Z. Naturforsch. 58b, 211 – 216 (2003); received Oktober 4, 2002 The oxidative coupling of various symmetric (5 7) as well as unsymmetric silicon bisnaphtholates (11, 12), initiated by different oxidants (iron(III), cerium(IV), copper(II) or hypervalent iodine), furnishes the corresponding symmetric and unsymmetric binaphthols 13 17. The coupling reaction of the substrates follows strictly an in...

The s-step Lanczos method is an attractive alternative to the classical Lanczos method as it enables an O(s) reduction in data movement over a fixed number of iterations. This can significantly improve performance on modern computers. In order for s-step methods to be widely adopted, it is important to better understand their error properties. Although the s-step Lanczos method is equivalent to...

Two of the commonly used versions of the Lanczos method for eigenvalues problems are the shift-and-invert Lanczos method and the restarted Lanczos method. In this talk, we will address two questions, is the shift-and-invert Lanczos method a viable option on massively parallel machines and which one is more appropriate for a given eigenvalue problem?

A well-known approach to compute the LU factorization of a general unsymmetric matrix A is to build the elimination tree associated with the pattern of the symmetric matrix A + A and use it as a computational graph to drive the numerical factorization. This approach, although very eÆcient on a large range of unsymmetric matrices, does not capture the unsymmetric structure of the matrices. We in...

An efficient palladium-catalyzed cross-coupling reaction of azides with isocyanides is developed, providing a general synthetic route to unsymmetric carbodiimides with excellent yields. This method shows a broad substrate scope, including not only aryl azides, but also unactivated benzyl and alkyl azides. Furthermore, from readily available substrates, Pd-catalyzed coupling with a tandem amine ...

The s-step Lanczos method is an attractive alternative to the classical Lanczos method as it enables an O(s) reduction in data movement over a fixed number of iterations. This can significantly improve performance on modern computers. In order for s-step methods to be widely adopted, it is important to better understand their error properties. Although the s-step Lanczos method is equivalent to...

Analysis and development of restarted Krylov subspace methods for computing f(A)b have proliferated in recent years. We present an acceleration technique for such methods when applied to Stieltjes functions f and Hermitian positive definite matrices A. This technique is based on a rank-one modification of the Lanczos matrix derived from a connection between the Lanczos process and Gauss–Radau q...

We use a recently developed technique, which allows to perform few Lanczos steps on a given wavefunction even for large system sizes, to investigate the t−J model in the physical parameter region and to check the stability of the BCS d-wave variational wavefunction [1]. Our statistical Lanczos algorithm, which extends and improves the one Lanczos step proposed in Ref. [2], has been extensively ...

The first one-pot selective synthesis of unsymmetric tertiary amines is reported by the amination of two types of alcohols with primary amines via the development of a simple CuAlOx-HT catalyst and enables the synthesis of unsymmetric amines in a wide variety of primary amines and alcohols.