In sections 1, 2, 3, 4 the many-time and one-time functional calculus is developed for the anharmonic oscilator in analogy to the requirements of nonlinear spinor theory. In section 5 the N.T.D.-method is discussed for the eigenvalue functional equation. It is shown that the N.T.D.method admits different representations, namely a symmetric one and an unsymmetric one. The proof of convergence is...

We review three algorithms that scale the in nity-norm of each row and column in a matrix to 1. The rst algorithm applies to unsymmetric matrices, and uses techniques from graph theory to scale the matrix. The second algorithm applies to symmetric matrices, and is notable for being asymptotically optimal in terms of operation counts. The third is an iterative algorithm that works for both symme...

We investigate several ways to improve the performance of sparse LU factorization with partial pivoting, as used to solve unsymmetric linear systems. We introduce the notion of unsymmetric supernodes to perform most of the numerical computation in dense matrix kernels. We introduce unsymmetric supernode-panel updates and two-dimensional data partitioning to better exploit the memory hierarchy. ...

The superscript H refers to the Hermitian transpose, which includes transposition and complex conjugation. That is, for any matrix A, AH = AT . An eigenvector of A, as defined above, is sometimes called a right eigenvector of A, to distinguish from a left eigenvector. It can be seen that if y is a left eigenvector of A with eigenvalue λ, then y is also a right eigenvector of AH , with eigenvalu...

A process for the gram scale synthesis of the oxygen bridged dimer of boron subphthalocyanine, μ-oxo-(BsubPc)2, has been developed. During the development it was found that a wide range of reaction pathways under diverse conditions lead to μ-oxo-(BsubPc)2 formation. However, obtaining μ-oxo-(BsubPc)2 as the main reaction product in appreciable yields and its subsequent isolation were extremely ...

A rhodium-catalysed stitching reaction between 2-(silylethynyl)arylboronates and 2-(silylethynyl)aryl bromides has been developed for the synthesis of unsymmetric dibenzo[a,e]pentalenes. The introduction of appropriately sized silyl groups on the starting substrates led to a high crossover selectivity without using an excess amount of either substrate. The present stitching reaction could produ...

We present greedy unsymmetric collocation schemes for solving linear elliptic partial differential equations using radial basis functions. The proposed approach circumvents the ill-conditioning problem associated with the standard collocation technique and enables the efficient solution of problems requiring a large set of collocation points. Numerical studies indicate that the accuracy of gree...