Results 41 to 50 of about 1,544,471 (165)
Sequences, Bent Functions and Jacobsthal Sums [PDF]
, 2010 The $p$-ary function $f(x)$ mapping $\mathrm{GF}(p^{4k})$ to $\mathrm{GF}(p)$ and given by $f(x)={\rm Tr}_{4k}\big(ax^d+bx^2\big)$ with $a,b\in\mathrm{GF}(p^{4k})$ and $d=p^{3k}+p^{2k}-p^k+1$ is studied with the respect to its exponential sum. In the case when either $a^{p^k(p^k+1)}\neq b^{p^k+1}$ or $a^2=b^d$ with $b\neq 0$, this sum is shown to be ...
Tor Helleseth, Alexander Kholosha
openaire +2 more sources
, 2022 summary:We study generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions. We present some properties of these quaternions and the relations between the generalized commutative Jacobsthal quaternions and ...
Bród, Dorota +2 more
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On ̄h-Jacobsthal and ̄h-Jacobsthal–Lucas sequences, and related quaternions
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2019 Abstract 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
Anatriello G., Vincenzi G.
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On the pulsating Padovan sequence [PDF]
Notes on Number Theory and Discrete MathematicsA novel kind of Padovan sequence is introduced, and precise formulas for the form of its members are given and proven. Furthermore, the pulsating Padovan sequence in its most general form is introduced and the obtained identity is proved.
Orhan Dişkaya +2 more
doaj +1 more source
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
wiley +1 more source
Uma visilização da sequê de Jacobsthal com o aporte do GeoGebra: A visualization of the Jacobsthal sequence with the contribution of GeoGebra [PDF]
, 2023 In Brazil, according to research, there are few works on the Jacobsthal sequence in undergraduate courses, and this motivated this work, given the intriguing particularity of its definition.
Carla Patrícia Souza Rodrigues Pinheiro +5 more
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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
wiley +1 more source
Non-Fisherian generalized Fibonacci numbers [PDF]
Notes on Number Theory and Discrete MathematicsUsing biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered ...
Thor Martinsen
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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
wiley +1 more source
A Generalization of Gaussian Balancing and Gaussian Balancing‐Lucas Numbers With Applications
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.In this paper, we study a generalization of Gaussian balancing and Gaussian Lucas‐balancing numbers, we find their generating functions, Binet formulas, related matrix representation, and many other properties. Also, we provide some applications in cryptography.
T. Al-Asoully +2 more
wiley +1 more source