Oxorhenium(V) dithiolates catalyze the oxidation by tert-butyl hydroperoxide of sulfoxides and sulfides, including 4,6-dimethyldibenzothiophene

tert-Butyl hydroperoxide (TBHP) efficiently converts a wide variety of sulfides to sulfoxides and sulfones. The method offers the advantage that one product or the other can be obtained in high purity by a modest variation of conditions. The reactions occur smoothly at 25minus sign50 C in chloroform and, to the extent studied, in toluene and methylene chloride. A catalyst is required; the most extensively studied was MeReO(mtp)PPh(3), 1, where mtpH(2) is 2-(mercaptomethyl)thiophenol. Other chelating dithiolate ligands can be used with comparable results. These oxidations were tested for dialkyl, alkylminus signaryl, and diaryl sulfides; thiophenes; and thianthrene. Even the "hard" sulfide, 4,6-dimethyldibenzothiophene (DMDBT) was quantitatively oxidized to the dioxide with TBHP:DMDBT 3.0-3.5 and 0.05-3.8 mol % 1. The mechanism was explored in kinetics studies carried out only for methyl tolyl sulfide. The product buildup curve was complex, with an induction period followed by a rapid growth phase. The kinetic data could be modeled adequately but not perfectly by allowing five rate constants to refine. Their values are consistent with the chemical sense of the mechanism.     

Sufficient Maximum Principle for Stochastic Optimal Control Problems with General Delays

Journal of Optimization Theory and Applications - This paper is to establish a sufficient maximum principle for one kind of stochastic optimal control problem with three types of delays: a discrete...     

Full-wave analysis of waveguide-to-microstrip transitions for millimeter wave applications

A full-wave solution is presented for the waveguide to microstrip transition. The exact Green's function of the transition is used in a moment method procedure. The behavior of the microstrip transition to a rectangular waveguide is studied with respect to the critical dimensions of the microstrip width, length and backshort location. The convergence characteristics of the full wave analysis method are investigated, along with the current distribution and the input impedance. Results given for the return loss is compared with measurements.     

On the ε-expansion procedure in the RNG theory of turbulence

Rescaling the equations of eliminating small scales, the physical justification for the-expansion procedure in the RNG theory of turbulence is proposed, in terms of that the inertial effects are small comparing with the viscous effects at the vicinity of the Kolmogorov dissipation wavenumber.We are grateful to Professor Chao-Hao Gu for numerous helpful suggestions. We would also like to acknowledge Professor Ke-Lin Wang and Bing-Hong Wang for many stimulating discussions of these problems.     

Level crossing resonance due to chlorine nuclei in a free radical

Muonium adds to allyl chloride, CH₂=CHCH₂Cl, to form two radicals: MuCH₂CHCH₂Cl (main product) and CH₂CHMuCH₂Cl (minor product). Both radicals were fully characterized bySR andLCR. In the main product, the LCR lines due to the³⁵Cl and³⁷Cl nuclei were observed. Also, the temperature dependence of various hyperfine coupling constants (hfc) indicates that both Mu and Cl eclipse the unpaired electronp ₂-orbital in the minimum energy conformation. For the fragment-CH₂Cl, the presence of Mu in the-position is found to affect significantly the hfc of Cl in the-position; an internal rotational barrier of 12 kJ mol^–1 was estimated using a simpleV ₂ torsional potential.