Construction of best Bregman approximations in reflexive Banach spaces

An iterative method is proposed to construct the Bregman projection of a point onto a countable intersection of closed convex sets in a reflexive Banach space.

     

Phospha-palladacycles and N-heterocyclic carbene palladium complexes: efficient catalysts for CC-coupling reactions

Due to the great importance of palladium-catalyzed Heck-type reactions in scientific and industrial chemistry, a lot of publications and reviews have been published during the last years describing this matter under different aspects. This article presents a summary of catalytic applications of palladium complexes with phosphorus ligands containing a metallated sp³-carbon centre (“palladacycles”) or with N-heterocyclic carbene ligands in C-C and C-N coupling reactions of aryl halides including recent results of mechanistic discussions about their role in the catalytic cycle.     

Solving Sequences of Refined Multistage Stochastic Linear Programs

Multistage stochastic programs with continuous underlying distributions involve the obstacle of high-dimensional integrals where the integrands' values again are given by solutions of stochastic programs. A common solution technique consists of discretizing the support of the original distributions leading to scenario trees and corresponding LPs which are – up to a certain size – easy to solve. In order to improve the accuracy of approximation, successive refinements of the support result in rapidly expanding scenario trees and associated LPs. Hence, the solvability of the multistage stochastic program is limited by the numerical solvability of sequences of such expanding LPs. This work describes an algorithmic technique for solving the large-scale LP of refinement ν based on the solutions at the previous ν?1 refinements. Numerical results are presented for practical problem statements within financial applications demonstrating significant speedup (depending on the size of the LP instances).     

Induced smectic C* phases

Induced ferroelectric S*_C phases are formed by non-chiral S_C host phases doped with chiral dipolar guest molecules. In those mixtures the spontaneous polarization P_s and the tilt angle Θ has been investigated as a function of the mole fraction x_G of the chiral dopant. In most cases the reduced polarization P₀ = P_S/ sin Θ has been found to depend linearly on x_G. The polarization power which is defined by δ_P=(∂P₀/∂x_G)ΔT is discussed in terms of the molecular structure of the chiral dopants. There are systems in which P₀(x_G) deviates positively from linearity. This behaviour can be understood by considering a local field correction to P₀. By assuming a local field of Lorentz type a theoretical relation for P₀(x_G) has been derived which explains the experimental results. The effect of a local field is considerable if the transverse dipole moment and the polarizability of the chiral dopant are large.     

Application of a digital signal processor to Fourier-transform infrared spectroscopy

Summary The application of a digital signal processor (DSP) to Fourier-transform infrared spectroscopy is described, which allows for near real-time display of the transformed interferograms as spectra.     

Biosynthetic Studies on Antibiotics

The intricacies of the synthetic chemistry executed by living cells in the assembly of complex organic natural products can be probed in great detail by stable-isotope labeling in conjunction with sophisticated 2D and multiple-quantum NMR methods of analysis. Mechanistic details are revealed by unraveling the “cryptic” stereochemistry of biosynthetic reactions with the aid of stereospecific isotope labeling. Analysis of blocked mutants and cloning of biosynthetic genes provides new tools for the study of biosynthetic pathways and for the exploitation of the chemical capabilities of living organisms.     

Complete structure determination of the astrophysically important nucleus Na below the proton threshold

The fusion–evaporation reaction ¹⁰B(¹²C, 2n) was used to make the first observation of in-beam γ decays from the astrophysically important nucleus ²⁰Na, lying adjacent to the proton drip-line. All states below the proton threshold in ²⁰Na were populated and identified in the experiment. These include new levels, previously unresolved levels, and states located with improved energy precision. The level structure of ²⁰Na, and its γ transitions, are compared to the mirror partner ²⁰F measured simultaneously in this experiment. In particular, a high degree of energy stability is found for all negative parity states. These results are discussed in the context of the nuclear shell model.