Borohydride reduction of the periodate-oxidized polysaccharide obtained from slippery-elm mucilage, affords, on partial hydrolysis with hot acid, three oligosaccharides: O-(3-O-methyl-β-D-galactopyranosyl)-(1→4)-O-(3-O-methyl-β-D-galactopyranosyl)-(1→4)-L-rhamnose (2), O-(3-O-methyl-β-D-galactopyranosyl)-(1→4)-L-rhamnose (3), and O-(3-O-methyl-β-D-galactopyranosyl)-(1→4)-3-O-methyl-D-galactose (4). The structure assigned to 3 was corroborated by a synthesis of the disaccharide.
By using a very general drop theorem in locally convex spaces we obtain some extended versions of Ekeland's variational principle, which only need assume local completeness of some related sets and improve Hamel's recent Nike Roshe Run Uk 5
results. From this, we derive some new versions of Caristi's fixed points theorems. In the framework of locally convex spaces, we prove that Daneš' drop theorem, Ekeland's variational principle, Roshe Run Woven
Caristi's fixed points theorem and Phelps lemma are equivalent to each other.
A method of solving the radiative transfer equation in two-dimensional X−Y geometry is proposed. Starting from the interaction principle, a set of linear equations for the intensities on a discrete grid in a rectangular domain are derived, by an extension of the one-dimensional method of Grant and Hunt. The method yields positive intensities and flux conservation, provided that the size of the cells of the grid is sufficiently small. A simple problem is presented to illustrate the method.