TY - CHAP
A1 - Kraußhar, Rolf Sören
A1 - Constales, Denis
A1 - Gürlebeck, Klaus
A1 - Sprößig, Wolfgang
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - APPLICATIONS OF QUATERNIONIC ANALYSIS IN ENGINEERING
N2 - The quaternionic operator calculus can be applied very elegantly to solve many important boundary value problems arising in fluid dynamics and electrodynamics in an analytic way. In order to set up fully explicit solutions. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one has to evaluate two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. Recently the theory of quaternionic holomorphic multiperiodic functions and automorphic forms provided new impulses to set up explicit representation formulas for large classes of hyperbolic polyhedron type domains. These include block shaped domains, wedge shaped domains (with or without additional rectangular restrictions) and circular symmetric finite and infinite cylinders as particular subcases. In this talk we want to give an overview over the recent developments in this direction.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29128
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Morais, Joao
A1 - Georgiev, Svetlin
A1 - Sprößig, Wolfgang
ED - Gürlebeck, Klaus
ED - Lahmer, Tom
ED - Werner, Frank
T1 - A NOTE ON THE CLIFFORD FOURIER-STIELTJES TRANSFORM
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar
N2 - The purpose of this article is to provide an overview of the real Clifford Fourier- Stieltjes transform (CFST) and of its important properties. Additionally, we introduce the definition of convolution of Clifford functions of bounded variation.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Computerunterstütztes Verfahren
Y1 - 2012
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27794
UR - http://euklid.bauing.uni-weimar.de/ikm2012
SN - 1611-4086
ER -
TY - CHAP
A1 - Le, Hoai Thu
A1 - Morais, Joao
A1 - Sprößig, Wolfgang
ED - Gürlebeck, Klaus
ED - Lahmer, Tom
ED - Werner, Frank
T1 - ORTHOGONAL DECOMPOSITIONS AND THEIR APPLICATIONS
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar
N2 - It is well known that complex quaternion analysis plays an important role in the study of higher order boundary value problems of mathematical physics. Following the ideas given for real quaternion analysis, the paper deals with certain orthogonal decompositions of the complex quaternion Hilbert space into its subspaces of null solutions of Dirac type operator with an arbitrary complex potential. We then apply them to consider related boundary value problems, and to prove the existence and uniqueness as well as the explicit representation formulae of the underlying solutions.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Computerunterstütztes Verfahren
Y1 - 2012
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27729
UR - http://euklid.bauing.uni-weimar.de/ikm2012
SN - 1611-4086
ER -