Personal aircraft: a more affordable luxury

Access to luxury products has been limited traditionally to the upper classes. Products and services related to the means of transport have usually been considered of luxury and industrialization has made accessible to much of the population in developed countries. An emerging market is personal aircraft which is currently restricted to certain layers of society but it is expected that their use will represent the next great advance in transport. This article has the object of presenting the results of ongoing research and it focuses on possible demand and the tendency to use this transport option in Spanish societ

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

On bounds for solutions of monotonic first order difference-differential systems

Many special functions are solutions of first order linear systems $y_n'(x)=a_n(x)y_n(x)+d_n(x)y_{n-1}(x)$, $y_{n-1}'(x)=b_n(x)y_{n-1}(x)+e_{n}(x)y_n(x)$. We obtain bounds for the ratios $y_n(x)/y_{n-1}(x)$ and the logarithmic derivatives of $y_n(x)$ for solutions of monotonic systems satisfying certain initial conditions. For the case $d_n(x)e_n(x)>0$, sequences of upper and lower bounds can be obtained by iterating the recurrence relation; for minimal solutions of the recurrence these are convergent sequences. The bounds are related to the Liouville-Green approximation for the associated second order ODEs as well as to the asymptotic behavior of the associated three-term recurrence relation as $n\rightarrow +\infty$; the bounds are sharp both as a function of $n$ and $x$. Many special functions are amenable to this analysis, and we give several examples of application: modified Bessel functions, parabolic cylinder functions, Legendre functions of imaginary variable and Laguerre functions. New Tur\'an-type inequalities are established from the function ratio bounds. Bounds for monotonic systems with $d_n(x)e_n(x)<0$ are also given, in particular for Hermite and Laguerre polynomials of real positive variable; in that case the bounds can be used for bounding the monotonic region (and then the extreme zeros)

A Multicultural Experience Boosted by Specialized European Master: A Real Approach to Internatioanl Project Management

When the Specialized Master in International Project Management started in Madrid in 2009, ESCP Europe, a high-level school of management with international scope, decided to reinforce the European institution and also to foster innovation sustaining a wide international partnership network. Students and executives came from around the world and the school offered them a model of Project Management which prepared them for the multicultural future where geographically dispersed projects teams must collaborate with a common goal. Created in 1988, this Master keeps evolving and is a truly international program with international students and a real methodological revolution in Project Management education including international seminaries and destinations in emerging countries: Either, India and China, or Brazil and Argentina. This Specialized Master makes significant use of inductive teaching methods and interactive activities (project simulations, case studies, business plan development, etc.). This guarantees the skills acquisition needed to work in multidisciplinary, international and multicultural teams. The teaching methods emphasize experimentation and simulation exercises including International Consultancy Projects which requests an intensive use of Information and Communications Technologies in order to enable the international experience