We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. also provide examples oriented graphs that have non-Cohen-Macaulay vertex-weighted ideals, while the ideal their underlying graph is Cohen-Macaulay. This disproves a conjecture posed by Pitones, Reyes, Toledo.

We demonstrate the first long-wavelength (Xc= 20 pm) quantum WN infrared photodetector using non-lattice matched InxGaj-xAs/GaAs materials system. High optical gains (low capture probabilities) were achieved by using GaAs as a barrier material in this system. The dctcctivity has been found to be comparable to those achieved with the usual lattice matched GaAs/AlxGal-XAS detectors.

Well-differentiated fetal adenocarcinoma (WDFA) is a very uncommon malignant tumor originating in the lung. This report describes the case of a 38-year-old woman with a WDFA treated by surgery. The malignancy is low grade and associated with a good prognosis, and so it is important for clinicians to be aware of and to identify this rare variant of adenocarcinoma.

Using Rogers’ nonterminating 6φ5 summation and elementary series manipulations, we give a simple proof of Bailey’s very-well-poised 6ψ6 summation. This proof extends M. Jackson’s first proof of Ramanujan’s 1ψ1 summation.

If sk denotes the number of stable sets of cardinality k in the graph G,

If sk equals the number of stable sets of cardinality k in the graph G, then I(G; x) = α(G) ∑ k=0 skx k is the independence polynomial of G (Gutman and Harary, 1983). Alavi, Malde, Schwenk and Erdös (1987) conjectured that I(G; x) is unimodal whenever G is a forest, while Brown, Dilcher and Nowakowski (2000) conjectured that I(G; x) is unimodal for any well-covered graph G. Michael and Traves (...