Universitätsbibliothek
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In this note, we describe quite explicitly the Howe duality for Hodge systems and connect it with the well-known facts of harmonic analysis and Clifford analysis. In Section 2, we recall briefly the Fisher decomposition and the Howe duality for harmonic analysis. In Section 3, the well-known fact that Clifford analysis is a real refinement of harmonic analysis is illustrated by the Fisher decomposition and the Howe duality for the space of spinor-valued polynomials in the Euclidean space under the so-called L-action. On the other hand, for Clifford algebra valued polynomials, we can consider another action, called in Clifford analysis the H-action. In the last section, we recall the Fisher decomposition for the H-action obtained recently. As in Clifford analysis the prominent role plays the Dirac equation in this case the basic set of equations is formed by the Hodge system. Moreover, analysis of Hodge systems can be viewed even as a refinement of Clifford analysis. In this note, we describe the Howe duality for the H-action. In particular, in Proposition 1, we recognize the Howe dual partner of the orthogonal group O(m) in this case as the Lie superalgebra sl(2 1). Furthermore, Theorem 2 gives the corresponding multiplicity free decomposition with an explicit description of irreducible pieces.

This paper describes the application of interval calculus to calculation of plate deflection, taking in account inevitable and acceptable tolerance of input data (input parameters). The simply supported reinforced concrete plate was taken as an example. The plate was loaded by uniformly distributed loads. Several parameters that influence the plate deflection are given as certain closed intervals. Accordingly, the results are obtained as intervals so it was possible to follow the direct influence of a change of one or more input parameters on output (in our example, deflection) values by using one model and one computing procedure. The described procedure could be applied to any FEM calculation in order to keep calculation tolerances, ISO-tolerances, and production tolerances in close limits (admissible limits). The Wolfram Mathematica has been used as tool for interval calculation.

Im vorliegenden Beitrag wird ein Framework für ein verteiltes dynamisches Produktmodell (FREAC) vorgestellt, welches der experimentellen Softwareentwicklung dient. Bei der Entwicklung von FREAC wurde versucht, folgende Eigenschaften umzusetzen, die bei herkömmlichen Systemen weitgehend fehlen: Erstens eine hohe Flexibilität, also eine möglichst hohe Anpassbarkeit für unterschiedliche Fachdisziplinen; Zweitens die Möglichkeit, verschiedene Tools nahtlos miteinander zu verknüpfen; Drittens die verteilte Modellbearbeitung in Echtzeit; Viertens das Abspeichern des gesamten Modell-Bearbeitungsprozesses; Fünftens eine dynamische Erweiterbarkeit sowohl für Softwareentwickler, als auch für die Nutzer der Tools. Die Bezeichnung FREAC umfasst sowohl das Framework zur Entwicklung und Pflege eines Produktmodells (FREAC-Development) als auch die entwickelten Tools selbst (FREAC-Tools).

Besides home entertainment and business presentations, video projectors are powerful tools for modulating images spatially as well as temporally. The re-evolving need for stereoscopic displays increases the demand for low-latency projectors and recent advances in LED technology also offer high modulation frequencies. Combining such high-frequency illumination modules with synchronized, fast cameras, makes it possible to develop specialized high-speed illumination systems for visual effects production. In this thesis we present different systems for using spatially as well as temporally modulated illumination in combination with a synchronized camera to simplify the requirements of standard digital video composition techniques for film and television productions and to offer new possibilities for visual effects generation. After an overview of the basic terminology and a summary of related methods, we discuss and give examples of how modulated light can be applied to a scene recording context to enable a variety of effects which cannot be realized using standard methods, such as virtual studio technology or chroma keying. We propose using high-frequency, synchronized illumination which, in addition to providing illumination, is modulated in terms of intensity and wavelength to encode technical information for visual effects generation. This is carried out in such a way that the technical components do not influence the final composite and are also not visible to observers on the film set. Using this approach we present a real-time flash keying system for the generation of perspectively correct augmented composites by projecting imperceptible markers for optical camera tracking. Furthermore, we present a system which enables the generation of various digital video compositing effects outside of completely controlled studio environments, such as virtual studios. A third temporal keying system is presented that aims to overcome the constraints of traditional chroma keying in terms of color spill and color dependency. ...

In recent years special hypercomplex Appell polynomials have been introduced by several authors and their main properties have been studied by different methods and with different objectives. Like in the classical theory of Appell polynomials, their generating function is a hypercomplex exponential function. The observation that this generalized exponential function has, for example, a close relationship with Bessel functions confirmed the practical significance of such an approach to special classes of hypercomplex differentiable functions. Its usefulness for combinatorial studies has also been investigated. Moreover, an extension of those ideas led to the construction of complete sets of hypercomplex Appell polynomial sequences. Here we show how this opens the way for a more systematic study of the relation between some classes of Special Functions and Elementary Functions in Hypercomplex Function Theory.