On equivalence of L p -norms related to Schrödinger type operators on Riemannian manifolds

In this paper, we study Schrödinger type operator on a Riemannian manifold. Under some assumptions on a potential function, we characterize the domain of the square root of the Schrödinger type operator on L ^p space. In the proof, the defective intertwining properties and the Littlewood-Paley inequalities play important roles.     

Reaction of poly(vinyl alcohol) with tetravalent ceric ion

Poly(vinyl alcohol) (PVAI) was oxidized by ceric ion, Ce(IV), in aqueous HNO₃ medium at different temperatures and found to be degraded as a result of selective cleavage of the 1,2-glycol unit existing in PVAl. The rate of oxidation increased with increasing temperature. The aldehyde groups formed at the ends of the degraded polymer upon oxidation were relatively stable at 0°C. With rise of temperature, the aldehyde groups reacted either with excess of Ce(IV) to carboxylic acids or with hydroxyl groups of PVAl molecules to give acetal linkage. When the acetalization predominated over the oxidation to carboxyl group, gelation of the reaction mixture was observed. Based on these results, a plausible mechanism of oxidation of PVAl with Ce(IV) and the subsequent reactions is discussed.     

Fine structures of zeolite-Linde-L (LTL): surface structures, growth unit and defects

High-resolution electron microscopy (HREM) has been used to image the surface structure of nano- and micrometer-sized synthetic crystals of zeolite-Linde-L (LTL). Columnar holes and rotational, nano-sized, wheel-like defects were observed within the crystals, where the hole has a minimum size equal to that of the rotational defect. Predictions of surface structure from atomistic computer simulation concur with the observations from HREM and provide insight into the crystal growth mechanism of perfect and defective LTL. Analysis of the energetics of the formation of rotational defect structures reveals that the driving force for defect creation is thermodynamic and furthermore, the rotational defects could be created in high concentrations. Formation of a columnar hole is found to be slightly energetically unfavourable and therefore we speculate that the incidence of both rotational and nano-sized vacancy defects is strongly dependent on kinetic factors and reaction conditions. The morphology of nano- and microcrystalline LTL is contradistinct and we use insights from simulation to propose an explanation of the disparity in crystal shape.     

Synthesis of dehydroxy-trans-resorcylide by intramolecular alkylation of the protected cyanohydrin using a butadiene telomer as a building block

Dehydrroxy-trans-resorcylide ($\text{15}$) was synthesized by efficient intramolecular alkylation of the protected cyanohydrin. The butadiene telomer obtained by the palladium catalyzed reaction of butadiene with acetic acid was used as a suitable block of the carbocycle.     

A new synthesis of δ-lactones from oxetanes

Oxetanes were reacted with lithium enolates generated from esters or amides in the presence of boron trifluoride etherate to give δ-hydroxyesters or amides in high yield, which were hydrolyzed and converted to δ-lactones.