Restricted expected multivariate least squares

A new approach of estimating parameters in multivariate models is introduced. A fitting function will be used. The idea is to estimate parameters so that the fitting function equals or will be close to its expected value. The function will be decomposed into two parts. From one part, which will be independent of the mean parameters, the dispersion matrix is estimated. This estimator is inserted in the second part which then yields the estimators of the mean parameters. The Growth Curve model, extended Growth Curve model and a multivariate variance components model will illustrate the approach.     

Ueber Indicatoren zur Alkalimetrie und Acidimetrie

Ohne Zusammenfassung     

Photo fragmentation of metal clusters stored in a penning trap

Photo fragmentation studies of stored mass selected metal cluster ions of a large size range are reported. The experimental method and the data evaluation are described in detail. Gold cluster ions were produced by laser vaporization and stored in a Penning trap. After size selection they were electronically excited by irradiation with a pulsed laser beam. Relaxation by evaporation of neutral atoms and dimers was observed as a function of photon energy. From these data upper and lower limits for dissociation energies are determined for Au⁺_n (n=3 to 23).     

Convergence analysis of a conforming adaptive finite element method for an obstacle problem

The adaptive algorithm for the obstacle problem presented in this paper relies on the jump residual contributions of a standard explicit residual-based a posteriori error estimator. Each cycle of the adaptive loop consists of the steps ‘SOLVE’, ‘ESTIMATE’, ‘MARK’, and ‘REFINE’. The techniques from the unrestricted variational problem are modified for the convergence analysis to overcome the lack of Galerkin orthogonality. We establish R-linear convergence of the part of the energy above its minimal value, if there is appropriate control of the data oscillations. Surprisingly, the adaptive mesh-refinement algorithm is the same as in the unconstrained case of a linear PDE—in fact, there is no modification near the discrete free boundary necessary for R-linear convergence. The arguments are presented for a model obstacle problem with an affine obstacle χ and homogeneous Dirichlet boundary conditions. The proof of the discrete local efficiency is more involved than in the unconstrained case. Numerical results are given to illustrate the performance of the error estimator.     

Possible transformation of YBa2Cu3O7 under pressure

Crystal structure measurements on the high-T _c material YBa₂Cu₃O₇ were carried out under pressure. Several X-ray reflections do not reveal a uniform shift with increasing pressure. Two models are presented, which show the experimental data to be consistent with an extensivec-axis orb-axis decrease, respectively.