Copper ratio obtained by generalizing the Fibonacci sequence
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DOI: 10.1063/5.0207147
Abstract: In this study, we define a new generalization of the Fibonacci sequence that gives the copper ratio, and we will call it the copper Fibonacci sequence. In addition, inspired by the copper Fibonacci definition, we… read more here.
Keywords: copper fibonacci; lucas; copper; sequence ... See more keywords
Leaky roots and stable Gauss-Lucas theorems
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DOI: 10.1080/17476933.2019.1571051
Abstract: ABSTRACT Let be a polynomial. The Gauss-Lucas theorem states that its critical points, , are contained in the convex hull of its roots. In a recent quantitative version, Totik shows that if almost all roots… read more here.
Keywords: gauss lucas; stable gauss; roots stable; leaky roots ... See more keywords
On Diophantine equations involving Lucas sequences
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DOI: 10.1515/math-2019-0073
Abstract: Abstract 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). read more here.
Keywords: involving lucas; lucas sequences; lucas; diophantine equations ... See more keywords
Fibonacci Cartan and Lucas Cartan numbers
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DOI: 10.1515/math-2025-0204
Abstract: Abstract This study introduces Fibonacci Cartan and Lucas Cartan numbers, extending the classical Fibonacci and Lucas sequences into the framework of Cartan numbers. By leveraging algebraic and geometric properties, we establish recurrence relations, generating functions,… read more here.
Keywords: lucas cartan; cartan numbers; lucas; cartan lucas ... See more keywords
Lung Cancer in Non-smokers in Czech Republic: Data from LUCAS Lung Cancer Clinical Registry
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DOI: 10.21873/anticanres.15368
Abstract: Background/Aim: LUCAS is a clinical lung cancer registry (ClinicalTrials.gov identifier is NCT04228237), prospectively collecting data from newly diagnosed lung cancer patients in seven pneumooncology centers in the Czech Republic, since June 1, 2018. The aim… read more here.
Keywords: non smokers; lung; lung cancer; lucas ... See more keywords
Some results on dual third-order Jacobsthal quaternions
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DOI: 10.2298/fil1907865c
Abstract: Dual Fibonacci and dual Lucas numbers are defined with dual Fibonacci and Lucas quaternions in Nurkan and G?ven [14]. In this study, we define the dual third-order Jacobsthal quaternion and the dual third-order Jacobsthal-Lucas quaternion.… read more here.
Keywords: dual third; lucas; third order; order jacobsthal ... See more keywords
Novel Classes on Generating Functions of the Products of (p,q)-Modified Pell Numbers with Several Bivariate Polynomials
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DOI: 10.3390/math12182902
Abstract: In this paper, using the symmetrizing operator δe1e22−l, we derive new generating functions of the products of p,q-modified Pell numbers with various bivariate polynomials, including Mersenne and Mersenne Lucas polynomials, Fibonacci and Lucas polynomials, bivariate… read more here.
Keywords: lucas polynomials; lucas; functions products; pell ... See more keywords
Pythagorean triples containing generalized Lucas numbers
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DOI: 10.3906/mat-1702-102
Abstract: Let $P$ and $Q$ be nonzero integers. Generalized Fibonacci and Lucas sequences are defined as follows: $U_{0}(P,Q)=0,U_{1}(P,Q)=1,$ and $ U_{n+1}(P,Q)=PU_{n}(P,Q)+QU_{n-1}(P,Q)$ for $n\geq 1$ and $ V_{0}(P,Q)=2,V_{1}(P,Q)=P,$ and $V_{n+1}(P,Q)=PV_{n}(P,Q)+QV_{n-1}(P,Q)$ for $n\geq 1,$ respectively. In this paper,… read more here.
Keywords: triples containing; pythagorean triples; generalized lucas; lucas numbers ... See more keywords
Repdigits as sums of two generalized Lucas numbers
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DOI: 10.3906/mat-2011-59
Abstract: A generalization of the well–known Lucas sequence is the k -Lucas sequence with some fixed integer k ≥ 2 . The first k terms of this sequence are 0, . . . , 0, 2,… read more here.
Keywords: generalized lucas; sums two; lucas; repdigits sums ... See more keywords
Genealogias de um mundo decadente: a ascensão e queda dos impérios de Thomas Sutpen e Lucas Procópio
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DOI: 10.5935/2179-0027.20180006
Abstract: Este artigo visa a investigar o valor simbolico atribuido a figura paterna expressa nos romances Absalao, Absalao! (1936), de William Faulkner, e Opera dos mortos (1967) e Lucas Procopio (2002), de Autran Dourado. Procuraremos enfatizar… read more here.
Keywords: decadente ascens; thomas sutpen; genealogias mundo; mundo decadente ... See more keywords