On the Feynman Path Integral for the Dirac Equation in the General Dimensional Spacetime

The Feynman path integral for the Dirac equation in the general dimensional spacetime is determined mathematically in the form of the sum-over-histories satisfying the superposition principle, i.e., the “sum” of the probability amplitudes with a common weight over all possible paths that go in any direction at any speed forward and backward in time. It is noted that our Feynman path integral is determined not in configuration space, but in phase space.     

Measurement of speed of sound in poly(lactic acid)-clay composite

We measured longitudinal speed of sound for matrix[poly(lactic acid)]-additive(clay particles) composite rectangular-solid specimen prepared by injection molding. It was found that the speed of sound measured in the direction along the longer side of the specimen was the highest at the middle of the specimen. This trend corresponded with that for crystallinity determined through differential scanning calorimetry (DSC). A cross section view of the specimen parallel to its longer side showed that there was a transverse flow trace of resin in the vicinity of the injection gate while the flow trace along the direction of the longer side spread wider as getting far from the gate toward the middle of the specimen. The high crystallinity appeared in the middle of the specimen was inferred to come from the promotion of crystallization by molecular orientation induced with the above flow trace parallel to the direction along the longer side of the specimen.     

A Generalized Proximal Point Algorithm and Implicit Iterative Schemes for a Sequence of Operators on Banach Spaces

The aim of this paper is to obtain weak convergence of an iterative scheme generated by a sequence of accretive operators defined on a real Banach space, which is a generalization of the result given by Kamimura and Takahashi (J. Approx. Theory 106:226–240, 2000). We also show several applications to the implicit iterative schemes with the Yosida approximations and with the W-mappings generated by a sequence of nonexpansive mappings.     

Brønsted acid catalyzed regioselective aza-Ferrier reaction: a novel synthetic method for alpha-(N-Boc-2-pyrrolidinyl) aldehydes

The 1,4-elimination reaction of (Z)-N-Boc-2-(4-methoxy-2-alkenyloxy)pyrrolidines is shown to proceed with high (1E,3E)-stereoselectivity to afford N-Boc-2-(1,3-dienyloxy)pyrrolidines; the Br?nsted acid catalyzed aza-Ferrier reaction of the N-Boc-2-(1,3-dienyloxy)pyrrolidines (3) provides alpha-(N-Boc-2-pyrrolidinyl) aldehydes in excellent yields with high alpha-regioselectivities.     

Synthesis, characterization and oxidizing properties of a diorgano tellurone carrying bulky aromatic substituents

Bis(2,4,6-triisopropylphenyl) tellurone (Tip(2)TeO(2)) was prepared, fully characterized by spectroscopic and X-ray crystallographic analyses, as well as theoretical calculations, and found to be an effective oxidizing agent that was capable of converting alcohols into carbonyl compounds under mild reaction conditions.     

Exceptionally strong Bragg diffraction from a mesoporous silica film pretreated with chlorotrimethylsilane toward application in X-ray optics

Exceptionally strong Bragg diffraction from a mesoporous silica film is achieved by exposing the as-deposited film to vapor of chlorotrimethylsilane (Me(3)SiCl) before extracting the surfactant. The intensity of the X-ray diffraction peak increased 7 times after the surfactant removal and it approached 30% reflectivity. This large increase of diffraction intensity cannot be explained simply by the improved contrast of the electron density, and rearrangement of the pore wall during the Me(3)SiCl vapor treatment is suggested. It is shown by infrared spectroscopy that Me(3)SiCl with a high grafting reactivity effectively caps the silanol groups and prevents the following condensation, which causes the structural degradation. The substitution of the hydrogen atom of hydroxyl groups with trimethylsilyl groups should help the improvement of the structural regularity by reducing the hydrogen bonds in the pore wall. The achieved strong diffraction opens the gate for the application of these regular mesoporous films prepared by a self-assembly process to optical elements in the X-ray region.     

Optical resolution of aromatic alcohols using silica nanoparticles grafted with helicene

Optically active silica nanoparticles, with a 70-nm diameter, grafted with (P)-1,12-dimethyl-8-methoxycarbonylbenzo[c]phenanthrene-5-carboxyamide were synthesized, and their use in the kinetic resolution of aromatic alcohols was examined. Up to 61% ee for (S)-2,2-dimethyl-1-phenyl-1-propanol was obtained by a preferential precipitation of aggregates formed with (P)-nanoparticles.     

Synthesis, Stability, and Photoluminescence Properties of PdAu10(PPh3)8Cl2 Clusters

We report on the synthesis, stability, and photoluminescence (PL) properties of triphenylphosphine (PPh₃)-stabilized PdAu₁₀(PPh₃)₈Cl₂ cluster, which is a mono-Pd-doped cluster of the well-studied Au₁₁(PPh₃)₈Cl₂ cluster. The PdAu₁₀(PPh₃)₈Cl₂ cluster was synthesized by simultaneously reducing two different metal complexes; AuCl(PPh₃) and Pd(PPh₃)₄. Experimental evaluation of the stability showed that PdAu₁₀(PPh₃)₈Cl₂ is more stable against degradation in solution than the monometal Au₁₁(PPh₃)₈Cl₂ cluster. PL measurements revealed that PdAu₁₀(PPh₃)₈Cl₂ exhibits PL at 950?nm with a quantum yield of 1.5?×?10^?3, which has not been observed for the monometal Au₁₁(PPh₃)₈Cl₂ cluster. The results indicate that Pd doping is a powerful method to produce clusters with higher stability and different physical properties than the monometal Au:PPh₃ clusters.     

Palladium doping of magic gold cluster Au38(SC2H4Ph)24: formation of Pd2Au36(SC2H4Ph)24 with higher stability than Au38(SC2H4Ph)24

A phenylethanethiolate-protected Pd(2)Au(36)(SC(2)H(4)Ph)(24) cluster, which is a two-Pd atom-doped cluster of the well studied magic gold cluster Au(38)(SC(2)H(4)Ph)(24), was synthesized in high purity and its stability was investigated. The results demonstrate that Pd(2)Au(36)(SC(2)H(4)Ph)(24) is more stable than Au(38)(SC(2)H(4)Ph)(24) against degradation in solution and core etching by thiols.