Compact operators without extended eigenvalues

A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Mechanically tunable multiband compact quadrifilar helix antenna with dual mode operation

We show that by introducing a gap at the center of the helical sections (where the current is minimum) of a lambda/2 quadrifilar helix antenna (QHA) and varying the axial length and radial gap between the overlapping volutes, the antenna gives a 28% impedance bandwidth which is nine times the bandwidth of a conventional QHA. A 16% bandwidth with a front to back ratio of >= 14 dB is achievable with 5-14% reduction in the size of the QHA. The structure can yield a monopole radiation pattern suitable for terrestrial applications or a hemispherical pattern suitable for satellite use. The simulation results are validated by measurements at L-band.

Dual-mode compact structure comprising of side-fed bifilar and quadrifilar helix antenna

A side-fed bifilar helix antenna can be integrated with a quadrifilar helix antenna in a piggy back configuration in order to achieve a dual-mode radiating structure. The overall length of the structure is 0.44 lambda at the resonant frequency (1.54 GHz) of the space mode antenna and 0.39 lambda at the resonant frequency (1.34 GHz) of the terrestrial mode antenna. The computed results are validated by experimental data.

Compact quadrifilar helix antenna

Introduction: The quadrifilar helix antenna (QHA) is used widely for terrestrial [1] and space communication systems [2], where it is necessary to generate a circularly polarised cardioid-shaped radiation pattern with a high front-to-back ratio and low cross-polarisation. The radiating structure comprises four helical conductors which are excited in phase quadrature at the feed point, which is usually located at the centre of the top radials. The physical size of the quadrifilar antenna can be reduced by dielectric loading [3] or by meandering the printed linear elements [4]. However, in the former arrangement dielectric absorption reduces the radiation efficiency of the antenna, and the latter technique is not suitable for constructing free standing wire structures, which are normally used for spacecraft payloads in the VHF and UHF bands [2]. This Letter shows that a significant reduction in the axial length of a 1/2 turn half-wavelength QHA can be achieved by modifying the geometry of the helices in the region around the midpoint where a current null exists. Simulated and experimental results at L band are used to show that a size reduction of up to 15% is possible without significantly degrading the pattern shape and the bandwidth.

Development of an ELISA screening test for nitroimidazoles in egg and chicken muscle

An antibody was generated that can bind metronidazole (MNZ), a nitroimidazole drug used in veterinary medicine to treat poultry for coccidiosis and histomoniasis. A direct competitive enzyme-linked immunosorbent assay (cELISA) is described. It was used to characterise binding of this antibody to a number of nitroimidazole drugs. It displayed cross-reactivity with dimetridazole (DMZ), ronidazole (RNZ), hydroxydimetridazole (DMZOH), and ipronidazole (IPZ).

Size-assortative pairing in Gammarus pulex (Crustacea : Amphipoda): a test of the timing hypothesis

We present the first empirical test of the timing hypothesis regarding the generation of size-assortative pairing in amphipods. The timing hypothesis proposes that, since large males are better able to afford the costs of mate guarding than small males, the former can take larger females into precopula earlier in the female moult cycle than is feasible for the latter. This leaves small males to form pairs with smaller females closer to moult, thus generating size assortment. We presented male Gammarus pulex, collected both in precopula and as singletons, with females that were (1) previously guarded and therefore near to copulatory moult and (2) previously unguarded and therefore far from copulatory moult. This comparison tested the prediction of the timing hypothesis, that size assortment should break down when the opportunity for time-based male decisions is removed, but that size assortment should occur where timing is not disrupted. Counter to the hypothesis, we found that size assortment did not break down upon removal of the time factor. Large males tended to initiate mate guarding earlier than small males in both female moult groups. However, only in the previously unguarded group did large males guard for longer than small males. This result suggests that, although size assortment occurred in all groups, the causative mechanisms that generated this pattern may differ between these groups. We therefore consider the possible importance of mechanisms such as aggression, simultaneous manipulation of females and female resistance in producing size assortment where males encounter numerous females that are close to moult. We also observed that prior recent guarding experience by males had no effect on latency to guard or size-assortative pairing. (C) 2002 The Association for the Study of Animal Behaviour. Published by Elsevier Science Ltd. All rights reserved.

Rarity and decline in bumblebees - A test of causes and correlates in the Irish fauna

Bees are believed to be in decline across many of the world's ecosystems. Recent studies on British bumblebees proposed alternative theories to explain declines. One study suggested that greater dietary specialization among the rarer bumblebee species makes them more susceptible to decline. A second study disputed this theory and found that declines in British bumblebees were correlated with the size of species' European ranges, leading to the suggestion that climate and habitat specialization may be better indicators of the risk of decline. Here we use a new and independent dataset based on Irish bumblebees to test the generality of these theories. We found that most of the same bumblebee species are declining across the British Isles, but that, within Ireland, a simple food-plant specialization model is inadequate to explain these declines. Furthermore, we found no evidence of a relationship between declines in Irish bumblebees and the size of species' European ranges. However, we demonstrate that the late emerging species have declined in Ireland (and in Britain), and that these species show a statistically significant westward shift to the extremity of their range, probably as a result of changing land use. Irish data support the finding that rare and declining bumblebees are later nesting species, associated with open grassy habitats. We suggest that the widespread replacement of hay with silage in the agricultural landscape, which results in earlier and more frequent mowing and a reduction in late summer wildflowers, has played a major role in bumblebee declines. (C) 2006 Elsevier Ltd. All rights reserved.