On the computation of confluent hypergeometric functions for large imaginary part of parameters b and z

The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-319-42432-3_30We present an efficient algorithm for the confluent hypergeometric functions when the imaginary part of b and z is large. The algorithm is based on the steepest descent method, applied to a suitable representation of the confluent hypergeometric functions as a highly oscillatory integral, which is then integrated by using various quadrature methods. The performance of the algorithm is compared with open-source and commercial software solutions with arbitrary precision, and for many cases the algorithm achieves high accuracy in both the real and imaginary parts. Our motivation comes from the need for accurate computation of the characteristic function of the Arcsine distribution or the Beta distribution; the latter being required in several financial applications, for example, modeling the loss given default in the context of portfolio credit risk.Peer ReviewedPostprint (author's final draft

Motility of small nematodes in disordered wet granular media

The motility of the worm nematode \textit{Caenorhabditis elegans} is investigated in shallow, wet granular media as a function of particle size dispersity and area density ($\phi$). Surprisingly, we find that the nematode's propulsion speed is enhanced by the presence of particles in a fluid and is nearly independent of area density. The undulation speed, often used to differentiate locomotion gaits, is significantly affected by the bulk material properties of wet mono- and polydisperse granular media for $\phi \geq 0.55$. This difference is characterized by a change in the nematode's waveform from swimming to crawling in dense polydisperse media \textit{only}. This change highlights the organism's adaptability to subtle differences in local structure and response between monodisperse and polydisperse media

Induced Representations of Quantum Kinematical Algebras and Quantum Mechanics

Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. We propose in this paper its generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper (olmo01), to induce representations of quantum bicrossproduct algebras we construct the representations of the family of standard quantum inhomogeneous algebras $U_\lambda(iso_{\omega}(2))$. This family contains the quantum Euclidean, Galilei and Poincar\'e algebras, all of them in (1+1) dimensions. As byproducts we obtain the actions of these quantum algebras on regular co-spaces that are an algebraic generalization of the homogeneous spaces and $q$--Casimir equations which play the role of $q$--Schr\"odinger equations.Comment: LaTeX 2e, 20 page

Representations of Quantum Bicrossproduct Algebras

We present a method to construct induced representations of quantum algebras having the structure of bicrossproduct. We apply this procedure to some quantum kinematical algebras in (1+1)--dimensions with this kind of structure: null-plane quantum Poincare algebra, non-standard quantum Galilei algebra and quantum kappa Galilei algebra.Comment: LaTeX 2e, 35 page

Scale morphology and specialized dorsal scales of a new teleosteomorph fish from the Aptian of West Gondwana

Scales of a new species of Teleosteomorpha from the continental Aptian of the south of South America are studied. These neopterygians are from the La Cantera Formation in central Argentina, and were previously identified as Pholidophoriformes. They present ganoid scales; most of them are rhombic with well-developed peg-and-socket articulations and possessing a smooth surface. They have a straight posterior margin, but occasionally, some scales of the flank have a sinuous posterior margin with one or two serrations. The shape of the scales varies along the body from large, rectangular and deeper than long scales behind the head to the preanal region to smaller and rhomboidal scales in the caudal region. There are a few horizontal rows along the flank and about 32 lateral line scales. Thick, round ganoid scales are present in the prepelvic region close to the ventral margin. The round and rhombic scales present growth lines, which form concentric ridges on the external side. A characteristic row of deep scales forms the dorsal margin on each side of the body; a row of median ridge scales is not present. This is a unique feature of the studied fishes. Scutes covered with unornamented ganoine precede the pelvic, dorsal, and anal fins, as well as the dorsal and ventral margins of the caudal fin. The posterior margin of the dorsal lobe of the caudal fin is formed by a single line of scales, which continues and covers the base of the first principal caudal ray. Histological studies reveal a lepisosteoid-scale type with multiple ganoine layers, lack of dentine, and the presence of canaliculi of Williamson. The macro- and micromorphology of the scales shows features that are found in other teleosteomorphs, but also in other neopterygians

Multiple solutions for asteroid orbits: Computational procedure and applications

We describe the Multiple Solutions Method, a one-dimensional sampling of the six-dimensional orbital confidence region that is widely applicable in the field of asteroid orbit determination. In many situations there is one predominant direction of uncertainty in an orbit determination or orbital prediction, i.e., a ``weak'' direction. The idea is to record Multiple Solutions by following this, typically curved, weak direction, or Line Of Variations (LOV). In this paper we describe the method and give new insights into the mathematics behind this tool. We pay particular attention to the problem of how to ensure that the coordinate systems are properly scaled so that the weak direction really reflects the intrinsic direction of greatest uncertainty. We also describe how the multiple solutions can be used even in the absence of a nominal orbit solution, which substantially broadens the realm of applications. There are numerous applications for multiple solutions; we discuss a few problems in asteroid orbit determination and prediction where we have had good success with the method. In particular, we show that multiple solutions can be used effectively for potential impact monitoring, preliminary orbit determination, asteroid identification, and for the recovery of lost asteroids