Results 11 to 20 of about 1,029,498 (122)

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
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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
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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
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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
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Some identities of bivariate Pell and bivariate Pell-Lucas polynomials

Journal of Amasya University the Institute of Sciences and Technology, 2023
In this paper, we obtain some identities for the bivariate Pell polynomials and bivariate Pell-Lucas polynomials. We establish some sums and connection formulas involving them.
Yashwant Panwar
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Dual Jacobsthal Quaternions

Communications in Advanced Mathematical Sciences, 2020
In this paper, dual Jacobsthal quaternions were defined. Also, the relations between dual Jacobsthal quaternions which connected with Jacobsthal and Jacobsthal-Lucas numbers were investigated. Furthermore, Binet's formula, Honsberger identity, D'ocagne'
Fügen Torunbalcı Aydın
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Higher-Order Jacobsthal–Lucas Quaternions

Axioms, 2022
In this work, we define higher-order Jacobsthal–Lucas quaternions with the help of higher-order Jacobsthal–Lucas numbers. We examine some identities of higher-order Jacobsthal–Lucas quaternions. We introduce their basic definitions and properties.
Mine Uysal, Engin Özkan
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Hyperbolic Fibonacci Sequence

Universal Journal of Mathematics and Applications, 2019
In this paper, we investigate the hyperbolic Fibonacci sequence and the hyperbolic Fibonacci numbers. Furthermore, we give recurrence relations, the golden ratio and Binet's formula for the hyperbolic Fibonacci sequence and Lorentzian inner product ...
Fügen Torunbalcı Aydın
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On a New One Parameter Generalization of Pell Numbers

Annales Mathematicae Silesianae, 2019
In this paper we present a new one parameter generalization of the classical Pell numbers. We investigate the generalized Binet’s formula, the generating function and some identities for r-Pell numbers.
Bród Dorota
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Deriving a Formula in Solving Reverse Fibonacci Means

Recoletos Multidisciplinary Research Journal, 2022
Reverse Fibonacci sequence $\{J_n\}$ is defined by the relation $J_n = 8(J_{n-1} - J_{n-2})$ for $n\geq2$ with $J_0=0$ and $J_1=1$ as initial terms. A few formulas have been derived for solving the missing terms of a sequence in books and mathematical ...
Steven Elizalde, Romeo Patan
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