Results 61 to 70 of about 316 (181)

A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL

Journal of New Theory, 2017
The Fibonacci polynomial Fn(x) defined recurrently by Fn+1(x) = xFn(x)+Fn−1(x), with F0(x) = 0, F1(0) = 1, for n ≥ 1 is the topic of wide interest for many years. In this article, generalized Fibonacci polynomials Fbn+1(x) and Lbn+1(x) are introduced and
A. D. Godase, M. B. Dhakne
doaj  

Bernoulli-Fibonacci Polynomials

, 2020
By using definition of Golden derivative, corresponding Golden exponential function and Fibonomial coefficients, we introduce generating functions for Bernoulli-Fibonacci polynomials and related numbers. Properties of these polynomials and numbers are studied in parallel with usual Bernoulli counterparts.
Pashaev, Oktay K., Ozvatan, Merve
openaire   +2 more sources

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

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

On convolved generalized Fibonacci and Lucas polynomials [PDF]

Applied Mathematics and Computation, 2014
We define the convolved h(x)-Fibonacci polynomials as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the h(x)-Fibonacci and h(x)-Lucas polynomials. Moreover we obtain the convolved h(x)-Fibonacci polynomials form a family of Hessenberg matrices.
openaire   +2 more sources

Design and Experimental Characterization of a Tendon‐Driven Anthropomorphic Finger With Adaptive Compliance

Journal of Robotics, Volume 2026, Issue 1, 2026.
The primary objective of a soft robotic finger is to reproduce the functional versatility of the human hand by incorporating intrinsic flexibility. By mimicking the human finger’s morphology, structural organization, and kinematic behavior, the system enables anthropomorphic motion that provides enhanced adaptability and dexterity.
Blanka Bakos, Andrea Deaconescu, Tudor Deaconescu, Smritijit Sen   +3 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

Generalized Fibonacci Polynomials and Their Properties

Symmetry
This study presents a unified framework for the simultaneous analysis of generalized Fibonacci numbers and their associated polynomial extensions, both of which play a significant role in combinatorial analysis and discrete mathematics. The generalized Fibonacci polynomials have been extended to four new families of polynomials, each defined through ...
Sibel Koparal, Nese Ömür, Sezer Boz, Khidir Shaib Mohamed, Waseem Ahmad Khan, Alawia Adam   +5 more
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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

From Fibonacci Sequence to the Golden Ratio

Journal of Mathematics, 2013
We consider the well-known characterization of the Golden ratio as limit of the ratio of consecutive terms of the Fibonacci sequence, and we give an explanation of this property in the framework of the Difference Equations Theory. We show that the Golden
Alberto Fiorenza, Giovanni Vincenzi
doaj   +1 more source