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The asymmetric dialkylzinc addition to imines catalyzed by [2.2]paracyclophane-based N,O-ligands

The first highly enantioselective dialkylzinc addition to imines in the presence of catalytic amounts of N,O-ligands is reported. N-formyl-alpha-(p-tolysulfonyl)benzylamines are the readily available starting materials easily obtained in a one-pot synthesis from benzaldehydes, formamide, and p-tolylsulfinic acid. Upon deprotonation, the sulfinate is eliminated to give the acyl imine. The acyl imines further react with alkylzinc reagents in the presence of catalytic amounts of [2.2]paracyclophane-based N,O-ligands L yielding the alkylated N-(1-phenylpropyl)formamides with excellent yields and enantioselectivities.     

Iterative Algorithms for Multiscale State Estimation, Part 1: Concepts

The objective of the present investigation is to explore the potential of multiscale refinement schemes for the numerical solution of dynamic optimization problems arising in connection with chemical process systems monitoring. State estimation is accomplished by the solution of an appropriately posed least-squares problem. To offer at any instant of time an approximate solution, a hierarchy of successively refined problems is designed using a wavelet-based Galerkin discretization. In order to fully exploit at any stage the approximate solution obtained also for an efficient treatment of the arising linear algebra tasks, we employ iterative solvers. In particular, we will apply a nested iteration scheme to the hierarchy of arising equation systems and adapt the Uzawa algorithm to the present context. Moreover, we show that, using wavelets for the formulation of the problem hierarchy, the largest eigenvalues of the resulting linear systems can be controlled effectively with scaled diagonal preconditioning. Finally, we deduce appropriate stopping criteria and illustrate the characteristics of the solver with a numerical example.     

Appending boundary conditions by Lagrange multipliers: Analysis of the LBB condition

Summary. This paper is concerned with the analysis of discretization schemes for second order elliptic boundary value problems when essential boundary conditions are enforced with the aid of Lagrange multipliers. Specifically, we show how the validity of the Ladyškaja–Babušska–Brezzi (LBB) condition for the corresponding saddle point problems depends on the various ingredients of the involved discretizations. The main result states that the LBB condition is satisfied whenever the discretization step length on the boundary, , is somewhat bigger than the one on the domain, . This is quantified through constants stemming from the trace theorem, norm equivalences for the multiplier spaces on the boundary, and direct and inverse inequalities. In order to better understand the interplay of these constants, we then specialize the setting to wavelet discretizations. In this case the stability criteria can be stated solely in terms of spectral properties of wavelet representations of the trace operator. We conclude by illustrating our theoretical findings by some numerical experiments. We stress that the results presented here apply to any spatial dimension and to a wide selection of Lagrange multiplier spaces which, in particular, need not be traces of the trial spaces. However, we do always assume that a hierarchy of nested trial spaces is given. Received October 23, 1998 / Revised version received December 27, 1999 / Published online October 16, 2000     

Depinning of a domain wall in the 2d random-field Ising model

We report studies of the behaviour of a single driven domain wall in the 2-dimensional non-equilibrium zero temperature random-field Ising model, closely above the depinning threshold. It is found that even for very weak disorder, the domain wall moves through the system in percolative fashion. At depinning, the fraction of spins that are flipped by the proceeding avalanche vanishes with the same exponent as the infinite percolation cluster in percolation theory. With decreasing disorder strength, however, the size of the critical region decreases. Our numerical simulation data appear to reflect a crossover behaviour to an exponent at zero disorder strength. The conclusions of this paper strongly rely on analytical arguments. A scaling theory in terms of the disorder strength and the magnetic field is presented that gives the values of all critical exponent except for one, the value of which is estimated from scaling arguments. Received: 13 February 1998 / Accepted: 30 March 1998     

Convexity and Bernstein polynomials onk-simploids

This paper is concerned with Bernstein polynomials onk-simploids by which we mean a cross product ofk lower dimensional simplices. Specifically, we show that if the Bernstein polynomials of a given functionf on ak-simploid form a decreasing sequence thenf +l, wherel is any corresponding tensor product of affine functions, achieves its maximum on the boundary of thek-simploid. This extends recent results in [1] for bivariate Bernstein polynomials on triangles. Unlike the approach used in [1] our approach is based on semigroup techniques and the maximum principle for second order elliptic operators. Furthermore, we derive analogous results for cube spline surfaces.This work was partially supported by NATO Grant No. DJ RG 639/84.     

Trace element determination of high-purity chemicals for the processing of semiconductors with high-resolution ICP-mass spectrometry using stable isotope dilution analysis (IDA)

The demand for trace element analysis in many fields of application has significantly increased in the last few years. Accuracy is fundamental to analysis and the importance of accurate measurements is widely accepted. Yet most instrumental analytical methods are relative methods and accuracy is established by using certified reference materials for method validation and calibration or by use of a definitive method as isotope dilution analysis (IDA). In this work a new high-resolution ICP mass spectrometer Finnigan MAT “ELEMENT”, which provides mass spectral resolution of 300 up to 7500 and thus eliminates most of the spectral interferences quadrupol mass analyzers are suffering from, is applied in combination with IDA to evaluate the capabilities of these techniques to the accurate determination of element traces in processing chemicals for semiconductor production.