On the limits of spectral methods for frequency estimation

An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicates the intrinsic limitations of spectral methods when it comes to the task of measuring frequencies. Other examples, one from medicine and one from bifurcation theory, are given, which also exhibit these limitations of spectral methods. For two methods of spectral estimation it is verified that the particular way end points are treated, which is specific to each method, is, for long enough time series, not relevant for the main result.

Unitary SK1 of unitary and graded division algebras

The reduced unitary Whitehead group $\SK$ of a graded division algebra equipped with a unitary involution (i.e., an involution of the second kind) and graded by a torsion-free abelian group is studied. It is shown that calculations in the graded setting are much simpler than their nongraded counterparts. The bridge to the non-graded case is established by proving that the unitary $\SK$ of a tame valued division algebra wih a unitary involution over a henselian field coincides with the unitary $\SK$ of its associated graded division algebra. As a consequence, the graded approach allows us not only to recover results available in the literature with substantially easier proofs, but also to calculate the unitary $\SK$ for much wider classes of division algebras over henselian fields.

A hypercyclic finite rank perturbation of a unitary operator

A unitary operator V and a rank 2 operator R acting on a Hilbert space H are constructed such that V + R is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.

Framework for Establishing Limits of Tabular Aerodynamic Models for Flight Dynamics Analysis

This paper describes the use of the Euler equations for the generation and testing of tabular aerodynamic models for flight dynamics analysis. Maneuvers for the AGARD Standard Dynamics Model sharp leading-edge wind-tunnel geometry are considered as a test case. Wind-tunnel data is first used to validate the prediction of static and dynamic coefficients at both low and high angles, featuring complex vortical flow, with good agreement obtained at low to moderate angles of attack. Then the generation of aerodynamic tables is described based on a data fusion approach. Time-optimal maneuvers are generated based on these tables, including level flight trim, pull-ups at constant and varying incidence, and level and 90 degrees turns. The maneuver definition includes the aircraft states and also the control deflections to achieve the motion. The main point of the paper is then to assess the validity of the aerodynamic tables which were used to define the maneuvers. This is done by replaying them, including the control surface motions, through the time accurate computational fluid dynamics code. The resulting forces and moments are compared with the tabular values to assess the presence of inadequately modeled dynamic or unsteady effects. The agreement between the tables and the replay is demonstrated for slow maneuvers. Increasing rate maneuvers show discrepancies which are ascribed to vortical flow hysteresis at the higher rate motions. The framework is suitable for application to more complex viscous flow models, and is powerful for the assessment of the validity of aerodynamics models of the type currently used for studies of flight dynamics.

Limits on HDS/H2S abundance ratios in hot molecular cores

We have searched for HDS emission in a small number of hot cores. Using observations of (H2S)-S-34, we have derived upper limits to the [HDS]/[H2S] abundance ratio. The upper limits, which are close to 10(-3) can be interpreted in two ways, depending on whether grain surface reactions contribute to the formation of H2S. If grains do not dominate, then the H2S observed is formed in hot, post-shocked gas and a ratio close to the cosmic [D]/[H] ratio is expected for [HDS]/[H2S]. This scenario is consistent with our upper limits and with the relatively low abundance ratio found for [HDO]/[H2O] in hot cores but does not seem to account for all of the molecular [D]/[H] ratios observed in hot cores. If grains do dominate the formation of HBS, then the observed upper limit to the ratio is consistent with the formation of 'hot core ices' at a temperature of 60-80 K, close to the temperature at which cometary ices are thought to form.

Distance limits to intermediate- and high-velocity clouds

We present optical spectra of 403 stars and quasi-stellar objects in order to obtain distance limits towards intermediate- and high-velocity clouds (IHVCs), including new Fibre-fed Extended Range Optical Spectrograph (FEROS) observations plus archival ELODIE, FEROS, High Resolution Echelle Spectrometer (HIRES) and Ultraviolet and Visual Echelle Spectrograph (UVES) data. The non-detection of Ca II K interstellar (IS) absorption at a velocity of −130 to −60 km s−1 towards HDE 248894 (d ∼ 3 kpc) and HDE 256725 (d ∼ 8 kpc) in data at signal-to-noise ratio (S/N) > 450 provides a new firm lower distance limit of 8 kpc for the anti-centre shell HVC. Similarly, the non-detection of Ca II K IS absorption towards HD 86248 at S/N ∼ 500 places a lower distance limit of 7.6 kpc for Complex EP, unsurprising since this feature is probably related to the Magellanic System. The lack of detection of Na I D at S/N = 35 towards Mrk 595 puts an improved upper limit for the Na I column density of log (NNaD <) 10.95 cm−2 towards this part of the Cohen Stream where Ca II was detected by Wakker et al. Absorption at ∼ −40 km s−1 is detected in Na I D towards the Galactic star PG 0039+049 at S/N = 75, placing a firm upper distance limit of 1 kpc for the intermediate-velocity cloud south (IVS), where a tentative detection had previously been obtained by Centurion et al. Ca ´ II K and Na I D absorption is detected at −53 km s−1 towards HD 93521, which confirms the upper distance limit of 2.4 kpc for part of the IV arch complex obtained using the International Ultraviolet Explorer (IUE) data by Danly. Towards HD 216411 in Complex H a non-detection in Na D towards gas with log(NH I) = 20.69 cm−2 puts a lower distance limit of 6.6 kpc towards this HVC complex. Additionally, Na I D absorption is detected at −43.7 km s−1 in the star HD 218915 at a distance of 5.0 kpc in gas in the same region of the sky as Complex H. Finally, the Na I/Ca II and Ca II/H I ratios of the current sample are found to lie in the range observed for previous studies of IHVCs.

Luminosity and mass limits for the progenitor of the type Ic supernova 2004gt in NGC 4038

We report on our attempts to locate the progenitor of the Type Ic supernova SN 2004gt in NGC 4038. We use high-resolution HST ACS images of SN 2004gt and have compared them with deep pre-explosion HST WFPC2 F336W, F439W, F555W, and F814W images. We identify the SN location on the pre-explosion frames with an accuracy of 5 mas. We show that the progenitor is below the detection thresholds of all the pre-explosion images. These detection limits are used to place luminosity and mass limits on the progenitor. The progenitor of SN 2004gt seems to be restricted to a low-luminosity high-temperature star, either a single WC star with an initial mass of > 40 M-circle dot or a low-mass star in a binary. The pre-explosion data cannot distinguish between the two scenarios.

Mass limits for the progenitor star of supernova 2001du and other Type II-P supernovae

The supernova SN 2001du was discovered in the galaxy NGC 1365 at a distance of 19 +/- 2 Mpc, and is a core-collapse event of Type II-P. Images of this galaxy, of moderate depth, have been taken with the Hubble Space Telescope approximately 6.6 yr before discovery and include the supernova position on the WFPC2 field of view. We have observed the supernova with the WFPC2 to allow accurate differential astrometry of SN 2001du on the pre-explosion frames. As a core-collapse event it is expected that the progenitor was a massive, luminous star. There is a marginal detection (3sigma) of a source close to the supernova position on the pre-discovery V -band frame, but it is not precisely coincident and we do not believe it to be a robust detection of a point source. We conclude that there is no stellar progenitor at the supernova position and derive sensitivity limits of the pre-discovery images that provide an upper mass limit for the progenitor star. We estimate that the progenitor had a mass of less than 15 M-circle dot . We revisit two other nearby Type II-P supernovae that have high-quality pre-explosion images, and refine the upper mass limits for the progenitor stars. Using a new distance determination for SN 1999gi from the expanding photosphere method, we revise the upper mass limit to 12 M-circle dot . We present new HST images of the site of SN 1999em, which validate the use of lower spatial resolution ground-based images in the progenitor studies and use a new Cepheid distance to the galaxy to measure an upper mass limit of 15 M-circle dot for that progenitor. Finally we compile all the direct information available for the progenitors of eight nearby core-collapse supernovae and compare their mass estimates. These are compared with the latest stellar evolutionary models of pre-supernova evolution which have attempted to relate metallicity and mass to the supernovae type. Although this is statistically limited at present, reasonable agreement is already found for the lower-mass events (generally the II-P), but some discrepancies appear at higher masses.

Theoretical and spatial limits to the value of rural environmental benefits: Evidence from the forestry sector

The valuation of environmental benefits has been well researched in the forestry sector. This is not generally the case in the agriculture sector although schemes to compensate farmers for provision of officially defined environmental benefits are already in place throughout the European Union. This paper draws on empirical findings from forestry and deductions from economic theory to challenge the notion of the universality of such benefits. Empirical findings from forestry suggest recreational use value is location specific rather than widely spread. Household utility theory predicts zero willingness to pay to maintain the status quo level of a previously unpaid for environmental benefit (when provision is not perceived as under risk) but a positive willingness to pay for an increase. Thus, non use values cannot be attributed to the major part of existing commercial forestry area but to spatially restricted schemes such as additional afforestation or preservation of ancient natural woodlands.