11 research outputs found
Comment on ``Large-space shell-model calculations for light nuclei''
In a recent publication Zheng, Vary, and Barrett reproduced the negative
quadrupole moment of Li-6 and the low-lying positive-parity states of He-5 by
using a no-core shell model. In this Comment we question the meaning of these
results by pointing out that the model used is inadequate for the reproduction
of these properties.Comment: Latex with Revtex, 1 postscript figure in separate fil
Karhunen-Lo\`eve expansion for a generalization of Wiener bridge
We derive a Karhunen-Lo\`eve expansion of the Gauss process , , where is a
standard Wiener process and is a twice continuously
differentiable function with and . This
process is an important limit process in the theory of goodness-of-fit tests.
We formulate two special cases with the function
, , and , ,
respectively. The latter one corresponds to the Wiener bridge over from
to .Comment: 25 pages, 1 figure. The appendix is extende
Several ways to a Berwald manifold - and some steps beyond
After summarizing some necessary preliminaries and tools, including Berwald derivative and Lie derivative in pull-back formalism, we present several equivalent conditions, each of which characterizes Berwald manifolds among Finsler manifolds. These range from Berwald’s classical definition to the existence of a torsion-free covariant derivative on the base manifold compatible with the Finsler function, the vanishing of the h-Berwald differential of the Cartan tensor and Aikou’s characterization of Berwald manifolds. Finally, we study some implications of V. Matveev’s observation according to which quadratic convexity may be omitted from the definition of a Berwald manifold. These include, among others, a generalization of Z.I. Szab´o’s well-known metrization theorem, and also lead to a natural generalization of Berwald manifolds, to Berwald { Matveev manifolds.The first two authors were supported by Hungarian Scientific Research Fund OTKA No. NK 81402.peerReviewe