

Influence of a Corpus Luteum Tissue Extract on Rabbit Ovarian Mesothelial Cells

This study investigates rabbit ovarian mesothelial (OM) cells exposed in vitro to a crude corpus luteum extract (CLE; 60 μg/ml). The growth of OM cells was evaluated by measuring the change in cell number (mean % ± standard error of mean, SEM), the number of cell population doublings (CPD ± SEM), and the cell population doubling time in hours (CPDT ± SEM) after 7.5 days of culture in a serum-poor medium. Quantitative estimates of surface morphology changes were obtained by analyzing the total number (mean no. ± SEM), density (mean no./100 μ.m2 ± SEM), and length-to-diameter ratio (mean L/D ± SEM) of microvilli. OM cells in control medium formed loosely cohesive monolayers, and grew 152.53 ± 11.01% with a CPD of 0.59 ± 0.08 and a CPDT of 117.29 ± 6.43 hours. The exposed surface area of these cells was over 8,000 μ.m2 and was covered in its epinuclear region by long and slender microvilli with a L/D of 6.01 ± 0.29. The total number of microvilli in each control cell was 1977.52 ± 120.49 with a density of 0.58 ± 0.03/100 μ.m2 in the epinuclear region and of 0.05 ± 0.003/150 μ.m2 in the remaining surface area (5,161.62 ± 354.43 μ.m2). In contrast, CLE-rich cells cultures grew 329.57 ± 16.65%, with a CPD of 1.71 ± 0.07 and a CPDT of 53.43 + 2.93 hours. These cells formed confluent monolayers of smaller (2104.86 ± 103.71 μ.m2), tightly juxtaposed epithelioid cells with a microvillar density of 0.70 ± 0.03/100 μ.m2 in over 78% of their surface. These data support the existence of an intra-ovarian factor capable of enhancing growth and differentiation of OM cells

Measurement of thin liquid film drainage using a novel high-speed impedance analyzer

This work describes the design and implementation of a new instrument, called the thin film impedance analyzer, which measures the rate of drainage of thin oil films. The instrument forms an oil film by elevating a planar oil–water interface into a water drop hanging from a stainless steel capillary tube immersed in the oil. The instrument measures the magnitude of the impedance of the matter between the capillary tube and a screen electrode immersed in the lower water phase. Under appropriate conditions, the capacitance of the oil film dominates the impedance. The instrument records the increase in the magnitude of the admittance associated with the draining and thinning of the oil film. The features of the drainage curves vary considerably with the type, amount, and location of surfactants in the oil and water phases, as well as with user-specified values of drop volume, drop equilibration time, and extent of drop compression. For this reason, the instrument has utility as a screening tool for selecting surfactants for emulsion formulations. Potential future uses include accelerated prediction of emulsion stability and extraction of oil–water interfacial rheological parameters

Measurement of Thin Liquid Film Drainage Using a Novel High-Speed Impedance Analyzer

This work describes the design and implementation of a new instrument, called the thin film impedance analyzer, which measures the rate of drainage of thin oil films. The instrument forms an oil film by elevating a planar oil–water interface into a water drop hanging from a stainless steel capillary tube immersed in the oil. The instrument measures the magnitude of the impedance of the matter between the capillary tube and a screen electrode immersed in the lower water phase. Under appropriate conditions, the capacitance of the oil film dominates the impedance. The instrument records the increase in the magnitude of the admittance associated with the draining and thinning of the oil film. The features of the drainage curves vary considerably with the type, amount, and location of surfactants in the oil and water phases, as well as with user-specified values of drop volume, drop equilibration time, and extent of drop compression. For this reason, the instrument has utility as a screening tool for selecting surfactants for emulsion formulations. Potential future uses include accelerated prediction of emulsion stability and extraction of oil–water interfacial rheological parameters