Results 11 to 20 of about 616 (205)
A Context-Free Grammar Associated with Fibonacci and Lucas Sequences [PDF]
Journal of Mathematics, 2023 We introduce a context-free grammar G=s⟶s+d,d⟶s to generate Fibonacci and Lucas sequences. By applying the grammar G, we give a grammatical proof of the Binet formula.
Harold Ruilong Yang
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Equations with Solution in Terms of Fibonacci and Lucas Sequences [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 The main results characterize the equations (2.1) and (2.10) whose solutions are linear combinations with rational coefficients of at most two terms of classical Fibonacci and Lucas sequences.
Andreescu Titu, Andrica Dorin
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On Fibonacci and Lucas sequences modulo a prime and primality testing
Arab Journal of Mathematical Sciences, 2018 We prove two properties regarding the Fibonacci and Lucas Sequences modulo a prime and use these to generalize the well-known property p∣Fp−p5. We then discuss these results in the context of primality testing.
Dorin Andrica +2 more
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Elliptic Solutions of Dynamical Lucas Sequences [PDF]
Entropy, 2021 We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system
Michael J. Schlosser, Meesue Yoo
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Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences [PDF]
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,
Yasemin Taşyurdu +1 more
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Global warming and obesity: External heat exposure as a modulator of energy balance. [PDF]
FASEB BioadvCore body temperature regulation can significantly influence metabolic processes to maintain energy balance. For example, geographic and environmental factors (global warming) can affect obesity rates and can be tracked along latitudinal boundaries.
Muhammad I +3 more
europepmc +2 more sources
On some new results for the generalised Lucas sequences [PDF]
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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ON THE SEQUENCES RELATED TO FIBONACCI AND LUCAS NUMBERS [PDF]
Journal of the Korean Mathematical Society, 2005 The sequences \(\{U_n\}_{n\geq 0}\) and \(\{V_n\}_{n\geq 0}\) are introduced by recurrence relations: \[ \begin{aligned} U_n &= (q- 2)(U_{n-2}- U_{n-4},\;n\geq 4,\\ V_n &= (q-2) V_{n-2}- V_{n-4},\;n\geq 4\end{aligned} \] with initial conditions \(U_0= 0\), \(U_1= 1\), \(U_2= 1\), \(U_4= q- 1\), \(V_0= 2\), \(V_1= 1\), \(V_2= q-1\), where \(q\geq 5\) is
exaly +5 more sources
The eccentricity sequences of Fibonacci and Lucas cubes
Discrete Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michel Mollard
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High-resolution X-ray scanning with a diffuse Huffman-patterned probe to reduce radiation damage. [PDF]
J Synchrotron RadiatThis paper introduces high‐resolution imaging using diffuse probes, which allow for lower energy deposition per unit area per unit time, by encoding Huffman‐like patterns onto them, enabling a tighter impulse response. The approach, demonstrated in X‐ray imaging, involves using specially fabricated masks to shape the probe and recover sharp object ...
Aminzadeh A +5 more
europepmc +2 more sources