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MAPLE TOOLS FOR MODIFIED QUATERNIONIC ANALYSIS

  • At the 16th IKM Bock, Falcão and Gürlebeck presented examples of the application of some specially developed Maple-Software in hypercomplex analysis. Other papers of those authors continued this work and showed the efficiency of such tools for concrete numerical calculations as well as for numerical experiments, supporting the detection of new relationships and even theorems in a highly technicalAt the 16th IKM Bock, Falcão and Gürlebeck presented examples of the application of some specially developed Maple-Software in hypercomplex analysis. Other papers of those authors continued this work and showed the efficiency of such tools for concrete numerical calculations as well as for numerical experiments, supporting the detection of new relationships and even theorems in a highly technical theoretical work. The mentioned software has been developed mainly for the use on mapping problems in the Euclidean spaces of dimension 3 and 4 by means of Bergman kernel methods (BKM), which are related to monogenic functions as solutions of generalized Cauchy-Riemann equations with respect to the Euclidean metric (Riesz system). The developed procedures concerning generalized powers of totally regular variables and the corresponding homogeneous polynomials basically rely on results and conventions introduced in the paper "Power series representation for monogenic functions in Rm+1 based on a permutational product", Complex Variables, 15, No.3, 181-191 (1990) by H. Malonek. Since 1992 H. Leutwiler, S. L. Eriksson and others developed in a number of papers a modified Clifford analysis and, particularly, a modified quaternionic analysis. The modification mainly consists in considering generalized Cauchy-Riemann equations with respect to a hyperbolic metric in a half space. The aim of this contribution is to show how through a change of the basic combinatorial relations used in the modified quaternionic analysis the aforementioned Maple-software (that has been recently published on CD-Rom as integrated part of the text book "Funktionentheorie in der Ebene und im Raum" by K. Gürlebeck, K. Habetha, and W. Sprössig, in the series "Grundstudium Mathematik" of Birkhäuser Verlag, 2006) can directly be used for numerical calculations in the modified theory.zeige mehrzeige weniger

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Metadaten
Dokumentart:Konferenzveröffentlichung
Verfasserangaben: Helmuth Robert MalonekORCiDGND, M. Irene Falcão, António Silva
DOI (Zitierlink):https://doi.org/10.25643/bauhaus-universitaet.2953Zitierlink
URN (Zitierlink):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170327-29535Zitierlink
URL:http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
Herausgeber: Klaus GürlebeckGND, Carsten KönkeORCiDGND
Sprache:Englisch
Datum der Veröffentlichung (online):24.03.2017
Datum der Erstveröffentlichung:14.07.2006
Datum der Freischaltung:27.03.2017
Veröffentlichende Institution:Bauhaus-Universität Weimar
Urhebende Körperschaft:Bauhaus-Universität Weimar
Institute und Partnereinrichtugen:Bauhaus-Universität Weimar / In Zusammenarbeit mit der Bauhaus-Universität Weimar
Seitenzahl:7
GND-Schlagwort:Architektur <Informatik>; CAD; Computerunterstütztes Verfahren
DDC-Klassifikation:500 Naturwissenschaften und Mathematik / 510 Mathematik
BKL-Klassifikation:56 Bauwesen / 56.03 Methoden im Bauingenieurwesen
Sammlungen:Bauhaus-Universität Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar, 17. 2006
Lizenz (Deutsch):License Logo Creative Commons 4.0 - Namensnennung-Nicht kommerziell (CC BY-NC 4.0)