General order Newton-Padé approximants for multivariate functions

Summary Padé approximants are a frequently used tool for the solution of mathematical problems. One of the main drawbacks of their use for multivariate functions is the calculation of the derivatives off(x ₁, ...,x _p ). Therefore multivariate Newton-Padé approximants are introduced; their computation will only use the value off at some points. In Sect. 1 we shall repeat the univariate Newton-Padé approximation problem which is a rational Hermite interpolation problem. In Sect. 2 we sketch some problems that can arise when dealing with multivariate interpolation. In Sect. 3 we define multivariate divided differences and prove some lemmas that will be useful tools for the introduction of multivariate Newton-Padé approximants in Sect. 4. A numerical example is given in Sect. 5, together with the proof that forp=1 the classical Newton-Padé approximants for a univariate function are obtained.     

Application of a fusion model using collective variables and microscopically related mass parameters

A calculation of nucleus-nucleus collisions is presented, using a model which starts from a TDHF equation and leads to classical equations of motion for a set of four collective variables. Restricting to axial symmetry and assuming the liquid drop mass formula to hold, a differential equation is derived, which describes nuclear deformations and energies and is used to construct a potential energy surface for the collective variables. The nuclear deformations are obtained without the need of shape parameters. The equations of motion for the collective variables are solved numerically.     

The He(Iα) Photoelectron Spectra of Substituted 1,2-Dithietes

The He(Iα) photoelectron (PE.) spectra of a series of substituted 1,2-dithietes have been recorded and assigned with respect to the orbital sequence derived from an STO-3G model calculation and by correlation with the PE. spectra of related compounds. The results provide additional support for the presence of a closed, four-membered ring moiety in all the 1,2-dithietes investigated. In all cases the two highest occupied molecular orbitals are b₂(π)= HOMO, a₂(π), with exception of 3,4-bis(trifluoromethyl)-1,2-dithiete where the sequence b₂(π), a₂(π) or a₂(π), b₂(π) is uncertain.     

Darstellung und Kristallstruktur von SrCu2Sb2 und SrZnBi2

Preparation and Crystal Structure of SrCu₂Sb₂ and SrZnBi₂ SrCu₂Sb₂ and SrZnBi₂ have been prepared and analytically and structurally characterized. SrCu₂Sb₂ crystallizes tetragonal in the CaBe₂Ge₂ structure type. SrZnBi₂ has its own structure type. In both structures the transition metal atoms form with the semimetal atoms tetragonal pyramids, which are connected by common edges of the basis to twodimensional sheets. These sheets are separated in the case of SrCu₂Sb₂ by single sheets of strontium atoms, in the case of SrZnBi₂ by double sheets of strontium atoms in which fourfold nets of Bi atoms are located.     

Instability of laser cw oscillation in the presence of a passive medium

For a homogeneously broadened two-level ring laser model the stability of the cw laser oscillation in the presence of a passive medium is investigated. The passive material is treated similar to the active material, but without an external pumping mechanism. Stable and unstable regions are shown for various parameters. The stability region of the cw solution becomes extremly small for certain parameters.