6 papers
Asymptotic Expansions for Neural Network Approximations of Quantum Channels
Rômulo Damasclin Chaves dos Santos
This paper establishes the Quantum Voronovskaya--Damasclin (QVD) Theorem, providing a complete asymptotic characterization of Quantum Neural Network Operators in the approximation…
Fractional Grönwall--Wendroff Inequalities for Implicit Systems with Distributed Memory
Rômulo Damasclin Chaves dos Santos
This work establishes a comprehensive analytical framework for studying implicit fractional differential systems with distributed memory and time delays. We develop novel fractiona…
Curvature-Enhanced Dynamics and Exponential Decay of the Non-Cutoff Boltzmann Equation on Riemannian Manifolds
Rômulo Damasclin Chaves dos Santos
In this work, we investigate the long-time behavior of solutions to the non-cutoff Boltzmann equation on compact Riemannian manifolds with bounded Ricci curvature. The paper introd…
Energy Dissipation and Regularity in Quaternionic Fluid Dynamics using Sobolev-Besov Spaces
Rômulo Damasclin Chaves dos Santos
This study investigates the dynamics of incompressible fluid flows through quaternionic variables integrated within Sobolev-Besov spaces. Traditional mathematical models for fluid…
Stochastic Regularity in Sobolev and Besov Spaces with Variable Noise Intensity for Turbulent Fluid Dynamics
Rômulo Damasclin Chaves dos Santos
This paper advances the stochastic regularity theory for the Navier-Stokes equations by introducing a variable-intensity noise model within the Sobolev and Besov spaces. Traditiona…
Mountain-Pass Solutions in 2D Turbulence with Generalized Sobolev Operators
Rômulo Damasclin Chaves dos Santos
This work extends the study of mean field equations arising in two-dimensional (2D) turbulence by introducing generalized weighted Sobolev operators. Employing variational methods,…