Results 41 to 50 of about 143 (119)
Invariance of recurrence sequences under a galois group
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 2, Page 327-334, 1996., 1995 Let F be a Galois field of order q, k a fixed positive integer and R = Fk×k[D] where D is an indeterminate. Let L be a field extension of F of degree k. We identify Lf with fk×1 via a fixed normal basis B of L over F. The F‐vector space Γk(F)( = Γ(L)) of all sequences over Fk×1 is a left R‐module. For any regular f(D) ∈ R, Ωk(f(D)) = {S ∈ Γk(F) : f(D)S
Hassan Al-Zaid, Surjeet Singh
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 In this paper, first we define Horadam octonions by Horadam sequence which is a generalization of second order recurrence relations. Also, we give some fundamental properties involving the elements of that sequence.
Karataş Adnan, Halici Serpil
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A Note on Two Fundamental Recursive Sequences
Annales Mathematicae Silesianae, 2021 In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc.
Farhadian Reza, Jakimczuk Rafael
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Generalized Chebyshev Polynomials
Discussiones Mathematicae - General Algebra and Applications, 2018 Let h(x) be a non constant polynomial with rational coefficients. Our aim is to introduce the h(x)-Chebyshev polynomials of the first and second kind Tn and Un. We show that they are in a ℚ-vectorial subspace En(x) of ℚ[x] of dimension n.
Abchiche Mourad, Belbachir Hacéne
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On Quaternion-Gaussian Fibonacci Numbers and Their Properties
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept gaussian Fibonacci numbers as coefficients.
Halici Serpil, Cerda-Morales Gamaliel
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Sum of Squares of Mulatu Numbers That Are Powers of 2
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.In this work, we fully characterize all nonnegative integer solutions (n, m, a) to the Diophantine equation Mn2+Mm2=2a, where Mkk≥0 is the Mulatu sequence. The argument employs Matveev’s explicit lower bound for linear forms in logarithms of algebraic numbers together with the reduction technique of Dujella and Pethö to obtain an absolute upper bound ...
Ahmed Gaber +3 more
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Generalized apostol-type polynomial matrix and its algebraic properties [PDF]
, 2019 The aim of this paper is to introduce the generalized Apostol-type polynomial matrix W [m−1,α](x;c,a;λ;µ;ν) and the generalized Apos-tol-type matrix W [m−1,α](c,a;λ;µ;ν).
Ramírez, William +2 more
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A Hybrid Matrix–Based Encoding Scheme With Error Detection via Third‐Order Recurrences
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, we propose a novel encoding–decoding algorithm based on third‐order linear recurrence sequences and their associated matrix representations. In particular, third‐order Jacobsthal and third‐order Jacobsthal–Lucas matrix sequences are combined with Padovan and Perrin matrix sequences to construct a hybrid block–based coding scheme.
Sukran Uygun, Smritijit Sen
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One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers
Annales Mathematicae Silesianae, 2023 In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover,
Bród Dorota +2 more
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On the ψ− Sheffer F− Polynomials and Their Degenerate Matrices
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this study, we systematically construct a novel framework within umbral calculus by integrating the structures of generalized F‐calculus and degenerate sequences. Utilizing Roman’s foundational approach to umbral calculus, we first introduce a new family of ψ − F− linear functionals and their corresponding ψ − F− differential operators on the ...
Semra Kuş, Smritijit Sen
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