Resummation of perturbation series and reducibility for Bryuno skew-product flows

We consider skew-product systems on T^d x SL(2,R) for Bryuno base flows close to constant coefficients, depending on a parameter, in any dimension d, and we prove reducibility for a large measure set of values of the parameter. The proof is based on a resummation procedure of the formal power series for the conjugation, and uses techniques of renormalisation group in quantum field theory.Comment: 30 pages, 12 figure

Power computation for the triboelectric nanogenerator

We consider, from a mathematical perspective, the power generated by a contact-mode triboelectric nanogenerator, an energy harvesting device that has been well studied recently. We encapsulate the behaviour of the device in a differential equation, which although linear and of first order, has periodic coefficients, leading to some interesting mathematical problems. In studying these, we derive approximate forms for the mean power generated and the current waveforms, and describe a procedure for computing the Fourier coefficients for the current, enabling us to show how the power is distributed over the harmonics. Comparisons with accurate numerics validate our analysis

HALOGAS: HI Observations and Modeling of the Nearby Edge-on Spiral Galaxy NGC 4565

We present 21-cm observations and models of the neutral hydrogen in NGC 4565, a nearby, edge-on spiral galaxy, as part of the Westerbork Hydrogen Accretion in LOcal GAlaxieS (HALOGAS) survey. These models provide insight concerning both the morphology and kinematics of HI above, as well as within, the disk. NGC 4565 exhibits a distinctly warped and asymmetric disk with a flaring layer. Our modeling provides no evidence for a massive, extended HI halo. We see evidence for a bar and associated radial motions. Additionally, there are indications of radial motions within the disk, possibly associated with a ring of higher density. We see a substantial decrease in rotational velocity with height above the plane of the disk (a lag) of -40 +5/-20 km/s/kpc and -30 +5/-30 km s/kpc in the approaching and receding halves, respectively. This lag is only seen within the inner ~4.75' (14.9 kpc) on the approaching half and ~4.25' (13.4 kpc) on the receding, making this a radially shallowing lag, which is now seen in the HI layers of several galaxies. When comparing results for NGC 4565 and those for other galaxies, there are tentative indications of high star formation rate per unit area being associated with the presence of a halo. Finally, HI is found in two companion galaxies, one of which is clearly interacting with NGC 4565.Comment: 17 pages, 16 figures, accepted for publication in the Astrophysical Journal, modified affiliatio

Bifurcation curves of subharmonic solutions

We revisit a problem considered by Chow and Hale on the existence of subharmonic solutions for perturbed systems. In the analytic setting, under more general (weaker) conditions, we prove their results on the existence of bifurcation curves from the nonexistence to the existence of subharmonic solutions. In particular our results apply also when one has degeneracy to first order -- i.e. when the subharmonic Melnikov function vanishes identically. Moreover we can deal as well with the case in which degeneracy persists to arbitrarily high orders, in the sense that suitable generalisations to higher orders of the subharmonic Melnikov function are also identically zero. In general the bifurcation curves are not analytic, and even when they are smooth they can form cusps at the origin: we say in this case that the curves are degenerate as the corresponding tangent lines coincide. The technique we use is completely different from that of Chow and Hale, and it is essentially based on rigorous perturbation theory.Comment: 29 pages, 2 figure

The population of hot subdwarf stars studied with Gaia I. The catalogue of known hot subdwarf stars

In preparation for the upcoming all-sky data releases of the Gaia mission we compiled a catalogue of known hot subdwarf stars and candidates drawn from the literature and yet unpublished databases. The catalogue contains 5613 unique sources and provides multi-band photometry from the ultraviolet to the far infrared, ground based proper motions, classifications based on spectroscopy and colours, published atmospheric parameters, radial velocities and light curve variability information. Using several different techniques we removed outliers and misclassified objects. By matching this catalogue with astrometric and photometric data from the Gaia mission, we will develop selection criteria to construct a homogeneous, magnitude-limited all-sky catalogue of hot subdwarf stars based on Gaia data.Comment: 11 pages, A&A accepte

Isolated and non-isolated dwarfs in terms of modified Newtonian dynamics

Within the framework of modified Newtonian dynamics (MOND) we investigate the kinematics of two dwarf spiral galaxies belonging to very different environments, namely KK 246 in the Local Void and Holmberg II in the M81 group. A mass model of the rotation curve of KK 246 is presented for the first time, and we show that its observed kinematics are consistent with MOND. We re-derive the outer rotation curve of Holmberg II, by modelling its HI data cube, and find that its inclination should be closer to face-on than previously derived. This implies that Holmberg II has a higher rotation velocity in its outer parts, which, although not very precisely constrained, is consistent with the MOND prediction.Comment: Accepted in A&A as a Research Note. 6 pages, 3 figure

Discovery of a red quasar with recurrent activity

We report a new double-double radio quasar, DDRQ, J0746$+$4526 which exhibits two cycles of episodic activity. From radio continuum observations at 607 MHz using the GMRT and 1400 MHz from the FIRST survey we confirm its episodic nature. We examine the SDSS optical spectrum and estimate the black hole mass to be (8.2$\pm$0.3)$\times$10$^7$M$_\odot$ from its observed MgII emission line, and the Eddington ratio to be 0.03. The black hole mass is significantly smaller than for the other reported DDRQ, J0935+0204, while the Eddington ratios are comparable. The SDSS spectrum is significantly red continuum dominated suggesting that it is highly obscured with ${E(B-V)}_{host}=0.70\pm0.16$ mag. This high obscuration further indicates the existence of a large quantity of dust and gas along the line of sight, which may have a key role in triggering the recurrent jet activity in such objects.Comment: 5 pages, 3 figures, 1 table. Accepted for publication in Ap

A comparison of two-coloured filter systems for treating visual reading difficulties

Copyright @ 2013 Informa UK Ltd.Purpose: Visual disturbances that make it difficult to read text are often termed “visual stress”. Coloured filters in spectacles may help some children overcome reading problems that are often caused by visual stress. It has been suggested that for optimal effect each child requires an individually prescribed colour for each eye, as determined in systems such as the “Harris Foundation” coloured filters. Alternatively, it has been argued that only blue or yellow filters, as used in the “Dyslexia Research Trust” (DRT) filter system, are necessary to affect the underlying physiology. Method: A randomised, double blind trial with 73 delayed readers, was undertaken to compare changes in reading and spelling as well as irregular and non-word reading skills after 3 months of wearing either the Harris or the DRT filters. Results: Reading improved significantly after wearing either type of filter (t = −8.4, p < 0.01), with 40% of the children improving their reading age by 6 months or more during the 3 month trial. However, spelling ability (t = 2.1, p = 0.05) and non-word reading (f = 4.7, p < 0.05) improved significantly more with the DRT than with the Harris filters. Conclusion: Education and rehabilitation professionals should therefore, consider coloured filters as an effective intervention for delayed readers experiencing visual stress

A gamma- and X-ray detector for cryogenic, high magnetic field applications

As part of an experiment to measure the spectrum of photons emitted in beta-decay of the free neutron, we developed and operated a detector consisting of 12 bismuth germanate (BGO) crystals coupled to avalanche photodiodes (APDs). The detector was operated near liquid nitrogen temperature in the bore of a superconducting magnet and registered photons with energies from 5 keV to 1000 keV. To enlarge the detection range, we also directly detected soft X-rays with energies between 0.2 keV and 20 keV with three large area APDs. The construction and operation of the detector is presented, as well as information on operation of APDs at cryogenic temperatures