Results 31 to 40 of about 7,195 (140)

Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial Sequences [PDF]

Kyungpook mathematical journal, 2017
In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for $F_p$, where $p$ is a prime of a certain type. We also define period of a Fibonacci sequence modulo an integer, $m$ and derive certain interesting properties related to them.
Laugier, Alexandre, Saikia, Manjil P.
openaire   +3 more sources

Computational Framework for Numerical Simulation of Fractional‐Order Financial Crime Model via Lucas Collocation Technique

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
The Lucas collocation approach is used in this study to approximate a fractional‐order financial crime model (FOFCM) numerically. The model categorizes the population into five groups: persons without a financial criminal past, those inclined toward financial crimes, active participants, individuals undergoing prosecution, and those imprisoned.
Mahmoud Abd El-Hady, Homan Emadifar, Mehdi Hariri, Atallah El-Shenawy, Chong Lin   +4 more
wiley   +1 more source

HOMFLY Polynomials of Torus Links as Generalized Fibonacci Polynomials [PDF]

The Electronic Journal of Combinatorics, 2015
The focus of this paper is to study the HOMFLY polynomial of $(2,n)$-torus link as a generalized Fibonacci polynomial. For this purpose, we first introduce a form of generalized Fibonacci and Lucas polynomials and provide their some fundamental properties.
Kemal Taskopru, Altıntaş, İsmet
openaire   +4 more sources

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

(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

Incomplete Bivariate Fibonacci and Lucas p‐Polynomials [PDF]

Discrete Dynamics in Nature and Society, 2012
We define the incomplete bivariate Fibonacci and Lucas p‐polynomials. In the case x = 1, y = 1, we obtain the incomplete Fibonacci and Lucas p‐numbers. If x = 2, y = 1, we have the incomplete Pell and Pell‐Lucas p‐numbers. On choosing x = 1, y = 2, we get the incomplete generalized Jacobsthal number and besides for p = 1 the incomplete generalized ...
TUĞLU, NAİM, TAŞCI, DURSUN, Firengiz, Mirac Cetin   +2 more
openaire   +3 more sources

“Generating matrix for Generalized Fibonacci numbers and Fibonacci polynomials

Journal of Physics: Conference Series, 2022
AbstractMany researchers have been working on recurrence relation sequences of numbers and polynomials which are useful topic not only in mathematics but also in physics, economics and various applications in many other fields. There are many useful identities on recurrence relation sequence but there main problem to find any term of recurrence ...
Mannu Arya, Vipin Verma
openaire   +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

Incomplete generalized Fibonacci and Lucas polynomials [PDF]

Hacettepe Journal of Mathematics and Statistics, 2015
In this paper, we define the incomplete h(x)-Fibonacci and h(x)-Lucas polynomials, we study recurrence relations and some properties of these ...
openaire   +3 more sources