@inproceedings{NguyenGuerlebeck,
author = {Nguyen, Manh Hung and G{\"u}rlebeck, Klaus},
title = {ON M-CONFORMAL MAPPINGS AND GEOMETRIC PROPERTIES},
series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom and Werner, Frank},
organization = {Bauhaus-Universit{\"a}t Weimar},
issn = {1611-4086},
doi = {10.25643/bauhaus-universitaet.2783},
url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27833},
pages = {7},
abstract = {Monogenic functions play a role in quaternion analysis similarly to that of holomorphic functions in complex analysis. A holomorphic function with nonvanishing complex derivative is a conformal mapping. It is well-known that in Rn+1, n ≥ 2 the set of conformal mappings is restricted to the set of M{\"o}bius transformations only and that the M{\"o}bius transformations are not monogenic. The paper deals with a locally geometric mapping property of a subset of monogenic functions with nonvanishing hypercomplex derivatives (named M-conformal mappings). It is proved that M-conformal mappings orthogonal to all monogenic constants admit a certain change of solid angles and vice versa, that change can characterize such mappings. In addition, we determine planes in which those mappings behave like conformal mappings in the complex plane.},
subject = {Angewandte Informatik},
language = {en}
}
@inproceedings{BockGuerlebeck,
author = {Bock, Sebastian and G{\"u}rlebeck, Klaus},
title = {A Coupled Ritz-Galerkin Approach Using Holomorphic and Anti-holomorphic Functions},
editor = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
organization = {Bauhaus-Universit{\"a}t Weimar},
doi = {10.25643/bauhaus-universitaet.2928},
url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29281},
pages = {14},
abstract = {The contribution focuses on the development of a basic computational scheme that provides a suitable calculation environment for the coupling of analytical near-field solutions with numerical standard procedures in the far-field of the singularity. The proposed calculation scheme uses classical methods of complex function theory, which can be generalized to 3-dimensional problems by using the framework of hypercomplex analysis. The adapted approach is mainly based on the factorization of the Laplace operator EMBED Equation.3 by the Cauchy-Riemann operator EMBED Equation.3 , where exact solutions of the respective differential equation are constructed by using an orthonormal basis of holomorphic and anti-holomorphic functions.},
subject = {Architektur },
language = {en}
}