Results 61 to 70 of about 1,108 (208)

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

Mersenne Primes in Certain Lucas Sequences [PDF]

EPJ Web of Conferences
Prime numbers are the most important numbers in number theory and cryptography. One of such special primes are given by the set of Mersenne primes, that are derived from the form Mn = 2n − 1, where n is a prime number.
Hadi Ahmed H., Hashim Hayder R.
doaj   +1 more source

Identities relating six members of the Fibonacci family of sequences

Karpatsʹkì Matematičnì Publìkacìï, 2022
In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences.
R. Frontczak, T. Goy, M. Shattuck
doaj   +1 more source

Trustworthy Distributed Load Forecasting in Resource‐Limited Smart Grids and Buildings via Random Layer Aggregation

International Journal of Intelligent Systems, Volume 2026, Issue 1, 2026.
Federated learning (FL) is a privacy‐preserving method for short‐term load forecasting in energy networks. However, current defense mechanisms against adversarial attacks often depend on supplementary machine learning frameworks, such as anomaly detection models or Byzantine‐robust aggregators.
Habib Ullah Manzoor, Attia Shabbir, Rao Naveed Bin Rais, Sajjad Hussain, Ahmed Zoha, Richard Murray   +5 more
wiley   +1 more source

Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix

Abstract and Applied Analysis, 2015
The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed.
Yanpeng Zheng, Sugoog Shon
doaj   +1 more source

Assessing the problem of excitation light scattering in high‐viscosity jets used in serial crystallography sample delivery

Journal of Applied Crystallography, Volume 58, Issue 6, Page 2078-2089, December 2025.
We experimentally demonstrate that the scattering‐induced decrease in light intensity experienced by a crystal embedded in a high‐viscosity jet is very limited in materials such as lipidic cubic phase or hydroxyethyl cellulose, and therefore cannot justify the use of pump energies exceeding the linear excitation regime under realistic experimental ...
Stanisław Niziński, Bogdan Marekha, Jochen Reinstein, Robert L. Shoeman, R. Bruce Doak, Ilme Schlichting   +5 more
wiley   +1 more source

Acerca de algunos exponentes de Mersenne (About some Mersenne exponents)

Revista Digital Matemática, Educación e Internet
Los números primos de Mersenne crecen de manera vertiginosa y se vuelven intratables con las herramientas de cómputo actuales. En este trabajo se repasan brevemente las cadenas de Mersenne para mostrar cómo ese crecimiento exponencial impone un límite en
Gerardo Miramontes de León
doaj   +1 more source

Fast, high-quality pseudo random number generators for heterogeneous computing [PDF]

EPJ Web of Conferences
Random number generation is key to many applications in a wide variety of disciplines. Depending on the application, the quality of the random numbers from a particular generator can directly impact both computational performance and critically the ...
Barbone Marco, Gaydadjiev Georgi, Howard Alexander, Luk Wayne, Savvidy George, Savvidy Konstantin, Rose Andrew, Tapper Alexander   +7 more
doaj   +1 more source

StorjLedger: An Innovative Distributed Storage Ecosystem That Overcomes Blockchain Trade‐Offs Using Erasure‐Coded Sharding and Proof‐of‐Storage Consensus

Engineering Reports, Volume 7, Issue 10, October 2025.
StorjLedger leverages erasure‐coded sharding and Proof‐of‐Storage to deliver nearly 1000 transactions per second with sub‐second latency, 98% data redundancy, and 76% lower storage costs, resolving the blockchain trilemma by harmonizing scalability, security, and decentralization.
Saha Reno, Koushik Roy
wiley   +1 more source

On the generalized sums of Mersenne, Fermat, Cullen and Woodall Numbers [PDF]

, 2019
Recently we have discussed Mersenne and Fermat numbers using generalized sums. Here we discuss Cullen and Woodall numbers, which are similar to Mersenne and Fermat numbers. The generalized sums are given for them.
Sparavigna, Amelia Carolina, Amelia Carolina Sparavigna   +1 more
core   +1 more source