Results 51 to 60 of about 1,467 (207)
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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Mind the Gap: Linking Refactorings and Code Smells in Elixir
Journal of Software: Evolution and Process, Volume 38, Issue 5, May 2026.ABSTRACT Elixir is a functional programming language increasingly used in the industry to develop scalable and fault‐tolerant concurrent systems more easily and with fewer computational resources. In previous studies, we cataloged 35 code smells and 82 refactorings tailored for this language, validating them with over 300 experienced developers ...
Lucas Vegi, Marco Túlio Valente
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Mathematika, Volume 72, Issue 2, April 2026.Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
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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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Device‐Independent Quantum Key Distribution: Protocols, Quantum Games and Security
IET Quantum Communication, Volume 7, Issue 1, January/December 2026.Device‐independent quantum key distribution (DIQKD) removes the need to trust internal device behaviour by certifying security through Bell‐inequality violations, thereby closing practical loopholes in conventional QKD. This paper systematically reviews DIQKD foundations (Bell tests and security definitions), protocol frameworks (CHSH‐based and ...
Syed M. Arslan +3 more
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Dual Proximal Groups Concisely Representing Complex Hosoya Triangles
Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.This paper introduces dual proximal groups (DPGs) that provide concise representation of complex Hosoya triangles (CHTs). An application is given in terms of the DPG representation of collections of Hosoya‐Hilbert circular triangles on modulated motion waveforms in sequences of video frames. MSC2020 Classification: 11B39,54E05,57S25.
Kübra Gül +3 more
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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
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On Chebyshev Polynomials, Fibonacci Polynomials, and Their Derivatives
Journal of Applied Mathematics, 2014 We study the relationship of the Chebyshev polynomials, Fibonacci polynomials, and their rth derivatives. We get the formulas for the rth derivatives of Chebyshev polynomials being represented by Chebyshev polynomials and Fibonacci polynomials.
Yang Li
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On the Two‐Term Zeckendorf Representations of the Padovan and Perrin Sequences
Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.In this paper, we completely solve the Diophantine equations Pm = Fn + Fk and Em = Fn + Fk under the condition n ≥ k + 2 ≥ 4, where Pm is the m‐th Padovan number, Em is the m‐th Perrin number, and Fk is the k‐th Fibonacci number. This work determines all terms of the Padovan and Perrin sequences that admit a unique two‐term Zeckendorf representation ...
Awaou Lare Ousseni +4 more
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Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients
Universal Journal of Mathematics and Applications, 2023 In this paper, we introduce hybrid numbers with Fibonacci and Lucas hybrid number coefficients. We give the Binet formulas, generating functions, and exponential generating functions for these numbers. Then we define an associate matrix for these numbers.
Emrah Polatlı
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