Results 31 to 40 of about 1,789,377 (77)
On complex gaussian jacobsthal and jacobsthal-lucas quaternions
Cumhuriyet Science Journal, 2020 The main aim of this work is to introduce the complex Gaussian Jacobsthal and Jacobsthal-Lucas quaternions and investigate their structures. We obtain the recurrence relations, Binet formulas and generating functions for these quaternions.
Hasan Arslan
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On Jacobsthal and Jacobsthal-Lucas Hybrid Numbers
Annales Mathematicae Silesianae, 2019 The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper we consider special kinds of hybrid numbers, namely the Jacobsthal and the Jacobsthal-Lucas hybrid numbers and we give some their properties.
Szynal-Liana Anetta, Włoch Iwona
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On the Norms of r−Hankel and r−Toeplitz Matrices
Mathematical Problems in Engineering, Volume 2019, Issue 1, 2019., 2019 In this paper, using the properties of r−Hankel and r−Toeplitz matrices, combining the properties of exponential form, we shall study the spectral norms of r−Hankel and r–Toeplitz matrices involving exponential form e(x).
Baijuan Shi, Fazal M. Mahomed
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Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials
Discrete Dynamics in Nature and Society, 2012 We define the incomplete bivariate Fibonacci and Lucas 𝑝-polynomials. In the case 𝑥=1, 𝑦=1, we obtain the incomplete Fibonacci and Lucas 𝑝-numbers. If 𝑥=2, 𝑦=1, we have the incomplete Pell and Pell-Lucas 𝑝-numbers.
Dursun Tasci +2 more
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Mersenne-Horadam identities using generating functions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
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On Power Sums Involving Lucas Functions Sequences
Mathematical Problems in Engineering, Volume 2017, Issue 1, 2017., 2017 We present some general formulas related to sum of powers, also with alternating sign, involving Lucas functions sequences. In particular, our formulas give a synthesis of various identities involving sum of powers of well‐known polynomial sequences such as Fibonacci, Lucas, Pell, Jacobsthal, and Chebyshev polynomials.
Stefano Barbero, Fazal M. Mahomed
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Explicit Form of the Inverse Matrices of Tribonacci Circulant Type Matrices
Abstract and Applied Analysis, Volume 2015, Issue 1, 2015., 2015 It is a hot topic that circulant type matrices are applied to networks engineering. The determinants and inverses of Tribonacci circulant type matrices are discussed in the paper. Firstly, Tribonacci circulant type matrices are defined. In addition, we show the invertibility of Tribonacci circulant matrix and present the determinant and the inverse ...
Li Liu, Zhaolin Jiang, Zidong Wang
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On some properties of Jacobsthal and Jacobsthal-Lucas numbers
Journal of Innovative Applied Mathematics and Computational SciencesIn this study, we first develop some helpful generating functions for the Jacobsthal and Jacobsthal-Lucas numbers. We have discussed generating functions for $\mathbf{J}_{2n}$ and $\mathbf{j}_{2n}$ with just even and odd terms and generating functions ...
Mirwais Mansoor kakar
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VanderLaan Circulant Type Matrices
Abstract and Applied Analysis, Volume 2015, Issue 1, 2015., 2015 Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and g‐circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The
Hongyan Pan, Zhaolin Jiang, Shen Yin
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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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