Note: Communicated by Nek Valous, National Center for Tumor Diseases (NCT), Heidelberg.
Title: Evaluation schemes in the ring of quaternionic polynomials
Journal: BIT Numerical Mathematics, Volume 58, Issue 1, pp 51–72, March 2018
Authors: M. Irene Falcão, Fernando Miranda, Ricardo Severino, M. Joana Soares
In this paper we focus on computational aspects associated with polynomial problems in the ring of one-sided quaternionic polynomials. The complexity and error bounds of quaternion arithmetic are considered and several evaluation schemes are analyzed from their complexity point of view. The numerical stability of generalized Horner’s and Goertzel’s algorithms to evaluate polynomials with quaternion floating-point coefficients is addressed. Numerical tests illustrate the behavior of the algorithms from the point of view of performance and accuracy.
Title: Multifluid plasma equations in terms of hyperbolic octonions
Journal: International Journal of Geometric Methods in Modern Physics, Volume 15, Issue 04, April 2018
Authors: Süleyman Demir and Erdinç Zeren
Stimulating from the hyperbolic octonionic generalization of the Maxwell-type equations of compressible fluids, an alternative reformulation has been proposed for the analogous multifluid plasma equations. In this paper, using both the fluid and electromagnetic behavior of the plasma, the compact and elegant expressions have been derived in terms of hyperbolic octonions as previously given for electromagnetic theory, linear gravity and fluid mechanics. Using the advantages of proposed model, the field equations of multifluid plasma have been combined in a single equation. Furthermore, the plasma wave equations in terms of generalized vorticity and Lamp vector have been expressed in a form similar to electromagnetic, gravitational counterparts previously given in relevant literature.
Source: Email from N. Velous, nek.valous_AT_nct-heidelberg.de, 17 Mar. 2018.