Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments

We describe a variety of methods to compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$. These functions are numerically satisfactory independent solutions of the differential equation $x^2 w'' +x w' +(a^2 -x^2)w=0$. In an accompanying paper (Algorithm xxx: Modified Bessel functions of imaginary order and positive argument) we describe the implementation of these methods in Fortran 77 codes.Comment: 14 pages, 1 figure. To appear in ACM T. Math. Sof

On the computation of moments of the partial non-central chi-squared distribution function

Properties satisfied by the moments of the partial non-central chi-square distribution function, also known as Nuttall Q-functions, and methods for computing these moments are discussed in this paper. The Nuttall Q-function is involved in the study of a variety of problems in different fields, as for example digital communications.Comment: 6 page

On Non-Oscillating Integrals for Computing Inhomogeneous Airy Functions

Integral representations are considered of solutions of the inhomogeneous Airy differential equation $w''-z w=\pm1/\pi$. The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions are used to confine the discussion to one function and to a certain sector in the complex plane. By using steepest descent methods from asymptotics, the standard integral representations of the Scorer functions are modified in order to obtain non-oscillating integrals for complex values of $z$. In this way stable representations for numerical evaluations of the functions are obtained. The methods are illustrated with numerical results.Comment: 12 pages, 5 figure

Integral Representations for Computing Real Parabolic Cylinder Functions

Integral representations are derived for the parabolic cylinder functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives. The new integrals will be used in numerical algorithms based on quadrature. They follow from contour integrals in the complex plane, by using methods from asymptotic analysis (saddle point and steepest descent methods), and are stable starting points for evaluating the functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives by quadrature rules. In particular, the new representations can be used for large parameter cases. Relations of the integral representations with uniform asymptotic expansions are also given. The algorithms will be given in a future paper.Comment: 31 pages, 3 figures. To appear in Numer. Mat

Comparative analysis of two genomic regions among four strains of Buchnera aphidicola, primary endosymbiont of aphids.

Preliminary analysis of two selected genomic regions of Buchnera aphidicola BCc, the primary endosymbiont of the cedar aphid Cinara cedri, has revealed a number of interesting features when compared with the corresponding homologous regions of the three B. aphidicola genomes previously sequenced, that are associated with different aphid species. Both regions exhibit a significant reduction in length and gene number in B. aphidicola BCc, as it could be expected since it possess the smallest bacterial genome. However, the observed genome reduction is not even in both regions, as it appears to be dependent on the nature of their gene content. The region fpr-trxA, that contains mainly metabolic genes, has lost almost half of its genes (45.6%) and has reduced 52.9% its length. The reductive process in the region rrl-aroK, that contains mainly ribosomal protein genes, is less dramatic, since it has lost 9.3% of genes and has reduced 15.5% of its length. Length reduction is mainly due to the loss of protein-coding genes, not to the shortening of ORFs or intergenic regions. In both regions, G+C content is about 4% lower in BCc than in the other B. aphidicola strains. However, when only conserved genes and intergenic regions of the four B. aphidicola strains are compared, the G+C reduction is higher in the fpr-trxA region

MÁSTER DE FORMACIÓN INICIAL DEL PROFESORADO DE ENSEÑANZA SECUNDARIA. ALGUNOS ANÁLISIS Y PROPUESTAS

Se presentan algunos análisis y propuestas en torno al nuevo máster de formación inicial de profesorado de secundaria, para contribuir al necesario y urgente debate acerca de su desarrollo futuro

Cambio climático: objetivo Durban

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