@inproceedings{MalonekFalcaoSilva,
  author    = {Malonek, Helmuth Robert and Falc{\~a}o, M. Irene and Silva, Ant{\´o}nio},
  title     = {MAPLE TOOLS FOR MODIFIED QUATERNIONIC ANALYSIS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2953},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29535},
  pages     = {7},
  abstract  = {At the 16th IKM Bock, Falc{\~a}o and G{\"u}rlebeck 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. G{\"u}rlebeck, K. Habetha, and W. Spr{\"o}ssig, in the series "Grundstudium Mathematik" of Birkh{\"a}user Verlag, 2006) can directly be used for numerical calculations in the modified theory.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{ConstalesKrausshar,
  author    = {Constales, Denis and Kraußhar, Rolf S{\"o}ren},
  title     = {ON THE NAVIER-STOKES EQUATION WITH FREE CONVECTION IN STRIP DOMAINS AND 3D TRIANGULAR CHANNELS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2938},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29387},
  pages     = {12},
  abstract  = {The Navier-Stokes equations and related ones can be treated very elegantly with the quaternionic operator calculus developed in a series of works by K. Guerlebeck, W. Sproeossig and others. This study will be extended in this paper. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one basically needs 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. With special variants of quaternionic holomorphic multiperiodic functions we obtain explicit formulas for three dimensional parallel plate channels, rectangular block domains and regular triangular channels. The explicit knowledge of the integral kernels makes it then possible to evaluate the operator equations in order to determine the solutions of the boundary value problem explicitly.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}