Nichtlineare Tschebyscheff Approximation mit Nebenbedingungen: Anwendungen

Summary In this paper we give some applications resulting from the theory of nonlinear approximation under side-conditions developed in a preceding paper [3]. Particularly a necessary condition for best approximation in terms of a generalized alternant is discussed, the approximating functions having restricted ranges. As special cases of this kind we deduce theorems for one-sided approximation and for approximations by positive functions. We conclude with a result in the theory of nonlinear programming.

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Zweiter Teil einer gekürzten Fassung der Dissertation des Verfassers [3].     

Configuration interaction calculations for the ground and excited states of ozone and its positive ion: Energy locations and transition probabilities

Large-scale configuration interaction calculations (including energy extrapolation) are reported for the various states of ozone and its positive ion. The first four dipole-forbidden electronic transitions in the O₃ spectrum are calculated to occur at 1.20, 1.44, 1.59, and 1.72 eV, respectively, while the corresponding low-energy-allowed species known as the Chappuis, Huggins, and Hartley bands are predicted to possess vertical excitation energies of 1.95, 3.60, and 4.97 eV, respectively. These results all appear to fit in quite well with the observed location of the pertinent spectral features, with respect to both energy and intensity. The 5- to 8-eV region of the ozone spectrum is found to be characterized by a series of double-excitation transitions out of the highest three occupied orbitals to the lowest unoccupied 2b₁(π^*) species. The strong features observed at 9.3 and 10.2 eV are thereupon calculated to result primarily from transitions into the 7a₁ (σ^*) MO (calculated 9.29 and 10.05 eV) and in the former case also from the 3s members of the various O₃ Rydberg series (calculated 9.21 and 9.38 eV). Finally the order of the first three ip's is found to be 6a₁, 4b₂, and 1a₂, while the feature in the neighborhood of 16 eV is attributed to a shake-up state of ²B₁ symmetry.     

Zur Koecherschen Reduktionstheorie in Positivitätsbereichen. I

Ohne ZusammenfassungGefördert durch National Science Foundation grant GP-3750.     

Zur Koecherschen Reduktionstheorie in Positivitätsbereichen. III

Ohne ZusammenfassungGefördert durch National Science Foundation Grant GP-3750     

Spectroscopy of stripe order in La1.8Sr0.2NiO4 using resonant soft x-ray diffraction

Strong resonant enhancements of the charge-order and spin-order superstructure-diffraction intensities in La1.8Sr0.2NiO4 are observed when x-ray energies in the vicinity of the Ni L2,3 absorption edges are used. The pronounced photon-energy and polarization dependences of these diffraction intensities allow for a critical determination of the local symmetry of the ordered spin and charge carriers. We found that not only the antiferromagnetic order but also the charge-order superstructure resides within the NiO2 layers; the holes are mainly located on in-plane oxygens surrounding a Ni2+ site with the spins coupled antiparallel in close analogy to Zhang-Rice singlets in the cuprates.     

Radio frequency selective addressing of localized atoms in a periodic potential

We study the localization and addressability of ultracold atoms in a combined parabolic and periodic potential. Such a potential supports the existence of localized stationary states and we show that applying a radio frequency field allows us to selectively address atoms in these states. This method is used to measure the energy and momentum distribution of the atoms in the localized states. We also discuss possible extensions of this scheme to address and manipulate atoms in single lattice sites.