Results 31 to 40 of about 92,778 (311)
On Bicomplex Jacobsthal-Lucas Numbers
Journal of Mathematical Sciences and Modelling, 2020 In this study we introduced a sequence of bicomplex numbers whose coefficients are chosen from the sequence of Jacobsthal-Lucas numbers. We also present some identities about the known some fundamental identities such as the Cassini's, Catalan's and Vajda's identities.
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The Third Order Jacobsthal Octonions: Some Combinatorial Properties
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018 Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many di erent ways.
Cerda-Morales Gamaliel
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On some series involving the binomial coefficients $binom{3n}{n}$ [PDF]
Notes on Number Theory and Discrete MathematicsUsing a simple transformation, we obtain much simpler forms for some series involving binomial coefficients $binom{3n}{n}$ derived by Necdet Batir. New evaluations are given and connections with Fibonacci numbers and the golden ratio are established ...
Kunle Adegoke +2 more
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On some new results for the generalised Lucas sequences
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits ...
Andrica Dorin +2 more
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Repdigits as difference of two Fibonacci or Lucas numbers
Математичні Студії, 2021 In the present study we investigate all repdigits which are expressed as a difference of two Fibonacci or Lucas numbers. We show that if $F_{n}-F_{m}$ is a repdigit, where $F_{n}$ denotes the $n$-th Fibonacci number, then $(n,m)\in \{(7,3),(9,1),(9,2 ...
P. Ray, K. Bhoi
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Congruences for $q$-Lucas Numbers
The Electronic Journal of Combinatorics, 2013 For $\alpha,\beta,\gamma,\delta\in{\mathbb Z}$ and ${\rm\nu}=(\alpha,\beta,\gamma,\delta)$, the $q$-Fibonacci numbers are given by$$F_0^{{\rm\nu}}(q)=0,\ F_1^{{\rm\nu}}(q)=1\text{ and }F_{n+1}^{{\rm\nu}}(q)=q^{\alpha n-\beta}F_{n}^{{\rm\nu}}(q)+q^{\gamma n-\delta}F_{n-1}^{{\rm\nu}}(q)\text{ for }n\geq 1.$$And define the $q$-Lucas number $L_{n}^{{\rm\nu}
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Impact of Metastatic Patterns on Survival and Response to Therapy in Neuroblastoma
Pediatric Blood &Cancer, EarlyView.ABSTRACT Background While the presence of metastases in neuroblastoma (NB) is a well‐established prognostic factor, the clinical significance of dissemination patterns and tumour burden and their impact on response and survival remains poorly understood.
Mariona Morell‐Daniel +15 more
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On the Intersections of Fibonacci, Pell, and Lucas Numbers [PDF]
Integers, 2011 AbstractWe describe how to compute the intersection of two Lucas sequences of the ...
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Modelling stem cell differentiation related processes—A practical overview for biologists
FEBS Letters, EarlyView.Stem cell differentiation is complex and difficult to control experimentally. This review introduces suitable computational modelling approaches that can support stem cell research, from mechanistic ODE and abstract models to multiscale and deep learning methods.
Ricco Zeegelaar +4 more
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Molecular Oncology, EarlyView.Breast cancer remains a major cause of cancer death in women, frequently developing endocrine therapy resistance. This study demonstrates that upregulated p21‐activated kinase 1 (PAK1) activity drives resistance to tamoxifen and long‐term estrogen deprivation in ER+ breast cancer models.
Luisa Schwarzmüller +10 more
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