Results 81 to 90 of about 7,705 (228)

The k‐Augmented Pascal Matrix and Its Properties

Journal of Mathematics, Volume 2025, Issue 1, 2025.
We define the k‐augmented Pascal matrix and present both a generalization and an alternative version of this matrix. We derive some properties of the defined matrices and establish a connection with generalized Stirling numbers and second‐order Eulerian numbers. Additionally, we provide a factorization of the k‐augmented Pascal matrix, highlighting its
Gonca Kizilaslan, Taekyun Kim, Pramita Mishra   +2 more
wiley   +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

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

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

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

Melham's sums for some Lucas polynomial sequences [PDF]

Notes on Number Theory and Discrete Mathematics
A Lucas polynomial sequence is a pair of generalized polynomial sequences that satisfy the Lucas recurrence relation. Special cases include Fibonacci polynomials, Lucas polynomials, and Balancing polynomials.
Chan-Liang Chung, Chunmei Zhong
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

ON THE ZEROS OF THE DERIVATIVES OF FIBONACCI AND LUCAS POLYNOMIALS

Journal of New Theory, 2015
The purpose of this article is to derive some functions which map the zeros of Fibonacci polynomials to the zeros of Lucas polynomials. Also we find some equations which are satisfied by F 0 n (x) and so L 00 n (x).
Nihal Yılmaz Özgür, Öznur Öztunç Kaymak   +1 more
doaj