Results 1 to 10 of about 46 (31)

Topologies of Bihyperbolic Numbers

Mathematics, 2022
In this paper, we establish a correlation between the bihyperbolic numbers set and the semi-Euclidean space. There are three different norms on the semi-Euclidean space that allow us to define three different hypersurfaces on semi-Euclidean space. Hence,
Marija Paunovic, Sóley Ersoy, Ana Savic   +2 more
exaly   +6 more sources

On Some Properties of Bihyperbolic Numbers of The Lucas Type

Communications in Advanced Mathematical Sciences, 2023
To date, many authors in the literature have worked on special arrays in various computational systems. In this article, Lucas type bihyperbolic numbers were defined and their algebraic properties were examined. Bihyperbolic Lucas numbers were studied by
Fügen Torunbalcı Aydın
doaj   +4 more sources

Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas Numbers

Journal of Advanced Research in Natural and Applied Sciences, 2023
In this study, we define a new type of Pell and Pell-Lucas numbers which are called Gaussian-bihyperbolic Pell and Pell-Lucas numbers. We also define negaGaussian-bihyperbolic Pell and Pell-Lucas numbers.
Hasan Gökbaş
doaj   +3 more sources

On the Combinatorial Properties of Bihyperbolic Balancing Numbers [PDF]

Tatra Mountains Mathematical Publications, 2020
Abstract In this paper, we introduce bihyperbolic balancing and Lucas-balancing numbers. We give some of their properties, among others the Binet formula, Catalan, Cassini, d’Ocagne identities and the generating function.
Dorota Brod, Anetta Szynal-Liana, Iwona Włoch   +2 more
exaly   +2 more sources

On Mersenne Numbers and their Bihyperbolic Generalizations

Annales Mathematicae Silesianae
In this paper, we introduce Mersenne and Mersenne–Lucas bihyperbolic numbers, i.e. bihyperbolic numbers whose coefficients are consecutive Mersenne and Mersenne–Lucas numbers.
Bród Dorota, Szynal-Liana Anetta
doaj   +2 more sources

On generalized bihyperbolic Mersenne numbers [PDF]

Mathematica Bohemica
In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained.
Dorota Bród, Anetta Szynal-Liana
exaly   +2 more sources

Bihyperbolic numbers of the Fibonacci type and triangular matrices (tables)

Azerbaijan Journal of Mathematics
Summary: In this paper, we compute paradeterminants and parapermanents of some triangular matrices that give bihyperbolic numbers of the Fibonacci type. Using connections between the paradeterminant of triangular matrix and the lower Hessenberg determinant, we also obtain the general term of these sequences.
Bednarz, P., Szynal-Liana, A.
exaly   +3 more sources

Special bihyperbolic numbers and their connections with triangular tables and matrices

Annales Universitatis Mariae Curie-Sklodowska Sectio A Mathematica
In this paper we express special bihyperbolic numbers as paradeterminants and parapermanents of some triangular matrices. Moreover, by applying the connections between these parameters of triangular tables and the determinants and permanents of lower Hessenberg matrices, we obtain another expressions of these numbers, using matrices which are not ...
Paweł Bednarz
exaly   +2 more sources

Bihyperbolic numbers of the Fibonacci type as tridiagonal matrix determinants

Boletim Da Sociedade Paranaense De Matematica
Bihyperbolic numbers are extension of hyperbolic numbers to four dimensions. In this paper, we construct a family of tridiagonal matrices which determinants (continuants) and permanents can represent the sequences of bihyperbolic numbers of the Fibonacci type.
Dorota Brod, Anetta Szynal-Liana
exaly   +2 more sources

On third-order Jacobsthal numbers and their bihyperbolic generalizations

Annales Universitatis Mariae Curie-Sklodowska Sectio A Mathematica
In this paper, we introduce bihyperbolic third-order Jacobsthal and third-order Jacobsthal--Lucas numbers. In other words, bihyperbolic numbers whose coefficients are consecutive third-order Jacobsthal and third-order Jacobsthal--Lucas numbers. Furthermore, we study one parameter generalizations of bihyperbolic third-order Jacobsthal and third-order ...
exaly   +2 more sources