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Geometric Aspects of Lucas Sequences, I

Tokyo Journal of Mathematics, 2020
From the text: ``We present a way of viewing Lucas sequences in the framework of group scheme theory. This enables us to treat the Lucas sequences from a geometric and functorial viewpoint, which was suggested by \textit{R. R. Laxton} [Duke Math. J. 36, 721--736 (1969; Zbl 0226.10010)] ] and by \textit{M. Aoki} and \textit{Y. Sakai} [Rocky Mt. J. Math.
openaire   +5 more sources

ON PERFECT POWERS IN LUCAS SEQUENCES [PDF]

International Journal of Number Theory, 2005
Let (un)n≥0be the binary recurrence sequence of integers given by u0= 0, u1= 1 and un+2= 2(un+1+ un). We show that the only positive perfect powers in this sequence are u1= 1 and u4= 16. We further discuss the problem of determining perfect powers in Lucas sequences in general.
Bugeaud, Yann, Luca, Florian, Mignotte, Maurice, Siksek, Samir   +3 more
openaire   +1 more source

A Concept of a Digital and Traceable Manufacturing Documentation Based on Formalized Process Description Applied on Composite Aircraft Moveable

Advanced Engineering Materials, EarlyView.
The documentation of component manufacture has become an essential part of today's production processes, especially for the analysis and optimization of production or component design with regard to structural performance, economic efficiency, and sustainability.
Björn Denker, Dominik Delisle, Christian Krombholz, Martin Rädel, Frank Dressel   +4 more
wiley   +1 more source

Shifted powers in Lucas–Lehmer sequences [PDF]

Research in Number Theory, 2019
We develop a general framework for finding all perfect powers in sequences derived by shifting non-degenerate quadratic Lucas-Lehmer binary recurrence sequences by a fixed integer. By combining this setup with bounds for linear forms in logarithms and results based upon the modularity of elliptic curves defined over totally real fields, we are able to ...
Bennett, Michael A., Patel, Vandita, Siksek, Samir   +2 more
openaire   +4 more sources

CO2 Reduction on Copper‐Nitrogen‐Doped Carbon Catalysts Tuned by Pulsed Potential Electrolysis: Effect of Pulse Potential

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, Janis Timoshenko, Andrea Martini, Hyo Sang Jeon, Eduardo Ortega, Martina Rüscher, Arno Bergmann, Aram Yoon, Uta Hejral, Antonia Herzog, Clara Rettenmaier, Felix T. Haase, Philipp Grosse, Beatriz Roldan Cuenya   +13 more
wiley   +1 more source

Self‐Assembling Peptide Hydrogels Support Stromal Vascular Fraction Viability to Promote In Vivo Nerve Regeneration

Advanced Healthcare Materials, EarlyView.
Stromal vascular fraction (SVF) may enhance nerve repair, especially when delivered in a self‐assembling peptide hydrogel (SAPH). In vitro, softer SAPH increased neuronal explant outgrowth and supported greater SVF viability and proliferation. In a rat sciatic defect, SVF in an optimized SAPH produced motor and sensory recovery equivalent to autograft ...
Liam A. McMorrow, Steffan Llewellyn, Jared McSweeney, Alessandro Faroni, Aline F. Miller, Alberto Saiani, Adam J. Reid   +6 more
wiley   +1 more source

Atomistic Mechanisms Triggered by Joule Heating Effects in Metallic Cu‐Bi Nanowires for Spintronics

Advanced Materials, EarlyView.
Bi doped metallic Cu nanowires are promising for spintronics thanks to the stabilization of a giant spin Hall effect. However, heat resulting from current injection forces Bi to leave solution, forcing segregation into monoatomic decorations which evolve into coherent crystalline aggregates.
Alejandra Guedeja‐Marrón, Juan Ignacio Beltrán, Matilde Saura‐Múzquiz, Paolo Perna, M. Carmen Muñoz, Lucas Pérez, Maria Varela   +6 more
wiley   +1 more source

Assembling a True “Olympic Gel” From over 16 000 Combinatorial DNA Rings

Advanced Materials, EarlyView.
Olympic gels are an elusive class of soft matter, consisting of molecular networks held together purely by mechanically interlocked rings. Their topological structure promises unique properties and functions, but their synthesis has proven notoriously difficult.
Sarah K. Speed, Yu‐Hsuan Peng, Azra Atabay, Krishna Gupta, Toni Müller, Carolin Fischer, Ilka M. Hermes, Jens‐Uwe Sommer, Michael Lang, Elisha Krieg   +9 more
wiley   +1 more source

Copper ratio obtained by generalizing the Fibonacci sequence

AIP Advances
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 also define copper Lucas sequences, and ...
Engin Özkan, Hakan Akkuş
doaj   +1 more source

A Study on the k-Mersenne and k-Mersenne-Lucas Sequences

Universal Journal of Mathematics and Applications
In this study, we examine an application of $k-$Mersenne and $k-$Mersenne-Lucas sequences. We present the Catalan transforms of these sequences and give the properties of these Catalan transforms. Catalan transforms of $k-$Mersenne and $k-$Mersenne-Lucas
Mine Uysal, Hakan Akkuş, Bayram Şen, Engin Özkan   +3 more
doaj   +1 more source