Results 71 to 80 of about 7,865 (225)

Symmetric and generating functions of generalized (p,q)-numbers

Kuwait Journal of Science, 2021
In this paper, we first define new generalization for (p,q)-numbers. Considering these sequence, we give Binet's formulas and generating functions of (p,q)-Fibonacci numbers, (p,q)-Lucas numbers, (p,q)-Pell numbers, (p,q)-Pell Lucas numbers, (p,q ...
Nabiha Saba, Ali Boussayoud, Abdelhamid Abderrezzak   +2 more
doaj   +1 more source

Properties of the Ammann–Beenker Tiling and its Square Periodic Approximants

Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.
This review article is intended for those seeking to understand the geometrical properties of one well‐known two‐dimensional quasiperiodic tiling, namely the Ammann‐Beenker tiling. This eight‐fold symmetric tiling has been a preferred starting point for studies of electronic properties of quasicrystals, due to its relatively simple structure as ...
Anuradha Jagannathan, Michel Duneau
wiley   +1 more source

Pure Point Diffraction and Almost Periodicity

Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.
Abstract This article deals with pure point diffraction and its connection to various notions of almost periodicity. We explain why the Fibonacci chain does not fit into the classical concept of Bohr almost periodicity and how it fits into the classes of mean, Besicovitch and Weyl almost periodic point sets.
Daniel Lenz, Timo Spindeler, Nicolae Strungaru   +2 more
wiley   +1 more source

Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials

Mathematics, 2018
This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials.
Taekyun Kim, Dae San Kim, Jongkyum Kwon, Dmitry V. Dolgy   +3 more
doaj   +1 more source

Substitutions and their Generalisations

Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.
Abstract Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and potentials.
Neil Mañibo
wiley   +1 more source

Perfect powers in elliptic divisibility sequences

Bulletin of the London Mathematical Society, Volume 56, Issue 11, Page 3331-3345, November 2024.
Abstract Let E/Q$E/\mathbb {Q}$ be an elliptic curve given by an integral Weierstrass equation. Let P∈E(Q)$P \in E(\mathbb {Q})$ be a point of infinite order, and let (Bn)n⩾1$(B_n)_{n\geqslant 1}$ be the elliptic divisibility sequence generated by P$P$. This paper is concerned with a question posed in 2007 by Everest, Reynolds and Stevens: does (Bn)n⩾1$
Maryam Nowroozi, Samir Siksek
wiley   +1 more source

Strong divisibility sequences and sieve methods

Mathematika, Volume 70, Issue 4, October 2024.
Abstract We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence that only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility sequences, discussing the limitations of our methods.
Tim Browning, Matteo Verzobio
wiley   +1 more source

Some identities of the generalized bi-periodic Fibonacci and Lucas polynomials

AIMS Mathematics
In this paper, we considered the generalized bi-periodic Fibonacci polynomials, and obtained some identities related to generalized bi-periodic Fibonacci polynomials using the matrix theory.
Tingting Du, Zhengang Wu
doaj   +1 more source

Asymptotic behavior of Laplacian eigenvalues of subspace inclusion graphs

Journal of the London Mathematical Society, Volume 110, Issue 3, September 2024.
Abstract Let Fln,q$\text{Fl}_{n,q}$ be the simplicial complex whose vertices are the nontrivial subspaces of Fqn$\mathbb {F}_q^n$ and whose simplices correspond to families of subspaces forming a flag. Let Δk+(Fln,q)$\Delta ^{+}_k(\text{Fl}_{n,q})$ be the k$k$‐dimensional weighted upper Laplacian on Fln,q$ \text{Fl}_{n,q}$.
Alan Lew
wiley   +1 more source