Results 51 to 60 of about 320 (182)

On the arguments of the roots of the generalized Fibonacci polynomial

Lithuanian Mathematical Journal, 2023
AbstractWe revisit the classical subject of equidistribution of the roots of Littlewood-type polynomials. More precisely, we show that the roots of the family of polynomials Ψk(z) = zk−zk−1−⋯−1, k ⩾ 1, are uniformly distributed around the unit circle in the strong quantitative form, confirming a conjecture from [C.-A. Gómez and F. Luca, Commentat. Math.
Alahmadi, Adel, Klurman, Oleksiy, Luca, Florian, Shoaib, Hatoon   +3 more
openaire   +1 more source

GENERALIZED IDENTITIES OF BIVARIATE FIBONACCI AND BIVARIATE LUCAS POLYNOMIALS

Journal of Amasya University the Institute of Sciences and Technology, 2020
In this paper, we present generalized identities of bivariate Fibonacci polynomials and bivariate Lucas polynomials and related identities consisting even and odd terms. Binet’s formula will employ to obtain the identities.
Jaya Bhandari, V. K. Gupta, Yashwant Panwar   +2 more
doaj  

Affine–Hill cipher from Hadamard-type Fibonacci–Mersenne and Fibonacci-balancing p-sequences [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we define two new sequences using the generalized Mersenne numbers, Fibonacci p-numbers, and m-balancing numbers. These sequences are constructed using the Hadamard-type product of their characteristic polynomials.
Elahe Mehraban, T. Aaron Gulliver, Evren Hincal   +2 more
doaj   +1 more source

Leonardo Cartan Numbers and Related Fibonacci–Lucas Structures

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper investigates the Leonardo Cartan numbers, defined as an extension of the classical Leonardo sequence through additional algebraic structures. The recurrence relations of these numbers are established, and various summation formulas are derived.
Hasan Çakır, İskender Öztürk, Smritijit Sen   +2 more
wiley   +1 more source

On an analytical study of the generalized Fibonacci polynomials [PDF]

Notes on Number Theory and Discrete Mathematics
In this work, we presented an analytical study of the generalized Fibonacci polynomial of order r≥2, by using properties of the fundamental system associated with the generalized Fibonacci polynomial.
Leandro Rocha, Gabriel F. Pinheiro, Elen V. P. Spreafico   +2 more
doaj   +1 more source

Split Quaternionic Representations of Horadam Sequences and Their Binet, Generating Function, and Cassini‐Type Identities

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study establishes a novel algebraic connection between Horadam numbers and the split quaternion algebra. To this end, two fundamental constructs are introduced: the Fibonacci Sq,r‐split quaternions and the Horadam sq,r‐split quaternions, which generalize Horadam numbers within the framework of split quaternions.
İskender Öztürk, Hasan Çakır, Smritijit Sen   +2 more
wiley   +1 more source

Some fundamental Fibonacci number congruences [PDF]

Notes on Number Theory and Discrete Mathematics
This paper investigates a number of congruence properties related to the coefficients of a generalized Fibonacci polynomial. This polynomial was defined to produce properties comparable with those of the standard polynomials of some special functions ...
Anthony G. Shannon, Tian-Xiao He, Peter J.-S. Shiue, Shen C. Huang   +3 more
doaj   +1 more source

(Random) Trees of Intermediate Volume Growth

Random Structures &Algorithms, Volume 67, Issue 4, December 2025.
ABSTRACT For every function g:ℝ≥0→ℝ≥0$$ g:{\mathbb{R}}_{\ge 0}\to {\mathbb{R}}_{\ge 0} $$ that grows at least linearly and at most exponentially, if it is sufficiently well‐behaved, we can construct a tree T$$ T $$ of uniform volume growth g$$ g $$, or more precisely, C1·g(r/4)≤|BG(v,r)|≤C2·g(4r),for allr≥0andv∈V(T),$$ {C}_1\cdotp g\left(r/4\right)\le \
George Kontogeorgiou, Martin Winter
wiley   +1 more source

Fundamental Solutions and Green's Functions for Certain Elliptic Differential Operators From a Pseudodifferential Algebra

Mathematical Methods in the Applied Sciences, Volume 48, Issue 13, Page 12654-12674, September 2025.
ABSTRACT We have studied possible applications of a particular pseudodifferential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The pseudodifferential algebra considered in the present work, comprises degenerate partial differential ...
Heinz‐Jürgen Flad, Gohar Flad‐Harutyunyan   +1 more
wiley   +1 more source

AI in Neurology: Everything, Everywhere, All at Once Part 1: Principles and Practice

Annals of Neurology, Volume 98, Issue 2, Page 211-230, August 2025.
Artificial intelligence (AI) is rapidly transforming healthcare, yet it often remains opaque to clinicians, scientists, and patients alike. This review, part 1 of a 3‐part series, provides neurologists and neuroscientists with a foundational understanding of AI's key concepts, terminology, and applications.
Matthew Rizzo, Jeffrey D. Dawson
wiley   +1 more source