Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

Effect of helix turn angle on the performance of a half wavelength quadrifilar antenna

The impedance and radiation pattern parameters of a lambda/2 quadrifilar helix antenna (QHA) with turn angles in the range 0 degrees to 235 degrees are analyzed. It is shown that by selecting the helix turn angle to satisfy the minimum bandwidth and beamwidth requirements, an improved electrical performance and a reduction in the physical size of the antenna is obtained. This is demonstrated by comparing the performance of a conventional half turn QHA with structures having a smaller pitch length. The computed results are validated by experimental data at L-band.

The rotational broadening of V395 Carinae. Implications on the compact object's mass

Context: The masses previously obtained for the X-ray binary 2S 0921-630 inferred a compact object that was either a high-mass neutron star or low-mass black-hole, but used a previously published value for the rotational broadening (v sin i) with large uncertainties. Aims: We aim to determine an accurate mass for the compact object through an improved measurement of the secondary star's projected equatorial rotational velocity. Methods: We have used UVES echelle spectroscopy to determine the v sin i of the secondary star (V395 Car) in the low-mass X-ray binary 2S 0921-630 by comparison to an artificially broadened spectral-type template star. In addition, we have also measured v sin i from a single high signal-to-noise ratio absorption line profile calculated using the method of Least-Squares Deconvolution (LSD). Results: We determine v sin i to lie between 31.3±0.5 km s-1 to 34.7±0.5 km s-1 (assuming zero and continuum limb darkening, respectively) in disagreement with previous results based on intermediate resolution spectroscopy obtained with the 3.6 m NTT. Using our revised v sin i value in combination with the secondary star's radial velocity gives a binary mass ratio of 0.281±0.034. Furthermore, assuming a binary inclination angle of 75° gives a compact object mass of 1.37±0.13 M_?. Conclusions: We find that using relatively low-resolution spectroscopy can result in systemic uncertainties in the measured v sin i values obtained using standard methods. We suggest the use of LSD as a secondary, reliable check of the results as LSD allows one to directly discern the shape of the absorption line profile. In the light of the new v sin i measurement, we have revised down the compact object's mass, such that it is now compatible with a canonical neutron star mass.

Effect of Loading, Voltage Difference and Phase Angle on the Synchronisation of a Small Alternator

Synchronisation of small distributed generation, 30 kVA–2 MVA, employing salient-pole synchronous machines is normally performed within a narrow range of tolerances for voltage, frequency and phase angle. However, there are situations when the ability to synchronise with non-ideal conditions would be beneficial. Such applications include power system islanding and rapid generator start-up. The physical process and effect of out-of-phase synchronisation is investigated both through simulation and experimental tests on a salient-pole alternator. There are many factors that affect synchronisation, but particular attention is given to synchronisation angle, voltage difference and, as generators will be loaded during islanding, the load angle. The results suggest that it would be acceptable for the maximum synchronisation angle of distributed generation to exceed that of current practice. Interesting observations on the nature of out-of-phase synchronisation are made, including some specific to small salient-pole synchronous machines. Furthermore, recommendations are made for synchronisation under different system conditions.

Small-angle scattering from long-chain alkylimidazolium-based ionic liquids

This paper compares the structure of 1-alkyl-3-methylim ridazolium salts using SAXS and X-ray reflectivity. A range of anions have been investigated namely chloride, bromide, trifluoromethanesulfonate (OTf), bis(trifluoromethanesulfonyl)imide (TFI) and tetrachloropalladate(II) with cation alkyl chains ranging from n = 12-20. In general, the salts show liquid crystalline behaviour whose structure is still observed on melting into an isotropic liquid.

Submillimeter wave frequency selective surface with polarisation independent spectral responses

This paper reports the design, construction and electromagnetic performance of a new freestanding frequency selective surface (FSS) structure which generates coincident spectral responses for dual polarisation excitation at oblique angles of incidence. The FSS is required to allow transmission of 316.5 - 325.5 GHz radiation with a loss = 0.6 dB and to achieve = 30 dB rejection from 349.5 - 358.5 GHz. It should also exhibit crosspolarisation levels below -25 dB, all criteria being satisfied simultaneously for TE and TM polarisations at 45° incidence. The filter consists of two identical, 30 mm diameter, 12.5 ?m thick, optically flat, perforated metal screens separated by 450 ?m. Each of the ˜5000 unit cells contains two nested, short circuited, rectangular loop slots and a rectangular dipole slot. The nested elements provide a passband spectral response centred at 320 GHz in the TE and TM planes; the dipole slot increases the filter roll-off above resonance. The FSS was fabricated from silicon-on-insulator wafers using precision micromachining and plating processes including the use of Deep Reactive Ion Etching (DRIE) to pattern the individual slots and remove the substrate under the periodic arrays. Quasi–optical transmission measurements in the 250 – 360 GHz range yielded virtually identical copolarised spectral responses, with the performance meeting or exceeding the above specifications. Experimental results are in excellent agreement with numerical predictions.