Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

Apostolova, Lilia N.. "Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials." Mathematica Balkanica New Series 26.1-2 (2012): 15-24. <http://eudml.org/doc/281461>.

@article{Apostolova2012,
abstract = {MSC 2010: 30C10, 32A30, 30G35The algebra R(1; j; j2; j3), j4 = ¡1 of the fourth-R numbers, or in other words the algebra of the double-complex numbers C(1; j) and the corresponding functions, were studied in the papers of S. Dimiev and al. (see [1], [2], [3], [4]). The hyperbolic fourth-R numbers form other similar to C(1; j) algebra with zero divisors. In this note the square roots of hyperbolic fourth-R numbers and hyperbolic complex numbers are found. The quadratic equation with hyperbolic fourth-R coefficients and variables is solved. The Cauchy-Riemann system for holomorphicity of fourth-R functions is recalled. Holomorphic homogeneous polynomials of fourth-R variables are listed.},
author = {Apostolova, Lilia N.},
journal = {Mathematica Balkanica New Series},
keywords = {algebra of fourth-R numbers; algebra of hyperbolic fourth-R numbers; hyperbolic fourth-R quadratic equation; holomorphic fourth-R function; holomorphic fourth- R polynomial; algebra of fourth- numbers; algebra of hyperbolic fourth- numbers; hyperbolic fourth- quadratic equation; holomorphic fourth- function; holomorphic fourth- polynomial},
language = {eng},
number = {1-2},
pages = {15-24},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials},
url = {http://eudml.org/doc/281461},
volume = {26},
year = {2012},
}

TY - JOUR
AU - Apostolova, Lilia N.
TI - Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials
JO - Mathematica Balkanica New Series
PY - 2012
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 26
IS - 1-2
SP - 15
EP - 24
AB - MSC 2010: 30C10, 32A30, 30G35The algebra R(1; j; j2; j3), j4 = ¡1 of the fourth-R numbers, or in other words the algebra of the double-complex numbers C(1; j) and the corresponding functions, were studied in the papers of S. Dimiev and al. (see [1], [2], [3], [4]). The hyperbolic fourth-R numbers form other similar to C(1; j) algebra with zero divisors. In this note the square roots of hyperbolic fourth-R numbers and hyperbolic complex numbers are found. The quadratic equation with hyperbolic fourth-R coefficients and variables is solved. The Cauchy-Riemann system for holomorphicity of fourth-R functions is recalled. Holomorphic homogeneous polynomials of fourth-R variables are listed.
LA - eng
KW - algebra of fourth-R numbers; algebra of hyperbolic fourth-R numbers; hyperbolic fourth-R quadratic equation; holomorphic fourth-R function; holomorphic fourth- R polynomial; algebra of fourth- numbers; algebra of hyperbolic fourth- numbers; hyperbolic fourth- quadratic equation; holomorphic fourth- function; holomorphic fourth- polynomial
UR - http://eudml.org/doc/281461
ER -