The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl

Isolation and Characterization of Bacteria from the Gut of Bombyx mori that Degrade Cellulose, Xylan, Pectin and Starch and Their Impact on Digestion

Bombyx mori L. (Lepidoptera: Bombycidae) have been domesticated and widely used for silk production. It feeds on mulberry leaves. Mulberry leaves are mainly composed of pectin, xylan, cellulose and starch. Some of the digestive enzymes that degrade these carbohydrates might be produced by gut bacteria. Eleven isolates were obtained from the digestive tract of B. mori, including the Gram positive Bacillus circulans and Gram negative Proteus vulgaris, Klebsiella pneumoniae, Escherichia coli, Citrobacter freundii, Serratia liquefaciens, Enterobacter sp., Pseudomonas fluorescens, P. aeruginosa, Aeromonas sp., and Erwinia sp.. Three of these isolates, P. vulgaris, K. pneumoniae, C. freundii, were cellulolytic and xylanolytic, P. fluorescens and Erwinia sp., were pectinolytic and K. pneumoniae degraded starch. Aeromonas sp. was able to utilize the CMcellulose and xylan. S. liquefaciens was able to utilize three polysaccharides including CMcellulose, xylan and pectin. B. circulans was able to utilize all four polysaccharides with different efficacy. The gut of B. mori has an alkaline pH and all of the isolated bacterial strains were found to grow and degrade polysaccharides at alkaline pH. The number of cellulolytic bacteria increases with each instar

Fluorous oxime palladacycle: A precatalyst for carbon-carbon coupling reactions in aqueous and organic medium

10.1021/jo202482hJournal of Organic Chemistry7762729-2742JOCE