Substituent effect investigation of 3‐(2, 4‐dichlorophenyl)‐1‐(4′‐X‐phenyl)‐2‐propen‐1‐one. Part 1. Correlation analysis of 13C NMR chemical shifts

A series of substituted chlorinated chalcones namely, 3‐(2,4‐dichlorophenyl)‐1‐(4′‐X‐phenyl)‐2‐propen‐1‐one, have been synthesized, X being H, NH₂, OMe, Me, F, Cl, CO₂Et, CN, and NO₂. Dual substituent parameter (DSP) models of ¹³C NMR chemical shift (CS) have revealed that π‐polarization concept could be utilized to explain the reverse field effect at CO, the enhanced substituent field effect at CO, C‐2, and C‐5, and the decreased sensitivity of substituent field effect at C‐6. Chlorine atoms dipole direction at the benzylidene ring either enhances or reduces substituent effect depending on how they couple with the substituent dipole at the probe site. The correlation of ¹³C NMR CS of C‐2, C‐5, and C‐6 with σ and σ indicates that chlorine atoms in the benzylidine ring deplete the ring from charges. Both MSP of Hammett and DSP of Taft ¹³C NMR CS models give similar trends of substituent effects at C‐2, C‐5, and C‐6. However, the former fail to give a significant correlation for CO and C‐6 ¹³C NMR CS. MSP of σ_q and DSP of Taft and Reynolds models significantly correlated ¹³C NMR CS of C_β. MSP of σ_q fails to correlate C‐1′ ¹³C NMR CS. Investigation of ¹³C NMR CS of non‐chlorinated chalcones series: 3‐phenyl‐1‐(4′‐X‐phenyl)‐2‐propen‐1‐one has revealed similar trends of substituent effects as in the chlorinated chalcones series for C‐1′, CO, C_α, and C_β. In contrast, the substituent effect of the non‐chlorinated chalcone series at C‐2, C‐5, and C‐6 did not correlate with any substituent constant. Copyright © 2010 John Wiley & Sons, Ltd.     

Error estimation in nonlinear optimization

Methods are developed and analyzed for estimating the distance to a local minimizer of a nonlinear programming problem. One estimate, based on the solution of a constrained convex quadratic program, can be used when strict complementary slackness and the second-order sufficient optimality conditions hold. A second estimate, based on the solution of an unconstrained nonconvex, nonsmooth optimization problem, is valid even when strict complementary slackness is violated. Both estimates are valid in a neighborhood of a local minimizer. An active set algorithm is developed for computing a stationary point of the nonsmooth error estimator. Each iteration of the algorithm requires the solution of a symmetric, positive semidefinite linear system, followed by a line search. Convergence is achieved in a finite number of iterations. The error bounds are based on stability properties for nonlinear programs. The theory is illustrated by some numerical examples.     

Theorie der Abelschen Gruppen

Ohne Zusammenfassung     

On the super-approximation property of Galerkin's method with finite elements

Summary For Galerkin's method with finite elements as trial functions for strongly elliptic operator equations in the Hilbert scaleH ^t the super-approximation property and the optimal convergence rate are obtained by using the Aubin-Nitsche lemma. This applies in particular to spline collocation methods for a wide class of pseudodifferential equations.Dedicated to the memory of Professor Lothar Collatz     

Living radical emulsion polymerization using the nanoprecipitation technique: An extension to atom transfer radical polymerization

Living radical polymerizations of styrene were performed under emulsion atom transfer radical polymerization conditions with latexes prepared by a nanoprecipitation technique recently developed for the stable free‐radical polymerization process. Latexes were prepared by the precipitation of a solution of low‐molecular‐weight polystyrene in acetone into a solution of a surfactant in water. The resulting particles were swollen with styrene and then heated. The effects of various surfactants and hydrophobic ligands, the reaction temperature, and the ligand/copper(I) bromide ratio were studied. The best results were obtained with the nonionic surfactant Brij 98 in combination with the hydrophobic ligand N,N‐bis(2‐pyridylmethyl)octadecylamine and a ligand/copper(I) bromide ratio of 1.5 at a reaction temperature of 85–90 °C. Under these conditions, latexes with good colloidal stability with average particle diameters of 200 nm were obtained. The molecular weight distributions of the polystyrenes were narrow, although the experimental molecular weights were slightly larger than the theoretical ones because not all the macroinitiator appeared to reinitiate. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4027–4038, 2006     

Qualitative behaviour of incompressible two-phase flows with phase transitions: The isothermal case

A thermodynamically consistent model for incompressible two-phase flows with phase transitions is considered mathematically. The model is based on first principles, i.e., balance of mass, momentum and energy. In the isothermal case, this problem is analysed to obtain local well-posedness, stability of non-degenerate equilibria, and global existence and convergence to equilibria of solutions which do not develop singularities.