Results 21 to 30 of about 137 (85)
On (k,p)-Fibonacci numbers and matrices [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, some relations between the powers of any matrices X satisfying the equation Xᵏ-pXᵏ⁻¹-(p-1)X-I=0 and (k,p)-Fibonacci numbers are established with ...
Sinan Karakaya +2 more
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Counting the sum of cubes for Lucas and Gibonacci numbers
Science and Technology Indonesia, 2019 Lucas and Gibonacci numbers are two sequences of numbers derived from a welknown numbers, Fibonacci numbers. The difference between Lucas and Fibonacci numbers only lies on the first and second elements.
Wamiliana Wamiliana +2 more
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On Generalized Jacobsthal and Jacobsthal–Lucas Numbers
Annales Mathematicae Silesianae, 2022 Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers.
Bród Dorota, Michalski Adrian
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On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers
Karpatsʹkì Matematičnì Publìkacìï, 2021 The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
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Some new identities for the sum of generalized Fibonacci numbers and generalized Lucas numbers [PDF]
Mathematica MoravicaLet UN and Vn denote the n-th generalized Fibonacci and generalized Lucas numbers, respectively. In this paper, we calculate the n-th powers of some square matrices by diagonalizing them with their eigenvalues and eigenvectors.
Lıman Gülsüm +2 more
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Using Generalized Fibonacci Sequences for Solving the One-Dimensional LQR Problem and its Discrete-Time Riccati Equation [PDF]
Modeling, Identification and Control, 2010 In this article we develop a method of solving general one-dimensional Linear Quadratic Regulator (LQR) problems in optimal control theory, using a generalized form of Fibonacci numbers.
Per-Ole Nyman +2 more
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Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,
Yasemin Taşyurdu +1 more
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Scalable Computation of Topological Abstractions for Scalar Data
Computer Graphics Forum, EarlyView.Abstract Topological data analysis has become an important tool for large scale scalar data analysis and visualization, efficiently extracting the inherent structure and features of interest of the data. However, with growing dataset sizes and complexity, it is increasingly becoming infeasible to compute topological abstractions of interest in serial ...
M. Will +6 more
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Radial Tiny Golden Angle UTE (tyGA‐UTE) for Cardiac MRI in the Small Animal Model
NMR in Biomedicine, Volume 39, Issue 11, November 2026.This study validates an 11.7‐T ultra‐high‐field tyGA‐UTE cardiac MRI workflow for murine models, featuring single‐acquisition dual reconstructions for real‐time visualization and quantitative functional assessment. It delivers performance equivalent to standard techniques, excellent reproducibility, and higher efficiency by eliminating repeated scans ...
Hao Li +4 more
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Exploring Generalized $2^k$-Fibonacci Sequence: A New Family of the Fibonacci Sequence
Communications in Advanced Mathematical SciencesThe focus of this paper is to study the $2^k$–Fibonacci sequence, which is defined for all integers $2^k$, and its connections with both the Fibonacci and the Fibonacci-Lucas sequences.
Elis Gardel Costa Mesquista +2 more
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