Results 21 to 30 of about 252 (37)

Quaternion quadratic equations in characteristic 2 [PDF]

, 2014
In this paper we present a solution for any standard quaternion quadratic equation, i.e. an equation of the form $z^2+\mu z+\nu=0$ where $\mu$ and $\nu$ belong to some quaternion division algebra $Q$ over some field $F$, assuming the characteristic of $F$
Chapman, Adam
core   +1 more source

Solving simple quaternionic differential equations [PDF]

, 2003
The renewed interest in investigating quaternionic quantum mechanics, in particular tunneling effects, and the recent results on quaternionic differential operators motivate the study of resolution methods for quaternionic differential equations. In this
Aslaksen H., Brenner J., Dyson F. J., Gisele C. Ducati, Leo S. De, Leo S. De, Leo S. De, Leo S. De, Leo S. De, Stefano De Leo, Study E.   +10 more
core   +3 more sources

Some properties of Fibonacci numbers, Fibonacci octonions and generalized Fibonacci-Lucas octonions

, 2015
In this paper we determine some properties of Fibonacci octonions. Also, we introduce the generalized Fibonacci-Lucas octonions and we investigate some properties of these ...
Savin, Diana
core   +1 more source

Quaternary quadratic lattices over number fields

, 2018
We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of (V,q).
Dieudonné J., Gabriele Nebe, Hasse H., Markus Kirschmer, Reiner I., Scharlau W., Vignéras M.-F., Voight J.   +7 more
core   +1 more source

On ̄h-Jacobsthal and ̄h-Jacobsthal–Lucas sequences, and related quaternions

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
In this paper, inspired by recent articles of A. Szynal-Liana & I. Włoch and F. T. Aydin & S. Yüce (see [26] and [2]), we will introduce the ̄h-Jacobsthal quaternions and the ̄h-Jacobsthal–Lucas sequences and their associated quaternions. The new results
Anatriello Giuseppina, Vincenzi Giovanni
doaj   +1 more source

Integral theorems for the quaternionic G-monogenic mappings

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
In the paper [1] considered a new class of quaternionic mappings, so- called G-monogenic mappings. In this paper we prove analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and ...
Shpakivskyi V. S., Kuzmenko T. S.
doaj   +1 more source

Irreducibility of Polynomials over Global Fields is Diophantine

, 2017
Given a global field $K$ and a positive integer $n$, we present a diophantine criterion for a polynomial in one variable of degree $n$ over $K$ not to have any root in $K$.
Dittmann, Philip
core   +1 more source

On a Generalization for Tribonacci Quaternions

, 2017
Let $V_{n}$ denote the third order linear recursive sequence defined by the initial values $V_{0}$, $V_{1}$ and $V_{2}$ and the recursion $V_{n}=rV_{n-1}+sV_{n-2}+tV_{n-3}$ if $n\geq 3$, where $r$, $s$, and $t$ are real constants. The $\{V_{n}\}_{n\geq0}$
Cerda-Morales, Gamaliel
core   +1 more source

The Third Order Jacobsthal Octonions: Some Combinatorial Properties

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018
Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many di erent ways.
Cerda-Morales Gamaliel
doaj   +1 more source

Fibonacci Cartan and Lucas Cartan numbers

Open Mathematics
This study introduces Fibonacci Cartan and Lucas Cartan numbers, extending the classical Fibonacci and Lucas sequences into the framework of Cartan numbers.
Öztürk İskender, Çakır Hasan
doaj   +1 more source