Differential equations for the cuspoid canonical integrals

Differential equations satisfied by the cuspoid canonical integrals I_n(a) are obtained for arbitrary values of n≥2, where n−1 is the codimension of the singularity and a=(ɑ_1,ɑ_2,...,ɑ_(n−1)). A set of linear coupled ordinary differential equations is derived for each step in the sequence I_n(0,0,...,0,0) →I_n(0,0,...,0,ɑ_(n−1)) →I_n(0,0,...,ɑ_(n−2),ɑ_(n−1)) →...→I_n(0,ɑ_2,...,ɑ_(n−2),ɑ_(n−1)) →I_n(ɑ_1,ɑ_2,...,ɑ_n−2,ɑ_(n−1)). The initial conditions for a given step are obtained from the solutions of the previous step. As examples of the formalism, the differential equations for n=2 (fold), n=3 (cusp), n=4 (swallowtail), and n=5 (butterfly) are given explicitly. In addition, iterative and algebraic methods are described for determining the parameters a that are required in the uniform asymptotic cuspoid approximation for oscillating integrals with many coalescing saddle points. The results in this paper unify and generalize previous researches on the properties of the cuspoid canonical integrals and their partial derivatives

THE PRODUCTIVITY OF AGRICULTURAL RESEARCH AND EXTENSION EXPENDITURES IN THE SOUTHEAST

Research and Development/Tech Change/Emerging Technologies,

Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography

By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty

Study of dopants for radiation-resistant silicon Final report

Radiation effects on electrical properties of both aluminum and lithium doped bulk silico

Investigating the prevalence of low energy availability, disordered eating and eating disorders in competitive and recreational female endurance runners

Eating disorders (ED), disordered eating (DE) and low energy availability (LEA) can be detrimental to health and performance. Previous studies have independently investigated prevalence of ED, DE or LEA, however limited studies have combined methods identifying risk within female runners. The aim of this study was to identify prevalence of ED, DE and LEA in United Kingdom-based female runners and associations between age, competition level and running distance. The Female Athlete Screening Tool (FAST) and Low Energy Availability in Females Questionnaire (LEAF-Q) were used in a cross-sectional study design. A total of n = 524 responses eligible for analysis were received. A total of n = 248 (47.3%), n = 209 (40%) and n = 49 (9.4%) athletes were at risk of LEA, DE and ED, respectively. LEAF-Q scores differed based upon age (Age: H(3) = 23.998, p≤0.05) and competitive level (Comp: H(1) = 7.682, p≤0.05) whereas FAST scores differed based on age (Age: F(3,523) = 4.753, p≤0.05). Tukey's post-hoc tests showed significantly higher FAST scores in 18-24 years compared to all other age categories (p≤0.05). Stepwise multiple regression demonstrated age and competitive level modestly predicted LEAF-Q scores (R2adj = 0.047, F(2,523) = 13.993, p≤0.05, VIF = 1.0) whereas age modestly predicted FAST scores (R2adj = 0.022, F(1,523) = 12.711, p≤0.05, VIF = 1.0). These findings suggest early identification, suitable screening methods and educational intervention programmes should be aimed at all levels of female endurance runners

Nitrification-denitrification in WSP: a mechanism for permanent nitrogen removal in maturation ponds

A pilot-scale primary maturation pond was spiked with 15N-labelled ammonia (15NH4Cl) and 15N labelled nitrite (Na15NO2), in order to improve current understanding of the dynamics of inorganic nitrogen transformations and removal in WSP systems. Stable isotope analysis of δ15N showed that nitrification could be considered as an intermediate step in WSP, which is masked by simultaneous denitrification, under conditions of low algal activity. Molecular microbiology analysis showed that denitrification can be considered a feasible mechanism for permanent nitrogen removal in WSP, which may be supported either by ammonia-oxidising bacteria (AOB) or by methanotrophs, in addition to nitrite-oxidising bacteria (NOB). However, the relative supremacy of the denitrification process over other nitrogen removal mechanisms (e.g., biological uptake) depends upon phytoplanktonic activity

Modeling the Void H I Column Density Spectrum

The equivalent width distribution function (EWDF) of \hone absorbers specific to the void environment has been recently derived (Manning 2002), revealing a large line density of clouds (dN/dz ~500 per unit z for Log (N_HI)> 12.4). I show that the void absorbers cannot be diffuse (or so-called filamentary) clouds, expanding with the Hubble flow, as suggested by N-body/hydro simulations. Absorbers are here modeled as the baryonic remnants of sub-galactic perturbations that have expanded away from their dark halos in response to reionization at z ~ 6.5. A 1-D Lagrangian hydro/gravity code is used to follow the dynamic evolution and ionization structure of the baryonic clouds for a range of halo circular velocities. The simulation products at z=0 can be combined according to various models of the halo velocity distribution function to form a column density spectrum that can be compared with the observed. I find that such clouds may explain the observed EWDF if the halo velocity distribution function is as steep as that advanced by Klypin (1999), and the halo mass distribution is closer to isothermal than to NFW.Comment: 21 pages, 15 figures. Paper in press; ApJ 591, n

Geogrid Reinforced Soil Retaining Wall on Compressible Soils

A geogrid reinforced soil wall with a wrap-around facing system was successfully constructed on soft, compressible alluvial and residual soils. An originally designed 20-foot (6.1 m) high, reinforced concrete cantilever retaining wall was not constructed because of the expected settlements induced by the wall and backfill. The geogrid reinforced wall was utilized because of its ability to withstand the estimated settlement and because it was considered less expensive than providing deep foundation support of a cantilever wall. This paper discusses the design, construction, and performance of the geogrid reinforced wall

Equivalence between Kaluza Klein modes of gravitinos and goldstinos in brane induced supersymmetry breaking

We identify the goldstino fields that give mass to the Kaluza Klein modes of five dimensional supergravity, when supersymmetry breaking is induced by brane effects. We then proof the four dimensional Equivalence Theorem that, in renormalizable gauges, allows for the replacement of Kaluza Klein modes of helicity $\pm1/2$ gravitinos in terms of goldstinos. Finally we identify the five dimensional renormalizable gauge fixing that leads to the Equivalence Theorem.Comment: Final version published in JHEP. Typo corrected in eq. 2.