Evans function and Fredholm determinants

We explore the relationship between the Evans function, transmission coefficient and Fredholm determinant for systems of first order linear differential operators on the real line. The applications we have in mind include linear stability problems associated with travelling wave solutions to nonlinear partial differential equations, for example reaction-diffusion or solitary wave equations. The Evans function and transmission coefficient, which are both finite determinants, are natural tools for both analytic and numerical determination of eigenvalues of such linear operators. However, inverting the eigenvalue problem by the free state operator generates a natural linear integral eigenvalue problem whose solvability is determined through the corresponding infinite Fredholm determinant. The relationship between all three determinants has received a lot of recent attention. We focus on the case when the underlying Fredholm operator is a trace class perturbation of the identity. Our new results include: (i) clarification of the sense in which the Evans function and transmission coefficient are equivalent; and (ii) proof of the equivalence of the transmission coefficient and Fredholm determinant, in particular in the case of distinct far fields.Comment: 26 page

Numerical heat transfer model for frost protection of citrus fruits by water from a spraying system

A simplified model is developed to simulate the conditions associated with the protection of fruits from frost damage using water from a spraying system. The model simulates the movement of the solidifying water front on a single fruit, and based on that determines the spray frequency needed for a water film to continuously surround the ice-coated fruit to prevent the fruit temperature from dropping below 0ºC. Simulations are presented for the frost protection of sweet oranges (citrus sinensis). The effect of environmental conditions such as air temperature, air velocity, surface radiation and water film evaporation on the development of the ice layer encasing is considered. Simulations show the effect the encasing ice sheet thickness has on the fruit temperature if water from a spraying system is turned off permanently. Experimental tests are also conducted to determine the change in the thermal properties of citrus sinensis for operating temperatures that range from above freezing to sub-freezing. The results of the experimental tests and the numerical simulations shall lead to a better understanding of fruit protection from frost damage by the application of water from a spraying system

First report of Metarhizium anisopliae IP 46 pathogenicity in adult Anopheles gambiae s.s. and An. arabiensis (Diptera; Culicidae).

The entomopathogenic fungus Metarhizium anisopliae isolate IP 46, originating from a soil sample collected in 2001 in the Cerrado of Central Brazil, was tested for its ability to reduce the survival of adult male and female Anopheles gambiae s.s. and An. arabiensis mosquitoes. A 6-h exposure to the fungus coated on test paper at a concentration of 3.3 x 106 conidia cm-2 reduced the daily survival of both mosquito species (HR = 3.14, p < 0.001), with higher risk of dying in An. gambiae s.s relative to An. arabiensis (HR = 1.38, p < 0.001). Fungal sporulation was observed in >95% of mosquito cadavers in the treatment groups. The results indicate that M. anisopliae IP 46 has the potential to be a bio-control agent for African malaria vector species, and is a suitable candidate for further research and development

Evaluation of High Impedance Surfaces for MRI RF Coil Applications ­ Simulations of RF Field and Specific Absorption Rate

This paper investigates the use of High Impedance Surfaces (HIS) to enhance the magnetic near-field within a dielectric phantom stimulated by a surface coil antenna resonating at 63.8 MHz for use in Magnetic Resonance Imaging (MRI) systems. Specifically, the optimization of the space between the surface of the coil and the HIS is presented here. The HIS incorporates interdigitated capacitive elements that produce an electrically small unit cell size. The magnetic field strength is shown to be improved by 42% as compared to a system which uses only an RF shield The associated Specific Absorption Rate (SAR) for the optimum design is simulated and compared to international standards. The work is aimed at 1.5T MRI applications

Metallicities of 0.3<z<1.0 Galaxies in the GOODS-North Field

We measure nebular oxygen abundances for 204 emission-line galaxies with redshifts 0.3<z<1.0 in the Great Observatories Origins Deep Survey North (GOODS-N) field using spectra from the Team Keck Redshift Survey (TKRS). We also provide an updated analytic prescription for estimating oxygen abundances using the traditional strong emission line ratio, R_{23}, based on the photoionization models of Kewley & Dopita (2003). We include an analytic formula for very crude metallicity estimates using the [NII]6584/Halpha ratio. Oxygen abundances for GOODS-N galaxies range from 8.2< 12+log(O/H)< 9.1 corresponding to metallicities between 0.3 and 2.5 times the solar value. This sample of galaxies exhibits a correlation between rest-frame blue luminosity and gas-phase metallicity (i.e., an L-Z relation), consistent with L-Z correlations of previously-studied intermediate-redshift samples. The zero point of the L-Z relation evolves with redshift in the sense that galaxies of a given luminosity become more metal poor at higher redshift. Galaxies in luminosity bins -18.5<M_B<-21.5 exhibit a decrease in average oxygen abundance by 0.14\pm0.05 dex from z=0 to z=1. This rate of metal enrichment means that 28\pm0.07% of metals in local galaxies have been synthesized since z=1, in reasonable agreement with the predictions based on published star formation rate densities which show that ~38% of stars in the universe have formed during the same interval. (Abridged)Comment: AASTeX, 49 pages, 16 figures, accepted for publication in The Astrophysical Journa

Association Studies and Legume Synteny Reveal Haplotypes Determining Seed Size in Vigna unguiculata.

Highly specific seed market classes for cowpea and other grain legumes exist because grain is most commonly cooked and consumed whole. Size, shape, color, and texture are critical features of these market classes and breeders target development of cultivars for market acceptance. Resistance to biotic and abiotic stresses that are absent from elite breeding material are often introgressed through crosses to landraces or wild relatives. When crosses are made between parents with different grain quality characteristics, recovery of progeny with acceptable or enhanced grain quality is problematic. Thus genetic markers for grain quality traits can help in pyramiding genes needed for specific market classes. Allelic variation dictating the inheritance of seed size can be tagged and used to assist the selection of large seeded lines. In this work we applied 1,536-plex SNP genotyping and knowledge of legume synteny to characterize regions of the cowpea genome associated with seed size. These marker-trait associations will enable breeders to use marker-based selection approaches to increase the frequency of progeny with large seed. For 804 individuals derived from eight bi-parental populations, QTL analysis was used to identify markers linked to 10 trait determinants. In addition, the population structure of 171 samples from the USDA core collection was identified and incorporated into a genome-wide association study which supported more than half of the trait-associated regions important in the bi-parental populations. Seven of the total 10 QTLs were supported based on synteny to seed size associated regions identified in the related legume soybean. In addition to delivering markers linked to major trait determinants in the context of modern breeding, we provide an analysis of the diversity of the USDA core collection of cowpea to identify genepools, migrants, admixture, and duplicates