Results 21 to 30 of about 884 (133)
Binomial transform of the bivariate Fibonacci quaternion polynomials and its properties [PDF]
Notes on Number Theory and Discrete MathematicsThe primary aim of this work is to deal with binomial transforms of bivariate Fibonacci quaternion polynomial sequence. The binomial sequence of the bivariate Fibonacci quaternion polynomial is found, and then results are obtained for the recurrence ...
Faruk Kaplan, Arzu Özkoç Öztürk
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The complex-type Pell p-numbers [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we define the complex-type Pell p-numbers and give the generating matrix of these defined numbers. Then, we produce the combinatorial representation, the generating function, the exponential representation and the sums of the complex-type ...
Yeşim Aküzüm +2 more
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A Context-Free Grammar Associated with Fibonacci and Lucas Sequences
Journal of Mathematics, 2023 We introduce a context-free grammar G=s⟶s+d,d⟶s to generate Fibonacci and Lucas sequences. By applying the grammar G, we give a grammatical proof of the Binet formula.
Harold Ruilong Yang
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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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On fourth-order jacobsthal quaternions
Journal of Mathematical Sciences and Modelling, 2018 In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions. In particular, we are interested in the generating function, Binet formula,
Gamaliel Cerda-morales
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On a generalization of the Gadovan numbers [PDF]
Mathematica MoravicaIn this paper, we define (k, l)-Gadovan numbers. We give the Binet-like formula, the generating functions, the exponential generating function of the (k, l)-Gadovan numbers. Also, we derive Cassinilike identity, Catalan-like identity, Vajda-like identity,
Özkan Engın, Eser Engın, Uysal Mıne
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A quantum calculus framework for Gaussian Fibonacci and Gaussian Lucas quaternion numbers [PDF]
Notes on Number Theory and Discrete MathematicsIn order to investigate the relationship between Gaussian Fibonacci numbers and quantum numbers and to develop both a deeper theoretical understanding in this study, q-Gaussian Fibonacci, q-Gaussian Lucas quaternions and polynomials are taken with ...
Bahar Kuloğlu
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On Some Properties of Bihyperbolic Numbers of The Lucas Type
Communications in Advanced Mathematical Sciences, 2023 To date, many authors in the literature have worked on special arrays in various computational systems. In this article, Lucas type bihyperbolic numbers were defined and their algebraic properties were examined. Bihyperbolic Lucas numbers were studied by
Fügen Torunbalcı Aydın
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Generalized Bronze Leonardo sequence [PDF]
Notes on Number Theory and Discrete MathematicsIn this study, we define the Bronze Leonardo, Bronze Leonardo–Lucas, and Modified Bronze Leonardo sequences, and some terms of these sequences are given. Then, we give special summation formulas, special generating functions, etc.
Engin Özkan, Hakan Akkuş
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Cancer Medicine, Volume 15, Issue 4, April 2026.ABSTRACT Disorders of lipid metabolism contribute to the occurrence and progression of hematological malignancies, including chronic lymp hocytic leukemia (CLL). The objective of this study was to investigate the association between serum lipid levels and prognosis in patients with CLL.
Weiran Lv +9 more
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