Language:
EN
| Published:
15-11-2025
|
Abstract
| pp. 13-26
Generalized commutative quaternions generalize elliptic, parabolic and hyperbolic quaternions, bicomplex numbers, complex hyperbolic numbers and hyperbolic complex numbers. In this paper, we use the Mersenne numbers and polynomials in the theory of these quaternions. We introduce and study generalized commutative Mersenne quaternion polynomials and generalized commutative Mersenne–Lucas quaternion polynomials.
Language:
EN
| Published:
10-01-2024
|
Abstract
| pp. 18-28
This article has two main parts. In the first part we show that some of the basic theory of generalized polynomials on commutative semigroups can be extended to all semigroups. In the second part we show that if a sub-semigroup S of a group G generates G in the sense that G = S·S−1, then a generalized polynomial on S with values in an Abelian group H can be extended to a generalized polynomial on G into H. Finally there is a short discussion of the extendability of exponential functions and generalized exponential polynomials.
Language:
EN
| Published:
26-10-2023
|
Abstract
| pp. 214-220
In this paper we consider a generalized polynomial f : ℝ → ℝ of degree two that satisfies the additional equation f(x)f(y) = 0 for the pairs (x,y) ∈ D, where D ⊆ ℝ2 is given by some algebraic condition. In the particular cases when there exists a positive rational m fulfilling D = { (x,y) ∈ ℝ2 | x2 - my2 = 1 }, we prove that f(x) = 0 for all x ∈ ℝ.
Language:
EN
| Published:
18-04-2022
|
Abstract
| pp. 206-214
In this note, we present an extension of the celebrated Abel–Liouville identity in terms of noncommutative complete Bell polynomials for generalized Wronskians. We also characterize the range equivalence of n-dimensional vector-valued functions in the subclass of n-times differentiable functions with a nonvanishing Wronskian.
Language:
EN
| Published:
13-09-2023
|
Abstract
| pp. 306-314
Let P(z) = Σj=0najzj be a polynomial of degree n such that an ≥ an-1 ≥ ... ≥ a1 ≥ a0 ≥ 0. Then according to Eneström-Kakeya theorem all the zeros of P(z) lie in |z| ≤ 1. This result has been generalized in various ways (see [1, 3, 4, 6, 7]). In this paper we shall prove some generalizations of the results due to Aziz and Zargar [1, 2] and Nwaeze [7].
2023-09-13
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English