Ueber Reactionen auf Solanin

Ohne Zusammenfassung     

Kalkstickstoff

Ohne Zusammenfassung     

Self-adaptive inexact proximal point methods

We propose a class of self-adaptive proximal point methods suitable for degenerate optimization problems where multiple minimizers may exist, or where the Hessian may be singular at a local minimizer. If the proximal regularization parameter has the form where η∈[0,2) and β>0 is a constant, we obtain convergence to the set of minimizers that is linear for η=0 and β sufficiently small, superlinear for η∈(0,1), and at least quadratic for η∈[1,2). Two different acceptance criteria for an approximate solution to the proximal problem are analyzed. These criteria are expressed in terms of the gradient of the proximal function, the gradient of the original function, and the iteration difference. With either acceptance criterion, the convergence results are analogous to those of the exact iterates. Preliminary numerical results are presented using some ill-conditioned CUTE test problems. This material is based upon work supported by the National Science Foundation under Grant Nos. 0203270, 0619080, and 0620286.     

The generalized triangular decomposition

Given a complex matrix , we consider the decomposition , where is upper triangular and and have orthonormal columns. Special instances of this decomposition include the singular value decomposition (SVD) and the Schur decomposition where is an upper triangular matrix with the eigenvalues of on the diagonal. We show that any diagonal for can be achieved that satisfies Weyl's multiplicative majorization conditions:

where is the rank of , is the -th largest singular value of , and is the -th largest (in magnitude) diagonal element of . Given a vector which satisfies Weyl's conditions, we call the decomposition , where is upper triangular with prescribed diagonal , the generalized triangular decomposition (GTD). A direct (nonrecursive) algorithm is developed for computing the GTD. This algorithm starts with the SVD and applies a series of permutations and Givens rotations to obtain the GTD. The numerical stability of the GTD update step is established. The GTD can be used to optimize the power utilization of a communication channel, while taking into account quality of service requirements for subchannels. Another application of the GTD is to inverse eigenvalue problems where the goal is to construct matrices with prescribed eigenvalues and singular values.

     

Dependence of enantioselectivity on the ligand/metal ratio in the asymmetric Michael addition of indole to benzylidene malonates: electronic influence of substrates

Simple bis(oxazoline) ligands, especially azabis(oxazolines), can promote the copper(II)-catalyzed Michael addition of indoles to benzylidene malonates with up to >99 % ee (ee=enantiomeric excess), provided that the ligand/metal ratio is tuned meticulously with particular regard to the electronic properties of the substrate. Despite a common paradigm followed in many asymmetric catalyses, an excess of chiral ligand is not always beneficial. In fact any excess of ligand has to be avoided to reach excellent enantioselectivities when electron-rich benzylidene malonates are used. On the contrary, malonates carrying an electron-withdrawing group require an excess of ligand for an optimum ee value. A correlation of optical yields versus the sigma(I) values of several para substituents shows a sigmoid trajectory. In the presence of an additive, such as triflate, the significance of the ligand/metal ratio vanishes and very good enantioselectivities are achieved at any rate--no matter whether electron-donating or withdrawing substituents are present.     

Frequency tunable single-line pulsed first-overtone carbon monoxide laser

Tunable single-line first-overtone (FO) CO lasing on wavelengths from 2.7 up to 4.2 μm corresponding to overtone vibrational transitions from 13→11 up to 38→36 on 413 ro-vibrational lines was experimentally obtained. A parametric study of energetic and spectral characteristics of the single-line FO CO laser was carried out. Energy distribution over ro-vibrational lines was measured. The maximum specific output energy (SOE) came up to 3 J/l Amagat, with single-line output efficiency being up to 0.6%. For the first time, a multi-quantum theoretical model was used to describe the tunable single-line FO CO laser. This multi-quantum approach demonstrated better agreement between theoretical calculations and observed experimental data for laser output as a function of vibrational quantum numbers.     

A theorem and a question about epicomplete archimedean lattice-ordered groups

An archimedean ?-group is called epicomplete (or universally σ-complete, or sequentially inextensible) if it is divisible, σ-complete and laterally σ-complete. Various characterizations of such G are known in case the G have weak order units. The “theorem” of the title is a characterization of such G which have no weak order unit; it involves the requirement that G have a certain kind of representation. The “question” of the title is whether every epicomplete G has such a representation.     

C. fumago chloroperoxidase is also a dehaloperoxidase: oxidative dehalogenation of halophenols

We have examined the H2O2-dependent oxidative dehalogenation of 2,4,6-trihalophenols and p-halophenols catalyzed by Caldariomyces fumago chloroperoxidase (CCPO). CCPO is significantly more robust than other peroxidases and can function under harsher reaction conditions, and so its ability to dehalogenate halophenols could lead to its use as a bioremediation catalyst for aromatic dehalogenation reactions. Optimal catalysis occurred under acidic conditions (100 mM potassium phosphate solution, pH 3.0). UV-visible absorption spectroscopy, high-performance liquid chromatography, and gas chromatography/mass spectrometry clearly identified the oxidized reaction product for CCPO-catalyzed dehalogenation of 2,4,6-trihalophenols as the corresponding 2,6-dihalo-1,4-benzoquinones. This reaction has previously been reported for two His-ligated heme-containing peroxidases (see Osborne, R. L.; Taylor, L. O.; Han, K. P.; Ely, B.; Dawson, J. H. Biochem. Biophys. Res. Commun. 2004, 324, 1194-1198), but this is the first example of a Cys-ligated heme-containing peroxidase functioning as a dehaloperoxidase. The relative catalytic efficiency (turnover number) of CCPO reported herein is comparable to that of horseradish peroxidase (Ferrari, R. P.; Laurenti, E.; Trotta, F. J. Biol. Inorg. Chem. 1965, 4, 232-237). The mechanism of dehalogenation has been probed using p-halophenols as substrates. Here the major product is a dimer with 1,4-benzoquinone as the minor product. An electron-transfer mechanism is proposed that accounts for the products formed from both the 2,4,6-trihalo- and p-halophenols. Finally, we note that this is the first case of a peroxidase known primarily for its halogenation ability being shown to also dehalogenate substrates.