Routh's procedure for non-Abelian symmetry groups

We extend Routh's reduction procedure to an arbitrary Lagrangian system (that is, one whose Lagrangian is not necessarily the difference of kinetic and potential energies) with a symmetry group which is not necessarily Abelian. To do so we analyse the restriction of the Euler-Lagrange field to a level set of momentum in velocity phase space. We present a new method of analysis based on the use of quasi-velocities. We discuss the reconstruction of solutions of the full Euler-Lagrange equations from those of the reduced equations.Comment: 30 pages, to appear in J Math Phy

On an exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions

We derive an exact solution to the Thomas-Fermi equation for a Bose-Einstein condensate which has dipole-dipole interactions as well as the usual s-wave contact interaction, in a harmonic trap. Remarkably, despite the non-local anisotropic nature of the dipolar interaction the solution is an inverted parabola, as in the pure s-wave case, but with a different aspect ratio. Various properties such as electrostriction and stability are discussed.Comment: 11 pages, 5 figure

The Distribution of C14 Labelled Salicylates in Rat Tissues

During the period of development of salicylate therapy, it was demonstrated that many body membranes were permeable to salicylates, and that appreciable quantities were excreted in the urine. With the development of a satisfactory quantitative method by Brodie et al. (1) the salicylate concentration in body fluids and urine could be determined. More recently the successful labelling of salicylates with C14 has placed investigation of salicylate distribution in animal tissues on a more practical basis. The carboxyl group of salicylic acid (2) (3) (4) and the acetyl group of acetylsalicylic acid (5) have been tagged with radioactive carbon. These labelled compounds have been employed in experiments on the metabolism and distribution of the salicylates (3) (4) (6). The most complete distribution study was performed by Schayer (3) after the administration of C11 carboxyl labelled salicylic acid to rats. He determined the radioactivity in various organs and the excretory products 24 hours after administration. Since Schayer found that practically all of the administered salicylate was excreted in 24 hours, it was thought that a shorter period should be employed in such studies. Preliminary experiments indicated that a three hour period would be satisfactory. The following study was undertaken to compare the distribution of carboxyl labelled salicylic acid and acetyl labelled acetylsalicylic acid in body fluids and tissues of rats

Project MOSI: rationale and pilot-study results of an initiative to help protect zoo animals from mosquito-transmitted pathogens and contribute data on mosquito spatio–temporal distribution change

Mosquito-borne pathogens pose major threats to both wildlife and human health and, largely as a result of unintentional human-aided dispersal of their vector species, their cumulative threat is on the rise. Anthropogenic climate change is expected to be an increasingly significant driver of mosquito dispersal and associated disease spread. The potential health implications of changes in the spatio-temporal distribution of mosquitoes highlight the importance of ongoing surveillance and, where necessary, vector control and other health-management measures. The World Association of Zoos and Aquariums initiative, Project MOSI, was established to help protect vulnerable wildlife species in zoological facilities from mosquito-transmitted pathogens by establishing a zoo-based network of fixed mosquito monitoring sites to assist wildlife health management and contribute data on mosquito spatio-temporal distribution changes. A pilot study for Project MOSI is described here, including project rationale and results that confirm the feasibility of conducting basic standardized year-round mosquito trapping and monitoring in a zoo environment

Rotating strings

Analytical expressions are provided for the configurations of an inextensible, flexible, twistable inertial string rotating rigidly about a fixed axis. Solutions with trivial radial dependence are helices of arbitrary radius and pitch. Non-helical solutions are governed by a cubic equation whose roots delimit permissible values of the squared radial coordinate. Only curves coplanar with the axis of rotation make contact with it.Comment: added to discussion and made small revisions to tex

Antibodies to Enteroviruses in Cerebrospinal Fluid of Patients with Acute Flaccid Myelitis.

Acute flaccid myelitis (AFM) has caused motor paralysis in >560 children in the United States since 2014. The temporal association of enterovirus (EV) outbreaks with increases in AFM cases and reports of fever, respiratory, or gastrointestinal illness prior to AFM in >90% of cases suggest a role for infectious agents. Cerebrospinal fluid (CSF) from 14 AFM and 5 non-AFM patients with central nervous system (CNS) diseases in 2018 were investigated by viral-capture high-throughput sequencing (VirCapSeq-VERT system). These CSF and serum samples, as well as multiple controls, were tested for antibodies to human EVs using peptide microarrays. EV RNA was confirmed in CSF from only 1 adult AFM case and 1 non-AFM case. In contrast, antibodies to EV peptides were present in CSF of 11 of 14 AFM patients (79%), significantly higher than controls, including non-AFM patients (1/5 [20%]), children with Kawasaki disease (0/10), and adults with non-AFM CNS diseases (2/11 [18%]) (P = 0.023, 0.0001, and 0.0028, respectively). Six of 14 CSF samples (43%) and 8 of 11 sera (73%) from AFM patients were immunoreactive to an EV-D68-specific peptide, whereas the three control groups were not immunoreactive in either CSF (0/5, 0/10, and 0/11; P = 0.008, 0.0003, and 0.035, respectively) or sera (0/2, 0/8, and 0/5; P = 0.139, 0.002, and 0.009, respectively).IMPORTANCE The presence in cerebrospinal fluid of antibodies to EV peptides at higher levels than non-AFM controls supports the plausibility of a link between EV infection and AFM that warrants further investigation and has the potential to lead to strategies for diagnosis and prevention of disease

The Rare Decay D^0 -> gamma gamma

We present a calculation of the rare decay mode D^0 -> gamma gamma, in which the long distance contributions are expected to be dominant. Using the Heavy Quark Chiral Perturbation Theory Lagrangian with a strong g coupling as recently determined by CLEO from the D^* -> D pi width, we consider both the anomaly contribution which relates to the annihilation part of the weak Lagrangian and the one-loop pi, K diagrams. The loop contributions which are proportional to g and contain the a_1 Wilson coefficient are found to dominate the decay amplitude, which turns out to be mainly parity violating. The branching ratio is then calculated to be (1.0+-0.5)x10^(-8). Observation of an order of magnitude larger branching ratio could be indicative of new physics.Comment: 16 pages, 5 figures, additional reference and several remarks added, results unchange

The falling chain of Hopkins, Tait, Steele and Cayley

A uniform, flexible and frictionless chain falling link by link from a heap by the edge of a table falls with an acceleration $g/3$ if the motion is nonconservative, but $g/2$ if the motion is conservative, $g$ being the acceleration due to gravity. Unable to construct such a falling chain, we use instead higher-dimensional versions of it. A home camcorder is used to measure the fall of a three-dimensional version called an $xyz$-slider. After frictional effects are corrected for, its vertical falling acceleration is found to be $a_x/g = 0.328 \pm 0.004$. This result agrees with the theoretical value of $a_x/g = 1/3$ for an ideal energy-conserving $xyz$-slider.Comment: 17 pages, 5 figure

qq-Classical orthogonal polynomials: A general difference calculus approach

It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator. In this paper we present a study of classical orthogonal polynomials in a more general context by using the differential (or difference) calculus and Operator Theory. In such a way we obtain a unified representation of them. Furthermore, some well known results related to the Rodrigues operator are deduced. A more general characterization Theorem that the one given in [1] and [2] for the q-polynomials of the q-Askey and Hahn Tableaux, respectively, is established. Finally, the families of Askey-Wilson polynomials, q-Racah polynomials, Al-Salam & Carlitz I and II, and q-Meixner are considered. [1] R. Alvarez-Nodarse. On characterization of classical polynomials. J. Comput. Appl. Math., 196:320{337, 2006. [2] M. Alfaro and R. Alvarez-Nodarse. A characterization of the classical orthogonal discrete and q-polynomials. J. Comput. Appl. Math., 2006. In press.Comment: 18 page

Low thrust propulsion in a coplanar circular restricted four body problem

This paper formulates a circular restricted four body problem (CRFBP), where the three primaries are set in the stable Lagrangian equilateral triangle configuration and the fourth body is massless. The analysis of this autonomous coplanar CRFBP is undertaken, which identies eight natural equilibria; four of which are close to the smaller body, two stable and two unstable, when considering the primaries to be the Sun and two smaller bodies of the solar system. Following this, the model incorporates `near term' low-thrust propulsion capabilities to generate surfaces of articial equilibrium points close to the smaller primary, both in and out of the plane containing the celestial bodies. A stability analysis of these points is carried out and a stable subset of them is identied. Throughout the analysis the Sun-Jupiter-Asteroid-Spacecraft system is used, for conceivable masses of a hypothetical asteroid set at the libration point L4. It is shown that eight bounded orbits exist, which can be maintained with a constant thrust less than 1:5 10􀀀4N for a 1000kg spacecraft. This illustrates that, by exploiting low-thrust technologies, it would be possible to maintain an observation point more than 66% closer to the asteroid than that of a stable natural equilibrium point. The analysis then focusses on a major Jupiter Trojan: the 624-Hektor asteroid. The thrust required to enable close asteroid observation is determined in the simplied CRFBP model. Finally, a numerical simulation of the real Sun-Jupiter-624 Hektor-Spacecraft is undertaken, which tests the validity of the stability analysis of the simplied model