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Aufgrund der vernetzten Strukturen und Wirkungszusammenhänge dynamischer Systeme werden die zugrundeliegenden mathematischen Modelle meist sehr komplex und erfordern ein hohes mathematisches Verständnis und Geschick. Bei Verwendung von spezieller Software können jedoch auch ohne tiefgehende mathematische oder informatorische Fachkenntnisse komplexe Wirkungsnetze dynamischer Systeme interaktiv erstellt werden. Als Beispiel wollen wir schrittweise das Modell einer Miniwelt entwerfen und Aussagen bezüglich ihrer Bevölkerungsentwicklung treffen.

Es wird die Aufgabe der vollständigen räumlichen Abdeckung von Regionen in durch mobile Roboter betrachtet. Da-bei können die Regionen in vollständig, teilweise oder nicht bekannten Umgebungen liegen. Zur Lösung wird ein Verfahren aus der Computer-grafik zum Füllen von Bildregionen zugrunde gelegt. Das Verfahren hat eine lokale Sichtweise und läßt somit den Einsatz von Sensordaten und das Auftreten von unvorhergesehenen Hindernissen zu. Die Regionen können durch Karten off-line vorgegeben sein oder durch Sensordaten on-line aufgebaut werden. Dennoch ist eine vollständige und genau einma-lige Flächenbearbeitung garantiert. Dies wird an Beispielen in einer graphischen Visualisierung der Realzeit-Steuerung des Roboters validiert.

Manipulating deformable linear objects - Vision-based recognition of contact state transitions -
(1999)

A new and systematic approach to machine vision-based robot manipulation of deformable (non-rigid) linear objects is introduced. This approach reduces the computational needs by using a simple state-oriented model of the objects. These states describe the relation of the object with respect to an obstacle and are derived from the object image and its features. Therefore, the object is segmented from a standard video frame using a fast segmentation algorithm. Several object features are presented which allow the state recognition of the object while being manipulated by the robot.

Diese Arbeit skizziert einen allgemeinen Ansatz zur Montage deformierbarer linearer Werkstücke (wie Kabel, Drähte, Schläuche, Blattfedern) mit Industrierobotern. Hierzu werden insbesondere die folgenden zwei Aspekte betrachtetet. Erstens die zuverlässige Ausführung der Montage unter Berücksichtigung der Werkstückdeformation und anderer Unsicherheiten, zweitens die numerische Simulation des Werkstückverhaltens. Zur robusten Ausführung der Montage wird das aus der Montage starrer Werkstücke bekannte Konzept der Manipulation-Skills auf deformierbare Werkstücke übertragen. Bei der numerischen Simulation wird insbesondere die Bestimmung der Greifertrajektorie bei gegebener Aufgabenstellung betrachtet.

Anwendungen effizienter Verfahren in Automation - Universität Karlsruhe auf der SPS97 in Nürnberg -
(1998)

Load balancing is one of the central problems that have to be solved in parallel computation. Here, the problem of distributed, dynamic load balancing for massive parallelism is addressed. A new local method, which realizes a physical analogy to equilibrating liquids in multi-dimensional tori or hypercubes, is presented. It is especially suited for communication mechanisms with low set-up to transfer ratio occurring in tightly-coupled or SIMD systems. By successive shifting single load elements to the direct neighbors, the load is automatically transferred to lightly loaded processors. Compared to former methods, the proposed Liquid model has two main advantages. First, the task of load sharing is combined with the task of load balancing, where the former has priority. This property is valuable in many applications and important for highly dynamic load distribution. Second, the Liquid model has high efficiency. Asymptotically, it needs O(D . K . Ldiff ) load transfers to reach the balanced state in a D-dimensional torus with K processors per dimension and a maximum initial load difference of Ldiff . The Liquid model clearly outperforms an earlier load balancing approach, the nearest-neighbor-averaging. Besides a survey of related research, analytical results within a formal framework are derived. These results are validated by worst-case simulations in one-and two-dimensional tori with up to two thousand processors.

We present a parallel path planning method that is able to automatically handle multiple goal configurations as input. There are two basic approaches, goal switching and bi-directional search, which are combined in the end. Goal switching dynamically selects a fa-vourite goal depending on some distance function. The bi-directional search supports the backward search direction from the goal to the start configuration, which is probably faster. The multi-directional search with goal switching combines the advantages of goal switching and bi-directional search. Altogether, the planning system is enabled to select one of the pref-erable goal configuration by itself. All concepts are experimentally validated for a set of benchmark problems consisting of an industrial robot arm with six degrees of freedom in a 3D environment.

Comprehensive reuse and systematic evolution of reuse artifacts as proposed by the Quality Improvement Paradigm (QIP) do not only require tool support for mere storage and retrieval. Rather, an integrated management of (potentially reusable) experience data as well as project-related data is needed. This paper presents an approach exploiting object-relational database technology to implement the QIP-driven reuse repository of the SFB 501. Requirements, concepts, and implementational aspects are discussed and illustrated through a running example, namely the reuse and continuous improvement of SDL patterns for developing distributed systems. Based on this discussion, we argue that object-relational database management systems (ORDBMS) are best suited to implement such a comprehensive reuse repository. It is demonstrated how this technology can be used to support all phases of a reuse process and the accompanying improvement cycle. Although the discussions of this paper are strongly related to the requirements of the SFB 501 experience base, the basic realization concepts, and, thereby, the applicability of ORDBMS, can easily be extended to similar applications, i. e., reuse repositories in general.

A practical distributed planning and control system for industrial robots is presented. The hierarchical concept consists of three independent levels. Each level is modularly implemented and supplies an application interface (API) to the next higher level. At the top level, we propose an automatic motion planner. The motion planner is based on a best-first search algorithm and needs no essential off-line computations. At the middle level, we propose a PC-based robot control architecture, which can easily be adapted to any industrial kinematics and application. Based on a client/server-principle, the control unit estab-lishes an open user interface for including application specific programs. At the bottom level, we propose a flexible and modular concept for the integration of the distributed motion control units based on the CAN bus. The concept allows an on-line adaptation of the control parameters according to the robot's configuration. This implies high accuracy for the path execution and improves the overall system performance.

Die Bewegungsplanung für Industrieroboter ist eine notwendige Voraussetzung, damit sich autonome Systeme kollisionsfrei durch die Umwelt bewegen können. Die Berücksichtigung von dynamischen Hindernissen zur Laufzeit erfordert allerdings leistungsfähige Algorithmen, zur Lösung dieser Aufgabenstellung in Echtzeit. Eine Möglichkeit zur Beschleunigung der Algorithmen ist der effiziente Einsatz von skalierbarer Parallelverarbeitung. Die softwaretechnische Umsetzung kann aber nur dann erfolgreich sein, wenn ein Parallelrechner zur Verfügung steht, der einen hohen Datendurchsatz bei geringer Latenzzeit bietet. Darüber hinaus muß dieser Parallelrechner unter vertretbarem Aufwand bedienbar sein und ein gutes Preisleistungsverhältnis aufweisen, damit die Parallelverarbeitung verstärkt in der Industrie zum Einsatz kommt. In diesem Artikel wird ein Workstation-Cluster auf der Basis von neun Standard- PCs vorgestellt, die über eine spezielle Kommunikationskarte miteinander vernetzt sind. In den einzelnen Abschnitten werden die gesammelten Erfahrungen bei der Inbetriebnahme, Systemadministration und Anwendung geschildert. Als Beispiel für eine Anwendung auf diesem Cluster wird ein paralleler Bewegungsplaner für Industrieroboter beschrieben.

This paper presents a new approach to parallel motion planning for industrial robot arms with six degrees of freedom in an on-line given 3D environment. The method is based on the A*-search algorithm and needs no essential off-line computations. The algorithm works in an implicitly descrete configuration space. Collisions are detected in the cartesian workspace by hierarchical distance computation based on the given CAD model. By decomposing the 6D configuration space into hypercubes and cyclically mapping them onto multiple processing units, a good load distribution can be achieved. We have implemented the parallel motion planner on a workstation cluster with 9 PCs and tested the planner for several benchmark environments. With optimal discretisation, the new approach usually shows linear, and sometimes even superlinear speedups. In on-line provided environments with static obstacles, the parallel planning times are only a few seconds.

The task of handling non-rigid one-dimensional objects by a robot manipulation system is investigated. To distinguish between different non-rigid object behaviors, five classes of deformable objects from a robotic point of view are proposed. Additionally, an enumeration of all possible contact states of one-dimensional objects with polyhedral obstacles is provided. Finally, the qualitative motion behavior of linear objects is analyzed for stable point contacts. Experiments with different materials validate the analytical results.

We present a parallel control architecture for industrial robot cells. It is based on closed functional components arranged in a flat communication hierarchy. The components may be executed by different processing elements, and each component itself may run on multiple processing elements. The system is driven by the instructions of a central cell control component. We set up necessary requirements for industrial robot cells and possible parallelization levels. These are met by the suggested robot control architecture. As an example we present a robot work cell and a component for motion planning, which fits well in this concept.

This paper is based on a path planning approach we reported earlier for industrial robot arms with 6 degrees of freedom in an on-line given 3D environment. It has on-line capabilities by searching in an implicit and descrete configuration space and detecting collisions in the Cartesian workspace by distance computation based on the given CAD model. Here, we present different methods for specifying the C-space discretization. Besides the usual uniform and heuristic discretization, we investigate two versions of an optimal discretization for an user-predefined Cartesian resolution. The different methods are experimentally evaluated. Additionally, we provide a set of 3- dimensional benchmark problems for a fair comparison of path planner. For each benchmark, the run-times of our planner are between only 3 and 100 seconds on a Pentium PC with 133 MHz.

In this paper, the problem of path planning for robot manipulators with six degrees of freedom in an on-line provided three-dimensional environment is investigated. As a basic approach, the best-first algorithm is used to search in the implicit descrete configuration space. Collisions are detected in the Cartesian workspace by hierarchical distance computation based on the given CAD model. The basic approach is extended by three simple mechanisms and results in a heuristic hierarchical search. This is done by adjusting the stepsize of the search to the distance between the robot and the obstacles. As a first step, we show encouraging experimental results with two degrees of freedom for five typical benchmark problems.

This paper presents a new approach to parallel path planning for industrial robot arms with six degrees of freedom in an on-line given 3D environment. The method is based a best-first search algorithm and needs no essential off-line computations. The algorithm works in an implicitly discrete configuration space. Collisions are detected in the Cartesian workspace by hierarchical distance computation based on polyhedral models of the robot and the obstacles. By decomposing the 6D configuration space into hypercubes and cyclically mapping them onto multiple processing units, a good load distribution can be achieved. We have implemented the parallel path planner on a workstation cluster with 9 PCs and tested the planner for several benchmark environments. With optimal discretisation, the new approach usually shows very good speedups. In on-line provided environments with static obstacles, the parallel planning times are only a few seconds.

The paper presents a novel approach to parallel motion planning for robot manipulators in 3D workspaces. The approach is based on a randomized parallel search algorithm and focuses on solving the path planning problem for industrial robot arms working in a reasonably cluttered workspace. The path planning system works in the discretized configuration space which needs not to be represented explicitly. The parallel search is conducted by a number of rule-based sequential search processes, which work to nd a path connecting the initial configuration to the goal via a number of randomly generated subgoal configurations. Since the planning performs only on-line collision tests with proper proximity information without using pre-computed information, the approach is suitable for planning problems with multirobot or dynamic environments. The implementation has been carried out on the parallel virtual machine (PVM) of a cluster of SUN4 workstations and SGI machines. The experimental results have shown that the approach works well for a 6-dof robot arm in a reasonably cluttered environment, and that parallel computation increases the efficiency of motion planning significantly.

This paper presents a new approach to parallel motion planning for industrial robot arms with six degrees of freedom in an on-line given 3D environment. The method is based on the A-search algorithm and needs no essential off-line computations. The algorithm works in an implicitly descrete configuration space. Collisions are detected in the Cartesian workspace by hierarchical distance computation based on the given CAD model. By decomposing the 6D configuration space into hypercubes and cyclically mapping them onto multiple processing units, a good load distribution can be achieved. We have implemented the parallel motion planner on a workstation cluster with 9 PCs and tested the planner for several benchmark environments. With optimal discretisation, the new approach usually shows linear speedups. In on-line provided environments with static obstacles, the parallel planning times are only a few seconds.

This paper discusses the problem of automatic off-line programming and motion planning for industrial robots. At first, a new concept consisting of three steps is proposed. The first step, a new method for on-line motion planning is introduced. The motion planning method is based on the A*-search algorithm and works in the implicit configuration space. During searching, the collisions are detected in the explicitly represented Cartesian workspace by hierarchical distance computation. In the second step, the trajectory planner has to transform the path into a time and energy optimal robot program. The practical application of these two steps strongly depends on the method for robot calibration with high accuracy, thus, mapping the virtual world onto the real world, which is discussed in the third step.

We consider wavelet estimation of the time-dependent (evolutionary) power spectrum of a locally stationary time series. Allowing for departures from stationary proves useful for modelling, e.g., transient phenomena, quasi-oscillating behaviour or spectrum modulation. In our work wavelets are used to provide an adaptive local smoothing of a short-time periodogram in the time-freqeuncy plane. For this, in contrast to classical nonparametric (linear) approaches we use nonlinear thresholding of the empirical wavelet coefficients of the evolutionary spectrum. We show how these techniques allow for both adaptively reconstructing the local structure in the time-frequency plane and for denoising the resulting estimates. To this end a threshold choice is derived which is motivated by minimax properties w.r.t. the integrated mean squared error. Our approach is based on a 2-d orthogonal wavelet transform modified by using a cardinal Lagrange interpolation function on the finest scale. As an example, we apply our procedure to a time-varying spectrum motivated from mobile radio propagation.

We describe a hybrid case-based reasoning system supporting process planning for machining workpieces. It integrates specialized domain dependent reasoners, a feature-based CAD system and domain independent planning. The overall architecture is built on top of CAPlan, a partial-order nonlinear planner. To use episodic problem solving knowledge for both optimizing plan execution costs and minimizing search the case-based control component CAPlan/CbC has been implemented that allows incremental acquisition and reuse of strategical problem solving experience by storing solved problems as cases and reusing them in similar situations. For effective retrieval of cases CAPlan/CbC combines domain-independent and domain-specific retrieval mechanisms that are based on the hierarchical domain model and problem representation.

Structured domains are characterized by the fact that there is an intrinsic dependency between certain key elements in the domain. Considering these dependencies leads to better performance of the planning systems, and it is an important factor for determining the relevance of the cases stored in a case-base. However, testing for cases that meet these dependencies, decreases the performance of case-based planning, as other criterions need also to be consider for determining this relevance. We present a domain-independent architecture that explicitly represents these dependencies so that retrieving relevant cases is ensured without negatively affecting the performance of the case-based planning process.

We derive minimax rates for estimation in anisotropic smoothness classes. This rate is attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis with separate scale parameter for every dimension. It is shown that this basis is superior to its one-scale multiresolution analog, if different degrees of smoothness in different directions are present.; As an important application we introduce a new adaptive wavelet estimator of the time-dependent spectrum of a locally stationary time series. Using this model which was resently developed by Dahlhaus, we show that the resulting estimator attains nearly the rate, which is optimal in Gaussian white noise, simultaneously over a wide range of smoothness classes. Moreover, by our new approach we overcome the difficulty of how to choose the right amount of smoothing, i.e. how to adapt to the appropriate resolution, for reconstructing the local structure of the evolutionary spectrum in the time-frequency plane.

With this article we first like to give a brief review on wavelet thresholding methods in non-Gaussian and non-i.i.d. situations, respectively. Many of these applications are based on Gaussian approximations of the empirical coefficients. For regression and density estimation with independent observations, we establish joint asymptotic normality of the empirical coefficients by means of strong approximations. Then we describe how one can prove asymptotic normality under mixing conditions on the observations by cumulant techniques.; In the second part, we apply these non-linear adaptive shrinking schemes to spectral estimation problems for both a stationary and a non-stationary time series setup. For the latter one, in a model of Dahlhaus on the evolutionary spectrum of a locally stationary time series, we present two different approaches. Moreover, we show that in classes of anisotropic function spaces an appropriately chosen wavelet basis automatically adapts to possibly different degrees of regularity for the different directions. The resulting fully-adaptive spectral estimator attains the rate that is optimal in the idealized Gaussian white noise model up to a logarithmic factor.

This paper is devoted to the mathematica l description of the solution of the so-called rainflow reconstruction problem, i.e. the problem of constructing a time series with an a priori given rainflow m atrix. The algorithm we present is mathematically exact in the sense that no app roximations or heuristics are involved. Furthermore it generates a uniform distr ibution of all possible reconstructions and thus an optimal randomization of the reconstructed series. The algorithm is a genuine on-line scheme. It is easy adj ustable to all variants of rainflow such as sysmmetric and asymmetric versions a nd different residue techniques.

In the automotive industry both the loca l strain approach and rainflow counting are well known and approved tools in the numerical estimation of the lifetime of a new developed part especially in the automotive industry. This paper is devoted to the combination of both tools and a new algorithm is given that takes advantage of the inner structure of the most used damage parameters.

The ideas of texture analysis by means of the structure tensor are combined with the scale-space concept of anisotropic diffusion filtering. In contrast to many other nonlinear diffusion techniques, the proposed one uses a diffusion tensor instead of a scalar diffusivity. This allows true anisotropic behaviour. The preferred diffusion direction is determined according to the phase angle of the structure tensor. The diffusivity in this direction is increasing with the local coherence of the signal. This filter is constructed in such a way that it gives a mathematically well-funded scale-space representation of the original image. Experiments demonstrate its usefulness for the processing of interrupted one-dimensional structures such as fingerprint and fabric images.

A survey on continuous, semidiscrete and discrete well-posedness and scale-space results for a class of nonlinear diffusion filters is presented. This class does not require any monotony assumption (comparison principle) and, thus, allows image restoration as well. The theoretical results include existence, uniqueness, continuous dependence on the initial image, maximum-minimum principles, average grey level invariance, smoothing Lyapunov functionals, and convergence to a constant steady state.

A straightforward formulation of a mathematical problem is mostly not ad-equate for resolution theorem proving. We present a method to optimize suchformulations by exploiting the variability of first-order logic. The optimizingtransformation is described as logic morphisms, whose operationalizations aretactics. The different behaviour of a resolution theorem prover for the sourceand target formulations is demonstrated by several examples. It is shown howtactical and resolution-style theorem proving can be combined.

Deduktionssysteme
(1999)

We show how to buildup mathematical knowledge bases usingframes. We distinguish three differenttypes of knowledge: axioms, definitions(for introducing concepts like "set" or"group") and theorems (for relating theconcepts). The consistency of such know-ledge bases cannot be proved in gen-eral, but we can restrict the possibilit-ies where inconsistencies may be impor-ted to very few cases, namely to the oc-currence of axioms. Definitions and the-orems should not lead to any inconsisten-cies because definitions form conservativeextensions and theorems are proved to beconsequences.

In most cases higher-order logic is based on the (gamma)-calculus in order to avoid the infinite set of so-called comprehension axioms. However, there is a price to be paid, namelyan undecidable unification algorithm. If we do not use the(gamma) - calculus, but translate higher-order expressions intofirst-order expressions by standard translation techniques, we haveto translate the infinite set of comprehension axioms, too. Ofcourse, in general this is not practicable. Therefore such anapproach requires some restrictions such as the choice of thenecessary axioms by a human user or the restriction to certainproblem classes. This paper will show how the infinite class ofcomprehension axioms can be represented by a finite subclass,so that an automatic translation of finite higher-order prob-lems into finite first-order problems is possible. This trans-lation is sound and complete with respect to a Henkin-stylegeneral model semantics.

Extending existing calculi by sorts is astrong means for improving the deductive power offirst-order theorem provers. Since many mathemat-ical facts can be more easily expressed in higher-orderlogic - aside the greater power of higher-order logicin principle - , it is desirable to transfer the advant-ages of sorts in the first-order case to the higher-ordercase. One possible method for automating higher-order logic is the translation of problem formulationsinto first-order logic and the usage of first-order the-orem provers. For a certain class of problems thismethod can compete with proving theorems directlyin higher-order logic as for instance with the TPStheorem prover of Peter Andrews or with the Nuprlproof development environment of Robert Constable.There are translations from unsorted higher-order lo-gic based on Church's simple theory of types intomany-sorted first-order logic, which are sound andcomplete with respect to a Henkin-style general mod-els semantics. In this paper we extend correspond-ing translations to translations of order-sorted higher-order logic into order-sorted first-order logic, thus weare able to utilize corresponding first-order theoremprover for proving higher-order theorems. We do notuse any (lambda)-expressions, therefore we have to add so-called comprehension axioms, which a priori makethe procedure well-suited only for essentially first-order theorems. However, in practical applicationsof mathematics many theorems are essentially first-order and as it seems to be the case, the comprehen-sion axioms can be mastered too.

In this paper we generalize the notion of method for proofplanning. While we adopt the general structure of methods introducedby Alan Bundy, we make an essential advancement in that we strictlyseparate the declarative knowledge from the procedural knowledge. Thischange of paradigm not only leads to representations easier to under-stand, it also enables modeling the important activity of formulatingmeta-methods, that is, operators that adapt the declarative part of exist-ing methods to suit novel situations. Thus this change of representationleads to a considerably strengthened planning mechanism.After presenting our declarative approach towards methods we describethe basic proof planning process with these. Then we define the notion ofmeta-method, provide an overview of practical examples and illustratehow meta-methods can be integrated into the planning process.

Extending the planADbased paradigm for auto-mated theorem proving, we developed in previ-ous work a declarative approach towards rep-resenting methods in a proof planning frame-work to support their mechanical modification.This paper presents a detailed study of a classof particular methods, embodying variations ofa mathematical technique called diagonaliza-tion. The purpose of this paper is mainly two-fold. First we demonstrate that typical math-ematical methods can be represented in ourframework in a natural way. Second we illus-trate our philosophy of proof planning: besidesplanning with a fixed repertoire of methods,metaADmethods create new methods by modify-ing existing ones. With the help of three differ-ent diagonalization problems we present an ex-ample trace protocol of the evolution of meth-ods: an initial method is extracted from a par-ticular successful proof. This initial method isthen reformulated for the subsequent problems,and more general methods can be obtained byabstracting existing methods. Finally we comeup with a fairly abstract method capable ofdealing with all the three problems, since it cap-tures the very key idea of diagonalization.

Most automated theorem provers suffer from the problem thatthey can produce proofs only in formalisms difficult to understand even forexperienced mathematicians. Effort has been made to reconstruct naturaldeduction (ND) proofs from such machine generated proofs. Although thesingle steps in ND proofs are easy to understand, the entire proof is usuallyat a low level of abstraction, containing too many tedious steps. To obtainproofs similar to those found in mathematical textbooks, we propose a newformalism, called ND style proofs at the assertion level , where derivationsare mostly justified by the application of a definition or a theorem. Aftercharacterizing the structure of compound ND proof segments allowing asser-tion level justification, we show that the same derivations can be achieved bydomain-specific inference rules as well. Furthermore, these rules can be rep-resented compactly in a tree structure. Finally, we describe a system calledPROVERB , which substantially shortens ND proofs by abstracting them tothe assertion level and then transforms them into natural language.

Planning Argumentative Texts
(1999)

This paper presents PROVERB a text planner forargumentative texts. PROVERB's main feature isthat it combines global hierarchical planning and un-planned organization of text with respect to local de-rivation relations in a complementary way. The formersplits the task of presenting a particular proof intosubtasks of presenting subproofs. The latter simulateshow the next intermediate conclusion to be presentedis chosen under the guidance of the local focus.

This paper deals with the reference choices involved in thegeneration of argumentative text. A piece of argument-ative text such as the proof of a mathematical theoremconveys a sequence of derivations. For each step of de-rivation, the premises (previously conveyed intermediateresults) and the inference method (such as the applica-tion of a particular theorem or definition) must be madeclear. The appropriateness of these references cruciallyaffects the quality of the text produced.Although not restricted to nominal phrases, our refer-ence decisions are similar to those concerning nominalsubsequent referring expressions: they depend on theavailability of the object referred to within a context andare sensitive to its attentional hierarchy . In this paper,we show how the current context can be appropriatelysegmented into an attentional hierarchy by viewing textgeneration as a combination of planned and unplannedbehavior, and how the discourse theory of Reichmann canbe adapted to handle our special reference problem.

Most automated theorem provers suffer from the problemthat the resulting proofs are difficult to understand even for experiencedmathematicians. An effective communication between the system andits users, however, is crucial for many applications, such as in a mathematical assistant system. Therefore, efforts have been made to transformmachine generated proofs (e.g. resolution proofs) into natural deduction(ND) proofs. The state-of-the-art procedure of proof transformation fol-lows basically its completeness proof: the premises and the conclusionare decomposed into unit literals, then the theorem is derived by mul-tiple levels of proofs by contradiction. Indeterminism is introduced byheuristics that aim at the production of more elegant results. This inde-terministic character entails not only a complex search, but also leads tounpredictable results.In this paper we first study resolution proofs in terms of meaningful op-erations employed by human mathematicians, and thereby establish acorrespondence between resolution proofs and ND proofs at a more ab-stract level. Concretely, we show that if its unit initial clauses are CNFsof literal premises of a problem, a unit resolution corresponds directly toa well-structured ND proof segment that mathematicians intuitively un-derstand as the application of a definition or a theorem. The consequenceis twofold: First it enhances our intuitive understanding of resolutionproofs in terms of the vocabulary with which mathematicians talk aboutproofs. Second, the transformation process is now largely deterministicand therefore efficient. This determinism also guarantees the quality ofresulting proofs.

Even though it is not very often admitted, partial functionsdo play a significant role in many practical applications of deduction sys-tems. Kleene has already given a semantic account of partial functionsusing a three-valued logic decades ago, but there has not been a satisfact-ory mechanization. Recent years have seen a thorough investigation ofthe framework of many-valued truth-functional logics. However, strongKleene logic, where quantification is restricted and therefore not truth-functional, does not fit the framework directly. We solve this problemby applying recent methods from sorted logics. This paper presents atableau calculus that combines the proper treatment of partial functionswith the efficiency of sorted calculi.

The semantics of everyday language and the semanticsof its naive translation into classical first-order language consider-ably differ. An important discrepancy that is addressed in this paperis about the implicit assumption what exists. For instance, in thecase of universal quantification natural language uses restrictions andpresupposes that these restrictions are non-empty, while in classi-cal logic it is only assumed that the whole universe is non-empty.On the other hand, all constants mentioned in classical logic arepresupposed to exist, while it makes no problems to speak about hy-pothetical objects in everyday language. These problems have beendiscussed in philosophical logic and some adequate many-valuedlogics were developed to model these phenomena much better thanclassical first-order logic can do. An adequate calculus, however, hasnot yet been given. Recent years have seen a thorough investigationof the framework of many-valued truth-functional logics. UnfortuADnately, restricted quantifications are not truth-functional, hence theydo not fit the framework directly. We solve this problem by applyingrecent methods from sorted logics.

Typical instances, that is, instances that are representative for a particular situ-ation or concept, play an important role in human knowledge representationand reasoning, in particular in analogical reasoning. This wellADknown obser-vation has been a motivation for investigations in cognitive psychology whichprovide a basis for our characterization of typical instances within conceptstructures and for a new inference rule for justified analogical reasoning withtypical instances. In a nutshell this paper suggests to augment the proposi-tional knowledge representation system by a non-propositional part consistingof concept structures which may have directly represented instances as ele-ments. The traditional reasoning system is extended by a rule for justifiedanalogical inference with typical instances using information extracted fromboth knowledge representation subsystems.

The introduction of sorts to first-order automated deduc-tion has brought greater conciseness of representation and a considerablegain in efficiency by reducing search spaces. This suggests that sort in-formation can be employed in higher-order theorem proving with similarresults. This paper develops a sorted (lambda)-calculus suitable for automatictheorem proving applications. It extends the simply typed (lambda)-calculus by ahigher-order sort concept that includes term declarations and functionalbase sorts. The term declaration mechanism studied here is powerfulenough to subsume subsorting as a derived notion and therefore gives ajustification for the special form of subsort inference. We present a set oftransformations for sorted (pre-) unification and prove the nondetermin-istic completeness of the algorithm induced by these transformations.

Higher-Order Tableaux
(1999)

Even though higher-order calculi for automated theorem prov-ing are rather old, tableau calculi have not been investigated yet. Thispaper presents two free variable tableau calculi for higher-order logicthat use higher-order unification as the key inference procedure. Thesecalculi differ in the treatment of the substitutional properties of equival-ences. The first calculus is equivalent in deductive power to the machine-oriented higher-order refutation calculi known from the literature, whereasthe second is complete with respect to Henkin's general models.

Many mathematical proofs are hard to generate forhumans and even harder for automated theoremprovers. Classical techniques of automated theoremproving involve the application of basic rules, of built-in special procedures, or of tactics. Melis (Melis 1993)introduced a new method for analogical reasoning inautomated theorem proving. In this paper we showhow the derivational analogy replay method is relatedand extended to encompass analogy-driven proof planconstruction. The method is evaluated by showing theproof plan generation of the Pumping Lemma for con-text free languages derived by analogy with the proofplan of the Pumping Lemma for regular languages.This is an impressive evaluation test for the analogicalreasoning method applied to automated theorem prov-ing, as the automated proof of this Pumping Lemmais beyond the capabilities of any of the current auto-mated theorem provers.

This paper addresses the decomposition of proofs as a means of constructingmethods in plan-based automated theorem proving. It shows also, howdecomposition can beneficially be applied in theorem proving by analogy.Decomposition is also useful for human-style proof presentation. We proposeseveral decomposition techniques that were found to be useful in automatedtheorem proving and give examples of their application.

This paper analyzes how mathematicians prove the-orems. The analysis is based upon several empiricalsources such as reports of mathematicians and math-ematical proofs by analogy. In order to combine thestrength of traditional automated theorem provers withhuman-like capabilities, the questions arise: Whichproblem solving strategies are appropriate? Which rep-resentations have to be employed? As a result of ouranalysis, the following reasoning strategies are recog-nized: proof planning with partially instantiated meth-ods, structuring of proofs, the transfer of subproofs andof reformulated subproofs. We discuss the represent-ation of a component of these reasoning strategies, aswell as its properties. We find some mechanisms neededfor theorem proving by analogy, that are not providedby previous approaches to analogy. This leads us to acomputational representation of new components andprocedures for automated theorem proving systems.

As global networks are being used by more and more people,they are becoming increasingly interesting for commercial appli-cations. The recent success and change in direction of the World-Wide Web is a clear indication for this. However, this success meta largely unprepared communications infrastructure. The Inter-net as an originally non-profit network did neither offer the secu-rity, nor the globally available accounting infrastructure byitself.These problems were addressed in the recent past, but in aseemingly ad-hoc manner. Several different accounting schemessensible for only certain types of commercial transactions havebeen developed, which either seem to neglect the problems ofscalability, or trade security for efficiency. Finally, some propos-als aim at achieving near perfect security at the expense of effi-ciency, thus rendering those systems to be of no practical use.In contrast, this paper presents a suitably configurable schemefor accounting in a general, widely distributed client/server envi-ronment. When developing the protocol presented in this paper,special attention has been paid to make this approach work wellin the future setting of high-bandwidth, high-latency internets.The developed protocol has been applied to a large-scale distrib-uted application, a WWW-based software development environ-ment.

In this paper, we compare the BERKOM globally ac-cessible services project (GLASS) with the well-knownWorld-Wide Web with respect to the ease of development,realization, and distribution of multimedia presentations.This comparison is based on the experiences we gainedwhen implementing a gateway between GLASS and theWorld-Wide Web. Since both systems are shown to haveobvious weaknesses, we are concluding this paper with apresentation of a better way to multimedia document en-gineering and distribution. This concept is based on awell-accepted approach to function-shipping in the Inter-net: the Java language, permitting for example a smoothintegration of GLASS92 MHEG objects and WWW HTMLpages within one common environment.

In this paper, a framework for globally distributed soft-ware development and management environments, whichwe call Booster is presented. Additionally, the first experi-ences with WebMake, an application developed to serve asan experimental platform for a software developmentenvironment based on the World Wide Web and theBooster framework is introduced. Booster encompasses thebasic building blocks and mechanisms necessary tosupport a truly cooperative distributed softwaredevelopment from the very beginning to the last steps in asoftware life cycle. It is thus a precursor of the GlobalSoftware Highway, in which providers and users can meetfor the development, management, exchange and usage ofall kind of software.

In order to reduce the elapsed time of a computation, a pop-ular approach is to decompose the program into a collection of largelyindependent subtasks which are executed in parallel. Unfortunately, it isoften observed that tightly-coupled parallel programs run considerablyslower than initially expected. In this paper, a framework for the anal-ysis of parallel programs and their potential speedup is presented. Twoparameters which strongly affect the scalability of parallelism are iden-tified, namely the grain of synchronization, and the degree to which thetarget hardware is available. It is shown that for certain classes of appli-cations speedup is inherently poor, even if the program runs under theidealized conditions of perfect load balance, unbounded communicationbandwidth and negligible communication and parallelization overhead.Upper bounds are derived for the speedup that can be obtained in threedifferent types of computations. An example illustrates the main find-ings.

We present two techniques for reasoning from cases to solve classification tasks: Induction and case-based reasoning. We contrast the two technologies (that are often confused) and show how they complement each other. Based on this, we describe how they are integrated in one single platform for reasoning from cases: The Inreca system.

We present an approach to systematically describing case-based reasoning systems bydifferent kinds of criteria. One main requirement was the practical relevance of these criteria and their usability for real-life applications. We report on the results we achieved from a case study carried out in the INRECA1 Esprit project.

In this paper we describe a framework for defining and operationalizing conceptual models of distributed knowledge-based systems which extends published approaches by the notion of ,agents" and multiple task decompositions. The main part deals with techniques underlying our distributed interpreter. We show how a client-server-architecture can be implemented which allows prototyping distributed knowledge-based systems. Further we describe our mechanism which manages task interactions and supports dependency-directed backtracking efficiently.

In this paper we present an interpreter which allows to support the validation of conceptual models in early stages of the development. We compare hypermedia and expert system approaches to knowledge processing and show how an integrated approach eases the creation of expert systems. Our knowledge engineering tool CoMo-Kit allows a "smooth" transition from initial protocols via a semi-formal specification based on a typed hypertext up to an running expert system. The interpreter uses the intermediate hypertext representation for the interactive solution of problems. Thereby, tasks are distributed to agents via an local area network. This means that the specification of an expert system can directly be used to solve real world problems. If there exist formal (operational) specifications for subtasks then these are delegated to computers. Therefore, our approach allows to specify and validate distributed, cooperative systems where some subtasks are solved by humans and other subtasks are solved automatically by computers.

In diesem Papier vergleichen wir Hypermedia- und Expertensystemansaetze zur Wissensverarbeitung. Wir zeigen, wie ein integrierter Ansatz die Erstellung von Expertensystemen erleichtert. Das von uns entwickelte und implementierte System ermoeglicht einen "sanften" Entwicklungsprozess ausgehend von initialen Protokollen zu einer semi-formale Strukturierung in Form eines getypten Hypertextes. Dem Hypertext ist eine aufgabenorientierte Struktur aufgepraegt, so dass eine anschliessende Operationalisierung in Form eines Expertensystems vereinfacht wird. Die in diesem Prozess erzeugte Zwischenrepraesentation (der Hypertext) wird von einem Interpreter direkt zur interaktiven Loesung von Problemen benutzt, wobei die einzelnen Aufgaben auf die verschiedenen Sachbearbeiter verteilt werden. Abschliessend erlaeutern wir, dass Hypertext und Expertensysteme nur die Raender eines Kontinuums einer allgemeinen Wissensverarbeitung sind.

In diesem Beitrag wird gezeigt, wie mit Hilfe von Knowledge Engineering Techniken eine komplexe Domäne, die Entwicklung von Bebauungsplänen, modelliert werden kann. Dabei wird insbesondere auf notwendige Erweiterungen bekannter Ansätze eingegangen, die sich aus einer praxisbezogenen Entwurfsdomäne ergeben. Der beschriebene Ansatz unterstützt die Koordination mehrerer Agenten durch die Verwaltung von Abhängigkeiten. Das beschriebene Projekt "Intelligenter Bebauungsplan" integriert GIS/CAD, Hypertext und Expertensystemtechnologie. Die Strukturierung der benötigten Informationen als Hypertext wurde von den beteiligten Stadtplanern gewünscht und ist eine natürliche Repräsentation für Gesetzestexte (und Kommentare), da sie ohnehin viele Querverweise enthalten.

In diesem Papier stellen wir einen Interpreter vor, der die Validierung von konzeptuellen Modellen bereits in fruehen Entwicklungsphasen unterstuetzt. Wir vergleichen Hypermedia- und Expertensystemansaetze zur Wissensverarbeitung und erlaeutern, wie ein integrierter Ansatz die Erstellung von Expertensystemen vereinfacht. Das von uns entwickelte Knowledge Engineering Werkzeug ermoeglicht einen "sanften" Uebergang von initialen Protokollen ueber eine semi-formale Spezifikation in Form eines getypten Hypertextes hin zu einem operationalen Expertensystem. Ein Interpreter nutzt die in diesem Prozess erzeugte Zwischenrepraesentation direkt zur interaktiven Loesung von Problemen, wobei einzelne Aufgaben ueber ein lokales Rechnernetz auf die Bearbeiter verteilt werden. Das heisst, die Spezifikation des Expertensystems wird direkt fuer die Loesung realer Probleme eingesetzt. Existieren zu einzelnen Teilaufgaben Operationalisierungen (d.h. Programme), dann werden diese vom Computer bearbeitet.

In diesem Papier beschreiben wir eine Methode zur Spezifikation und Operationalisierung von konzeptuellen Modellen kooperativer wissensbasierter Arbeitsabläufe. Diese erweitert bekannte Ansätze um den Begriff des Agenten und um alternative Aufgabenzerlegungen. Das Papier beschreibt schwerpunktmäßig Techniken, die unserem verteilten Interpreter zugrunde liegen. Dabei gehen wir insbesondere auf Methoden ein, die Abhängigkeiten zwischen Aufgaben behandeln und ein zielgerichtetes Backtracking effizient unterstützen.

Die Lösung einer Konfigurationsaufgabe in technischen Domänen besteht aus einer Menge von Bauteilen, die miteinander verträglich sind und in ihrem Zusammenspiel die gegebenen Anforderung erfüllen. Eine gängige Vorgehensweise bei der Suche nach einer Lösung ist die schrittweise Spezialisierung einer abstrakten Aufgabenstellung oder ihre Zerlegung in Teilaufgaben. Ein Konfigurationssystem, das diese Vorgehensweise unterstützt, muss Wissen enthalten, wie eine Aufgabe spezialisiert oder in Teilaufgaben zerlegt werden kann, welche konkreten Bauteile zur Erfüllung einer ausreichend detaillierten Teilaufgabe verwendet werden können und ob alle Teile einer Lösung miteinander verträglich sind. Aufgrund dieses Wissens kann eine konsistente Lösung durch Tiefensuche hergeleitet werden.

This paper describes how knowledge-based techniques can be used to overcome problems of workflow management in engineering applications. Using explicit process and product models as a basis for a workflow interpreter allows to alternate planning and execution steps, resulting in an increased flexibility of project coordination and enactment. To gain the full advantages of this flexibility, change processes have to be supported by the system. These require an improved traceability of decisions and have to be based on dependency management and change notification mechanisms. Our methods and techniques are illustrated by two applications: Urban land-use planning and software process modeling.

About the approach The approach of TOPO was originally developed in the FABEL project1[1] to support architects in designing buildings with complex installations. Supplementing knowledge-based design tools, which are available only for selected subtasks, TOPO aims to cover the whole design process. To that aim, it relies almost exclusively on archived plans. Input to TOPO is a partial plan, and output is an elaborated plan. The input plan constitutes the query case and the archived plans form the case base with the source cases. A plan is a set of design objects. Each design object is defined by some semantic attributes and by its bounding box in a 3-dimensional coordinate system. TOPO supports the elaboration of plans by adding design objects.

INRECA offers tools and methods for developing, validating, and maintaining classification, diagnosis and decision support systems. INRECA's basic technologies are inductive and case-based reasoning [9]. INRECA fully integrates [2] both techniques within one environment and uses the respective advantages of both technologies. Its object-oriented representation language CASUEL [10, 3] allows the definition of complex case structures, relations, similarity measures, as well as background knowledge to be used for adaptation. The objectoriented representation language makes INRECA a domain independent tool for its destined kind of tasks. When problems are solved via case-based reasoning, the primary kind of knowledge that is used during problem solving is the very specific knowledge contained in the cases. However, in many situations this specific knowledge by itself is not sufficient or appropriate to cope with all requirements of an application. Very often, background knowledge is available and/or necessary to better explore and interpret the available cases [1]. Such general knowledge may state dependencies between certain case features and can be used to infer additional, previously unknown features from the known ones.

Let \(X\) be a Banach lattice. Necessary and sufficient conditions for a linear operator \(A:D(A) \to X\), \(D(A)\subseteq X\), to be of positive \(C^0\)-scalar type are given. In addition, the question is discussed which conditions on the Banach lattice imply that every operator of positive \(C^0\)-scalar type is necessarily of positive scalar type.

Hyperbolic planes
(1995)

We prove that there exists a positive \(\alpha\) such thatfor any integer \(\mbox{$d\ge 3$}\) and any topological types \(\mbox{$S_1,\dots,S_n$}\) of plane curve singularities, satisfying \(\mbox{$\mu(S_1)+\dots+\mu(S_n)\le\alpha d^2$}\), there exists a reduced irreducible plane curve of degree \(d\) with exactly \(n\) singular points of types \(\mbox{$S_1,\dots,S_n$}\), respectively. This estimate is optimal with respect to theexponent of \(d\). In particular, we prove that for any topological type \(S\) there exists an irreducible polynomial of degree \(\mbox{$d\le 14\sqrt{\mu(S)}$}\) having a singular point of type \(S\).

In the scalar case one knows that a complex normalized function of boundedvariation \(\phi\) on \([0,1]\) defines a unique complex regular Borel measure\(\mu\) on \([0,1]\). In this note we show that this is no longer true in generalin the vector valued case, even if \(\phi\) is assumed to be continuous. Moreover, the functions \(\phi\) which determine a countably additive vectormeasure \(\mu\) are characterized.

The Filter-Diagonalization Method is used to ,nd the broad and even overlapping resonances of a 1D Hamiltonian used before as a test model for new resonance theories and computational methods. It is found that the use of several complex-scaled cross-correlation probability amplitudes from short time propagation enables the calculation of broad overlapping resonances, which can not be resolved from the amplitude of a single complex-scaled autocorrelation calculation.

A formalism is developed for calculating the quasienergy states and spectrum for time-periodic quantum systems when a time-periodic dynamical invariant operator with a nondegenerate spectrum is known. The method, which circumvents the integration of the Schr-odinger equation, is applied to an integrable class of systems, where the global invariant operator is constructed. Furthermore, a local integrable approximation for more general non-integrable systems is developed. Numerical results are presented for the doubleresonance model.

We consider N coupled linear oscillators with time-dependent coecients. An exact complex amplitude - real phase decomposition of the oscillatory motion is constructed. This decomposition is further used to derive N exact constants of motion which generalise the so-called Ermakov-Lewis invariant of a single oscillator. In the Floquet problem of periodic oscillator coecients we discuss the existence of periodic complex amplitude functions in terms of existing Floquet solutions.

Quantum Chaos
(1999)

The study of dynamical quantum systems, which are classically chaotic, and the search for quantum manifestations of classical chaos, require large scale numerical computations. Special numerical techniques developed and applied in such studies are discussed: The numerical solution of the time-dependent Schr-odinger equation, the construction of quantum phase space densities, quantum dynamics in phase space, the use of phase space entropies for characterizing localization phenomena, etc. As an illustration, the dynamics of a driven one-dimensional anharmonic oscillator is studied, both classically and quantum mechanically. In addition, spectral properties and chaotic tunneling are addressed.

Mn-Si-C alloy films are prepared by e-beam coevaporation onto a Si substrate held at 600 °C. Ferromagnetism is observed below T = (360 +/- 5) K with SQUID magnetometry and magneto-optical Kerr effect. This is the highest Curie temperature T yet observed for a Mn-based alloy. Although the composition determined by Auger depth profiling varies appreciably for different films, their T is the same indicating that ferromagnetism is caused by an alloy of well-defined composition independent of precipitations.

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 static and spin wave properties of regular square lattices of magnetic dots of 0.5-2 microm dot diameter and 1-4 microm periodicity patterned in permalloy films have been investigated by Brillouin light scattering. The samples have been structured using x-ray lithography and ion beam etching. The Brillouin light scattering spectra reveal both surface and bulk spin wave modes. The spin wave frequencies can be well described taking into account the demagnetization factor of each single dot. For the samples with smallest dot separation of 0.1 microm a fourfold in-plane magnetic anisotropy with the easy axis directed along the pattern diagonal is observed, indicating anisotropic coupling between the dots.

A computer control for a Sandercock-type multipath tandem Fabry-Perot interferometer is described, which offers many advantages over conventionally used analog control: The range of stability is increased due to active control of the laser light intensity and the mirror dither amplitude. The alignment is fully automated enabling start of a measurement within a minute after start of align, including optionally finding the optimum focus on the sample. The software control enables a programmable series of measurements with control of, e.g., the position and rotation of the sample, the angle of light incidence, the sample temperature, or the strength and direction of an applied magnetic field. Built-in fitting routines allow for a precise determination of frequency positions of excitation peaks combined with increased frequency accuracy due to a correction of a residual nonlinearity of the mirror stage drive.

Wall energy and wall thickness of exchange-coupled rare-earth transition-metal triple layer stacks
(1999)

The room-temperature wall energy sw 54.0310 23 J/m 2 of an exchange-coupled Tb 19.6 Fe 74.7 Co 5.7 /Dy 28.5 Fe 43.2 Co 28.3 double layer stack can be reduced by introducing a soft magnetic intermediate layer in between both layers exhibiting a significantly smaller anisotropy compared to Tb+- FeCo and Dy+- FeCo. sw will decrease linearly with increasing intermediate layer thickness, d IL , until the wall is completely located within the intermediate layer for d IL d w , where d w denotes the wall thickness. Thus, d w can be obtained from the plot sw versus d IL .We determined sw and d w on Gd+- FeCo intermediate layers with different anisotropy behavior ~perpendicular and in-plane easy axis! and compared the results with data obtained from Brillouin light-scattering measurements, where exchange stiffness, A, and uniaxial anisotropy, K u , could be determined. With the knowledge of A and K u , wall energy and thickness were calculated and showed an excellent agreement with the magnetic measurements. A ten times smaller perpendicular anisotropy of Gd 28.1 Fe 71.9 in comparison to Tb+- FeCo and Dy+- FeCo resulted in a much smaller sw 51.1310 23 J/m 2 and d w 524 nm at 300 K. A Gd 34.1 Fe 61.4 Co 4.5 with in-plane anisotropy at room temperature showed a further reduced sw 50.3310 23 J/m 2 and d w 517 nm. The smaller wall energy was a result of a different wall structure compared to perpendicular layers.

This paper presents the different possibilities for parallel processing in robot control architectures. At the beginning, we shortly review the historic development of control architectures. Then, a list of requirements for control architectures is set up from a parallel processing point of view. As our main topic, we identify the levels of parallel processing in robot control architectures. With each level of parallelism, examples for a typical robot control architecture are presented. Finally, a list of keywords is provided for each previous work we refer to.

Struktur und Werkzeuge des experiment-spezifischen Datenbereichs der SFB501 Erfahrungsdatenbank
(1999)

Software-Entwicklungsartefakte müssen zielgerichtet während der Durchführung eines Software- Projekts erfasst werden, um für die Wiederverwendung aufbereitet werden zu können. Die methodische Basis hierzu bildet im Sonderforschungsbereich 501 das Konzept der Erfahrungsdatenbank. In ihrem experiment-spezifischen Datenbereich werden für jedes Entwicklungsprojekt alle Software-Entwicklungsartefakte abgelegt, die während des Lebenszyklus eines Projektes anfallen. In ihrem übergreifenden Datenbereich werden all die jenigen Artefakte aus dem experiment-spezifischen Datenbereich zusammengefasst, die für eine Wiederverwendung in nachfolgenden Projekten in Frage kommen. Es hat sich gezeigt, dass bereits zur Nutzung der Datenmengen im experiment- spezifischen Datenbereich der Erfahrungsdatenbank ein systematischer Zugriff notwendig ist. Ein systematischer Zugriff setzt jedoch eine normierte Struktur voraus. Im experiment-spezifischen Bereich werden zwei Arten von Experimenttypen unterschieden: "Kontrollierte Experimente" und "Fallstudien". Dieser Bericht beschreibt die Ablage- und Zugriffsstruktur für den Experimenttyp "Fallstudien". Die Struktur wurde aufgrund der Erfahrungen in ersten Fallstudien entwickelt und evaluiert.

The following two norms for holomorphic functions \(F\), defined on the right complex half-plane \(\{z \in C:\Re(z)\gt 0\}\) with values in a Banach space \(X\), are equivalent:
\[\begin{eqnarray*} \lVert F \rVert _{H_p(C_+)} &=& \sup_{a\gt0}\left( \int_{-\infty}^\infty \lVert F(a+ib) \rVert ^p \ db \right)^{1/p}
\mbox{, and} \\ \lVert F \rVert_{H_p(\Sigma_{\pi/2})} &=& \sup_{\lvert \theta \lvert \lt \pi/2}\left( \int_0^\infty \left \lVert F(re^{i \theta}) \right \rVert ^p\ dr \right)^{1/p}.\end{eqnarray*}\] As a consequence, we derive a description of boundary values ofsectorial holomorphic functions, and a theorem of Paley-Wiener typefor sectorial holomorphic functions.

In this paper we are interested in using a firstorder theorem prover to prove theorems thatare formulated in some higher order logic. Tothis end we present translations of higher or-der logics into first order logic with flat sortsand equality and give a sufficient criterion forthe soundness of these translations. In addi-tion translations are introduced that are soundand complete with respect to L. Henkin's gen-eral model semantics. Our higher order logicsare based on a restricted type structure in thesense of A. Church, they have typed functionsymbols and predicate symbols, but no sorts.