We show that the equation a2 +b6 = cn has no nontrivial positive integer solutions with (a, b) = 1 via a combination of techniques based upon the modularity of Galois representations attached to certain Q -curves, corresponding surjectivity results of Ellenberg for these representations, and extensions of multi-Frey curve arguments of Siksek.

Previous work with growing swine indicated that the lysine requirement, expressed as a percentage of the diet, decreased by .02 percentage units with each 1% reduction in dietary protein level. Thus, the dietary lysine needed for optimal performance may be less than the reported requirement when a portion of the soybean meal in a corn-soybean meal diet is replaced with crystalline lysine. An ex...

In particulate soft matter systems the average number of contacts Z of a particle is an important predictor of the mechanical properties of the system. Using x-ray tomography, we analyze packings of frictional, oblate ellipsoids of various aspect ratios α, prepared at different global volume fractions ϕg. We find that Z is a monotonically increasing function of ϕg for all α. We demonstrate that...

The cholangiocarcinoma (CCA) is a relatively rare cancer worldwide but it is highly prevalent in Thailand where the liver fluke, Opisthorchis viverrini is endemic. There are reports that interleukin 6 (IL-6) may play an important role in the pathogenesis of opisthorchiasis associated CCA. Functionally, IL-6 can act on target cells through its receptor, IL-6R, and IL-6R polymorphisms may affect ...

Background: Recent studies have shown that cytokines have an important role in the pathogenesis of inflammatory diseases and can be used as prognostic markers. Objective: To evaluate the IL-6/IL-10 ratio in patients with Inherited Epidermolysis Bullosa (EB) as a prognostic marker. Methods: Serum levels of IL-6 and IL-10 were measured in 13 patients with recessive dystrophic EB (RDEB) as well as...