Results 41 to 50 of about 1,789,377 (77)
Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix
Abstract and Applied Analysis, Volume 2015, Issue 1, 2015., 2015 The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed. Meanwhile, the exact determinants and inverse matrices of these special matrices are presented.
Yanpeng Zheng, Sugoog Shon, Zidong Wang
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Some Special Identities for Jacobsthal and Jacobsthal-Lucas Generalized Octonions
, 2022 Summary: We study on Jacobsthal and Jacobsthal-Lucas generalized octonions over the algebra \(\mathbb{O}(a, b, c)\) where \(a\), \(b\) and \(c\) are real numbers. We present Binet formulas for these types of octonions.
Mert, Tuğba +3 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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Total Graph Interpretation of the Numbers of the Fibonacci Type
Journal of Applied Mathematics, Volume 2015, Issue 1, 2015., 2015 We give a total graph interpretation of the numbers of the Fibonacci type. This graph interpretation relates to an edge colouring by monochromatic paths in graphs. We will show that it works for almost all numbers of the Fibonacci type. Moreover, we give the lower bound and the upper bound for the number of all (A1, 2A1)‐edge colourings in trees.
Urszula Bednarz +3 more
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On Jacobsthal and Jacobsthal-Lucas hybrid numbers [PDF]
, 2018 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 ...
Szynal-Liana, Anetta, Włoch, Iwona
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Journal of Mathematics, Volume 2024, Issue 1, 2024.Spinors can be expressed as Lie algebra of infinitesimal rotations. Spinors are also defined as elements of a vector space which carries a linear representation of the Clifford algebra typically. The motivation for this study is to define a new and particular sequence.
Tülay Erişir, Serkan Araci
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A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Given a vector space X, we investigate the solutions f:R→X of the linear functional equation of third order f(x) = pf(x − 1) + qf(x − 2) + rf(x − 3), which is strongly associated with a well‐known identity for the Fibonacci numbers. Moreover, we prove the Hyers‐Ulam stability of that equation.
Soon-Mo Jung +2 more
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Invertibility and Explicit Inverses of Circulant‐Type Matrices with k‐Fibonacci and k‐Lucas Numbers
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Circulant matrices have important applications in solving ordinary differential equations. In this paper, we consider circulant‐type matrices with the k‐Fibonacci and k‐Lucas numbers. We discuss the invertibility of these circulant matrices and present the explicit determinant and inverse matrix by constructing the transformation matrices, which ...
Zhaolin Jiang +3 more
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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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Applications and properties of Jacobsthal and Jacobsthal Lucas numbers [PDF]
, 2008 Bu çalışmada, Horadam tarafından tanımlanmış olan Jacobsthal ve Jacobsthal Lucas sayılarının verilen özelliklerine ek olarak bazı özellikler elde edildi. Jacobsthal sayılarının bölünebilme özellikleri verildi.
Köken, Fikri
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