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REGULAR QUATERNIONIC FUNCTIONS AND THEIR APPLICATIONS

  • 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 areThe 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.show moreshow less

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Metadaten
Document Type:Conference Proceeding
Author: Yuri Grigor'ev
DOI (Cite-Link):https://doi.org/10.25643/bauhaus-universitaet.2798Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170314-27988Cite-Link
ISSN:1611-4086
Parent Title (English):Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar
Editor: Klaus GürlebeckGND, Tom LahmerORCiDGND
Language:English
Date of Publication (online):2017/03/03
Date of first Publication:2015/08/28
Release Date:2017/03/14
Publishing Institution:Bauhaus-Universität Weimar
Creating Corporation:Bauhaus-Universität Weimar
Institutes:Bauhaus-Universität Weimar / In Zusammenarbeit mit der Bauhaus-Universität Weimar
Pagenumber:6
Tag: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
GND Keyword:Angewandte Informatik; Angewandte Mathematik; Building Information Modeling; Computerunterstütztes Verfahren
Dewey Decimal Classification:000 Informatik, Informationswissenschaft, allgemeine Werke / 000 Informatik, Wissen, Systeme
500 Naturwissenschaften und Mathematik / 510 Mathematik
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
56 Bauwesen / 56.03 Methoden im Bauingenieurwesen
Collections: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, 20. 2015
Licence (German):License Logo Creative Commons 4.0 - Namensnennung-Nicht kommerziell (CC BY-NC 4.0)