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.     

Non-surface activity and micellization behavior of cationic amphiphilic block copolymer synthesized by reversible addition-fragmentation chain transfer process

Cationic amphiphilic diblock copolymers of poly(n-butylacrylate)-b-poly(3-(methacryloylamino)propyl)trimethylammonium chloride) (PBA-b-PMAPTAC) with various hydrophobic and hydrophilic chain lengths were synthesized by a reversible addition-fragmentation chain transfer (RAFT) process. Their molecular characteristics such as surface activity/nonactivity were investigated by surface tension measurements and foam formation observation. Their micelle formation behavior and micelle structure were investigated by fluorescence probe technique, static and dynamic light scattering (SLS and DLS), etc., as a function of hydrophilic and hydrophobic chain lengths. The block copolymers were found to be non-surface active because the surface tension of the aqueous solutions did not change with increasing polymer concentration. Critical micelle concentration (cmc) of the polymers could be determined by fluorescence and SLS measurements, which means that these polymers form micelles in bulk solution, although they were non-surface active. Above the cmc, the large blue shift of the emission maximum of N-phenyl-1-naphthylamine (NPN) probe and the low micropolarity value of the pyrene probe in polymer solution indicate the core of the micelle is nonpolar in nature. Also, the high value of the relative intensity of the NPN probe and the fluorescence anisotropy of the 1,6-diphenyl-1,3,5-hexatriene (DPH) probe indicated that the core of the micelle is highly viscous in nature. DLS was used to measure the average hydrodynamic radii and size distribution of the copolymer micelles. The copolymer with the longest PBA block had the poorest water solubility and consequently formed micelles with larger size while having a lower cmc. The "non-surface activity" was confirmed for cationic amphiphilic diblock copolymers in addition to anionic ones studied previously, indicating the universality of non-surface activity nature.     

Proton-coupled electron-transfer processes in photosystem II probed by highly resolved g-anisotropy of redox-active tyrosine YZ

The oxidation of a redox-active tyrosine residue Y(Z) in photosystem II (PSII) is coupled with proton transfer to a hydrogen-bonded D1-His190 residue. Because of the apparent proximity of Y(Z) to the water-oxidizing complex and its redox activity, it is believed that Y(Z) plays a significant role in water oxidation in PSII. We investigated the g-anisotropy of the tyrosine radical Y(Z)(?) to provide insight into the mechanism of Y(Z)(?) proton-coupled electron transfer in Mn-depleted PSII. The anisotropy was highly resolved by electron paramagnetic resonance spectroscopy at the W-band (94.9 GHz) using PSII single crystals. The g(X)-component along the phenolic C-O bond of Y(Z)(?) was calculated by density functional theory (DFT). It was concluded from the highly resolved g-anisotropy that Y(Z) loses a phenol proton to D1-His190 upon tyrosine oxidation, and D1-His190 redonates the same proton back to Y(Z)(?) upon reduction.     

Target-selective fluorescent "switch-on" protein labeling by 6π-azaelectrocyclization

Application of azaelectrocyclization and FRET techniques to lysine groups enabled the selective and sensitive detection of a target protein from a mixture, with high fluorescence contrast.     

Enantiocontrolled total syntheses of breviones A, B, and C

Enantiocontrolled total syntheses of the breviones A, B, and C have been accomplished using a highly diastereoselective oxidative coupling of an α-pyrone with a tricyclic diene prepared from an optically pure Wieland-Miescher ketone derivative through the 7-endo-trig mode of acyl radical cyclization.     

Expansion of Photostable Luminescent Radicals by Meta-Substitution

Polychlorinated pyridyldiphenylmethyl radicals having substituents meta to the position bearing the carbon-centered radical (α-carbon) are synthesized. All of them are stable in ambient conditions in solutions and fluorescent in cyclohexane. The fluorescence of the radicals with bromo, phenyl, 4-chlorophenyl, or 2-pyridyl substituents are enhanced in chloroform, while the emission of the radicals with 2-thienyl or 2-furyl substituents are quenched in chloroform. DFT and TD-DFT calculations indicate that the first doublet excited states of the former are locally excited, while the first doublet excited states of the latter are charge transfer states from the π-electron-donating substituent to the accepting radical. The latter also show much higher photostability under 370-nm light irradiation compared with the first reported photostable fluorescent radical, (3,5-dichloro-4-pyridyl)bis(2,4,6-trichlorophenyl)methyl radical (PyBTM), with pronounced bathochromic shifts of the fluorescence.