Reproducing Kernels for Iterated Parabolic Operators on the Upper Half Space with Application to Polyharmonic Bergman Spaces

We consider parabolic operators of fractional order and their iterates on the upper half space of the euclidean space. We deal with Hilbert spaces of solutions of those parabolic equations. We shall show, in this note, the existence of reproducing kernels and give a formula by using their fundamental solutions. As an application, we also discuss the polyharmonic Bergman spaces and give their reproducing kernels by using the Poisson kernel on the upper half space.     

Aerobic oxidation of alcohols using bismuth bromide as a catalyst

We developed an environmentally friendly method for aerobic oxidation of alcohols using a commercially available, relatively benign bismuth salt as a catalyst. We found that the catalytic combination of BiBr₃ with nitric acid is key for enhancing the reactivity. The reaction proceeds well under air, making the use of pure oxygen unnecessary. Each of the primary or secondary alcohols tested was oxidized to the corresponding aldehydes or ketones using this protocol.     

Internal radiocesium contamination of adults and children in Fukushima 7 to 20 months after the Fukushima NPP accident as measured by extensive whole-body-counter surveys

The Fukushima Dai-ichi NPP accident contaminated the soil of densely-populated regions in Fukushima Prefecture with radioactive cesium, which poses significant risks of internal and external exposure to the residents. If we apply the knowledge of post-Chernobyl accident studies, internal exposures in excess of a few mSv/y would be expected to be frequent in Fukushima.Extensive whole-body-counter surveys (n = 32,811) carried out at the Hirata Central Hospital between October, 2011 and November, 2012, however show that the internal exposure levels of residents are much lower than estimated. In particular, the first sampling-bias-free assessment of the internal exposure of children in the town of Miharu, Fukushima, shows that the ¹³⁷Cs body burdens of all children (n = 1,383, ages 6–15, covering 95% of children enrolled in town-operated schools) were below the detection limit of 300 Bq/body in the fall of 2012. These results are not conclusive for the prefecture as a whole, but are consistent with results obtained from other municipalities in the prefecture, and with prefectural data.     

Novel enantioselective direct aldol-type reaction promoted by a chiral phosphine oxide as an organocatalyst

Chiral phosphine oxide successfully catalyzed the direct aldol-type reactions of cyclohexanone derivatives and benzaldehyde derivatives in high stereoselectivities. The reaction mechanism involves the in situ formation of trichlorosilyl enol ethers. The present reaction could be extended to the cross-aldol reactions between two aldehydes.     

Room Temperature Solution ENDOR of some Super Stable Fluorocarbon Radicals

Room temperature fluorine electron nuclear double resonance (ENDOR) has been successfully observed for several superstable fluorocarbon radicals ·C(C₂F₄R)(i-C₃F₇)₂ in solution. Three radicals were employed in which CF₃, F, and O-c-C₆F₁₀SO₃C₂F₅ were introduced as R, and all the hyperfine couplings (hfcs) obtained by ENDOR were assigned with the help of ESR simulation and ab initio MO calculation. In case of ·C(i-C₃F₇)₃ large ¹³C and considerable β-fluorine couplings suggest the nonplaner arrangement for the central and three carbons at the β-position, in spite of the fact that all the methyl fluorine show the same hfc. Therefore, a rapid puckering motion along the C₃ axis together with the methyl rotation should average the hfc’s of the 18 fluorine nuclei to give the same value. When one of the CF₃ groups is substituted with an F nucleus, the five CF₃ groups give two hfc values, suggesting some dynamics still exists for the molecular frame. When a large group, O-c-C₆F₁₀SO₃C₂F₅, is substituted for CF₃, all the five CF₃ groups become nonequivalent and the ENDOR signal becomes intensive and sharp even at 290 K, indicating that the molecular frame becomes rigid. The relation between the ENDOR spectra of these systems and the intramolecular dynamics is discussed.     

DFT Study of a 5‐endo‐trig‐Type Cyclization of 3‐Alkenoic Acids by Using Pd–Spiro‐bis(isoxazoline) as Catalyst: Importance of the Rigid Spiro Framework for Both Selectivity and Reactivity

The reaction pathway of an enantioselective 5‐endo‐trig‐type cyclization of 3‐alkenoic acids catalyzed by a chiral palladium–spiro‐bis(isoxazoline) complex, Pd–SPRIX, has been studied by density functional theory calculations. The most plausible pathway involves intramolecular nucleophilic attack of the carboxylate moiety on the C?C double bond activated by Pd–SPRIX and β‐H elimination from the resulting organopalladium intermediate. The enantioselectivity was determined in the cyclization step through the formation of a π‐olefin complex, in which one of the two enantiofaces of the olefin moiety was selected. The β‐H elimination occurs via a seven‐membered cyclic structure in which the acetate ligand plays a key role in lowering the activation barrier of the transition state. In the elimination step, the SPRIX ligand was found to behave as a monodentate ligand due to the hemilability of one of the isoxazoline units thereby facilitating the elimination. Natural population analysis of this pathway showed that the more weakly electron‐donating SPRIX ligand, compared with the bis(oxazoline) ligand, BOX, facilitated the formation of the π‐olefin complex intermediate, leading to a smaller overall activation energy and a higher reactivity of the Pd–SPRIX catalyst.