Optimal Lβ\mathfrak{L}^{\beta}-Control for the Global Cauchy Problem of the Relativistic Vlasov-Poisson System

Recently, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh proved that a unique global classical solution to the relativistic Vlasov-Poisson system exists whenever the positive, integrable initial datum is spherically symmetric, compactly supported in momentum space, vanishes on characteristics with vanishing angular momentum, and for $\beta \ge 3/2$ has $\mathfrak{L}^{\beta}$-norm strictly below a positive, critical value $\mathcal{C}_{\beta}$. Everything else being equal, data leading to finite time blow-up can be found with $\mathfrak{L}^{\beta}$-norm surpassing $\mathcal{C}_{\beta}$ for any $\beta >1$, with $\mathcal{C}_{\beta}>0$ if and only if $\beta\geq 3/2$. In their paper, the critical value for $\beta = {3}/{2}$ is calculated explicitly while the value for all other $\beta$ is merely characterized as the infimum of a functional over an appropriate function space. In this work, the existence of minimizers is established, and the exact expression of $\mathcal{C}_{\beta}$ is calculated in terms of the famous Lane-Emden functions. Numerical computations of the $\mathcal{C}_{\beta}$ are presented along with some elementary asymptotics near the critical exponent ${3}/{2}$.Comment: 24 pages, 2 figures Refereed and accepted for publication in Transport Theory and Statistical Physic

Pricing Upward-Only Adjusting Leases

This paper presents a stochastic pricing model of a unique, path-dependent lease instrument common in the United Kingdom and numerous commonwealth countries, the upward-only adjusting lease. In this lease, the rental rate is fixed at lease commencement but will be reset to the market rate at predetermined intervals (usually every five years) if it exceeds the contract rent. Numerical results indicate how the initial coupon rate should be set relative to that on a symmetric up-and-downward adjusting variable rate' lease under various economic conditions (level of real interest rates and expected drift and volatility of the underlying rental service flow). We also consider the calculation of effective rents when free rent periods are given during either a market collapse or a steady-state drift.

Exploring Infrared Properties of Giant Low Surface Brightness Galaxies

Abridged: We present analysis of Spitzer Space Telescope observations of the three low surface brightness (LSB) optical giant galaxies Malin 1, UGC 6614 and UGC 9024. Mid- and far-infrared morphology, spectral energy distributions, and integrated colors are used to derive the dust mass, dust-to-gas mass ratio, total infrared luminosity, and star formation rate (SFR). The 8 micron images indicate that polycyclic aromatic hydrocarbon molecules are present in the central regions of all three metal-poor LSB galaxies. The diffuse optical disks of Malin 1 and UGC 9024 remain undetected at mid- and far-infrared wavelengths. The dustiest of the three LSB galaxies, UGC 6614, has infrared morphology that varies significantly with wavelength. The 8 and 24 micron emission is co-spatial with H\alpha emission previously observed in the outer ring of UGC 6614. The estimated dust-to-gas ratios, from less than 10^{-3} to 10^{-2}, support previous indications that the LSB galaxies are relatively dust poor compared to the HSB galaxies. The total infrared luminosities are approximately 1/3 to 1/2 the blue band luminosities, suggesting that old stellar populations are the primary source of dust heating in these LSB objects. The SFR estimated from the infrared data ranges ~0.01-0.88 M_sun yr^{-1}, consistent with results from optical studies.Comment: Accepted in ApJ (2007, July 20 issue), 34 pages, 10 postscript figures, 2 table

How should you evaluate an asymptomatic patient with a femoral or iliac artery bruit?

Perform an ankle-arm index (AAI, or ankle- brachial index) test to evaluate for peripheral artery disease (PAD) (strength of recommendation [SOR]: B, cohort studies). If the test detects PAD, recommend steps to modify cardiovascular risk factors (SOR: B, extrapolation from randomized clinical trials [RCTs])

The Influence of Topology on Hydraulic Conductivity in a Sand-and-Gravel Aquifer

A field experiment consisting of geophysical logging and tracer testing was conducted in a single well that penetrated a sand-and-gravel aquifer at the U.S. Geological Survey Toxic Substances Hydrology research site on Cape Cod, Massachusetts. Geophysical logs and flowmeter/pumping measurements were obtained to estimate vertical profiles of porosity ϕ, hydraulic conductivity K, temperature, and bulk electrical conductivity under background, freshwater conditions. Saline-tracer fluid was then injected into the well for 2 h and its radial migration into the surrounding deposits was monitored by recording an electromagnetic-induction log every 10 min. The field data are analyzed and interpreted primarily through the use of Archie’s (1942) law to investigate the role of topological factors such as pore geometry and connectivity, and grain size and packing configuration in regulating fluid flow through these coarse-grained materials. The logs reveal no significant correlation between K and ϕ, and imply that groundwater models that link these two properties may not be useful at this site. Rather, it is the distribution and connectivity of the fluid phase as defined by formation factor F, cementation index m, and tortuosity α that primarily control the hydraulic conductivity. Results show that F correlates well with K, thereby indicating that induction logs provide qualitative information on the distribution of hydraulic conductivity. A comparison of α, which incorporates porosity data, with K produces only a slightly better correlation and further emphasizes the weak influence of the bulk value of ϕ on K

The Influence of Topology on Hydraulic Conductivity in a Sand-and-Gravel Aquifer

A field experiment consisting of geophysical logging and tracer testing was conducted in a single well that penetrated a sand-and-gravel aquifer at the U.S. Geological Survey Toxic Substances Hydrology research site on Cape Cod, Massachusetts. Geophysical logs and flowmeter/pumping measurements were obtained to estimate vertical profiles of porosity ϕ, hydraulic conductivity K, temperature, and bulk electrical conductivity under background, freshwater conditions. Saline-tracer fluid was then injected into the well for 2 h and its radial migration into the surrounding deposits was monitored by recording an electromagnetic-induction log every 10 min. The field data are analyzed and interpreted primarily through the use of Archie’s (1942) law to investigate the role of topological factors such as pore geometry and connectivity, and grain size and packing configuration in regulating fluid flow through these coarse-grained materials. The logs reveal no significant correlation between K and ϕ, and imply that groundwater models that link these two properties may not be useful at this site. Rather, it is the distribution and connectivity of the fluid phase as defined by formation factor F, cementation index m, and tortuosity α that primarily control the hydraulic conductivity. Results show that F correlates well with K, thereby indicating that induction logs provide qualitative information on the distribution of hydraulic conductivity. A comparison of α, which incorporates porosity data, with K produces only a slightly better correlation and further emphasizes the weak influence of the bulk value of ϕ on K

Longitudinal stability augmentation of seaplanes in planing

The towing tank experiments conducted at Yokohama National University from November 30 to December 9 in 2005 suggested a new way of suppressing a dangerous coupled motion between heave and pitch called porpoising. The research in this paper was developed on the observations made in the experiments and conducted numerical simulations to further investigate the parametric design space. Two linear-time-invariant models were developed: rigid-body planing craft (conventional float planes or flying boats), and flexibly supported planing craft. The latter could simulate the new method found in the experiments for suppressing porpoising. In this study, the stability of the oscillatory motions was analyzed to see the effect of design variables on the inception of porpoising. The parametric study of flexibly supported float planes in the context of porpoising was a new contribution in the conceptual design of seaplanes

SN1991bg-like supernovae are associated with old stellar populations

SN1991bg-like supernovae are a distinct subclass of thermonuclear supernovae (SNe Ia). Their spectral and photometric peculiarities indicate their progenitors and explosion mechanism differ from `normal' SNe Ia. One method of determining information about supernova progenitors we cannot directly observe is to observe the stellar population adjacent to the apparent supernova explosion site to infer the distribution of stellar population ages and metallicities. We obtain integral field observations and analyse the spectra extracted from regions of projected radius $\sim\,\mathrm{kpc}$ about the apparent SN explosion site for 11 91bg-like SNe in both early- and late-type galaxies. We utilize full-spectrum spectral fitting to determine the ages and metallicities of the stellar population within the aperture. We find that the majority of the stellar populations that hosted 91bg-like supernovae have little recent star formation. The ages of the stellar populations suggest that that 91bg-like SN progenitors explode after delay times of $>6\,\mathrm{Gyr}$, much longer than the typical delay time of normal SNe Ia, which peaks at $\sim 1\,\mathrm{Gyr}$.Comment: 12 pages, 3 figures, 3 tables, submitted to Publications of the Astronomical Society of Australi