Results 81 to 90 of about 916 (205)

On Values of Cyclotomic Polynomials. V [PDF]

, 2003
In this paper, we present three results on cyclotomic polynomials. First, we present results about factorization of cyclotomic polynomials over arbitrary fields K.
Motose, Kaoru, Kaoru Motose
core   +1 more source

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

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

Binomials transformation formulae for scaled Fibonacci numbers

Open Mathematics, 2017
The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined
Hetmaniok Edyta, Piątek Bożena, Wituła Roman   +2 more
doaj   +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

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

Bivariate Gaussian Fibonacci and Lucas polynomials [PDF]

, 2013
In this study we define and study the Bivariate Gaussian Fibonacci and Bivariate Gaussian Lucas Polynomials. We give generating function, Binet formula, explicit formula and partial derivation of these polynomials. By defining these bivariate polynomials
Gurel, E., Aşcı, Mustafa
core  

Tiling Models for Palindromic and n‐Colored Compositions With 1 s and 3 s

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this work, we explore compositions of positive integers into parts consisting of 1 and 3 s, highlighting their close connection to the Narayana numbers. We also examine palindromic compositions of this type and introduce arithmetic functions that reflect their structural properties.
Orhan Dişkaya, Bahar Kuloğlu, Hayrullah Özimamoğlu, Ahmet Kaya, Hamza Menken, Smritijit Sen   +5 more
wiley   +1 more source

Trivariate Fibonacci and Lucas polynomials [PDF]

, 2018
Yüksek Lisans TeziBu çalışma beş bölümden oluşmaktadır. Birinci bölümde Tribonacci sayıları ve polinomlarının tanımları ve bazı özellikleri verilmiştir.
Kılınç, Hatice
core  

Coefficient Estimate and Fekete-Szeg\"{o} Problems for Certain New Subclasses of Bi-univalent Functions Defined by Generalized Bivariate Fibonacci Polynomial [PDF]

Sahand Communications in Mathematical Analysis
This article deals with two new subclasses of analytic and bi-univalent functions in the open unit disk, which is defined  by applying subordination principle between analytic functions and the generalized Bivariate Fibonacci polynomials.
Rumeysa Öztürk, İbrahim Aktaş
doaj   +1 more source