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We present a complete derivation of the semiclassical limit of the coherent state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial value representation for the semiclassical propagator, based on an initial gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed gaussian approximation. It is very different from the Herman - Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.

Mit der vorliegenden Veröffentlichung soll der Versuch unternommen werden, mathematischen Schulstoff aus konkreten Problemen herzuentwickeln. Im Mittelpunkt der vorliegenden Arbeit stehen betriebswirtschaftliche Planungs- und Entscheidungsprobleme, wie sie von fast allen Wirtschaftsunternehmen zu lösen sind. Dabei wird im besonderen auf folgende Optimierungsprobleme eingegangen: Berechnung des Rohstoffbedarfs bei gegebenen Bestellungen, Aufarbeitung von vorhandenen Lagerbeständen und das Stücklistenproblem.

A natural extension of point facility location problems are those problems in which facilities are extensive, i.e. those that can not be represented by isolated points but as some dimensional structures such as straight lines, segments of lines, polygonal curves or circles. In this paper a review of the existing work on the location of extensive facilities in continuous spaces is given. Gaps in the knowledge are identified and suggestions for further research are made.

Fragestellungen der Standortplanung sollen den Mathematikunterricht der Schule bereichern, dort behandelt und gelöst werden. In dieser Arbeit werden planare Standortprobleme vorgestellt, die im Mathematikunterricht behandelt werden können. Die Probleme Produktion von Halbleiterplatinen, Planung eines Feuerwehrhauses und das Zentrallagerproblem, die ausnahmlos real und nicht konstruiert sind, werden ausführlich durchgearbeitet, so dass es schnell möglich ist, daraus Unterrichtseinheiten zu entwickeln.

Abstract: The basic concepts of selective multiscale reconstruction of functions on the sphere from error-affected data is outlined for scalar functions. The selective reconstruction mechanism is based on the premise that multiscale approximation can be well-represented in terms of only a relatively small number of expansion coefficients at various resolution levels. A new pyramid scheme is presented to efficiently remove the noise at different scales using a priori statistical information.

By means of the limit and jump relations of classical potential theory the framework of a wavelet approach on a regular surface is established. The properties of a multiresolution analysis are verified, and a tree algorithm for fast computation is developed based on numerical integration. As applications of the wavelet approach some numerical examples are presented, including the zoom-in property as well as the detection of high frequency perturbations. At the end we discuss a fast multiscale representation of the solution of (exterior) Dirichlet's or Neumann's boundary-value problem corresponding to regular surfaces.

The purpose of satellite-to-satellite tracking (SST) and/or satellite gravity gradiometry (SGG) is to determine the gravitational field on and outside the Earth's surface from given gradients of the gravitational potential and/or the gravitational field at satellite altitude. In this paper both satellite techniques are analysed and characterized from mathematical point of view. Uniqueness results are formulated. The justification is given for approximating the external gravitational field by finite linear combination of certain gradient fields (for example, gradient fields of single-poles or multi-poles) consistent to a given set of SGG and/or SST data. A strategy of modelling the gravitational field from satellite data within a multiscale concept is described; illustrations based on the EGM96 model are given.

Wannier-Stark states for semiconductor superlattices in strong static fields, where the interband Landau-Zener tunneling cannot be neglected, are rigorously calculated. The lifetime of these metastable states was found to show multiscale oscillations as a function of the static field, which is explained by an interaction with above-barrier resonances. An equation, expressing the absorption spectrum of semiconductor superlattices in terms of the resonance Wannier-Stark states is obtained and used to calculate the absorption spectrum in the region of high static fields.

In this work, we discuss the resonance states of a quantum particle in a periodic potential plus static force. Originally this problem was formulated for a crystalline electron subject to the static electric field and is known nowadays as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and, in this sense, solves the Wannier-Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier-Stark resonances appearing in different physical systems like optical or semiconductor superlattices.

Given a railway network together with information on the population and their use of the railway infrastructure, we are considering the e ffects of introducing new train stops in the existing railway network. One e ffect concerns the accessibility of the railway infrastructure to the population, measured in how far people live from their nearest train stop. The second effect we study is the change in travel time for the railway customers that is induced by new train stops. Based on these two models, we introduce two combinatorial optimization problems and give NP-hardness results for them. We suggest an algorithmic approach for the model based on travel time and give first experimental results.

Abstract: Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fields "doubble Phi", CC and "Phi"C, the conformal fields which are symmetric traceless tensors of rank l and have dimensions "delta" = 2+l or 8+l+ "eta"(l) and "eta"(l) = O(N ^ -2) are identified. The unidentified field have dimension "delta" = "lambda"+l+eta(l) with "lambda" >= 10. The anomalous dimensions eta(l) are calculated at order O(N ^ -2) for both 2 ^ -1/2(-"doubble Phi" + CC) and 2 ^ -1/2(-"Phi"C + C"Phi") and are found to be the same, proving U(1)_Y symmetry. The relevant coupling constants are given at order O(1).

Industrial Ecology's Hidden Philosophy of Nature. Fundamental Underpinning to Use Nature as Model
(2001)

In its scientific sense, industrial ecology represents an emerging transdisciplinary field of studying industrial systems and their fundamental linkage with natural ecosystems. As a short form, industrial ecology is called the "science of sustainability". At the bottom of industrial ecology there is a refreshingly different perspective of understanding nature as model in comparison with other scientific disciplines and concepts of understanding nature e.g. in terms of "sack of resources", "biophysical limit", "something outside", "surrounding", or just "environment" as opposed to industrial systems. The keynote of industrial ecology's specific perspective of understanding nature is to balance the development of industrial systems with the constraints of natural eco-systems, analogous to an "industrial symbiosis". The goal is to contribute for laying a fundamental underpinning for industrial ecology in its scientific sense, in this case especially for its use of nature as model. Therefore an impressive battery of philosophical arguments is provided bringing to bear against the sort of probably raised fallacies and facile or hasty proclaimed critics by sceptics, hard-liners, and mainstream-scientists who often overlook industrial ecology's stimulating role towards sustainability.

In this article, we investigate the maximum entropy moment closure in gas dynamics. We show that the usual choice of polynomial weight functions may lead to hyperbolic systems with an unpleasant state space: equilibrium states are boundary points with possibly singular fluxes. In order to avoid singularities, the necessary arises to find weight functions which growing sub-quadratically at infinity. Unfortunately, this requirement leads to a conflict with Galilean invariance of the moment systems because we can show that rotational and translational invariant, finite dimensional function spaces necessarily consist of polynomials.