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#### Erscheinungsjahr

- 1997 (66) (entfernen)

#### Dokumenttyp

- Preprint (66) (entfernen)

#### Schlagworte

- AG-RESY (1)
- Brownian motion (1)
- CAx-Anwendungen (1)
- CoMo-Kit (1)
- Dense gas (1)
- Elliptic-parabolic equation (1)
- Enskog equation (1)
- Function of bounded variation (1)
- Integral transform (1)
- Intelligent Object Fusion (1)

#### Fachbereich / Organisatorische Einheit

We report on the observation of quantized surface spin waves in periodic arrays of magnetic Ni81Fe19 wires by means of Brillouin light scattering spectroscopy. At small wavevectors (q_1 = 0 - 0.9*100000 cm^-1 ) several discrete, dispersionless modes with a frequency splitting of up to 0.9 GHz were observed for the wavevector oriented perpendicular to the wires. From the frequencies of the modes and the wavevector interval, where each mode is observed, the modes are identified as dipole-exchange surface spin wave modes of the film with quantized wavevector values determined by the boundary conditions at the lateral edges of the wires. With increasing wavevector the separation of the modes becomes smaller, and the frequencies of the discrete modes converge to the dispersion of the dipole-exchange surface mode of a continuous film.

The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite dimensional superspaces, and construct superanalogs of the classical function spaces with a reproducing kernel - including the Bargmann-Fock representation - and of the Wiener-Segal representation. The latter representation requires the investigation of Wick ordering on Z 2 -graded algebras. As application we derive a Mehler formula for the Ornstein-Uhlenbeck semigroup on the Fock space.

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.

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.

In this paper a group of participants of the 12th European Summer Institute which took place in Tenerifa, Spain in June 1995 present their views on the state of the art and the future trends in Locational Analysis. The issue discussed includes modelling aspects in discrete, network and continuous location, heuristic techniques, the state of technology and undesirable facility location. Some general questions are stated reagrding the applicability of location models, promising research directions and the way technology affects the development of solution techniques.

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.

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.

In this paper we provide a semantical meta-theory that will support the development of higher-order calculi for automated theorem proving like the corresponding methodology has in first-order logic. To reach this goal, we establish classes of models that adequately characterize the existing theorem-proving calculi, that is, so that they are sound and complete to these calculi, and a standard methodology of abstract consistency methods (by providing the necessary model existence theorems) needed to analyze completeness of machine-oriented calculi.

MP Prototype Specification
(1997)

A first explicit connection between finitely presented commutative monoids and ideals in polynomial rings was used 1958 by Emelichev yielding a solution tothe word problem in commutative monoids by deciding the ideal membership problem. The aim of this paper is to show in a similar fashion how congruenceson monoids and groups can be characterized by ideals in respective monoid and group rings. These characterizations enable to transfer well known resultsfrom the theory of string rewriting systems for presenting monoids and groups to the algebraic setting of subalgebras and ideals in monoid respectively grouprings. Moreover, natural one-sided congruences defined by subgroups of a group are connected to one-sided ideals in the respective group ring and hencethe subgroup problem and the ideal membership problem are directly related. For several classes of finitely presented groups we show explicitly howGröbner basis methods are related to existing solutions of the subgroup problem by rewriting methods. For the case of general monoids and submonoidsweaker results are presented. In fact it becomes clear that string rewriting methods for monoids and groups can be lifted in a natural fashion to definereduction relations in monoid and group rings.

The concept of algebraic simplification is of great importance for the field of symbolic computation in computer algebra. In this paper we review somefundamental concepts concerning reduction rings in the spirit of Buchberger. The most important properties of reduction rings are presented. Thetechniques for presenting monoids or groups by string rewriting systems are used to define several types of reduction in monoid and group rings. Gröbnerbases in this setting arise naturally as generalizations of the corresponding known notions in the commutative and some non-commutative cases. Severalresults on the connection of the word problem and the congruence problem are proven. The concepts of saturation and completion are introduced formonoid rings having a finite convergent presentation by a semi-Thue system. For certain presentations, including free groups and context-free groups, theexistence of finite Gröbner bases for finitely generated right ideals is shown and a procedure to compute them is given.

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.

In dieser Arbeit wird die Problematik der sich rapide wandelnden industriellen CAx-Anwendungen betrachtet. Durch die Einfu"hrung der Feature-Technologie scheinen einige Probleme der Parallelisierung der Prozesse, des Simultaneous und des Concurrent Engineering sowie des Outsourcing überwindbar zu sein. Allerdings entwickelte sich die Feature-Technologie bisher ohne ausreichenden Bezug zur Konstruktionspraxis, was zu erheblichen Defiziten im industriellen Einsatz führte. Untersuchungen in der Automobilindustrie (AIFEMInitiative) zeigen, dass dies vielfach auf mangelnde Kommunikation zwischen Konstrukteuren und CAx-Experten zurückgeführt werden kann. Aufgrund des jetzigen Ansatzes der Feature-Technologie im Zusammenwirken mit dem extremen Zeitdruck in der Produktentwicklung besteht aber die Gefahr, die Produktdefinitionsprozesse nur nach den Kriterien Entwicklungszeit, Kosten und Produktqualität zu optimieren. Features dienen dabei nur als speziell angepasste Werkzeuge. Damit wird eine echte Innovation der Produkte behindert. Es wird aufgezeigt, wie die Feature-Technologie erweitert werden muss, um die Kreativität der Konstrukteure zu fördern und somit neuartige Produkte zu ermöglichen. Näher ausgeführt werden die Aspekte der benutzerdefinierten Features, der Datenstandardisierung, der Verarbeitung unvollsta"ndiger Information und der dynamischen Prozessunterstützung.

Ist "Programmieren ganz ohne Code" auch im CAx-Bereich möglich? Die Vielzahl heterogener CAx-Anwendungen und die wachsende Komplexität der Entwicklungsprozesse bedarf neuer Lösun-gen in der CAx-Technik. Ziel dieses Beitrages ist es, die richtungsweisende Rolle der Komponenten-technologie im CAx-Bereich aufzuzeigen. Es werden die Grundlagen der Komponenten sowie die wichtigen Komponentenarchitekturen (ActiveX und Java Beans) vorgestellt. Die Erwartungen der Anwender und der Systemhersteller, die Potentiale und die Auswirkungen dieser Technologie auf die neuen Systeme werden analysiert. Die zur Zeit verfügbaren ersten Ansätze werden präsentiert. Die Rolle der internationalen Standards für die technische Umsetzung und für die Akzeptanz von CAx-Komponentensystemen wird aufgezeigt.

Process Chain in Automotive Industry - Present Day Demands versus Long Term Open CAD/CAM Strategies
(1997)

The automotive industry was a pioneer in using CAD/CAM technology. Now the car manufacturers development process is almost completely done with this technology. Substantial initiative for the standardisation of CAD/CAM technics comes from the automotive industry, as e.g. for neutral CAD data interfaces. The R&D departments of German car manufacturers have founded a working group ii with the aim to develop a common long term CAD/CAM strategy. One important result is the concept of a future CAx iii architecture based on the standard data structure STEP iv . The commitment of the car manufactures to STEP and open system architectures is in contradiction to their attitude towards suppliers and subcontractors: Recently, more and more contractors are contractually bound to use exactly the same CAD system as the orderer. The German car industry tries to find a way out of this contradiction and to improve the co-operation between the companies in short term. Therefore they proposed a "Dual CAD Strategy", i.e. to put improvements in CAD communication into practice which are possible today - even proprietary solutions - and in parallel to invest in strategic concepts to prepare tomorrow's open system landscape.

In the modeling of biological phenomena, in living organisms whether the measurements are of blood pressure, enzyme levels, biomechanical movements or heartbeats, etc., one of the important aspects is time variation in the data. Thus, the recovery of a "smooth" regression or trend function from noisy time-varying sampled data becomes a problem of particular interest. Here we use non-linear wavelet thresholding to estimate a regression or a trend function in the presence of additive noise which, in contrast to most existing models, does not need to be stationary. (Here, nonstationarity means that the spectral behaviour of the noise is allowed to change slowly over time.). We develop a procedure to adapt existing threshold rules to such situations, e.g., that of a time-varying variance in the errors. Moreover, in the model of curve estimation for functions belonging to a Besov class with locally stationary errors, we derive a near-optimal rate for the L2-risk between the unknown function and our soft or hard threshold estimator, which holds in the general case of an error distribution with bounded cumulants. In the case of Gaussian errors, a lower bound on the asymptotic minimax rate in the wavelet coefficient domain is also obtained. Also it is argued that a stronger adaptivity result is possible by the use of a particular location and level dependent threshold obtained by minimizing Stein's unbiased estimate of the risk. In this respect, our work generalizes previous results, which cover the situation of correlated, but stationary errors. A natural application of our approach is the estimation of the trend function of nonstationary time series under the model of local stationarity. The method is illustrated on both an interesting simulated example and a biostatistical data-set, measurements of sheep luteinizing hormone, which exhibits a clear nonstationarity in its variance.

Starting from the mollified version of the Enskog equation for a hard-sphere fluid, a grid-free algorithm to obtain the solution is proposed. The algorithm is based on the finite pointset method. For illustration, it is applied to a Riemann problem. The shock-wave solution is compared to the results of Frezzotti and Sgarra where a good agreement is found.