TY  - CONF
A1  - Grigor'ev, Yuri
A2  - Gürlebeck, Klaus
A2  - Lahmer, Tom
T1  - REGULAR QUATERNIONIC FUNCTIONS AND THEIR APPLICATIONS
T2  - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar
N2  - The theory of regular quaternionic functions of a reduced quaternionic variable is a 3-dimensional generalization of complex analysis. The Moisil-Theodorescu system (MTS) is a regularity condition for such functions depending on the radius vector r = ix+jy+kz seen as a reduced quaternionic variable. The analogues of the main theorems of complex analysis for the MTS in quaternion forms are established: Cauchy, Cauchy integral formula, Taylor and Laurent series, approximation theorems and Cauchy type integral properties. The analogues of positive powers (inner spherical monogenics) are investigated: the set of recurrence formulas between the inner spherical monogenics and the explicit formulas are established. Some applications of the regular function in the elasticity theory and hydrodynamics are given.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Building Information Modeling
KW  - Computerunterstütztes Verfahren
KW  - 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
Y1  - 2015
UR  - https://e-pub.uni-weimar.de/opus4/frontdoor/index/index/docId/2798
UR  - https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170314-27988
SN  - 1611-4086
ER  -