Results 41 to 50 of about 183 (115)

Magic numbers in the music of Sofia Gubaidulina [PDF]

Muzikologija, 2002
Sofia Gubaidulina's compositions are characterized by a special kind of symbolism and constructivism both based on numbers, i.e. mathematical proportions. In almost all her works so-called numerical plots can be detected. The proportions of the Fibonacci
Tsenova Valeria
doaj   +1 more source

Design of a Tunable Multi-Band Transmitting and Band-Stop Photonic Crystal IR Filter Utilizing Lucas Numbers

Mathematics
In this study, a novel aperiodic photonic crystal (PC) structure is designed using the golden ratio-based Lucas sequence, and its infrared (IR) transmission characteristics are investigated.
Çiğdem Seçkin Gürel, Berker Yalçın
doaj   +1 more source

On a unified approach to homogeneous second-order linear difference equations with constant coefficients and some applications

Special Matrices
In this article, we establish a new closed formula for the solution of homogeneous second-order linear difference equations with constant coefficients by using matrix theory.
Kaddoura Issam, Mourad Bassam
doaj   +1 more source

THE SQUARE TERMS IN GENERALIZED LUCAS SEQUENCES

Mathematika, 2013
Summary: Let \(P\) and \(Q\) be non-zero integers. The generalized Fibonacci sequence \(\{U_n\} \) and Lucas sequence \(\{V_n\}\) are defined by \(U_0 = 0\), \(U_1 = 1\) and \(U_{n+1} = PU_n + QU_{n-1}\) for \(n\geq 1\) and \(V_0 = 2\), \(V_1 = P\) and \(V_{n+1} = PV_n + QV_{n-1} \) for \(n\geq 1\), respectively.
Sakarya Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü, Keskin, Refik, Keskin, Refik   +2 more
openaire   +4 more sources

On the emergence of the Quanta Prime sequence

Arab Journal of Basic and Applied Sciences
This paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications.
Moustafa Ibrahim
doaj   +1 more source

Geometric Aspects of Lucas Sequences, I

Tokyo Journal of Mathematics, 2020
From the text: ``We present a way of viewing Lucas sequences in the framework of group scheme theory. This enables us to treat the Lucas sequences from a geometric and functorial viewpoint, which was suggested by \textit{R. R. Laxton} [Duke Math. J. 36, 721--736 (1969; Zbl 0226.10010)] ] and by \textit{M. Aoki} and \textit{Y. Sakai} [Rocky Mt. J. Math.
openaire   +5 more sources

On the Lucas property of linear recurrent sequences [PDF]

International Journal of Number Theory, 2016
Let [Formula: see text] be an arithmetic function. [Formula: see text] has Lucas property if for any prime [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] In this paper, we discuss the Lucas property of Fibonacci sequences and Lucas numbers. Meanwhile, we find some other interesting results.
Zhong, Hao, Cai, Tianxin
openaire   +2 more sources

Pell–Lucas diffractive lenses for trifocal multi-trap optical tweezers

JPhys Photonics
In this work, we introduce a new family of trifocal diffractive lenses based on the Pell–Lucas number sequence. Two phase configurations are considered: binary-phase and kinoform-type.
Arlen B Pérez-Hernández, Juan C Castro-Palacio, Emilio Sánchez-Ortiga, Walter D Furlan, Juan A Monsoriu, Francisco M Muñoz-Pérez   +5 more
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Horadam–Lucas Cubes

Axioms
In this paper, we introduce a novel class of graphs referred to as the Horadam–Lucas cubes. This class extends the concept of Lucas cubes and retains numerous desirable properties associated with them.
Elif Tan, Luka Podrug, Vesna Iršič Chenoweth   +2 more
doaj   +1 more source

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
doaj   +1 more source