A superlinearly convergent method for minimization problems with linear inequality constraints

A method is described for minimizing a continuously differentiable functionF(x) ofn variables subject to linear inequality constraints. It can be applied under the same general assumptions as any method of feasible directions. IfF(x) is twice continuously differentiable and the Hessian matrix ofF(x) has certain properties, then the algorithm generates a sequence of points which converges superlinearly to the unique minimizer ofF(x). No computation of secondorder derivatives is required.Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462 and by the National Science Foundation under Research Grant GP.33033.     

Gesichtspunkte bei der Stoffauswahl für dünne Schichten in der Optik

Ohne Zusammenfassung     

Evaluation of the Fe2+/Fe3+ ratio from57Co Mössbauer emission spectra: Influence of the relaxation of Fe3+

The Fe³⁺ fraction after the EC of⁵⁷Co is usually evaluated supposing that ferric ions contribute a quadrupole doublet to Mössbauer emission spectra. It is shown that a not sufficiently fast relaxation of the electron spins may falsify the evaluated intensity even by a factor 2. Additional information can be gained from measurements performed in a large velocity span at low temperatures in high magnetic fields.     

Probabilistic clustering via Pareto solutions and significance tests

The present paper proposes a new strategy for probabilistic (often called model-based) clustering. It is well known that local maxima of mixture likelihoods can be used to partition an underlying data set. However, local maxima are rarely unique. Therefore, it remains to select the reasonable solutions, and in particular the desired one. Credible partitions are usually recognized by separation (and cohesion) of their clusters. We use here the p values provided by the classical tests of Wilks, Hotelling, and Behrens–Fisher to single out those solutions that are well separated by location. It has been shown that reasonable solutions to a clustering problem are related to Pareto points in a plot of scale balance vs. model fit of all local maxima. We briefly review this theory and propose as solutions all well-fitting Pareto points in the set of local maxima separated by location in the above sense. We also design a new iterative, parameter-free cutting plane algorithm for the multivariate Behrens–Fisher problem.     

Untersuchung von Mischvorgängen bei der Herstellung von Kohlenstoffund SiC-Werkstoffen mit Hilfe der Methodik der radioaktiven Markierung

Fūr die Herstellung von Kohlenstoff- und SiC-Werkstoffen ist eine gute Vermischung der festen und flüssigen Komponenten die notiwendige Voraussetzung. Da andere Methoden meist zu zeitaufwendig sind, wurden im VEB EKL seit mehr als 10 Jahren Versuchsreihen mit der Methodik der radioaktiven Markierung einer der Mischungskomponenten zur Untersuchung des Mischvorgangs für Maschinen bis zu 2000 kg Fülung angewandt, wobei sich die Fremdmarkierung mit ⁸²Br-Naphthalin als vorteilhaft erwiesen hat. Der Mischungszustand wird durch statistische Auswertung der Radioaktivität von Probenserien, deren γ-Strahlung gemessen wird und deren Masse in Abhängigkeit von der Mischergröβ 1 bis 100 g je Probe beträgt, charakterisiert. Zusätzlich wird die Feinverteilung durch Kontaktautoradiographie von ebenen Probenoberflächen, ebenfalls für Probenserien, bestimmt.     

Temperature dependence of Bi2O3 structural parameters close to the α–δ phase transition

This article presents the results of in situ X-ray powder diffraction, Raman spectroscopy, and electrical impedance spectroscopy of the α-phase of Bi₂O₃, at 0.1 MPa in the temperature range below and above the α–δ-phase transition. This work demonstrated subtle nonlinear temperature variations of the cell parameters, of the hard-mode Raman shift, and of the activation energy of electrical conductivity in the temperature range about 100–120°C below the α–δ phase transition temperature T _Tr ≈ 725°C in Bi₂O₃. At T < 600°C, the linear variation of the inverse dielectric susceptibility (χ ^?1) correlates well with the hard mode frequency shift Δ(ω ²) of Raman A_1g mode as Δ(χ ^?1)/Δ(ω ²) ≈ 5.5 × 10^?7 cm². A structural model describing the mechanism of O^2? anion distribution and electric dipole disordering in the vicinity of T _Tr is discussed.     

Probability of fatigue failure in glass fibers

Abstract

Fracture mechanics provides the background for making long-term failure predictions to assure the mechanical reliability of glass fibers. The fatigue parameters necessary for making these predictions can be obtained from static and dynamic fatigue strength experiments. The failure calculations are best understood by expressing the predictions in terms of a design diagram. The probability of failure in service as well as the proof test stress necessary to ensure a minimum lifetime in service can be obtained from a design diagram.     

Divergent Late‐Stage (Hetero)aryl C−H Amination by the Pyridinium Radical Cation

(Hetero)arylamines constitute some of the most prevalent functional molecules, especially as pharmaceuticals. However, structurally complex aromatics currently cannot be converted into arylamines, so instead, each product isomer must be assembled through a multistep synthesis from simpler building blocks. Herein, we describe a late‐stage aryl C?H amination reaction for the synthesis of complex primary arylamines that other reactions cannot access directly. We show and rationalize through a mechanistic analysis the reasons for the wide substrate scope and the constitutional diversity of the reaction, which gives access to molecules that would not have been readily available otherwise.