Results 51 to 60 of about 248,402 (331)
Complete solutions of the simultaneous Pell equations $ (a^2+1)y^2-x^2 = y^2-bz^2 = 1 $
AIMS Mathematics, 2021 In this paper, we consider the simultaneous Pell equations $ (a^2+1)y^2-x^2 = y^2-bz^2 = 1 $ where $ a > 0 $ is an integer and $ b > 1 $ is squarefree and has at most three prime divisors.
Changsheng Luo, Jiagui Luo
doaj +1 more source
On the discriminator of Lucas sequences. II
, 2023 25 pages, 7 ...
Ferrari, ., Luca, F., Moree, P.
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Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective The optimal treatment for neurosarcoidosis myelitis is uncertain. We characterize incident neurosarcoidosis myelitis and assess treatment response by MRI and clinical scales. Methods Incident probable or definite neurosarcoidosis myelitis in adults was retrospectively identified from 13 academic medical centers.
Giovanna S. Manzano +39 more
wiley +1 more source
Complete solutions of the simultaneous Pell's equations $ (a^2+2)x^2-y^2 = 2 $ and $ x^2-bz^2 = 1 $
AIMS Mathematics, 2023 In this paper, we consider the simultaneous Pell equations $ (a^2+2)x^2-y^2 = 2 $ and $ x^2-bz^2 = 1 $ where $ a $ is a positive integer and $ b > 1 $ is squarefree and has at most three prime divisors.
Cencen Dou, Jiagui Luo
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Versatile Cell Penetrating Peptide for Multimodal CRISPR Gene Editing in Primary Stem Cells
Advanced Functional Materials, EarlyView.CRISPR machinery in diverse molecular formats (DNA, RNA, and ribonucleic protein) is complexed into nanoparticles with the cell‐friendly arginine‐alanine‐leucine‐alanine (RALA) cell‐penetrating peptide. Nanoparticles are delivered to primary mesenchymal stem cells ex vivo or locally in vivo to facilitate multimodal CRISPR gene editing. This RALA‐CRISPR
Joshua P. Graham +9 more
wiley +1 more source
Advanced Functional Materials, EarlyView.In operando neutron diffraction reveals the real‐time structural evolution of O3‐type NaxNi1/3Mn1/3Fe1/3O2 in commercial sodium‐ion batteries that is coupled with electrochemical and tomography data. The study establishes a direct link between current‐dependent phase transitions, lattice kinetics, and electrochemical behavior, offering mechanistic ...
B. D. K. K. Thilakarathna +4 more
wiley +1 more source
On the Lucas property of linear recurrent sequences [PDF]
International Journal of Number Theory, 2016 Let [Formula: see text] be an arithmetic function. [Formula: see text] has Lucas property if for any prime [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] In this paper, we discuss the Lucas property of Fibonacci sequences and Lucas numbers. Meanwhile, we find some other interesting results.
Tianxin Cai, Hao Zhong
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Exact divisibility by powers of the integers in the Lucas sequences of the first and second kinds
AIMS Mathematics, 2021 Lucas sequences of the first and second kinds are, respectively, the integer sequences $ (U_n)_{n\geq0} $ and $ (V_n)_{n\geq0} $ depending on parameters $ a, b\in\mathbb{Z} $ and defined by the recurrence relations $ U_0 = 0 $, $ U_1 = 1 $, and $ U_n ...
Kritkhajohn Onphaeng +1 more
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Lucas sequence, its properties and generalisation [PDF]
, 2013 Fibonacci AND Lucas sequences are most interesting among recurrent sequences.
Barik, Biswajit
core
Advanced Functional Materials, EarlyView.This study demonstrates that pulsed potential electrolysis significantly improves CO2 reduction performance on copper‐nitrogen doped carbon electrodes. The formation of cationic copper sites and metallic clusters as a function of applied intermittent potential leads to notable selectivity changes compared to potentiostatic reduction.
Dorottya Hursán +13 more
wiley +1 more source