Hardy-Sobolev-Maz'ya inequalities for arbitrary domains

We prove a Hardy-Sobolev-Maz'ya inequality for arbitrary domains \Omega\subset\R^N with a constant depending only on the dimension N\geq 3. In particular, for convex domains this settles a conjecture by Filippas, Maz'ya and Tertikas. As an application we derive Hardy-Lieb-Thirring inequalities for eigenvalues of Schr\"odinger operators on domains.Comment: 19 page

The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space

It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the three dimensional upper half space is given by the Sobolev constant. This is achieved by a duality argument relating the problem to a Hardy-Littlewood-Sobolev type inequality whose sharp constant is determined as well.Comment: 9 page

Dynamic Web File Format Transformations with Grace

Web accessible content stored in obscure, unpopular or obsolete formats represents a significant problem for digital preservation. The file formats that encode web content represent the implicit and explicit choices of web site maintainers at a particular point in time. Older file formats that have fallen out of favor are obviously a problem, but so are new file formats that have not yet been fully supported by browsers. Often browsers use plug-in software for displaying old and new formats, but plug-ins can be difficult to find, install and replicate across all environments that one may use. We introduce Grace, an http proxy server that transparently converts browser-incompatible and obsolete web content into web content that a browser is able to display without the use of plug-ins. Grace is configurable on a per user basis and can be expanded to provide an array of conversion services. We illustrate how the Grace prototype transforms several image formats (XBM, PNG with various alpha channels, and JPEG 2000) so they are viewable in Internet Explorer.Comment: 12 pages, 9 figure

Vitis vinifera (Vitales: Vitaceae) as a Reproductive Host of Spissistilus festinus (Hemiptera: Membracidae).

Feeding by the three-cornered alfalfa hopper, Spissistilus festinus (Say) (Hemiptera: Membracidae) results in girdling of grapevine petioles and shoots. Its significance as an economic pest of grape has increased since it was shown to transmit Grapevine red blotch virus (GRBV) in a greenhouse study. However, the status of grapevines as a reproductive host for S. festinus remained undetermined. Adult S. festinus were caged onto three regions of the grapevines: apical shoot, green shoot, and dormant cane. Their ability to reproduce was determined by weekly destructive sampling for 7 wk. Successful oviposition and nymphal emergence were observed on apical and green shoots, but not on dormant canes. However, insect development beyond the second nymphal instar did not occur. Knowledge of S. festinus reproduction on grapevines will be an important consideration in designing management guidelines to minimize the spread of GRBV in vineyards

Tracking Pacific bluefin tuna (Thunnus thynnus orientalis) in the northeastern Pacific with an automated algorithm that estimates latitude by matching sea-surface-temperature data from satellites with temperature data from tags on fish

Data recovered from 11 popup satellite archival tags and 3 surgically implanted archival tags were used to analyze the movement patterns of juvenile northern bluefin tuna (Thunnus thynnus orientalis) in the eastern Pacific. The light sensors on archival and pop-up satellite transmitting archival tags (PSATs) provide data on the time of sunrise and sunset, allowing the calculation of an approximate geographic position of the animal. Light-based estimates of longitude are relatively robust but latitude estimates are prone to large degrees of error, particularly near the times of the equinoxes and when the tag is at low latitudes. Estimating latitude remains a problem for researchers using light-based geolocation algorithms and it has been suggested that sea surface temperature data from satellites may be a useful tool for refining latitude estimates. Tag data from bluefin tuna were subjected to a newly developed algorithm, called “PSAT Tracker,” which automatically matches sea surface temperature data from the tags with sea surface temperatures recorded by satellites. The results of this algorithm compared favorably to the estimates of latitude calculated with the lightbased algorithms and allowed for estimation of fish positions during times of the year when the lightbased algorithms failed. Three near one-year tracks produced by PSAT tracker showed that the fish range from the California−Oregon border to southern Baja California, Mexico, and that the majority of time is spent off the coast of central Baja Mexico. A seasonal movement pattern was evident; the fish spend winter and spring off central Baja California, and summer through fall is spent moving northward to Oregon and returning to Baja California