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Retrieving multiple cases is supposed to be an adequate retrieval strategy for guiding partial-order planners because of the recognized flexibility of these planners to interleave steps in the plans. Cases are combined by merging them. In this paper, we will examine two different kinds of merging cases in the context of partial-order planning. We will see that merging cases can be very difficult if the cases are merged eagerly. On the other hand, if cases are merged by avoiding redundant steps, the guidance of the additional cases tends to decrease with the number of covered goals and retrieved cases in domains having a certain kind of interactions. Thus, to retrieve a single case covering many of the goals of the problem or to retrieve fewer cases covering many of the goals is at least equally effective as to retrieve several cases covering all goals in these domains.

It is of basic interest to assess the quality of the decisions of a statistician, based on the outcoming data of a statistical experiment, in the context of a given model class P of probability distributions. The statistician picks a particular distribution P , suffering a loss by not picking the 'true' distribution P' . There are several relevant loss functions, one being based on the the relative entropy function or Kullback Leibler information distance. In this paper we prove a general 'minimax risk equals maximin (Bayes) risk' theorem for the Kullback Leibler loss under the hypothesis of a dominated and compact family of distributions over a Polish observation space with suitably integrable densities. We also find that there is always an optimal Bayes strategy (i.e. a suitable prior) achieving the minimax value. Further, we see that every such minimax optimal strategy leads to the same distribution P in the convex closure of the model class. Finally, we give some examples to illustrate the results and to indicate, how the minimax result reflects in the structure of least favorable priors. This paper is mainly based on parts of this author's doctorial thesis.

The Multiple Objective Median Problem involves locating a new facility so that a vector of performance criteria is optimized over a given set of existing facilities. A variation of this problem is obtained if the existing facilities are situated on two sides of a linear barrier. Such barriers like rivers, highways, borders, or mountain ranges are frequently encountered in practice. In this paper, theory of the Multiple Objective Median Problem with line barriers is developped. As this problem is nonconvex but specially-structured, a reduction to a series of convex optimization problems is proposed. The general results lead to a polynomial algorithm for finding the set of efficient solutions. The algorithm is proposed for bi-criteria problems with different measures of distance.

An asymptotic-induced scheme for kinetic semiconductor equations with the diffusion scaling is developed. The scheme is based on the asymptotic analysis of the kinetic semiconductor equation. It works uniformly for all ranges of mean free paths. The velocity discretization is done using quadrature points equivalent to a moment expansion method. Numerical results for different physical situations are presented.

Due to continuously increasing demands in the area of advanced robot control, it became necessary to speed up the computation. One way to reduce the computation time is to distribute the computation onto several processing units. In this survey we present different approaches to parallel computation of robot kinematics and Jacobian. Thereby, we discuss both the forward and the reverse problem. We introduce a classification scheme and classify the references by this scheme.

We develop a test for stationarity of a time series against the alternative of a time-changing covariance structure. Using localized versions of the periodogram, we obtain empirical versions of a reasonable notion of a time-varying spectral density. Coefficients w.r.t. a Haar wavelet series expansion of such a time-varying periodogram are a possible indicator whether there is some deviation from covariance stationarity. We propose a test based on the limit distribution of these empirical coefficients.

This paper shows an approach to profit from type information about planning objects in a partial-order planner. The approach turns out to combine representational and computational advantages. On the one hand, type hierarchies allow better structuring of domain specifications. On the other hand, operators contain type constraints which reduce the search space of the planner as they partially achieve the functionality of filter conditions.

This paper is a continuation of a joint paper with B. Martin [MS] dealing with the problem of direct sum decompositions. The techniques of that paper areused to decide wether two modules are isomorphic or not. An positive answer to this question has many applications - for example for the classification ofmaximal Cohen-Macaulay module over local algebras as well as for the study of projective modules. Up to now computer algebra is normally dealing withequality of ideals or modules which depends on chosen embeddings. The present algorithm allows to switch to isomorphism classes which is more natural inthe sense of commutative algebra and algebraic geometry.

An asymptotic-induced scheme for nonstationary transport equations with thediffusion scaling is developed. The scheme works uniformly for all ranges ofmean free paths. It is based on the asymptotic analysis of the diffusion limit ofthe transport equation. A theoretical investigation of the behaviour of thescheme in the diffusion limit is given and an approximation property is proven.Moreover, numerical results for different physical situations are shown and atheuniform convergence of the scheme is established numerically.

This paper describes an Internet-scalable knowledge base infrastructure for managing the knowledge used by an in-telligent software productivity infrastructure system. The infrastructure provides workable solutions for several significant issues: (1) Internetunique names for pieces of knowledge; (2) multi-platform, multi-language support; (3) distributed knowledge base synchronization mechanisms; (4) support for extensive customized variations in knowledge content, and (5) knowledge caching mechanisms for improved system performance. The infrastructure described here is a workable example of the kind of infrastructure that will be required to manage the evolution and reuse of millions of pieces of knowledge in the future.

An unusual interlayer coupling, recently discovered in layered magnetic systems, is analysed from the experimental and theoretical points of view. This coupling favours the 90 orientation of the magnetization of the adjacent magnetic films. It can be phenomenologically described by a term in the energy expression, which is biquadratic with respect to the magnetizations of the two films. The main experimental findings, as well as the theoretical models, explaining the phenomenon are discussed.

The tunneling splitting of the energy levels of a ferromagnetic particle in the presence of an applied magnetic field - previously derived only for the ground state with the path integral method - is obtained in a simple way from Schr"odinger theory. The origin of the factors entering the result is clearly understood, in particular the effect of the asymmetry of the barriers of the potential. The method should appeal particularly to experimentalists searching for evidence of macroscopic spin tunneling.

An analogue of the classical Riemann-Siegel integral formula for Dirichlet series associated to cusp forms is developed. As an application of the formula, we give a comparatively simple proof of the approximate functional equation for this type of Dirichlet series.

A formula suitable for a quantitative evaluation of the tunneling effect in a ferromagnetic particle is derived with the help of the instanton method. The tunneling between n-th degenerate states of neighboring wells is dominated by a periodic pseudoparticle configuration. The low-lying level-splitting previously obtained with the LSZ method in field theory in which the tunneling is viewed as the transition of n bosons induced by the usual(vacuum) instanton is recovered.The observation made with our new result is that the tunneling effect increases at excited states. The results should be useful in analyzing results of experimental tests of macroscopic quantum coherence in ferromagnetic particles.

We present a general framework for developing search heuristics for au-tomated theorem provers. This framework allows for the construction ofheuristics that are on the one hand able to replay (parts of) a given prooffound in the past but are on the other hand flexible enough to deviate fromthe given proof path in order to solve similar proof problems. We substanti-ate the abstract framework by the presentation of three distinct techniquesfor learning appropriate search heuristics based on soADcalled features. Wedemonstrate the usefulness of these techniques in the area of equational de-duction. Comparisons with the renowned theorem prover Otter validatethe applicability and strength of our approach.