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.     

Asymmetric hydrogenation of N-sulfonylated-alpha-dehydroamino acids: toward the synthesis of an anthrax lethal factor inhibitor

A novel and highly enantioselective Ru-catalyzed hydrogenation of N-sulfonylated-alpha-dehydroamino acids has been discovered and demonstrated in the synthesis of an anthrax lethal factor inhibitor (LFI). Herein, this methodology is used to prepare N-sulfonylated amino acids in up to 98% ee. This unprecedented hydrogenation uses a chiral Ru catalyst rather than Rh as typical for acylated dehydroamino acids and esters, and this work reports the first asymmetric hydrogenation of a tetrasubstituted dehydroamino acid derivative using a Ru catalyst. [reaction: see text]     

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.     

Use of two-dimensional liquid fractionation for separation of proteins from cell lysates without the presence of methionine oxidation

A novel two-dimensional (2D) chromatographic method is developed to separate proteins from malignant breast cancer whole cell lysates. Protein mixtures are first separated according to their pIby chromatofocusing followed by an orthogonal non-porous reversed-phase separation. An important advantage of this 2D chromatographic method is that, unlike gel-based methods, it does not result in methionine oxidation. The lack of methionine oxidation during separation is demonstrated by the analysis of protein tryptic digests using matrix-assisted laser desorption ionization time-of-flight (MALDI-TOF) MS. Our novel 2D chromatographic method used in combination with on-target light-induced methionine oxidation provides a means for studying methionine-containing peptides. Methionine residues in peptide sequences are partially oxidized with light exposure. Neither the location nor the modification of methionine in the peptide sequence affects the oxidation. As a result, multiple peaks are observed in MALDI-TOF-MS spectra after light exposure. Sequence information derived from light-induced methionine can be applied to enhance the database search results obtained through peptide mass fingerprinting.     

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.