We correct an error in the proof of the main result of our original paper.
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.
Background Noise sensitivity is a key individual-level predictor of noise response, yet the Weinstein Noise Sensitivity Scale (WNSS), one of the most widely used instruments, has been subject to arbitrary classification approaches—including median splits and Z-score-based groupings—that may fail to reflect the inherent group structure of the data. This study applied Latent Class Analysis (LCA) to derive an empirically grounded classification scheme for the Korean WNSS. Methods A self-report survey using the 21-item Korean WNSS was administered to 1,929 Korean adults. Reliability and validity of the scale were examined prior to LCA. LCA was conducted using Mplus 8, and classification stability was evaluated through 1,000 repeated random sampling iterations. The derived LCA-based classification was compared with conventional median- and Z-score-based classification methods, and data-driven cut-off scores were determined using kernel density estimation. Results A four-class solution was identified as optimal (Entropy = 0.909, BIC = 125,318.9), with a replication rate of 43.2 % across repeated sampling iterations (n = 1,000). The four classes differed not only in mean noise sensitivity scores (Class 1: 2.92, Class 2: 3.57, Class 3: 4.38, Class 4: 4.77) but also in the item-level response patterns, particularly on items measuring emotional reactions to noise and everyday discomfort. Compared with conventional classification methods, median-based classification was found to systematically underestimate the size of the low group and overestimate the size of the high group, with 54.1 % of the conventional low-sensitivity group reclassified into LCA Class 2. Data-driven cut-off scores of 3.27, 3.96, and 4.76 were identified as class boundaries, showing high agreement with LCA-based classification (Class 4 specificity = 0.92, Class 2 sensitivity = 0.76). Conclusions The four-class classification scheme and data-driven cut-off scores proposed in this study serve as empirically grounded criteria that complement conventional arbitrary classification, and may contribute to enhancing the reproducibility and cross-study comparability of noise sensitivity research. The proposed classification framework can provide a basis for formulating differentiated intervention strategies according to noise sensitivity level in environmental impact assessment, occupational health screening, and noise-related policy development.
Coffee shops are strongly influenced by their location, which determines customer accessibility and pedestrian traffic potential, thereby impacting sales performance. The irrevocability of location decisions further amplifies their strategic importance. Coffee shops operate in highly competitive environments oriented toward profit and sales maximization. However, existing studies have predominantly conducted static trade area analyses centered on macroeconomic physical variables such as distance, population density, and store size. Additionally, entrepreneurs often rely on intuition and experience rather than scientific analysis for site selection. We analyzed various trade area characteristics, including competitive factors, potential demand, and infrastructure, using machine learning models to predict coffee shop locations and business sustainability. By identifying key variables that significantly influence post-opening business continuity, we highlight the need to reconsider several traditional assumptions related to site selection. Furthermore, we suggest that sufficient data combined with machine learning techniques can generate meaningful insights into business phenomena.
Estuary-to-bay water-quality coupling in Gwangyang Bay, Korea, was assessed based on observations collected at 12 freshwater inflows and 12 bay sampling points across three hydrological phases operationally classified by antecedent precipitation: immediate post-rain (May), lagged post-rain (July), and dry baseline (October). Concentrations of dissolved silicate (DSi), total nitrogen (TN), and total phosphorus (TP) in freshwater inflows differed significantly among these phases. Riverine nutrient loads exhibited a pronounced event-phase gradient (July > May > October). The Seomjin River contributed 67–91
