3 citations · 4 across the 5 of their papers we have counts for
5 papers
Cauchy formulae and Hardy spaces in discrete octonionic analysis
Rolf Sören Kraußhar, Dmitrii Legatiuk
In this paper, we continue the development of a fundament of discrete octonionic analysis that is associated to the discrete first order Cauchy-Riemann operator acting on octonions…
Towards discrete octonionic analysis
Rolf Sören Kraußhar, Anastasiia Legatiuk, Dmitrii Legatiuk
In recent years, there is a growing interest in the studying octonions, which are 8-dimensional hypercomplex numbers forming the biggest normed division algebras over the real numb…
Brownian motion, martingales and Itô formula in Clifford analysis
Swanhild Bernstein, Dmitrii Legatiuk
Clifford analysis has been the field of active research for several decades resulting in various methods to solve problems in pure and applied mathematics. However, the area of sto…
Mathematical modelling by help of category theory: models and relations between them
Dmitrii Legatiuk
The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, th…
Coupling of complex function theory and finite element method for crack propagation through energetic formulation: conformal mapping approach and reduction to a Riemann-Hilbert problem
Dmitrii Legatiuk, Daniel Weisz-Patrault
In this paper we present a theoretical background of a coupled analytical-numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of th…