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pro vyhledávání: '"Alfaya, A."'
We classify all solution triples with $k$-Fibonacci components to the equation $x^2+y^2+z^2=3xyz+m,$ where $m$ is a positive integer and $k\geq 2$. As a result, for $m=8$, we have the Markoff triples with Pell components $(F_2(2), F_2(2n), F_2(2n+2))
Externí odkaz:
http://arxiv.org/abs/2409.13885
Artificial Neural Networks (ANNs) have significantly advanced various fields by effectively recognizing patterns and solving complex problems. Despite these advancements, their interpretability remains a critical challenge, especially in applications
Externí odkaz:
http://arxiv.org/abs/2409.11078
Given a holomorphic Lie algebroid on an m-pointed Riemann surface, we define parabolic Lie algebroid connections on any parabolic vector bundle equipped with parabolic structure over the marked points. An analogue of the Atiyah exact sequence for par
Externí odkaz:
http://arxiv.org/abs/2406.15828
Artificial Neural Networks (ANNs) have become a powerful tool for modeling complex relationships in large-scale datasets. However, their black-box nature poses ethical challenges. In certain situations, ensuring ethical predictions might require foll
Externí odkaz:
http://arxiv.org/abs/2406.08525
We classify all solution triples with Fibonacci components to the equation $a^2+b^2+c^2=3abc+m,$ for positive $m$. We show that for $m=2$ they are precisely $(1,F(b),F(b+2))$, with even $b$; for $m=21$, there exist exactly two Fibonacci solutions $(1
Externí odkaz:
http://arxiv.org/abs/2405.08509
Publikováno v:
Journal of Geometry and Physics 207 (2025) 105350
Given any irreducible smooth complex projective curve $X$, of genus at least $2$, consider the moduli stack of vector bundles on $X$ of fixed rank and determinant. It is proved that the isomorphism class of the stack uniquely determines the isomorphi
Externí odkaz:
http://arxiv.org/abs/2310.07666
As Machine Learning models are considered for autonomous decisions with significant social impact, the need for understanding how these models work rises rapidly. Explainable Artificial Intelligence (XAI) aims to provide interpretations for predictio
Externí odkaz:
http://arxiv.org/abs/2305.02368
Autor:
Alfaya, David, Pauly, Christian
Publikováno v:
Journal of Algebra 634 (2023) 306-335
Building on Simpson's original definition over the complex numbers, we introduce the notion of restricted sheaf $\Lambda$ of rings of differential operators on a variety defined over a field of positive characteristic. We define the notion of $p$-cur
Externí odkaz:
http://arxiv.org/abs/2303.02359
Autor:
Alfaya, David, Biswas, Indranil
Publikováno v:
International Mathematics Research Notices 2023 (2023) 19546-19591
We provide an explicit algebraic construction for the pullback and direct image of parabolic bundles, parabolic Higgs bundles and parabolic connections through maps between Riemann surfaces. We show that these constructions preserve semistability and
Externí odkaz:
http://arxiv.org/abs/2303.00475
Autor:
Ferreira-Alfaya, Francisco Javier1 (AUTHOR) fcoferalf@correo.ugr.es
Publikováno v:
Discover Public Health. 11/20/2024, Vol. 21 Issue 1, p1-12. 12p.
