Computation of the Marcum Q-function

Methods and an algorithm for computing the generalized Marcum $Q-$function ($Q_{\mu}(x,y)$) and the complementary function ($P_{\mu}(x,y)$) are described. These functions appear in problems of different technical and scientific areas such as, for example, radar detection and communications, statistics and probability theory, where they are called the non-central chi-square or the non central gamma cumulative distribution functions. The algorithm for computing the Marcum functions combines different methods of evaluation in different regions: series expansions, integral representations, asymptotic expansions, and use of three-term homogeneous recurrence relations. A relative accuracy close to $10^{-12}$ can be obtained in the parameter region $(x,y,\mu) \in [0,\,A]\times [0,\,A]\times [1,\,A]$, $A=200$, while for larger parameters the accuracy decreases (close to $10^{-11}$ for $A=1000$ and close to $5\times 10^{-11}$ for $A=10000$).Comment: Accepted for publication in ACM Trans. Math. Soft

Asymptotic approximations to the nodes and weights of Gauss-Hermite and Gauss-Laguerre quadratures

Asymptotic approximations to the zeros of Hermite and Laguerre polynomials are given, together with methods for obtaining the coefficients in the expansions. These approximations can be used as a standalone method of computation of Gaussian quadratures for high enough degrees, with Gaussian weights computed from asymptotic approximations for the orthogonal polynomials. We provide numerical evidence showing that for degrees greater than $100$ the asymptotic methods are enough for a double precision accuracy computation ($15$-$16$ digits) of the nodes and weights of the Gauss--Hermite and Gauss--Laguerre quadratures.Comment: Submitted to Studies in Applied Mathematic

UV Surface Environment of Earth-like Planets Orbiting FGKM Stars Through Geological Evolution

The UV environment of a host star affects the photochemistry in the atmosphere, and ultimately the surface UV environment for terrestrial planets and therefore the conditions for the origin and evolution of life. We model the surface UV radiation environment for Earth-sized planets orbiting FGKM stars at the 1AU equivalent distance for Earth through its geological evolution. We explore four different types of atmospheres corresponding to an early Earth atmosphere at 3.9 Gyr ago and three atmospheres covering the rise of oxygen to present day levels at 2.0 Gyr ago, 0.8 Gyr ago and modern Earth (Following Kaltenegger et al. 2007). In addition to calculating the UV flux on the surface of the planet, we model the biologically effective irradiance, using DNA damage as a proxy for biological damage. We find that a pre-biotic Earth (3.9 Gyr ago) orbiting an F0V star receives 6 times the biologically effective radiation as around the early Sun and 3520 times the modern Earth-Sun levels. A pre-biotic Earth orbiting GJ 581 (M3.5V) receives 300 times less biologically effective radiation, about 2 times modern Earth-Sun levels. The UV fluxes calculated here provide a grid of model UV environments during the evolution of an Earth-like planet orbiting a range of stars. These models can be used as inputs into photo-biological experiments and for pre-biotic chemistry and early life evolution experiments.Comment: 10 pages, 5 figure

Investigation of acceptor levels and hole scattering mechanisms in p-gallium selenide by means of transport measurements under pressure

The effect of pressure on acceptor levels and hole scattering mechanisms in p-GaSe is investigated through Hall effect and resistivity measurements under quasi-hydrostatic conditions up to 4 GPa. The pressure dependence of the hole concentration is interpreted through a carrier statistics equation with a single (nitrogen) or double (tin) acceptor whose ionization energies decrease under pressure due to the dielectric constant increase. The pressure effect on the hole mobility is also accounted for by considering the pressure dependencies of both the phonon frequencies and the hole-phonon coupling constants involved in the scattering rates.Comment: 13 pages, Latex, 4 ps figures. to appear in High Pressure Research 69 (1997

An exploratory study of the effect of social capital on supply chain relationships: the case of Romania

This study examines the relationship of social capital among buyers and their principal supplier and their most recently chosen supplier in Romania. The study provides an understanding of the transition from a command to a market economy. Responses from 96 managers were analyzed and revealed that supply chain practices are unevenly applied, the practices are used to greater degree with the principal supplier, and a statistically significant link was found between measures of the buyer’s social capital and its supply chain relationships with the principal supplier. No such link was found between the buyer and its most recently chosen supplier.buyer, relationships, Romania, social capital, supplier, supply chain, transition.