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.     

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.     

Kinetic determination of trace cobalt(II) by visual autocatalytic indication

A highly sensitive and simple visual autocatalytic method has been developed for the determination of trace cobalt. The cobalt ion released by the oxidative decomposition of inert bis[2-(5-bromo-2-pyridylazo)-5-(N-propyl-N-sulfopropyl-amino-phenolato] cobaltate (Co(III)-5-Br-PAPS) with peroxomonosulfate acts as a catalyst for the oxidative degradation of the complex. Thus a definite time lapse of degradation is observed by the sudden disappearance of colored Co(III) complexes. The degradation time varies inversely with the logarithm of the initial concentration of cobalt(II). The determination range of cobalt(II) was from 3x10(-9) to 2x10(-7) M in the presence of 5x10(-6) M of 5-Br-PAPS. The relative standard deviation of the spot size method (10 mul) was 3.5% at 1x10(-7) M cobalt(II). This autocatalytic indicator reaction system has been successfully applied for the visual determination of urinary cobalt.     

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.     

Microwave spectroscopic study on the molecular structure and the quadrupole coupling constants of thionyl chloride

Microwave spectra of thionyl chloride, SO³⁵Cl₂ and SO³⁵Cl³⁷Cl, in the frequency range 8–25 GHz have been analyzed. The rotational constants have been obtained from the low J transition frequencies. The r_S coordinates of Cl atoms and the r_o structure have been evaluated with some assumptions: r(S-O) = 1.435 ± 0.011± Å, r(S—Cl) = 2.072 0.005 Å, ∠ OSCl = 108.00 ± 0.06°, ∠ ClSCl = 97.15 ± 0.30°. Nuclear quadrupole coupling constants have been obtained for the SO³⁵Cl₂, species: x_aa = ?25.02 ± 0.04 MHz, x(_bb = ?0.25 ± 0.04 MHz, X_cc = 25.27 ± 0.08 MHz, and X_zz = ?96.75 MHz. The values obtained are compared with those of other workers.