TY - CHAP A1 - Kraußhar, Rolf Sören ED - Gürlebeck, Klaus ED - Lahmer, Tom ED - Werner, Frank T1 - SOME HARMONIC ANALYSIS ON MÖBIUS STRIP DOMAINS AND THE KLEIN BOTTLE IN Rn 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 aim of this paper we discuss explicit series constructions for the fundamental solution of the Helmholtz operator on some important examples non-orientable conformally at manifolds. In the context of this paper we focus on higher dimensional generalizations of the Klein bottle which in turn generalize higher dimensional Möbius strips that we discussed in preceding works. We discuss some basic properties of pinor valued solutions to the Helmholtz equation on these manifolds. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Computerunterstütztes Verfahren Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27692 UR - http://euklid.bauing.uni-weimar.de/ikm2012 SN - 1611-4086 ER - TY - CHAP A1 - Kraußhar, Rolf Sören A1 - de Almeida, Regina ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - FUNDAMENTALS OF A WIMAN VALIRON THEORY FOR POLYMONOGENIC FUNCTIONS 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 - In this paper we present some rudiments of a generalized Wiman-Valiron theory in the context of polymonogenic functions. In particular, we analyze the relations between different notions of growth orders and the Taylor coefficients. Our main intention is to look for generalizations of the Lindel¨of-Pringsheim theorem. In contrast to the classical holomorphic and the monogenic setting we only obtain inequality relations in the polymonogenic setting. This is due to the fact that the Almansi-Fischer decomposition of a polymonogenic function consists of different monogenic component functions where each of them can have a totally different kind of asymptotic growth behavior. 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 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28100 SN - 1611-4086 ER - TY - CHAP A1 - Cacao, Isabel A1 - Constales, Denis A1 - Kraußhar, Rolf Sören ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - A UNIFIED APPROACH FOR THE TREATMENT OF SOME HIGHER DIMENSIONAL DIRAC TYPE EQUATIONS ON SPHERES N2 - Using Clifford analysis methods, we provide a unified approach to obtain explicit solutions of some partial differential equations combining the n-dimensional Dirac and Euler operators, including generalizations of the classical time-harmonic Maxwell equations. The obtained regular solutions show strong connections between hypergeometric functions and homogeneous polynomials in the kernel of the Dirac operator. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Architektur KW - Computerunterstütztes Verfahren KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28343 UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html SN - 1611-4086 ER -