Search Results (154)

Korea’s rising shares of variable renewable energy (VRE) and inflexible baseload increases the need for fast-responding and cost-effective flexibility. Most studies on power-to-heat (P2H) emphasize district-heating (DH) economics or load shifting, leaving the system-level impacts of its reserve provision capability unclear. We develop a mixed-integer linear programming model for reserve-constrained unit commitment (RCUC) that co-optimizes the power and DH systems. In addition, the model incorporates a P2H system capable of providing multiple reserve services. Reserve requirements are divided into static and dynamic terms, with the dynamic term represented as a piecewise-linear approximation of short-term VRE variability derived from weather-based generation profiles and evaluated at the scheduled VRE output. Using a 2030 winter week for Korea, we compare five cases: no EB; EB as load only; and EB contributing only to the secondary/regulation reserve requirement, only to the primary reserve requirement, or both. Under the KRW 1000/kWh curtailment-penalty case, EB as load reduces system operating cost compared to the baseline, and enabling reserve provision yields additional cost savings, with the largest benefit observed when primary reserve is provided. EB operation also shifts dispatch from coal and gas toward nuclear, VRE, and pumped storage, while reducing renewable curtailment. Overall, enabling P2H to contribute to reserve procurement, particularly in the primary reserve, delivers substantially greater value than representing P2H solely as a controllable load for energy shifting. Full article

Differential equations with fractional order play an important role in modeling some natural phenomena. This paper investigates the dynamics of the fractional-order commensal symbiosis model with the Allee effect. This model describes the relationship between prey and predator populations. The piecewise-constant approximation technique is applied to discretize this model. Equilibrium points are established, and local stability conditions are calculated using fractional-order linearization and eigenvalue-based arguments. Moreover, the bifurcation theory is successfully invoked to discuss the period-doubling bifurcation. In particular, sufficient conditions are effectively determined for the emergence of the period-doubling bifurcation. We utilize the hybrid control approach to control the behavior of the considered system. Then, some numerical examples are presented to demonstrate the accuracy and validity of the theoretical results. The findings indicate that fractional order and Allee effects improve system dynamics and substantially improve stability limits and bifurcation structures, providing new insights into how to handle the dynamics of ecological systems. Full article

Large-scale photovoltaic (PV) deployment in arid deserts may alter land–atmosphere interactions and influence groundwater systems, yet such impacts remain poorly quantified due to limited high-resolution observations. To overcome the coarse spatial resolution of GRACE data, this study develops a CNN-LSTM-Attention deep learning framework to downscale terrestrial water storage anomalies (TWSA) from 0.25° × 0.25° to 0.1° × 0.1° over the Huadian PV base in the Tengger Desert, China, during 2004–2024. Groundwater storage anomalies (GWSA) were derived using a water-balance approach, and piecewise linear regression was applied to detect trend shifts associated with PV development. Results show a persistent decline in TWSA and GWSA before 2022, followed by short-term recovery signals afterward. Groundwater responses exhibit greater magnitude and delayed behavior relative to soil moisture. Spatial analysis reveals stronger variability and more frequent deficits in the western subregion, indicating intra-base heterogeneity. A seasonal phase analysis identifies an approximately six-month lag between soil moisture and groundwater, highlighting constraints from deep vadose-zone processes. The findings suggest that groundwater dynamics reflect the combined effects of climate variability, infiltration lag, and PV-related land surface modification rather than a single driver. This study demonstrates the potential of deep-learning-based GRACE downscaling for groundwater monitoring in human-modified arid regions and provides insights for sustainable water management under renewable energy development. Full article

As urbanization intensifies, improving street thermal comfort has become a critical issue in urban renewal. While existing studies generally assume that increasing the Green View Index (GVI) linearly improves pedestrian thermal comfort, this study identifies a significant “Decoupling Effect” in high-density commercial areas through field measurements and numerical simulations of three typical street types (commercial–service, ecological–recreational, and historical–cultural) in Shenyang. Integrating DeepLab V3 semantic segmentation with ENVI-met version 5.1.1 microclimate simulation, the results demonstrate a robust monotonic negative correlation between GVI and Physiological Equivalent Temperature (PET) in ecological streets (Spearman’s ρ = −0.692, p < 0.001), confirming the consistent cooling benefit of greenery in nature-dominated environments. However, a distinct “Threshold Effect” was identified in commercial streets using Piecewise Linear Regression (PLR). A critical breakpoint was detected at GVI = 22.08%. Below this threshold, visual greenery effectively contributes to cooling (slope = −0.454); yet, once GVI exceeds 22.08%, the cooling efficacy diminishes significantly (slope = −0.109), marking the onset of a “decoupling” phase. Specifically, despite Wenhua Road achieving a GVI of ~24.5% with a complex “three-board, four-belt” structure, its PET peak reaches 46.15 °C, approximately 5.5 °C higher than ecological streets. Mechanism analysis reveals that under peak thermal stress (Traffic Heat ≈ 75 W/m²), the high-intensity anthropogenic heat and hardscape radiation exceed the evaporative cooling threshold of vegetation. This study reveals the non-linear relationship between visual greenery and the physical thermal environment, suggesting that simply pursuing visual green quantity is ineffective in commercial canyon renewal; instead, a threshold-based synergistic optimization of canopy shading and pavement thermal performance is required. These findings provide a quantitative basis for sustainable street landscape planning and urban climate adaptation strategies in high-density cities. Full article

This paper will present a constant-force vibration isolator (CFVI), in which the isolated load is supported by two pulley-roller mechanisms, while the dynamic stiffness is modified by a cam mechanism with the piecewise profile redefined by the user. As a result, this model can generate the constant force-displacement response within the working region, thereby obtaining quasi-zero stiffness in this range. Because of the piecewise configuration of the cam, the system motion governed by the piecewise dynamic equation under base motion excitation will be analyzed and established. The approximate solution of the piecewise dynamic equation is derived by using the average method, from which the relative amplitude–frequency relation and the absolute amplitude transmissibility of the CFVI will be obtained. The effects of the key working parameters involving the damping coefficient, critical position, and excited amplitude on the dynamic behavior and isolation effectiveness of the CFVI are considered through numerical simulations. The simulation result reveals that the dynamic response of the CFVI offers two branches: resonance and isolation. The former is significantly affected by the working parameters, whereas the latter is weakly influenced. Furthermore, the isolation effectiveness of the CFVI will be compared with that of its linear counterpart and the quasi-zero stiffness vibration isolation model using a semicircle cam (QZSI). The results demonstrate that the CFVI outperforms the other models for base motion excitations. Full article

This paper investigates the transition behaviour and stochastic resonance phenomenon in a class of bifurcation systems with a symmetric piecewise smooth potential, induced by a control parameter, under the combined influence of multiplicative white noise, additive white noise, and a periodic force. As the control parameter increases, the symmetric piecewise smooth potential of the system evolves from tristability to bistability. To study stochastic resonance in this system, an approximate Fokker–Planck equation is first derived based on Novikov’s theorem and the Fox approximation method. Subsequently, the approximate stationary probability density of the system is obtained from the Fokker–Planck equation, revealing the occurrence of a stochastic P-bifurcation. Then, within the bistable and multistable regimes, the effects of the bifurcation parameter, multiplicative noise intensity, and additive noise intensity on the mean first passage time (MFPT) are analysed. Finally, based on the mean first passage time, the response amplitude for stochastic resonance is derived via linear response theory, and the influences of the bifurcation parameter, noise intensities, correlation time, and signal frequency on the response amplitude are examined. In the bifurcation regime, the correctness of the expressions is verified numerically. It is found that multistability reduces the mean first passage time, and stochastic resonance is further analysed using the Fokker–Planck equation. Full article

This paper studies the dynamic adjustment of bilateral trade following Economic Integration Agreements (EIAs) and examines how financial development and labor market rigidity moderate the timing of trade responses. We approximate the event time adjustment path using a Piecewise Linear Trend (PLT) specification that relaxes global linearity restrictions common in dynamic gravity models. Event study evidence reveals heterogeneous pre-entry and post-entry slopes, particularly at the product-margin level. Split joint pre-trend tests show that aggregate trade satisfies long-run parallel trends, while product-level margins exhibit significant secular restructuring prior to implementation, motivating explicit slope parameterization. Within the PLT framework, financial development is associated with short-run anticipation effects, whereas labor rigidity corresponds to delayed post-entry adjustments. Industry-level interactions indicate that these dynamics vary systematically with sectoral characteristics. The results remain robust to zero-inclusive estimators, alternative institutional proxies, and alternative event time discretizations. Overall, the findings demonstrate that institutional conditions shape the temporal profile of trade adjustment and that flexible slope modeling is essential for identifying dynamic responses to trade liberalization. Full article

This paper investigates a fairness-aware task assignment problem, where traditional models prioritize operational effectiveness while overlooking workload fairness. Motivated by real-world airport operations, we propose a multi-objective task assignment model that penalizes deviations between actual and expected workloads. Expected workloads are computed from the aggregated task density over each shift’s time window. To capture the nonlinear nature of perceived unfairness, we define the imbalance cost using a quadratic penalty function. We develop three piecewise linear approximations to solve the model efficiently and further simplify them by exploiting convexity to remove binary variables. Experiments on real-world data from a major airport in China show that the proposed methods significantly reduce solution time while preserving solution quality. Under a one-hour time budget, the piecewise linear approximation models achieve up to 5.12% cost savings in large-scale instances compared to the original nonlinear model. Moreover, our proposed fairness-aware task assignment model yields substantial improvements in workload balance (over 90%) at a limited cost to service quality (approximately 20%), even with small imbalance penalties. Full article

Suppose $K_Y$ and $K_X$ are the image and the preimage of a nonlinear operator $\mathcal{F}:K_Y\to K_X$. It is supposed that the cardinality of each $K_Y$ and $K_X$ is N and N is large. We provide an approximation to the map $\mathcal{F}$ that requires prior information only on a few elements p from $K_Y$, where $p\ll N$, but still effectively represents $\mathcal{F}\left(K_Y\right)$. It is achieved under Lipschitz continuity assumptions. The device behind the proposed method is based on a special extension of the piecewise linear interpolation technique to the case of sets of stochastic elements. The proposed technique provides a single operator that transforms any element from the arbitrarily large set $K_Y$. The operator is determined in terms of pseudo-inverse matrices so that it always exists. Full article

Uncertainty in optimization models often causes awkward properties in their deterministic equivalent formulations (DEFs), even for simple linear models. Chance-constrained programming is a reasonable tool for handling optimization problems with random parameters in objective functions and constraints, but it assumes that the distribution of these random parameters is known, and its DEF is often associated with the complicated computation of multiple integrals, hence impeding its extensive applications. In this paper, for optimization models with chance constraints, the historical data of random model parameters are first exploited to construct an adaptive approximate density function by incorporating piecewise linear interpolation into the well-known histogram method, so as to remove the assumption of a known distribution. Then, in view of this estimation, a novel confidence set only involving finitely many variables is constructed to depict all the potential distributions for the random parameters, and a computable reformulation of data-driven distributionally robust chance constraints is proposed. By virtue of such a confidence set, it is proven that the deterministic equivalent constraints are reformulated as several ordinary constraints in line with the principles of the distributionally robust optimization approach, without the need to solve complicated semi-definite programming problems, compute multiple integrals, or solve additional auxiliary optimization problems, as done in existing works. The proposed method is further validated by the solution of the stochastic multiperiod capacitated lot-sizing problem, and the numerical results demonstrate that: (1) The proposed method can significantly reduce the computational time needed to find a robust optimal production strategy compared with similar ones in the literature; (2) The optimal production strategy provided by our method can maintain moderate conservatism, i.e., it has the ability to achieve a better trade-off between cost-effectiveness and robustness than existing methods. Full article

Objective: This study aimed to investigate the association between time to admission (TTA) and long-term mortality in patients with hip fractures, enabling surgeons to assess individual risks and prevent adverse outcomes. Methods: Demographic and clinical data of patients with hip fractures were obtained from medical records in our hospital. Patients aged 65 years or older were included. TTA was defined as the time from injury to first presentation at our institution. The primary outcome was long-term all-cause mortality. The regular multivariate Cox regression, restricted cubic spline, and two-piecewise model were used to explain the linear and curvilinear association between TTA and long-term mortality. The analyses were performed using EmpowerStats and R. Results: A total of 2361 patients were included in our study. There were 743 males and 1618 females, with a mean age of 79.44 ± 6.71 years. There were 1745 intertrochanteric fractures and 616 femoral neck fractures. We divided the patients into four groups according to TTA distribution: TTA ≤ 6 h, 6 h < TTA ≤ 12 h, 12 h < TTA ≤ 24 h, and TTA > 24 h, and the corresponding long-term mortality rates were 254 (25.53%), 85 (32.20%), 127 (32.56%), and 267 (37.50%). A curvilinear association was observed between TTA delay and long-term mortality in geriatric hip fractures, with 24 h serving as an inflection point. When TTA was less than 24 h, every one-hour increase in TTA was associated with a 1.6% increase in long-term mortality (HR = 1.016, 95% CI: 1.008–1.024; p < 0.001). When TTA exceeded 24 h, the long-term mortality risk showed no significant further increase with TTA (HR = 1.000, 95% CI: 1.000–1.000; p = 0.531). Conclusions: This study suggests that delayed admission is associated with a worse prognosis, and the mortality risk increases by approximately 1.6% per hour of delay within the first 24 h, after which the risk appears to stabilize. The first 24 h post-injury may represent a critical window for intervention. Full article

With the growing number of applications in embedded systems—such as IoT modules, smart sensors, and wearable devices—there is an increasing demand for fast and accurate computations on resource-constrained platforms. In this paper, we present a new method for computing n-th roots in floating-point arithmetic based on an initial estimate generated by a “magic constant,” followed by one or two iterations of a modified Newton–Raphson or Householder algorithm. For cubic and quartic roots, we provide C implementations operating in single-precision floating-point format. The proposed algorithms are evaluated in terms of maximum relative error and execution time on selected microcontrollers. They exhibit high accuracy and noticeably reduced computation time. For example, our methods for computing cubic roots outperform the standard library function cbrtf() in both speed and precision. The results may be useful in a variety of fields, including biomedical and biophysical applications, statistical analysis, and real-time image and signal processing. Full article

This paper presents a two-stage stochastic programming model for the joint optimization of fleet deployment and sailing speed in liner shipping under fuel price volatility and carbon tax uncertainty. The integrated framework addresses strategic fleet planning by determining optimal fleet composition in the first stage, while the second stage optimizes operational decisions, including vessel assignment to routes and sailing speeds on individual voyage legs, after observing stochastic parameter realizations. The model incorporates nonlinear fuel consumption functions that are approximated using piecewise linearization techniques, with the resulting formulation being solved using the Sample Average Approximation (SAA) method. To enhance computational tractability, we employ big-M methods to linearize mixed-integer terms and introduce auxiliary variables to handle nonlinear relationships in both the objective function and constraints. The proposed model provides shipping companies with a comprehensive decision-support tool that effectively captures the complex interdependencies between long-term strategic fleet planning and short-term operational speed optimization. Numerical experiments demonstrate the model’s effectiveness in generating optimal solutions that balance economic objectives with environmental considerations under uncertain market conditions, highlighting its practical value for resilient shipping operations in volatile fuel and carbon pricing environments. Full article

Liner shipping companies commonly pursue strategies such as forming strategic alliances and attracting new customers to strengthen competitiveness and improve operational performance. However, in the shipping of perishable goods, inadequate ship scheduling and bunker management can result in substantial customer loss and increased operational costs. This paper examines a scenario in which a large volume of perishable goods is shipped by liner ships. The specific demand characteristics of perishable goods—requiring rapid port handling and expedited shipping—are analyzed. To address these challenges, we propose a mixed-integer nonlinear programming (MINLP) model to optimize ship scheduling and refueling decisions for liner cold chain services under cooperative agreements. The model minimizes total liner shipping service costs while explicitly accounting for the decay of perishable goods. Nonlinear elements are linearized using a piecewise linear secant approximation, enabling efficient solution of the model with commercial solvers. Numerical experiments based on the AEU6 route operated by China COSCO Shipping Group validate the model and provide practical managerial insights. The results indicate that: (1) incorporating collaborative agreements can reduce total route service costs by 4.5% and total port handling costs by 7.5%, while also lowering late arrival penalties and losses from perishable goods decay; (2) joint consideration of refueling strategies and collaborative agreements improves both decision flexibility and solution accuracy; (3) the shipping of perishable goods has differentiated effects across voyage legs, highlighting the need for liner shipping companies to enhance cooperation with ports and refine bunker fuel procurement planning; and (4) it is essential to improve ship performance and appropriately design bunker fuel tank capacity to respond to dynamic changes in the shipping market. Full article

We consider discrete best approximation problems in the setting of tropical algebra, which is concerned with the theory and application of algebraic systems with idempotent operations. Given a set of input–output pairs of an unknown function defined on a tropical semifield, the problem is to determine an approximating rational function formed by two Puiseux polynomials as numerator and denominator. With specified numbers of monomials in both polynomials, the approximation aims at evaluating the exponent and coefficient for each monomial in the polynomials to fit the rational function to the data in the sense of a tropical distance function. To solve the problem, we transform it into an approximation of a vector equation with unknown vectors on both sides, where one side corresponds to the numerator polynomial and the other side to the denominator. Each side involves a matrix with entries dependent on the unknown exponents, multiplied by the vector of unknown coefficients of monomials. We propose an algorithm that constructs a series of approximate solutions by alternately fixing one side of the equation to an already-found result and leaving the other side intact. Each equation obtained is approximated with respect to the vector of coefficients, which yields this vector and approximation error, both parameterized by exponents. The exponents are found by minimizing the error with an optimization procedure based on an agglomerative clustering technique. To illustrate, we present results for an approximation problem in terms of max-plus algebra (a real semifield with addition defined as maximum and multiplication as arithmetic addition), which corresponds to an ordinary problem of piecewise linear approximation of real functions. As our numerical experience shows, the proposed algorithm converges in a finite number of steps and provides a reasonably accurate solution to the problems considered. Full article