Two-dimensional gauge theory and matrix model

We study a matrix model obtained by dimensionally reducing Chern–Simons theory on S³$S^3$. We find that the matrix integration is decomposed into sectors classified by the representation of SU(2)$\mathit{SU}(2)$. We show that the N  -block sectors reproduce SU(N)$\mathit{SU}(N)$ Yang–Mills theory on S²$S^2$ as the matrix size goes to infinity.     

Preparation of a novel bromine complex and its application in organic synthesis

Although molecular bromine (Br₂) is a useful brominating reagent, it is not easy to handle. Herein, we describe the preparation of a novel air-stable bromine complex prepared from 1,3-dimethyl-2-imidazolidinone (DMI) and Br₂, which was identified to be (DMI)₂HBr₃ by spectral and X-ray techniques. This complex was then used to brominate olefins, carbonyl compounds, and aromatics, as well as in the Hofmann rearrangement. Yields of reaction products using this complex were almost the same or superior to those using other bromine alternatives.     

Heck-type 5-endo-trig cyclization promoted by vinylic fluorines: synthesis of 5-fluoro-3H-pyrroles

A 5-endo-trig alkene insertion proceeds under palladium catalysis via aminopalladium species starting from 3,3-difluoroallyl ketone O-pentafluorobenzoyloximes, providing a facile access to 5-fluoro-3H-pyrroles.     

Putnam’s Inequality for log-Hyponormal Operators

Let T be a bounded linear operator on a complex Hilbert space H. T $/in$ B(H) is called a log-hyponormal operator if T is invertible and log (TT ^*) log (T ^* T). Since a function log : (0,) (-,) is operator monotone, every invertible p-hyponormal operator T, i.e., (TT ^*) ^p (T ^* T ^p is log-hyponormal for 0 < p 1. Putnams inequality for p-hyponormal operator T is the following:$ \| (T^*T)^p-(TT^*)^p \|\leq\frac{p}{\pi}\int\int_{\sigma(T)}r^{2p-1}drd\theta $.In this paper, we prove that if T is log-hyponormal, then$ \| log(T^*T)-log(TT^*) \|\leq\frac{1}{\pi}\int\int_{\sigma(T)}r^{-1}drd\theta $.     

Pyrolysis of sulfoxide. III. Conversion of 2-(phenylsulfinyl)enoate to 2,4-dienoate and synthesis of pellitorine

2,4-Dienoate was prepared by pyrolysis of 2-(phenylsulfinyl)enoate. N-Isobutyl-E,E-2,4-decadieneamide (pellitorine) was synthesized from decanoic acid in a satisfactory yield.     

Electrochemical processes of meso-tetrakis (4-sulfonatophenyl) porphine at a silver electrode studied by surface-enhanced resonance raman spectroscopy

The potential dependence of surface-enhanced resonance Roman spectra of meso-tetrakis (4-sulfonatophenyl) porphine (TSPP) in 0.05 M H₂SO₄ reveals two electrochemical processes at a silver electrode surface. One which begins around ?0.3 V is interpreted as dissociation of aggregated TSPP to monomers. The other which occurs near ?0.4 V is ascribed to a partial Ag incorporation of TSPP molecules.     

Formation pathways of HO2 and OH changing as a function of temperature in photolytically initiated oxidation of dimethyl ether

The time resolved product formation in oxidation of dimethyl ether (DME) has been studied between 298-625 K and 20-90 torr total pressure. Near-infrared frequency modulation spectroscopy (FMS) with Herriott type multi pass optics and UV absorption spectroscopy (UV) were conducted in the same cell. The reaction was initiated by pulsed photolysis in a mixture of Cl₂, O₂, and DME via CH₃OCH₂ radical formation. The reaction process was investigated through FMS measurement of HO₂ and OH, and UV measurement of CH₃OCH₂O₂. The yields of HO₂ and OH are obtained by comparison with reference mixtures, Cl₂, O₂, and CH₃OH for HO₂, and Cl₂, O₂, CH₃OH, and NO for OH, which convert 100% of initial Cl to HO₂ and OH. The CH₃OCH₂O₂ yield is also obtained. It was found that the HO₂ yield increases sharply over 500 K mainly with a longer time constant than that of R + O₂ reaction, while a prompt component exists throughout the temperature range at a few percent yield. OH was found to be produced promptly at a yield considerably larger than that known for the simplest alkanes. The CH₃OCH₂O₂ profile has a prompt rise followed by a gradual decay whose rate is consistent with the slow HO₂ formation. The species profiles were successfully predicted with a model constructed by modifying the existing one to suit the reduced pressure condition. After modification, it was inferred that the HO₂ formation over 500 K is secondary from HCHO + OH and HCO + O₂ and a part of HCO is formed directly from the O₂ adduct, whereas the HO₂ formation below 500 K is governed by CH₃OCH₂O₂ chemistry. The HCO forming pathway via isomerization-decomposition of the O₂ adduct, which was not included in the former models, was supported by our quantum-chemical calculations.     

High-resolution ESR study of the H...CH3, H...CHD2, D...CH2D, and D...CD3 radical pairs in solid argon

High-resolution electron spin resonance (ESR) spectra of radical pairs of a hydrogen atom that coupled with a methyl radical (H...CH3, H...CHD2, D...CH2D, and D...CD3) were observed for X-ray irradiated solid argon containing selectively deuterium-labeled methanes, CH4, CH2D2, and CD4, at 4.2 K. The double-quartet 1H-hyperfine (hf) splittings of ca. 26 and 1.16 mT at the Deltam(s) = +/-1 and Deltam(s) = +/-2 transitions, which are one-half of the isotropic 1H-hf splittings of an isolated H-atom and a CH3 radical, were attributed to the H...CH3 pair. The 1H-hf splittings at the Deltam(s) = +/-1 transition were further split by the fine structure (fs) due to the electron dipole-dipole coupling. Because of the high-resolution spectra, three different sets of the fs splitting, d, are clearly resolved in the spectra of both the H...CH3 and the D...CD3 pairs. The separation distance (inter-spin distance), R, between the H-atom and the CH3 radical being in pairs was evaluated from the d values based on a point-dipole interaction model. For the case of the H...CH3 pair, the observed d values of 4.2, 4.9, and 5.1 mT yield the respective separations, R = 0.87, 0.83, and 0.82 nm, to probe the trapping site of the pair in an Ar crystalline lattice (fcc). For the pair with R = 0.87 nm, for example, we propose that the CH3 radical occupies a substitutional site and the counter H-atom occupies either the interstitial tetrahedral sites directed away from the CH3 radicals by a distance of 0.87 nm or the interstitial octahedral sites by a distance of 0.88 nm. When a mixture of CH4 and CD4 in a solid Ar matrix was irradiated, only two different radical pairs, H...CH3 and D...CD3, were observed. This result clearly demonstrates that the hydrogen atom and methyl radicals, which undergo a pairwise trapping, can originate from the same methane molecule.     

Metal-catalyzed radical polyaddition as a novel polymer synthetic route

A new class of polymerizations was developed via metal-catalyzed C-C bond forming radical polyaddition; the monomers were designed to have a reactive C-Cl bond, which can be activated by the metal catalysts to generate a carbon radical species, along with a C=C double bond, to which the carbon radical generated from another molecule adds to form a C-C backbone polymer with an inactive C-Cl pendant.