A comparison of some algorithms for the nonlinear least squares problem

The problem of minimizing a sum of squares of nonlinear functions is studied. To solve this problem one usually takes advantage of the fact that the objective function is of this special form. Doing this gives the Gauss-Newton method or modifications thereof. To study how these specialized methods compare with general purpose nonlinear optimization routines, test problems were generated where parameters determining the local behaviour of the algorithms could be controlled. The order of 1000 test problems were generated for testing three algorithms: the Gauss-Newton method, the Levenberg-Marquardt method and a quasi-Newton method.     

Convergence acceleration by means of numerical quadrature

By regarding a series as a Stieltjes integral to which classical numerical methods are applied, very accurate expressions for the sum are obtained. Convergence and stability are investigated in some cases of practical importance. When certain conditions are satisfied, realistic and strict error bounds for the sum can be found. Some generalizations are also indicated.     

Diffusion in phases with several components and sublattices

Diffusion in multicomponent alloys is discussed in order to extend earlier treatments to phases with sublattices. Both a phenomenological approach and some physical models are applied. Care is taken so that the driving forces and the fluxes are chosen in a way obeying the requirements of irreversible thermodynamics. The Onsager reciprocal relation will thus be obeyed. Two kinds of models have been considered, exchange between two atoms and exchange between an atom and a vacancy.For phases with several sublattices a number of difficulties arise and only a few cases of great practical importance are considered. The connection between practical diffusion coefficients and phenomenological coefficients is given. The use of different concentration variables in Fick's second law is discussed.     

Interpretation of electron spectra I. Spectra of furan,pyrrole and cyclopentadiene,studied with HAM/3

The interpretation of spectra of molecules by use of semi-empirical methods, of which SPINDO is an example, is usually possible for only one property of the molecule. If several properties of the molecules are used in the parametrization process the resulting method will have a more general applicability. This possibility is illustrated by the use of HAM/3 to interpret ionization energies, excitation energies and electron affinities of furan, pyrrole and cyclopentadiene.     

An experimental study of the 9Be(p, π+)10Be and 9Be(p, π−)10C reactions at 185 MeV

A magnetic spectrometer was used for the momentum analysis of pions produced by 185 MeV protons on a ⁹Be target. The obtained energy resolution (0.55 MeV FWHM) made it possible to resolve a number of discrete final states in ¹⁰Be and ¹⁰C. Energy spectra were measured in the angular region 15°–130° (lab). Angular distributions for six peaks in ¹⁰Be and four peaks in ¹⁰C are presented in tables and graphs. A peak corresponding to a not previously reported level in ¹⁰Be was observed at 11.75 ±0.11 MeV excitation energy. The measured $\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}$ ratio for the ground state analogues was found to be angular dependent and varied from 30 at 35° (lab) to 2 at 125° (lab). The results are compared with theoretical predictions and discussed in terms of one- and two-nucleon models.     

Über die Kapazität einer verallgemeinerten Cantorschen Punktmenge

Ohne ZusammenfassungIch bin Herrn ProfessorGunnar af Hällström für wertvolle Ratschläge bei der Ausarbeitung dieser Untersuchung großen Dank schuldig.     

Shaking processes in β-decay

A discussion of theoretical treatments of atomic rearrangement processes accompanying β-decay is presented. A schematic model for K-shell ejection or excitation is developed and the expected accuracy of this model and other theoretical treatments using approximate wave functions is discussed. Comparison with experimental evidence reveals that there is some evidence of direct processes but that uncertainties in calculations exist for low energy processes.