Results 11 to 20 of about 1,163,634 (140)

A Training Algorithm for Locally Recurrent Neural Networks Based on the Explicit Gradient of the Loss Function

Algorithms
In this paper, a new algorithm for the training of Locally Recurrent Neural Networks (LRNNs) is presented, which aims to reduce computational complexity and at the same time guarantee the stability of the network during the training.
Sara Carcangiu, Augusto Montisci
doaj   +2 more sources

Multiparameter Quantum Cauchy-Binet Formulas [PDF]

Algebras and Representation Theory, 2020
The quantum Cayley-Hamilton theorem for the generator of the reflection equation algebra has been proven by Pyatov and Saponov, with explicit formulas for the coefficients in the Cayley-Hamilton formula. However, these formulas do not give an \emph{easy} way to compute these coefficients.
Karlin, Samuel, Rinott, Yosef
  +12 more sources

Exploring Generalized $2^k$-Fibonacci Sequence: A New Family of the Fibonacci Sequence

Communications in Advanced Mathematical Sciences
The focus of this paper is to study the $2^k$–Fibonacci sequence, which is defined for all integers $2^k$, and its connections with both the Fibonacci and the Fibonacci-Lucas sequences.
Elis Gardel Costa Mesquista, Eudes Antonio Costa, Paula Maria Machado Cruz Catarino   +2 more
doaj   +2 more sources

Algorithm for Constructing an Analogue of the Binet Formula [PDF]

Programming and Computer Software, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kuzovatov, V. I., Kytmanov, A. A., Kuzovatova, O. I.   +2 more
openaire   +5 more sources

Elliptic curve and k-Fibonacci-like sequence

Scientific African, 2023
In this paper, we will introduce a modified k-Fibonacci-like sequence defined on an elliptic curve and prove Binet’s formula for this sequence. Moreover, we give a new encryption scheme using this sequence.
Zakariae Cheddour, Abdelhakim Chillali, Ali Mouhib   +2 more
doaj   +1 more source

The generalized Binet formula for $k$-bonacci numbers

Elemente der Mathematik, 2023
Using Vandermonde determinants, we give a simple proof of the generalization of the Binet formula to the k -bonacci numbers.
Parks, Harold R., Wills, Dean C.
openaire   +1 more source

Dirichlet Convolution and the Binet Formula

, 2023
Summary: The main aim of this note is to show that the set of closed triples of generalized Fibonacci arithmetic functions under the Dirichlet convolution is a singleton set. This unique Dirichlet convolution identity is the Binet Fibonacci number formula in terms of arithmetic functions and the Dirichlet convolution.
Schwab, Emil Daniel, Schwab, Gabriela
openaire   +2 more sources

Hybrid Quaternions of Leonardo

Trends in Computational and Applied Mathematics, 2022
In this article, we intend to investigate the Leonardo sequence presenting the hybrid Leonardo quaternions. To explore Hybrid Quaternions of Leonardo, the priori, sequence of Leonardo, quaternions and hybrid numbers were presented.
M. C. S. Mangueira, F. R. V. Alves, P. M. M. C. Catarino   +2 more
doaj   +1 more source

Some New Representations of the Binet's Function Involving Euler Sums

American Review of Mathematics and Statistics, 2022
We consider a method for transforming divergent series arising from the Euler - Maclaurin formula into convergent ones. Applying it to the Stirling series forlog 𝛤(𝑧)we obtain some new representations of the J. Binet function.
N. Naĭdenov
semanticscholar   +1 more source

On Quaternion Gaussian Bronze Fibonacci Numbers

Annales Mathematicae Silesianae, 2022
In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defined and studied. Binet’s formula, generating function and certain properties and identities are provided.
Catarino Paula, Ricardo Sandra
doaj   +1 more source