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.     

Motion of redox molecules in solution monitored by the highly-sensitive EQCM technique

The behavior of redox molecules in solution that was not detected by electrochemical techniques was measured by a highly-sensitive electrochemical quartz crystal microbalance (EQCM) technique that has been improved in this study to obtain a high sensitivity of EQCM measurement in solution. The improved EQCM technique allowed to monitor the motion of a redox molecule, that is an access of the molecule to an electrode surface and repulsion from the surface during redox. An EQCM technique currently in use has measured adsorption of redox molecules on an electrode surface or polymerization on the surface caused by a chemical reaction following redox, which exhibits an enough large mass change response to detect with an EQCM measurement. However, access and repulsion of redox molecule, which is a slight motion of the molecule near on electrode surface, has not been detected and investigated by an EQCM technique, because the mass change response seems to be very small. In this study, the redox behavior of methyl viologen on a bare gold surface, pyridinethiol surface and methylpyridinethiol surface was investigated. Although the three electrodes give the same cyclic voltammogram of methyl viologen, the three are different in QCM response recorded at the same time as the voltammetry. Access/repulsion of methyl viologen within an electrical double layer was monitored by the highly-sensitive EQCM technique.     

Palladium-catalyzed reaction of allyl carbamates; allylation of carbonucleophiles,and protection-deprotection of amines

Allylation of carbonucleophiles with allylic carbamates under neutral conditions has been studied. The C-allylation of carbonucleophile is competitive with the N-allylation of amines, and the structure of amines is crucial for the selectivity. Bulky secondary amines gave the best results. Also a new method of protection-deprotection of amines as carbamates has been developed. Smooth deprotection is possible by the palladium-catalyzed reaction of allyl carbamates with formic acid. This method is particulary useful for primary amines, including optically active amino acids.     

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.     

The Electronic Structure of Azuleno[1,2,3-cd]phenalene and Azuleno[5,6,7-cd]phenalene,a Comparison

The photoelectron (PE.) spectra of azuleno[l, 2, 3-cd]phenalene ( 1 ) and azuleno- [5,6,7-cd]phenalene( 2 ) have been recorded. The first five bands of both compounds could be assigned to transitions corresponding to removal of electrons from 4a₂, 6b₁, 5b₁, 3a₂ and 4b_l orbitals. This assignment is based mainly on a comparison between the observed ionization potentials and orbital energies calculated in a HMO and a PPP model. The UV./VIS. polarized absorption spectrum of 1 in the region 10000–45000 cm^?1 has been measured by means of the stretched film technique. The measurements were performed in polyethylene sheets at 77°K. Several bands could be assigned to π* ← π transitions calculated by a PPP-CI method. A comparison between the electronic structures of 1 and 2 is made by means of a simple HMO diagram.     

Lewis acid catalysis in supercritical carbon dioxide. Use of poly(ethylene glycol) derivatives and perfluoroalkylbenzenes as surfactant molecules which enable efficient catalysis in ScCO2

Lewis acid catalysis in supercritical carbon dioxide (CO(2)) was investigated. While solubility of most organic materials is low in scCO(2), poly(ethylene glycol) derivatives or perfluoroalkylbenzenes were found to work as surfactants to dissolve organic materials in scCO(2). In the presence of these molecules, Lewis acid catalyzed organic reactions such as aldol-, Mannich-, and Friedel-Crafts-type reactions proceeded smoothly in scCO(2). Formation of emulsions was observed in these reactions, and the systems were studied in detail.