Results 91 to 100 of about 145,594 (304)
On Diophantine equations involving Lucas sequences
Open Mathematics, 2019 In this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequence and R, P and Q are polynomials (under weak assumptions).
Trojovský Pavel
doaj +1 more source
On Lucas Sequences Computation
Int'l J. of Communications, Network and System Sciences, 2010 This paper introduces an improvement to a currently published algorithm to compute both Lucas "sister" sequences Vk and Uk. The proposed algorithm uses Lucas sequence properties to improve the running time by about 20% over the algorithm published in [1].
openaire +2 more sources
Machine Learning‐Enabled Drug‐Induced Toxicity Prediction
Advanced Science, EarlyView.Unexpected toxicity accounts for 30% of drug development failures. This review highlights ML innovations in predicting drug‐induced toxicity, emphasizing comparative analyses, interpretable algorithms, and multi‐source data integration. It categorizes toxicity types, summarizes ML models, and organizes key databases, offering strategies to address ...
Changsen Bai +5 more
wiley +1 more source
A note on the bi-periodic Fibonacci and Lucas matrix sequences [PDF]
Applied Mathematics and Computation 320 (2018): 400-406, 2016 In this paper, we introduce the bi-periodic Lucas matrix sequence and present some fundamental properties of this generalized matrix sequence. Moreover, we investigate the important relationships between the bi-periodic Fibonacci and Lucas matrix sequences. We express that some behaviours of bi-periodic Lucas numbers also can be obtained by considering
arxiv
Advanced Science, EarlyView.In this work, the synthesis of carbon nanotubes (CNTs) supported sub‐5 nm dominant intermetallic RuCu, RuRh, and RuPd NPs are succeeded by the proposed method of nanosecond laser ultrafast confined alloying (LUCA), which is featured by its unique ultrafast heating and cooling rates and high stability for long‐term alkaline HER catalysis application ...
Taiping Hu +9 more
wiley +1 more source
A Matrix Approach for Divisibility Properties of the Generalized Fibonacci Sequence
Discrete Dynamics in Nature and Society, 2013 We give divisibility properties of the generalized Fibonacci sequence by matrix methods. We also present new recursive identities for the generalized Fibonacci and Lucas sequences.
Aynur Yalçiner
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Powers in Lucas Sequences via Galois Representations [PDF]
arXiv, 2013 Let $u_n$ be a nondegenerate Lucas sequence. We generalize the results of Bugeaud, Mignotte, and Siksek, 2006 to give a systematic approach towards the problem of determining all perfect powers in any particular Lucas sequence. We then prove a general bound on admissible prime powers in a Lucas sequence assuming the Frey-Mazur conjecture on isomorphic ...
arxiv
The power sum of balancing polynomials and their divisible properties
AIMS MathematicsIn recent years, many scholars have studied the division properties of polynomials and sequence power sums. In this paper, we use Girard-Waring formula and combinatorial method to study the power sum problem of balancing polynomials and Lucas-balancing ...
Hong Kang
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On members of Lucas sequences which are products of factorials [PDF]
arXiv, 2019 Here, we show that if $\{U_n\}_{n\ge 0}$ is a Lucas sequence, then the largest $n$ such that $|U_n|=m_1!m_2!\cdots m_k!$ with $1
arxiv
A Privacy‐Preserving System for Confidential Carpooling Services Using Homomorphic Encryption
Advanced Intelligent Systems, EarlyView.This research presents a homomorphic encryption‐based solution to enhance privacy in carpooling without compromising functionality. Rigorous experiments confirm its robustness, accuracy, and efficiency in securely matching users while preserving confidentiality.
David Palma +3 more
wiley +1 more source