In this paper, we study the dynamics of the limiting equation (i.e., non-autonomous ODE) of non-autonomous parabolic linear PDEs with dynamic boundary conditions. For this, we first show the well posedness of the PDEs and investigate how the solutions of given PDEs converge to those of the limiting equation. We show that, under certain standard conditions, bounded solutions exhibit additional smoothness – specifically Hölder continuity – which allows us to obtain the uniform convergence of solutions. Consequently, the large-time behavior can be described by analyzing the limiting problem. Our approach involves non-autonomous singular perturbations of a reaction-diffusion equation with large diffusion in all domain and its boundary.
The strawberry consists of two main parts: the dry achenes (the true fruit) and an enlarged receptacle (the fleshy part). These parts exhibit high metabolic synchrony during the development and ripening stages. Due to the low rates of ethylene production and respiration during ripening, strawberries are currently classified as non-climacteric fruits. However, studies suggest that ethylene, along with its interactions with other plant growth regulators like abscisic acid and auxin influences the ripening process in strawberries. Auxins are crucial for the initial development of fruits, promoting cell expansion and modulating non-climacteric ripening. Recent research indicates that cytokinins and gibberellins might play a role in enhancing fruit development and ripening by promoting cell expansion. Additionally, the literature suggests that increased sugar concentration, accompanied by cell wall degradation and changes in pulp osmotic pressure, is linked to hormonal crosstalk between growth promoters, abscisic acid and ethylene. Although traditionally classified as non-climacteric, recent evidence may suggest that strawberries operate under a model similar to ‘suppressed climacteric’. In this system, ethylene does not act as the primary trigger, but rather as an essential modulator of late ripening. Thus, strawberry ripening reflects a sophisticated hormonal interaction essential to the strawberry ripening cascade. Strawberry ripening is regulated by coordinated hormonal crosstalk involving auxin, abscisic acid, cytokinins, gibberellins, and ethylene, suggesting an alternative ripening model in which ethylene functions as a late-stage modulator rather than the primary trigger.
To evaluate the efficacy of a new orthodontic primer (Ambar APS Ortho; FGM Dental Products, Joinville, SC, Brazil) on shear bond strength (SBS) and degree conversion (DC) of metallic brackets bonding. 240 sound maxillary premolars were randomized into 24 experimental groups based on: (1) Orthodontic primer (Ambar APS Ortho, Orthoprimer and Transbond XT); (2) Light-curing time (3-seconds and 10-seconds); (3) Light-curing unit (Valo Cordless and Quazar); and (4) Storage condition (immediate time [IT] and after thermocycling [TC]). After each storage time, specimens were subjected to SBS testing at a crosshead speed of 1 mm/min until failure, and values were recorded in MPa. For DC (
This study analyzes the determinants of commuting between cities in the Londrina Metropolitan Region (LMR) using a Structural Gravity model with Fixed Effects, estimated by Poisson Pseudo-Maximum Likelihood (PPML), and an XGBoost model. The two approaches were used for predictive performance comparison, and spatial aspects were incorporated into both models by introducing an interaction between distance and labor market development as a regressor. The results suggest that distance acts as a repelling factor for commuting flows and while labor market dynamics in the origin city serve as a repelling factor, it acts as an attractive factor in the destination city. Although spatial effects were significant, their inclusion did not greatly enhance the predictive power of the models. Moreover, the Structural Gravity model and the XGBoost showed identical performances, suggesting that the Gravity model remains relevant for commuting research.
Optical limiting materials have been developed to protect optical sensors and photonic devices from laser-induced damage. In this study, the optical properties of five vegetable oils (olive, sesame, cherry, pumpkin, and grape seed) combined with molybdenum diselenide (MoSe2) nanosheets under continuous-wave laser radiation at 532 and 405 nm were investigated. Molybdenum diselenide nanosheets were added at different concentrations to evaluate improvements in the optical limiting threshold performance. At 532 nm, sesame and cherry seed oils showed no inherent optical limiting behavior, but with MoSe2 (0.5 g/L), both exhibited a threshold decrease to 76.24 mW. Pumpkin seed oil showed the greatest improvement, with its threshold reducing from 80.5 to 63.42 mW with MoSe2. At 405 nm, all oils exhibited native optical limiting responses, with grape, cherry, and pumpkin seed oils showing the lowest initial thresholds. MoSe₂ enhanced the performance, with pumpkin seed oil reaching 63.2 mW at 0.5 g/L concentration. These results confirm that MoSe2 nanosheets improve the nonlinear optical response of vegetable oils, indicating their potential as economical alternatives for optically limited applications.
