Ill-posedness of degenerate dispersive equations

In this article we provide numerical and analytical evidence that some degenerate dispersive partial differential equations are ill-posed. Specifically we study the K(2,2) equation $u_t = (u^2)_{xxx} + (u^2)_{x}$ and the "degenerate Airy" equation $u_t = 2 u u_{xxx}$. For K(2,2) our results are computational in nature: we conduct a series of numerical simulations which demonstrate that data which is very small in $H^2$ can be of unit size at a fixed time which is independent of the data's size. For the degenerate Airy equation, our results are fully rigorous: we prove the existence of a compactly supported self-similar solution which, when combined with certain scaling invariances, implies ill-posedness (also in $H^2$)

Evolution of the nuclear ribosomal DNA intergenic spacer in four species of the Daphnia pulex complex

<p>Abstract</p> <p>Background</p> <p>Concerted evolution refers to the pattern in which copies of multigene families show high intraspecific sequence homogeneity but high interspecific sequence diversity. Sequence homogeneity of these copies depends on relative rates of mutation and recombination, including gene conversion and unequal crossing over, between misaligned copies. The internally repetitive intergenic spacer (IGS) is located between the genes for the 28S and 18S ribosomal RNAs. To identify patterns of recombination and/or homogenization within IGS repeat arrays, and to identify regions of the IGS that are under functional constraint, we analyzed 13 complete IGS sequences from 10 individuals representing four species in the <it>Daphnia pulex </it>complex.</p> <p>Results</p> <p>Gene conversion and unequal crossing over between misaligned IGS repeats generates variation in copy number between arrays, as has been observed in previous studies. Moreover, terminal repeats are rarely involved in these events. Despite the occurrence of recombination, orthologous repeats in different species are more similar to one another than are paralogous repeats within species that diverged less than 4 million years ago. Patterns consistent with concerted evolution of these repeats were observed between species that diverged 8-10 million years ago. Sequence homogeneity varies along the IGS; the most homogeneous regions are downstream of the 28S rRNA gene and in the region containing the core promoter. The inadvertent inclusion of interspecific hybrids in our analysis uncovered evidence of both inter- and intrachromosomal recombination in the nonrepetitive regions of the IGS.</p> <p>Conclusions</p> <p>Our analysis of variation in ribosomal IGS from <it>Daphnia </it>shows that levels of homogeneity within and between species result from the interaction between rates of recombination and selective constraint. Consequently, different regions of the IGS are on substantially different evolutionary trajectories.</p

Atlas of Avoidable Hospitalisations in Australia: ambulatory care-sensitive conditions

Avoidable hospitalisations represent a range of conditions for which hospitalisation should be able to be avoided because the disease or condition has been prevented from occurring, or because individuals have had access to timely and effective primary care. This report addresses the level and extent of regional variation in Australia in a sub-set of avoidable hospitalisations, namely those arising from ambulatory care-sensitive (ACS) conditions. ACS conditions are certain conditions for which hospitalisation is considered potentially avoidable through preventive care and early disease management, usually delivered in a primary care setting, for example by a general medical practitioner, or at a community health centre

Development of a DNA-Liposome Complex for Gene Delivery Applications

The association structures formed by cationic liposomes and DNA(Deoxyribonucleic acid)-liposome have been effectively utilized as gene carriers in transfection assays. In this research study, cationic liposomes were prepared using a modified lipid film hydration method consisting of a lyophilization step for gene delivery applications. The obtained results demonstrated that the mean particle size had no significant change while the polydispersity (PDI) increased after lyophilization. The mean particle size slightly reduced after lyophilization (520 ± 12 nm to 464 ± 25 nm) while the PDI increased after lyophilization (0.094 ± 0.017 to 0.220 ± 0.004). In addition. The mean particle size of vesicles increases when DNA is incorporated to the liposomes (673 ± 27 nm). According to the Scanning Electron Microscopy(SEM) and transmission electron microscopy (TEM) images, the spherical shape of liposomes confirmed their successful preservation and reconstitution from the powder. It was found that liposomal formulation has enhanced transfection considerably compared to the naked DNA as negative control. Finally, liposomal formulation in this research had a better function than Lipofectamine® 2000 as a commercialized product because the cellular activity (cellular protein) was higher in the prepared lipoplex than Lipofectamine® 2000

Rare Kaon Decays

The current status of rare kaon decay experiments is reviewed. New limits in the search for Lepton Flavor Violation are discussed, as are new measurements of the CKM matrix.Comment: 8 pages, 3 figures, LaTeX, presented at the 3rd International Conference on B Phyiscs and CP Violation, Taipei December 3-7, 199

Pollen dimorphism and dioecy in Vitis aestivalis

Problems of low production and sterile pollen in varieties of Vitis vinifera may be tracable to their ancestral relations with dioecious wild grapes.Like V. riparia, the wild summer grape V. aestivalis has dimorphic male and female flowers; but unlike V. riparia it also has dimorphic pollen grains with the pollen from the female flower being significantly smaller.It seems fairly certain that V. aestivalis is truly dioecious

Response of selected plant and insect species to simulated solid rocket exhaust mixtures and to exhaust components from solid rocket fuels

The effects of solid rocket fuel (SRF) exhaust on selected plant and and insect species in the Merritt Island, Florida area was investigated in order to determine if the exhaust clouds generated by shuttle launches would adversely affect the native, plants of the Merritt Island Wildlife Refuge, the citrus production, or the beekeeping industry of the island. Conditions were simulated in greenhouse exposure chambers and field chambers constructed to model the ideal continuous stirred tank reactor. A plant exposure system was developed for dispensing and monitoring the two major chemicals in SRF exhaust, HCl and Al203, and for dispensing and monitoring SRF exhaust (controlled fuel burns). Plants native to Merritt Island, Florida were grown and used as test species. Dose-response relationships were determined for short term exposure of selected plant species to HCl, Al203, and mixtures of the two to SRF exhaust