Photochemistry of the SO2, 2-pentene system at 3660 Å

The photolysis of SO₂ in the presence of cis- and trans-2-pentene has been investigated at 3660 Å and 22°C. Quantum yield measurements of the SO₂ photosensitized conversion of one isomer into the other are consistent with a mechanism in which the only participating excited electronic state of SO₂ is the SO₂(³B₁) state. Quantum yield measurements were made for a variation in P_SO2/P_isomer reactant ratios of 4.01–283 and 57.5–351 for the cis and trans isomers, respectively. The data are consistent with a mechanism in which a (SO₂-olefin)³ collision intermediate is the precursor to the photosensitized isomeric products. The intermediate undergoes unimolecular decay to yield the cis and trans isomers with probabilities of 0.26 ± 0.05 and 0.69 ± 0.04, respectively. Estimates of the quenching rate constants at 22°C for removal of SO₂(³B₁) molecules by cis- and trans-2-pentene are (0.633 ± 0.125) × 10¹¹ l./mole/sec and (1.00 ± 0.27) × 10¹¹ l./mole/sec, respectively. An experimentally determined photostationary composition, [trans-2-pentene]/[cis-2-pentene] = 2.3 ± 0.1 was in fair agreement with that of 1.7 ± 0.7 as predicted from kinetic data derived in this study.     

Aspects of supersymmetric quantum mechanics

We review the properties of supersymmetric quantum mechanics for a class of models proposed by Witten. Using both Hamiltonian and path integral formulations, we give general conditions for which supersymmetry is broken (unbroken) by quantum fluctuations. The spectrum of states is discussed, and a virial theorem is derived for the energy. We also show that the euclidean path integral for supersymmetric quantum mechanics is equivalent to a classical stochastic process when the supersymmetry is unbroken (E₀ = 0). By solving a Fokker-Planck equation for the classical probability distribution, we find P_c(y) is identical to |Ψ₀(y)|² in the quantum theory.     

The Evolution of Large-Horizontal-Scale Disturbances in Marginally Stable,Inviscid, Shear Flows. II. Solutions of the Boussinesq Equation

In part I the Boussinesq equation was found to describe large-horizontal-scale disturbances in certain marginally stable flows. In this paper the properties of the solutions of this equation are explored. Solutions that are bounded for all time and those that blow up in finite time are observed analytically and numerically. Sufficient conditions for both boundedness and blowup are given.     

Eigenwerte und Minimalpolynome symmetrischer Matrizen in kommutativen Körpern

Ohne Zusammenfassung     

Manganese(I) poly(mercaptoimidazolyl)borate complexes: spectroscopic and structural characterization of Mn...H-B interactions in solution and in the solid state

The manganese(I) tricarbonyl complexes (Bm(R))Mn(CO)3(R = Me, Bz, But, p-Tol) and (PhBmMe)Mn(CO)3, the first bis(mercaptoimidazolyl)borate derivatives for this metal, have been readily prepared and fully characterized. In particular, the presence of three-center-two-electron Mn...H-B interactions in these species, both in solution and in the solid state, has been investigated using a combination of IR and NMR spectroscopies and, in the case of the methyl-, tert-butyl- and para-tolyl-substituted derivatives, by X-ray crystallography. To complement these synthetic and structural studies, the tris(mercaptoimidazolyl)borate complexes (TmMe)Mn(CO)3(R = Me, Bz, But, p-Tol) and (PhTm(Me))Mn(CO)3, as well as the related pyrazolylbis(mercaptoimidazolyl)borate (pzBmMe)Mn(CO)3, have also been synthesized and characterized by a combination of analytical and spectroscopic techniques.     

Cross-linked aggregates of (R)-oxynitrilase: a stable, recyclable biocatalyst for enantioselective hydrocyanation

[Reaction: see text] The (R)-oxynitrilase from almonds was immobilized as a cross-linked enzyme aggregate (CLEA) via precipitation with 1,2-dimethoxyethane and subsequent cross-linking using glutaraldehyde. The resulting preparation was a highly effective hydrocyanation catalyst under microaqueous conditions, which suppress the nonenzymatic background reaction. The beneficial effect of these latter conditions on the hydrocyanation of slow-reacting aldehydes is demonstrated. The oxynitrilase CLEA was recycled 10 times without loss of activity.     

Asymmetric transfer hydrogenation in water with a supported Noyori-Ikariya catalyst

[reaction: see text] The poly(ethylene glycol)-supported ruthenium precatalyst shown above is highly effective for asymmetric transfer hydrogenation of unfunctionalized aromatic ketones by HCOONa in neat water, affording fast rates, good to excellent enantioselectivities, and outstanding reusability.