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The hybrid numerical-asymptotic (HNA) approach aims to reduce the computational cost of conventional numerical methods for high-frequency wave scattering problems by enriching the numerical approximation space with oscillatory basis functions, chosen based on partial knowledge of the high-frequency solution asymptotics. In this paper, we propose a new methodology for the treatment of shadow boundary effects in HNA boundary element methods, using the classical geometrical theory of diffraction phase functions combined with mesh refinement. We develop our methodology in the context of scattering by a class of sound-soft non-convex polygons, presenting a rigorous numerical analysis (supported by numerical results) which proves the effectiveness of our HNA approximation space at high frequencies. Our analysis is based on a study of certain approximation properties of the Fresnel integral and related functions, which govern the shadow boundary behaviour.
This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalizations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces
and an open
. We exhibit examples in one and two dimensions of sets
for which these scales of Sobolev spaces are not interpolation scales. In the cases where they are interpolation scales (in particular, if
is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.
The debate regarding the number of dust-reddened quasars has been ongoing for several years. Selecting quasars based on a UV excess will exclude any quasar that has an SED that departs from the standard power-law or is experiencing obscuration from dust. As longer wavelengths are less affected by dust attenuation, it is advantageous to select quasar candidates in the NIR, but until now, there did not exist a dataset of sufficient depth and coverage suitable for undertaking such an experiment.
We increase the number of remote halo tracers by using blue horizontal branch (BHB) stars out to Galactocentric distances of 130 kpc. We use SDSS EDR photometry and the VLT to detect 16 BHB stars at Galactocentric distances 70 <r < 130 kpc, and to measure their radial velocities. We find the mass of the Milky Way is M = 1.7+3.0–0.6 × 1012M⊙. When completed this survey will: (i) substantially reduce the errors in the total mass and extent of the Milky Way halo, and (ii) map the velocity space in a hitherto unexplored region of the halo.
The discovery of gravitationally lensed radio-rings (Hewitt et al. 1988) opened up a new line of attack on the problem of dark matter in galaxies. High–resolution radio observations (Langston et al. 1989) resolve structure tangentially and radially within the rings, providing sophisticated analysis routines (Kochanek & Narayan 1992, Wallington, Narayan & Kochanek 1994) with enough constraints to compute realistic models of the mass distribution within the deflectors (Kochanek 1995). Five such systems are now known and extensive programs to identify further examples are underway.
There is still debate as to whether wide separation (Δθ ≳ 3″) double quasars are physical binaries or gravitationally lensed sources. We proceed under the assumption that most of these objects are the result of lensing, and use maximum likelihood techniques (Kochanek 1993) to infer information about the mass distribution of deflectors that would be required to produce these wide image separations. Under the above assumptions, the most consistent explanation is the existence of a significant population of dark objects with the mass of groups of galaxies.
By characterising the range of quasar UV-optical spectral indices and any correlation with it e.g. luminosity or line parameters, we hope to remove one more bias from the quasar luminosity function (QLF).
An automated system to measure and analyse large numbers of objective prism spectra from photographic plates using the Automated Plate Measuring (APM) facility at Cambridge is described. The system is being applied in a number of ways including automated quasar detection and subsequent clustering analyses, galaxy redshift surveys, and wide field searches for rare objects, such as carbon stars.
Three units, correlatable with recent Lake Champlain, late-glacial marine Champlain Sea, and proglacial Lake Vermont sediments, have been identified from about 200 km of high-resolution seismic reflection profiles and eight piston cores collected in southern Lake Champlain. Lake Vermont deposits are nonfossiliferous and range from thin to absent nearshore and on bedrock highs to more than 126 m thick near Split Rock Point. Champlain Sea sediments contain marine foraminifers and ostracodes and are fairly uniform in thickness (20–30 m). Recent Lake Champlain sediments range in thickness from 0 to 25 m. Average sedimentation rates for Lake Vermont are considerably higher (4–8 cm/yr) than those for the Champlain Sea (0.8–1.2 cm/yr) and Lake Champlain (0.14–0.15 cm/yr). Bedrock, till, and deltaic and alluvial deposits were also identified on the acoustic records but were not sampled. An unconformity separating Champlain Sea deposits from Lake Champlain deposits is associated with numerous benches at water depths of 20–30 m. These benches, the alluvial deposits, and the onset of deltaic deposition are probably associated with a low water level stillstand at the close of the Champlain Sea episode.
A latex agglutination test to identify the sources of blood-meals of Culicoides is described. The method requires the minimum amounts of reagents and apparatus and would be suitable for rapid tests under field conditions. Blood-meals of Culicoides nubeculosus (Mg.) and C. variipennis (Coq.) from laboratory cultures, which had engorged on blood from several species of domestic animals, were differentiated without difficulty. In a series of ‘blind’ tests, the blood-meals of 49 C. variipennis from seven species of domestic animal were identified with 100% accuracy. The differentiation of blood-meals from closely related hosts, such as mouse and guineapig or ox and sheep, is entirely dependent upon the specificity of the antisera conjugated to the latex. Blood-meals could be identified reliably for about 48 h after ingestion at 20–25°C, but at higher temperatures the reaction became less reliable after 24 h. Detergents commonly used in collecting midges had no effect on the latex agglutination test, but 0–01% mertbiolate, often used as a preservative, caused auto-agglutination and cannot be used when this test is to be applied.