Article
Multidisciplinary Sciences
Valerio Faraoni, Farah Atieh
Summary: Continuous generalizations of the Fibonacci sequence can be described through ODEs analogous to the Friedmann equation in general relativity, with Lagrangian and Hamiltonian formulations and an invariant specific to the Fibonacci sequence.
Article
Mathematics, Interdisciplinary Applications
B. Prasad
Summary: This paper introduces dual complex Fibonacci p-numbers and discusses some properties related to complex Fibonacci numbers and complex Fibonacci p-numbers. (c) 2021 Elsevier Ltd. All rights reserved.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Yasemin Alp, E. Gokcen Kocer
Summary: This paper introduces the hybrid Leonardo numbers using the Leonardo numbers, along with discussing their algebraic properties such as recurrence relation, generating function, Binet's formula, sum formulas, Catalan's identity, and Cassini's identity.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics
Elif Tan, Mehmet Dagli, Amine Belkhir
Summary: In this paper, the authors introduce bi-periodic incomplete Horadam numbers as a natural extension of incomplete Horadam numbers. They investigate the fundamental properties and provide recurrence relations for these numbers. Moreover, they derive the generating function of these numbers.
TURKISH JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
Cristiano Maria Verrelli, Cristian Romagnoli, Roxanne Jackson, Ivo Ferretti, Giuseppe Annino, Vincenzo Bonaiuto
Summary: The study found that elite swimmers exhibit a harmonically self-similar temporal partition at middle distance pace. Quantitative indices were proposed to assess this time structure based on the generalized Fibonacci sequence and the golden ratio. Experimental validation indicated the presence of this structure in international and national-level swimmers.
Article
Mathematics
Natalia Bednarz
Summary: This paper introduces and studies a new two-parameters generalization of Fibonacci numbers, which also generalizes Pell numbers and Narayana numbers. The paper proves identities that generalize well-known relations for Fibonacci and Pell numbers, and provides a matrix representation for generalized Fibonacci numbers.
Article
Multidisciplinary Sciences
Jonatan Pena Ramirez, Erick Espinoza, Ricardo Cuesta
Summary: The golden number, an irrational number widely observed in nature and man-made systems, is shown to appear in the periodic solutions of an underactuated mass-spring oscillator. Analytical and numerical methods confirm its presence in the amplitude ratios and oscillation frequency of the solutions, which are referred to as golden solutions. Stability of these solutions is also demonstrated using the Poincare method.
SCIENTIFIC REPORTS
(2022)
Article
Mathematics, Applied
Abdul Hamid Ganie, Mashael M. AlBaidani
Summary: This paper introduces a new sequence of Jacobsthal type with a generalized order j and studies some basic properties related to it, as well as establishes the generalized Binet formula.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Mathematics, Interdisciplinary Applications
Songul Celik, Inan Durukan, Engin Ozkan
Summary: This study explores the placement of different number sequences at the vertices of polygons, deriving relationships among the corresponding numbers and obtaining formulas for the terms of the sequences formed.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Mehmet Dagli, Elif Tan, Oktay Olmez
Summary: This paper discusses the spectral and Frobenius norms of r-circulant matrices defined by generalized bi-periodic Fibonacci numbers, providing explicit formulas for the computation of eigenvalues and determinants.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Multidisciplinary Sciences
Semra Kaya Nurkan, Ilkay Arslan Guven
Summary: In this paper, a new sequence of quadruple numbers called ordered Leonardo quadruple numbers is introduced using Leonardo numbers. The properties of ordered Leonardo quadruple numbers, including their relations with Leonardo, Fibonacci, and Lucas numbers, are determined. The proofs make use of the symmetric and antisymmetric properties of Fibonacci numbers. Well-known identities, the Binet formula, and a generating function for these numbers are obtained. Illustrations of the identities are also provided.
Article
Physics, Multidisciplinary
Akio Tsuneda
Summary: This paper discusses the auto-correlation functions of m-bit random numbers obtained from chaotic binary sequences generated by one-dimensional nonlinear maps. It shows how the auto-correlation properties of the m-bit sequences can be controlled by the auto-correlation functions of the original binary sequences. Numerical experiments demonstrate that the generated m-bit sequences closely match the theoretical values and can have various auto-correlation properties.
Article
Evolutionary Biology
Torsten H. Struck, Anja Golombek, Christoph Hoesel, Dimitar Dimitrov, Asmaa Haris Elgetany
Summary: The variability and evolution of the annelid gene order were investigated using a comprehensive and systematic approach. The study found that the gene order with and without tRNAs is generally conserved, but individual taxa exhibit higher degrees of variability. Molecular evolutionary aspects, such as substitution rate and base composition, were found to be the main driving forces behind gene order evolution. Life history and ecological factors did not explain the observed variability. The study also discussed the molecular properties of annelid mitochondrial genomes and potential reasons for the discrepancies with canonical views on gene evolution.
SYSTEMATIC BIOLOGY
(2023)
Article
Mathematics
Sid Ali Bousla
Summary: This paper presents a method for estimating the least common multiple of binary linear recurrence sequences, and discusses its characteristics and applications.
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics
Elif Tan, N. Rosa Ait-Amrane
Summary: This paper introduces a new generalization of hybrid numbers, called bi-periodic Horadam hybrid numbers. The generating function, Binet formula, and some basic properties of these new hybrid numbers are given. Furthermore, the relationships between generalized bi-periodic Fibonacci hybrid numbers and generalized bi-periodic Lucas hybrid numbers are investigated.
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
S. P. Glasby, Frederico A. M. Ribeiro, Csaba Schneider
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
(2020)
Article
Mathematics
S. P. Glasby
COMMUNICATIONS IN ALGEBRA
(2020)
Article
Mathematics
S. P. Glasby, Cheryl E. Praeger, Colva M. Roney-Dougal
JOURNAL OF ALGEBRA
(2020)
Article
Mathematics
Mariagrazia Bianchi, Stephen P. Glasby, Cheryl E. Praeger
JOURNAL OF GROUP THEORY
(2020)
Article
Mathematics, Applied
Stephen P. Glasby, Emilio Pierro, Cheryl E. Praeger
Summary: In this paper, recent progress on the classification of point-primitive generalised polygons is discussed, reducing the problem to primitive actions of almost simple groups of Lie type. The study illustrates how the natural geometry of these groups can be used and describes a strategy to prove the non-existence of such generalised polygons.
ARS MATHEMATICA CONTEMPORANEA
(2021)
Article
Mathematics, Applied
S. P. Glasby, G. R. Paseman
Summary: The weighted binomial sum, commonly seen in coding theory and information theory, was investigated in this study. It was proven that for most values of m, the maximum value of the sum occurs when r = left perpendicular m/3 right perpendicular + 1. Additionally, it was shown that this maximum value approaches 3/root pi m (3/2)(m) as m approaches infinity.
ELECTRONIC JOURNAL OF COMBINATORICS
(2022)
Article
Mathematics
Dominik Bernhardt, Tim Boykett, Alice Devillers, Johannes Flake, Stephen P. Glasby
Summary: In this paper, we study groups with a special property called J-group. We prove that finite nilpotent groups with certain conditions and finite p-groups with certain conditions are all J-groups. We also prove that regular p-groups or power-closed groups are J-groups.
JOURNAL OF GROUP THEORY
(2022)
Article
Mathematics, Applied
S. P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger
Summary: This article studies the proportion estimation of non-degenerate subspaces in a vector space equipped with a non-degenerate alternating, hermitian or quadratic form over a finite field. The proportion is estimated when the non-degenerate subspaces U and U' are added up to equal the whole vector space V, usually without being perpendicular to each other. In the symplectic or unitary cases, the proportion is shown to be at least 1-c/|F| for some constant c < 2, while in the orthogonal case, c < 3.
FINITE FIELDS AND THEIR APPLICATIONS
(2022)
Article
Mathematics, Applied
Stephen P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger
Summary: This article investigates the proportion estimation of specific non-degenerate pairs of subspaces (U, U') in a d-dimensional vector space V over a finite field, equipped with a non-degenerate hermitian, alternating, or quadratic form. The proportion is shown to be positive and at least 1 - c/q, where q is the size of the finite field F and c is a constant.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2022)
Article
Mathematics
Gordon F. Royle, Cheryl E. Praeger, S. P. Glasby, Saul D. Freedman, Alice Devillers
Summary: A graph is called odd if it has an orientation that can be reversed by an automorphism that reverses the sense of an odd number of its edges. Otherwise, it is called even. Pontus von Bromssen (formerly Andersson) showed that the existence of such an automorphism is independent of the orientation and conjectured that the number of pairwise non-isomorphic even graphs on n vertices is equal to the number of pairwise non-isomorphic tournaments on n vertices. We prove this conjecture using a counting argument with multiple applications of the Cauchy-Frobenius theorem.
JOURNAL OF ALGEBRAIC COMBINATORICS
(2023)
Article
Computer Science, Theory & Methods
S. P. Glasby, Ferdinand Ihringer, Sam Mattheus
Summary: Given positive integers e(1), e(2), let Xi denote the set of ei-dimensional subspaces of a fixed finite vector space V = (F-q)(e1+e2). Let Y-i be a non-empty subset of Xi and let ai = |Yi |/|Xi |. We give a positive lower bound, depending only on a(1),a(2), e(1), e(2), q, for the proportion of pairs (S-1, S-2) E Y-1 X Y-2 which intersect trivially. As an application, we bound the proportion of pairs of non-degenerate subspaces of complementary dimensions in a finite classical space that intersect trivially. This problem is motivated by an algorithm for recognizing classical groups. By using techniques from algebraic graph theory, we are able to handle orthogonal groups over the field of order 2, a case which had eluded Niemeyer, Praeger, and the first author.
DESIGNS CODES AND CRYPTOGRAPHY
(2023)
Article
Mathematics
Vishnuram Arumugam, Heiko Dietrich, S. P. Glasby
Summary: Given a finite group G acting on a set X, the proportion of elements in G that have exactly k fixed points in X is denoted as & delta;k(G,X). The symmetric group Sn represents the action on the set [n]={1,2,···,n}. For A ≤ Sm and B ≤ Sn, the permutational wreath product A wreath product B has two natural actions, and formulas for & delta;k(A wreath product B,[m]x[n]) and & delta;k(A wreath product B,[m][n]) are provided. It is proven that for k=0, the values of these proportions are dense in the intervals [& delta;0(B,[n]),1] and [& delta;0(A,[m]),1]. Further results include estimates for & delta;0(G,[m][n]) for subgroups G ≤ Sm wreath product Sn containing Am[n].
JOURNAL OF ALGEBRAIC COMBINATORICS
(2023)
Article
Mathematics
Michael Giudici, S. P. Glasby, Cheryl E. Praeger
Summary: In this study, we classify the subgroups of finite classical groups that act transitively on a G-invariant set of subspaces of the natural module. These subspaces can either be totally isotropic or nondegenerate. Our proof relies on the classification of the maximal factorisations of almost simple groups. As an application, we classify all point-transitive sub-groups of automorphisms of finite thick classical generalised quadrangles.
JOURNAL OF ALGEBRA
(2023)
Article
Mathematics
S. P. Glasby, Cheryl E. Praeger, W. R. Unger
Summary: In most permutations of degree n, there exists a power which is a cycle of prime length approximately log n. Specifically, for sufficiently large n, the proportion of such elements is at least 1 - 5/ log log n with the prime between log n and (log n)(log log n). The proportion of even permutations with this property is at least 1 - 7/ log log n.
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
(2021)
Article
Mathematics, Applied
John Bamberg, S. P. Glasby, Scott Harper, Cheryl E. Praeger
ELECTRONIC JOURNAL OF COMBINATORICS
(2020)
