Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar, 20. 2015
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Institute
- In Zusammenarbeit mit der Bauhaus-Universität Weimar (15)
- Professur Angewandte Mathematik (8)
- Graduiertenkolleg 1462 (4)
- Institut für Strukturmechanik (ISM) (4)
- Professur Informatik im Bauwesen (4)
- Institut für Konstruktiven Ingenieurbau (IKI) (2)
- Professur Computer Vision in Engineering (2)
- Professur Stochastik und Optimierung (2)
- Professur Baubetrieb und Bauverfahren (1)
Keywords
- Angewandte Informatik (35)
- Angewandte Mathematik (35)
- Building Information Modeling (35)
- Computerunterstütztes Verfahren (35)
- Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications (34)
- Data, information and knowledge modeling in civil engineering (1)
- Function theoretic methods and PDE in engineering sciences (1)
- Mathematical methods for (robotics and) computer vision (1)
- Numerical modeling in engineering (1)
- Optimization in engineering applications (1)
What is nowadays called (classic) Clifford analysis consists in the establishment of a function theory for functions belonging to the kernel of the Dirac operator. While such functions can very well describe problems of a particle with internal SU(2)-symmetries, higher order symmetries are beyond this theory. Although many modifications (such as Yang-Mills theory) were suggested over the years they could not address the principal problem, the need of a n-fold factorization of the d’Alembert operator. In this paper we present the basic tools of a fractional function theory in higher dimensions, for the transport operator (alpha = 1/2 ), by means of a fractional correspondence to the Weyl relations via fractional Riemann-Liouville derivatives. A Fischer decomposition, fractional Euler and Gamma operators, monogenic projection, and basic fractional homogeneous powers are constructed.