Das Recht auf gleiche ursprüngliche Freiheit : Hillel Steiners empirischer Ansatz einer liberalen Gerechtigkeitstheorie

Gerade bei Rechten auf Freiheit stellt sich die Frage, ob und wie sie sich begründen lassen. Ein naheliegender Zugang sind liberale Theorien der Gerechtigkeit. Sie rechtfertigen individuelle Anrechte auf ein Maß an Freiheit. Begründungsbedürftig ist die Annahme subjektiver Rechte auf Freiheit schon deshalb, da sie eine fundamentale Weichenstellung für jede politische Theorie darstellt, die sie beinhaltet. Für diesen Bereich der Freiheit ist die Begründungslast umgekehrt; eine Einschränkung der Freiheit muß begründet werden, nicht das Verlangen danach, frei zu sein. Der "Zweck" einer liberalen Theorie der Gerechtigkeit ist die wertneutrale Entscheidung auch antagonistischer Konflikte. Es sind Situationen, in denen zwei Parteien handeln wollen, die Handlungen sich aber gegenseitig ausschließen und die Parteien sich über die Bewertung der Handlungsziele uneinig sind. In der hier erörterten Theorie Hillel Steiners werden die fraglichen Entscheidungen aufgrund subjektiver Rechte gefällt. Gerechtigkeit begründet subjektive Rechte auf ein Maß an Freiheit, durch die selbst antagonistische Konflikte neutral entschieden werden können. Im folgenden wird im Kontext dieser Art liberaler Gerechtigkeitstheorie argumentiert. ..

Gaussian limits for discrepancies. I: Asymptotic results

We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit $N\to\infty$. We then examine the circumstances under which this distribution approaches a normal distribution. For large classes of non-uniformity measures, a Law of Many Modes in the spirit of the Central Limit Theorem can be derived.Comment: 25 pages, Latex, uses fleqn.sty, a4wide.sty, amsmath.st

Multidimensional sampling for simulation and integration: measures, discrepancies, and quasi-random numbers

This is basically a review of the field of Quasi-Monte Carlo intended for computational physicists and other potential users of quasi-random numbers. As such, much of the material is not new, but is presented here in a style hopefully more accessible to physicists than the specialized mathematical literature. There are also some new results: On the practical side we give important empirical properties of large quasi-random point sets, especially the exact quadratic discrepancies; on the theoretical side, there is the exact distribution of quadratic discrepancy for random point sets.Comment: 51 pages. Full paper, including all figures also available at: ftp://ftp.nikhef.nl/pub/preprints/96-017.ps.gz Accepted for publication in Comp.Phys.Comm. Fixed some typos, corrected formula 108,figure 11 and table

Discrepancy-based error estimates for Quasi-Monte Carlo. I: General formalism

We show how information on the uniformity properties of a point set employed in numerical multidimensional integration can be used to improve the error estimate over the usual Monte Carlo one. We introduce a new measure of (non-)uniformity for point sets, and derive explicit expressions for the various entities that enter in such an improved error estimate. The use of Feynman diagrams provides a transparent and straightforward way to compute this improved error estimate.Comment: 23 pages, uses axodraw.sty, available at ftp://nikhefh.nikhef.nl/pub/form/axodraw Fixed some typos, tidied up section 3.

Statistical evaporation of rotating clusters. IV. Alignment effects in the dissociation of nonspherical clusters

Unimolecular evaporation in rotating, non-spherical atomic clusters is investigated using Phase Space Theory in its orbiting transition state version. The distributions of the total kinetic energy release epsilon_tr and the rotational angular momentum J_r are calculated for oblate top and prolate top main products with an arbitrary degree of deformation. The orientation of the angular momentum of the product cluster with respect to the cluster symmetry axis has also been obtained. This statistical approach is tested in the case of the small 8-atom Lennard-Jones cluster, for which comparison with extensive molecular dynamics simulations is presented. The role of the cluster shape has been systematically studied for larger, model clusters in the harmonic approximation for the vibrational densities of states. We find that the type of deformation (prolate vs. oblate) plays little role on the distributions and averages of epsilon_tr and J_r except at low initial angular momentum. However, alignment effects between the product angular momentum and the symmetry axis are found to be significant, and maximum at some degree of oblateness. The effects of deformation on the rotational cooling and heating effects are also illustrated.Comment: 15 pages, 9 figure