Results 31 to 40 of about 128 (124)

Fractional Dynamics of Nonlinear Liquid Dispersion Pattern Drops: A Robust Analytical Study of Modulation Instability and Compacton Structures

Computational and Mathematical Methods, Volume 2026, Issue 1, 2026.
Nonlinear dispersion phenomena in liquid media often lead to the formation of localized structures such as compact wave packets and dispersion drops. The present investigation demonstrates that the proposed analytical framework yields accurate approximate solutions, successfully captures compacton‐like structures, and clearly reveals the critical ...
Yogeshwari F. Patel, Mohammad Izadi, Hany M. Ahmed, Rajesh Kumar   +3 more
wiley   +1 more source

Tridiagonal matrices representations of generalized bivariate complex polynomials

Journal of Innovative Applied Mathematics and Computational Sciences
This paper introduces a closed-form expression for generalized bivariate complex polynomials using a tridiagonal determinant in symbolic form. Subsequences with even and odd indices are also represented as tridiagonal determinants.
K. L. Verma
doaj   +1 more source

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

A Generalization of Gaussian Balancing and Gaussian Balancing‐Lucas Numbers With Applications

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
In this paper, we study a generalization of Gaussian balancing and Gaussian Lucas‐balancing numbers, we find their generating functions, Binet formulas, related matrix representation, and many other properties. Also, we provide some applications in cryptography.
T. Al-Asoully, A. Al-Kateeb, Abdul Rauf Khan   +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

Sum of Squares of Mulatu Numbers That Are Powers of 2

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
In this work, we fully characterize all nonnegative integer solutions (n, m, a) to the Diophantine equation Mn2+Mm2=2a, where Mkk≥0 is the Mulatu sequence. The argument employs Matveev’s explicit lower bound for linear forms in logarithms of algebraic numbers together with the reduction technique of Dujella and Pethö to obtain an absolute upper bound ...
Ahmed Gaber, Mohiedeen Ahmed, Walid Wannes, Shikha Binwal   +3 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

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

A Note on Generalized k-Order F&L Hybrinomials

Axioms
In this study, we introduce generalized k-order Fibonacci and Lucas (F&L) polynomials that allow the derivation of well-known polynomial and integer sequences such as the sequences of k-order Pell polynomials, k-order Jacobsthal polynomials and k-order ...
Süleyman Aydınyüz, Gül Karadeniz Gözeri   +1 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