Perturbed eigenvalues of polyharmonic operators in domains with small holes

We study singular perturbations of eigenvalues of the polyharmonic operator on bounded domains under removal of small interior compact sets. We consider both homogeneous Dirichlet and Navier conditions on the external boundary, while we impose homogeneous Dirichlet conditions on the boundary of the removed set. To this aim, we develop a notion of capacity which is suitable for our higher-order context, and which permits to obtain a description of the asymptotic behaviour of perturbed simple eigenvalues in terms of a capacity of the removed set, in dependence of the respective normalized eigenfunction. Then, in the particular case of a subset which is scaling to a point, we apply a blow-up analysis to detect the precise convergence rate, which turns out to depend on the order of vanishing of the eigenfunction. In this respect, an important role is played by Hardy-Rellich inequalities in order to identify the appropriate functional space containing the limiting profile. Remarkably, for the biharmonic operator this turns out to be the same, regardless of the boundary conditions prescribed on the exterior boundary

Multiwavelength Studies of PSR J1420-6048, a Young Pulsar in the Kookaburra

We present X-ray, radio, and infrared observations of the 68 ms pulsar PSR J1420-6048 and its surrounding nebula, a possible counterpart of the gamma-ray source GeV J1417-6100/3EG J1420-6038. Pulsed X-ray emission at the radio period is marginally detected by ASCA from a source embedded in the hard spectrum X-ray nebula AX J1420.1-6049. At radio wavelengths, the pulsar is found to be strongly linearly and circularly polarized, and the polarization sweep is measured. A comparison of high resolution ATCA radio imaging of the Kookaburra's upper wing (G313.6+0.3), which contains the pulsar and the X-ray nebula, with infrared images suggests the radio emission is partly non-thermal.Comment: 8 pages, 4 figures, to appear in Astrophysical Journal Letter

Ultrastructural and functional aspects of the spermatheca in the american harlequin bug, Murgantia histrionica (Hemiptera: Pentatomidae)

The spermatheca of Murgantia histrionica (Hahn) was investigated using fluorescence, scanning and transmission electron microscopy. The aim of the study was to elucidate the structure of this organ, pointing out differences between mated and unmated females. Results have shown an elaborated cuticular structure associated with muscular and glandular tissues. The spermatheca is joined with the common oviduct by the spermathecal duct, forming a thin saccular dilation through two consecutive invaginations. The distal part of the organ is formed by a series of two communicating cuticular chambers. The first cylindrical-shaped chamber, corresponding to the coiled region, is wrapped by longitudinal muscular fibers suspended between two cuticular flanges. The contractions of these fibers compress a deformable zone of the cylinder, pumping the sperm toward the spermathecal duct. Without contractions the cylinder results to be isolated from the proximal part of the spermatheca by means of a valve. The second chamber, corresponding to the spermatheca, is made of two parts: a truncated-conical sub chamber, with a constant cuticular thickness, bearing on itself the distal flange, where muscular fibers are attached. The second part is a bulb-like structure wrapped in a glandular epithelium. The secretory units are composed by two cells: a secretory cell and an associated duct cell. Every evacuating duct shows a little reservoir just after the terminal apparatus, and converge inside the distal bulb after a tortuous path. The functional implications of this structure in the reproductive biology of M. histrionica are discussed

Development and distribution of the non-indigenous Pacific oyster (Crassostrea gigas) in the Dutch Wadden Sea

Pacific oysters (Crassostrea gigas) were first observed in the Dutch Wadden Sea near Texel in 1983. The population increased slowly in the beginning but grew exponentially from the mid-1990s onwards, although now some stabilisation seems to be occurring. They occur on a variety of substrates such as mussel beds (Mytilus edulis), shell banks, dikes and poles. After initial settlement spat may fall on older individuals and congregate to dense clumps and subsequently form reefs. Individual Pacific oysters grow 3–4 cm long in their first year and 2–3 cm in their second year. Many mussel beds (Mytilus edulis) are slowly taken over by Pacific oysters, but there are also several reports of mussel spat settling on Pacific oyster reefs. This might in the end result in combined reefs. Successful Pacific oyster spat fall seems to be related to high summer temperatures, but also after mild summers much spat can be found on old (Pacific oyster) shells. Predation is of limited importance. Mortality factors are unknown, but every now and then unexplained mass mortality occurs. The gradual spread of the Pacific oyster in the Dutch Wadden Sea is documented in the first instance based on historical and anecdotal information. At the start of the more in-depth investigation in 2002, Pacific oysters of all size classes were already present near Texel. Near Ameland the development could be followed from the first observed settlement. On dense reefs each square metre may contain more than 500 adult Pacific oysters, weighing more than 100 kg per m² fresh weigh

Rings and Jets around PSR J2021+3651: the `Dragonfly Nebula'

We describe recent Chandra ACIS observations of the Vela-like pulsar PSR J2021+3651 and its pulsar wind nebula (PWN). This `Dragonfly Nebula' displays an axisymmetric morphology, with bright inner jets, a double-ridged inner nebula, and a ~30" polar jet. The PWN is embedded in faint diffuse emission: a bow shock-like structure with standoff ~1' brackets the pulsar to the east and emission trails off westward for 3-4'. Thermal (kT=0.16 +/-0.02 keV) and power law emission are detected from the pulsar. The nebular X-rays show spectral steepening from Gamma=1.5 in the equatorial torus to Gamma=1.9 in the outer nebula, suggesting synchrotron burn-off. A fit to the `Dragonfly' structure suggests a large (86 +/-1 degree) inclination with a double equatorial torus. Vela is currently the only other PWN showing such double structure. The >12 kpc distance implied by the pulsar dispersion measure is not supported by the X-ray data; spectral, scale and efficiency arguments suggest a more modest 3-4 kpc.Comment: 22 pages, 5 figures, 3 tables, Accepted to Ap