Elementary excitations in antiferromagnetic Heisenberg systems

The structure of the (eigen)states of antiferromagnetic Heisenberg systems is discussed. These systems are shown to be equivalent to classical systems of coupled harmonic oscillators. Most attention will be paid to the first excited state. This state is supposed to be a triplet. An approximation method, which is a generalization of a method, used to describe the ground state of Heisenberg systems, will be used to describe elementary excitations. The working of the method is demonstrated by some small-system calculations

Exact spectrum for n electrons in the single band Hubbard model

The energy spectrum and the correlation functions for n electrons in the one-dimensional single band Hubbard model with periodic boundary conditions are calculated exactly. For that purpose the Hamiltonian is transformed into a set of Hamiltonians, corresponding to systems of spinless fermions.\ud Our results include the results of Mei and Chen, presented in a recent paper

A mechanism for symmetry breaking in antiferromagnetic Heisenberg systems

An approximation method, based on dimer coverings, for the ground state of the antiferromagnetic Heisenberg lattice is described. The working of the method is demonstrated by some small-system calculations. The method introduces a possible mechanism for symmetry breaking for two- and higher-dimensional systems

A thermodynamic approximation of the ground state of antiferromagnetic heisenberg spin−1/2 lattices

The exact ground state of finite Heisenberg spin−1/2 lattices isstudied. The coefficients of the so-called Ising configurations contributing to the ground state are approximated by Boltzmann-like expressions. These expressions contain a parameter that may be related to an inverse temperature

Image reconstruction from scattered Radon data by weighted positive definite kernel functions

We propose a novel kernel-based method for image reconstruction from scattered Radon data. To this end, we employ generalized Hermite–Birkhoff interpolation by positive definite kernel functions. For radial kernels, however, a straightforward application of the generalized Hermite–Birkhoff interpolation method fails to work, as we prove in this paper. To obtain a well-posed reconstruction scheme for scattered Radon data, we introduce a new class of weighted positive definite kernels, which are symmetric but not radially symmetric. By our construction, the resulting weighted kernels are combinations of radial positive definite kernels and positive weight functions. This yields very flexible image reconstruction methods, which work for arbitrary distributions of Radon lines. We develop suitable representations for the weighted basis functions and the symmetric positive definite kernel matrices that are resulting from the proposed reconstruction scheme. For the relevant special case, where Gaussian radial kernels are combined with Gaussian weights, explicit formulae for the weighted Gaussian basis functions and the kernel matrices are given. Supporting numerical examples are finally presented

Kernel-based Image Reconstruction from Scattered Radon Data

Computerized tomography requires suitable numerical methods for the approximation of a bivariate function f from a finite set of discrete Radon data, each of whose data samples represents one line integral of f . In standard reconstruction methods, specific assumptions concerning the geometry of the Radon lines are usually made. In relevant applications of image reconstruction, however, such assumptions are often too restrictive. In this case, one would rather prefer to work with reconstruction methods allowing for arbitrary distributions of scattered Radon lines. This paper proposes a novel image reconstruction method for scattered Radon data, which combines kernel-based scattered data approximation with a well-adapted regularization of the Radon transform. This results in a very flexible numerical algorithm for image reconstruction, which works for arbitrary distributions of Radon lines. This is in contrast to the classical filtered back projection, which essentially relies on a regular distribution of the Radon lines, e.g. parallel beam geometry. The good performance of the kernel-based image reconstruction method is illustrated by numerical examples and comparisons

Methodologische Fragen der Verwendung von Bild-, Ton- und Textdaten zur Navigationsanalyse

Lernende eignen sich bei der Navigation in Online-Lernumgebungen Wissen an. Studien, die diese Aneignung von Wissen untersuchen, stellen dabei häufig die Frage nach dem Resultat des Aneignungsprozesses in den Mittelpunkt. Dieser Zugang mit der Frage nach Effektivität und Effizienz dominiert die gegenwärtige Perspektive auf E-Learning – gerade auch im Vergleich zu traditionellen Medien wie dem Buch