The current high cost of producing green hydrogen, for use as an energy vector, has motivated the search for the development of non-conventional technologies for its production, joining forces on the path towards energy transition. Hydrogen production by aluminum corrosion in aqueous acid solutions seems to be a promising alternative. In order to evaluate its technical feasibility, a kinetic study was carried out, analyzing the impact of HCl concentration (1.125 to 1.75 M) on the aluminum corrosion capacity under the presence of a saline environment and using a promoter, fitting the proposed models to the data obtained through experimental runs. Although other studies use the shrinking core model to describe the kinetics of this type of reaction, in most cases, it does not fit well with the experimental data and needs to be modified. Finally, by considering the corrosion dynamics (variations in diffusion coefficients and shell thickness) in the kinetic model equations, it was possible to describe its behavior. For low HCl concentrations, a single resistance controls the reaction of the particle throughout; however, for high HCl concentrations, a combination of related equations must be used. The results of this study enable viable continuous reactor designs for a given amount of green hydrogen production.

This paper develops a rigorous operator-theoretic framework for learning-augmented quasi-gradient methods in constrained optimization. We consider the minimization of an objective function over a closed convex feasible set, where feasibility is enforced via projection and directional updates may incorporate data-driven corrections. Such settings arise naturally in modern optimization algorithms that integrate artificial intelligence components under structural constraints. The proposed formulation introduces an explicit contraction–bias–variance decomposition of the iterative dynamics. Curvature induces deterministic contraction, alignment distortion—quantified by a geometric parameter—modifies the effective contraction margin, and stochastic learning components inject controlled dispersion. Explicit error recursions yield convergence guarantees under strong convexity, the Polyak–Łojasiewicz condition, and smooth nonconvexity. The analysis establishes that stability regions and first-order complexity bounds are preserved whenever alignment distortion remains below unity and bounded second-moment conditions hold. A fully reproducible computational study provides quantitative validation: the empirically observed steady-state error closely matches the theoretical prediction proportional to ${\sigma }^2/\mu (1-\eta )$. Comparative experiments with gradient, stochastic gradient, and momentum methods confirm that the proposed operator retains classical stability margins and conditioning sensitivity while enabling principled integration of learned directional components. The results provide a transparent mathematical bridge between stochastic approximation theory and contemporary AI-enhanced constrained optimization.

The integrity of cold chains is critical for preserving the quality, safety, and efficacy of temperature-sensitive products, including pharmaceuticals, vaccines, and perishable goods. However, real-world cold-chain operations are subject to environmental variability, operational disturbances, and transport-related uncertainties that are often inadequately captured by deterministic models. This study presents a stochastic modeling methodology that integrates a physics-based heat-transfer model with a machine-learning residual correction to predict temperature dynamics and product degradation under uncertainty. Temperature evolution is represented through a stochastic heat-transfer model incorporating random perturbations, while product degradation is quantified using Arrhenius-based kinetics that link thermal exposure to quality loss. A machine-learning-based residual correction is subsequently incorporated to improve predictive accuracy while preserving the physical structure of the governing model. The proposed methodology is evaluated through computational experiments using a representative pharmaceutical cold-chain transportation scenario. Numerical experiments based on the Euler–Maruyama method and Monte Carlo analysis are performed to assess the proposed methodology under representative operating conditions. Results indicate that stochastic variability can produce transient temperature excursions even when average operating conditions remain acceptable, leading to increased degradation and higher failure probabilities. The computational results demonstrate the feasibility of the proposed methodology for the probabilistic estimation of thermal risk and product quality deterioration by integrating physics-based modeling, uncertainty analysis, and data-driven residual correction within a unified computational methodology. The proposed methodology provides a computational basis for the future development of intelligent cold-chain monitoring and decision-support systems. Overall, it offers practical capabilities for uncertainty quantification, reliability assessment, and informed decision making in temperature-sensitive supply chains.

This paper develops a variational analysis of projected optimization over nonconvex constraint sets, with emphasis on the geometry and regularity of the metric projection. For a closed feasible set, the metric projection is treated as a set-valued mapping whose loss of local uniqueness may induce nonsmoothness and nonunique feasible continuations. Projection multiplicity and local projection regularity are related to the differentiability properties of the squared distance function, tangent-normal geometry, and first-order stationarity. These relationships provide a geometric characterization of regimes in which projected dynamics are locally single-valued or may branch. Smooth embedded manifolds arise as a locally regular case, where the existence of tubular neighborhoods ensures local uniqueness of the metric projection and the corresponding stationarity condition reduces to the vanishing of the Riemannian gradient. This framework, termed Nonconvex Constraint Geometry (NCG), connects set-valued projection, variational regularity, nonsmoothness, and manifold-constrained optimization within a unified geometric setting.

The integrity of cold chains is critical for preserving the quality, safety, and efficacy of temperature-sensitive products, including pharmaceuticals, vaccines, and perishable goods. However, real-world cold-chain operations are subject to environmental variability, operational disturbances, and transport-related uncertainties that are often inadequately captured by deterministic models. This study presents a physics-informed stochastic framework for modeling temperature dynamics and product degradation under uncertainty. Temperature evolution is represented through a stochastic heat-transfer model incorporating random perturbations, while product degradation is quantified using Arrhenius-based kinetics that link thermal exposure to quality loss. The framework integrates stochastic simulation, degradation modeling, and machine-learning-based correction to capture nonlinear effects not explicitly represented by the governing equations. Numerical experiments based on the Euler–Maruyama method and Monte Carlo simulation are used to generate physically consistent synthetic datasets and evaluate system performance. Results indicate that stochastic variability can produce transient temperature excursions even when average operating conditions remain acceptable, leading to increased degradation and higher failure probabilities. The proposed methodology provides improved estimates of thermal risk and product quality deterioration compared with deterministic approaches. Overall, the framework offers a practical tool for uncertainty quantification, reliability assessment, and decision support in temperature-sensitive supply chains.