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

Mathematica Balkanica New Series (2012)

- Volume: 26, Issue: 1-2, page 15-24
- ISSN: 0205-3217

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topApostolova, 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 -

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