https://www.db-thueringen.de/receive/dbt_mods_00037019https://www.db-thueringen.de/servlets/MCRFileNodeServlet/dbt_derivate_00043169/man_173_pdfa.pdfhttps://www.db-thueringen.de/rsc/thumbnail/dbt_mods_00037019.png Malonek, Helmuth R. aut Author Malonek Helmuth R. Falcão, M. Irene aut Author Falcão M. Irene Cruz, Carla aut Author Cruz Carla 000 510 Angewandte Informatik article Angewandte Mathematik Computerunterstütztes Verfahren The aim of our contribution is to clarify the relation between totally regular variables and Appell sequences of hypercomplex holomorphic polynomials (sometimes simply called monogenic power-like functions) in Hypercomplex Function Theory. After their introduction in 2006 by two of the authors of this note on the occasion of the 17th IKM, the latter have been subject of investigations by different authors with different methods and in various contexts. The former concept, introduced by R. Delanghe in 1970 and later also studied by K. Gürlebeck in 1982 for the case of quaternions, has some obvious relationship with the latter, since it describes a set of linear hypercomplex holomorphic functions all power of which are also hypercomplex holomorphic. Due to the non-commutative nature of the underlying Clifford algebra, being totally regular variables or Appell sequences are not trivial properties as it is for the integer powers of the complex variable z=x+ iy. Simple examples show also, that not every totally regular variable and its powers form an Appell sequence and vice versa. Under some very natural normalization condition the set of all para-vector valued totally regular variables which are also Appell sequences will completely be characterized. In some sense the result can also be considered as an answer to a remark of K. Habetha in chapter 16: Function theory in algebras of the collection Complex analysis. Methods, trends, and applications, Akademie-Verlag Berlin, (Eds. E. Lanckau and W. Tutschke) 225-237 (1983) on the use of exact copies of several complex variables for the power series representation of any hypercomplex holomorphic function. his Host institution Gürlebeck, Klaus edt Editor Gürlebeck Klaus 1015214991 Lahmer, Tom edt Editor Lahmer Tom 0000-0002-1251-7301 135943620 Werner, Frank edt Editor Werner Frank 0000-0002-0709-3591 134070666 article urn:nbn:de:gbv:wim2-20170314-27751 en oai:opus4.weimar:2775 10.25643/bauhaus-universitaet.2775 2012-07-04 2012-07-04 text International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar 19, 2012 261 265 IKM 000 conference_publication 510 Angewandte Informatik Angewandte Mathematik Computerunterstütztes Verfahren The 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 4th till 6th July 2012. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference! http://uri.gbv.de/document/gvk:ppn:835105016 his Host institution his Host institution his Host institution Gürlebeck, Klaus edt Editor Gürlebeck Klaus 1015214991 Lahmer, Tom edt Editor Lahmer Tom 0000-0002-1251-7301 135943620 Werner, Frank edt Editor Werner Frank 0000-0002-0709-3591 134070666 urn:nbn:de:gbv:wim2-20150916-24571 en oai:opus4.weimar:2457 1611-4086 10.25643/bauhaus-universitaet.2457 2012-09-01 2012-09-01 text International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering 434 Seiten dbt_mods_00037019https://www.db-thueringen.de/receive/dbt_mods_00037019