Konvergenz von quadratischen Interpolations- und Flächenabgleichssplines

The purpose of this paper is to show that for continuous functions the related quadratic splines converge without any assumption on the spline grid. The points of the interpolatory grid can be chosen between the corresponding points of the spline grid with a division ratio from \(\frac{{\sqrt 2 }}{2}\) to \(1 - \frac{{\sqrt 2 }}{2}\) . In the case of continuously differentiable functions the division ratio can even be taken between 0 and 1; in addition, the order of convergence is increased. For twice differentiable functions the full order of convergence is obtained. Analogous results about the convergence of histo splines are proved.     

Computing turning points of curves implicitly defined by nonlinear equations depending on a parameter

Let the space curveL be defined implicitly by the (n, n+1) nonlinear systemH(u)=0. A new direct Newton-like method for computing turning points ofL is described that requires per step only the evaluation of one Jacobian and 5 function values ofH. Moreover, a linear system of dimensionn+1 with 4 different right hand sides has to be solved per step. Under suitable conditions the method is shown to converge locally withQ-order two if a certain discretization stepsize is appropriately chosen. Two numerical examples confirm the theoretical results.     

On a lower bound theorem for the buckling load of elastic beams subjected to nonconservative,compressive follower loads

Summary For beams loaded withuniformly distributed follower forces, there exists a lower bound theorem, which allows to evaluate the actual buckling load approximately by means of the buckling load of the same beam loaded correspondingly with conservative unidirectional forces of the same magnitude. In this paper it is shown that the theorem remains valid for monotonically decreasing or at least not increasing follower forces. Moreover, a modified lower bound theorem can be formulated for follower loads which monotonically increase over a part or even over the whole length of the beam. In that case, a lower bound curve has to be constructed using the eigenvalue curve of the conservatively loaded beam. The intersection of the lower bound curve with the vertical axis yields a lower bound for the buckling load of the nonconservatively loaded beam.

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Zu einem Satz über die untere Schranke der Knicklast elastischer, durch Folgekräfte belasteter Stäbe

Zusammenfassung Ein für Stäbe untergleichförmig verteilten Folgekräften gültiger Satz für die untere Schranke der Knicklast gestattet die näherungsweise Ermittlung der tatsächlichen Knicklast aus der desselben Stabes unter richtungstreuer Belastung derselben Größe. In dieser Arbeit wird gezeigt, daß dieser Satz auch für monoton abnehmende oder zumindest nicht zunehmende Folgekräfte gilt. Weiters kann ein modifizierter Satz für über einen Teil des Stabes oder die ganze Stablänge monoton zunehemende Folgekräfte formuliert werden. In diesem Fall muß unter Verwendung der Eigenwertkurve des konservativ belasteten Stabes eine untere Grenzkurve ermittelt werden. Der Schnittpunkt dieser Kurve mit der vertikalen Achse ergibt eine untere Schranke der Knicklast des nichtkonservativ belasteten Stabes.

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With 8 Fugures     

Estimating errors of numerical approximation for periodic analytic functions

We give a simple method based on Cauchy's integral formula for estimating the errors of numerical approximation for periodic analytic functions. We then obtain error estimates for the quadrature formulas of Chawla and Ramakrishnan [1] for the numerical evaluation of the Cauchy principal value integral $$I\left( {f;a} \right) = \int\limits_0^{2\pi } {f(x)\cot \left( {\left( {x - a} \right)/2} \right)dx,} $$ and for the quadrature formula of Garrick [2] for the evaluation ofI (f;o), Based on these error estimates, we are led to conclude that for the evaluation ofI (f;o), Garrick's formula has a better error estimate than the formula of Chawla and Ramakrishnan with the same number of function evaluations. Finally, we extend Garrick's formula for the evaluation ofI (f;a) for arbitrarya∈[0,2π); the extended formula has, for alla, the same error estimate as Garrick's formula. While, for a=x_j, the extended formula is identical with the quadrature formula of Wittich [3], fora≠x _j, the extended formula is much better in that it uses only half the number of function evaluations of Wittich's formula for the same accuracy.     

Approximation der optimalen Vorhersage der Ausgabe stochastischer Quellen

This paper discusses the prediction of the output of a stochastic sourceQ having positive transition function. If the sourceQ has two output alphabets,X andY, then there exists such a stochastic automaton \(\mathfrak{A}(V_{opt} )\) with input alphabetX, output alphabetY, and a countable set of states, that realizes the optimal predictionV _opt fromX toY. Here it will be shown thatV _opt can be approximated with any precision by a predictionV which is realized by a stochastic automaton with finite set of states.     

Discovering invariants via simple component analysis

We propose a new technique combining dynamic and static analysis of programs to find linear invariants. We use a statistical tool, called simple component analysis, to analyze partial execution traces of a given program. We get a new coordinate system in the vector space of program variables, which is used to specialize numerical abstract domains. As an application, we instantiate our technique to interval analysis of simple imperative programs and show some experimental evaluations.     

Situative Managementunterstützungssysteme

Digital natives increasingly populate organizations?? management. These new-generation managers more naturally accept management support systems (MSS), but also have higher expectations about how they should accommodate their individual user preferences. As a result, managers question MSS that have been developed without configuration mechanisms to accommodate their working style, relevant MSS use cases, and different MSS access modes. The objective of this article is to reveal managers?? different MSS use situations and propose levers for tailoring (conceptual) MSS design to them. Use situations generalize classes of similar user-group preferences. We first apply findings from a literature review to cluster managers?? user-group preferences into 36 MSS use situations. Second, we propose that the selection of end-user devices can serve as a main lever for MSS configuration. Third, we complete the configuration with a MSS user-interface design. Finally, we demonstrate utility of our configuration model by presenting and evaluating a prototype.     

Lieferantenportfolio-Management für IT-Services unter Berücksichtigung von Diversifikationseffekten

By means of service-oriented architectures the IT support of processes can be designed as a portfolio of individual IT services provided by different suppliers. The processes are designed based on selection decisions between IT services that potentially have to be included. Many companies formulate a multitude of requirements for investments in IT services at ever shorter intervals. However, the scope of the desired investments usually exceeds the available budget. Thus, companies face the challenge of allocating the limited budget to investments in the most promising combination of IT services. This is hardly possible without methodical support. In addition, the allocation is often done intuitively and subject to the decision-makers?? affinity with IT. Therefore, this paper develops a quantitative, multi-period procedure model for the purpose of maximizing the enterprise value in accordance with value based management, which considers the dependencies of the periodical selection decisions. In the following, a decision logic for the heuristic solution to the selection problem is presented and its application is demonstrated by means of an illustrative case example.     

Discrete time sliding mode control of robotic manipulators: Development and experimental validation

This paper presents a robust discrete-time sliding mode control coupled with an uncertainty estimator designed for planar robotic manipulators. Experimental evidence shows satisfactory trajectory tracking performances and noticeable robustness in the presence of model inaccuracies, disturbances and payload perturbations. Ultimate boundedness of the tracking errors is proved, as well as boundedness of the estimation error with arbitrary precision.     

On grammar forms with terminal context

Summary A context-free grammar form G defines a family of context-free grammars {ie397-01}(G). In this paper {ie397-02}(G) is extended to give the family of terminal context grammars {ie397-03}(G), which were introduced by Book [4]. It is shown that the families of languages defined by {ie397-04}(G) and {ie397-05}(G) are equal when G is an -free context-free grammar form. This generalizes the result of Book [4] for context-free grammars and underlines the usefulness of the notion of grammar forms in formal language theory.The work of the second author was carried out partially under a National Research Council of Canada Grant. No. A-7700 and partially under the auspices of the University of Karlsruhe