Results 71 to 80 of about 975,787 (327)
A Note on Two Fundamental Recursive Sequences
Annales Mathematicae Silesianae, 2021 In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc.
Farhadian Reza, Jakimczuk Rafael
doaj +1 more source
FGF14 GAA Intronic Expansion in Unsolved Adult‐Onset Ataxia in the Care4Rare Canada Consortium
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Background and Objectives Spinocerebellar ataxias (SCA) represent a clinically and genetically heterogeneous group of progressive neurodegenerative diseases with prominent cerebellar atrophy. Recently, a novel pathogenic repeat expansion in intron 1 of FGF14 was identified, causing adult‐onset SCA (SCA27B). We aimed to determine the proportion
Alexanne Cuillerier +20 more
wiley +1 more source
A Lucas analogue of Eulerian numbers [PDF]
arXiv, 2023 The generalized Lucas numbers are polynomials in two variables with nonnegative integer coefficients. Lucas versions of some combinatorial numbers with known formulas in terms of quotient and products of nonnegative integers have been recently given by replacing the integers in those formulas with their corresponding Lucas analogues.
arxiv
On Pell, Pell-Lucas, and balancing numbers [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers. Moreover, we obtain the set of positive integer solutions of some specific Pell equations in terms of the
openaire +4 more sources
Digital Methods for the Fatigue Assessment of Engineering Steels
Advanced Engineering Materials, EarlyView.The use of engineering steels is often limited by their fatigue strength. In the sake of a faster product development, the fatigue behavior can be predicted by machine learning (ML). In this work, ML is applied on a heterogeneous database, covering a wide range of steel types.
Sascha Fliegener +7 more
wiley +1 more source
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
doaj +1 more source
q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
, 2019 We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding $q$-supercongruence. Similar $q$-supercongruences are established for binomial coefficients and the Ap\'{e}ry numbers, by means of a general criterion ...
Gorodetsky, Ofir
core +1 more source
Advanced Engineering Materials, EarlyView.A hybrid system for de‐icing made of gradient polymer coatings, deposited on aluminum coupled with an electromechanical system, is demonstrated as an effective and durable strategy for reducing drastically ice adhesion. The system is capable of detaching ice blocks over the coating in less than 1 s, regardless of the ice type and covered area ...
Gabriel Hernández Rodríguez +8 more
wiley +1 more source
Generalized Balancing and Balancing-Lucas numbers [PDF]
arXiv, 2022 In this paper, we introduce a generalization of Balancing and Balancing-Lucas numbers. We describe some of their properties also we give the related matrix representation and divisibility properties.
arxiv
Indagationes Mathematicae, 1993 AbstractIf (um)m∈N0 denotes a Lucas sequence, i.e. a binary integer recurrence sequence with initial values u0=0 and u1=1, then the equation kum=lun with k,l∈Z⧹{0} and max{m,n}≥5 can be valid only for finitely many Lucas sequences with coprime roots and finitely many indices m,n∈N, which can - both - be effectively bounded. This yields lower bounds for
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